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Fast load flow algorithms Jalali-Kushki, Hossein 1977

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'FAST LOAD-FLOW ALGORITHMS by Hossein Jalali-Kushki B.Sc, Arya-Mehr-University of Technology, Tehran, Iran, 1971 M.A.Sc., University of British Columbia, Vancouver, Canada, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF DOCTOR OF PHILOSOPHY THE FACULTY OF GRADUATE STUDIES in the Department of Electrical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1977 © Hossein Jalali-Kushki, 19 77 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Co lumb ia , I a g ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t ten pe rm i ss ion . Department o f Eleotrieal Engineering The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date September 1, 1977 ABSTRACT New, fast and reliable algorithms for solving load-flow problems are presented in this thesis. Each of these algorithms iteratively solves a set of linear equations i n terms of voltage magnitude squared and phase angles, and converges onto the f i n a l solution i n a few iterations. Although the lin e losses of the system are used i n deriving the equations of the basic line-loss load-flow algorithm, knowledge of their (approximate) values i s not a pre-requisite to using the algorithm. The basic line-loss load-flow algorithm i s s l i g h t l y modified to give an incremental-change line-loss algorithm which proves to be always preferable to the basic algorithm. By exploiting the weak interdependence between active power and voltage magnitude, and between reactive power and phase angle, two decoupled versions of the incremental-change line-loss algorithm were also developed. A l l these algorithms have constant gradient characteristics, and their storage requirements are, at most, the same as those of the standard Newton-Raphson algorithm. If need be, the storage requirements can be reduced to those of the triangularized Y-matrix iterative algorithms. Tests on various systems indicate fast and reliable convergence characteristics better than those of the Newton-Raphson algorithm and comparable, to those obtained by Stott and Alsac with their decoupled Newton-Raphson load-flow algorithm. i i TABLE OF CONTENTS Page ABSTRACT . . . . . . . i i TABLE OF CONTENTS . I i i i LIST OF TABLES . . " v LIST OF ILLUSTRATIONS v i NOMENCLATURE . . . . . . . . v i i ACKNOWLEDGEMENT ix 1. INTRODUCTION . . . . . . . . . . . . . . . . 1 1.1 The Load-Flow Problem . . . . . . . . . . . . . . . . . . 1 1.2 The Review of Available Load-Flow Algorithms . . . . . . 5 1.3 The Newton-Raphson Algorithm . 9 1.4 The Fast Decoupled (Newton-Raphson) Load Flow, / 12 1.5 The Line-Loss Algorithm 15 2. THE LINE-LOSS ALGORITHM 17 2.1 Derivation of the Algorithm . . 19 2.2 The Iterative Process 25 2.3 Programming and Storage Requirements . 28 2.4 The Numerical Results 30 3. THE INCREMENTAL-CHANGE LINE-LOSS ALGORITHM 38 3.1 Derivation of the Algorithm 38 3.2 The Iterative Process . . . 42 3.3 Programming and Storage Requirements . . 44 3.4 The Numerical Results . 48 4. FAST DECOUPLED LINE-LOSS ALGORITHMS 60 4.1 Derivation of the Algorithm 60 4.2 The Iterative Process 63 4.3 Programming and Storage Requirements 65 4.4 The Numerical Results 66 i i i Page 5. CONCLUSIONS 7 3 BIBLIOGRAPHY • • 7 5 APPENDIX A . •'. 83 APPENDIX B 160 iv LIST OF TABLES Table Page 2.1 Dimensions of "Element" (i,k) of the Matrix of Coefficients 28 2.2 Test Systems Used 31 2.3 Comparison of Number of Iterations 32 2.4 Comparison of Computation Times 32 3.1 Comparison of Number of Iterations . 49 3.2 Comparison of Computation Times . 49 4.1 Comparison of Number of Iterations 68 4.2 Comparison of Computation Times 68 v LIST OF ILLUSTRATIONS Figure Page 2.1 A Simple Branch Representation 19 2.2 The Branch Corresponding to that of Fig. 2.1 21 '2.-3 TT-Representation of Branch (i,k) 23 2.4. Typical Voltage Magnitude (a) and Phase Angle (b) Variations for Test System 9 35 2.5 Typical Voltage Magnitude (a) and Phase Angle (b) "^Variations for Test System 3 ,36 2.6 Typical Voltage Magnitude (a) and Phase Angle (b) Variations for Test System 6 37 3.1 Typical Voltage Magnitude and Phase Angle Variations for Test System 9 51 3.2 Typical Voltage Magnitude and Phase Angle Variations For Test System 10 52 3.3 Comparison of the Algebraic Sum of a l l the Power Mismatches (Test System 8) 56 3.4 Comparison of Maximum Power Mismatches (Test System 8) 57 3.5 Comparison of Sum of a l l the Absolute Values of Power Mismatches (Test System 8) 58 4.1 Flow-Chart Indicating the Logic of Decoupled Algorithms 64 ?4.2 ^Comparison of the Algebraic Sum of a l l the Power Mismatches (Test System 8) 69 4.3 Comparison of the Maximum Power Mismatches 70 4.4 Comparison of Sum of a l l the Absolute Values of Power Mismatches . . . 71 vi 'NOMENCLATURE Voltage . -'.V\ 'complex voltage of .bus i U^ magnitude of ^ 6^  phase angle of V e^ complex voltage of bus i in the (S-U^) system Power 'S k^ complex power flowing *from bus i towards bus k total complex power injection at bus i complex power loss in line (i,k) P i^,P i,P i^ real parts of S i k, S^, respectively Q i k » Q i , Q i k imaginary parts of S i k, S i k, respectively Admittance y^ k value of admittance connecting buses i and k y. total shunt admittance at bus i Y nodal admittance matrix Y.. elements ( i , j ) of Y G real part of Y B imaginary part of Y G„,B^_. elements ( i , j ) of G and B, respectively g^ total shunt conductance at bus i b^ total shunt susceptance at bus i x^ k reactance of branch (i,k) vi 1 General (i,k) * , 3 Im Re E i k n "PV i e P-Q or P-V superscript (V) branch connecting buses i and k complex conjugate complex operator, S-T imaginary part of a complex number r e a l part of a complex number '.correction term corresponding to branch (i,k) number of buses -number of P-V buses number of P-Q buses i i s a P-Q (or P-V) bus dif f e r e n t i a l operator indicates iteration number v i i i ACKNOWLEDGMENT I would like to express my deepest gratitude to my supervisor, Dr. M.D. Wvong, for his continued encouragement, help and guidance throughout the research and writing of this thesis. I would also like to thank Dr. Y.N. Yu, for his constant encouragement during the research work and for proof-reading the thesis and offering valuable suggestions. I am also grateful to Dr. H.W. Dommel for proof-reading the thesis and also for providing me the excellent opportunity to visit the Bonneville Power Administration and have valuable discussions with the people there. Thanks are also due to Miss Sannifer Louie for typing the thesis. The financial support from the National Research Council of Canada is gratefully acknowledged. ix 1. INTRODUCTION 1.1 The Load-Flow Problem "A power system continuously experiences changes in i t s opera-ting state. These changes can be due to load demand variations, re-scheduling of power generation, redistribution of reactive power genera-tion, changing tap settings of transformers or phase shifters and dis-connecting lines, transformers and generators for maintenance or as a consequence of system faults. The effect of these variations is inves-tigated both during system planning and operation. One of the objec-tives i s to ensure that the quality of service provided to the consumers is acceptable. Another is to confirm that these operations do not cause overloading of system elements. Yet another objective during system planning is to determine the range of tap settings of transformers and the capacities of the excitors required for proper steady-state and transient operation. The real and reactive power flow patterns are also studied as an important part of system security monitoring process .... A large number of load flow solutions w i l l have to be obtained for a present day power system." [G16] "Power flow studies are the backbone of the design of a power system. They are the means by which the future operation of the system is known ahead of time .... The continual expansion of the demand for ele c t r i c a l energy due to the growth of industries, commercial centers, and residential sections, require never-ending additions to existing power systems. The system engineer must decide what components must be added to the system many years before they are put into operation and he does this by means of power flow studies." [R5] 2. "The power flow program is indispensible for the analysis of ac power systems. Although improved solution methods and faster com-puters have extended i t s capabilities, this gain has been largely offset by the increased number and size of studies that must be made." [D7] "An increasing use is being made of Power Flow algorithms in the electric u t i l i t y industry, and recently the interest has been in applying a form of the algorithm to real time situations. The new uses of Power Flow imply that faster and more eff i c i e n t algorithms are desired." [N7] "The load-flow program is certainly the most frequently used computer program for power system applications. It consumes the largest computer time per year. This time has been growing as power system planners see the need for solving ever larger cases in succession of base case and many contingent solutions .... The great demand that load-flow applications place on computing resources accounts for the continued interest in the development of techniques that are faster, exhibit quicker convergence for a variety of system conditions, and make efficient use of core." [D8] These statements of the "authorities" in the f i e l d - from American Electric Power Services Corporation, to IBM S c i e n t i f i c Center, to Bonneville Power Administration - should suffice to indicate the great importance of load-flow studies and the necessity of developing even faster and more efficient load-flow algorithms in order to deal with the huge interconnected power systems of today. The problem is to specify a set of complex voltages for the system nodes (or buses) that satisfy certain requirements. Depending upon these requirements, the buses of the system can be divided into three main categories: 3. (a) The load or P-Q buses; whose active and reactive power injec-tions are given and whose voltage magnitudes and phase angles have to be determined. A system may have any number of these buses. (b) The voltage regulated, generator or P-V buses; whose voltage magnitudes and active power injections are given and whose phase angles have to be specified. A system may have any number of these buses. (c) The reference, swing or slack buses; whose voltage magnitudes and phase angles are pre-determined and have no constraints on their power injections. A system can have any number of these buses but must at least have one. The problem can be formulated in terms of node or mesh variables. The most commonly used formulation is the one using the nodal equations: where I is the vector of injected nodal currents, Y i s the nodal admit-tance matrix and V is the vector of nodal voltages. However, since neither the voltages nor the currents are known, the nodal equations alone w i l l not be adequate. Additional equations are required to relate the known quantities, the active and reactive power injections, to the nodal voltages and currents. These are: I = Y-V (1-1) S. - V. I 1 i 1 = 1, •. •, n (1-2) 4. where is the total complex power injection at node i and * is used to indicate the conjugate of a complex number. The nonlinearity of the load-flow problem arises from the fact that: (1) equation (1-2) is nonlinear, and (2) for P-V buses, the problem is further complicated because, in equation (1-2), only the real part of and the magnitude of V. are known. l Equations (1-1) and (1-2) represent the basic formulation of the load-flow problem. A l l the load-flow algorithms that use nodal analysis, use some combination of these equations to correct the voltages -in steps - from a set of i n i t i a l estimates onto the final solution. The differences in the convergence characteristics and the computing speed of various algorithms are due to the fact that each algorithm uses (1-1) and (1-2) differently. Normally the per unit quantities of the variables are used and certain practical assumptions are usually made in developing the load-flow algorithms. Among these are the facts that for any practical power system: (1) The voltage magnitudes are approximately 1 P.U. and a l l the phase differences across various branches are small; (2) The transmission lines are highly inductive; (3) The interdependence between active powers and voltage magni-tudes and between reactive powers and phase angles are weak and may be neglected; and (4) The losses of the system constitute a small percentage of the total generated power. 5. The f i r s t assumption is made not only in developing load-flow algorithms, but also in choosing a reliable starting point. This i s normally referred to as a "flat-s t a r t " , and is obtained by setting a l l P-Q bus voltage magnitudes to 1 P.U. and a l l the phase angles to zero . Other practical considerations, such as the required speed and accuracy of the solution, play a role both in developing load-flow algorithms and in choosing a particular algorithm for a specific study. 1.2 Review of Available Load-Flow Algorithms Before d i g i t a l computers became available, the load-flow pro-blem was solved on network analysers. The f i r s t totally automatic algori-thm for solving the load-flow problem on a d i g i t a l computer was presented by Ward and Hale in 1956 [Y4]. Since then, considerable attention has been paid to the development of faster, more eff i c i e n t and more reliable load-flow algorithms and enormous progress has been made in this direc-tion . This section i s intended to give a general account of the deve-lopment of load-flow algorithms. It is by no means a complete and ex-haustive survey of the literature. The Ward-Hale algorithm [Y4], as i t i s normally referred to, is one of a group of load-flow algorithms classified as the "Y-matrix Iterative Methods" [Y1-Y4]. The reason for this classification is that a l l these algorithms are based on the iterative solution of the set of linear equations in (1-1). Their storage requirements are minimal and, for that reason, they were very suitable to the early generation of computers. Furthermore, the Y-matrix iterative methods are easy to Other starting points are also used. For example, in assessing the system outages, the base case solution may be preferable to the flat-start values. See "Bibliography" for a partial listing. 6. program and perform satisfactorily on many problems. The changes in the system configuration can be easily accounted for and the automatic con-trols can be easily included in these algorithms. On the other hand, the Y-matrix iterative methods converge very slowly and sometimes do not converge at a l l . In practice, acce-leration techniques are invariably used to speed up the convergence of these algorithms. However, even with the use of the "best" acceleration factors, for large systems, the total computation time of these algori-thms is far greater than that of the newer methods. Nowadays, with the constant growth of the power systems and the increase in the number of load-flow problems that have to be solved for each system, and also due to the appearance of the modern and very powerful d i g i t a l computers with storage capabilities far beyond those of the earlier computers, the Y-matrix iterative methods are becoming less and less attractive. In the early 1960's another group of load-flow algorithms, classified as the "Z-matrix Methods" [Z1-Z4], were introduced. These algorithms, which are based on the direct solution of the linear set of equations in (1-1), have more reliable convergence characteristics than the Y-matrix iterative methods. On the other hand, their storage re-quirements and computation times are considerably more and grow enor-mously with system size. They are rarely competitive with the Y-matrix iterative methods and s t i l l less competitive with the newer load-flow algorithms. The Z-matrix methods did not become very popular. In 1959, the Newton-Raphson method of solving the load-flow problem was shown to have powerful convergence characteristics [N13, N14]. Due to i t s large storage and computer time requirements, however, i t was not competitive with the Y-matrix iterative methods. It was not until 7. 1967, when, by using sparsity programming and ordered Gaussian elimina-tion these problems were overcome [G23,N11], that the algorithm became practical and widely used. Because of i t s quadratic convergence, the Newton-Raphson algorithm converges very rapidly to very accurate solutions. For prac-t i c a l accuracies, i t always converges in a few iterations, irrespective of the system size. It i s far superior to any of the Y-matrix iterative methods but i t is also far more complicated to program. Its storage requirements, even with sparsity programming and ordered elimination, are much more than those of the Y-matrix iterative methods, but impose no serious problem on most present-day computers. Soon after the appearance of the paper by Tinney and Hart in 1967 [Nil], the Newton-Raphson algorithm became very popular and replaced the "cla s s i c a l " Ward-Hale algorithm. Subsequently, a great deal of work was done in the direction of developing the Newton-Raphson load-flow algorithm and improving upon certain aspects of i t . The polar form of this algorithm became to be widely regarded as the standard method of solving load-flow problems. Even today, the Newton-Raphson method of solving load-flow problems is the algorithm which is most widely used by the industry. Also, this algorithm is almost invariably used as the basis of comparison for the newly developed load-flow algorithms. In 1967, Bonaparte and Maslin [DI] presented a new load-flow algorithm which was based on exploiting the weak interdependence between real power flows and voltage magnitudes. In this algorithm - the DC load-flow as i t is normally called - a set of linear equations relating the real power injections to voltage phase angles i s directly solved at each iteration. The matrix of coefficients remains constant throughout 8. the process and, therefore, the computation time per iteration is greatly reduced. The algorithm was proposed as a means of obtaining fast and approximate real power flow solutions and as such, i t became very popular and widely used. The idea of exploiting the weak interdependence between the real powers and voltage magnitudes and between the reactive powers and voltage phase angles of any practical power system was used in several subsequent papers. In the proposed decoupled algorithms, the P-U and Q-<5 couplings are altogether neglected and the load-flow equations are simplified. The idea of decoupling the load-flow equations did not become very popular u n t i l , in a recent paper by Stott and Alsac [Dll], i t was shown that a decoupled version of the Newton-Raphson algorithm has better characteristics than the original undecoupled algorithm. The Fast Decoupled (Newton-Raphson) Load Flow, as the authors called i t , is becoming increasingly popular [D5,D8] and is expected to replace the Newton-Raphson algorithm. Many other load-flow algorithms have been developed during the past two decades which do not belong to any of the above categories. In fact, with the incredible growth of power systems, the scope of the problem has become so wide and the number of publications related to the subject so numerous that i t would be practically impossible for this survey to give a complete coverage. A more complete account of the development in this f i e l d can be found in several review papers [R1-R6] that have appeared on the subject. 9. (*) 1.3 The Newton-Raphson Algorithm [Nil] Combining equations (1-1) and (1-2) we obtain: s • = V, ? Y* V* (1-4) l i , , ik k k=l where Y . , is the (i,k)tlih element of the nodal admittance matrix, Y . ik Using polar coordinates: V, ^ TJ. e J ( S i i l in ( 1 _ 5 ) Y 4 I Y I e J ik *ik " 1 ik 1 where j is the complex operator, V-T, equation (1-4) becomes: s±.?t + Ki. J u. ±u k |y | " «!. " Ik) k=l The Newton-Raphson technique i s then used to solve the set of nonlinear equations in (1-6). The elements of the Jacobian matrix are the partial derivatives of P^ and with respect to voltage magnitudes and phase angles: and n AU A p i • X ( H i k A \ + N i k ( 1 ~ 7 a ) k=l k n AU, A Q i = J- < Jik A 6 k + L i k i f ( 1 " 7 b ) k=l k where: 3P. 9P. r r A 1 . vr A 1 „ ik = 86, ' ik " 3U. uk k k A 3Qj A 3Qj J i k • " 86^ ; L i k 9Uk Uk (1-8) Throughout this thesis, the phrase "the Newton-Raphson algorithm" refers to the application of this well-known algorithm for solving a set of nonlinear equations to the polar formulation of the load-flow problem. 10. and AP± k rescheduled) - P (calculated) AQ± k Q^scheduled) - Q±(calculated) The partial derivatives defined in (1-8) are real functions of the admittance matrix and node voltages. Even though the problem is formulated in polar coordinates, these partial derivatives should be calculated by rectangular complex arithmetic. Assuming the following rectangular expressions for the admittances and voltages: V = e i + ^ f i Y i k = G i k + ^ B i k we have for i 4 k: and for i = k: H i k = L i k " \ f i " bk e i N i k = " J i k " *k e i + bk f i H.. = -Q. - B.. U? n l i i l L i i = Q i - B i i u i N. . = P. + G.. U? i i l i i i j i i = p i ^ G i i u i (1-9) and defining: \ + J b k - ( e k + J f k ) < G i k + JBlk> ( 1 - 1 0 ) (1-lla) (1-llb) 11. For a system of n nodes (not including the slack buses) of which n ^ are P-Q type, the number of unknowns is n + n p^. The number of equations is likewise n + np(^ because for every P-V or P-Q bus we can write (l-7a) and for every P-Q bus we can also write (l-7b). In this way, for every P-Q bus, there is a "double row" and a "double column" in the Jacobian matrix; for every P-V bus there is a single row and a single column; and there are no rows or columns corresponding to the slack buses. The element (i,k) of the Jacobian matrix is therefore a submatrix whose di-mensions are 2-by-2, 2-by-l, l-by-2, or 1-by-l, depending upon the types of buses i and k. The structure of the Jacobian matrix would then be the same as that of the nodal admittance matrix, but the former will not be symmetrical even i f the latter is. At every step of the iterative process, the Jacobian matrix is evaluated and the following set of linear equations is directly solved: "AP" ' H N" "A6" AQ J L AU U (1-12) using Gaussian elimination; i.e., through the process of triangulariza-tion and back substitution. Although the original Jacobian matrix is highly sparse, because of the new elements that are created in the course of the triangular!zation process, its triangularized form may not be sparse any more. In order to prevent this, Tinney and Hart [Nil] sug-gested several ordering schemes for the nodes of the system that tend to reduce the number of newly accumulated elements to a minimum. One of these schemes, which the authors used in their program and which is also used 12. in LFP*, calls for numbering the nodes "so that at each step of the elimination the next node to be eliminated is the one having the fewest connected branches. This method requires simulation of the elimination process to take into account the changes in the node-branch connections effected at each step". Using the above scheme, the rows of the Jacobian matrix are ordered only once in the beginning of the process. The same order is then used at every iteration step. The augmented Jacobian matrix is formed and triangularized, row by row in that order, and the result is stored in compact form. The sign of integer row and column pointers indicate types of rows and columns and, therefore, number and order of the elements of the Jacobian submatrices. This storage scheme, which is explained in detail in [Nil] was also used in programming the Newton-Raphson algorithm in LFP. 1.4 The Fast Decoupled (Newton-Raphson) Load-Flow [Dll] This algorithm was first presented in 1973 in a paper by Stott and Alsac [Dll]. The polar form of the Newton-Raphson algorithm is taken as the starting point. This means starting with equation (1-12), repeated here for convenience: AP H N" AS " AQ J » L AU U The algorithm takes advantage of the weak interdependence between real powers and voltage magnitudes and between the reactive powers and phase LFP is a collection of programs for solving the load-flow problem using various algorithms. The programs were written for the purpose of com-paring the performance of various algorithms. See Appendix A. 13. angles (for practical power systems operating in steady state) to de-couple P-5 and Q-U problems. "The f i r s t step" in this direction i s to neglect the coupling submatrices [N] and [J] in (1-12) , obtaining two separated sets of equations: [AP] = [H][A6] (l-13a) [AQ] = [ L ] [ ^ ] (l-13b) where the elements of [H] and [ L ] , for i ^  k, are H i k - L i k = u i V G i k s i n ( 6 i - V - B i k c o s ( 6 i - V ] (1"14a) and: H i i = - B i i u i - Q± (l-14b) L. . = - B. . U? + Q, i i i i i x i However, i t was found that the decoupled equations of (1-13) represent an unstable algorithm unless other practical assumptions are made and an alternative equation is used instead of (l-13b) [D9]. The "best" stable algorithm was derived in [Dll] using further physically j u s t i -fiable simplifications as follows: "In practical power systems the following assumptions are almost always valid: cos( < s i - <5fc) ~ 1 ; G i k s l n ( 6 i " «k> « B i k ; Q. « B, . I i i i so that good approximations to (l-13a) and (l-13b) are: 14. [AP] = [U-B'-U][A6] (l-15a) [AQ] = [U-B"-U][^j] (l-15b) where [B'] and [B11] are matrices whose elements are strictly elements of [-B] and [U'B'*U] represents a matrix whose element (i,k) has the expression u\ -B^'U^. The decoupling process and the final algorithmic forms are now completed by: (a) omitting from [B'] the representation of those network ele-ments that predominantly affect MVAR flows; i.e., shunt reac-tances and off-nominal in-phase transformer taps (b) omitting from [B"] the angle shifting effects of phase shifters (c) taking the left-hand U terms in (l-15a) and (l-15b) onto the left-hand sides of the equations, and then in (l-15a) removing the influence of MVAR flows on the calculation of [A5] by setting a l l the right-hand U terms to 1 P.U. Note that the U terms on the left-hand sides of (l-15a) and (l-15b) affect the behaviour of the defining functions and not the coupling (d) neglecting series resistances in calculating the elements of [B']> which then becomes the DC approximation load-flow matrix. This is of minor importance, but is found experimentally to give slightly improved results." With the above modifications the final fast decoupled load-flow equations become: [^j] = [B'][A6] (l-16a) [^ §] = [B"][AU] (l-16b) 15. In the above algorithm, both [B'] and [B11] are constant, real and sparse matrices that need to be triangularized only once at the beginning of the study. Equations (l-16a) and (l-16b) are solved se-parately and repeatedly until a l l the power flows are within the desired tolerance of their scheduled values. Starting with (l-16a), equations (l-16a) and (l-16b) are solved alternatively unless a l l the active powers or a l l the reactive powers are within the desired tolerance of their f i n a l values in which case the solution of the corresponding set of equations is skipped. The solution of either (l-16a) or (l-16b) i s considered to be one half iteration. Experiments have shown that the convergence of this algorithm is very fast and reliable [D5,D8,D11] and that the algori-thm i s much preferred to the undecoupled Newton-Raphson algorithm. In LFP, (l-16a) and (l-16b) are solved using ordered Gaussian elimination. The buses are numbered such that at each stage of the elimination process of [B']» the next row to be eliminated is the one having the fewest number of off-diagonal elements. The ordering is assumed to be the same for [B'] and [B"]. Both these matrices are formed and triangularized row by row and the results are separately stored in compact form. Negative pointers are used to indicate P-V type buses. 1.5 The Line-Loss Algorithms [09,014,04] Applied numerical methods are most eff i c i e n t when they take advantage of the physical properties of the system being solved. For example, exploiting the weak (P-U) and (Q-6) interdependencies and other physical properties of the practical power systems, resulted in the development of the Fast Decoupled (Newton-Raphson) Load-Flow, which is 16. shown to have much better characteristics than the undecoupled Newton-Raphson algorithm. In any practical e l e c t r i c a l power transmission network, the line losses of the system form a very small percentage of the system's total power generation. In the following chapters, this physical pro-perty of the system is exploited and a number of very fast and reliable load-flow algorithms are developed. The idea of using the line losses of the system in a load-flow algorithm is new and results in.a set of linear equations in terms of voltage magnitudes squared and voltage phase angles. The solution of the load-flow problem is obtained by repeatedly solving this set of equations. 1 Although knowledge of the approximate values of line losses can be effectively used with the line-loss algorithms, such knowledge is not a pre-requisite to using the algorithms. Since losses are usually small, their values may be i n i t i a l l y set to zero. Alternatively, a f l a t start may be used to start the algorithms. Two slightly different formulations of the line-loss algorithm, as well as two decoupled versions of this algorithm, are presented in this thesis. In Chapter 2, the basic line-loss algorithm is derived. Chapter 3 contains a modified version of this algorithm which is faster and has better convergence characteristics. The decoupled versions of the algorithm are introduced in chapter 4. The performance of these algorithms are compared with those of the Newton-Raphson algorithm and the Fast Decoupled (Newton-Raphson) Load-Flow in respective chapters. 17. 2. THE LINE-LOSS ALGORITHM During the last two decades, remarkable progress has been made in developing better algorithms for the d i g i t a l solution of the load-flow problem. On the other hand, the same period has witnessed a tremen-dous growth in the size of power systems and the emergence of huge interconnected e l e c t r i c a l power transmission networks involving many u t i l i t i e s , which has resulted in a sizeable increase in the number and size of load-flow problems to be solved. This growth has been so enormous that i t has largely offset the gains of the aforementioned development. Consequently, due to the ever-increasing system size and the growing complexity of the problems associated with i t , even today, there is s t i l l a need for faster, more efficient and more reliable load-flow algorithms. This is why the constant-gradient fast-converging algorithms, such as the Fast Decoupled (Newton-Raphson) Load-Flow [Dll] are becoming very popular. The line-loss load-flow algorithm presented here, is a constant-gradient algorithm with very fast and reliable con-vergence. This algorithm was developed as the result of an attempt to transform the nonlinear load-flow problem into an ordinary linear circuit problem. It was noticed that, i n a lossless* system, the power flow through a line remains constant and that, in any system, the algebraic sum of powers entering any node is zero. Both of these are character-i s t i c s of current. Therefore, in a lossless system, the nodal power injections may be assumed nodal currents. The solution to the load-flow _ Throughout this thesis the word "loss" always refers to "complex power loss". A lossless system, likewise, refers to an ideal system with zero impedances. 18. problem for the former case would then be the same as the solution of the current flow problem for the latter. At the same time we know that, in any practical power system, the losses represent only a small percentage of the generated power. Therefore, we expect the above power/current analogy to be approximately valid for a practical power system. Furthermore, we expect this approxi-mation to be even better i f we know the (approximate) values of the line losses for our system. As a matter of fact i t can be easily shown that, for a DC system, knowing the exact values of line losses means that we can transform the nonlinear load-flow problem into an exact linear equivalent. The variables in the linear equivalent model, are the square of the voltages in the original DC system. Of course, for an ordinary AC system, the problem is far more complicated. On the one hand, for P-V buses, only the real power i n -jections are specified and, on the other hand, the magnitudes of voltages for these buses are constrained. The problem is further complicated by the fact that there is not a one to one relationship between the voltages of our original AC network and the voltages which w i l l be obtained by assuming nodal power injections to be currents. Hence, for an AC system, even i f the exact values of line losses are known, the problem cannot be solved in-one step. Using certain approximations, however, would result in an iterative algorithm for the d i g i t a l solution of the load-flow problem. This algorithm, which may be derived using the expression for the line losses of the system, is called the line-loss algorithm. From a mathematical point of view, the line-loss algorithm transforms the load-rflow equations into a set of "almost linear" equa-tions in terms of voltage magnitudes squared and voltage phase angles. 19. The nonlinear terms in the resulting formulation are very small. These terms are grouped together and taken to the known side of. the equations. Their values are set to some i n i t i a l estimates (usually zero) in the beginning of the process and are calculated using the updated nodal voltages at each subsequent iteration. 2.1 Derivation of the Algorithm The algorithm can be derived in two different ways. The f i r s t is to use circuit analysis concepts and power/current analogy, while the second is to derive the algorithm by manipulating the power-flow equa-tions from a mathematical point of view. The former approach led to the development of the algorithm while the latter approach was later used to indicate the relationship between the equations used in the line-loss algorithm and the exact load-flow equations. The following presentation w i l l be made in the same order. The s t r i c t l y mathematical derivation is given in section 3.1. The idea, as mentioned earlier, is to extend the analogy that exists between the power flows and the currents of a lossless system, to practical systems for which the losses are usually very small. Assume a branch (i,k), represented - as shown in Fig. 2.1 - by an admittance y., connecting nodes i and k. Fig. 2.1. A Simple Branch Representation. 20. We know that, in a- lossy system, the power "sent" from node i through the branch (i,k) is different from the power "received" by node k. The difference between the two (or more precisely, the algebraic sum of the power flow from node i to node k and the power flow from node k to node i) is equal to the complex power losses in the branch (i,k): S i k = [ U i + Uk " 2 U i Uk C O s ( < S i " 6k ) ]4k <2"1> where U\ and 6^  (IL^  and 6^ ) represent the magnitude and the phase angle of voltage at node i (node k) and is the complex power loss in the branch (i,k). Now, i f we subtract the losses from the actual power flow in branch (i,k), the branch can be considered lossless. In other words, after subtracting the line losses, the power flow in the branch remains constant and can be treated as current. In order to subtract the line losses, which are in reality distributed along the branch, we can either introduce a new node at the center of the branch (i,k) whose total in-jected power equals negative of in (2-1), or we can subtract s^/2 from the powers flowing into both nodes i and k. The first approach resembles the way the T-equivalent of a line is obtained while the second approach would be similar to finding the u-equivalent of the line. The two methods are identical in every way except that the former requires introduction of new nodes into the system while the latter does not. For this reason, the second approach was chosen. a Subtracting half of the line losses, S^ as given in (2-1), from the powers flowing into nodes i and k, would leave two identical values. The fact that these values, which s t i l l have the dimension of power, are equal indicate that we can use them as the power flowing 21. (*) through a lossless line and, subsequently, use them as currents . We represent the resulting power flow from node i to.node k, after sub-4 tracting — — , by the symbol S fc to show that: 1) i t i s power, and, 2) i t i s different from the actual power flow (before subtracting the losses) which we c a l l S i k. Using equations (1-1), (1-2) and (2-1), the expression for can be easily found: S A S b i k = S i k lk i [ u 2 - u 2 - 2 j U . ^ s M S . - S ^ (2-2) where j is the complex operator, / ^ l . As mentioned earlier, we can now treat s!^ as a current flowing through the branch. Equation (2-2) indicates that the best results would be obtained when the admittance of the branch i s conjugated, as shown in Fig. 2.2 ,\ ek - 1 / 2 Uk " ^ k Fig. 2.2. The Branch Corresponding to that of Fig. 2.1. If current flows through the branch (i,k) of Fig. 2.2, the voltage across the branch would be e - e, i k u 2 U 2 -T- " "2 " j ui uk ^ l n ( 6 i - V (2-3) The value of this "power-flow" through the lossless line i s exactly equal to the power that was flowing through the middle point of the original branch. 22. where e^ and e^ represent the nodal voltages for the branch of Fig. 2.2, The real part of each voltage, e , can be readily equated to U 2 1 —2 . This would be consistent with the results obtained for a DC net-work. The imaginary parts of the voltages cannot be so easily related to the voltages of the original branch, as the imaginary part of (2-3) represents a coupling between the voltages of nodes i and k. However, we can write: U. ^ aln(6 1 - 6k) - 6 ± - 6 k - e ± k (2-4) where e^ k is a correction term which is usually very small since in practical power systems a l l the voltage magnitudes are approximately 1 P.U. and a l l the phase differences across the branches are small. Using.(2-3) and.(2-4), we can assume the imaginary part of e^ i to be -6^ and modify the current S^k according to the value of the correction term In other words, using e. = i U* - j 6 ± i = 1, n (2-5) would result in a current equal to S^k - j e^ k y^ k flowing through the branch (i,k) of Fig. 2.2. For convenience, from now on, werrefer to the original system as the (I-V) system and to the system whose admit-2 tances and voltages are as shown in Fig. 2.2,.as the (S-U ) system. Writing the voltage/current relationship - equation (1-1) -2 for the (S-U ) system, and considering the fact that, Y^k, the element (i,k) of the nodal admittance matrix has the value of -Y£ k» w e obtain: I 2 n S , n . n U, h-x-r+s x Y i k e i k = x Yxk (4 - v-v k=l k=l k=l i = 1, ..., n 23. The above equation has to be slightly modified when the branches of the (I-V) system are represented, as shown in Fig. 2.3, by. their rr-equivalents. S. x y i k Fig. 2.3. u-Representation of Branch (i,k). The problem can be handled by treating each "leg" of the ir-equivalent as the simple branch in Fig. 2.1, but there is an easier approach: f i r s t we subtract the power consumed by each n-equivalent "leg" from the net power injection at the corresponding node. The remaining values would represent power flows through simple branches, like that in Fig. 2.1. Therefore, equation (2-6) becomes: 2 * r 5 i " U i y i " I 2 1 k=l n S ik n n U. .1. Yik<-T- J«k> < 2 " 7 ) + j I Y k=l ik fcik k=l L i k v 2 where y^ represents the total shunt admittance at node i : n y i = I' Y i k 1 k=i l l c (2-8) Using (2-8), equation (2-7) can be rewritten as: 24. £ 2 n S n ^ , n ^ U, S ± " I f + J I Y e = I Y (-| - j 6 ) k=l k=l 1 K 1 R k=l l k z K U 2 k^i + - | ( Y i i + V 3 fii^-yi) (2-9) i = 1, . .., n The above equation represents what we c a l l the line-loss 2 algorithm. It is the current flow equation for the (S-U ) system. At the same time, i t has to (and does^) correspond to the power-flow equa-tion for the (I-V) system. Note that irrespective of the fact that the branches of the (I-V) system may have been represented by their TT-equivalents, the corresponding branches in the (S- system are always represented as in Fig. 2.2. By separating the real and imaginary equations in (2-9) we obtain the f i n a l form of the line-loss algorithm: 2 2 n p* n n IT p- " I -4=- + I e.. B.. = Y (G M ~ - B.. 6, ) 1 k-i 2 k-i i k i k kil i k 2 i k k k ^ i + (G ± ± + g±) - y - (B ± 1 - b ±) 6. (2-10a) a 2 n %u n " n uv Q i - J x — + kl± eik G"ik" (-Bik -r - Gik66k> k^i u 2 - ( B i i + V -r- ( G i i " ^ 6 i ( 2" 1 0 b ) (*y See section 3.1. 25. where: Y ± k = G i k + J B i k ' y± - « ± +JI>1 For each P-Q bus, there are two unknowns, U\ and 6^ V- both equations (2-10a) and (2-10b) are written. For each P-V bus, there i s only one unknown, 6^ , and only equation (2-10a) can be written. There are no equations written for slack buses whose voltages are known ahead of time. In the resulting set of equations, a l l the U terms correspon-ding to P-V buses and a l l the U and 6 terms corresponding to the slack buses are calculated and moved to the known side of the equations. 2.2 The Iterative Process Once the set of equations in (2-10) is formed, i t w i l l be used in the following iterative process: (1) I n i t i a l l y , a l l the e^'s are set to zero. The line losses are set to their i n i t i a l estimates when such estimates are available. Otherwise, they are set to zero. (2) The resulting set of linear equations i s directly solved using ordered Gaussian elimination and back substitution. The results w i l l provide an i n i t i a l set of voltages. (3) If the present set of voltages satisfy the power constraints the problem i s solved. Otherwise, using the present values of voltages and equations (2-1) and (2-4), the new values of e^k a 1 1^ a r e calculated and the known side of the equations (2-10a) and (2-10b) are updated. 26. (4) The linear set of equations i s solved again, using the updated known vector. Note that since the matrix of coefficients remains constant, the triangularization/back substitution process need to be performed on the known vector only. (5) The new values of voltages obtained as the result of step 4 replace the previous values of voltages. The process then continues with step 3. The algorithm is very fast and has reliable convergence. It i s very fast because-of the fact that the matrix of co-efficients remains constant throughout the process; i t is triangularized only once. The statement with respect to r e l i a b i l i t y of the convergence is not easy to prove. Indeed, the usual practice for confirming the r e l i a b i l i t y of a particular algorithm is to test i t by using several numerical examples. With respect to the line-loss algorithm, the test results confirm the r e l i a b i l i t y of convergence. The following explana-tion i s added to indicate why consistently good convergence character-i s t i c s can be expected from this algorithm. The basic equations of the algorithm, equations (2-10a) and (2-10b), represent the following recursion formula: S + F(X ( V )) = A'X ( V + 1 ) V = 0, 1 n F(X<°>) = 0 ( 2 " n ) where S is the vector of injected active and reactive powers, F(X) is the nonlinear vector comprising a l l the line loss terms and e terms in (2-10), A is the matrix of coefficients in (2-10) and X i s the vector of unknown voltage magnitudes squared and voltage phase angles. Superscript 27. (v) indicates the iteration number. As mentioned earlier, for any practical power system, the loss terms and.the e terms are very small. In other words, for practical power systems we have I 1*00 I I « 1 (2-12) l|s|| where | | • | | indicates the norm of a vector. From (2-11) and (2-12) we can conclude that the condition for (2-11) to converge onto the f i n a l solution i s that matrix A should be "well conditioned". Although there i s no definition for what i s a "well-conditioned" system and what i s not, the matrices with dominant diagonal elements are normally considered to be well conditioned. Hence, since the matrix of coefficients, A in (2-11), which is directly related to the nodal admittance matrix, has dominant diagonal terms, i t is well conditioned and, therefore, (2-11) converges. We can also use the condition number, u, of A to show that i t i s a well conditioned matrix. Here again, there is not a set of values of u corresponding to the "well conditioned" matrices and another set corresponding to.the " i l l conditioned" ones. However, the matrices whose condition numbers are of about the same order as the matrix i t s e l f are considered to be well conditioned. The condition number of A was calcu-lated for a.few of the test systems and i t was found that the above condition was satisfied. The condition numbers for Test Systems 3 (IEEE 14-bus system) and 5 (IEEE 30-bus system) were 10.89 and 24.46, respectively. Although the condition numbers may be used to calculate an upper bound for the voltage mismatches at the end of each iteration, such bounds would be far greater than the actual mismatches and, there-fore, would have no practical significance. 28. 2.3 Programming and Storage Requirements In matrix form, we have a double-row and a double-column for each P-Q bus; a single-row and a single-column for eabh P-V bus; and no row and column for slack buses. The "element" (i,k) of the matrix of coefficients would be a submatrix whose dimensions are given in Table 2.1. P-Q P-V P-Q 2 x 2 2 x 1 P-V 1 x 2 l x l Table 2.1. Dimensions of "Element" (i,k) of the Matrix of Coefficients. The elements of these submatrices are the elements of the (modified) nodal admittance matrix. Therefore, i f there is no branch connecting buses i and k, the corresponding (i,k) element would be n u l l . It follows that: (1) The matrix of coefficients is highly sparse; (2) The matrix of coefficients has exactly the same structure as the Jacobian matrix of the Newton-Raphson algorithm in polar coordinates; (3) The matrix of coefficients remains constant throughout the algorithm; and ~ u: (4) Using (-6^) and 2 — a s o u r variables and assuming symmetry for the nodal admittance matrix, the matrix of coefficients would also be symmetrical except in some of i t s diagonal "elements". 29. The last proposition can be verified by examining equations (2-10a) and (2-10b): The "element" (i,k) of the matrix of coefficients, when both i and k are P-Q buses and i ^ k, would be: G i k G i k - B i k "ik r "I "I (2-13) i e P-Q k e P-Q i * k which is equal to the transpose of "element" (k,i). It can be easily seen that this is s t i l l valid when one or both of the buses are of P-V type. Therefore, we have symmetry as far as the off-diagonal "elements" are concerned. The diagonal "elements" of P-V buses are scalar ( B ^ - b^) and, as such, do not alter the symmetry of the matrix. For P-Q type buses, however, the diagonal "elements" are: B i i " b i G i i + Si D±i i e P-Q G i i " g i " < B i i + V (2-14) which would not be symmetric i f ^ 0. It must be mentioned, however, that g^ is usually equal to zerol Even in cases where g_^  ^ 0, i t can be accounted for in other ways such that the matrix of coefficients becomes completely symmetrical. The above features of the matrix of coefficients play an im-portant role in programming the algorithm: Since this matrix is highly sparse, the ordered Gaussian elimination can be effectively u t i l i z e d to minimize the storage requirements; and since i t remains unchanged 30. throughout the process, the t r i a n g u l a r i z a t i o n process need be c a r r i e d out only once. Furthermore, we can e x p l o i t the (almost) symmetry of t h i s matrix and further reduce the storage requirements: I t can be e a s i l y shown that the upper h a l f of a t r i a n g u l a r i z e d symmetrical matrix contains a l l the information necessary f o r carrying out forward and back-substitution processes on any R.H.S. vector. In t h i s case, how-ever, due to s l i g h t asymmetry, we have to store an a d d i t i o n a l n ^ elements. Taking advantage of the fact that the matrix of c o e f f i c i e n t s contains a l l the information about the nodal admittance matrix, the storage requirements of the algorithm, which are equal to those of the standard Newton-Raphson algorithm, can be f u r t h e r reduced. This r e s u l t s i n a considerable increase i n computation time but may be desirable for smaller computers. 1 2.4 The Numerical Results A load-flow program (LFP^*^) was written - mostly i n FORTRAN IV language - to compare the performance of the various algorithms. The program, e x p l o i t i n g the s p a r s i t y of the matrices, can handle very large systems. I t contains the l i n e - l o s s algorithm (including the v a r i a t i o n s of t h i s algorithm to be presented i n the following chapters), as w e l l as the w e l l known Newton-Raphson and Fast Decoupled (Newton-Raphson) Load-Flow algorithms. A l l the algorithms share the same input/output as w e l l as some other routines which are common to a l l of them. Furthermore, since a l l the programs were written by the author and a l l the tests were performed on the same d i g i t a l computer - UBC's IBM 370/168 - the r e s u l t s are not biased by programming or computer e f f i c i e n c y . (*) See Appendix A for d e t a i l s . 31. Several test systems of various sizes and configurations were used to compare the algorithms. These are lis t e d in Table 2.2. System No. No. of Buses No. of Lines No. of Transf. Source 1 5 6 0 [G21] 2 6 7 2 [Y4] 3* 14 17 3 [R2] 4 21 29 3 [DI] 5* 30 37 4 [R2] 6 33 23 11 [G14] 7 38 39 9 [G16] 8* 57 63 17 [R2] 9 93 99 57 [G13] 10 138 219 75 [G6] Table 2.2 Test Systems Used. * IEEE Test Systems A l l the recorded computation times are CPU time spent in the main part of the algorithm; in other words, the time taken for input/ output operations, formation of the nodal admittance matrix, dynamic storage allocations, etc., are not included. This ensures that the recorded times can be taken as very good measures of comparing the speed of various algorithms. Tables 2.3 and 2.4 compare the line-loss algorithm with the well-known Newton-Raphson algorithm and the Fast Decoupled Load-Flow. System N-R FDL line loss alg. 1 2 2 2 2 2 2i 3 3* 2 2* 3 4 2 2i 2 5* 2 2 2 6 3 4 NC 7 3 2i 6 8* 2 3 3 9 3 6 12 10 4 4* 13 Table 2. 3. Comparison of Number (NC: No Convergence) of Iterations. System N-R FDL line loss alg. 1 7 9 7 2 13 12 - 13 3* 36 31 32 4 79 54 49 5* 112 75 7,0 6 119 101 NC 7 162 98 153 8* 336 224 218 9 808 563 836 10 2337 1091 1751 Table 2.4. Comparison of Computation Times. (Times in milliseconds; NC: No Convergence) 33. A l l the results were obtained by specifying a tolerance of .01 P.U. (1 MW/1 MVAR) on maximum power mismatch. In the case of the Newton-Raphson algorithm and the Fast Decoupled Load-Flow, a flat-start was used. For the line-loss algorithm two different alternatives were tested: (1) setting the i n i t i a l estimates of line losses to zero and; (2) using a flat-start to calculate the i n i t i a l values of line losses and e's. The two approaches proved to be identical*. It can be seen from Tables 2.3 and 2.4 that, even when the (approximate) values of line losses are not specified i n i t i a l l y , the line-loss algorithm performs very satisfactorily. For most systems, the algorithm converges in a few iterations and i t s overall computation time is less than that of the Newton-Raphson algorithm. Of course, the algorithm performs even better when some i n i t i a l estimates of line losses are available. Figures 2.4, 2.5 and 2.6 show the typical voltage magnitude and phase angle variations for various test systems. It is interesting to note the similarity of these patterns to that of an underdamped, c r i t i c a l l y damped or overdamped second-order system. Nevertheless, the line-loss algorithm, in this present form, may have a considerable computational round-off error: which, in some cases, can.delay or even prevent convergence. This can be seen by ex-amining equations (2-10a) and (2-10b). At a point f a i r l y close to the The number of iterations were exactly the same while, because of the increased computation during the i n i t i a l stage of the latter case, the computing times increased slightly. 34, f i n a l solution, the corrected R.H.S. values of equations differ by a very small percentage from their previous values. The resulting correc-tions to voltage magnitudes and phase angles would also be a small per-centage of their previous values. Since the equations are in terms of the voltage magnitudes and phase angles and not in terms of corrections to these values, the roundoff error may completely offset the effect of these corrections. In other words, at some point in the process, the corrections are lost due to numerical errors and i t would be impossible to get any closer to the solution point. This is precisely what happens in the case of Test System 5. ^ The line-loss algorithm, however, can be reformulated to over-come this problem. In the next chapter, f i r s t the s t r i c t l y mathematical derivation of the line-loss algorithm is presented. Then the equations are slightly modified and reformulated in terms of incremental changes to variables. The new formulation does not have the roundoff error problem and as well has several other advantages over the basic line-loss algorithm. 35,. Fig. 2.4. Typical Voltage Magnitude (a) and Phase Angle (b) Variations for Test -System 9. 36. Fig. 2.5. Typical Voltage Magnitude (a) and Phase Angle (b) Variations for Test System 3. 37. Fig. 2.6. Typical Voltage Magnitude (a) and Phase Angle (b) Variations for Test System 6. 38. 3. THE INCREMENTAL-CHANGE LINE-LOSS ALGORITHM In previous chapter the line-loss algorithm was derived using circuit theory concepts and current/power analogy. Since the algorithm represents the exact expression of the power flows in the system, we'must be able to derive i t directly from.the power flow equations. It must be mentioned, however, that we are able to do so precisely because we know what we are looking for and why. Without such knowledge, there would have been no reason to "regroup" the terms in this particular way while there are almost endless other po s s i b i l i t i e s . In this chapter, f i r s t we present the new way of deriving the basic equation of the line-loss algorithm. This derivation enables us to proceed to reformulate the equations in terms of the incremental changes to variables. The modified-version, which we c a l l the incremental-change line-loss algorithm, has a l l the advantages of the basic line-loss algo-rithm while i t does not have the serious drawback of being vulnerable to roundoff errors. It also takes less computation time per iteration and less storage as compared with the basic line-loss algorithm. 3.1 Derivation of the Algorithm For an n-bus system the total complex power, S^, injected at any bus, i , i s given by: S i = V i I, Y i k v i k = I Y i k < v i V + Y i i u i < 3- x ) k=l k=l k ^ i where represents the complex voltage at bus i , Y ^ represents the (i,k)th element of the nodal admittance matrix, U\ i s the magnitude of V. and * indicates the conjugate of a complex number. At the same time, 39. i f y ^ i s the value of admittance connecting buses i and k in the IT-equivalent representation of the branch (i,k), we have the following expression for the complex power losses in that branch: S5, = (v - V )v* (V - V )' ik y 1 V y i k ^ i V = y i k [ U i + U k - 2 R e ( V i V k > ] (3-2> where Re( ) represents the real part of a complex number. Now, from the fact that the element (i,k) of the nodal admittance matrix is equal to the negative of y ^ J i.e.: Y i k = - y i k ( 3 " 3 ) i t follows that: Re(V. V*) = i [ U 2 + U 2 + (3-4) Y i k We also know that the imaginary part of i s : Im(V V*) = U Ufc sin(6 1 - 6fc) (3-5) which we assume to be U i Uk S l n ( 5 i " 6 k } " 6 i " 6k " e i k ( 3 " 6 ) where is the correction, or error term. Note that equation (3-6) presents no approximation. From equations (3-4), (3-5) and (3-6) i t follows that: V i Vk " * [ U1 + Uk + + J < 5i " 6k " eik> ( 3 " 7 ) ik Replacing for V. V, in equation (3-1) and rearranging the terms we obtain: 1 K. 40. n. s ! , n . n j, . .uf k=l k=l k=l kH k^i kH U- n * * 2 ("T + J V J = 1 4 + Y i i u i ( 3 " 8 ) k^i Considering the fact that: X Y ^ + Y i i = y i ( 3 _ 9 ) k=l k^i equation (3-8) becomes a 2 n S.. n . n . U k=l k=l k=l k/i k^i kjl u 2 + - i ( Y±i + y ± } - j 6 i ( Y i i - y±> ( 3 " 1 0 ) which is exactly the same as equation (2-9), the basic equation of the line-loss algorithm. The recursion formula, (2-11) in the line-loss algorithm, uses the above equation in the following way: (v) 2 n S,, n . , . n IL (v+1) k=l k=l k=l k^i k^i Wi + - r < Y i i + V - i \ ( Yu " Y i } <3-"> where superscripts (v) and (v+1) denote the iteration cycle. At the same time, we know that equation (3-10) was obtained without any approxi-mation and, therefore, i t expresses the exact relationship between the 41. nodal power injections and nodal voltages. It can be written for any set of voltages and their corresponding powers. In other words, i f we use S^V^ to represent the calculated value of injected power at bus i at the end of iteration cycle v, we have: , \ n ( v ) n . ( . n U? (v) s± " J ~r + j I Y±k e±k " I Y*kHi -3 V k=l k=l k=l k ^ i k ^ i k ^ i u 2 ( v ) + 1 (Y* + y * ) - j 6<V> (Y*. - yf) (3-12) 2 i i J± l i i i Equation (3-12) does not represent any recursion formula. On the con-trary i t expresses the exact power-flow equations at the end of itera-tion cycle v. Now, subtracting equations (3-11) and (3-12) we obtain: k=l k ^ i - j A 6<v) (Y* ± -.y*) (3-13) where: (v) A g(v) l _ i i = power mismatch at the end of iteration cycle v; 2(v) 2(v+l) 2(v) i A l _ i A 2 . " 2 2 and (v) A 6(v+D _ 6(v) I - I I 42. Note that in the R.H.S. of equations (2-10) and (3-10) we included a l l the buses connected to bus i . However, the constant terms, corresponding to the voltage magnitudes of P-V buses and to the voltage magnitudes and phase angles of slack buses, cancel out. i n the subtrac-tion and do not appear in the R.H.S. of equation (3-13). Since equation (3-13) applies to any ( v ) , we drop the super-script (v) from this equation. Then, separating the real and imaginary equations in (3-13), we obtain the f i n a l equations used in the incremental-change line-loss algorithm: n U 2 U 2 A P i = j=1 ( G i k A -T " B i k A V + ( G i i + V A - \ k ^ i - ( B ± i - b ± ) A 6 ± (3-14a) A Q i " j , ( " B i k A \ ~ G i k A 6 k ) " ( B i i + V A k ^ i - ( G ± 1 - g.) A6. (3-14b) For any P-Q bus, both equations (3-14a) and (3-14b) can be written and two correction terms have to be calculated. For a P-V type bus, only equation (3-14a) can be written and only one correction term has to be calculated. Slack buses have no unknowns and none of the above equations can be written for them. 3.2 The Iterative Process The set of equations in (3-14), in matrix form, have exactly the same matrix of coefficients as the set of equations i n (2-10). The reason for this is that although i n the R.H.S. of equation (2-10) the 43. terms corresponding to any bus connected to i are included, nevertheless, a l l the U terms corresponding to P-V buses and a l l the ,U and 6 terms corresponding to slack buses are known. The matrix of coefficients is not affected by these terms and, hence, there is the complete similarity between the matrices of coefficients. Another point to be.mentioned here is that, contrary to the basic line-loss algorithm of equation (2-10), the incremental-change line-loss algorithm cannot be started without having an i n i t i a l set of estimates for the voltages. Once a set of estimates are available, they can be corrected using equation (3-14). If the approximate values of line losses are available, we can obtain these i n i t i a l estimates by performing one cycle of the basic line-loss algorithm. Note that, since the matrices of coefficients are exactly identical, this step can be very easily implemented. If no approximate values of losses are initially specified, we can either use a flat-start or perform one cycle of the line-loss algorithm with losses set to zero. Both approaches were found to be equally good. The iterative process can be summarized as follows: (1) If some i n i t i a l estimates for the line losses of the system are available, a cycle of the basic line-loss algorithm is performed to obtain the i n i t i a l values of voltages. Otherwise, (*) a flat-start is used (2) Using the present estimates of voltages, the power flows of the system are calculated. If they are within the desired toler-ance of their specified values, the problem is solved. Otherwise, (*) Alternatively, one cycle of the basic line-loss algorithm with i n i -t i a l estimates of line losses set to zero may be performed. LFP permits both options. See Appendix A. 44. (3) the power mismatches calculated in step 2 are used i n equation (3-14) to calculate the corrections to the voltage magnitudes and phase angles. The set of equations is solved by Gaussian elimination and back substitution. Note that since the matrix of coefficients remains constant i t need.be triangularized only once. At each step of the process, the triangularization/ back substitution process i s only performed on the vector of power mismatches. (4) Using the answers obtained as the result of step 3, the present estimates of the voltages are corrected. The new values of voltages, then, would be the new estimates and the process continues with step 2. The algorithm has a very fast convergence since the matrix of coefficients remains constant and does not have to be formed and triangularized at every step. Furthermore, the algorithm i s very r e l i a -ble. The test results confirm this fact. Furthermore, a l l the comments made about the r e l i a b i l i t y of the basic line-loss algorithm apply here as well. In fact, this version of the line-loss algorithm i s more reliable since i t i s formulated in terms of incremental changes to vari-ables and, therefore, is not vulnerable to roundoff errors. 3.3 Programming and Storage Requirements As mentioned earlier, the matrix of coefficients in this algorithm is exactly the same as that i n the basic line-loss algorithm of Chapter 2. Therefore, a l l the comments about programming and storage requirements of the latter apply here as well; viz, i f we use (-A6.) and ..Df A —^ • as our variables: 45. (a) The matrix of coefficients i s a highly sparse, constant and almost symmetrical matrix which can be very easily constructed; therefore, (b) sparsity programming techniques and ordered Gaussian elimina^ tion can be effectively used to minimize the storage require-ments. The matrix of coefficients i s triangularized only once. Only the upper half of the triangularized matrix of coeffic-ients plus an additional n^^ elements need be stored; and, (c) i f need be, the storage requirements of the algorithm can be reduced to those of the Y-matrix algorithms, at the expense of increased computation time. The storage requirements.of the algorithm, are, at most, equal to those of the standard Newton-Raphson algorithm. This statement can be verified by comparing the structure of the matrix of coefficients in this algorithm and the Jacobian matrix in the Newton-Raphson algorithm. The "element" (i,k) in both of them is a submatrix whose dimensions depend on the type of buses i and k. For the same bus types, these submatrices w i l l have the same dimensions in both cases. Also, in both cases, the slack buses are not included in these matrices. This means that the structure of the matrix of coefficients in (3-14) (and also in (2-10)) is exactly the same as that of the Jacobian matrix in the Newton-Raphson algorithm with polar coordinates. However, the Newton-Raphson.algorithm does not store the entire Jacobian matrix, but only i t s triangularized half. In other words, the Jacobian matrix is formed and triangularized, row by row, and the triangularized Jacobian i s the only thing that is stored. Exactly ther 46. same procedure can be followed in case of the incremental-change line-loss algorithm. In the Newton-Raphson algorithm this i s possible because the Jacobian has to be formed at every step of the iterative process and, hence, no information other than the upper half of the triangularized matrix is required. In the incremental-change line-loss algorithm this is possible because the matrix of coefficients is symme-t r i c a l . Thanks to this symmetry, only the upper half of the triangular-ized matrix of coefficients would contain sufficient information to carry out triangularization and back substitution processes on any right hand side vector. However, we need to store a l l the diagonal elements, as well as n-pq additional elements i f the matrix is not completely symmetrical. These elements can be stored in place of the active and reactive power mismatches in the Newton-Raphson algorithm. The storage scheme used (in LFP) for calculating and storing the elements of the matrix of coefficients can be summarized as follows: A l l the triangularized elements of the matrix of coefficients, along with proper pointers, are stored in a vector, from now on referred to as the vector of the triangularized elements. In another vector the pointers to the starting location of each row are stored. These pointers are positive for P-Q rows (double rows) and negative for P-V rows (single rows). The elements of the triangularized row are stored in locations starting with the one specified by the pointer for that row and ending with the one specified by the next pointer. The f i r s t one or three locations, depending upon whether the row is P-V or P-Q, are used for storing the diagonal elements. This is followed by an integer pointer indicating the column number of an "element" in the row. This pointer, too, is positive for P-Q columns (double columns) and negative for P-V 47. columns (single columns). The number and the order of the elements that follow this pointer are dependent upon, and determined by the sign of both row and column pointers. In the location following the last item for that particular column (which may be one, two or four locations away) the column pointer for the next element in the row is stored, followed by the value of i t s elements. And so i t continues. Each row is formed and triangularized in a vector, from now on referred to as the working-row, prior to being stored in the vector of the triangularized elements. Each element of the working-row consists of four locations in which the four possible elements of the submatrix (i,k) are stored. It also has a column pointer which follows the same rule as any other pointer with respect to P-Q and P-V elements. The length of the working-row is sufficient to store a f u l l row of the matrix of coefficients. Once the row i s formed, a linear combination of the previously stored rows is added to i t such that i t w i l l not have any elements in the column range that has been processed before. During this process, new elements may be created and some of the elements may be deleted and modified. New elements are added to the end of the working-row and deleted elements are indicated by a zero column pointer. At the end of the process, only the elements with non-zero column pointers w i l l be stored in the compact vector of the triangularized elements. It should be mentioned that the storage requirements of the basic line-loss algorithm is roughly the same as those of the incremental-change line-loss algorithm. The former requires slightly more space for storing additional terms corresponding to P-V and slack buses and other information necessary for updating the known vector. 48. 3.4 The Numerical Results The incremental-change line-loss algorithm was programmed using sparse matrix techniques and tested upon the test systems l i s t e d in Table 2.2. Tables 3.1 and 3.2 compare the required number of itera-tions and the CPU time taken by this algorithm with those of the Newton-Raphson algorithm and the Fast Decoupled (Newton-Raphson) Load-Flow. The number of iterations and the CPU times taken by the basic line-loss algorithm are also included for comparison. A l l the results were obtained by specifying a tolerance of .01 P.U. (1 MW/ MVAR) on maximum power mis-match. Furthermore, for the Newton-Raphson algorithm and the Fast Decoupled (Newton-Raphson) Load-Flow, a flat-start was used while, the incremental-change line-loss algorithm was started by using equations (2-10a) and (2-10b) during the f i r s t iteration and switched to equations (3514a) and (3-14b) thereafter. The correction terms and the line-losses were assumed to be i n i t i a l l y zero. It i s evident from Tables 3.1 and 3.2 that the incremental-change line-loss algorithm has a l l the advantages of the basic line-loss algorithm while, at the same time, i t is not vulnerable to computational roundoff error. In case of Test System 6, where the original line-loss algorithm failed to converge, the new version converges in 5 iterations. Table 3.2 also shows that the incremental-change line-loss algorithm is faster than the basic line-loss algorithm, because the line losses and correction terms need not be computed at each iteration. Even without any approximate values of line losses specified, the incremental-change line-loss algorithm converges considerably faster than Newton-Raphson algorithm and, in most cases, even faster than the Fast Decoupled (Newton-Raphson) Load-Flow. System N-R FDL line loss alg. Inc. change line loss alg. 1 2 2 2 2 2 2 2i 3 3 3* 2 2i 3 3 4 2 2i 2 2 5* 2 - 2 2 2 6 3 4 NC 5 7 3 2* 6 6 8* 2 3 3 3 9 3 6 12 12 10 4 4i 13 13 Table 3.1. Comparison of Number of Iterations. (NC: No Convergence) System N-R FDL line loss alg. Inc. change line loss alg. 1 7 9 7 6 2 13 12 13 10 3* 36 31 32 25 4 79 54 49 42 5* 112 75 70 61 6 119 101 NC 80 7 162 98 153 113 8* 336 224 218 188 9 808 563 836 616 10 2337 1091 1751 1247 Table 3.2. Comparison of Computation Times. (Times in milliseconds; NC: No Convergence) 50. The algorithm always converges in a few iterations, except for Test Systems 9 and 10, where the number of iterations required are 12 and 13, respectively. This was found to be caused by very large phase differences (up to about 70°j); across some of the branches of these systems. Such large phase differences do not occur in practice. However, even in these cases, the computation time i s significantly reduced as compared with the Newton-Raphson algorithm. It is interesting to note that the pattern of voltage magnitude and phase angle variations for these systems (*) - as shown in Figures 3.1 and 3.2 - resemble the pattern of an under-damped second-order system. Several other modifications were tried to see i f the perfor-mance of this algorithm, especially with respect to the number of itera-tions taken for Test Systems 9 and 10, can be further improved. Some of these actually did reduce the number of iterations considerably. Un-fortunately, however, these modifications were those that required changing the matrix of coefficients at every step and, consequently, also increased the total computation time considerably. Nevertheless, their improved performance with respect to the number of iterations makes them attractive alternatives. They are also of special interest to those who may want to pursue this research work.further. A few of these alterna-tives which showed the greatest improvement are briefly mentioned below: One such alternative was to use another equation instead of (3-6), which would provide us with better values at the end of f i r s t iteration. Since we know that: ' For a l l the plots a flat-start was used. If one cycle of the line-loss algorithm with zero i n i t i a l estimates was performed, the plots would start at the points corresponding to iteration 1. Fig. 3.1. Typical Voltage Magnitude and Phase-Angle Varia-tions for Test System 9. (Incremental-Change Line-Loss Algorithm with a Flat-Start) 52. ~ l r~ 8 12 ITERRTION (b) -1 20 16 Fig. 3.2. Typical,Voltage Magnitude (a) and Phase-Angle Variations for Test-System 10. (Incremental-Change Line-Loss Algorithm with a Flat-Start) '• ,'~ ' " 53. 3 ? sin x £ x - l y % x [ | + ^ |-^] (3-15) we can use the following equation instead of (3-6): U. U k sin (6 1 - y = (6 ± - + I Cos(6. - 6fc) ] - ( C ° r ^ l 0 n ) (3-16) Furthermore, we can replace for cos(5. - 6 ) an expression of the line losses. Assuming that the magnitudes of voltages are almost 1 P.U., we obtain: i k % cos(6, - 6, ) - 1 (3-17) * u x " i "k 2Y Therefore, (3-16) becomes 4 u i \ s l "< 6 i " V " < !i " V I1 + dr' " e i k » - 1 8 > oY., ik where represents the new correction term which is different from (and much smaller than) the correction term used in (3-6). Using (3-18) instead of (3-6), and following the same procedure as explained in section 3.1, we get: n 2 a s . - f " ^ + J I Y* £., = I ^ Y * - j I 6.<Y* 1 k=l 2 k=l l k l k k=l 2 i k k=l k l k 6 k ^ i k ^ i k # L k ^ i which should replace the basic equation (3-10). It can be seen that the matrix of coefficients is no longer constant. Using the above equation 54. reduced the number of iterations taken for Test System 9 by one third. On the other hand, the total computation time was much more than that of the incremental-change line-loss algorithm. When the variable terms in the matrix of coefficients were transferred to the other side of the equations and evaluated on the basis of the present values of voltages the performance of the algorithm became worse than that of the incremental-change line-loss algorithm. Another alternative which showed a great reduction in the num-ber of iterations was to leave the sine terms in (3-6) intact. The deriva-tion of the incremental-change line-loss algorithm, would then include the difference between two sine terms. In other words, A(sin(S)) will appear in equation (3-13) instead of AS. However, assuming that the (*) change in 5 from one step to the next is small , we can write: sin[(S i - 6k) + A(S± - 6 k)] £ sin(6 ± - 6fc) + A(6± - 6 k)cos(6 ± - 5fc) (3-20) Here again, due to the cosine term in the right-hand side of (3-20), we will get.a matrix of coefficients which changes from one iteration step to the next. Using this approach, the number of iterations taken for Test System 9, was reduced to 6. The computation time, on the other hand, increased threefold. Once again, taking the variable terms in the matrix of coefficients to the other side of the equations, and evaluating them on the basis of the present values of the voltages resulted in a worse performance. Tie) This assumption is indeed valid. Test results showed that after one cycle of the basic line-loss algorithm, even when the i n i t i a l esti-mates were set to zero, the calculated voltages were within less than 10% of their final values. 55. Yet another approach was to use the following expression, 2 instead of equation (2-5), for the voltages of the (S-U ) system: for a l l i and k. The problem with this approach is that the phase angle for each bus can be calculated from several different routes; and the values do not necessarily agree with each other. The approach would be unsuccessful i f the f i r s t route that becomes available i s chosen and the phase angle is calculated from that route. On the other hand, when a l l the possible values for each bus are calculated and a least squares hyper-plane i s f i t t e d to these values the algorithm improves tremen-dously (with respect to the number of iterations). This latter approach, however, involves finding the parameters of the least squares hyper-plane, which requires £he direct solution of another set of equations. Although the matrix of coefficients for the new set of equations is the same as the system's incidence matrix, nevertheless, the increased storage and computation time requirements offset the gains achieved in reducing the number of iterations from 12 to 6 (in case of Test System 9). f u l . In particular, the use of various acceleration factors, including the ones that are related to power mismatches and vary from one iteration to the next, did not improve the performance of the algorithm. Except for decoupling, which improved the overall results, the best algorithm remained the one derived in section 3.1 - the incremental-change line-loss algorithm. Figures 3.3, 3.4 and 3.5 compare the performance of this (3-21) such that: A i - Ak • U i uk s i n ( 6 i - V (3-22) Many other alternatives were tried but proved to be unsuccess-£-< 56 F i g . 3.3. Comparison of t h e A l g e b r a i c Sum of a l l t h e Power Mismatches. (Test System 8) 5? 5 7 F i g . 3.4. Comparison o f the Maximum Power Mismatches. ( Te s t System 8) NEWTON-RAPHSON L INE-LOSS ALG. INCREMENTAL-CHANGE 4.0 5.0 ITERAT I O N 6.0 "I— 7.0 8.0 .5. Comparison of Sum of a l l the A b s o l u t e Values o f Power Mismatches. (Test System 8) 59. algorithm, and that of the basic line loss algorithm, with the perfor-mance of the Newton-Raphson algorithm. Note that, for the sake of clarity, the three curves are displaced by one iteration step from one another. The figures show that the line-loss algorithms have a much greater rate of convergence during the first iterations than during the later itera-tions. This is due to the constant-gradient characteristic of these algorithms. The overall performance of the line-loss algorithms was greatly improved when the weak (P-U) and (Q-6) interdependencies were exploited and the incremental-change line-loss algorithm was decoupled. The decoupled version, as we will see in the next chapter, has a remark-able resemblance to the Fast Decoupled (Newton-Raphson) Load-Flow. 60. 4. FAST DECOUPLED LINE-LOSS ALGORITHMS In a practical power system, the interdependence between active powers and voltage magnitudes, and between reactive powers and phase angles are weak and may be neglected. This i s usually referred to as "the decoupling principle". In this chapter, we exploit this feature of practical power systems and decouple the incremental-change line-loss algorithm. It w i l l be seen that, contrary to the Newton-Raphson algorithm, applying the decoupling principle to the incremental-change line-loss algorithm w i l l result in a stable decoupled algorithm. Two slightly different decoupled algorithms w i l l be presented and compared with the Fast Decoupled (Newton-Raphson) Load-Flow. Both these algorithms are very fast and reliable. Test results indicate that the performance of these decoupled versions is even better than that of the undecoupled incremental-change line-loss algorithm. Indeed, the decoupled formulations are nothing but approximations to the original formulation. The reason for their improved performance seems to be that, in the decoupled versions, the corrections are calculated and applied at the end of every "half-iteration" rather than every iteration. 4.1 Derivation of the Algorithm The incremental-change line-loss algorithm uses equations (3-14a) and (3-14b), rewritten below, u 2 u 2 = X ( G i k A -T " B i k A V + ( G i i + *i> A ~T k ^ l . k ^ i - (B.. - b.) AS . (3-14a) n l i 61. n r 2 u 2  A 0 - i " I ( " B i k A - - G i k A6k> " ( B i i + V A -i k=l k^i ( G i i " g i ) A 6 i O-lAb) which, in matrix form, can be written as: AP - B ' •' G ' i i -AQ l i - G " '< - B " t • , TJ2 (4-1) (a) Algorithm A Assuming that submatrices [G '] and [G M ] in the above equation are null, we get: [ AP ] = [ - B ' ] • [ A<5 ] U 2 [ AQ ] = [ - B " ] • [ A \ ] (4-2a) (4-2b) This follows the decoupling technique commonly used [Dll]; namely, that of neglecting P-U and Q-6 interdependencies altogether. From equations (3-14a) and (3-14b), i t is seen that the sub-matrices [B '] and [B " ] are identical with the nodal susceptance matrix entries, except for the main diagonal elements. (b) Algorithm B In this algorithm we also neglect the effect of the series resistances in calculating the elements of [ B ' ] . The equations used are s t i l l (4-2a) and (4-2b) but the elements of [ B ' ] are different: 62. 1 (4-3a) X ik lite and (4-3b) In other words, the DC load-flow algorithm [DI] is used instead of equa-tion (4-2a) for calculating the voltage phase angles. Equation (4-2b) remains unchanged. This was found, experimentally, to slightly improve the results. Stott and Alsac experienced the same results when they applied the above approximation to the decoupled Newton-Raphson algorithm [Dll]. (4-2b) , which are the basic equations for the decoupled line-loss algorithms, with equations (l-16a) and (l-16b), which represent the Fast Decoupled (Newton-Raphson) Load-Flow. The two sets of equations are remarkably similar. Indeed, the matrices of coefficients in equations (4-2a) and (l-16a) are exactly identical. Equation (4-2b) is only slightly different from equation (l-16b); but i f the approximation u 2 A — j £ U AU is made, then the two w i l l become almost identical. It must be mentioned, however, that equations (l-16a) and (1-I6b) were obtained by making a number of practical assumptions after applying the decoupling principle while, equations (4-2a) and (4-2b) are obtained simply by neglecting P-U and Q-6 couplings. Between the two decoupled line-loss algorithms, algorithm B is more similar to the Fast Decoupled (Newton-Raphson) Load-Flow. It is very interesting to compare the equations (4-2a) and 63. 4.2 The Iterative Process Like the incremental-change line-loss algorithm, the decoupled algorithms A and B need a set of i n i t i a l estimates for the voltages of the system. However, unlike the former algorithm, the matrices of coefficients in the latter are not the same as that of the basic l i n e -loss algorithm. Therefore, although i t is possible to start these algo-rithms by f i r s t performing one cycle of the basic line-loss algorithm, this would require forming and solving a different set of equations during the f i r s t iteration step. This is a very time consuming process. For this reason, the decoupled line-loss algorithms are always started using a f l a t - s t a r t . The solution of either (4-2a) or (4-2b) i s considered to be one "half iteration". Prior to solving (4-2a) or (4-2b), the active or re-active power mismatches are checked against the desired tolerance. If a l l these mismatches are within the desired limits, the solution of the corresponding set of equations is skipped. Hence, depending upon the convergence characteristics of different systems, one set of equations may have to be solved more often than the other. The algorithm always starts by trying to solve (4-2a), because this was found (experimentally) to be always preferable. The flow-chart of Figure 4.1 summarizes the iterative process for decoupled algorithm A and B. Note that since the matrices of coefficients, [B'] and [B 1 1], are symmetrical and constant, they need to be triangularized only once. As before, the solution of (3-2a) or (3-2b) is always obtained by using the information in the upper triangularized half of these matrices. 64. C START ^ Calculate AP Yes KP = max AP Solve (3-2a) and correct phase angles! Calculate AQ KQ = max IAQ Yes Solve (3-2b) and correct voltage magnitudes' Yes C RETURN Yes Fig. 4.1. Flow-Chart Indicating the Logic of Decoupled Algorithms. 65. 4 . 3 P r o g r a m m i n g a n d S t o r a g e R e q u i r e m e n t s B o t h [ B ' ] a n d [ B " ] , i n e q u a t i o n s ( 4 - 2 a ) a n d ( 4 - 2 b ) , a r e c o n s -t a n t , s y m m e t r i c a l a n d h i g h l y s p a r s e m a t r i c e s . Due t o t h e s p a r s i t y o f t h e s e m a t r i c e s , t h e d e c o u p l e d a l g o r i t h m s A a n d B c a n b e n e f i t a g r e a t d e a l f r o m o r d e r e d G a u s s i a n e l i m i n a t i o n a n d s p a r s i t y p r o g r a m m i n g t e c h n i -q u e s . T h e s t o r a g e r e q u i r e m e n t s o f t h e s e a l g o r i t h m s , t h e n , w o u l d b e m u c h l e s s t h a n t h o s e o f t h e N e w t o n - R a p h s o n a l g o r i t h m a n d e x a c t l y t h e s ame a s t h o s e o f t h e F a s t D e c o u p l e d ( N e w t o n - R a p h s o n ) L o a d - F l o w . F u r t h e r m o r e , i f s t o r a g e i s a v e r y s e r i o u s l i m i t a t i o n , t h e s t o r a g e r e q u i r e m e n t s o f t h e s e a l g o r i t h m s c a n b e s u b s t a n t i a l l y r e d u c e d , o f c o u r s e , a t t h e e x p e n s e o f i n c r e a s e d c o m p u t a t i o n t i m e p e r i t e r a t i o n . S i n c e b o t h m a t r i c e s a r e s y m m e t r i c a l a n d c o n s t a n t , t h e y n e e d t o b e t r i a n g u l a r i z e d o n l y o n c e a n d o n l y t h e u p p e r h a l f o f t h e i r t r i a n -g u l a r i z e d r e s u l t s n e e d b e s t o r e d . T h e o r d e r i n g o f t h e r o w s i s e x a c t l y t h e s ame f o r [ B ' J a n d f o r t h e J a c o b i a n m a t r i x i n t h e N e w t o n - R a p h s o n a l g o r i t h m a n d t h e m a t r i x o f c o e f f i c i e n t s i n t h e i n c r e m e n t a l - c h a n g e l i n e -l o s s a l g o r i t h m . T h e same o r d e r i n g i s a s s u m e d f o r t h e r o w s o f [ B 1 1 ] . W i t h s u c h o r d e r i n g o f t h e r o w s , h o w e v e r , t h e d e c o u p l e d a l g o r i t h m s r e -q u i r e j u s t s l i g h t l y o v e r h a l f t h e c o m p u t e r s t o r a g e n e e d e d b y t h e o t h e r a l g o r i t h m s m e n t i o n e d a b o v e . T h e s t o r a g e s c h e m e u s e d f o r t h e s e a l g o r i t h m s , w h i c h i s t h e ( * ) s ame a s t h e o n e u s e d f o r p r o g r a m m i n g t h e F a s t D e c o u p l e d ( N e w t o n -R a p h s o n ) L o a d - F l o w , i s v e r y s i m i l a r t o t h a t o f t h e i n c r e m e n t a l - c h a n g e l i n e - l o s s a l g o r i t h m , a s e x p l a i n e d i n s e c t i o n 3 . 3 . B o t h [ B ' ] a n d [ B " ] ( * ) T h i s i s t h e s t o r a g e s c h e m e u s e d i n L F P . S t o t t a n d A l s a c d i d n o t m e n t i o n w h a t s t o r a g e s c h e m e t h e y u s e d i n I D11 ] . 66. are formed and triangularized, row by row, and stored in compact form in two separate vectors. There are two vectors of pointers, indicating the starting locations of each row in [B'] and [B"]. The compact forms of [B'] and [B11] consist of integer column pointers followed by respec-tive entries of the triangularized matrices. The scheme is considerably simpler than that used for the incremental-change line-loss algorithm (and also for.the Newton-Raphson algorithm) since there is no necessity of distinguishing between P-Q and P-V pointers. As was the case with the incremental-change line-loss algorithm, however, each row is formed in a working-row, combined with the previously processed rows and trian-gularized, and then stored in compact form. Here again, only the entries in the upper half of the triangularized matrices (plus the diagonal elements) are stored. This information is sufficient for carrying out triangularization/back substitution process on any right-hand side vector. 4.4 The Numerical Results The results of comparison between decoupled algorithms A and B, and other algorithms are shown in Tables 4.1 and 4.2. A flat-start and a tolerance of .01 P.U. (1 MW/1 MVAR) on maximum power mismatch was specified for a l l the runs. The test systems are those l i s t e d in Table 2.2. The rate of convergence of these algorithms are compared with that of the Fast Decoupled (Newton-Raphson) algorithm in Figures 4.1, 4.2 and 4.3. Since [B'] and |B"] are of smaller dimensions than the matrix of coefficients of the incremental-change line-loss load-flow algorithm, a reduction in computation time per iteration i s expected as a result of decoupling. However, Table 4.2 shows that this i s not the case. The reason for this is that in the decoupled algorithms almost a l l the search operations are duplicated. This cannot be avoided i f the f l e x i b i -l i t y of performing each half iteration separately is to be preserved. The only way to eliminate this problem would be to solve (4-2a) and (4-2b) simultaneously which, however, greatly degrades the performance of the decoupled algorithms. Tables 4.1 and 4.2 indicate that the performance of the de-coupled line-loss algorithms is comparable to that of the Fast Decoupled (Newton-Raphson) Load-Flow. This was to be expected since there i s a remarkable similarity between the equations used by the two algorithms. However, in order to better compare the r e l i a b i l i t y of the decoupled line-loss algorithms A and B with that of the Fast Decoupled (Newton-Raphson) Load-Flow, i t was decided to check their behaviour with respect to heavily overloaded systems. Test System 5 (IEEE 30-bus system) was overloaded, step by step, and the load-flow problem was solved for each loading level using various algorithms. The Newton-Raphson algorithm, the Basic line-loss algorithm and the incremental-change line-loss algorithm a l l diverged for the same loading level. This breaking point was when a l l the power injections (both loads and generations) were 1.8 times greater than their original values. On the other hand, a l l the decoupled algorithms converged for this loading level: the Fast Decoupled (Newton-Raphson) Load Flow converged in 27 half-iterations (216 milliseconds); algorithm A converged in 16 half iterations (164 milliseconds)"; and algorithm B converged in 20 half iterations (187 milliseconds). The differences in computation times and the number of iterations are noticeably in favour of the 68. System N-R FDL line loss alg. Inc. line change Decoupled line loss alg. J L O S S arg. Alg. A Alg. B 1 2 2 2 2 14 i i 2 2 24 3 3 24 24 3* 2 24 3 3 7 ' 24 4 2 24 2 2 34 2± 5* 2 2 2 2 3 2 6 3 4 NC 5 34 44 7 3 24 6 6 3 3 8* 2 3 3 3 34 24 9 3 6 12 12 44 44 10 4 44 13 13 6i 44 Table 4. 1. Comparison D f Number of Iterations (NC: No Convergence). System N-R FDL line loss alg. Inc. line change Decoupled line loss alg. Alg. A Alg. B 1 7 9 7 6 8 :7 2 13 12 13 10 12 12 3* 36 31 32 25 57 30 4 79 54 49 42 63 53 5* 112 75 70 61 87 73 6 119 101 NC 80 94 107 7 162 98 153 113 108 108 8* 336 224 218 • 188 235 210 9 808 563 836 616 505 495 10 2337 1091 1751 1247 1263 1063 Table 4.2. Comparison of Computation Times. (Times in milliseconds) (NC: No Convergence) 69. •* F i g . 4 .2 . Comparison of the A l g e b r a i c Sum of a l l the Power Mismatches. (Test System 8) 70. DECOUPLED N-R ALGORITHM A . ALGORITHM B . 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 6.0 ITERATION F i g . 4.3. Comparison of the Maximum Power Mismatches. (Test System 8) 71. F i g . 4.4. Comparison of Sum of a l l the A b s o l u t e V a l u e s o f Power Mismatches. (Test System 8) 72. decoupled line-loss algorithms, especially algorithm A, which has less similarity with the Fast Decoupled (Newton-Raphson) Load-Flow. When the system was slightly (one per cent) more overloaded, the Fast Decoupled (Newton-Raphson) Load-Flow diverged while both de-coupled line-loss algorithms converged, each taking 20 half iterations. As the overloading continued, in small one per cent steps, both de-coupled algorithms converged for three more steps u n t i l , f i n a l l y , algorithm B diverged. For this loading level, algorithm A was the only algorithm that solved the problem. After this point, none of the load-f'low algorithms converged. The above test indicates that while the decoupled line-loss algorithms have the same performance as the Fast Decoupled (Newton-Raphson) Load-Flow, they are more reliable. The assumption made in deriving algorithm B, slightly improves the performance of this algor-ithm while, at the same time, makes i t slightly less reliable. 7 3 . 5. CONCLUSIONS In a power system, the l i n e losses can be used to derive the constant gradient, f a s t converging l i n e - l o s s load-flow algorithm. The algorithm i t e r a t i v e l y solves a set of l i n e a r equations i n terms of voltage magnitudes squared and phase angles, and converges onto the f i n a l s o l u t i o n i n a few i t e r a t i o n s . Although the performance of the algorithm improves i f the (approximate) values of l i n e - l o s s e s are i n i t i a l l y known, such knowledge i s not a p r e - r e q u i s i t e to using the algorithm. For p r a c t i c a l accuracies, even when the i n i t i a l estimates of l i n e - l o s s e s are assumed zero, the l i n e - l o s s algorithm converges considerably f a s t e r than the standard Newton-Raphson algorithm. A s l i g h t l y modified version of the l i n e - l o s s algorithm, written i n terms of the incremental changes to the voltage magnitudes squared and phase angles, performs even better than the o r i g i n a l version. For a l l the test systems used, i t converges considerably f a s t e r than the Newton-Raphson algorithm - i n some cases i t i s almost twice as f a s t . The decoupled versions of the incremental change l i n e - l o s s algorithm have convergence c h a r a c t e r i s t i c s s i m i l a r to those of the Fast Decoupled (Newton-Raphson) Load-Flow [ D l l ] . As compared with the undecoupled version of t h i s algorithm, they show d e f i n i t e improve-ment with respect to the required number of i t e r a t i o n s ; but not with respect to computation time. In the decoupled algorithms, the corrections are calculated and applied at the end of every h a l f i t e r a t i o n ; r e s u l t i n g i n improved o v e r a l l performance and the increased computation time per i t e r a t i o n . J 74. A l l the line-loss algorithms have very reliable convergence. In particular, the results of using these algorithms for solving the load-flow problem on heavily overloaded systems showed that the con-vergence of the line-loss algorithms is at least as reliable as that of the Newton-Raphson algorithm. The results also showed that the decoupled line loss algorithms are more reliable than the Newton-Raphson algorithm and the Fast Decoupled (Newton-Raphson) Load-Flow. The storage requirements of the line-loss algorithms are, at most, equal to those of the standard Newton-Raphson algorithm. The decoupled versions of the line-loss algorithm have the same storage requirements as the Fast Decoupled (Newton-Raphson) Load-Flow. However, i f storage is a serious limitation, in both cases, the storage require-ments can be reduced to those of the Y-matrix algorithms. The matrix of coefficients in the line-loss algorithms is very easy to construct and is directly related to the system nodal admittance matrix. Hence, slight changes in the system configuration can be easily reflected in the algorithm. Furthermore, approximate load-flow solutions can be obtained after performing only one iteration of the line-loss algorithm. These characteristics make the line-loss algorithms particularly attractive for study of system outages, where numerous load-flow problems, only slightly different from one another, have to be solved and only approximate answers are required. BIBLIOGRAPHY General: [Gl] Arsov, D. and Hammam, M.S.A.A.; "Sensitivity of Load Flow"; Presented at the IEEE PES Winter Meeting; New York, N.Y.; Jan. 27-Feb. 1, 1974, Paper C74 018-8. 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[D7] Peterson, N.M., Tinney, W.F. and Bree, D.W.; "Iterative Linear AC Power Flow Solution for Fast Approximate Outage Studies"; IEEE Trans, on PAS; Vol. PAS-91; Sept./Oct. 1972; pp. 2048-2056. [D8] Sasson, A.M., Snyder, W. and Flam, M.; "Comments on 'Review of Load-Flow Calculation Methods'"; Proc. of IEEE; Vol. 63, no 4; April 1975; pp. 712-715. [D9] Stott, B.; "Decoupled Newton Load Flow"; IEEE Trans, on PAS; Vol. PAS-91; Sept./Oct. 1972; pp. 1955-1959. [D10] Stott, B.; "Effective Starting Process for Newton-Raphson Load Flows"; Proc. IEE; Vol. 118, no 8; Aug. 1971; pp. 983-987. [Dll] Stott, B. and Alsac, 0.; "Fast Decoupled Load Flow"; IEEE Trans, on PAS; Vol. PAS-93; May/June 1974; pp. 859-869. [D12] Uemura, K.; "Power Flow Solution by a Z-matrix Type Method and i t s Application to Contingency Evaluation"; PICA Conference Paper; 1971; pp. 386-390. Diakoptics (Tearing): [Tl] Happ, H.H.; "Diakoptics - The Solution of System Problems by Tearing"; Proc. of the IEEE; Vol. 62, no 7; July 1974; pp. 930-940. [T2] Happ, H.H.; "Multi-Level Tearing and Application"; IEEE Trans, on PAS, Vol. PAS-92, Mar/April-1973, pp. 725-733. [T3] Jain, M.K. and Rao, N.D.; "A Piecewise Solution of Z-Bus Load Flow"; Presented at the IEEE PES Summer Meeting & Energy Resources Conf.; Anaheim, Calif.; July 14-19, 1974; Paper C74 348-9. .81. [T4] Kesavan, H.K, and Bhat, M.V.; "Piecewise Newton-Raphson Method: An Exact Model"; Presented at the IEEE PES Winter Meeting; New York, N.Y.; Jan. 27-Feb. 1, 1974; Paper C74 165-7. [T5] Sasson, A.M.; "Decomposition Technique Applied to the Nonlinear Programming Load-Flow"; 1969 PICA Conference Papers; pp. 242-248. [T6] Sasson, A.M. and Brown, H.E.; "Deductions and Clarifications on the Diakoptics Approach"; 1971 PICA Conference Papers; pp. 433-439. Other Load Flow Algorithms: [01] Birt, K.A., Graffy, J.J. and McDonald, J.D.; "Three Phase Load Flow Program"; IEEE Trans, on PAS, Vol. PAS-95, No. '1," Jan/ Feb. 1976, pp. 59-65. ' [02] Borkowska, B. ; "Probablistic Load Flow"; IEEE'-Trans. on PAS, Vol. PAS-93, May/June 1974,-pp .-k 752-759. : • [03] Bosarge Jr., W.E., Jordan, J.A. and Murray, W.A.: "A Nonlinear l° Block SOR-Newton Load-Flow Algorithm"; Presented at the IEEE PES Summer Meeting & EHV/UHV Conference; Vancouver, Canada; July 15-20, 1973; Paper C73 464-5. [04] Cheann, H.R. and Jalali-Kushki, H.; "A New Formulation of the Load-Flow Problem"; Presented at the IEEE PES Winter Meeting; New York, N.Y.; Jan. 27-Feb. 1, 1974; Paper C74 164-0. [05] Dopazo, J.F., K l i t i n , O.A. and Sasson, A.M.; "Stochastic Load Flows"; IEEE Trans, on PAS; Vol. PAS-92, no 2; March-April, 1975; pp. 299-309. [06] Dusonchet, Y.P., Talukdar, S.N., Sinnott, H.E. and El-Abiad, A.H, "Load Flows Using a Combination of Point Jacobi and Newton's Methods"; IEEE Trans, on PAS; Vol. PAS-90; May/June 1971; pp. 941-949. [07] Galloway, R.H., Taylor, J., Hogg, W.D. and Scott, M.; "New Approach to Power-System Load-Flow Analysis in a Digital Computer"; Proc. IEE; Vol. 117; Jan. 1970; pp. 165-169. [08] Jalali-Kushki, H.; A New Formulation of the Load-Flow Problem; MASc Thesis; University of B.C.; Vancouver, Canada; 1973. [09] Jalali-Kushki, H. and Wvong, M.D.; "A Load-Flow Algorithm Using Approximate Line Losses"; Presented at the IEEE Winter Power Meeting; New York, N.Y.; Jan. 31-Feb. 4, 1977; Paper A77 142-3; IEEE Pub. 77 CH 1190-8-PWR. 82. [010] Okamura, M., et a l ; "A New Power Flow Model and Solution Method" IEEE Trans, on PAS, Vol. PAS-94, May/June 1975, pp. 1042-1050. [Oil] Roy, L. and Menon, K.B.; "A Generalized Piecewise Load Flow Method"; Presented at the IEEE PES Summer Meeting & Energy Resources Conf.; Anaheim, Calif.; July 14-19, 1974; Paper C 74 329-9. [012] Sachdev, M.S. and Medicherla, T.K.P.; "A Second Order Load Flow Technique"; IEEE Trans, on PAS, Vol. PAS-96, No. 1, Jan/Feb. 1977, pp. 189-197. , , [013] Semlyen, A. and Pervaiz, S.Z.; "Power Flow Calculation by Comple Waves"; Presented at the IEEE PES Summer Meeting & Energy Resources Conf.; Anaheim, Calif.; July 14-19, 1974; Paper C 74 332-3. [014] Wvong, M.D. and J a l a l i - K u s h k i , H.; "Comparison of the Line-Loss Load-Flow Algorithm with the Newton-Raphson Load-Flow"; 1977 PICA Proceedings^::pp.i.321=324v, , 83. APPENDIX A USER'S MANUAL FOR LFP A . l Introduction LFP stands f o r the "Load Flow Package". I t r e f e r s to a c o l l e c -t i o n of computer programs written for the purpose of comparing the per-formance of various load-flow algorithms. At the present time, only the Newton-Raphson algorithm, the Fast Decoupled (Newton-Raphson) Load-Flow, and the d i f f e r e n t versions of the l i n e - l o s s algorithm described i n t h i s t h e s i s , are a v a i l a b l e . However, the structure of the package i s such that any other algorithm can be added to i t without d i f f i c u t l y . Also, LFP has f a i r l y extensive monitoring features which make i t p a r t i -c u l a r l y a t t r a c t i v e f o r research work. The package consists of three d i s t i n c t modules, which operate i n succession "to one another i n the following order: (1) The input module; t h i s module reads the input data, rearranges t h i s data according to an i n t e r n a l format while saving the external bus numbers and other information not required by the load-flow algorithm, provides a l i s t i n g o o f input data i f necessary, forms the compact nodal admittance matrix, i n i t i a -l i z e s the proper vectors, sets proper pointers to the load-flow algorithm requested by the user, etc., etc. The output from this module i s ready to be processed.by the proper load-flow algorithm. (2) The process module; t h i s module performs the proper i t e r a t i v e process on the data provided by the input module. I t also p r i n t s the values of v a r i a b l e s at the end of various i t e r a t i o n steps i f such information i s required. The output from t h i s 84. module is the f i n a l values of voltages along with some other information such as the number of iterations and the computa-tion time taken by that particular algorithm. (3) The output module; this module prints and/or plots the output information. The same input and output modules are shared by a l l the algorithms while each algorithm has i t s own process module. LFP was written for use on UBC's IBM 370/168 d i g i t a l computer. Except for two small routines in IBM 370 assembly language, the programs are written in FORTRAN IV. They make use of several MTS features as well as some of the programs provided by UBC Computing Centre. A l l the pro-grams use single precision arithmetic. Dynamic storage allocation and sparsity programming techniques are employed to ensure efficient use of storage. With these features, LFP is capable of handling very large power systems - systems of the order of few thousand buses and trans-mission lines. The main purpose of this Appendix i s to explain •'the data preparation and use of the LFP. When necessary, comments are also made about the programming details and the structure of the package. A.2 How to Use The object module i s in the f i l e LFP. The prefix & i s used to specify the package (especially useful in terminal mode). The pro-gram may be used by issuing the following command: $R LFP SCARDS = ... SPRINT = ... PAR - (Parameter l i s t as) defined below SCARDS may be assigned to the f i l e or device from which the load-flow data is to be read and SPRINT to the unit on which the output should 85. appear. In terminal mode, the communication with the user is done via GUSER and SERCOM. The PAR f i e l d contains the information about the load-flow algorithm to be used, the starting point and the data f i l e . This i n -formation is provided using the following Keyword parameters. (Only the f i r s t letter of each Keyword would suffice): (1) ALGORITHM = name of the load-flow algorithm to be used. Only one name must be specified and i t must be one of those speci-fied in section A. 3, or names of other algorithms which may be added to the package at a later date. There i s no default for this Keyword. Not specifying i t either w i l l terminate the job (batchrmode) or w i l l result in an error message followed by a request for that information (terminal mode). (2) DATA - name of the f i l e or device that contains the laod-flow data. The default for this Keyword is *SOURCE*? The format of the data must be as explained in section A.4. (3) START - F or N. The default value i s F, which indicates a flat-start or zero i n i t i a l estimates for the losses, depending upon the load-flow algorithm being used. START = N indicates a non-flat starting point. The i n i t i a l estimates of losses or voltages must be provided at a later point in the program. See section A.5 for more details. Except for the name of the algorithm, these Keywords are optional. Their order i s not important and they may be separated by commas and/or blanks. If a Keyword is specified several times the last value w i l l be used. Note that using SCARDS = ... or DATA = ... Keywords, gives identical results. 86. If no PAR f i e l d i s specified, either the job would be ter-minated (batch mode) or the user is requested to provide a PAR f i e l d (terminal mode). The information in this f i e l d i s printed as part of the heading on every page of the output (unless other heading informa-tion i s provided; see section A. 4). If an error is detected in the PAR f i e l d , either the job is terminated (batch) or the user is requested to respecify the PAR f i e l d (terminal). A.3 The Algorithms At the present time, only the algorithms l i s t e d in this sec-tion may be specified. Other load-flow algorithms may be programmed and added to LFP, in which case the name of their respective entry points (SUBROUTINE or ENTRY) are used to specify the algorithms. The only restriction (apart from those imposed by the programming language) is that these names should not start with the letter "L". Names which start with L are considered as belonging to the line-loss algorithms. For these algorithms, START = N means that the i n i t i a l estimates of line losses (not voltages) are specified. The algorithms that may be specified are one of the following: NEWTON: The Newton-Raphson algorithm. STOTT: The Fast Decoupled (Newton-Raphson) Load-Flow. L0SS1: The basic line-loss algorithm. The algorithms starts by setting the line losses either to zero or to their i n i t i a l estimates, depending upon whether START = F or N." FL0SS1: The basic line loss algorithm starting from a fla t - s t a r t or from another point specified by the user, depending upon whether START = F or N. This is another' entry point in L0SS1. 87. LSS1M: The incremental-change line-loss algorithm. Starts with one cycle of the basic line-loss algorithm in which the losses are i n i t i a l l y set to zero or to their estimated values, depending upon whether START = F or N. FLSS1M: The incremental-change line-loss algorithm, starting either from a flat-start or from another starting point specified by the user. This is another entry point in LSS1M. DECPLl: The decoupled line-loss algorithm A. DECPL2: The decoupled line-loss algorithm B. This is another entry point in DECPLl. Apart from the above algorithms, the following names may also be specified: TEST: Used only for testing the input module. Prints out the infor-mation processed by this module. FLOWS: This i s an entry point in LFP which may be specified i f the power flows corresponding to a set of voltages are to be cal-culated. In that case, the START = N must be specified. A. 4 The Data Preparation Each data f i l e contains several different kinds of data re-cords. Some records contain information about different elements in the system; some contain the general information controlling the number of iterations, the length and the type of the output, etc; and some contain comments or the heading information which is to be printed on the top of every output page. Different records are distinguished by means of the character in their f i r s t column. For example, a record starting with letter B contains the information about one of the system's buses while a record starting with letter H contains the heading information. 88. Because of this, the input records may be arranged in any arbitrary order. The following is a brief description and format of each data record. A.4.1 Bus Information Records: Letter in the f i r s t column is "B". Each record contains the information about one particular bus in the system. This information (and i t s format, in parenthesis) i s as follows: BUS TYPE: A one digit integer number in column 2; (II). 1 is used for P-Q buses; 2 is used for P-V buses; 3 i s used for the slack buses. BUS NUMBER: A five digit.integer number in columns 3 to 7; (15). This can be any arbitrary number. Used in communications with the user. BUS NAME: An eight character alphanumerical string in columns 9 to 16; (A8). This can be any arbitrary combination of eight characters. Used as the bus name in the output printout. BUS GENERATION: A complex number in columns 19 to 32; (2F7.2). Specifies the total active and reactive power generation of the bus in MW. Positive signs are used for generation. BUS LOAD: A complex number i n columns 33 to 48; (2F8.2). Speci-fies the total active and reactive bus load in MW. Positive signs are used for load. GENERATOR Q LIMITS: Two real numbers in columns 49 to 63. These are the lower and upper limits for the reactive power genera-tion of P-V buses in MW. At present, LFP does not use this information. 8 9 . BASE "VOLTAGE: A r e a l n u m b e r i n c o l u m n s 64 t o 7 0 ; ( E 7 . 2 ) . S p e c i f i e s t h e b a s e v o l t a g e o f t h e b u s i n K V . VOLTAGE MAGN ITUDE : A r e a l n u m b e r i n c o l u m n s 7 1 t o 7 7 ; ( F 7 . 2 ) . S p e c i -f i e s t h e d e s i r e d m a g n i t u d e o f v o l t a g e f o r P - V a n d s l a c k b u s e s i n K V . A . 4 . 2 T r a n s m i s s i o n L i n e I n f o r m a t i o n R e c o r d s L e t t e r i n t h e f i r s t c o l u m n i s " L " . E a c h r e c o r d c o n t a i n s t h e i n f o r m a t i o n a b o u t o n e p a r t i c u l a r t r a n s m i s s i o n l i n e i n t h e s y s t e m . T h i s i n f o r m a t i o n ( a n d i t s f o r m a t , i n p a r e n t h e s i s ) i s a s f o l l o w s : L I N E NUMBER: A s i x d i g i t i n t e g e r n u m b e r i n c o l u m n s 2 t o 7 ; ( 1 6 ) . T h i s i s a n a r b i t r a r y n u m b e r a s s i g n e d b y t h e u s e r a n d u s e d i n t h e p r i n t o u t . L I N E NAME : A n e i g h t c h a r a c t e r a l p h a n u m e r i c s t r i n g i n c o l u m n s 9 t o 1 6 ; ( A 8 ) . SEND ING END BUS N O . : A f i v e d i g i t i n t e g e r n u m b e r i n c o l u m n s 17 t o 21 i n d i c a t i n g t h e b u s n u m b e r o f o n e e n d o f t h e t r a n s m i s s i o n l i n e ; ( 1 5 ) . T h i s n u m b e r m u s t a l s o b e s p e c i f i e d o n a b u s i n f o r m a t i o n r e c o r d . R E C E I V I N G END BUS N O . : A f i v e d i g i t i n t e g e r n u m b e r i n c o l u m n s 22 t o 26 i n d i c a t i n g t h e b u s n u m b e r o f t h e o t h e r e n d o f t h e t r a n s m i s s i o n l i n e ; ( 1 5 ) . T h i s n u m b e r m u s t a l s o b e s p e c i f i e d o n a b u s i n f o r m a t i o n r e c o r d . L I N E I M P E D A N C E : A c o m p l e x n u m b e r i n c o l u m n s 2 9 , 4 4 ; ( 2 F 8 . 5 ) . S p e c i f i e s t h e p e r u n i t v a l u e o f t h e l i n e i m p e d a n c e . 90. SENDING END SUSCEPTANCE: A real number in columns 49 to 55; (F7.5). Specifies, the per unit value of shunt admittance at the sending end of the line. RECEIVING END SUSCEPTANCE: A real number in columns 56 to 62; (F7.5). Specifies the per unit value of shunt admittance at the receiving end of the line. TRANSFORMER INDICATOR: A logical value in column 64; (LI). A "T" in that column indicates that the line has a transformer as well. In this case, the data f i l e must also contain a trans-former record with the same number. Otherwise, an error occurs. A.4.3 Transformer Records Letter in the f i r s t column is "T". Each record contains the information about one transformer in the system. Transformer taps must be fixed. If there i s a transmission line which also has a transformer, the information about the transmission line must appear on a separate "L" record. (The order of the records i s not important). The information on each record i s as follows: TRANSFORMER NUMBER: A six digit integer number in columns 2 to 7; (16). This number is used to specify the- transformer in the output printout. If a transformer i s part of a trans-mission line, this number must be the same as the transmission line number on the "L" record. TRANSFORMER NAME: An eight digit character string in columns 9 to 16; (A8). SENDING END NUMBER: A five digit integer number in columns 17 to 21; (15). Specifies the bus number of the sending end of 91. the transformer. This number must be specified on a bus information record. If the transformer i s part of a transmission line which i s specified on a "L" record, this number should be the same on the two records. RECEIVING END NUMBER: A five digit integerunumber in columns 22 to 26; (15). Specifies the bus number of the receiving end of the transformer. The comments made about the above item apply here as well. TRANSFORMER IMPEDANCE: A complex number in columns 27 to 41; (2F8.5). Specifies the per unit value of transformer impedance. SENDING END TAP: A real number in columns 43 to 50; (F8.4). Specifies the transformer tap (rturn ratio) on the sending end side of the transformer. RECEIVING END TAP: A real number in columns 51 to 58; (F8.4). Speci-fies the transformer tap (turn ratio) on the receiving end of the transformer. A.4.4 The Heading Records Letter in the f i r s t column i s "H". The information in the f i r s t 48 columns of this record, with the exception of column 1, are printed at the top of every page as part of the heading information. The remaining positions In the heading w i l l contain date and time. If no such record i s given the default heading w i l l be used. If there are several "H" records in a data f i l e , the last one w i l l overwrite the previous ones. 92. A.4.5 The Comment Records Letter in the f i r s t column is "C". The information in columns 2 to 80 of these records are printed before the f i r s t output page is printed. Up to ten "C" records may be specified for each data f i l e . This data is printed in the same order that i t appears in the data f i l e . A.4.6 The General Control Records Letter in the f i r s t column is "G". This record may contain the information about the maximum number of iterations permitted, the length and type of output, the desired tolerance (on maximum power mismatches), the "ZERO" of the run (values with absolute values smaller than "ZERO" are assumed zero.), and the MVA base of the system. If no "G" record i s specified, or i f any of the above information is not specified on the "G" record, the default values would be used. If any of the values is assigned several times, the last assignment would be used. The information on this record is specified by using several Keywords as follows. Only the f i r s t character of each Keyword would be sufficient: ITERATIONS = maximum number of iterations permitted. This must be a positive integer number. The default value i s 100. LIST = an integer number indicating the length and the type of output to be produced. The following is an explanation of various p o s s i b i l i t i e s : LIST = 1 indicates that only the f i r s t page of the out-put should be printed. This page contains a summary of the results. 9 3 . LIST = 2 is used i f the fullooutput i s to be printed. The output for this case is the output of LIST = 1 plus the complete printout of power flows through various branches. This is the default value. LIST = 6 or 7: is identical to LIST = 1 or 2 except that, in this case, the input data is printed as well. LIST = n l , n2, n6 or n7, where n is any positive inte-ger, is exactly identical to LIST = 1, 2, 6 or 7 except that, i n this case, the values of desired voltage magni-tudes and phase angles and also the values of power mis-matches are printed at the end of every n iteration. (See section A.5 for details). LIST = -1, -2, -6 or -7 i s the same as LIST = 1, 2, 6 or 7, respectively except that, in this case, the values of power mismatches and the voltage magnitudes and phase angles of the desired buses (see section A.5 for details), w i l l be plotted as well. LIST = - n l , -n2, -n6 or -n7 where n is any positive integer, is the same as LIST = -1, -2, -6 or -7, res-pectively except that, here, the values of power mis-matches and the voltage magnitudes and phase angles of the desired buses are also printed at the end of every n iteration. In other words, the effect is that of the two above categories combined. TOLERANCE = any real-number indicating the desired tolerance for the load-flow study in P.U. The default value is .005 E.U. ZERO = any real number; specifying the minimum non-zero absolute 94. value of a number. Numbers with an absolute value less than "ZERO" are assumed zero. The default value is .00005. BASE MVA: any real number; specifying the MVA base of the system. This value is used in converting the P.U. quantities back into their real values. The default value is 100 MVA. A.4.7 Data Set Definition Records Letter in the f i r s t column is "D". This record i s used to indicate to LFP that the rest of data records are to be read from the unit specified on this record. The format of this record i s a "D" in the f i r s t column and, a two digit integer number, indicating^the number of a logical unit, in columns 10 and 11. This record is usually used as the last record in a data f i l e . In this way, after the data in the f i l e is read, the control is trans-ferred to GUSER, enabling the user to enter any particular commands (data records) he may have for that run. A.4.8 The End Record Letter in the f i r s t column "E". The f i r s t letter i s the only information used from this re-cord. As soon as an "E" record i s encountered, the input module stops reading any other input records. The effect of "E" records is identical to, and can be achieved by, using $END OF FILE. If any record with an i n i t i a l other than those mentioned above is encountered, either the job w i l l be terminated (batch mode) or the user w i l l be asked to intervene (terminal mode). A sample data f i l e i s l i s t e d below. This i s the data for Test System 6: 9 5 . G 1=1C T=.C1 Z=.00C05 L=2 B3 1 ING230 230. B2 3 JHT 13 127. 13.8 BI 4 LOR 13 47.C 5.0 13.8 BI 5 SCA 13 25.8 5.0 13.8 B2 6 PUN 13 24.5 17.8 - 8.15 13.8 62 7 ASH 13 26. 7 13.8 B2 8 GGA 13 72.0 13.8 B I 10 JHT132 132.0 BI 11 DBY132 64. 6.4 132.0 BI 12 L0R132 C O 0.0 0.0 0.0 132.0 61 13 SCA122 C.C 0.0 0.0 0.0 132. BI 14 GLD132 0.0 0.0 5.0 2.5 132. B I 16 TAS132 C O 0.0 18.0 5.4 132.0 BI 17 CTI132 C O 0.0 0.0 0.0 132.0 BI 19 CBL132 0.0 0.0 10.6 5.3 132.0 B I 20 PUN132 C.C 0.0 10.0 3.0 132.0 61 22 DMR132 C.C 0.0 0.0 0.0 132.0 B I 23 PAL132 0.0 0.0 107.3 36.3 132.0 61 24 GCL132 C.C 0.0 6.9 2.6 132.0 BI 25 ASH132 0.0 0.0 0.0 0.0 132.0 BI 26 N0R132 0.0 0.0 9.6 4.8 132.0 B I 27 HMC132 C.C 0.0 24.0 7.2 132.0 B I 29 JPT132 C O 0.0 0.0 0.0 132.0 B I 30 VIT230 C O 0.0 0.0 0.0 230.0 BI 31 VIT 12 C O 0.0 0.0 0.0 12.6 BI 33 JPT 60 0.0 0.86 27.i B 15.9 60.0 BI 34 JPT 12 C.C 15. 0 0.0 0.0 12.0 BI 35 GGA132 0.0 0.0 0.0 0.0 132.0 BI 36 CFT132 0.0 0.0 65.4 20.3 132.0 B I 37 ARN230 C O 0.0 0.0 0.0 230.0 BI 38 ARN132 0.0 0.0 0.0 0.0 132.0 61 39 ST0132 25. C 93.0 197.5 140. 5 132.0 BI 40 VIT132 C.C 0.0 0.0 0.0 132.0 L 15 TAS132 14 16 .01575 .C393 .0088 .0088 L 17 DBY132 10 11 .0017 .0052 • C044 .0044 L 19 GL0132 13 14 .0516 . 129 .0286 .0286 F L 20 SCA132 12 13 .0168 .0448 .009 .009 F L 21 LDR132 10 12 .0017 • CC86 .0064 .0084 F ' L 22 CBL132 17 19 .00416 .01228 .0028 .0028 F L 23 C T l 1 3 2 10 17 .00208 .C0614 .0014 .0014 F L 24 P U M 3 2 17 20 .04102 .12C86 .0266 .0266 F L 25 DMR132 10 22 .04095 .12270 .1042 .1042 F L 26 OMR132 20 22 .04C4 . 1194 .0262 .0262 F L 27 ASH132 24 25 .0161 . C427 .0084 .0084 F L 28 GCL132 23 24 .0176 .0458 .0092 .0092 F L 29 PAL132 22 23 • 01C7 .C326 .0276 .0276 F L 30 JPT132 22 29 .02 54 . C75 .0656 .0656 F L 31 JPT132 26 29 .0165 .0431 .0086 .0086 F L 32 JPT132 27 29 .0165 .C431 .0086 .0086 F L 33 ST0132 29 39 .0440 . 1299 .0264 .0284 F L 34 GGA132 29 35 .0416 .1231 .0268 .0268 F L 35 CFT132 35 36 .0128 . C3 8 .0C82 .0082 F L 36 ST0132 36 39 .0094 .0279 .0C62 .0062 F L 37 VIT132 39 40 .00C37 .C0313 .0030 .0030 F L 39 VIT132 38 40 .02842 .C6428 .8190 .8190 F L 40 ARN230 1 37 .0026 .01584 .0306 .0306 F T 1 SCA132 5 13 .01632 . 272 1. 131 1.0 1 2 L0R132 4 12 .00949 . 1583 1. 125 1.0 T 3 JHT132 3 10 .00375 . C6245 1. 149 1.0 T 4 PUN132 6 20 .03534 . 5893 1.045 1.0 T 5 ASH132 7 25 .02202 . 3671 1.098 1.0 T 6 JPT 60 29 33 .01184 . 2960 1. 028 1.0 T 7 JPT 12 33 34 .00641 . 1602 1. 0 1.0 T 8 GGA132 8 35 .00393 . 0982 1.099 1.0 T 10 VIT132 30 40 .003 06 1. 019 1.0 T 11 VIT 12 30 31 .00334 . 0667 .975 1.0 T 12 ARN132 37 38 .00114 . 0228 1.032 1.0 CATA SET 15 96. A.5 Comments and Restrictions (1) If START = N i s specified, LFP expects to read the i n i -t i a l estimates of line loss or voltages - depending upon the load-flow algorithm being used - from a f i l e or device. The name of this f i l e or device i s read from GUSER. In terminal mode, the user is asked to pro-vide this information while, in batch mode, the program expects to find this information immediately after the data records. (There is one exception to this. See the next comment). The name of this f i l e or device must be found in the f i r s t 20 columns of the input record. This f i l e or device must contain the i n i t i a l values of voltages - for algorithms whose name does not start with "L" - or line losses - for algorithms whose names start with "L". If no name is given, the data i s expected to come from GUSER. The format of the data for entering the values of voltages is different from that for entering the i n i t i a l values of line losses. In the former case, the i n i t i a l values of bus voltages must be specified, in the same order as that of the input bus records but skipping over the slack buses, using 2F10.5 format. In other words, no bus numbers are necessary since the order i s already fixed. The voltage magnitudes (in P.U.) and the voltage phase angles (in degrees) are specified using the above format. In the latter case, the sending and receiving end bus numbers are specified, followed by the P.U. values of line losses. The order of the records is not important since the sending and receiving end numbers are specified. The format of each record is 215, 2F10.5. Note that the Per Unit values of line-losses have to be specified. In each case the terminal user is given any necessary informa-tion with respect to the points mentioned here. 97. (2) When the LIST Keyword (on the "G" record) is specified such that printing and/or plotting of variables at the end of various iteration steps is desired, the program expects to read the bus numbers whose voltage magnitudes and phase angles are wanted. The terminal user is asked for this information at the proper place. The batch user is expected to enter this information (from *MSOURCE*) immediately after the "E" record. Note that, i f START = N is specified at the same time, the information with respect to the i n i t i a l estimates must follow the information mentioned here. The format of the data is 2014. Unspecified bus numbers are ignored;. However, i f a bus number is entered, and later the negative value of the same number is encountered, the information with respect to that bus is not printed/plotted. In other words, the negative bus numbers may be used to cancel the positive numbers previously entered. If the information about a l l the voltages (except the slack buses) is required, the word ALL can be entered on the first three columns of the record. Otherwise, the bus numbers are read, using 2014 format, until a zero bus number is encountered at which point the information is con-sidered to be complete. The power mismatches will always be printed, along with the information about the desired voltages, at the end of the respective iterations. Therefore, i f only the power mismatches are wanted, a blank record must follow the "E" record, to indicate that there are no bus numbers specified. (3) The following routines were used from UBC Computing Centre's library. They must be available at the time of the run: Character Manipulation Routines: MOVEC, SETC, FINC, FINDST, IGC, DTB, EQUC. 9 8 . Input/Output and Dynamic Storage Allocation Routines: SERCOM, GUSER, SETPFX, GUINFO, CUINFO, FTNCMD, EMPTYF, CREPLY, GSPACE, FSPACE, CALLER. Bit Manipulation Routines: SHFTL, SHFTR, LOR, LXOR. Plotting (Metric): PLCTRL, SYMBOL, NUMBER, PLOT, AXCTRL, SCALE, AXPLOT. Other Routines: CDATE, PAR, LDINFO, TIME. Apart from the above routines, manyoof the MTS features are also used. The program has to be updated according to the changes that may occur to :these features. A listing of the program follows. 99. 1 SUBROUTINE PARR 2 L C G I C A L * ! I ST (2 5 5 ) , B A T C H , H D N G S I 8 0 ) » M T S U l 3 0 J , N A N E ( 1 6 ) , 3 COMMON /C1UTINF/ N P A G E , N L I N E , H D N G S , I S T N O 4 COMMCN /ADS/ I A , I D , I S , A L G , B A T C H 5 I NT EC ER*2 LEN 6 INTEGER S T A R T , F I N I S H 7 LNUM=1 8 CALL MCVECC14,•ASSIGN S C A R C S = ' , M T S U l 9 CALL S E T C ( 8 0 ,HDNGS,* ' 1 10 CALL MOVEC 1 5 , « A L G . = • ,HDNGS) 11 CALL K Q V E C ( 5 , ' C A T A = ' , H D N G S ( 1 4 1 ) 12 CALL M 0 V E C ( 6 , » S T A R T = ' , H D N G S ( 3 9 ) ) 13 CALL COATEIHCNGSC49)) 14 10 CALL PAR(1ST , N I , 2 5 5 , £ 1 0 0 ) 15 GO TO 300 16 ICC I F I B A T C H ) GO TC 150 17 LEN = 6 18 CALL S E R C O M C P A R = ? • , L E N , 0 ) 19 110 CALL S E T P F X P 7 S 1 ) 20 CALL GUSERJI S T , L E N , 0 , L N U M , S I 5 0 1 21 CALL S E T P F X ( ' £ ' , 1 ) 22 NI=LEN 23 GO TO 300 24 150 LEN=19 25 160 CALL SERCOMC NO PAR FIELD GIVEN •, LEN, 0) 26 CALL EXIT 27 300 START= 1 28 IA = 0 29 10=0 30 I S=0 i l . 35C CALL FINDCI I S T . N I , ' A D S S 3 , ST A RT, F I NI SH , I C F , £ 4 0 0 , £ 4 0 0 32 GO TC 500 33 400 IF < IA . N E . 0 ) GC TC 5000 34 LEN=27 35 CALL SERCOM(' ALGORITHM DOES NOT D E F A U L T ' , L E N , C) 36 450 I F ( P A T C H ) CALL EXIT 37 LEN=24 38 CALL SERCOMC R E S P E C I F Y THE PAR FI ELD* , LEN , 0 ) 39 GC TC 110 40 5 CO START=FIN I S H U 41 CALL FINDC( 1 S T , N l , ' = S 1 . S T A R T . F I N I S H , I C E , £ 6 0 C . £ 6 0 0 ) 42 GO TO 700 43 600 LEN=19 44 CALL SERCOMC ERROR IN PAR F I E L D S L E N . O ) 45 GC TG 450 46 700 START=FINISH+1 1 7 GC TC ( 1 0 0 0 , 2 0 0 0 , 3 0 0 0 ) , I C F 48 1000 CALL I G C ( I S T , M , ' • , 1, ST ART , FI NI SH , £ 4 0 0 . £400 ) 49 STAR T= FIN I S H 50 CALL FINDC( I S T . N I , ' , • , 2 , S T A R T , F I N I S H , I C F . E 1 2 0 C ) a l I F ( S T A R T . E O . F I N I S H ) GO TC 350 52 GC TC 1300 33 12CC FIN ISH = N I * l 54 L300 IA = FIN ISH-START 55 IF( IA . G T . 6 ) IA = 6 56 CALL S E T C ( 8 , A L G , » •) 57 CALL MOVECt I A , I S T ( S T A R T ) , A L G ) 58 CALL N G V E C ( 8 , A L G , H D N G S ( 6 ) ) 59 START=FINISH* l ( 100. 60 GO TO 350 61 C F I R S T IGNORE ALL THE PRECEDING BLANKS: 62 20G0 CALL I G C ( I S T , N I , « 1 , S T A R T , F I N I S H , 6 4 0 0 , £ 4 0 0 » o3 START=FIN I SH 64 CALL F I N D C ( I S T , N I , ' • ' , 2 . S T A R T . F I N I S H . I C F . £ 2 1 0 0 « £ 4 0 0 ) 65 C CHECK TO SEE IF "DATA= , " HAS HAPPENED: 66 I F ( F I N I S H . E C . START i GO TO 350 6 7 GO TO 2200 68 2100 FINISH=NI+1 69 2200 NUMB=FINISH-START 70 IO=NUHB 71 CALL MOVEC(NUMB,IST(START) ,HDNGS(19>) 72 CALL MOVEC{ NLMBi1ST(START 1.MTSUI15 t1 73 NCMTS=NUMB*14 74 LL=19+NUMB 75 NUMB=20-NUMB 76 CALL S E T C ( N U M E , H D N G S I L L ) t * ' ) /7 CALL FTNCMD(rTSU.NOMTS) 78 START=FINISH*1 79 GO TO 350 30 C F I R S T IGNORE ALL THE PRECEDING BLANKS: til 3000 CALL I G C U S T . N I , ' • , 1 , S T A R T , F I N I S H , £ 3 1 0 0 , £ 3 1 0 0 1 62 START=FINISH 83 CALL F I N O C ( I S T . N I , « , F N • , 3 , S T A R T , F I N I S H , I S , £ 3 1 0 0 . £ 3 1 0 0 » b4 START=FINISH+1 <i5 IF ( IS . E Q . 1) GG TO 3050 86 CALL F I N D C ( I S T . N I , ' ,• ,2 , S T A R T , F I N I S H . I C F , £ 3 0 2 0 , £ 3 0 2 0 ) . d7 START = F I N I S H U 38 GC TG 3050 09 302C START=NI+1 90 30 50 IF( IS . L T . 3) GO TO 3200 91 CALL MGVEC(4,«N •,HDNGSt45»» 92 IS = 2 93 GC TO 350 94 3100 START=NI~1 95 3200 I S = l 96 GC TC 350 97 5000 I F ( I D . N E . 0» GC TC 5500 98 CALL GTNAME('SCAROS • , N A M E , L I 99 CALL M O V E C ( L . N A M E , H O N G S J 1 9 H 1J0 LL=19+L 1G1 L=20-L U 2 CALL S E T C ( L , r C N C S ( L L ) , « •) lu3 5500 I F ( I S . E C . C» I S = l 104 I F J I S . E O . 1) CALL M 0 V E C ( 4 , ' F ' , H 0 N G S ( 4 5 » ) 105 RETURN 1C6 END 107 SUBROUTINE INPUT(COMNT,J 2 I u e INTEGER F I N I S H , D S E T , S T A R T 109 COMMON/IN I N F / I 1 , 1 2 , 1 3 , I T M A X , T 0 L E R N , Z E R O , B M V A , L I N E , L I S T , I E N D 110 CCPMCN /OUTINF/ N P AGE,NLINE ,HDNGS.ISTNO 111 CCMMCN /ADS/ I A , I 0 , I S , A L G , B A T C H 112 INTEGER*? T Y P E , N 0 , F R 0 M , T 0 , L E N , B U S E S ( 2 0 ) 1 13 L0GICAL*1 C O C E . C C D E S I S I / ' B ' . ' L ' . ' T ' . ' H ' . ' C ' E ' . ' G ' . ' O ' / 114 LOGICAL* 1 HCNC-Sl EC ) , COMNT ( I J , E PR OR (8 C) ,TX , B ATC H. ALG( 8» 115 LOGICAL EOUC 1 16 R EAL*8 NAME 117 EQUIVALENCE ( B U S E S l I ) , E R R O R ( I ) ) 118 REAL+4 B A S E , S L S E , S U R E , P T A P . O T A P . U 119 COMPLEX G E N . L O . Z 1 0 1 . 120 BMVA=100o 121 ICD=-10 122 L I S T = 2 123 ITMAX=100 124 TOLERN=O.C05 125 Z E R O . 00005 126 11=0 127 12=0 128 I 3=0 129 U N E = 0 130 J2 = 0 131 DSET=5 132 CALL FTNCMD(* ASSIGN 1 = - B U S I N F • , 1 6 » 133 CALL E M P T Y F ( l ) 134 CALL FTNCMD{'ASSIGN 2=-LIN I N F • , 1 6 ) 135 CALL EMPTYF12I 136 CALL FTNCMD( 'ASS IGN 3= -TX I N F • , 1 5 ) 137 CALL FMPTYF(3) 138 CALL FTNCMD( 'ASS IGN 4= -SCRATCH ' , 171 139 CALL EMPTYF(4) 140 50 CONTINUE 141 IF( ICD . L T . 0) GO TO 60 142 DSET=IOD 143 ICD=-10 144 CALL SETPFX l ,1) 145 60 REAC ICSET,61,END=850)COOE 146 61 FORM A T ( A I ) ' 147 BACKSPACE D SET 148 CALL FIN OST l C O D E S , 8 , C O D E , 1 , 1 , F I N I S H . U O O O ) 149 GO TCI 1 0 0 , 2 C C . 3 0 0 , 4 0 0 , 5 0 0 , 8 0 0 , 6 0 0 , 7 0 0 1 , F I N I S H 1 50 C BUS CATA CARDS 151 100 I 1 = 1 1*1 1=2 READ(DSET,101(TYPE,NO,NAKE,GEN,LD,eASE ,U 153 WR ITE ( I )TYPE , NO,NAME ,GEN,LD,BASE ,U 154 101 F C P M A T 1 1 X , I 1 , I 5 . 1 X , A 8 , 2 X , 2 F 7 . 2 , 2 F 8 . 2 , 1 5 X , 2 F 7 . 2 ) 155 GC TC 50 156 C TRANSMISSION L INE DATA CARDS 157 200 12= 12 + 1 158 RE AD(DSET » 201)NC,NAME,FROM,TO,Z ,SUSE.SURE ,TX 159 WRITE12) NC,NAME,FROM,TO,Z,SUSE.SURE ,TX 16C 2C1 F 0 R M A T U X , I 6 , 1 X , A 8 , 2 I 5 , 2 X , 2 F 8 . 5 , 4 X , 2 F 7 . 5 , I X ,L I 1 161 I F l . N O T . TX )LINE = LINE+1 162 GC TC 50 l o 3 C TRANSFORMER CATA CARD: 164 300 13=13+1 165 REACIDSET ,301 )N0,NAME,FROM,TO,Z.PTAP ,OTAP 166 WRITE13) NC ,NAME,FROM,T0 .Z .PTAP,OTAP lt.7 301 FORM ATI I X , I 6 , 1 X , A 8 , 2 I 5 , 2 F 8 . 5 , 2 F 8 . 4 , 2 F 7 . 5 ) 168 GC TC 50 169 C HEADING CARD, IUCN 'T WRITE OVER T I f E AND D A T E ) : 1/0 400 READ(OSET,401)(HDNGSI I ) , I = 1,48) 1/1 401 FCRMAT11X,48A1) 172 GO TO 50 173 C CCMKENT CARD: 1 /4 500 I F I J 2 . E Q . 7<=0IGO TO 50 1/5 J l = J 2 + l 176 J2=J2+79 1/7 READ ( DSET, 5C1 M C C M N T U ) , J = J 1 , J 2 » ' 1/8 501 FORM AT I I X ,79A1 ) 179 GC TC 50 102. 180 C GENERAL INFORMATION RECORD: 181 600 REAC(DSETt601)ERROR 182 601. FORMAT!8CA1> 183 LEN 2 = 80 184 STAR T=2 185 605 CALL FINDCIERROR, L E N 2 . • I T Z L B • , 5 , S T A R T , F I N I S H , I C F , 6 5 0 , £ 5 0 ) l d 6 START=FINISH+l 187 CALL F I N D C ( E P P 0 R , L E N 2 , • = • , 1 , S T A R T , F I N I S H , I C E , £ 6 0 5 , £6051 188 START=FINISH+1 189 LI MIT = LFN2-START + 1 190 GO TO ( 6 1 0 , 6 2 C 6 2 C , 6 1 0 , 6 2 0 1 , I C F 191 610 CALL D T B I E R R O R ( S T A R T ) , I N T , L I M I T , N S D , ' ' , £ 6 1 5 1 192 IF( ICF . E O . 1) GC TO 6 12 193 LIST=INT 194 GO TO 615 195 612 I TMAX=INT 196 615 START=START*LIMIT*1 197 GC TO 605 198 620 CALL D T B ( E R R C P I S T A R T > , I N T 1 , L I M I T , N S O , « ' , £ 6 2 2 1 199 START=START+LIMIT 200 622 I F ( E C U C ( E R R C F ( S T A R T ) , ' . • ) J G O TO 625 201 START=START+1 202 GO TO 605 203 625 LIMIT=LEN2-START+1 204 CALL D T 8 ( E R R 0 R ( S T A R T ) , I N T 2 . L I M I T , N S O . « , 6 6 3 0 ) / 205 START=START+LIMIT 2C6 L I M I T = L I M I T - 1 207 IF( INT1 . E O . C . A N D . INT2 . E O . 0) GO TO 605 2u8 A1=INT1 209 A2=INT2 210 A = A 1 + A 2 * 1 0 . * * ( - L I M I T ) 2 i l 626 GO TO ( 6 2 7 , 6 2 7 , 6 2 8 , 6 2 8 , 6 2 9 ) , I C F 212 627 TOLERN-A 213 GC TO 605 214 628 Z ERG =A 215 GO TO 605 216 629 BMVA=A 217 GO TO 605 218 63C START=START+LIMIT+1 219 IF( INT1 . E O . 0) GO TO 605 220 A=INT1 2il GO TO 626 222 700 REAC1DSET,701)NEWO 223 7C1 F 0 R M A T I 9 X , 1 2 > 224 IF( IOD . G T . 0)IOO=NEWD 225 DSET=NEWD 226 IFIDSET . E O . 15( CALL FTNCMD( 'ASSIGN SCARDS=*SCURCE*•,22) 227 GO TO 50 228 800 R E A C ( C S E T , 6 1 )CCDE 229 850 LINE = LINE-«-I3 230 I F ( L I S T . G T . 10 . O R . L I S T . L T . 0) GO TO 900 2 i l RETUPN 2 i 2 9 CO ! F ( . N O T . BATCH)WRITEC16 ,901) 233 901 FORMAT(* ENTER THE DESIRED BUS NUMBERS IN 2014 FORMAT OR 2->4 * / , • (A ZERO EUS NUMBER INDICATES END OF S E R I E S ) '1 235 R E A 0 ( 1 5 , 6 1 ) C C D E 236 I F ( E C U C ( C O D E , ' A ' ) 1 GC TO 950 237 BACKSPACE 15 238 910 R E A C ( 1 5 , 9 l l ) B L S E S 239 S l l FORM/IT (2014 ) 103. 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 2 64 2e5 266 267 268 269 270 271 272 273 2 74 275 2/6 2/7 278 279 2ao 281 232 2 63 284 285 266 267 2d8 2d9 2*0 291 292 2v3 294 295 296 257 298 299 950 1CC0 10C1 1100 1200 15C0 1501 101 INITIAL ON THE FOLLOWING RECORD:•.LEN.O) H R I T E ( l ) BUSES I F I B U S E S 1 2 0 J . E O . 0) RETURN GO TO 910 B U S E S d I=-999 K R I T E I D B U S E S RETURN READIDSET, l O O D E R R O R F CRMAT(80Al1 LEN=4l CALL S E R C O M C INVALID LEN=80 CALL SERCCM(ERROR»LEN,OI IF (BATCH) GO TO 1500 LEN=54 CALL S E R C O M C ENTER Y TO REPLACE N TO TERMINATE OR RETURN TO IGNOR * E ' , L E N . O ) CALL S E T P F X l , 1 1 P E A D ( 1 6 , 6 1 ) C 0 D E CALL SETPFX I ' £ ' , 1 ) I F I E C U C I C O D E , " •) ) GO TO 1100 I F I E C U C I C C C E . ' Y ' ) » GC TO 1200 W R I T E l 1 6 , 1 5 0 1 I CALL EXIT LEN=15 CALL S E T P F X l • £ ' , 1 ) CALL S E R C O M C RECORD I GNORED • , L E N , 0) GO TO 50 IOD=DSET DSET=15 GC TC 60 j CALL S E T P F X l ' £ ' , 1 ) WRITE16 ,15011 FORMAT(' JOB TERMINATED BY ERROR") STOP END SUBROUTINE HEAD COMMCN /OUTINF/ N P A G E , N L I N E , H D N G S , I S T N O L C G I C A L M HCNGS180) NPAGE = NPAGE + 1 j WRITE16, D H C N G S , N P A G E \ FORMAT(1 H I , 5 X , 8 C A 1 , 1 5 X , • P A G E ' , 1 3 / 1 1 0 ( ' * • ) / I ! NLIN E= 3 RETURN END SUBROUTINE BLSHDR CCMMCN /OUT INF/ N P A G E , N L I N E . H O N G S , I S T N O LOG ICAL*1 H0NGS180) CALL HEAD fcRITEI6,101) FORMAT I / ' B U S I N F O R M A T I O N : • / I X , 301 •«-')//5X , ' BUS # ' , 3 * X , •BUS NAME' ,3X , ' T Y P E ' , 1 2 X , ' G E N E R A T I O N ' , 10X. ' L O A D ' , 1 2 X , ' B A S E • ,6X * , ' V O L T A G E ' / 4 0 X , •MW•,6X , • M V A R ' , 8 X , • K W , 6 X , • M V A R • , 2 1 7 X , • K V • , 2 X ) / ) NL INE=NLINE*6 RETURN END SUBROUTINE LFDR CCMMCN /OUT INF/ NPAGE,NLINE,HDNGS, ISTNO LOGICAL*1 HDNGS(80) CALL HEAC fcRITE(6,l» i 104. 300 1 FORMAT(/• L I N E I N F O R M A T I O N S ' ! 301 200 W R I T E I 6 . 2 0 1 ) 302 2C1 FORMAT! I X , 3 2 { • • • ) , / / , 5 X , ' L I N E #•, 5 X , ' L I N E N A M E ' , 9 X , ' S . E . • » 3 X , ' R . E 303 * . ' , 1 0 X , , P E R UNIT R « , 4 X , ' P E R UNIT X ' . I O X . ' S . E . S U S E P . ' , 3 X , » R . E . SUS 304 * E P . ' , 6 X , • T X ? • , / 1 305 NLINE=NLINE*5 306 RETURN 3C7 END 3C8 SUBROUTINE TXHDR 3*9 COMMCN /OUTINF/ N P A G E , N L I N E , H D N G S , I S T N O 310 LCGICAL*1 HDNGS!801 3 i l CALL HEAC 312 U R I T E ( 6 t l l 313 1 FORMAT(/• T R A N S F O R M E R I N F O R M T I O N : •) 314 200 W R I T E I 6 . 2 0 1 ) 315 201 F O R M A T ! 1 X . 4 4 1 > , / / , 5 X , ' T X # ' , 8 X , ' T X N A M E • . 1 2 X , ' S . E . • , 5 X , ' R . E . ' , 316 * 1 OX, "LEAKAGE IMPEDANCE•,1 OX, ' S . E . T A P • , 7 X , ' R . E . T A P ' / ) 317 NLINE=NLINE+5 318 RETURN 319 END 320 SUBROUTINE BUS I N F { S C H E C , V , U , A N G , N O , T Y P E , I N P R T 1 321 LOGICAL* I B A T C H , H D N G S ( 8 0 ) , I N P R T , M T S U ( 3 0 ) , A L G ( 8 ) 3i2 CCMMCN/ININF/I1 , 12, 13, ITMAX,TO LE RN , ZERO , BM VA , L I N E . L I S T , I END 323 COMMCN /OUT INF/ N P A G E , N L I N E , H D N G S , I S T N O 3 i 4 COMMCN /ADS/ I A , ID, I S , A L G , B A T C H 325 LOGICAL EOUC 326 REAL*8 NAME 327 INTEGER*2 NO( 1 ) , B U S E S ! 2 0 ) , T Y P E ( I ) 328 REAL*4 U (1 ) ,/!NG( 1) .BASE 329 COMPLEX SCHEC!1 ) , V ( 1 ) , G E N , L O 330 EQUIVALENCE (NBUS.U) 231 EQUIVALENCE (MTSU!13 1 ,NRTRN) 332 CATA N R T S T / Z 4 C 4 0 4 0 4 0 / 3J3 REWIND 1 334 I F ! I N P R T I CALL BUSHDR 3J5 I END = NBUS 336 1 = 1 337 5C READ!11 TYPE ! I ) , N 0 ( I ) . N A M E , G E N , L O , B A S E , U ! I ) 338 I F ! . N O T . INPRT) GO TO 75 339 I F I N L I N E . G T . 50) CALL BUSHOR 340 WRITE!6,51 INC!I 1 . N A M E , T Y P E ! I 1 , G E N , L O , B A S E,U( I ) 341 NLINE=NLINE+1 342 51 FORMAT 1 3 X , I 5 , 6 X , A 8 , 4 X , U , 8 X , 2 F 8 . 2 , 2 X , 2 ( 2 X , F 8 . 2 ) , 4 X , F 6 . 2 , 5 X , F 6 . 2 » 343 75 I F I T Y P E ( I ) . F Q . 3 ) G 0 TO 100 344 U(I ) = U ( I (/BASE 345 SCHEDII)=(GEN-LDI/BMVA 346 A N G ! I ) = 0 . 347 I F ( I . E C . IENC) GO TO 200 348 1 = 1-1 249 GC TO 50 330 100 T Y P E ! IENO ) =TYPE( I ) 351 N O ! I E N D ) = N 0 ! I ) 352 U! IEND) = U( I J/BASE 353 V!IENC)=U(IENC> 354 A N G ! I E N D 1 = 0 . 355 IEND=IENC-1 356 I F ! I E N D . L T . I ) GO TO 200 357 GO TO 50 358 200 DO 220 1 = 1 , 1 END 359 I F ! T Y P E ( I ) . E C . l ) U ! I ) = l . 105. 3b0 v m - u m 3 o l 220 CONTINUE 362 225 R E A D ! I , E N D = 2 5 0 ) B U S E S 363 I F ( B U S E S I l ) . L T . 0) GO TO 243 364 OC 240 1=1 ,20 365 IFI B U S E S d ) . E O . 0) GO TO 250 366 DO 230 J = l , N B U S 367 I F I N C ( J ) . E C . BUSES I D ) GO TO 235 368 230 CONTINUE 369 GO TG 240 370 235 N 0 ( J ) = - N 0 ( J ) 371 24C CONTINUE 3 72 GC TC 22 5 3/3 243 DO 246 I = l , N B U S 374 246 N O ( I ) = - N O ( I ) 375 250 I F ( I S . E O . 1 . O R . E Q U C ( A L G ( 1 ) , « L • ) ) RETURN 376 • I F ( 9 A T C H I GO TO 260 377 W R I T E ( 1 6 , 2 5 1 ) 378 251 FORMAT(* ENTER NAME OF THE UNIT CONTAINING STARTING •/• VALUE DATA 379 * (RETURN OR EOF IF * M S O U R C E * ) ' l 380 CALL S E T P F X l ' ? » , 1 ) 381 260 R E A D ! 1 5 . 2 6 1 , E N D = 2 7 0 I ( M T S U l I ) , 1=13 , 3 0 1 3d2 261 FGRMAT120A1) 363 C GC TC 270 IF ' R E T U R N ' CR * EOF• 384 IF1NRTRN . E G . NRTSTI GC TO 270 335 C ASSIGN LOGICAL UNIT 8 TO FDS 3fc6 CALL MOV E C ( 1 2 , ' A S S I G N 8 = ' , M T S U ) 387 CALL FTNCMD(NTSU,30) 368 GC TC 280 339 27C CALL FTNCMDI•ECUATE 8=GUSER«,14) 3*0 I F ( B A T C H ) GC TO 280 391 W R I T E ( 1 6 , 2 7 1 ) 392 271 FORMAT!* ENTER '•M AG ' • , '* ANG*' IN 2 F 1 0 . 5 FORMAT'/ 393 *•' ORDER THE SAME AS BUS DATA. SKIP OVER SLACK B U S E S . * ) 394 C VOLTAGES ARE REAC IN P . U . , ANGLES IN DEGREES: 395 C THE ORDER IS THE SAME AS BUS DATA RECORDS EXCEPT THAT NO DATA 3*6 C IS GIVEN FOR SLACK B U S ( E S ) . 397 280 DO 290 I=1,IEND 398 R E A D t 8 , 2 8 1 , E N D = 3 0 0 ) U ( I ) , A N G ( I ) 399 281 F C R M A T 1 2 F 1 0 . 5 ) 4J0 ANG <I I=A NG(I 1 * 3 . 1 4 1 5 6 / 1 8 0 . 401 A1 = U ( I ) * C O S ( A N G l I I) 402 A2 = U ( I ) * S I N ( A N G I I I ) 4 J 3 V<I I=CMPLX(A1,A2I 404 290 CONTINUE 405 300 CALL SETPFXI•£•,I) 406 RETURN 407 END 408 SUBRCUT INE L I M N F l INPRT, Y, C P O N T , N X T R , R P O N T , N X T C , N O , T X Z , P T A P , O T A 409 * P , T X N O , P S I D E , O S I D E ) 410 CCMMCN/IN I N F / I I , 1 2 , 1 3 , I T M A X , T O L E R N , Z E R 0 , B M V A , L I N E . L I S T , I END 411 CCMMCN /OUTINF/ NPAGE,NLINE,HDNGS, ISTNO 412 L 0 G I C A L * 1 TX , HDNGS(8C) , INPRT 413 INTEGER* 2 CFONT ( 1 ) ,NXTR1 1 ) ,RPONT(1 ) , N X T C ( I ) 414 INTEGER*2 L T N C , F R O M , T O , N 0 ( I I .TXNO(1 I , P S I D E ( 1 » , C S I D E ( 1 ) 415 COMPLEX Y l 1 ) , Z , T X Z ( 1 ) , Y P 1 , Y P 2 , Y B , Z A , Z C , Z l , Y 2 , Y 3 416 REAL*4 P T A P ( 1 ) , F I L L E R ( 4 ) , 0 T A P ( 1 ) 417 REAL*8 NAME 418 INTEGER G P . V P . P P 419 E O U I V A L E N C E ( I l . N B U S ) i i 106. 420 REWIND 2 421 REWIND 3 422 C TC SET POINTERS FOR DIAGONAL ELEMENTS! 423 K=l 424 CO 20 I=1,NBUS 425 Y ( 2 * I> = 0 . 426 CPONT(K)=I 427 RPONT(K»=I 428 NXTR(K1=K 429 NXTC(KI=K 430 K=K+8 431 20 CONTINUE 432 C TO SET POINTERS FOR OFF-DIAGONAL ELEMENTS: 433 GP=K 4 34 LAST=GP+ L I N E * 8 - 1 6 435 IF (GP . G T . LAST) GO TO 35 436 DO 30 I=GP,LAST,8 437 NXTRI I ) = I*8 438 3C CONTINUE 439 35 NXTR(LAST+8) = 0 4 H 0 I F ( 1 3 . E C . 0)G0 TO 60 441 I F ( I N P R T J CALL TXHDR 4*2 DO 50 1=1,13 4 t 3 READ(3)TXN0< I ) , N A M E , P S IDE< I) .0S I DE( I ) , T X Z ( I ) . P T A P ( I ) , O T A P ( I I 444 I F ( . N O T . INPRT) GO TO 50 445 I F t NL INE . L E . 50JGO TO 40 446 CALL TXHDR 447 40 W R I T E ( 6 , 4 1 I T X N O I I ) , N A M E , P S I D E ( I ) , OS I DE( I ) , T X Z ( I J , P T A P ( I ) , O T A P ( I I 4<t8 NLINE =NLINE*1 449 41 F 0 R M A T ( 3 X , I 5 , 1 0 X , A 8 , 4 X , 2 ( 5 X , I 4 I , 7 X , 2 ( 3 X , F 8 . 4 I . 1 X . 2 ( 8 X , F 7 .21 1 4;>0 50 CONTINUE 451 60 I F ( I N P R T ) CALL LrOR 4S2 00 7C0 J = L , I 2 453 R E A D ( 2 ) L T N 0 , N A M E , F R C M , T O , Z , S E S U , R E S U , T X 4o4 IF{ . N O T . INPRT) GO TO 75 455 I F ( N L I N E . L E . 501GO TO 70 456 CALL LHDR 4 s 7 70 WRTTF(6 ,7 1 ILTNC,NAME . F R O M . T O , Z . S E S U . R E S U . T X 458 71 F 0 R M A T ( I 9 , 7 X , A 8 , 6 X , 2 ( 3 X , I 4 ) , 4 X . 2 ( 6 X , F 9 . 4 ) , 7 X , 2 ( 7 X , F 7 . 5 ) , 8 X . L 1 ) 459 NLINE=NLINE+1 460 75 Y P 1 = C M P L X ( 0 . , S E S U ) 461 YP2=CMPLX(0 . ,RESU» 462 IF( .NOT . TX )G0 TO 300 463 DO 150 1=1,13 4o4 I F ( T X N O ( I I . E C . LTNGIGO TO 160 465 150 CONTINUE 466 160 TXNOII 1=0 4o7 C TRANSFORMERS ARE ALWAYS ASSUMEO TO BE AT S . E . 4o8 Ff'CM = PSIDE ( I ) 4o9 T C = Q S I D E ( It 470 R AT I 0= QT AP(I l / P T A P J I t 471 I F t C A B S ( T X Z ( I ) ) . N E . 0 . ) G O TO 200 472 Z = l . / Z 473 ZA=YP1+Z 4 74 YB=RATIO*RAT10*(YP2+ZI 475 Z=-RATIO+Z 476 YP2=ZA+Z 477 YP1=YB+Z 478 GO TO 350 479 200 ZA=Z 107. 480 ZC=TXZ(I>/RATIO 4 d l YB=(l.-RATIO)/TXZ( I ) * Y P l 482 Z1=ZA+ZC+ZA*2C*YB 483 Y 3= Y e*ZA/Zl 484 Y2=YB*ZC/Zl 485 YP2=YP2+Y2 486 Y P l = RATIO*(RATIO-l.)/TXZU» +Y3 487 Z=-1./Z1 488 GO TO 350 489 300 Z=-l./Z 490 35C CONTINUE 491 WRITE(4)LTN0,NANE,FR0M,TO,YP1.YP2.Z 492 CALL SETIFRCf,T0,Z,YPi,YP2,NO,Y,CPCNT,RPONT.NXTR.NXTC,GP) 493 700 CONTINUE 494 IF( 13 .EO. C »GC TO 1C00 495 REWIND 3 496 DO 8C0 1=1,13 497 REA0(3)l.TN0, NAME, FROM, TO, FILLER 498 I F ( T X N O I I ) .EC. 0)GC TO 800 459 R A T I C = O T A P ( I l / P T A P I I I 500 IF(CABS(TXZ( I) ) .EO. 0.)TXZCI)=CMPLX(0.,ZERO) 5 u l YP2 = 1./TXZ( I ) 502 Z=-YP2*RATI0 503 YP2=YP2*Z 504 YP1=-RATIC*YF2 505 WRI TE{ 4) LTNCNAME.FRCM.TO, Y P l , YP2, Z 506 CALL SET(FRCM,TG,Z,YPl,YP2 ,NO,Y,CPCNT,RPONT,NXTR,NXTC,GP) 507 8CC CONTINUE 508 1C00 RETURN 509 END 51C SUB R CUT I NE SET { F POM , TO , SY, YP 1 , YP2 . NO ,Y ,CP CNT,RPGNT,NXTR,NXTCGPJ 511 COMMCN/IN INF/11, 12,13, IT MA X,TOLERN,ZERO,BMVA,LINE,LI ST,I END 512 INTEGER GP.VP.PP 513 INTEGER*2 FROM,T0,NO(1),CPCNT(1J ,RFCNT(1»,NXTR(I),NXTC11 I 514 COMPLEX S Y , Y P l , Y P 2 . Y ( l ) 515 EQUIVALENCE! Il,N B U S I 516 C SY IS THE NEGATIVE CF SELF ADMITTANCE 517 C Y P l AND YP2 £ R E THE LOCAL ADMITTANCES AT SENDING AND RECEIVING ENDS. 518 C TO AND FROM /> R E THE EXTERNAL BUS NUMBERS OF SENDING AND RECEIVING ENDS. 519 C FIRST FIND THE INTERNAL NUMBERS CORRESPONDING 10 "TO" AND "FROM".: 520 DC ICO I=l,NBLS 5^1 NOI=NO!I» 522 K=IABS(NOI) 523 IF(K .EO. TOI TO=-I 524 IF(K .EO. FRCM) FROM=-I 525 100 CONTINUE 526 TC=-TC 527 FROM=-FROM 528 C CHANCE THE SELF ADMITTANCES OF BOTH ENDS: 529 KK=FPCM*2 5J0 Y ( K K ) = Y ( K K l - S Y + Y P l 531 JJ=TC*2 532 Y I J J I =Y(JJ)-SY-YP2 533 C SET THE MUTUAL ADMITTANCE ELEMENT! 534 C IF THE ELEMENT EXISTS, MODIFY IT: 535 CALL SCAN(Y,CPONT,NXTR,FfiOM,TO,VP.PPI 536 I F I V P .EQ. 0)GO TO 600 537 Y(VP)=Y(VP)+SY 538 GO TO 700 5J9 C IF THE ELEMENT IS NEW, INSERT IT: ! 108. 540 600 CALL INSRTIY,CPCNT,RPONT,NXTR,NXTC.GP,FROM,TG.SY.S7001 541 7C0 RETURN 5*2 END 543 SUBROUTINE SCAN(Y .CPCNT,NXTR,FRO*,TC,VP,PP) 544 INTEGER*2 CPCNT( 1),NXTR(1) ,FROM , TOtTEMP 545 INTEGER FIRST,VP,PP 546 COMPLEX Y(11 54 7 C ONLY UPPER HALF OF THE ADMITTANCE MATRIX IS FORMED. 548 c THEREFORE, ELEMENT (ROW.COLI EXISTS IF (ROW .LE. COL). 549 IF(FRCM-TO) 1CC,2C0,300 550 100 VP = 0 551 PP=0 552 FIRST=FR0M*8-7 553 NEX T = NXTR(FIRSTJ 554 120 IF(NEXT.EO.FIRST)GO TO 150 555 IF(CPCNT(NEXT) .EO. TO) GO TO 130 556 NEXT=NXTR(NEXT) 557 GC TO 120 558 13C PP=NEXT 559 VP=(NEXT+7)/4 560 15C RETURN 561 200 VP=FR0M*2 562 FP=VP*4-7 5o3 RETURN 5o4 300 TEMP=FROM 565 FPCM=TO 566 TO=TEMP 567 GO TO 100 568 END 569 SUHROUTINE INSRTtY,CFCNT,RPONT,NXTR,NXTC,GP,FROM,TC,VALUE,*,*) 5 70 INTEGER VP.PP.GP 5/1 COMPLEX VALUE ,Y(1) 5/2 INTEGER*2 CPCNTI 1),RPONT(1 ),NXTR(1),NXTC(11,FRCM,TO 5 73 c ERROR RETURN 1 = NO INSERTION REQUIRED 5 74 c ERROR RETURN 2 = THERE IS NO SPACE IN GARBAGE C 575 C GARBAGE POINTER(GP) IS THE (PP) CF THE SPECIFIED LOCATION. 576 IF(CABS(VALUE ) .EQ. 0.)RETURN 1 577 IFIGP .EO. OJRETURN 2 578 LL =NXTR(GP) 5 79 PP=FRCM*8-7 580 L=NXTR(PP) 581 NXTR(PP)=GP 562 NXTR(GP)=L 563 RPON T(GP ) = FRCM 584 PP=TC*8-7 5b5 L=NXTC(PP) 566 NXTC(PP)=GP 587 NXTC(C-P)=L 568 CPCNT(GPI=TC 569 VP=(GP+7)/4 590 Y( VP)=VALUE 591 GP = LL 592 RETURN 593 END 594 EXTERNAL BUSINF.LININF.PROSS.FLOWS.LNFST 595 INTEGER ASCHEC,AV,AU.AANG,ANO,ATYPE,AY,AJO,FT 5 56 INTEGER ECH01,ECH02/1/,ATZ.OUT (20) 557 LOGICAL* 1 CCfNT(79C),HDNGS(80),BATCH,INPRT,ALG(8) 598 CCMMCN/IN I N F / I I , 1 2 , 1 3 , ITMA X,TOLERN,ZERO,BMVA .L INE,LI ST,I END 599 COMMON /OUTINF/ NPAGE,NLINE,HDNGS, ISTNO 109. 600 COMMON /ADS/ IA, ID,IS,ALG,BATCH 601 LOGICAL EOUC 602 COMMCN /LOSSES/ SL 603 EOUIVALENCEINBUS.II) 604 C STORE ECHO STATLS OF USER 605 CALL GUINFOCECHCOFF »,ECH01> 606 C THEN SET ECHC=OFF: 607 CALL CUINFOI'ECHOOFF '.ECHG2I 608 NPAGE=0 609 ISTNC=0 61C BA TCH=.TRUE• 611 CALL CREPLY(£101 612 BATCH=.FALSE. 613 10 CALL SETPFXI•€•, 11 614 CALL FTNCMD(•EQUATE 5=SCARDS«.15) 615 CALL FTNCMDI 1ECUAT E 6=SPRINT',15» 616 CALL FTNCMD(•EQUATE 15=GUSER•,15J 617 CALL FTNCMDf'EQUATE 16=SERCOM',16) 618 CALL PARR 619 CALL INPUT(CCMNT,J2) 620 I F I J 2 .EQ. CIGC TO 100 621 CALL HE AO 622 WRITE(6,1)(CCMNT(J),J=1,J2) 623 I FORMAT(/' C O M M E N T S : • / I X , 17{•+')//{/5X, •*',79A1 I I 624 100 CALL GSPACE1ASCHED,N8US*28I 625 AV=ASCHED+NBUS*8 626 AL = AV--NBUS*8 627 AANG=AU*NBUS*4 628 ANC=AANG+NBUS*4 629 4TYPE=ANC*NBLS*2 630 IN'PRT=IABS(MCC<LIST,10) ) .GT. 5 631 CALL CALLER(BCSINF,ASCHED,AV,AU,AANG,ANC.ATYPE,IPTR(INPRT)I 632 C GET SPACE FOR COMPACT ADMITTANCE MATRIX AND TRANSFORMER DATA: 633 M M N E U S + LINEI+16 634 CALL GSPACE I AY,NI> 635 IF( 13 .EQ. 0)G0 TO I 10 636 CALL GSPACECATZ, 13+221 637 C REAO LINE INFORMATION AND FORM Y MATRIX 638 CALL CALLER!LININF,IPTR(INPRT),AY,AY,AY+2,AY+4,AY<-6,ANO,AT2.ATZ+I3 639 **8,ATZ*-I3 : n2,ATZ + 13*16,ATZ + I3*18,ATZ + I 3*201 640 CALL FSPACE(ATZ) 641 GO TO 120 642 110 CALL CALLERILININF,IPTR(INPRT»,AY,AY,AY*2,AY+4,AY+6,ANO) 643 120 CONTINUE 644 IFI.NCT. EGUC (ALG( I) ,'L' ) ) GO TO 150 645 CALL GSPACEISL,NBUS*8I 646 I F ( I S .EQ. 1 ) GO TO 150 6*7 CALL C A L L E R t L N F S T . A N C S L ) 648 1 5C CALL LDINF0(1 , ALG,BITS,OUT ) 649 CALL GSPACEIASEQ,NBUS*21 650 CALL CALLER(PFOSS,IPTR(GUT(3)I,AY,AY,AY + 2,AY-4,AY + 6,ANO,A TYPE, 6 a l *ASCHED,A V,AU,AANG,ASEQ.S 11 11) 652 CALL FSPACE(ASEO) 653 L I S T = I A B S ( L I S T I 654 I F ( M C C ( L I S T , 5 ) .EQ. 1) GO TO 200 6a5 CALL CALLER{FLOWS,AV.AU,AANG,ANO» 656 200 CALL FSPACE(ASCHED) 6 i 7 C RESTORE USER'S ECHO STATUS 658 CALL CUINFOC ECFCCFF '.ECHOU 659 WPITE(6,201) \ 120. 660 201 FORMAT ClHI I 661 STOP 662 1111 W R I T E ( 6 , l l l 2 ) I S T N 0 663 1112 FORMAT(//» ***ERROR RETURN •//5X,• ISTNO=«,171 664 GG TC 200 665 END 666 SUBROUTINE PROSS(ALG ,Y,CPONT,NXTR,RPONT,NXTC,NO,TYPE,SCHED,V.U. 667 *ANG,SEQ,*I 668 EXTERNAL NEWTON 669 COMPLEX Y ( l I,SCHED(1»,V<1) 670 INTEGER*2 CPCNT(1),NXTR(1J,RPONT(1),NXTC(1),NC(1),TYPE ( 1 1 671 I NT EGER*2 S E C d ) 672 REAL U(l»,ANG(1» 673 CALL ALG(V,U,ANG,NO,SCHED,TYPE ,SEO,Y,CPONT,NXTR,RPONT,NXTC,Cl) 6/4 RETURN 6 75 1 RETURN 1 676 END 6 77 SUBROUTINE TEST(V,U ,ANG,NO.SCHED,TYPE,SEO,Y,CPONT,NXTR,RPONT,NXTCI 678 INTEGER*2 S E C d l 679 COMPLEX Y ( l ) ,SCFED(1 ),V(1) 680 INTEGERS CPCNT(1),NXTR(U,RP0NT(1 1, NXTC ( I I, NO ( I J, TYPE d ) 681 REAL U( 1) . ANG(1) 682 CCMMCN/IN INF/11,12,13. ITMAX,TOLERN,ZER0,BMVA,LINE,LIST,I END 683 COMMON /OUTINF/ NPAGE,NLINE.HDNGS,ISTNO 664 COMMON /ADS/ IA, ID, IS,ALG,BATCH 6(35 LCGICAL»1 HCNGSI80 ),BATCH,ALG(8) 686 F QUIVALENCEJNBUS,111 667 Nl=(NBUS + LINE 1*2 6d8 WPITE16.1) 689 1 FORM AT(* 1*//2CX,• A O M I T T A N C E M A T R I X:«//7X, 'VALUE', 690 *7X, 'CPONT *,5X,'NXTR«,5X,•RPONT',5X,'NXTC•//) 691 K = l 692 1 = 2 653 10 WRITE(6,2)Y(I).CPCNT(K),NXTR(K),RPCNT(K),NXTC(K) 6 54 2 F0RMAT(2F10.4,41101 695 . 1=1+2 656 K = K + 8 657 I F ( I .GT. N1IGC TO 100 698 GO TO 10 699 100 WPITE(6,101 ) 7uC 10 1 FCRMATC l ' / / 2 0 X . ' I N T E R N A L B U S A R R A G E M E N T : ' , 701 «//5X,"NO • ,5X, 'TYPE' , 10 X,•SCHED' ,10X,'V',5X,'U',5X,•ANG'//» 702 WRITE!6,102 ) (N0( I ),TYPE(I) ,SCHED< I ) ,V( I ),U(I ),ANG( I I,I=l,NBUS» 703 102 FORMAT(3X,2I5,6F10.4» 7 04 WRITE(6,103) 7u5 103 FORMAT!' l'//20X,'C. 0 M M O N A R E A S: • //5X , «/ IN INF/: • / » 706 WRITE(6,104)I1,12,13.1TMAX,TOLERN,ZERO,BMVA,LINE,LIST,I END 707 104 F0RMAT(4I7,3F10.4,2I71 7o8 WRITE!6,105 »NPAGE,NL(NE,HONGS 709 105 FORMAT(//5X,«/OUTINF/:«/2I 10//80AI) 710 WRITE(6,106)IA, IC, I S , ALG,BATCH 711 1C6 FORMAT(//5X, •/ADS/:'/3I10,5X,8A1,5X.LII 712 CALL EXIT 713 RETURN 714 END 715 SUBROUTINE ORDER{CONN,N1,CPONT„NXTR,RPONT,NXTC.NO,TEMP,NPO,NPV 716 *,TYPE) 717 CCMMCN /ININF/ 11,12,13, ITMAX,TOLERN , ZERO,BMVA, L I N E , L I S T , I END 718 INTEGER SHFTR,FIRST,PP,COL,SHFTL 1 719 INTEGER CCNN(M,1),CNE/Z80C0C000/ i I 1 720 INT EGER*2 TENP(1>,NO(1),TYPE I 1) 721 INTEGER*2 CPONT( 1) ,NXTR(1),RPONT11l,NXTC(1) 722 C AT RETURN TINE "NO" IS CHANGEO TO INDICATE THE OPTIMAL 723 c ORDERING OF THE NODES. ALSO NO(IENO+1I=0 724 NPO=0 725 NPV=0 726 JJ=1 727 c TO FORM CONNECTION MATRIX: 728 c ROWS OF "Y» ARE IN COLUMNS OF "CONN" 729 DO 100 1=1,IEND 73C DO 10 J=1,N1 731 1C CCNN(J,I)=0 732 c D I A G O N A L E L E M E N T : 733 TEMPI I 1=1 734 c J IS WORD INDICATOR; K IS SHFTR INDICATOR: 735 J = ( I - l ) / 3 2 * l 736 K=I-J*32+31 737 L = S H FTR(ONE,K) 738 CCNN(J,II=L 739 FIRST=I*8-7 74C PP=NXTR(FIRST» 741 20 I F I P P .EO. FIRSTIGG TO 50 742 CCL=CPCNT(PP) 743 IFJCCL .GT. IENDJGO TO 30 7-»4 TEMPI I 1 = TEMP(I) + l 745 J = ( C 0 L - l ) / 3 2 * l 746 K=CCL-J*32+31 747 L = SHFTR < ONE , K) 74 8 CCNNIJ,I ) = L C R ( C C N N ( J , I ) , L ) 749 30 PP = NXTR(PP ) 75C GO TO 20 731 50 PP=MXTC(FIRST) 752 7C I F I P P .EQ. FIRST)GC TO 100 753 COL=RPCNT(PP) 734 IFICCL .GT. IENDIGO TO 80 735 TEMPI I l = TEMPII1 + 1 756 J = ( C C L - l ) / 3 2 + l 737 K=CCL-J*32+3l 758 L=SHFTR{ONE ,K ) 759 CCNNIJ,I ) =LOR(CCNNIJ,I),L) 760 80 PP=NXTC(PP) 761 GO TO 70 7b2 100 CONTINUE 763 C TO FIND MININUM COUNT OF ROWS NOT YET PROCESSED 7c4 c (AT PROCESSED ROWS TEMP = 0) : 7t>5 150 MIN=IEND+1 766 INOEX=0 7o7 UO 200 1 = 1, IEND 7o8 I F ( T E M P t l ) .EC. 0)G0 TO 200 769 IF(TEMP(I> .GE. MINIGO TO 200 770 M IN =T EMP(I ) 771 INDEX=I 772 200 CONTINUE 773 IFIINOEX .EQ. 0)G0 TO 400 774 NC(JJ)=INDEX 775 IF{TYPE!INDEX) .EQ. 1) GO TO 210 776 NFV = NPV*-M N 777 GO TO 220 778 210 NPQ=NPQ+MIN 779 220 I F ( J J .EG. IENDIGO TO 400 122. 780 J J = J J * 1 7 a l T EMP (INDEX 1 = 0 7U2 C TO CHANGE THE OTHER ROWS t FIND NEW COUNTS: 783 00 3C0 1=1,IEND 784 I F I T E M P ( I ) .EC. 0)G0 TO 300 785 J = l 786 K=IN0EX-1 787 230 I F ( K .LE. 31IG0 TO 240 788 K=K-32 7b9 J = J * i 790 GC TO 230 791 C CHECK TO SEE IF ROW " I " HAS AN LEHENT IN POSITION COL=INDEX 792 240 L=SHFTLI C C N M J , I > ,K) 793 I F I L .GE. OIGO TO 300 794 DC 250 M=l,Nl 795 250 CCNN(M,I) = LCR (CCNNIM,I ),CONN(M,INDEX)) 796 L = SHFTR(CNE ,K) 797 C C N N I J , I J = LXCR(CONN(J, I ) , L ) 7*8 TEMPI I)=NAMEER(CCNN( 1, I ) , I END! 799 3CC CONTINUE 800 GO TO 150 801 8CC RETURN 8^2 END 803 SUBROUTINE NEWTCN(V,U,ANG,NO.SCHED ,TYPE.SE0,Y,CPONT,NXTR,RPONT, 804 *NXTC,*) 805 EXTERNAL ORDER,JCBN,BACK,CHANGE .DRAW 806 COMPLEX Y (1 ) , V ( I ) , SC HE D ( 1) 807 INTEGER*2 CPCNT(11,NXTRI 11,RPONT(1 > .NXTC(1 I .NO<1 I.TYPE(1) 808 INT C G ER* 2 SECID.NSTEP 809 INTEGER ATENF,AC CNN,AWR,RES(2) 810 REAL U ( l I ,ANG(l ) 811 LOGICAL*! BATCH,ALG(8),HDNGS(80) .PLOT,PRINT 812 COMMON/IN INF/ I I , 12, 13,ITMAX,TOLERN,ZERO,BMVA.L INE,L1ST,I END 813 COMMCN /ADS/ IA , ID, IS,ALG.BATCH ' 814 COMMCN /OUTINF/ NPAGE,NLINE,HDNGS,ISTNO 815 COMMCN /TYM/ RES 816 EQUIVALENCE ( N B U S . U ) 617 CALL TIME(O) 618 PLOT=LIST .LT. 0 819 I F ( P L C T ) REWIND 3 820 IF(PLCT) CALL EMPTY F ( 3 ) 821 PRINT=IAeS(LIST) .GT. 10 822 NSTEP=IABS(LIST)/10 823 N l = ( I E N D - l ) / 3 2 + i 624 NN=N1*IEND*4 825 CALL GSPACE(ACCNN.NN) 826 CALL GSPACE(ATEMP,IEND*2» 827 CALL CALLER!CRDER.ACONN,IPTR(Nl),IPTR(CPONTJ,1PTR(NXTR),IPTRIRPONT 82 8 * ) , 1 PTR(NXTC) , IPTR (SEC),ATEMP,IPTRINPQ),IPTR(NPV),IPTR(TYPE)) 829 CALL FSPACE(ATE«P) 830 CALL FSPACE(ACCNN) 831 NWORDS = NPQ*5 + NPV*3-I END*2 832 CALL GSPACE(AJC.NWGRDS*4) 833 CALL GSPACEfAWR,NBUS*16) 834 CALL GSPACE(AWI,NBUS*2) 835 CALL GSPACE(APNTR,NBUS*2) 836 IT=0 837 LIMIT=0 838 2C0 CALL CALLER(JCBN , AWR , AW I,A JO,A JO , I P T R ( S E Q ) , I P T R ( Y ) , I P T R ( C P O N T ) , I PT 839 * R(NX TRI, IPTRIRPCNT),IPTR(NXTC) , I P T R ( V ) , I P T R ( S C H E D ) , I P T R I U ) , I P T R I T Y 123. 840 «PF), APNTR,IPTR(ERR1),IPTR(ERR2).IPTR(IERR2),IPTR(ERR3) , £ 4 0 0 ) 841 IERR2=NO(IERF2) 842 IF(PLOT) CALL FLCTR(U,ANG,ERR 1,ERR2,ERR3. NO) 843 I F U E R R 2 .LT. 0) IERR2=-IERR2 844 I F t . N C T . PRINT .OR. IT .NE. LI M I T ) GO TO 210 845 LIMIT=LIMIT*NSTEP 846 CALL PRINTR( IT,V,U,ANG,ERR 1,ERR2 ,1ERR2,ERR3.NO) E47 210 IF(ERR2 .LE. TOLERNI GC TO 300 848 I F ( I T .GE. ITMAX) GO TO 250 849 CALL CALLER <eACK,AJO.AJO,APNTR,IPTR (SEQ),AWR ,AWR +NBUS*4, £400) 850 CALL CALLER(CHANGE,AWR,AWR+NBUS*4, IPTR(U »,IPTR(ANG).IPTR(V).IPTR(:S 651 * E C ) , IPTR(TYPEJ) 852 I T = I T t l 853 GC TC 20C 8 54 250 ISTNC=250 e-j5 3CC CALL FSPACE(AJC) 856 CALL FSPACE(AUR) 857 CALL FSPACE(AWI) 858 CALL FSPACE(APNTR) 859 CALL TIME(3,C,RES) 860 IF( .NOT. PLOT) GO TO 350 861 IT=IT+1 E62 NN=(IEND*2+3 )*IT*4 863 CALL GSPACElARRAY,NN) 864 CALL CALLER(DRAW , IPTR( IT 1 , I PTR (NC 1 ,ARRAY) 865 CALL F SP AC E(ARR AY) 866 I T = I T - l 867 35C CALL CUTKIT.ERR 1 ,ERR2 , IERR2.ERR3) 8o8 IF( ISTNO .NE. 0) RETURN 1 869 RETUFN 87C 400 RETURN 1 8 71 END 872 SUB ROUT INE PR INTR(IT,V,U,ANG,ERR 1,ERR2, IERR2,EPR3,NO) 873 COMMCN /ININF/ I 1,I 2,1 3,ITMA X,TOLERN,ZERO,BMVA ,LINE,LI ST,I END 8 74 CCMMCN /CUTINF/ NPAGE,NLINE,HDNGS, ISTNO 875 COMMCN /ADS/ I A,ID,IS,ALG,BATCH 876 L C G I C A L M ALG(8),BATCH 877 LOGICAL EOUC 8 78 REAL U(1»,ANG(1I 8 79 LOG ICAL*1 HDNGS(80) 860 COMPLEX V ( l ) 861 INTEGER*2 NC(1) 862 I F ( I T .EO. 0 .OR. NL INE .GE. 40) CALL HEAD 863 I F t I T .EO. 1 .AND. ECUCIALG(11,'L' ) 1 CALL HEAD 884 WRTTE< 6, I ) IT 8o5 1 FORMAT(//2X , • ITERATION :•, I4/2X, 15( • *' 1//9X,"BUSNO•,15X,•V•, 15X,•U 8d6 *',15X,'ANG' > 867 NLINE=NLINE+5 6d8 CC 100 I=1,IEND 689 I F ( N O ( I 1 .GT. 0) GC TO 100 850 K=-NO(I) 891 ANG 1 = ANG ( I )* 180./3.141592 8*2 WRI TE(6,2»K ,V( I ),U(I »,ANGI 89 3 2 F0RMATI10X,I4,5X,F8.5,4X,F8.5,3X,F9.4,5X,F10.5) 894 NLINE=NLINE*1 655 100 CONTINUE 8 96 WRITE(6,1011ERR1.ERR2,IERR2,ERR3 897 101 F0RMAT(/5X,'ERP. 1 = ',F10.6,5X,«EPR2= ,,F10.6,5X, ,IEPR2=»,I4,5X, 898 *'ERR2= ,,F10.6) 899 NL I NE = NL INE + 2 \ 124. 900 RETURN 901 END 902 SUBROUTINE BACK(CR,0 I,PCI NTR,SEO,DV,DANG,*l 903 COMMON / I N I N F / l l , 12,13, I TM AX, TCLERN, ZERO, BMVA, L I N E , L I S T , IENO 904 CCMMCN /OUTINF/NPAGE.NL INE,HDNGS,ISTNO SJ5 LCGICAL*1 HDNGS(SO) 906 EQUIVALENCE t N B U S t l l ) 907 RE AU*4 C R ( U , C V I U , D A N G ( 1 I 9C8 INTEGER C I ( I ) .FRCM,TC,COL 909 I NT EGER* 2 POINTR(1J,SEO(I) 910 DC 1CC0 I=1,IEND 911 RCW1=0. 912 RCW2=0.0 913 J=IEND-I+l 914 JP1=J+1 915 FROM=PCINTR(J) 516 TO=PCINTR(JP1> 917 IFITO .LT. C)TO=-TO 918 IF ( FRCM .LT. 0)C-0 TO 500 919 INDEX=FR0M+3 920 50 IF1IN0EX .EQ. TO) GO TO 200 521 CCL=CI(INDEX) 922 IFICCL .LT. C) CCL=-COL 923 DO 100 K=JP1,IEND 924 I F ( S E O I K ) .EC. COLIGC TO 150 925 100 CONTINUE 526 ISTNC=100 527 RETURN 1 928 150 COL = 01 <INDEX ) 929 INDEX=INDEX+1 930 ROW 1=R0W1-CR(INC EX)*DANG(K> 931 INOEX=INDEX+1 932 R0W2=R0W2+QR(INDEX)*0ANG(K) 533 INDEX=INDEX+1 934 IF(CCL .LT. 0)GO TO 50 935 RCWl = ROWlt-OR 1 INDEX )*OV(K ) 936 INDEX=(NDEX+1 937 P0W2 = R0W2 + QR( INDEX )*0V(K) 538 INDEX=INDEX+1 939 GO TO 50 940 200 X2=CP(FRCM+i)-RCW2 941 DV(JI=X2 942 RCWl=Pnwi+QR(FRCM+2)*X2 943 CANGIJ)=GR(FPCM)-RCWl 944 GO TO 1000 945 500 FROM=-FROM 546 INDEX=FROM+l 947 550 IF( INDEX .EO. TOGO TO 700 548 CCL=CI(INDEX) 949 I F ( C G L . L T . 0)CCL=-CGL 550 DO 6C0 K=JP1,IEND 951 I F ( S E C I K ) .EC. CCDGQ TO 650 532 600 CONTINUE 933 ISTNC=600 554 RETURN 1 555 65C COL=QI(INDEX) 956 INDEX=INDEX+1 957 ROHl=ROWl+OR(INDEX)*DANG(K» 958 INDEX=INDEX+1 959 IFICCL .LT. 0)GG TO 550 125. 960 P0W1=R0WI+0R(INDEX )*DV(K I 961 INDEX=INDEX*1 962 GO TO 550 963 70C OANGl J)=QRCFRCM)-RCW1 964 1000 CONTINUE 96 5 RETURN 966 END 967 SUBROUTINE CFANCE(DV,DANG,U, ANG. V, SEO. TYPE 1 968 COMMON / I N I N F / 1 1 , 1 2 . 13 , IT MAX, T OLE'RN, ZERO, BMVA.I LINE,L 1ST,IEND 9t>9 EQUIVALENCE ( N B U S . I l ) 9/0 REAL*4 D V l l J ,CANG(1),U(1),ANG(1I 971 COMPLEX V ( l ) 972 INTEC-ER*2 SEC( 1) ,TYPE< 11 973 DC 100 1=1, I E N D 974 J=SEC(I» 975 ANG(J ) = ANG< J )+OANG(I 1 9 76 I F ( T Y P E ( J J .EQ. 1) U ( J ) = U ( J ) + D V ( I I * U ( J ) 977 A1=U(J)*C0S(ANG(J) ) 978 A2 = U ( J ) * S I N ( A N G ( J ) ) 9 79 VIJ)=CMPLX(A1,A2» 90C 100 CONTINUE 9ttl RETURN 982 END 983 SUBROUTINE WRfKR(Y,V,TYPE,NXT,PONT , hRR,WRI) 9t*4 CCMMCN /PINF/IK.K,FIRST,ROW 985 COMMCN /1NINF/ I 1, 12,13, ITMAX,TQLERN ,ZERO.BMVA .LINE,LI ST. IEND 986 INTEGER*2 TYPE! 1),NXT( 1) , PCNTI I) ,WRI(1) 967 INTEGER FIRST,PP,VP,ROW 9d8 COMPLEX YI11 ,V( 11 , I J K , I K 989 REAL WRR(4,1),NKM 9S)0 P P = NX T ( F I R S T ) 991 50 I F I P P .EO. FIRSTJGO TO 300 992 J=PONT(PP) 993 WRI( K)=J 994 I F ( T Y P E ( J ) .EQ. 2 ) W R I ( K ) = - J 995 VF=(PP*7)/4 996 I J K = V ( J ) * Y ( V P ) 997 IK=IK+IJK 998 I F ( J .GT. IEND)G0 TO 200 999 IJK=V(ROW)*CCNJG(IJK) 1000 HKM = A IMAG(IJK) IC01 NKM=REAL(IJK) 1002 WRR( l,K)=HKf 1003 WRR(2 ,K)=-NKf 1004 WR R(3,K)=NKM 1005 WRR(4,K)=HKM 1006 K = K+1 1 C 7 2C0 PP=NXT(PPI 1008 GO TO 50 1CU9 300 RETURN 1 010 END 1011 SUBROUTINE JCBN(WRR»WR I,QR.QI.SEQ.Y,CPONT,NXTR .RPONT,NXTC ,V, 1012 *SCHED,U,TYPE,P0INTR,ERR1,ERR2,IERR2,ERR3,*I 1013 REAL WRR(4, 1 ) ,CR(1),U( 1) 1014 IN TEG ER* 2 W R111),CPONT(1),NXTR(1),RPONT( 1) .NX TCI l» 1015 INTEGER*2 S E C ( 1 1 , P C I N T P ( 1 1 , T Y P E ( I ) 1016 COMPLEX Y(1 ) ,V(1 ) , IK.SK.DS.TEMP,SCHED(1) 1017 INTEGER RCW,FIFST,CIAG,QI(I),COL 1018 CCMMCN /I N I N F / I I , 12 , 13 , I T MA X , TO LE RN , Z ERO , BMV A .LINE,LIST, IEND 1019 CCMMCN /OUTINF/ NPAGE ,NLINE,HONGS ,ISTNO 126. 1020 LOGICAL*I TYFE2,TYPEl,H0NGS( 80» 1021 COMMON /PINF/IK.K,FIRST,ROW 1022 EQUIVALENCE ( I U N B U S ) 1023 C CAUTION : BE VERY CAREFUL WITH THIS PROGRAM. 1024 c IT WCRKS! AND IT HAS TAKEN A LOT OF TIME TO DO SO. 1025 c SO, IF SOMETHING DOES NCT LOOK RIGHT IN THE FIRST GLANCE 1026 c DCNOT CHANGE IT QUICKLY. READ THE WHOLE PROGRAM AND THINK AGAIN. 1027 c 1028 c ROUTINE TC FOPM TRIANGULARIZED JACOBIAN. 1029 c WRR IS REAL-PART WORKING R GW; CONTAINS H,J,N,L. 1030 c WRI IS INTEGER-PART WORKING ROW: CONTAINS COL. 1031 c NO SHOWS THE CRDER IN WHICH THE NODES ARE TO BE PROCESSED. 1032 c QI £ OR ARE EQUIVALENT.! JACOB IAN MATRIX COMPACT FORM). 1033 c 1C34 DVl=C. 1035 DV2=C. 1 036 ERR2=0. 1C37 ERR3=0. 1038 P C I N T R I l ) = 1 1039 DO 1000 1=1,IEND 1040 ROW = SEO( I J 1041 IK=0.0 1042 r TC FORM WORKING ROW: 1043 WRI(1)=R0W I 0 t 4 TYPE2=TYPE(PCW) .EO. 2 IC45 TYPE1=.N0T. TYPE2 1046 IF(TYPE2)WRI(l)=-R0W 1 C47 K=2 1C48 FIRST=R0V»*8-7 1C49 c NOTE THE INFORMATION SHARED THROUGH /PINF/ IODO CALL WRMKRIY.V,TYPE,NXTC,RPONT,WRR,WRI ) 1051 CALL WRMKR(Y,V,TYPE,NXTR,CPONT, hRR , WRI1 1052 TEMP=YIR0W*2J 1C53 !K=IK+V(ROW»*TEMP 1054 SK=V(ROWI*CCNJG(IK) 1035 DS=SCHED(ROW)-SK 1056 OF=REAL(OS) 1C57 DVI=DV1+DP ' 1058 ADD=ABS(CP) 1C59 IF(ERR2 .GE. ADO) GO TG 50 1C<JO ERR 2 = A0D 1061 IERR2=P0W 1C62 50 E R R3 = ERR 3 + A DC I0o3 IF1TYPE2) GO TO 70 1 C64 DQ = A I MAG IDS 1 1065 DV2=DV2~00 1066 ACC=ABS(DO) 10o7 IFIERR2 .GE. ACC) GO TO 60 1C6B E R R 2 = A D D 10o9 IERR2=R0W 1G7C 6G ERR 3 = EPR3+ADD 1C 11 70 TEMP=TEMP*U(RCW)**2 1072 WRR ( 1 ,1)=-A IMAGtSK+TEMP) 1073 loRR (2,1) =REAL ( SK-TEMP) 1074 WRR(3,1)=REAL(SK+TEMP) 10/5 WRR(4,I)=A I MAGISK-TEMP) 1C76 K = K-1 1077 I F( I .EO. 1)GC TO 300 10 78 C TC PERFORM TRlANGULARIZATICN PROCESS ON THE ROW BEFORE STORING IT: 10 79 J = l 127. i c a e 9 0 IC0NE=SE0«J» 1081 I F ( T Y P E ! I DONE 1 .EO. 2» ID0NE=-ID0NE 1082 J J = 0 1083 100 J J = J J * 1 IC84 IF1ICCNE .EO. W R I I J J U G O TO 5 0 0 1085 150 I F U J .LT. K» GO TO 1 0 0 1086 J = J * l 1C87 I F ( J .LT. I J GO TO 9 0 1088 C . ROW TRIANGULARIZED. DIVIDE THE ROW BY ITS DIAGONAL ELEMENT IC89 c AND STORE THE RESULTS: 1C90 3CC RATI0=1./WRRI1 . 1 ) IC91 DC 350 J=1,K 1C92 I F I W R K J I .EC. CtGG TO 3 5 0 1093 WRR(l,J)=WRR(l,J ) * R A T i a 1C94 I F ( W R K J ) .GT. 0)WRR13,J)=WRR< 3,J)*RATI0 1C95 350 CGNTINUE 1096 DF=OP*RATIO 1C97 IF(TYPE21G0 TO 4 0 0 1C98 RATI0=-WRR(2,1) 1099 WRR <4,1>=WRR(4,lI+WRR13,1)*RATI0 1 U 0 RATI02=1./WRR(4,1I 1 101 DC 36C J=1,K 1102 I F ( W R K J ) .EC. OIGO TO 360 1103 WRR(2,JI=<WRP(2,JI-WRR(l,JI*RATICl*RATI02 I 104 I F ( W R K J ) .GT. 0)WRR(4,J)=(WRR(4,JI*WRR(3 ,J)*RATIO) *RATI02 1105 36C CONTINUE 1106 00=(DO+DP*RATIC I + RATI0 2 1 107 C ROW IS READY TC BE STORED 1 l o 8 4CC INDEX=POINTR(II 1109 IF!TYPE2)P0INTR(I)=-INDEX 1110 J=2 1111 OR IINDEXI=DP 1112 INDEX=IN0EX * 1 1113 IF1TYPE21G0 TO 420 1114 OR(INDEXI=DC 1 l i 5 INDEX=INDEX+ 1 1116 CR(INDEX )=WRR ( 3 , 1 ) 1117 INDEX=INDEX+1 1118 42C I F ( J .GT. K) GO TO 460 1119 J J =WRIIJI 1120 I F ( J J .EO. 0)G0 TO 450 1 121 OK INDEX J = J J 1122 INDEX=INDEX+ 1 1 123 0R( INDEX ) = WRRI I , J ) 1 124 INDEX=INDEX +1 1125 IF(TYPE2IGC TC 430. 1 126 CR(INCEX)=WRR(2,J) 1 127 IN0EX=INDEX+1 I 128 430 I F U J .LT. CIGC TO 450 1129 QP(INDEX)=WRR(3,J) 1130 INDEX=INCEX+l 1131 IF(TYPE2)G0 TO 450 1 132 OR t INDEX )=WRR(4,J) 1133 INQEX=INDEX+1 1 134 45C J = J«-1 1135 GO TO 420 1136 46C PCINTR(I+1)=INDEX 1137 GO TO 1000 1138 C TC CCNBINE A PCW WITH A PREVIOUSLY PROCESSED ROW: 1139 5 CO INDEX=PDINTR(JJ 128. 1140 IF(INDEX .LT. 0) INDEX=-INOEX 1141 LAST=PGI NTfUJ+U 1142 I F < L AST .LT. C) LAST=-LAST 1 143 RATIC=-WPR(l.JJI 1 144 C FIRST COMBINE THE PRESENT ROW WITH CNLY THE FIRST ROW OF THE 1145 C PREVIOUSLY PROCESED ROW. 1146 IFITYPEi>RATI02=-WRR(2»JJI 1147 DP=DP+OR(INDEX)*RATIC 1148 I F ( T Y P E l >DC = CC + OR(INDEX)*RAT 102 . 1149 52C INQEX=INDEX+l 1150 I F I W R I U J ) .LT. 0)G0 TO 540 1151 IN0EX=INDEX+1 I 152 WRR(3,JJI = WRP(3,JJ»-<-QR (INDEX)* RATIO 1153 IF(TYPE1)WRR(4,JJ)=WRR(4,JJ»+0R(INDEX)*RATI02 1154 INDEX=INDEX+1 I 155 54C COL=0I(INDEX) 1156 INDEX=INDEX+1 1 1 57 C SEE IF THE CCRRSEPODING OFF DIAGONAL ELEMENT EXISTS : 1 158 DO 550 NA=1,K 1 155 IFICCL .EC. WRI(NA))C-0 TO 600 1160 55C CONTINUE 1161 C IF NOT, CREATE ONE WITH ZERO VALUES: 1 162 K = K + l 1 163 WRI(K)=CCL 1164 DO 560 NB=1,4 l l o 5 56C WRR(NB,K)=0. 1 166 NA=K I 167 C CHANGE THE VALUE OF THE OFF DIAGONAL ELEMENT (THAT CERTAINLY 1 168 C EXISTS NCW) : 1165 6CC WRR (1,NA) = WRR(1,NA ) + QR(INDEX >*RATIO 1170 IF(TYPE11WRR(2,NA)=WRR (2.NA )+CR(INDEX)*RAT102 1171 INDEX=INDEX+1 11 72 I F ( W R K J J ) .GT. 0) INDEX=INDEX+l 1 173 IF(COL -LT. CI GC TO 700 I 174 WRR(3,NA)=WRR(3,NA)+0R(INDEX)*RATIC 11 75 I F( TYPE I )WPP. (4,NA1=WRR (4,NA)+0R( INDEX ) *RA T102 1 176 INDEX=INDEX+1 1177 I F I W R I U J ) .GT. C) I NDEX = INDEX*l 11/8 70C IF( INDEX .LT. LAST) GO TO 540 1 179 C IF THE PREV PROC. ROW IS T Y P E l , COMBINE THE SECONE ROW OF THAT: 1 160 I F I W R I U J ) .LT. 0)G0 TO 800 1181 RATIC = -WRR 13 , J J ) 1182 I F I T Y P E l )RATIC2=-WRR(4,JJ) 1 l d 3 INDEX = POINTR I J) 1184 INDEX=IA3S(INDEXI+1 1165 DP = OP +QR(INDEX)*RATIO I 166 IF ITYPEl)DC=CC + 0P( IN CEX)*RAT 102 1167 INDEX=INDEX*2 1 168 73C CCL=CI(INDEX) 1185 lNDEX=INDEX+2 1190 DO 740 NA=1,K 1 191 IF(CCL .EO. WRI(NA))GO TO 760 1 152 74C CONTINUE 1193 ISTNO=740 1 194 RETURN 1 1195 76C WPR(1,NA)=WRR(1,NA)+CR(INDEX)*RATIO 1196 IF(TYPE1)WP.R(2,NA)=WRR (2,NA)+QR( INDEX) *RAT 102 1197 II\DEX=IN0EX*1 1 198 IFICCL .LT. CIGC TO 780 1199 INDEX=INDEX+l 129. 12o0 WRR<3,NAI=WPR<3,NA)*CR(INDEX)*RATI0 1201 IF(TYPEIROW) .EO. 1)WRR(4,NA) =WRR(4,NA)*0RCINDEX)*RATI02 1202 INDEX=INDEX+1 1203 78 0 IF(INDEX .LT. LAST) GO TO 730 1204 800 WRI<JJ)=0 1205 GO TO 150 1206 1000 CONTINUE 1207 EPR1=SQRT(CV1*DV1*DV2*DV2) 1208 RETURN 1209 END 1210 SUBROUTINE OUT1(IT,ERR 1,ERR2,1ERR2,ERR3) 1211 COMMCN/I N I N F / U ,12,13, IT MA X , TO LE RN , ZERO, BMVA , L INE , L 1ST , I END 1212 COMMCN /OUTINF/ NPAGE,NLINE,HONGS,ISTNO 1213 CCMMCN /TYM/ RES 1214 INTEGER R E S ( 2 I 1215 L O G I CALM HCNGSI 80) 1216 CALL HEAD 1217 WRITE(6,1111,12,13,LINE 1218 1 FORMAT(/' T A B L E O F P A R A M E T E R S : • / 1 X , 3 8 ( • + ' ) , 4 ( / ) , 5 1219 *'X,«NC. OF BUSES=', I4,18X,'N0. CF TRANSMISSION L IN ES= • , I 5///5X, • NO. 1220 * CF TRANSFORMERS^ ,15,10X,'TCTAL NUMBER OF 6RANCHES=•, 15//) 1221 WPITE(6,2)BMVA,LIST 1222 2 F0RMATI5X,'BASE MVA SP EC I F I ED= • , F7 .2, I OX, »L I ST= •, 14// ) 1223 WRITE(6,3)IT,ITMAX,ERR1,T0LERN,ERR2.IERR2,ERR3 1224 3 FORMAT (5 X , •NC . OF I TERAT IONS=• , 16///5X, •MA X NO. OF ITERATI ONS=•, 16 1225 *///5X,'TOTAL POWER MISMATCHES =' , F l 0 . 6///5X,•TOLERANCE SPECIFIE0=', 1 226 *F10.6///5X,'MAX POWER HISMATCHES = • ,F 10.6,5X,•AT BUS ',I4///5X,•TOT 1227 + AL A BS POWER MISMATCHES 5 5* ,F10.6) 1228 WRITE(6,4)RES 1229 4 F0RMAT(//5X,'CPU TIME USED IN PR OSS=•,I 6///,5X, • ELAPSED TIMF IN PR 1230 *OSS=«,I6///I 1231 I F ( L I S T .LT.OJ CALL PLCTND 1232 RETURN 1233 END 1234 SUBROUTINE FLOWS(V,U,ANG,NC) 1235 EXTEFNAL OUTPUT 1236 COMMON/IN INF / 11, 12,13. I TMAX,TOLERN , ZER0,BMVA,LINE, L1ST, I END 1237 COMMCN /OUTINF/ NPAGE,NLINE,HDNGS,ISTNO 1238 EQUIVALENCE ( I l . N B U S I 1235 LOGICAL*! HCNGS(80) 1240 COMPLEX V ( l ) 1241 REAL U ( l ) ,ANG(l) 1242 INTEGER*2 N0(1) 1243 INTEGER FT 1244 CALL GSPACE(LTN0,LINE*2) 1245 CALL GSPACE(NAME,NBUS*18) 1246 CALL GSPACE t FT,LINE*4) 1247 CALL GSPACEIIMP,LINE*24) 1248 CALL GSPACE(EASE,NBUS*4) 1249 CALL CALLER(CUTPUT,IPTR( V) ,IPTR(U(,IPTR(ANG),NAME,IPTR(NO),FT , FT *L 1250 *INE*2,IMP,IMP+LINE*8,IMP+LINE* 16,BASE,LTNO ) 1251 CALL FSPACE(NAME) 1252 CALL FSPACE(FT) 1253 CALL FSPACE(IMP) 1254 CALL FSP AC E ( EASE ) 1255 CALL FSP ACE(LTNC) 1256 RETURN 1257 END 1258 SUBROUTINE OUTPUT(V,U, ANG,NAME,NC,FPCM,T0,YP1,YP2,Z.BASE,LTNO1 1259 COMMCN/ININF/I 1,12,13, ITMA X,TOLERN,ZERO,BMVA.LINE,LIST,IEND 130. 1260 COMMCN /OUTINF/ NPAGE,NIINE,HDNGS.ISTNO 1261 COMMCN /ADS/IA, ID,IS,ALG,BATCH 1262 EQUIVALENCE ( I l . N B U S ) 1263 L0GICAL*1 HDNGSI 80»,ALG(8),BATCH 1264 L O GICAL*l T E S T ( 8 ) / • F • , • L • , ' 0 • , •W•,•S• . ' •,• •/ 1265 COMPLEX V ( I I , Z ( 1 ) , Y P 1 < 1 1 , Y P 2 I 1 I , S , S T , Y P l 1266 REAL U( 1) , ANC-I 1 ) , F I L L E RI 4) , BASE( 1) 1267 INTEG ER*2 NC(1),TYPE,FROM I 1),T0(1).LTNOI1) 1268 REA L* 8 NAME(It,LTNAME 1269 INTEGER ITEST(2),IALGI2» 1270 EQUIVALENCE IALG(1 ), IALG11 ) ),(TEST(1),ITEST I 1)) 1271 REWIND 1 1272 REWIND 4 1273 IEND=NBUS 1274 PI=3.14159 1275 1=1 12 76 100 READIllTYPE.NOII»,NAMEII),FILLER,BASEI II,VOLT 1277 . IFITYPE .NE. 3) GO TO 200 1278 NC(IEND)=NO(I» 1279 NAME I I END I = NAME I I I 1280 BASEl IEND) = BASEI I ) 1281 IEN0=IEND-1 1282 1=1-1 1283 2C0 1=1+1 1264 I F I I .LE. IEND) GO TO 100 1285 00 30C 1=1,LINE 12o6 R E A D ( 4 ) L T N 0 ( I ) , L T N A M E , F R O M ( I ) , T O ( I ) , Y P 1 ( I ) , Y P 2 ( I J , Z ( I ) 1287 3CC Z ( H = - Z ( I ) 12o8 CALL HEAD 1269 DO 1000 I=1,NBUS 1290 K=NC(I) 1291 IC=NLINF*6 1292 DC 400 J=1,LINE 1293 IFIFRCM(J> .EC. K .OR. TOIJI .EQ. K I IC=IC + 1 1294 400 CONTINUE 1295 I F I I C .GT. 601 CALL HFAD 1296 ST=0. 1297 VOLT = U<I 1*BASE< I > 1298 DEG = ANG( I ) * 1 8 0 . / P I 1299 WRITE(6.401)K,NAME(I J . U I I ) ,VCLT,OEG 1300 401 F0RMATI//10X,'BUS NO•,I 5,2X,A8,4X,F5.3,• PU« ,4X,F8.3,• KV«,4X,F8.3 1301 DEG'/30X , * TO: •> 1302 NLINE=NLINE+4 1303 00 700 J=1,LINE 13J4 I F ( K .EO. FPCM(J)»GO TO 500 1305 I F I K .NE. T C ( J J ) GO TO 700 1306 KK=FPCM(J) 1307 YPI=YP2(J» 1308 GO TO 550 I3i.9 500 KK = T C ( J I 13iO YPI=YP1(JI I 2 i l 55C DC 60C 11=1,NBUS 1312 IF (KK .EC. N C ( I H ) GC TO 650 1313 6CC CONTINUE 1314 65C S = V ( I ) * ( Z t J ) + Y P I ) - V I II ) * Z ( J ) 1315 S=V(I»*CCNJGISJ*BMVA 1316 ST=ST+S 1317 WRITE(6,651)KK,NAME( II ),S,LTNO(J) 1318 651 F0RMATI35X,I5,2X,A8,2(10X,F10.3I , 4 X , ' ( . 1 4 , » ) • ! 1319 NLINE = NLINE+ 1 131. 1320 1321 1322 1323 1324 1325 132 6 1327 132 8 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1335 1340 1341 1342 1343 13*4 1345 1346 1347 1348 1349 135C 13 51 13 52 1353 1354 1355 1 356 1 357 13 58 1359 1300 1361 13o2 1 3 63 1364 1365 1366 1367 !3o8 13o9 1370 1371 1 3 72 13 73 13 74 1375 1376 13/7 1378 1379 •1/35X,' T O T A L S : •,3X.2(1 OX,F10.3)) I T E S T d l .AND. IALG(2) .EO. ITESTI2) ) STOP 7C0 CONTINUE WRITE(6,701)ST 7C1 F0RMAT(38X,52(»-NLINE=NLINE+2 1C00 CONTINUE I F ( I A L G d ) .EQ. RETURN END SUBROUTINE LOSS 11V,U.ANG,NO,SCHED,TYPE,SEO,Y,CPONT.NXTR,RPONT, NXTC *,*» EXTERNAL CRCER,MOCEF,FORMBP,FOPBKW,LCHNGE,DRAW .ERSLC COMPLEX Y( I I , V U I ,SCHED( I I INTE0ER*2 CPONT(1),NXTR(1),RP0NT(11.NXTC!1),NOUI.TYPE(11 I NT EG ER* 2 S E C l l l . N S T E P INTEGER RES(2)»ACCNN'»ATEMP REAL U ( l ) , A N C - d ) LCGICAL*1 BATCH,ALG(8I,HDNGS(801,PLCT,PRINT COMMGN /I N I N F / I 1,12,13,ITMAX,TOLERN,ZERO,BMVA,LINE.LI ST,IEND CCMMCN /ADS/ I A , I C , IS,ALG,6ATC H COMMCN /OUTINF/ NPAGE,NLINE,HDNGS.ISTNO COMMON /TYM/ RES COMMON /LOSSES/ SL EQUIVALENCE ( I l . N B U S I IA = 1 GC TC 10 ENTRY FLCSS1{V,U.ANG .NO.SCHED.TYPE,SEO,Y,CPONT,NXTR,RPCNT,NXTC,*) CALL GSPACE(SL,NBUS*8) IA=2 1C CALL TIME(O) PLOT=LIST .LT. 0 IF(PLC T ) REWIND 3 IFIPLOTJ CALL EMPTYF(31 PRINT=IARS(LIST) .GT . 10 NSTEF=IABS(LISTI/10 N l = ( I E N D - l l / 3 2 + 1 NN=N1+IEN0*4 CALL GSPACE(ACGNN.NN I CALL GSPACEIATEMP,IEN0*2I CALL CALLER(CRDER,ACCNN, IPTR(Nl),IPTR(CPONTI,IPTR(NXTR),IPTR(RPONT * l , I P T R ( N X T C ) , I P T R ( S E O I , A T E N P , I P T R ( N P C ) , I P T R ( N P V ) , I P T R ( T Y P E I ) CALL FSPACE(ATEMP) CALL FSPACE(ACCNM NV»ORDS=NPO*5tN'PV*3-I END*2 CALL GSPACE(/!M,NWCRDS*4) GSPACE(AWR,NBUS*16I GSPACE(AWI,NBUS*2I GSPACE(AFNTR,NBUS*2) GSPACE(BV.IEN0*8I GSPACE(NUMB,IEND*2) CALLER(MCCEF,AWR,AWI,AM,AM,BV,IPTR(SEO),IPTR(Y>,IPTR(CPONTI,1 *PTR(NXTRI,IPTR(RPCNT),IPTR(NXTC),IPTR(SCHED),IPTR{U),IPTR{TYPE I , *APNTR.NUMB,G400I CALL FSPACE(AWRI CALL FSPACE(AWI) CALL GSPACE(EP,IEND*8) I T=0 I F ( I A .EO. 1) GO TO 50 CALL CALLER(ERSLC. BP,NUMB,IPTR(SEQ),IPTR(TYPE 1 , I P T R ( V ) , I P T R ( U ) , I P * TR(ANG1,IPTR(SCHEDI, IPTR(IT I ,SL, IPTR(Y I,IPTR(CPONT I.IPTR(NXTRI.IPT *R( RPCNT) , IPTR (NXTC) . I P T R ( E R R l ) .1 PTR.IERR2) , IPTR (IERR2) , IPTR (ERR31) CALL CALL CALL CALL CALL CALL 132. 1380 IERR2=NO(IERP2I 1381 I F I I E R R 2 .LT. 0) IERR2=-IERR2 1382 IF(PLOT) CALL PLOTR(U,ANG,ERR1.ERR2.ERR3,NO) 13 83 IF{.NOT. PRINT) GO TC 20 1384 LIMIT=NSTEP 1385 CALL PRINTRUT,V,U,ANG,ERR1,ERR2,IERR2,ERR3,N0I 1386 20 IFIERR2 .LE. TOLERN) GO TO 300 1387 GO TO 100 1388 50 LIMIT=1 1389 100 CALL CALLER IFCRMBP.BV,BP,IPTRISEC),SL.IPTRI I T ) , I P T R ( V ) , IPTR ( AN G), 1390 * I P T R ( Y ) , I P T R ( C P O N T ) , I P T R I N XTR),IPTR(RPCNT).IPTR(NXTC),IPTR(TYPE). 1 391 *IPTR(U)» 1392 CALL CALLER(F0RBKW,AM,AM,9F,APNTP,NUCB,IPTR(SEC)) 1393 CALL CALLER(LCHNGE.BP,NUMB,IPTR(SEO),IPTR(TYPE),IPTR(V»,IPTRIU),IP 1394 *TRIANG),IPTR (SCHED1, I P T R ( I T ( , S L , IPTR (Y 1,IPTR(CPONT 1, IPTRINXTR),IPT 1395 *R(RPCNT).IPTRINXTC),IPTR(ERR 1)VIPTRIERR2),IPTR11ERR2),IPTR(ERR3)) 1396 IT=IT*1 1397 IERR2=NC(IERP2) 1398 I F I I E R R 2 .LT. CJ IERR2=-IERR2 13*9 I F ( P L C T ) CALL PLOTR(U,ANG,ERR 1,ERR2,ERR3,NO) 1400 IF( .NOT. PRINT .OR. IT .NE. LIMIT) GO TO 20C 1401 LIMIT=LIMIT + NST EP 1402 CALL PR INTR(IT,V,U,ANG,ERR 1,ERR2,IERR2,ERR3,NO) 1403 20C IF(ERR2 .LE. TOLERN) GO TO 300 14 04 I F ( IT .GE. UMAX ) GO TO 250 1405 GO TO 100 1406 25C ISTNG=250 14o7 300 CALL FSPACE(AM) 14u8 CALL FSPACE(AFNTRI 1409 CALL FSPACEIBV) 1410 CALL FSPACEIEP) 1411 CALL FSP ACE I NUMB) 1412 CALL TIME(3,C,RES) 1413 IFf.NOT. PLOT) GC TO 350 1414 I F ( I A .EO. 2) IT=IT*1 1415 NN=( IENO*2+3 )*IT*4 1416 CALL GSPACE(ARRAY.NN) 1417 CALL CALLER(DRAW,IPTRI IT 1 ,IPTR(NC).ARRAY) 1418 CALL FSPACE(ARRAY) 1419 I F ( I A .EO. 2) IT=IT-1 1420 35G CALL CUT1(IT,ERR1,ERR2,IERR2.ERR3) 1421 IF(ISTNO .NE. 0) RETURN 1 1422 RETURN 1423 4CC RETURN 1 1424 END 1425 SUBROUTINE LCFNGE(BP,NUMB,SEC,TYPE,V,U,ANG,SCHED.IT,SL,Y,CPONT,NXT 1426 *R,RPONT,NXTC,ERR I,ERR2,IERR2.ERR3) 1427 REAL RP(I ) ,U ( 1 ) , A N G ( l ) 1428 INTEGER*? NUMB 1 1),CPONT(1),NXTRI 1) ,RPONT(I ),NXTC(1),SE0(I).TYPE(I) 1429 COMPLEX Y ( 1 ) , V ( 1 ) , S L ( 1 ),SCHEDI I),IK,DV,SLK,DS 1430 INTEGER FIRST,PP,VP 1431 CCMMCN /ININ F / I 1, 12,13, ITNAX,TOLERN,ZERO,BMVA,LINE,LIST,IEND 1432 EQUIVALENCE (U.NBUS) 14J3 DO ICO 1=1,IEND 1434 K=SEO(I» 1435 KP = NL'MB I K) 1436 ANG(K1=-BP(KB) 1437 I F(TYPE(K ) .EC . 1)U(K1 = S0RT(BP(KB+1)*2.) 143 8 A1=U(KI*C0S1ANG(KI ) 1439 A2 = U(K)*SIN(ANG(K) ) 133. 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 14 52 1453 14 54 1455 1456 1457 1458 1459 146C 1461 1462 1463 1464 !4o5 1466 1467 14t>8 1469 1470 1471 1472 14 73 1474 1475 1476 1477 14 78 1479 1480 1 4 d l 1482 1483 1484 1485 I486 1487 14d8 1469 1490 14*1 1492 1 4*3 1494 1495 1496 1497 1498 1499 V(K)=CMPLXtAi,A2> 100 CONTINUE ENTRY ERSLCIBP,NUMB.SEQ,TYPE,V,U,ANG,SCHEO,IT,SL»Y,CPONT,NXTR, *RPONT,NXTC,ERR 1,ERR2,IERR2,ERR3 ) OVl=0. OV2=0. ERR2=0. ERR3=0. DO 200 1 = 1. 1 END IK=0. SLK=0. FIRST=I*8-7 PP=NXTR(FIRST) 110 I F I P P .EO. FIRST) GO TO 120 VP=IPP+7)/4 J=CPCNT(PP) I K = I K + Y ( V P ) * V ( J I DV=V<I)-V(J) SLK=SLK-DV*CCNJG(OV*Y(VP)) PP=NXTR(PP) GO TO 110 120 PP=NXTC(FIRST) 130 I F I P P .EO. FIRST) GO TC 150 VP=(PPW»/4 J=RPCNT(PPJ I K = I K + Y ( V P ) * V ( J ) DV = V( I )-V< J ) SIK=SLK-DV*CCNJG(DV*Yl V P ) ) PP=NXTC(PP) GO TO 130 150 S L t l ) = S L K / 2 . IK=IK*YC1*2l*VC n IK = V ( I I * CON J G ( IK I OS=SCFEDf I I - I K OP=REALIDS) DV1=DV1+0P ACC=ABSIDP) IF(ERR2 .GE. ADD) GO TO 160 ERR2=ADD IERR2=I 16C ERR 3 = ERR 3 + ACD I F ( T Y P E ( I ) .EO. 2) GO TO 200 DO=AIMAG(CS) DV2=CV2*DQ ACC=ABS(DQ) IFIERR2 .GE. ADD) GO TO 170 ERR 2 =AOD IERR2=I 17C ERR 3 = ERR3+A0C 2CC CONTINUE EPRl=SQRT(DVl**2+DV2+*2> RETURN END SUBRCLTINE LWRMKR(WRR,WRI,Y,PONT,NXT,U,FIRST,K,TYPE,NB,3,SUM) COMMCN /ININF/ I I , I 2,1 3,ITMA X,TOLERN,ZERO,BMVA,LINE,LI ST,I END EQUIVALENCE ( I l . N B U S I COMPLEX Y I H ,SUM INTEGER*2 PCNT(1),NXT( 1 ) , W R I ( I ) , T Y P E ( 1 1 REAL W R R ( 4 , l ) , U ( l ) , B ( l ) INTEGER VP,PP.FIRST 134. 1500 1501 50 1502 15u3 1504 1505 1506 1507 1508 15uS 1510 1511 1512 1513 1514 1515 1516 1517 100 1518 11C 1519 1520 1521 1522 1 5<!3 15C 1524 1525 2CC 1526 1527 1528 1525 I 530 1531 1532 1 533 1 534 1535 1 536 1537 1 5 j 8 1 1539 1540 1541 100 1542 1C1 15*3 1 544 15*5 1 546 1547 20C 1 548 15*9 1550 201 1551 15a2 2 1C 1553 22C I 554 250 1555 1556 251 1 5 57 1558 1559 PP = NXT(F IRST ) I F ( P P .EC. FIRSTI GO TO 200 J=PCNT<PP1 WRI(K)=J I F J T Y P E I J ) .EC. 2IWRI<K>=-J VP=(PP*7)/4 SUM = SUM+YI VP ) GIK=REAL<Y(VPII BIK = AIMAG(Y(VP) J I F ( J .GT. I END • GO TC 110 WRR(1,K)=BIK WRR(2,K)=GIK I F ( T Y P E ( J I .EC. 21 GC TO 100 WRR(3,K)=GIK WPR(4,K)=-BIK K=K*1 GO TO 150 K = K + 1 Ul=U(J 1**2/2. e(NBt=B(N9)-GIK * U l I=(FIRST+7»/8 I F ( T Y P E ( I J .EO. 2) GO TO ISO 8(NB+1»=B(NB+1)+BIK*Ul PP=NXT(PP) GO TO 50 RETURN END SUBROUTINE LNFST(NO,SL ) INTEGER*2 NC(1I COMPLEX SL ID .TEMP CCMNCN / I N INF/ 11, 12 , 13. IT MA X . TO LE RN, Z ERO , BMVA ,L I NE , L I ST , I END ECUIVALENCE ( I l . N B U S I COMMCN /ADS/ IA , I D , IS,ALG,BATCH L0GICAL*1 eATCF,ALG(8),MTSU(30l DATA NRTST/Z4C404040/ EQUIVALENCE (MTSUl13),NRTRN) IF(BATCH I GO TO 100 WRITEl16,1) FCRMATC ENTER NAME CF THE UNIT CONTAINING STARTING'/ *• VALUES (RETURN OR EOF IF *MSOURCE*)' l CALL SETPFXJ '?• , 1) READ( 15, 1C1 ,END = 2 0CMMTSU( I ) , 1=13,30 ) FORMAT(20Al ) IFINRTRN .EC. NRTST) GO TO 200 CALL MOVECl 12,"ASSIGN 8=',MTSU) CALL FTNCMD(MT SU,30) GO TO 210 CALL FTNCMD!'ECLATE 8=GUSER',14) IF(BATCH) GO TC 210 ViPITE(16,201» FORMAT(' ENTER P.U. VALUES OF " 4 1 IN ( 2 I 5 . 2 F 1 0 . 5 ) FORMAT*) DO 220 1 =1,NEL S S L ( I ) = 0 . DO 290 1=1,LINE READ(8.2 5l,EN0=3C0)NCl .N02.TEMP F0RMAT(2I5,2F10.5) DC 280 J=1,N8LS K=NG(J) I F I K .LT. 0) K=-K N01« •N02' **SL***/ 135. 1560 IF(K .EO. N01» N01=-J 1561 I F I K . E O . N02) N02=-J 1562 IF(NC1 .LT. 0 ./INC. N02 . L T . 0» G O T O 285 1563 2eo CONTINUE 1 564 285 N0l=-N01 1565 N02=-N02 1566 SLJN01)=SL(NCl)+TEMP/2. 1567 SLt NC2)=SL(NC2)«-TEMP/2. 1568 290 CONTINUE 1569 30 C CALL S E T P F X l , 1 ) 157C RETURN 1571 END 1572 SUBROUTINE FORBKW(AM , MA,BP,PCI NTR,NUMB,SEO» 1573 REAL A M I 1 ) , E P ( 1 I 1574 INTEGER M A ( l ) 1575 COMMCN /INI N F / I 1,12,13,ITMAX,TOLERN,ZERO,BMVA ,LINE.LI ST,I END 15/6 EQUIVALENCE (I1,NBUS» 1577 I N T EGEP>2 PCINTRJ 1) , NUM8(1),SEQ(11 15/8 OC 500 I=1,I£ND 1579 K = S E Q < I ) 1580 NB=NUMB(K) 1 581 J=PGINTR(I) 1582 LAST=PCINTR(I-1> 1 583 I F ( L AST .LT. C) LA ST = -LAST 1564 I F ( J .LT. 0) J=-J 1585 I F ( P O I N T R t l ) .LT. 0) G O TO 200 1586 BP (NB<-1) = R P (NB+l > - B P ( N B ) * A M ( J*2) 1567 ICC J = J-3 1568 IF( J .EO. LAST J GO TC 300 1569 K=IAES(MACJ)| 1550 KB=NUMB(Kl 1591 B P ( K B ) = B P ( K B)-BP(NB)«AM(J + l ) - B P I N B + 1)* AM (J»2) 1592 I F I M A t J ) .LT. 0 1 GO TO 100 1553 K B = K B * 1 15S4 J = J + 2 1 595 e P ( K e ) = B P ( K B ) - B P ( N B ) * A M ( J + l l - B P ( N B * l » * A M ( J + 2 J 1596 GO TC 100 1597 200 J = J+1 1598 I F ( J .EQ. LAST! GO TO 300 1599 K = IARS(MAIJ) ) 1600 KB=NUMB(K) 1601 J = J*1 1602 B P(KB)=RP<KB)-BP ( N B)*AM<J» 1 603 I F ( M A ( J - 1 ) .LT. 0) GC TO 200 1604 KB=KB+1 1605 J = J+1 1606 EP(Ke)=BP(KB»-BP(NB1*AM(J) 16C7 GO TO 200 1608 3 CC J=POINTR(I) 1609 I F ( J .LT. 01 J=-J 1610 BP ( N B)=BP(NB l*AM{J) 1 6 l l I F I P C I N T R U ) .GT. 0) B P l N B + l )=BP INB•1)*AM<J+11 16 12 50C CCNTINUE 1613 C RACK SUBSTITUTION STARTS: 1614 DC 1C00 11 = 1,IEND 1615 I=IEND-II+1 1616 J=PGINTR<I) 1617 I F ( J .LT. 01 J = - J 1618 LAST=P0INTR(I+1) 1619 IFILAST .LT. 0) LAST=-LAST 1620 SUM1=0. 1621 I F I P O I N T R I I ) .LT. 0) GO TO 700 1622 SUM2=0. 1623 600 J=J+3 1624 IF<J .EO. LAST) GO TO 800 1625 K = IABSIMAU>> 1626 KR=NUMB(KI 1627 SUM1 = S U M + A M J + l I*BP(KB1 1628 SLM2=SUM2-AM(J+2I*8P(KB> 1629 1 F I M A U ) .LT. 0) GO TO 600 1630 J=J+2 1631 KB=K3+1 1632 SUM1 = SUM1 + A M J * 1 ) * B P I K B ) 1633 SUM2=SUM2 + Ar'(J + 2>*BP(KB) 1634 GO TO 60C 1635 7CC J = J + 1 1636 I F ( J .EO. LAST I GO TO 800 1637 K=IABSIMAIJI I 1638 KB=NUMB ( K ) 1639 J = J->-l 1640 SUM1 = SUMI*-AM J J*eP(KB) 1641 I F ( M A U - l ) -LT. 0) GO TO 700 164? J = J->-l 1643 KB=KB+1 1644 SUM1=SUMI+AM(J|*EP(KB) 1645 GO TO 70C 1646 8C0 J=PCINTR(I1 1647 I F t J .LT. 0) J=-J 1648 K=SEG<II 1649 NB=NUMB(K) 1650 I F I P C I N T R U I .LT. 01 GO TO 900 1651 BP1NB+1)=8P(N0*1I-SUM2 1652 SLMl = SUMl»-BP(Ne + l J*A«U*2) 1653 9C0 BP(NBI=BP(NBI-SUKl 1654 1000 CONTINUE 1655 RETURN 1656 ENO 16 57 SUB POUT INE FGRMBP(B,BP,SEO,SL,IT,V,ANG,Y,CPCNT,NXTR,RPONT,NXTC 1658 *,TYPE,U) 1659 INTEGER FIRST,PP,VP 1660 REAL Bt1 1 ,BP(1»,ANGI H , U ( 1 ) 1661 INTEGER* 2 SEQUI,CPONT I I I . NXTR (I I, PPONT 11 I ,NXTC I 11 ,TYPE( 1 I 1662 COMPLEX SL( 1 I,V I 1J , Y(1),SUM 1663 COMMCN /IN IN F/ I I , 12 , 13, ITMAX,TOLERN.ZERO,BMVA ,L INE,LIST,I END 1664 COMMCN /AOS/ IA,10,IS,ALG,BATCH 16o5 L0GICAL*1 A LG(8),BATCH 1666 EQUIVALENCE ( I l . N B U S I 1667 IF t I A .EQ. 2 1 GC TC 100 1608 I F I I S .EO. 2 .OR. IT .NE. C) GO TO 100 1609 00 5C 1=1,IEND 16/0 5C S L ( I ) = 0 . 1671 100 NB=0 1672 DO 200 1=1,IEND 1673 K=SEO(I) 1674 NB=Nfi+l 1675 B P ( N B I = B ( N B I - P E A L ( S L ( K I I 1676 I F ( T Y P E I K ) .EO. 2) GO TO 200 1677 NB = NB*1 1678 3P (Nei=B(NBI-AIMAGISL(K»| 16/9 2C0 CONTINUE 137. 1680 I F ( I T .EQ. 0 .AND. (IA+ I S I .NE. 4) GO TO 450 1681 C NOTE THAT IT WILL NOT BRANCH IF IA=IS=2. 1682 NB=0 1683 DO 400 1=1,IEND 1684 NB=NB+1 1685 K=sEcm 1686 SUM=0. 1687 FIRST=K*8-7 1688 PP=NXTfilFIRST) 1689 C NOTE THAT -EPS (ACCORDING TO THE DEFINITION) IS BEING FORMED 1690 250 I F ( P P .EQ. FIRST) GO TO 300 1691 J=CFCNT{PP) 1692 VP=(PP+7)/4 1693 DANG = ANG IK)-ANG(J) 1 694 EPS = U(K> * U ( J ) * S I M DANG)-DANG 1695 SUM=SUM + EPS*CCNJG(Y(VP) ) 1696 PP=NXTRIPP) 1697 GO TG 250 1698 300 PP=NXTC(FIRST) 1699 320 I F ( P F .EC. FIRST) GO TO 350 1700 J=RPCNT(PP) 1701 VP=(PP*7)/4 1702 CANG=ANG(K)-ANG(J) 1703 EPS = l i ( K ) * U ( J )"S IN ( DA NG I-DANG 1704 SUM=SUM+EPS*CCNJG(YIVP)) I 705 PP=NXTC(PP) 1706 GO TO 320 1707 350 BP(NB) =BP (NB ) -»A I MAG I SUM ) 1708 IF(TYPE IK) .EC. 2) GO TO 400 1709 NB=NB+l 1710 BP(NB)=BP(NE)-REAL(SUM) 1711 400 CONTINUE 1 7 i 2 45C CONTINUE 1713 RETURN 1 714 END 1715 SUBROUTINE MCCEF(WRR,WRI.AM,MA,B,SEQ,Y,CPONT,NXTR,RPONT,NXTC ,SCHED 1716 *,L,TYPE,POINTP.NUMB,*) 1717 REAL WRR(4, 1),AM(1),U( 1 ) , B ( 1 ) 1718 INTEGER*2 WR1(1),SEQ(l ),CPONT(1),RPONT( 1).NXTR11).NXTC11) 1719 INTEGER*2 TYPE( 1 ) .PCINTRIl I,NUMB(1 ) 1720 INTEGER MA(1),ROW,PP,VP,FIRST,COL 1721 COMPLEX Y U ) . S C F E C I l ),SUM,TEMP 1722 COMMCN /I N I N F / 11,12,13,ITMAX,TOLERN,ZERO,BMVA,LINE,LIST,I END 1723 EQUIVALENCE ( I l . N B U S ) 1724 COMMCN /OUT INF/ NPAGE,NLINE,HDNGS, ISTNO 1725 L0GICAL*1 HDNGS(80),PV,PQ 1726 KB = 0 1 727 DO 10 1=1,1 END 1728 KB=KB+1 172 9 K=SEC(I) 1730 B(KB)=REAL(SCHECIK 1) 1731 I F(TYP E(K) .EC. 2) GO TO 10 1732 KE=KB+1 17J3 B(K B t =A I MAG ISCHEO(K)1 1734 10 CONTINUE 1735 PCINTRIl1=1 1736 KB=0 1737 DO 1000 1 = 1 , IEND 1738 KB=KB+l 1739 R0W=SE0II) 138. 1740 NUMB(POWI=KB 1741 WRI(1»=RCW 1742 PV=TYPE(ROW) .EO. 2 1743 PC= .NCT. PV 1744 I F ( P V ( WRI(1)=-RCW 1745 K = 2 1746 FIRST=R0W*8-7 1 747 SUM=0. 1748 CALL LWRMKR(WRR,WRI,Y,CPONT,NXTR,U,FIRST,K,TYPE.KB,B,SUM I 1 749 CALL LWRMKRURR,WRI,Y,RPONT,NXTC,U,FIRST,K,TYPE,KB,B,SUM) 1750 TEMP=YtR0W*2) 1 751 SUM=SUM+TEMP 1752 GII=REAL(TEMPI 1753 BII=AIMAG(TEPP) 1 754 GI=REAL(SUM) I 755 BI=AIMAG(SUP) 1756 WRR ( 1 , 1 ) = B I I - B I 1757 I F I P V ) GC TC 20 1758 KR=KB+1 1759 WRR(2,1 )=GII-GI !7eC WRR(3.1)=GII+GI l 7 o l WPR(4,1)=-BII-BI 1 7o2 GO TO 30 1763 2C U1=U(R0W(** 2/2• !7o4 E ( K B ) = B ( K B ) - ( G l l + G I ) * U l 17o5 30 K = K-1 1766 I F I I .EO. 1IGC TC 300 1767 C TC PERFORM TRIANGULARIZATI ON PROCESS ON THE ROW BEFORE STORING IT: 1768 J = l 1 769 5C IDCNE=SEC(J) 1770 IF I T Y P E ! IDONE) .EO. 2) ID0NE=-IDONE 1771 J J = 0 17/2 ICO J J = J J * 1 17 73 IFI ICCNF .EC. WRIIJJIIGO TO 500 I 7 74 150 I F ( J J .LT.. K) GO TC 100 17/5 J=J*1 17/6 I F ( J .LT . I ) GC TO 90 1777 C RCW TRIANGULARIZEC. DIVIDE THE ROW BY ITS DIAGONAL ELEMENT 17/8 C AND STORE THE RESULTS: 1779 3C0 R A T I O = l . / W R R ( l , l ) 1760 DIAG1=RATIC 1 7 o l DO 350 J = l , K 1762 I F ( W R K J ) .EC. 0)GO TO 350 1763 WRR( I , J)=WRR ( I , J l*RATIO 17o4 I F ( W R K J ) .GT. 0)WRR(3,J) = WRR( 3, J)*RATIC 1 765 350 CONTINUE 1766 IFtPVIGO TO 4C0 I 767 RAT IO=-WRR(2,1 ) 1768 WRR (4,1)=WRR (4,1 )+WRR(3, I)*RAT 10 1769 RATI 02 = 1 ,/WRR(4,1) 17*0 DI AG2 = RATI02 1791 DC 360 J=1,K 1792 I F ( W R K J ) .EQ. 0)G0 TO 360 1 793 WRR(2,J)=(WRP(2,J)+WRR«1,J)*RATIG)*RATI02 1 794 I F ( W R K J ) .GT. 0 IWRR (4, J »= (WRR (4, J l+WRR (3 , JI*RAT IC )*RATI02 1795 36C CONTINUE 1796 r ROW IS READY TC BE STORED 1797 4 CO INDEX=POINTR(I) 1798 IF(PV)POINTR(I)=-INDEX 1799 J = 2 139. 18J0 AMIINDEX)=DIAG1 1801 INDEX=INDEX+1 1802 IFC PVIGO TO 420 1803 AMI INCEX )=DIAG2 1804 INDEX=INDEX+l 1805 AMIINDEX>=WRRI3,1) 1806 INDEX=INDEX* 1 1807 420 I F ( J .GT. K ) GO TO 460 1808 JJ=WRI(J) 1809 I F U J .EQ. OIGO TO 450 1810 MAIINDEX)=JJ 1811 INDEX=INDEX+1 1812 AMI INDEX)=WRRtl,J) 1813 INOEX=INDEX+1 1814 IFIPVJGO TO 430 1815 AMIN0EXI=WRPI2,JI 1816 INDEX=IN0EX+1 1817 430 I F U J .LT. 0)GO TO 450 1818 AMI INDEX)=WRRI3?JI 1819 IN0EX=INDEX+1 1820 IF!PV1G0 TO 450 1821 AMI INDEX i=WR R ( 4 i J I 1822 INDE X=INDEX+1 1823 450 J = J + l 1824 GO TG 420 1825 460 PCINTRII+l)=INDEX 1826 GC TC 1000 1827 C TO CCM3INE A RCW WITH A PREVIOUSLY PROCESSED RCW: 1828 500 INDEX = P0INTR.(J) 1829 I FIINCEX .LT. 0) INDEX=-INCEX 18 i C LAST = POINTRIJ + l ) 1831 I F1 LA ST .LT. 0) LA ST=-LAST 1832 RATIO=-WRR( l , J J ) 1 833 C FIRST COMBINE THE PRESENT ROW WITH ONLY THE FIRST ROW OF THE 1 834 c PREVIOUSLY PRCCESED ROW: 1835 IF(PC)RATI02=-WRR(2,JJ) 1836 520 INDEX=IN0EX+1 1837 I F I W R I I J J ) .LT. 0)G0 TO 540 1838 INDEX=IN0EX+1 1839 WRR(3,JJI=WRR(3,JJ)+AM(INDEX)*RATI0 1840 IF(PC)WRRI4,JJ»=WRR|4,JJ)+AM|INDEX)*RATI02 1841 INDEX=INOEX+1 1842 540 COL=VA( INDEX ) 18*3 INDEX=INDEX+1 18*4 C SEE IF THE CCRRSEPODING OFF DIAGONAL ELEMENT EXI STS: 1845 DO 550 NA = 1 ,K 1 846 IFICOL .EC. WRIINAIIGO TO 600 16*7 550 CONTINUE 18*8 C IF NOT, CREATE ONE WITH ZERO VALUES: 1849 K = K+l 1850 WRt(K)=COL 1851 DC 560 NB=l,4 1852 56C WRRINB,K)=0. 1853 NA = K 1854 c CHANGE THE VALUE OF THE OFF DIAGONAL ELEMENT ITHAT CERTAINLY I 855 c EXISTS NOW): 1 656 600 WRR (1 ,NA) =WRR II,NA l+AMI INDEX)+RATI0 1857 IF(PCIWRRI2,NA)=WRR(2,NA) + AM«I NO EX)*RAT102 1858 INDEX=INDEX+1 1859 I F U R K J J ) .CT. 0) INDEX=INOEX+1 140. I860 1861 1862 1863 1864 1 8o5 1866 1867 1868 1869 1870 1871 1872 1873 18/4 18 75 1876 1 £77 1878 18 79 1880 1881 1882 1863 1884 1885 18o6 1867 1868 I £89 1890 1 891 1892 1 853 1894 1855 1 856 I 897 1398 I 89 9 19u0 1901 1902 1903 1 5 04 19o5 1906 1907 1908 1909 1910 1911 1 9 i 2 1913 1914 I 515 1516 1917 1918 1919 7CC C 73 C 740 760 78C 8CC 10C0 1C IF(COL .LT. 01 GO TO 700 WPR(3,NA)=WRR(3,NA )•AM I INDEX ) *RAT10 IF( PC)WRR(4tNA)=WRR(4,NA| + AMUNDEXI*RATI02 IN0EX=INCEX*1 I F I W R I U J ) .GT. 01 INDEX=INDEX*1 IFI INDEX .LT. LAST) GO TO 540 IF THE PREV PROC. ROW IS PC. COMBINE THE SECONE ROW OF THAT: I F ( W R K J J ) . LT. 0)GG TO 800 RATIC=—WRR(3,JJ) IF(PC)RATI02=-WRR14,JJI INDEX=PCINTR(JI INDEX=IABS(INDEXI+l IN0EX=INDEX+2 COL = MA(INDEX) INDEX=INDEX+2 DO 740 NA = 1 ,K IFICOL .EO. WRl{NA))GO TO 760 CONTINUE ISTN0=740 RETURN I WRRII ,NA)=WRR ll,NA)*AM|INDEX)*RAT10 IF ( POI WRR( 2 ,NAI = WRR(2 ,NAl->-AMI I NDEX )*RAT 102 INDEX=IN0EX*-1 IF(CGL .LT. OJGO TO 780 INDEX=INDEX+1 WRR(3.NA ) = WRR (3,NA ) + AM(INDEX)*RATIO IF«TYPF(ROW( .EO. 11WRRI4,NA)=WRR(4,NAl+AM(INDEX»*RATI02 INDEX=INDEX+1 IFI INDEX .LT. LAST) GO TO 730 WRU JJ)=0 GO TO 150 CCNTINUE RETURN END SUBROUTINE *,*) EXTERNAL CRCEP,MOCEF,FORMBP,FORBKW.MODCHG,DRAW.MODER COMPLEX Y(1 I,V(1 I.SCHED(l) IN TEGER*2 CPCNT( 1),NXTR t1),RPONT(1).NXTC(I),NC<1) .TYPE(1) IfJTEGER*2 SECU),NSTEP INTEGER RES(2),ACCNN,ATEMP REAL U ( l ),ANG(1) LCGICAL*1 BATCH,ALG(8t,HDNGS(80 I.PLOT,PR I NT COMMON /IMIN F/ I 1,12,13.ITMAX,TOLERN,ZERO,BMVA,LINE,LIST,I END /ADS/ IA, IC, IS,ALG,EATCH /OUTINF/ NPAGE,NLINE.HONGS,ISTNO /TYM/ RES /LOSSES/ SL ( I I .NBUS) LSS1M(V.U.ANG.NC.SCHEC.TYPE,SEO.Y.CPONT,NXTR,RPONT.NXTC COMMCN COMMCN COMMON C C M V C N EQUIVALENCE I A=l GC TC 10 ENTRY FLSSIMI ViU ,ANG,NO,SCHEO,TYFE,SEQ,Y,CPONT,NXTR,RPCNT,NXTC .* J IA = 2 CALL TIME(O) PLOT=LIST .LT. 0 IF( P L C T ) REWIND 3 I F I F LOT I CALL E MPTYF(31 PRINT=IABS(LIST) .GT. 10 NS T E F = I A e s ( L I S T ) / l O N l = l I E N D - l ) / 3 2 + l 141. 1920 1921 1922 1923 1924 192 5 1926 1927 1928 1929 1930 1931 1932 19 J3 1934 . 1935 1 936 1937 19 J8 1939 194C 1941 1942 1943 1944 1945 1946 1947 1948 1949 1930 1951 1952 1 953 1954 1955 1936 1957 1958 1939 I960 1961 1962 1963 19o4 1905 19c6 1967 19o8 1969 197C 1971 1972 1 973 1974 1 975 1976 19 77 1978 1979 20 50 100 200 250 30C NN=N1*IEND*4 CALL GSPACE(ACCNN.NN) CALL GSPACE(ATEMP,IENO*2) CALL CALLER ICRDER.ACONN, IPTRINl),IPTRICPONT),IPTR(NXTR),IPTRIRPONT *>,1PTR(NXTCI . I P T R I S E Q I , A T E P P , I P T R ( N P C ) . I P T R I N P V ) , I P T R ( T Y P E ) ) CALL FSPACE IATEMP) CALL FSPACE(ACCNNI NKQRDS=NP0*5+NPV*3-IEND*2 CALL GSPACEtAM,NW0RCS*4l CALL GSPACE(AWR,NBUS*16) CALL GSPACE(AM,NBUS*2) CALL GSPACEIAFNTR,N3US*2) CALL GSPACE(EV,IEND*8> CALL 0SPACE(NUM8,IEND*2» CALL CALLER (MGCEF, AWR, AW I , A M.AM, P.V, I PTR IS EC) , IPTRI YI , I PTR ICPON T I , I *PTR(NXTR),IPTRIR PCNT),IPTR(NXTC),IPTR(SCHED),IPTRIU),IPTRI TYPE), *APNTP,NUMB,C400) CALL FSPACE IA l»R I CALL FSPACE(AKI) CALL GSPACEieP,IEND*8) IT=0 IF( IA .EQ. 1) GO TO 50 CALL CALLER I CODER ,3P,NUMB,IPTRISEQ) ,IPTR(TYPE ) , I P T R ( V ) , I P T R I U ) . I P *TR(ANG),IPTR(SCHED I, IPTR I IT »,SL,IPTR(Y I ,IPTRICPONT I,IPTR(NXTR I,IPT *R(RPONT),IPTRINXTC ) ,IPTRIERR11 ,1PTR I ERR2) , I P T R ( I E R R 2 ) , I P T R I E R R 3 ) ) IERR2=N0(IEPP2) I F I I E R R 2 .LT. Cl IERR2=-IERR2 IFIPLC1T) CALL PL0TRIU,ANG,ERRl,ERR2,ERR3,NC) IFI.NCT. PRINT) GO TO 20 LIMI T = NSTEP CALL PR INTRI IT,V.U.ANG,ERR l.ERR2,IERR2.ERR3.Na» IF(ERR2 .LE. TOLERNI GC TO 300 GO TC 100 LIM1T=1 CALL CALLERIFCRMBP,EV,PP,IPTR(SECI,SL, I P T R ( I T ) , I P T R ( V I , I P T R I A N G ) . *IPTR(Y),IPTRtCPONT),IPTRINXTR) .IPTR(RPCNT),IPTRINXTC),IPTR(TYPE). * IPTR(U)) CALL CALLEP(FCRBKW,AM,AM,8F.APNTP,NUMB,IPTRISEC)) CALL CALLER(MOCCHG,BP,NUMB,IPTRISEQ),IPTR(TYPE),IPTR(V>.IPTRlU).IP * T R I A N G ) , I P T R ( S C H E D ) . I P T R ( I T ) , S L , I P T R ( Y ) , IPTR(CFONT ), IPTR(NXTR),IPT "RIRPCNT) , IPTR(NXTC ),IPTR(ERR1) . I P T R I E R R 2 ) , I P T R I I E R R 2 ) , I P T R J E R R 3 ) ) IT=IT+l IERR2=N0(IERP2) IF( IERR2 .LT. 0) IERR2=-IERR2 IF(PLOT) CALL PLOTR(U,ANG,ERR 1,ERR2,ERR3,NO) IF( .NOT. PRINT .OR. IT .NE. LI M I T ) GO TO 200 L IM IT = L IMIT + NSTEP CALL FRINTPIIT.V.U.ANG.ERR 1.ERR2,IERR2,ERR3,NO) IFIERR2 .LE. TOLERN) GO TO 300 I F I I T . G E . ITMAX) GO TO 250 GC TC 100 ISTN0=250 CALL FSPACE(AM) CALL FS PAC E(A FN TRI CALL FSPACE(EV) CALL F S P A C E i e P ) CALL FSPACE < NLMBI CALL TIMEI3,C,RES) I F ! .NCT. PLOT) GO TO 350 I F I I A .EO. 21 IT=I T + l 1980 1981 1982 1983 1984 1965 1986 1S87 1588 1989 1990 1991 1592 1 9 9 3 1994 1995 1996 1997 1998 1999 2 C J O 2 0 0 1 2002 20u3 2C04 20J5 20U6 2007 2Co8 2005 2010 2011 2012 2 0 i 3 2C14 2015 2 0 i 6 2C17 2018 2019 2020 2021 2022 2023 2C24 2025 2026 2027 2C28 2029 2C30 2031 2C->2 2033 2034 2CJ5 2C36 2C37 2038 2C39 N N = ( I E N 0 * 2 » 3 ) * I T * 4 CALL GSPACE(AFRAY.NN) CALL CALLER(CRAW,IPTR( I T ) , IPTR(NC).ARRAY) CALL FSPACE I ARRAY) I F I I A .EO. 2 » IT=IT-1 350 CALL CUT1UT,ERR1,ERR2,IERR2,ERR3> IFIISTNO . N E . 01 RETURN 1 RETURN 400 RETURN 1 END SUBROUTINE fCCCHGIBP.NUMB,SEO,TYPE,V,U «ANG,SCHED,IT,SL,Y.CPONT,NXT *R,RPCNT,NXTCEPR1.ERR2, IERR2, ERR3) REAL PP( l ) , L ( l l , A N G ( l l INTEGER* 2 NUMe ( 1 ) , C P O N T ! 1 ) , N X T R ( 1) ,RPONT{I),NXTC<1),SEC(1J .TYPEU) C CM PL E X Y ( 1 ) , V ( 1 ) , S L t 1 > , SC HEO ( 1 ) , I K, DS INTEGER F I R S T , P P , V P COMMCN /ININ F / I I , 12,13,ITMAX,TOLERN,ZERO.BMVA,LINE,LIST.IEND COMMON /ADS/ IA,1 0 , 1 S , A L G , B A T C H LOGICAL*! ALG(8 I,BATCH EQUIVALENCE ( I l . N E U S ) DV1=0. D V 2 = 0 . ERR2-0. ERR3=0. IFI IA .EO. 2) GO TO 150 I F ( I T . N E . 0 ) GO TO 150 DO I C C 1 = 1 , I E N D K=SECU> KB=NUMB(K) ANG(K»=-8P(KBI I F I T Y P E ( K ) .EO. l ) U ( K ) = S 0 R T ( B P ( K B * l ) * 2 . » A 1 = U ( K I * C O S ( A N G ( K ) ) A 2 = U l K ) * S I N ( A N G ( K I ) V ( K ) = C V P L X ( A l , A 2 ) 1 0 0 CONTINUE GO TO 200 150 DC 170 1 = 1, IEND K=SEC(I) KB=NUMBIK) ANG(K)=ANG(K)-EPIKB) I F t T Y P F ( K ) . EQ. 1 ) U ( K ) = S Q R T ( U ( K ) * * 2 + B P < K B * 1 ) * 2 . I A 1 =U(K ) * C 0 S ( A N G ( K ) ) A2 = U ( K ) * S I N ( A N G ( K M V(K )=CMPLX(A1.A2) 1 7 0 CONTINUE ENTRY MODER(BP,NUMB,SEC,TYPE,V,U,ANG,SCHED,IT.SL.Y.CPONT,NXTR, *RPONT,NXTC,ERR1,ERR2,IERR2.ERR3) 200 DC 4 0 0 1=1,IEND IK = C. K=SEO(I) KB=NLMBIK) F I R S T = K * 8 - 7 PP=NXTR(FIRST) 3 1 C I F ( P P . EQ. FIRST) GO TC 320 V P = ( P P + 7 ) / 4 J = C P C N T ( P P ) I K = I K * Y ( V P » * V ( J I P P = N X T R ( P P ) GC TG 310 32C P P = NXTC(FIRST I 143. 20*0 330 IF'PP .EQ. FIRST) GO TO 350 20*1 VP=(PP~7>/4 20*2 J=RPCNT(PP> 20*3 I K = I K + Y ( V P ) * V I J ) 2 0** PP=NXTC(PP) 20*5 GO TO 330 20*6 350 CONTINUE 2C*7 IK=IK+YIK*2)*V(KI 20*8 IK=V(K)*CCNJG(IK) 2C49 OS=SCHED<K)-IK 2050 DP=REAL(DS> 2C51 BP(KE)=DP 2052 DV1=CV1+DP 2C53 ACO=ABS(DP 1 2054 IF(ERR2 .GE. ADO 1 GO TO 360 2C55 ERR2=ADD 2056 IERR2=K 2C57 36C ERR 3 = ERR 3+ADD 2058 IF(TYPE!K ) .EQ. 2) GO TO 400 2059 DC=AIMAG(OS) 20o0 BP{KB*1> =0Q 20t.l DV2=CV2+D0 2C62 ACO=ABS(OQ) 2063 IF{ERR2 .GE. ADD) GO TO 370 20o4 ERR2 =ADD 2065 IERR2 =K 2066 37C ERR3=ERR3+ACD 2C67 400 CONTINUE 2Co8 ERR1=SQRT(0V1**2*0V2**2> 2 0o9 RETURN 2070 END 2071 SUBROIJTINE STCTT(V,U,ANG,NO,SCHED.TYPE.SEQ.Y.CPONT,NXTR.RPONT,NXTC 20/2 *,*) 2C73 EXTERNAL ORCER .EPBPP.DPDC, CVDD ,CRAVi 2074 COMPLEX Y(11 ,VI1) .SCHED(l) 2075 INTEGER*2 CPONT( 1 ),NXTR(1),RPONT(1),NXTC(1),NC(1),TYPE 11 ) 2076 INTEGERS S E C ( l ) , N S T E P 2077 INTEGER AW I,RE S(2) 2078 REAL U ( l ),ANG(1) 2C79 LCG I C AL*1 BATCH,ALG(8),HDNGS(80),PLOT, PRINT 2080 COMMCN /ININF/ I 1,12,1 3,UMAX,TOLERN,ZERO,BMVA,LINE,LIST,IEND 2C61 COMMCN /ADS/ IA,ID,IS,ALG,BATCH 20d2 COMMCN /OUTINF/ NPAGE,NLINE,HDNGS,ISTNO 2063 COMMCN /TYM/ RES 2C84 EQUIVALENCE (I1,NBUS) 2085 CALL TIME(O) 2C86 PLOT=LIST .LT. C 2067 IF(PL C T ) REWIND 3 2068 I F t P L C T I CALL EMPTYFI3) 20d9 PRINT=IABSIL 1ST ) .GT. 10 2090 NSTEP=IABS(LIST)/10 2C91 Nl=(IEND-1J/32+1 2092 NN = M*IEN0*4 2C93 CALL GSPACE(ACCNN.NN) 2094 CALL GSPACE(ATEMP,IEND*2) 20*5 CALL CALLER(ORDER,AC CNN, IPTR(N 1) ,IPTR(CPONT),IPTR(NXTR),IPTR (RPONT 2096 *» ,1 PTR (NXTC) .IPTR(SEO) ,ATEI»P, IFTR( NFC) .IPTR(NPV) ,IPTR( TYPE)) 2097 CALL FSPACE(ATEMP) 2058 CALL FSPACE(ACCNN) 2099 C 144. 2100 2101 2102 2103 2104 2105 2106 2107 2108 2109 2110 2 111 2112 2113 2114 2115 2116 2117 2118 2 U 9 2120 2121 2122 2123 2124 2125 2126 2127 2128 2129 2130 21^1 2132 21J3 2134 2135 2136 2137 2138 2 139 2 140 2 U l 2142 2143 2 144 2 1*5 2 1*6 2147 2 148 2149 2 1 50 2151 2152 2 153 2 154 2 155 21 56 2137 21 58 2 159 C C THE STORAGE IS SLIGHTLY OVER - ALLOCATED. ICC 11C 12C 13C 140 NW1=INPV+NPC)*2 NW2 = NPC*2 CALL GSPACE(BI,NW1*4» GSPACE(e2,NW2*4» GSPACE I AV>R »NBUS*4) GSPACE (AWI ,NBUS*2) GSPACE (MJMB.NBUS + 21 GSPACE ( PIST,NBIIS*2» GSPACE(B2ST,NBUS*2) CALL CALL CALL CALL CALL CALL IND = 1 150 CALL CALLER!BPBPP,B1,B1,AWR,AW I,BI3T,IPTRIY),IPTRICPONT),IPTRINXTR *) , IPTRIRPONT),IPTR! NXTC),IPTRISEO) , IPTR(TYPE),NUMB,IPTRIIND)I IND = 2 CALL CALLER IBPPPP,B2 ,B2,AWR,AW I ,B2ST,IPTR(Y) ,1PTR I CPONT),IPTRINXTR *>,IPTRlRPONT),IPTR(NXTC ),IPTR I SEO),IPTRI TYPE I.NUMB,IPTR< INDI I CALL FSPACEIAWR) CALL FSPACE(AWI) CALL GSPACE(CEL1,IENC*4) CALL GSPACE(CEL2,IEND*4) IT=0 LIMIT=0 ITL AS T=ITMAX*2 KP=1 K0=1 IND = 1 00 110 I=1,1 END A 1=U(I I*COSIANG(I ) I A 2 = U ( I ) * S I N ( A N G ( l ) l V ( I )=CMPLXI A 1,A2) CALL CALLER(DPOC,DELl.IPTR(YI,IPTR(CPONT), IPTR(NXTR),IPT R(RPONT), *IPTR I NXTC), IPTR(SEO) , IPTR(TYPE ),IPTRIV),IPTR(SCHED) ,I P T R ( U ) . I P T R ( * E R R l ) , I P T R ( E R R 2 ) , I P T R ( I ERR 2),IPTR(ERR 3 ) , I P T R ( K P ) , I P T R I I N D ) ) 1 ERR2=NO( IERR2) IFIIE R R 2 .LT. 0) IERR2=-IERR2 I F I PLOT) CALL PLOTR Ul,ANG,ERRl,EPR2,ERR3,NO) IFI .NOT• PRINT .OR. IT .NE. LIMIT) GO TO 120 CALL PR INTR( IT,V,U,ANG,ERR1,ERP2,IERR2,ERR3,N0) LIMIT=LIMIT+NSTEP I F ( K P .EO. C) GO TO 200 I F ( I T .GE. ITLAST) GO TO 350 CALL CALLER(CVCC,81,B1,BIST,DELI,IPT R(ANG),IPTR(TYPE), I PTR ISEO), *NUM8,IPTR(INO) IT=IT+1 IND=2 DO 140 1=1,IEND Al=um*COSlANG(I II A2=U( I)*SIN(ANG(I)» VII)=CMPLX(A1,A2) CALL CALLER (DFDCDEL2, IPTRI Y ) , IPTR (CPONT I , IPTR (NXTR I, I PTR ( RPONT) , * IPTR(NXTC), IPTR(SEO ) ,1 PTR(TYPE ) , I P T R I V ) , I P T R ( S C H E D I , I P T R ( U ) , IPTRI *ERR1),IPT»(ERR2),IPTR(IERR2I,IPTR(ERR3),IPTR(KQ),IPTR(IND)) IERR2=N0(1EPR2) 1FIIERR2 .LT. 0) IERR2=-IERR2 IF(PLOT) CALL PL0TR(U,ANG,ERR1,ERR2,ERR3.N0) IFI.NOT. PRINT .OR. IT .NE. LIMIT) GO TO 150 CALL PRINTR(IT,V,U,ANG,ERR1.ERR2,IERR2.ERR3,N0) LIMIT=LIMIT*N STEP IF(KO .EQ. 0) GO TO 300 145. 2160 I F ( I T .GE. ITLASTI GO TO 350 2161 CALL CALLER(CVDD,B2.B2,B2ST,DEL2,IPTR(U) , I P T R ( T Y P E ) , IPTR(SEQ). 2162 • NUMB » IPT R ( I N D ) ) 2163 IT=IT*1 21t>4 GO TC 100 2165 200 IF(KQ .EQ. 0» GO TC 400 2166 GO TO 130 2167 3CC I F ( K P .EO. CJ GO TO 400 2 168 GC TO 100 21o5 35C IST=350 2170 400 CALL F S P A C E I B l l 2 171 CALL FSPACE(e2) 2172 CALL FSPACEIB1ST) 2173 CALL FSPACE I E2ST) 2174 CALL FSPACE(NUMB) 2175 CALL TIME!3,C,RES) 2176 IFI .NOT. PLOT) GC TO 450 2 177 I T = IT*1 2178 ITMAX=-ITMAX 2179 NN=(IEND*2*3 )*IT*4 2180 CALL GSPACE!ARRAY,NN) 2161 CALL CALLER!CRAW,IPTRI I T ) , IPTR(NC) ,ARRAY) 2 l d 2 ITMAX=-ITMAX 2183 CALL FSPACE!ARRAY) 2164 IT=IT-1 2185 45 C CALL OUTK IT ,ERR 1,ERR2,1 ERP2,E PR3 ) 2186 IF! ISTNO -NE. 0) RETURN I 2167 RETURN 2168 END 2 189 SUBROUTINE BPBPP(BR,BI,WRR,WRI,BST,Y,CPONT ,NXTR,RPCNT,NXTC,SEQ,TYP 2190 *E,NUr*3,TND) 2 191 REAL R R d l . W R R d l 2192 INTEGER BI!1).FIRST,VP,PP 2193 COM F L EX Y d ) 2194 INTEGER*2 CPCNT!1),NXTR(I),RPONT!1),NXTC!1),SEC(1).TYPE(I) 2195 INTEGER* 2 W R K D . B S T d ) , NUMB ( 1) 2196 COMMCN /ININF/ I 1,12,13,ITNAX,TOLERN,ZERO,BMVA ,L INE,L I ST,I END 2157 EQUIVALENCE!Il.NBUS) 2158 LCGICAL*1 DPPIME 2159 DPR IME = IND .NE. 1 220C IF!CPRIME) GC TO 15 2201 DC 10 1=1.1ENC 2202 K=SEC(II 2203 NUMB !K) = I 2204 10 CONTINUE 2205 15 B S T ( l ) = l 2206 DC 1000 1 1 = 1,IENC 2207 I =SEC( 11 1 2208 IF(DPR IME .AND. T Y P E I I ) .NE. 1) GO TO 700 22J9 K=2 2210 FIRST=I*8-7 2211 SUM=C. 2 2 i 2 PP=MXTR{FIRSTI 2213 20 I F ( P P . EQ. FIRST) GO TC 50 2214 VP= (PP+71/4 2215 J = CPCNT JPP) 2216 IFIDPRIME .AND. TYPE(J ) .NE. 11 GO TC 30 2217 8IJ=AIMAG(Y(VP)) 2218 IF(CFRIME) GO TO 25 2219 GIJ=REAL!Y!VP)» 146. 2220 R A T I C = G I J / B I J 2221 BIJ=BIJ*{1.*RAT10**21 2222 SUM=SUM*8IJ 2223 I F I J .GT. IENCI GO TO 30 2224 25 WRR(K)=-BIJ 2225 WRI(K)=J 2226 K = K * l 2227 30 PP=NXTR(PPI 2228 GO TO 20 2229 5C PP=NXTC(FIRST 1 2230 70 IF{PP .EO. FIRST) GO TO 100 2231 VP=(PP+71/4 2232 J=RPCNT(PP) 2233 IF(DFRIME .AND. T Y P E ( J ) .NE. 1) GO 10 2234 BIJ=AIMAGtY(VP)) 2235 IFIOPRIMEI GC TO 75 2236 GI J = REAL ( Y ( V P ) l 2237 RAT I C = G I J / B I J 2238 B I J = B I J * ( 1 . + RAT 10**2 ) 2239 SUM = SUM+BIJ 224C I F ( J .GT . IEND) GO TO 80 2241 75 WRR(K )=-BIJ 22*2 WRI(K)=J 2 24 3 K = K~1 2244 80 PP=NXTC(PP) 2245 GO TO 70 2246 100 WRU i » = i 2247 IF(.NOT. OPRIME) WRR(1)=SUM 2248 IF(OPRIME) WRRIl ) =-A IMAGIY(1*2 ) 1 2245 K=K- 1 2230 C 2251 c WORKING ROW FORMATION IS COMPLETED 2252 c 2253 I F ( I I .EO. 1) GO TO 500 2254 IM1=II-1 2255 DO 2CC J J = l , I M l 2256 J = S E Q ( J J ) 2 2 57 IFIDFRIME .ANC. T Y P E I J ) .NE. 1) GO TO 2258 INDEX=BST(JJ)+1 2259 J J l = J J 22o0 105 J J 1 = J J l + 1 2261 L A S T= B S T ( J J 1 ) 2262 IFt LAST .EO. 0) GO TO 105 22fc3 IF(INDEX .GE. LA ST 1 GO TC 200 2264 DO 110 KK=1,K 2265 IF(WR IIKK) .EC. J ) GO TO 115 22o6 11C CONTINUE 2267 GO TO 200 22o8 115 RATIC = -WRR (KK) 2269 WRI(KK»=0 22/0 120 JK=3I(INDEX) 22/1 00 130 JKK=1,K 2 2/2 I F ( W R K J K K ) .EC. JK) GO TO 140 2273 130 CONT INUE 2 2/4 K = K + 1 2275 WRR(K)=0. 2276 WRI {K) = JK 2277 JKK = K 22/8 140 WRR (JKK) =WRR{JKK) + BR(IN'DEX + 1 ) * RATIO 2 2/9 IN0EX=INDEX*2 147. 2280 2281 2282 2283 2284 2285 2286 2287 2268 2269 2290 2291 2292 2293 2294 2295 2296 2297 2298 2299 2300 2301 2302 2303 2304 2305 2306 23u7 2308 2309 2310 2311 2312 2313 2314 2315 2316 2317 2318 2319 2320 23<il 2322 2323 2324 2325 2326 2327 2328 2329 2330 2331 2332 2333 2334 2335 2336 2337 2338 2 339 200 C C C C 5CC IF(INDEX .LT. CONTINUE LAST) GO TO 120 600 65C 70C 1G00 30 5C 80 ICO WORKING ROW COMB INATICN PROCESS COMPLETED NOW DIVIOE ThE ROW BY ITS DIAGONAL ANO STORE THE RESULTS RATI0=1./WRRI1) INOEX = BST( I I I BR I INDEX)=RAT 10 INDEX=INDEX+1 IFIK .EO. 11 GC TO 650 DO 600 KK=2,K IF(WRIIKK> .EC. 0) GO TO 600 B K INDEX)=WRKKK) SR(IN9EX + l l = l«RRlKKI*RATIC INDEX= INDEX + 2 CONTINUE BST( I I + l )=INDEX GO TO 1000 BSTI I I - l M B S T I I I I B S T ( I I ) = 0 CONTINUE RETURN END SUBROUTINE CP CO(CEL.Y,CPONT,NXTR,RPONT,NXTC,SE0,TYPE,V,SCHED.U.ERR *1,EKR2, IERR2.ERR3,KP0,IND) REAL 0EL(1),U<1) COMPLEX Y ( l ) ,V( 1 I ,SCHED{1 I , IK, SK.DS INTEGER*2 CPCNTI 1),NXTR(1),RPONT(1J,NXTCI 1),SEC(1).TYPE I 1) COMMON /ININF/ I I , 12 . 13, ITMAX,TOLERN,ZERO.BMVA ,LINE.LIST,IEND EQUIVALENCE (I1.N8US) LCGICAL*1 DPRIME INTEGER FIRST,VP.PP KPQ=C ERR2=0. ERR3=0. DV1=0. DV2 = 0. DPRIME=IND .EC. 2 00 200 11=1,IEND I=SEQ(11) FIRST=I*8-7 IK = Y( I * 2 ) * V ( I I FF=NXTR t FIRST) I F l P P .EO. FIRST) GO TO 50 VP=(PP+7)/4 J=CPCNT(PP) I K = I K + Y ( V P ) * V ( J ) PF=NXTRIPP) GO TO 30 PP=NXTCIFIRST) I F I P P .EO. FIRST) GO TC 100 V P = ( P P + 7 I / 4 J=RPCNT(PP) IK = I K + Y ( V P ) * V ( J ) PP=NXTC(PP) GO TO 80 SK=V(I)*CONJG(IK) DS=SCFED( I )-SK DP= REAL(OS) 148. 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 2350 2351 2352 2353 . 2354 2355 2356 2357 2358 2359 2360 2361 23o2 2363 2364 2365 2366 2367 2368 2365 2370 2371 2372 2373 2374 2 3 75 2376 2377 2378 23 79 2360 2361 2362 2383 2384 2365 2366 23d7 2368 2369 2390 2391 2392 2393 2354 2395 2356 2397 2358 2399 120 130 140 200 40 50 ICO 200 C C C C C AC0=ABS(OP> IF(DPRIME) GO TO 120 DEL 1 II>=DP/UfI» IFIACD .GT. TCLERN) KP0=1 DVl=CVl+DP ERR3=ERR3+A0D IF(ERR2 .GE. ADD) GO TO 130 ERR2=ADD IERR2=I I F ( T Y P E ( I ) . E O . 21 GO T O .200 D0 = A I MAG(OS) ACD=ABS(DQ> IF I .NOT. CPRIME) GO TC 140 DELI I I »=D0/UIII IFIACD .GT. TCLERN) KP0=1 DV2=CV2+DQ £RR3=ERR3*ADD IFIERR2 .GE. ADD) GO TO 200 ERR 2 =ADD IERR2=I CCNTINUE ERR 1 = SORT IDVl«*2*DV2**2) RETURN END SUBROUTINE DVCDI BR,BI,BST,CEL.UANG.TYPE,SE0,NUMB,IND» REAL BR I 1).C EL I 1 ).UA NG I 1) INTEGER e i ( l ) INTEGER*2 8ST I 1).TYPEI 1).SEO11 I.NUMB 11 I I M F / t l . n . n , - r . -COMMCN /ININ  I 1, 12 13 EQUIVALENCE ( I l . N B U S l L OGICALM OPRIME DPR I^E= IND .EC. 2 DO 2C0 I 1 = 1,I END I = SEOI11) IFIOPRIME .ANC. T Y P E I I ) INDEX = BSTI I I ) + l 111 = 11 111=111+1 L AS T = BSTI I I I ) IF(LAST .EO. 0) GO TO 40 IFI INDEX .GE. LAST) GO TO JJ=B1(INDEX) J=NUMBIJ J ) D E L ( J ) = D E L I J ) - D E L ( I I I * B R IINDEX + l I INDEX=INDEX+2 GO TC 50 INDEX = BSTII I » DEL I m=OEL< I I ) * B R ( I N D E X I CONTINUE FORWARD PROCESS COMPLETED START BACK SUBSTITUTION. ITMAX.TOLERN,ZERO,BMVA.LINE.LIST.IEND •EO. 2) GO TO 100 200 I.IEND I I DO 400 I I JJ=IEND+1 I=SEO|JJ) IFIDPRIME SUM=0. INDEX=BSTIJJ) + ). AND. T Y P E I I , .EC. 2) GO TO 400 149. 2400 J J l = J J 2401 240 J J 1 = J J 1 * 1 2402 LAST = B S T ( J J 1 | 2403 I F ( I A ST .EO. 0) GO TO 240 2404 250 IF( INDEX .GE. LAST) GO TO 300 2405 J=BIIINDEX) 2406 J=NUMB(J) 2407 SUM=SUM+BR(INCEX*1 J+DELIJ) 2408 INDEX=INDEX+2 2409 GO TO 250 2 4 i 0 300 DEL! J J ) = D E L ( J J ) - S U M 2411 400 CONTINUE 2412 C 2413 C BACK SUBSTITUTION ENDED. 2414 c 2415 DO 500 1 = 1,IEND 2416 J = S E C ( I ) 2417 IF!OPRIME) GC TO 450 2418 UANG!J)=UANG!J)+DEL<II 2419 GO TO 500 2420 45C I F I T Y P E I J ) .EQ. 2) GO TO 5C0 2 4 . i l UANG!J) = UANG!J)+OEL( I)*UANG!J) 24<±2 5 CC CONTINUE 2423 RETURN 24^4 END 2425 SUBROUTINE CRAW<IT ,NC,ARRAY» 2426 REAL ARRAY! I T , I ) 2427 I NTEGER*2 NC(1) 2428 COMMON / I N I N F / I 1, 12 , 13 , IT M A X , TO L E RN , Z ERO , BMV A , L I NE, L I ST , 2429 COMMCN /OUTINF/ NPAGE,NLINE,HDNGS,ISTNO 243C LCGICAL*1 HDNGS (80) 2431 EQUIVALENCE ( I l . N B U S ) 2432 IF! IT .LE. 1) RETURN 2433 CALL FTNCMDI'ASS IGN 9=PLCTFILE•,17 I 2434 CALL EMPTYFI9) 2435 REWIND 3 2436 J = l 2437 50 K=l 2438 CO 100 1 = 1,I END 2439 I F ( N C ( I ) .GT. 0) GO TO 100 2440 REA0!3)ARRAY(J,K),ARRAY!J,K+1) 24*1 K = K + 2 2442 ICC CONTINUE 2443 READ!3)ARRAY (J,K ),ARRAY(J.K+l),ARRAY(J,K+2) 2444 J=J + 1 2445 I F ( J .LE. IT) GO TO 50 24*6 CALL PLCTRL(•METR•,1 ) 2447 K = l 2448 DO 20C 1 = 1 , IEND 2449 I F ( N C ( I ) .GT. 0) GO TO 200 2430 ANO=-N0( I 1 2451 CALL DRAW2I IT,ITNAX,ARRAY,K) 2432 CALL SYMBOL! 10.5,2., .35, 'BUS #',90. ,5) 2453 CALL NUMBER(1C.5,4.,.35,AN0,9C.,-1) 2434 CALL SYMBCL(1C.5,5.2,.35,'(U)',90.,3) 2435 CALL SYMBOLl10.5,14.5,.35,'BUS #',90.,5) 2456 CALL NUMBER(1C.5,16.5,.35,ANO ,90.,-1) 2457 CALL SYMPOL(10.5,17.7, .35, • (ANG) ',90.,5) 2458 CALL P L 0 T ( 1 5 . ,C. ,-3) 2459 K = K + 2 IEND 150. 2460 2461 2462 2463 2464 2465 2466 2467 2468 2469 24 70 2471 24 72 2473 24 74 2475 24 76 2477 2478 2479 24fi0 2481 2482 2483 2464 2485 2486 24d7 24d8 2489 249C 2491 2492 2493 2494 2495 2496 2497 2498 2499 25u0 2501 2502 2503 2504 2505 2506 25*7 2508 2509 2510 2 5 i l 2 5 i 2 2513 2514 2515 2516 2517 2518 2519 100 20 50 60 65 67 7C .90.,5) 2',90.,5) 200 CONTINUE CALL 0RAW2I IT,ITMAX,ARRAY,K) CALL SYMBOL!10.5,2.,.35,'ERR I CALL SYMBCL(1C.5,14.5,.35,"ERR CALL PLOT(l£.,0.,-3) K = K+2 K=-K DRAW2IIT.ITMAX.ARRAY.K) AN INVISIBLE BOUNDARY: PLOTUC.5,24.5,3) SYMBOL(10.5,2.,.35,'ERR 3',90.,51 SYMBOL(0.,18., .25,HONGS,0.,48) SYMBOL(3.,16.,.25,HONGS I 4 9),0.,32) CALL PLOT CALL CALL CALL CALL RETURN END SUBROUTINE PLOTRIU,ANG,ERR 1,ERR2,ERR3,NO) REAL U ( l ) , ANC- 111 INTEGER*2 N0I1) COMMCN /ININ F / II,12,13,ITMAX,TOLERN,ZERO,BMVA,LINE,LIST,IEND EQUIVALENCE ( I l . N B U S ) 00 ICC 1=1,IEND IFIMOI I ) .GT. 0) GO TO 100 ANG 1 = ANGI I ) * 180./3.14159 WRITE13 )U(I I.ANGI CONTINUE WRITEI3IERR I ,ERR2,ERR3 RETURN END SUBROUTINE CRAW2 ( I T , ITMAX,ARRAY » KK) REAL ARR AY(IT , 1) COMMON /ACS/ IA,IC,IS,ALG,BATCH LOGICAL*! ALG(8),BATCH LOGICAL EQUC INDEX=0 IFIKK .GT KK=-KK INDEX=1 Y = l . K = KK FACT0R = l . IF( ITMAX .LT CX=I ABS( ITMAX 1/10. XINC=FACTOR/DX CALL AXC TR L( ' YORIG *,Y) CALL A X C T R L C C I G I T S ' . - l ) CALL AXPLOTC ITERATION;" ,0.,10 PIFF=ARR AY( 1,K)-ARRAY( IT.K ) TO 70 0) GC TO 20 0) FACT0R=.5 ,0. ,DX) • GT. .EQ. .0000011 GO 0) GO TO 65 I F ( A f i S I D I F F ) IF(M0C(K,2) • Y M N = .8 DY=.05 DC 6C 1=1.IT APR A Y ( I , K ) = (ARRAY!I,K >- .8)*20 . GO TC 80 YMIN=-4. DY=l. DO 67 1 = 1, IT ARRAY(I»K)=ARRAYI!,K)+4. GO TO 80 CALL SCALE! ARRAY! l , K ) , IT, l C . Y M I N . D Y , 1» 151. 2520 2521 2522 2 523 2 524 2525 2526 2527 2 52 8 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 2539 2540 2541 25*2 2543 25*4 2545 25*6 2547 2 54 8 2549 2 550 2551 2552 2553 2 554 2555 2556 2557 2558 2539 25o0 2 5 o l 2562 25o3 2564 2565 25c6 25o7 25o8 2569 25/C 2571 2572 2573 2574 25 75 2576 25/7 2 5 78 2579 80 AXCTRH'CIGITS',-21 AXPLOTI•.9C..10.,YMIN.DY) X = X I N C 100 1C c c c CALL CALL X=0. I F l E C U C I A L G t n . ' L ' )) YSCLC=APRAY(1,K)+Y CALL PL0TIX,YSCLD,3) CALL PLOTJX ,YSCLD,2> DO ICO 1=2,IT X=X+XINC YSCLO=ARRAY<I,Kt+Y CALL PLOTIX.YSCLO.l) CONTINUE IF(INDEX .NE. 01 RETURN K = K + 1 INDEX=INOEX+l Y=13.5 GO TO 50 END SUBROUTINE CECPL1(V,U,ANG,NO,SCHED,TYPE,SEO,Y.CPCNT,NXTR,RPONT, *NXTC,*I EXTERNAL CRDEF,fC1MC2,CECS,CU2CD,ORAW COMPLEX Y(1 I,V( I I ,SCHEDI1) INTEGER*2 CFCNT I 1 1 ,NXTRI 1 ) ,RPONT11),NXTCI 1),NO 11).TYPE(1) INTEGER* 2 S E C I l l ,NSTEP INTEGER AWI,RES(2> REAL U l l KANC - U > LOG ICAL*1 BATCH,ALGI81.HDNGS(8 0),PLCT,PRINT COMMON / I N I N F / I 1,I 2,1 3,ITMA X,TOLERN,ZER0,BMVA,LINE,LI ST,I END COMMON /ADS/ I A , ID, IS,ALG,BATCH COMMCN /OUTINF/ NPAGE,NLINE,HDNGS,ISTNO COMMCN /TYM/ RES EQUIVALENCE (U.NBUS) IA=1 GC TC 10 ENTRY DECPL2(V,U,ANG,NO,SCHED,TYPE .SEO.Y,CPONT,NXTR,RPCNT.NXTC,*) IA=2 CONTINUE CALL TIMEIOI PLOT=LIST .LT. 0 IF ( P L C T ) REWIND 3 IF( P L C T ) CALL EMPTYF(3) PRINT=IABS(LIST) .GT. 10 NSTEF=IABS(LISTI/10 Nl=(IEND-11/32+1 NN=N1*IEND*4 CALL GSPACEIACCNN.NNI CALL GSPACE(ATEMP,IEND*2) CALL CALLERICRDERjACCNN, I P T R ( N l ) , IPTRICPONT),IPTR(NXTR),IPTR(RPONT *),IPTRINXTC ).IPTRISEO).ATE MP,IPTRINPC).IPTR(NPV),IPTRITYPED CALL FSPACE(ATEMP) CALL FSPACE(ACCNN) THE STORAGE IS SLIGHTLY OVER - ALLOCATED. NWl=(NPV+NPQ)+2 NW2=NPC*2 CALL GSPACE(ei,NWl*4) CALL GSPACE(B2,NW2*4) CALL GSPACE(AWR,NBUS*4) CALL GSPACEJAWI,NBUS*2J 152. 2580 CALL GSPACE(NUME»N8US*2I 2581 CALL GSPACE(EIST,NBUS*2I 2582 CALL GSPACE(e2ST,NBUS*2) 2583 IND = 1 2584 CALL CALLER(MClMC2,Bl,Bi,AWR,AWI,BlST,IPTR(Y),IPTR(CPCNT),IPTRlNXT 2 585 *R ) . I P T R ( R P C N T ) , I P T R ( N X T C ) , IPTR (SEO ) ,IPTR(TYPE).NUMB,IPTR(IND)) 2586 IND=2 2587 CALL CALLER (MC 1MC2,B2,B2,AWR,AWI,B2ST,IPTR(Y),IPTR(CPCNT),IPTR(NXT 2 5o8 * R ) , I P T R ( R P C N T ) , IPTR(NXTC ». IPTR (SEO ),IPTRITYPEl,NUMB.IPTR(INDII 2585 CALL FSPACE(AWR) 2590 CALL FSPACE(AWI) 2591 CALL GSPACE (CEL1,IENC*4) 2592 CALL GSPACE(CEL2 ,1END*4) 2593 IT=0 2594 LIMIT=0 2595 ITL A S T=ITMAX* 2 2556 KP=l 2557 KC=1 2598 100 IND=1 2559 DO 110 1=1,1 END 26uC A1=U(Il*CCS(ANG(I I I 2601 A 2 = U ( I ) * S I N ( A N G ( I ) ) 26u2 11C V(I)=CMPLX(A1,A2) 2 6 03 CALL CALLER(DECS.DEL I.IPTR(YI,IPTR(CPONT),IPTR(NXTR).IPTR(RPONTI, 2604 * I P T R ( N X T C ) , IPTR(SEO) , IPTRITYPE ),IPTR(V),IPTR(SCHED),1PTR1U).IPTR( 2605 * E R R 1 ) , I P T R ( E R R 2 ) , I P T R ( I ERR 2 ) , I P T R ( E R R 3 ) , I P T R ( K P , , I P T R ( INDI I 2606 IERR2 = N0(I ERR2 I 2607 IFI IERR2 .LT. 01 IERR2 = -IERR2 26^8 IF(PLOT) CALL PLOTR(U,ANG,ERR1,ERR2,ERR3,NO I 2609 IF(.NOT. PRINT .CR. IT .NE. LIMIT) GO TO 120 2610 CALL PRINTR (IT,V,U,ANG,ERR 1,ERR2,IERR2,ERR 3,NO) 2611 LIMIT=LIMIT-NSTEP 2612 12C I F I K P .EO. C) GO TO 200 2613 I F I I T .GE. I TLAST) GO TO 350 2 614 CALL CALLER(DU2DD.B1 , B l , B l S T , D E L 1, I PTR(ANG).IPTR(TYPE),IPTR(SEO). 2615 *NUMB,IPTR I INC)) 2616 I T = I T U 2617 13C IND=2 2618 DO 140 1=1,IEND 2619 A1 = U ( I ) * C O S I A N G I I I I 2620 A2 = UI 1 )*SINIANG(I) ) 2621 140 V(I )=CMPLX(A I ,A2 ) 2 622 CALL CALLER(DECS,DEL2,IPTR(Y»,IPTR(CP0NT|,IPTR(NXTRI,IPTR(RPONTI, 26^3 *IPTR(NXTC) , IPTR(SEQ) ,1PTR(TYPE I,IPTRI V ) , I P T R I S C H E D ) . I P T R ( U ) , IPTR( 26<J4 * E R R 1 ) , I P T R ( E R R 2 ) , I P T R ( I E R R 2 ) , I P T R ( E R R 3 ) . I P T R ( K Q ) , I P T R ( I N D ) ) 2625 IERR2=N0(IERR2I 2626 I F U E R R 2 .LT. 0) IERR2=-IERR2 Zbtl IFIPLOT) CALL PLOTR(U.ANG,ERR1,ERR 2,ERR3, NO) 2628 IF( .NOT. PRINT .OR. IT .NE. LIMIT) GO TC 150 2629 CALL PR INTR( I T,V,U , ANG,ERR 1,ERR2,1ERR2.ERR3.NO) 2630 LIMIT=LIMIT-NSTEP 2631 15C IF(KC .EQ. 0) GO TO 300 2632 I F ( I T .GE. ITLAST) GC TO 350 2633 CALL CALLER(DU2DD.e2.B2,B2ST,DEL2,IPTR(U) , IPTR1TYPE) , IPTR(SEO), 2634 *NUMB , IPTR( INC ) ) 2635 I T = I T * l 2636 GO TC 100 2637 20C IF(KQ .EQ. C) GO TO 400 2638 GC TC 130 2635 3CC I F I K P .EQ. C) GO TO 40C 153. 2640 GC TC 100 2641 350 IST=350 2642 40C CALL F S P A C E ( B l ) 2643 CALL FSPACE(B2) 2644 CALL FSPACEieiSTI 2645 CALL FSPACE(B2ST) 2646 CALL FSPACE (NUMd 2647 CALL TIME(3,C.RE SI 2648 IFJ.NCT. PLOT) GO TO 450 2649 I T = I T * l 2650 ITMAX=-ITMAX 2651 NN=(IEND*2«-3 )*IT*4 2652 CALL GSPACE(APR AY,NN I 2633 CALL CALLER(DRAV«, I PTR ( I T ) , IPTRCNC),ARRAY) 2654 ITMAX=-ITMAX 2655 CALL FSPACE(ARRAY I 2656 IT=IT-1 2657 450 CALL OUT I ( I T , ERR 1,ERR2,1ERP2,ERR3 I 2658 IF( ISTNO -NE. 0) RETURN 1 2659 RETURN 2660 END 2 661 SUBROUTINE MC1MC2IBR,Bl,WRR,WRI,BST,Y,CPONT.NXTR,RPONT,NXTC,SEO, 2662 +TYPE,NUMB,INC) 2663 REAL BP ( I I , WP.RI1 I 2664 INTEGER B l ( I ) , F I R S T , V P , P P 2665 COMPLEX Y (1 ) 2606 INTEGER*2 CPONT(1 ) ,NXTR( 1) ,RPONT( 1) , NXTCI 1 ) , S EC(1),TYPE(11 2607 INTECER*2 WRI(1 ) ,BST(1),NUMBJ 1) 2668 .CCMMCN /ININF/ I 1,12,13,IT MA X,TOLERN,ZERO,EMVA,L INE,L I ST,I END 2669 COMMCN /ADS/ IA,ID,IS,ALG,BATCH 2670 LCGICAL*1 ALGI8),BATCH 2671 EOUIVALENCE!Il.NBUSI 2672 LCGICAL*1 OPRIME 2673 OPRIME= IND .NE. 1 2674 IF(DPRIME) GC TC 15 2675 DO 10 I=1,IENC 2676 K=SEC(I) 2677 NUMB(K)=I 2678 10 CONTINUE 2679 15 BST(1)=1 2660 DO 1C00 11=1,IEND 2661 I=SEO(II ) 2662 IF(DPR I ME .AND. TYPE (I I .NE. II GC TO 700 2683 K=2 2664 FIRST=I*8-7 2665 SUM=C. 2666 PP=NXTR(FIRST) 2667 20 I F I P P .EO. FIRST) GO TO 50 2668 VP=(PP<-7)/4 2669 J=CPCNT(PPI 2650 B I J = AIMAG(Y (VP)) 2691 IF1 I A .EO. 1 .CR. DPRIME) GO TO 23 2692 G I J = REAL ( Y ( V P ) ) 2653 RATIC=GIJ/BIJ 2654 GIJ = B I J * ( l.+RATIC* + 2) 2655 23 SUM=SUM+BIJ 2696 IFIIDPRIME .AND. T Y P E ( J ) .NE. I ) .OR. J .GT. I END I GO TO 30 2697 25 WRR(K)=-BIJ 2698 WRI(KI=J 2699 K=K+1 154. 2700 30 PP=NXTR(PP) 2701 GO TC 20 2702 50 PP=NXTC(FIRST) 2703 70 I F I P P .EQ. FIRST) GO TO 100 2704 VP=(PP+7)/4 27C5 J=RPCNT(PP) 2706 BI J = AIMAGIY(VP)) 27C7 I F I I A .EQ. 1 .OR. DPRIME) GO TO 73 2708 GIJ=REAL I Y I V P ) ) 2709 R A T I C = G I J / 3 I J 2710 BI J = 3 I J * ( l . + R A T I C * * 2 J 2711 73 SUM=SUM+BIJ 2712 IFIIDPRIME .AND. T Y P E ( J ) .NE. 1) .OR. J .GT. IENO) 2713 75 WRR ( K ) = - B I J 2714 WRI(K)=J 2715 K = K~1 2716 80 PP=NXTC(PP) 2717 GO TO 70 2718 100 WRI(1I=I 2719 IFI.NOT. DPRIME) WRR(1)=+SUM 272C IFIDPRIME) WRPI1)=-2.*AIMAG(Y<1*21>-SUM 2 721 K = K-1 2722 C 2723 C WORKING ROW FORMATION IS COMPLETED 2724 C 2725 I F ( I I .EO. 1) GO TO 500 2726 IMl=I1-1 2727 DO 200 J J = l , I M l 2728 J=SEC(JJ) 2729 IF(0PRIME .ANO. T Y P E I J I .NE. 11 GO TC 200 2730 INDEX=BST(JJ)+l 2731 J J 1 = J J 2732 1C5 J J 1 = J J I + 1 2733 LAS T=BST(JJ1) 2 734 IF (LAST .EQ. 0) GOTO 105 2 73 5 IF( INDEX .GE. LAST) GO TO 200 2736 DO 110 KK=1,K 2737 I F ( W R K K K ) .EC. J) GC TO 115 2 738 U O CONTINUE 2739 GC TC 200 2740 115 RATIO =-W RRIK K t 2741 WRI(KK)=0 2742 120 JK=BI(INDEX) 27*3 00 13C JKK=1,K 27*4 I F ( W R K J K K ) .EQ. JK) GO TO 140 2745 130 CONTINUE 2746 K = K + 1 2747 WRR(K)=0. 2748 WR I (K ) =JK 2749 JKK =K 27a0 140 WRR(JKK)=WPR(JKK )+BR(INDEX + 1)*RATIO 2751 INDEX=INDEX+2 2 7 52 IF( INDEX .LT. LAST) GO TO 120 2 753 200 CONTINUE 2754 C 2755 C WORKING ROW COMBINATION PROCESS COMPLETED 2756 C NOW DIVIDE ThE ROW EY ITS DIAGONAL AND STORE THE 2757 C 2758 50C RATI0=1./WRR( 1) 2759 INDEX=BST(I I ) 155. 2760 BR( INDEX)=RATIO 2761 INDEX=INDEX*1 2762 I F I K .EO. 1» GO TO 650 2763 DO 6C0 KK=2,K 2 764 I F ( W R K K K ) .EC. 0) GC TO 600 2765 Bl(INDEX»=WRI(KK» 27o6 BR( INCEX+1)=WRR(KK)*RATIO 2767 IN0EX=INCEX*2 27o8 6CC CONTINUE 2769 650 HST<II+1)=INDEX 277C GC TG 1000 2771 70C B S T I I I + l ) = B S T ( I I ) 2 7 72 B S T ( I I ) = 0 2773 10C0 CONTINUE 2 7 74 RETURN 2775 END 2 7 76 Sl.'BRCUTI NE DECS (DEL. Y, CPCNT, NXTR .RFCNT, NXTC. SEC, TYPE, V.SCHED. U, ERR 2777 * 1, ERR2, I ERR 2,ERR3,KPC,INDI 2778 REAL C E L ( l ) , U ( l ) 2779 COMPLEX Y d 1 .V( 1 1 , SCHED(l) .IK.SK.DS 2760 I N T E G E R S CPONT!I),NXTR( 1),RP0NT(1),NXTC(1) ,SEO( 1) ,TYPE(I) 2761 COMMON /ININ F / 11,12,13,IT MAX,TOLERN,ZERO,BMVA,LINE,LIST,IEND 2762 EQUIVALENCE ( I l . N B U S ) 2763 L C G I C A L M DPPIME 2764 INTEGER F I R S T , V P , P P 2785 KPQ=0 2766 ERR2=0. 2767 ERR3=0. 2738 DV1=0. 27d9 DV2=0. 2790 DPR IME=IND .EC. 2 2791 DO 200 I 1 = 1, IEND 2752 I=SECt11 I 2753 FIRST=I*8-7 2794 I K = Y ( 1*2 i * v m 2795 PP=NXTR(FIRSTI 2796 30 I F ( P P .EQ. FIRST) GO TO 50 2757 VP=(PP+7)/4 2 798 J=CPCNT(PP) 2799 1K = I K+YIV.P)*V(J) 2 8-0 PP=NXTR(PP) 2801 GC TO 30 2802 50 PP = NXTCI FIRST) 28-3 80 I F ( P P .EC. FIRST) GO TO 100 2804 VP=(po+7)/4 2805 J=RFCNT(PF) '2 8 06 I K = I K - Y ( V P I * V ( J ) 2807 PP=MXTC(PP) 2808 GC TC 80 2809 100 S K = V ( I ) * C G N J G ( I K ) 2 8 i 0 CS=SCFED(I )-SK 2 611 DP=REAL(0S) 2812 ACD=ABS(DP) 2813 IF(DPRIME) GC TC 120 2814 D E L ( I I I = D P 2815 IFIACD .GT. TCLERN) KPQ=1 2816 120 DVI=CV1+DP 2817 ERR3=ERR3+ADD 2818 IF(ERR2 .GE. ADD) GO TO 130 2819 ERR2 =ADD 156. 2820 IERR2=I 2821 130 I F ( T Y F E I I ) -EQ. 2) GO TO 200 2822 DO=AIMAG(DS) 2823 ADD=ABS(C0) 2824 IF( .NOT. DPRIME! GO TO 140 2825 D E L ( I I ) = 0 0 2826 IF!ADD .GT. TOLERN) KPQ=1 2827 14C 0V2=CV2+D0 2828 ERR3=ERR3+AD0 2829 IFIERR2 .GE. ADD) GO TO 200 2830 ERR 2 = ADD 2831 IERR2=I 2 832 200 CONTINUE 2833 ERR1=S0RT(DVl**2+DV2**2> 2 8 34 RETURN 2 835 END 2 836 SU8RCUTI NE DU2DD IBR . Rl , BST , DEL,UANG.TYPE,SEO.NUMB.INDI 2837 REAL BRI l ) . D E L ( l ) t U A N G I l ) 2838 INTEGER B U I ) 2839 INTEGER*2 BSTI1),TYPE!11,SEQ(1).NUMBII 1 2840 CCMMCN /ININF/ I 1, 12 . I 3 , IT MA X, TO LE RN , Z ERO , BM VA ,L I NE , L I ST , I END 2841 EQUIVALENCE ( I l . N B U S I 2 842 LCGICAL*1 DPRIME 2 8*3 D PR IfE= INO .EO. 2 2844 DO 2C0 11 = 1,I END 2845 I=SEQ(II ) 2846 IFICPRIME .AND. T Y P E I I ) -EQ. 2) GO TO 200 2847 INOEX = BSTl I I ) * 1 2848 111=11 2849 4C 111=111+1 2850 L AS T = BST( I I I ) 2851 IF I LAST .EQ. 0) GO TO 40 2852 5C IFIINDEX .GE. LAST) GO TO 100 2853 J J = B I I I N D E X I 2854 J=NUMB(JJ) 2855 DEL ( J )=DEL t J )-OEL( I I l*BRUNDEX + l ) 2856 IN0EX=lN0EX+2 2857 GO TO 50 2858 100 IND E X = B ST 11 I ) 2859 DEL( II)=DEL( I I ) * B R ( I N D E X ) 28o0 200 CCNTINUE 2861 C 2862 C FORWARD PROCESS COMPLETED 2863 c 2864 c START BACK SUBSTITUTION. 2865 c 2866 DO 400 I 1 = 1 , IEND 2867 JJ=IEND+1-II 28o8 I=SEO(JJ) 2869 IF(DFRI ME .AND. T Y P E I I ) .EO. 2) GO TO 400 28/0 SUM=C. 28/1 INDEX=BSTIJJ)+1 2872 J J 1 = J J 28/3 24C JJ1=JJ1+1 2874 LAST=BST(JJ1 ) 28/5 I F ( L A ST .EO. 0) GO TO 240 2876 250 IFf INDEX .GE. LAST) GO TO 300 28/7 J=BIIINDEX) 2878 J=NUMBIJ) 28/9 SUM=SUM + BR UNDEX + 1 )*DEL (J I 2 8 8 0 2 8 8 1 2 8 8 2 3 C C 2 8 3 3 4 0 0 2 8 3 4 C 2 8 8 5 C 2 8 8 6 C 2 8 8 7 2 8 8 8 2 8 8 9 2 8 9 C 2 8 9 1 2 8 9 2 4 5 C 2 8 9 3 2 8 9 4 5 C C 2 8 9 5 2 8 9 6 END O F F I L E I N D E X = I N D E X * 2 GO T O 2 5 0 D E L ( J J ) = D E L ( J J I - S U H C O N T I N U E B A C K S U B S T I T U T I O N E N D E D . DC 5 0 0 1 = 1 , I E N D J = S E Q U ) I F I D P R I M E ) GC TO 4 5 0 UANGl J ) = U A N C U ) * O E L ( I ) G C T C 5 0 0 I F I T Y P E I J ) . E O . 2 ) G C TO 5 0 0 U A N G ( J ) = S C R T ( U A N G ( J ) * * 2 + 2 . * 0 E L 1 1 ) 1 C C N T I N U E R E T U R N E N D 158. J '} . : J . J 1 GTNAME CSECT 2 *********************************************************************** 3 * CALLING SEQUENCE FROM FGRTRAN: * A * CALL GTNAME(MTU,NAME,LEN) * 5 * WHERE * 6 * MTU IS THE LOCATION OF AN ARRAY THAT CONTAINS THE NAME * 7 * OF TH E MTS UNIT. NAME MUST BE 8 CHARACTERS. IF IT IS LESS * 8 * THAN 8, IT MUST BE LEFT JUSTIFIED WITH TRAILING BLANKS. * 9 * EG. •SCARDS 10 * NAME(11 IS A LOGICAL*! ARRAY THAT IN RETURN WILL CONTAIN 11 * . THE NAME OF THE F I L E ASSIGNED TO THAT UNIT. * 12 * LEN IS AN INTEGER VARIABLE THAT IN RETURN WILL CONTAIN * 13 * THE NUMBER OF CHARACTERS IN N A M F ( l ) . * 14 *tt****4**»T*****!(<********4****$********* ******************************* 15 L SING *,9 16 STM 14,12,12113) STORE ALL THE REGISTERS BUT 13. 17 LR 9,15 SET BASE REGISTER 18 LA 10,SAVE 15 ST 10,8(0,13) SET THE FORWARD LINK 20 ST 13,4(0,101 SET THE BACKWARD LINK 21 LR 13,10 ESTABLISH THE SAVE AREA 22 L 5,0(C,1) GR5=A(MTU) 23 L 6,4(C,1I GR6=AINAME) 2A L 7 , 8 ( C , l ) GR 7 = A{LEN) 25 LM 0 , l , C ( 5 ) GET THE NAME OF THE UNIT. 26 L 15,=V(GDINF0) THEN 27 e ALR 14, 15 CALL THE SUBROUTINE GDINFO 28 LTR 15 ,15 CHECK RETURN CODE 29 BNZ. ERRCR AND BR ANCH IF NON-ZERO 30 L 1,36(0,1 ) GR 1= A(L ENGTH AND NAME) 31 LH 2,0(0,1) GR2=LENGTH CF NAME 32 LA 1,2(0,1 ) GR 1 = FIRST LOCATION OF NAME 33 ST 2,0(0,7) SET LEN = LENGTH 3A BCTR 2.C SUBTRACT ONE FROM LENGTH 35 EX 2,MOVE EXECUTE MOVE 36 L 13,4(0,131 RESTORE SAVE AREA ADDRESS 37 LM 14,12,12(13) RESTORE GENERAU REGISTERS . 38 SR 15,15 INDICATE ZERO RETURN CODE 39 BCR 15,14 RETURN AO ERROR L 13,4(0,13) RESTORE SAVE AREA ADORESS A l L 14, 12(0,13) RESTGRE RETURN ADDRESS 42 LM 0,12,201131 RESTORE GRO TO GR12 43 3C 15,14 RETURN *4 MOVE MVC 0 ( 0 , 6 ) , 0 ( 1 ) MOVE 'FILE NAME' TC 'NAME• 45 NAME DS 4F 46 SAVE OS 18F SAVE AREA 47 END 48 NAMBER CSECT *9 USING *,9 50 STM 14,12,12(131 S i LR 9, 15 52 LA 11 .SAVE 53 ST 11,8(0,13) SET BACKWARD L I N K . 54 ST 13,4(0,11) SET FORWARD LINK. 55 LR 13, 11 ESTABLISH SAVE AREA. 56 L 4,C(C,1, LOAD A (ARR AY) 57 L 5 , 4 ( d ) LOAD A ( I END) 58 L 5,0(0,5) LOAD I END 59 * 159. 60 * TO I N I T I A L I Z E 61 * 62 LA 7,0(0,0) WORD INDICATORS 63 LA 3,33(0,0) BIT INDICAT0R=33 64 LP, 6,7 COCNT=0 65 L 2,0(7,4) LOAD PROPER WORD. 66 GCCN BCT 3,NEXT CECREMENT BIT INDI. :G0 TO NEXT IF NON 67 LA 3,3210,0) RE-INIT. BIT INDICATOR. 68 LA 7,4(0,71 MODIFY WORC INDICATOR. 69 L 2,0(7,41 LOAD PROPER WORD. 70 NEXT LTR 2,2 TEST REGISTER 2 71 BC 11,ZERO BRANCH IF NGN-NEGATIVE. 72 LA 6,1(C,6) MODIFY COUNT 73 ZERO SLL 2 , H O SHIFT LEFT. 74 BCT 5,GCCN DECREMENT IEND; BRANCH IF NOT ZERO. 75 FINISHED LR 0,6 STORE COUNT. 76 L 13,410,13) RESTORE SAVE AREA ADDRESS. 77 LM 14,15,12113) RESTORE GENERAL REGISTERS. 78 LM 1, 12,24113) EXCEPT GR 0. 79 SR 15,15 INDICATE ZERO RETURN CODE. 80 BC R 15, 14 RETURN. 61 SAVE DS 18F 82 END END OF F I L E 160. APPENDIX B DATA FOR TEST SYSTEMS 6, 9 AND 10 The data for Test Systems 6, 9 and 10 are given below. This data was obtained from B.C. Hydro and is published here with their permission. The data for a l l the other test systems, are published in the respective references, mentioned in Table 2.2. For the sake of clarity, the listing of input data, produced by LFP, is used. The format of the input data (for LFP) is as explained in Appendix A, section A.4. In the listing that follows, the names SAMPLE (4001), SAMPLE (5001) and BCH.138 in the heading refer, respec-tively, to Test Systems 6, 9 and 10. ALG.=TEST CATA=SAMPLE<4001I START=F 09:27 P.M. JULY 24. 1977 PAGE bd H-1 B U S I N F O R M A T I O N U BUS * BUS NAME TYPE GENERATION MW MVAR LOAD BASE K.V VOLTAGE KV 1 ING230 3 0.0 0.0 0.0 0.0 230.00 235.00 3 JHT 13 2 127.00 0.0 0.0 0.0 13.80 13.80 4 LDR 13 1 47.00 5.00 0.0 0.0 13.80 0.0 5 SCA 13 1 " 25.80 5.00 . 0.0 0.0 13.80 0.0 6 PUN 13 24.50 0.0 17.80 8.15 13.80 14.30 7 ASH 13 26.70 0.0 0.0 0.0 13.80 13.80 8 GGA 13 2 72.00 0.0 0.0 0.0 13.80 13.80 10 JHT 132 1 0.0 0.0 0.0 0.0 132.00 0.0 11 CBY132 1 0.0 0.0 64.00 6.40 132.00 0.0 12 LDR132 1 0.0 0.0 0.0 0.0 132.00 0.0 13 SCA132 I 0.0 0.0 0.0 0.0 132.00 0.0 14 GL0132 1 0 .0 0.0 5.00 2.50 132.00 0.0 16 TAS132 1 0.0 0.0 18.CO 5.40 132.00 0.0 17 CTI132 1 0.0 0.0 0.0 0.0 132.00 0.0 19 CEL132 1 0.0 0.0 10.60 5.30 132.00 0.0 20 PUN132 1 0.0 0.0 10.00 3.00 132.00 0.0 . 22 CMR132 1 0.0 0.0 0.0 0.0 132.00 0.0 23 PAL132 1 0.0 0.0 107.30 36.30 132.00 0.0 24 GCL132 1 0.0 0.0 6.90 2.60 132.00 0.0 25 ASH132 1 0.0 0.0 0.0 0.0 132.00 0.0 26 NOR 132 I 0.0 0.0 9.60 4.80 132.00 0.0 27 KMC 132 I 0.0 0.0 24.00 7.20 132.00 0.0 29 JPT132 I 0.0 0.0 0.0 0.0 132.00 0.0 30 VIT230 1 0.0 0.0 0.0 0.0 230.00 0.0 31 • VIT 12 1 0.0 0.0 0.0 0.0 12.60 0.0 33 JPT 60 0.0 0.86 27.80 15.90 60.00 0. 0 34 JPT 12 1 0.0 15.00 0.0 0.0 12.00 0.0 35 GGA132 1 0.0 0.0 0.0 0.0 132.00 0.0 36 CFT132 1 0.0 0.0 65.40 20.30 132.00 0.0 37 ARN230 I 0.0 0.0 0.0 0.0 230.00 0.0 38 ARN132 I 0.0 0.0 0.0 0.0 132.00 0.0 39 ST0132 1 25.00 93.00 197.50 140.50 132.00 0.0 40 VIT132 1 0.0 0.0 0.0 0.0 132.00 0.0 o l-i CD CO r t on CO r t ro a H ON M ALG.=TEST DATA=SAMPLE<4001> »*•*•**»**»»*»********************* START=F T R A N S F O R M E R I N F C R M T I C N : -> TX » TX NAKE S.E. R . E . 1 SCA122 5 13 2 LDR132 4 12 -) 3 J H T 1 3 2 3 10 4 PUN122 . 6 20 5 ASH132 7 2 5 ") 6 JPT 60 29 33 7 J P T 12 33 34 8 GGA132 8 35 10 V I T 1 2 2 3 0 40 11 V I T 12 30 31 12 ARN132 37 38 i • LEAKAGE IMPEDANCE S.E. TAP R . E . T A P 0 . 0 1 6 3 0 . 2 7 2 0 1.13 I.00 0.C095 0 . 1 5 8 3 1.13 1.00 0 . 0 0 3 7 0.0624 1.15 1.00 0.C353 0 . 5 8 9 3 1.05 1.00 0.0220 0 . 3 6 7 1 1.10 1.00 0.01 18 0 . 2 9 6 0 1.03 1.00 C.0064 0 . 1 6 0 2 1 .00 1.00 0.0029 0 . 0 9 8 2 1.10 1.00 0.0030 0 . 0 6 0 0 1.02 1.00 0 . 0 0 3 3 0 . 0 6 6 7 0.98 1.00 0.0011 0 . 0 2 2 8 1.03 1.00 ( ALG.=TEST C A T A = S A M P L E ( 4 0 0 1 I START=F 0 9 : 2 7 P.M. L I N E I N F O R M A T I O N : L I N E » L I N E NAME S.E. R.E. PER U M T 15 TAS132 14 16 0 . 0 1 5 7 17 DBY132 10 11 0 . 0 0 1 7 19 GLD132 13 14 0.0516 2 0 SCA132 12 13 0 . 0 1 6 8 2 1 LDR132 10 12 0.OC17 22 C B L 1 3 2 17 19 0.00*2 2 3 C T l 132 10 17 0.0021 24 PUN132 17 20 0 . 0 4 1 0 25 0MR132 10 22 0 . 0 4 1 0 26 OMR132 20 22 0. 0 4 0 4 2 7 ASH132 24 25 0 . 0 1 6 1 28 G C L 1 3 2 2 3 24 0 . 0 1 7 6 29 P A L 1 3 2 22 23 0.0107 3 0 J P T 1 3 2 22 2 9 0 . 0 2 5 4 3 1 J P T 1 3 2 26 29 0 . 0 1 6 5 ~ 32 J P T 1 3 2 27 29 0 . 0 1 6 5 3 3 STD132 2 9 39 0 . 0 4 4 0 34 GGA132 29 35 0 . 0 4 1 6 3 5 C F T 1 3 2 35 36 0.0128 36 STO 132 36 39 0.0094 37 V I T 1 3 2 39 4 0 0.0004 3 9 V I T 1 3 2 38 40 0 . 0 2 8 4 4 0 ARN230 1 37 0 . 0 0 2 6 J U L Y 2 4 , 1977 PAGE 3 U N I T X S . E . S U S E P . R . E . S U S E P . TX? 0. 0 3 9 3 0 . 0 0 8 8 0 0 . 0 0 8 8 0 F 0 . 0 0 5 2 0 . 0 0 4 4 0 0 . 0 0 4 4 0 F 0. 1290 0 . 0 2 8 6 0 0 . 0 2 8 6 0 F 0 . 0 * 4 8 0 . 0 0 9 0 0 0 . 0 0 9 0 0 F 0 . 0 0 8 6 0 . 0 0 8 4 0 0 . 0 0 8 * 0 F 0.0123 0 . 0 0 2 8 0 0 . 0 0 2 8 0 F 0 . 0 0 6 1 0 . 0 0 1 4 0 0 . 0 0 1 * 0 F 0. 1209 0 . 0 2 6 6 0 0 . 0 2 6 6 0 F 0. 1227 0. 1 0 * 2 0 0. 10*20 F 0 .1194 0 . 0 2 6 2 0 0 . 0 2 6 2 0 F 0. 0 4 2 7 0 . 0 0 8 * 0 0 . 0 0 8 * 0 F 0 . 0 4 5 8 0 . 0 0 9 2 0 0 . C 0 9 2 0 F 0 . 0 3 2 6 0 . 0 2 7 6 0 0 . 0 2 7 6 0 F 0 . 0 7 5 0 0 . 0 6 5 6 0 0 . 0 6 5 6 0 F 0 . 0 * 3 1 0 . 0 0 8 6 0 0 . 0 0 8 6 0 F 0 .0*31 0 . 0 0 8 6 0 0 . 0 0 8 6 0 F 0 . 1 2 9 9 0 . 0 2 8 * 0 0 . 0 2 3 * 0 F 0. 1231 0 . 0 2 6 8 0 0 . 0 2 6 8 0 F 0 . 0 3 8 0 0 . 0 0 8 2 0 0 . 0 0 8 2 0 F 0 . 0 2 7 9 0 . 0 0 6 2 0 0 . 0 0 6 2 0 F 0.0031 0 . 0 0 3 0 0 0 . 0 0 3 0 0 F 0. 0 6 4 3 0 . 8 1 9 0 0 0 . 8 1 9 0 0 F 0.0158 0 . 0 3 0 6 0 0 . 0 3 0 6 0 F C7v V v ALG.-TEST 0ATA«SAMPLE(5001I START=F 09:26 P.M. JULY 24, 1977 PAGE 1 ********************************************* S I N r c R MAT I O N : BUS • BUS NAME TYPE GENERATION LOAO BASE VOLTAGE MW MVAR MW MVAR KV KV 21 BUS 21 0.0 0.0 0.0 0.0 500.00 0.0 22 BUS 22 1 0.0 0.0 0.0 0.0 500.00 0.0 23 BUS 23 1 0.0 0.0 0.0 0.0 500.00 0.0 24 BUS 24 1 0.0 0.0 . 0.0 0.0 500.00 0.0 25 BUS 25 1 0.0 0.0 0.0 0.0 500.00 0. 0 27 BUS 27 I 0.0 0.0 44.40 21.50 138.00 0.0 28 BUS 28 333.00 0.0 0.0 0.0 13.80 14. 15 29 BUS 29 1 0.0 0.0 0.0 0.0 230.00 0.0 30 BUS 30 1 0.0 0.0 259.00 0.0 230.00 0.0 31 BUS 31 1 0.0 0.0 0.0 0.0 230.00 0.0 32 BUS 32 1 0.0 0.0 0.0 0.0 360.00 0.0 33 BUS 33 1 0.0 0.0 0.0 0.0 360.00 0.0 34 BUS 34 208.00 0.0 0.0 0.0 13.80 14. 15 35 BUS 35 I 0.0 0.0 0.0 0.0 230.00 0.0 36 eus 36 1 0.0 0.0 0.0 0.0 360.00 0.0 37 BUS 37 1 0.0 0.0 124.00 29.00 230.00 0.0 38 BUS 38 1 0.0 0.0 0.0 0.0 230.00 0.0 39 EUS 39 1 0.0 0.0 0.0 0.0 230.00 0.0 40 BUS 40 1 0.0 0.0 0.0 0.0 230.00 0.0 41 BUS 41 1 0.0 0.0 66.40 32.10 230.00 0.0 42 BUS 42 1 0.0 0.0 0.0 0.0 230.00 0.0 43 BUS 43 1 0.0 0.0 0.0 0.0 230.00 0.0 44 BUS 44 I 0.0 0.0 83.50 40.40 230.00 0.0 45 BUS 45 1 0.0 0.0 111.70 54. 10 230.00 0.0 46 BUS 46 1 0.0 0.0 0.0 0.0 230.00 0.0 47 EUS 47 1 0.0 0.0 0.0 0.0 230.00 0.0 48 BUS 48 1 0.0 0.0 682.00 45.00 230.00 0.0 49 BUS 49 1 0.0 0.0 23.60 22.20 230.00 0.0 50 BUS 50 972.00 0.0 0.0 0.0 13.80 14. 15 51 BUS 51 306.00 0.0 0.0 0.0 13.80 14. 15 52 BUS 52 2 42.00 0.0 0.0 0.0 13.80 13.80 53 BUS 53 2 22.00 0.0 0.0 0.0 13.80 13. 80 54 BUS 54 2 60.00 0.0 12.00 5.80 13.80 13.80 55 BUS 55 2 140.00 0.0 0.0 0.0 13.80 14.15 56 BUS 56 2 50.00 0.0 0.0 0.0 13.80 13.80 57 BUS 57 2 52 .50 0.0 0.0 0.0 4.40 4.40 58 BUS 58 2 105.60 0.0 0.0 0.0 13.80 13.80 59 BUS 59 2 3241.00 756.OC 1955.00 70.00 230.00 241.30 60 BUS 60 3 11337.00 -886.50 9C92.00 -3645.00 100.00 113.00 61 BUS 61 2 826.00 292.00 411.00 -24.00 100.00 110.00 62 BUS 62 2 936.00 711.00 389.00 -290.00 100.00 115.00 63 BUS 63 2 0.0 0.0 0.0 0.0 12.30 12.60 ALG.=TEST C A T A = S A y P L E ( 5 0 0 1 ) START*F 0 9 : 2 6 P.P. J U L Y 2 4 , 1 9 7 7 PAGE 2 ************************************************************************************************************** B U S I U F C P M A T I O N : BUS # BUS NAME TYPE 64 BUS 64 2 6 5 BUS 65 2 66 EUS 66 2 67 BUS 67 2 68 BUS 68 69 BUS 69 70 BUS 70 71 BUS 71 72 BUS 72 73 BUS 73 74 BUS 74 75 BUS 75 76 BUS 76 77 BUS 77 78 BUS 78 79 BUS 79 80 BUS 80 81 BUS 81 82 BUS 82 83 BUS 83 84 BUS 84 85 BUS 85 86 BUS 86 87 BUS 87 88 EUS 88 89 BUS 89 90 eus 90 91 BUS 91 9 2 BUS 92 95 BUS 9 5 96 BUS 96 97 BUS 97 98 BUS 98 99 BUS 9 9 100 BUS100 101 B U S 1 0 1 A 02 BUS102 103 0 U S 1 0 3 104 BUS104 105 B U S 1 0 5 106 BUS106 10 7 BUS1C7 GENERATION LOAD BASE VOLTAGE MW MVAR MW MVAR KV KV 0.0 0.0 0.0 0.0 1 2 . 5 0 1 2 . 5 0 0.0 0.0 0.0 0.0 1 2 . 5 0 1 2 . 50 0.0 0.0 0.0 0.0 1 3 . 8 0 1 4 . 1 5 2 9 0 . 0 0 2 0 0 . 0 0 0.0 0.0 1 6 . 5 0 1 6 . 5 0 0.0 0.0 7 0 . 2 0 1 7 . 5 0 2 3 0 . 0 0 0.0 0.0 0.0 1 5 0 . 0 0 6 1 . 0 0 6 6 . 0 0 0.0 0.0 0.0 0.0 7 6 . 8 7 1 2 . 0 0 0.0 0.0 0.0 3.70 1.80 66 .00 0.0 0.0 0.0 9.30 4.50 6 6 . 0 0 0.0 0.0 0.0 0.40 0.20 6 6 . 00 0.0 0.0 0.0 0.0 0.0 3 6 0 . 0 0 0.0 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 0.0 0.0 1 4 0 . 6 0 4 3 . 5 0 6 0 . 0 0 0.0 0.0 0.0 4 7 . 2 0 1 6 . 4 0 6 0 . 0 0 0.0 0.0 0.0 3 1 . 6 0 1 4 . 5 0 6 0 . 0 0 0. 0 0.0 0.0 1 0 6 . 8 0 4 9 . 9 0 6 0 . 0 0 0.0 0.0 0.0 3.30 1 .30 6 0 . 0 0 0.0 0.0 0.0 5.70 1.90 6 0 . 0 0 0. 0 0.0 0.0 8 1 . 6 0 3 9 . 5 0 6 0 . 0 0 0.0 0.0 0.0 9 5 . 2 0 4 6 . 10 6 0 . 0 0 0.0 0.0 0.0 1 1 0 . 1 0 53.3 0 6 0 . 0 0 0. 0 0.0 0.0 155.7C 6 9 . 8 0 6 0 . 0 0 0.0 0.0 0.0 2 8 . 5 0 1 2 . 3 0 6 0 . 0 0 0.0 0.0 0.0 2 9 . 0 0 1 2 . 4 0 6 0 . 0 0 0.0 0.0 0.0 7 1 1 . 0 0 - 3 4 3 . 0 0 2 3 0 . 0 0 0.0 0.0 0.0 3 1 5 2 . 0 0 -756.OC 5 0 0 . 0 0 5 0 6 . 8 0 0.0 0.0 3 1 2 . 0 0 2 4 3 . 0 9 2 3 0 . 0 0 0. 0 0.0 0.0 2 0 0 . 0 0 4 8 . 1 1 1 3 2 . 0 0 0.0 0.0 0.0 33 .90 11 . 2 0 6 0 . 0 0 0. 0 0.0 0.0 28 .90 1 1 . 3 0 2 3 0 . 0 0 0.0 0.0 0.0 3 6 . 7 0 17.80 2 3 0 . 0 0 0.0 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 0.0 0.0 0.0 - 6 9 . 0 2 12 .00 0.0 0 .0 0.0 18.90 8.10 6 0 . 0 0 0. 0 0.0 0.0 7.90 3.80 6 0 . 0 0 0.0 0.0 0.0 0.0 0.0 6 0 . 0 0 0.0 0.0 0.0 8 5 . 8 0 1 8 . 9 0 6 0 . 0 0 0.0 0.0 0.0 7.30 3.50 6 0 . 0 0 0.0 0.0 0.0 9.30 4.50 6 0 . 0 0 0.0 0.0 0.0 3 1 . 3 0 15.10 6 0 . 0 0 0.0 0.0 0.0 8.60 * . 2 0 6 0 . 0 0 0.0 0.0 0.0 16 . 4 0 28.42 6 0 . 0 0 0.0 A I G . = T E S T C A T A = S A M P L E C 5 0 0 1 ) START=F 0 9 : 2 6 P.M. J U L Y 2 4 . 1977 PAGE 3 B U S I n F C B M A T I C N : BUS » BUS NAME TYPE 108 e u s i o s 1 109 BUS 109 1 110 BUS110 1 111 BUS111 2 112 8US112 1 113 BUS113 1 114 BUS114 1 115 BUS 115 1 270 EUS270 2 GENERATION MW MVAR 0.0 0.0 0.0 0.0 0.0 0.0 2 7 5 . 0 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 LOAD MW MVAR 3 6 . 9 0 2 7 . 8 6 3 8 . 6 0 1 3 . 2 0 0.0 - 7 6 . 8 7 0.0 0.0 2 1 . 4 0 8.50 3 0 . 3 0 1 0 . 7 0 0.0 0.0 3 6 0 . 0 0 3 6 0 . 6 8 0.0 0.0 BASE VOLTAGE KV KV 6 0 . 0 0 0. 0 3 6 0 . 0 0 0.0 1 2 . 0 0 0.0 1 3 . 8 0 1 4 . 15 2 3 0 . 0 0 0.0 6 0 . 0 0 0.0 2 3 0 . 0 0 0.0 1 3 . 8 0 0.0 1 0 0 . 0 0 1 1 3 . 0 1 ALG.=TEST CATA=SAHPLE<5001 > START=F 0 9 : 2 6 P.M. J U L Y 2 4 , 1 9 7 7 PAGE 4 ********************************************************* T R A N S F C R M E R I N F C R M T 1 0 N : TX U TX NAME S.E. R . E . LEAKAGE IMPEDANCE S . E . TAP R . E . TAP 96 2 1 28 0.0 0 . 0 5 5 8 1.00 0.98 97 21 5 0 0.0 0 . 0 1 4 3 1.00 0.98 98 69 6 3 0.0 0 . 0 9 5 9 1.00 0.93 99 9 0 91 0.0 0 . 0 9 6 8 1.00 1.03 100 9 0 9 2 0.0 0 . 2 2 5 3 1.00 1.02 301 4 6 85 0.0 0 . 0 7 1 4 1.00 1.02 302 46 85 0.0 0 . 0 7 6 8 1.00 1.06 303 31 76 0.0 0.1 LOS 1.00 1.03 304 24 31 0.0 0 . 0 1 9 3 1.00 1.03 305 3 9 82 0.0 0 . 2 2 8 0 1 .00 1.07 3 0 6 39 82 0.0 0 . 2 2 8 0 I .00 1.07 3 0 7 22 29 0.0 0 . 0 3 0 5 1.00 1.00 3 0 8 29 69 0.0 0.1 112 1.00 1.05 3 0 9 29 69 0.0 0 . 1 1 3 2 1.00 1.05 3 1 0 21 27 0.0 0 . 0 6 * 8 1.00 1.00 3 1 1 9 0 91 0.0 0 . 0 5 0 0 1.00 1.03 312 90 9 1 0.0 0 . 0 5 0 0 1.00 1.03 313 9 0 91 0.0 0 . 9 5 5 0 1.00 1.03 314 23 30 0.0 0 . 0 3 0 9 1.00 1.00 315 30 98 0.0 0 . 0 7 2 0 1.00 0.97 3 1 6 3 7 99 0.0 0 . 4 2 8 5 1.00 0.97 3 1 7 37 99 0.0 0 . 4 1 1 0 1.00 0.97 318 101 9 7 0.0 0 . 1 1 4 7 1.00 0.91 319 38 102 0.0 0 . 0 4 0 4 1.00 0.97 J 2 1 101 97 0.0 0 . 1 1 4 7 I . 0 0 0.91 3 2 3 22 29 0.0 0 . 0 3 0 0 1.00 1.00 324 21 111 0.0 0 . 0 5 5 8 1.00 0.98 3 2 6 29 110 0.0 0 . 0 7 1 5 1.00 1. 06 68 44 83 0.0 0 . 1 3 3 5 1.00 1.07 6 9 2 5 47 0.0 0 . 0 1 1 7 1.00 1.00 70 75 55 0.0 0 . 0 8 3 5 1.00 1.00 71 40 67 0.0 0 . 0 1 5 4 1.00 0.95 72 4 2 66 0.0 0 . 1 1 3 7 1.00 0.96 73 44 83 0.0 0 . 1 3 3 3 1.00 1.07 74 46 85 0.0 0 . 0 7 6 8 1.00 1.06 75 31 76 0.0 0 . 1 1 0 8 1.00 1.03 76 3 2 31 0.0 0 . 0 1 5 8 1.00 1.08 77 24 31 0.0 0 . 0 1 9 3 1.00 1.03 78 39 82 0.0 0 . 2 3 8 5 1.00 1.07 79 56 80 0.0 0. 1180 1.00 1.09 80 57 78 0.0 0 . 3 2 0 6 1.00 1. 16 81 58 77 0.0 0 . 1 7 3 4 1.00 1. 14 82 74 5* 0.0 0 . 1 9 4 8 1.00 0.97 C ' i . v. C o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ^ co H> « - " * ' 0 » — • o o L M O o r s j o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o •— o o •—»-••-••—oo»— *~ o 0 * 0 * 0 0 0 0 0 0 ^ 0 * 0 0 0 0 0 O u J O C ' O O ^ , O ^ * 0 U J N » - J N * • * * * —t • > * X * > z • r-* o 4> o » t • « H 4- •n * -4 » m 4- n » </> * -4 » * • » z » X 4- * • rn » O z 4> * > > * TO * > m + ft It + * C/t • ft » 4- Z * X » -o -n ft r-* m 4- o * —• • • m 4- TO * o + « a 4- •m » *-4- * — cn 4- * • • * rn * • • * 4- o * 4- « • z * 4- « 4- * c/» • -4 • ft > m ft JO • t -4 ft II ft T l ft • ft S3 »•• » IM » 0> r- • rn i> * • 7C > » • O * m • » <_  c » r-TJ » < m » O * IM > » J> z » • o * m * r-» .O »  -J # * • * • • • • » m • • • * * > # »  * » • * * • * "0 • * > m * <T> • * m * » » » KJ, • » • c r r ' ...'.89T ALG.=TEST DATA=SAMPLE<5001> START=F 09:25 P.M. JULY 24. 1977 PAGE 6 L I N E I N F O R M A T I O N : LINE * LINE NAME S.E. R.E. PER UNIT R PER UNIT X S.E. SUSEP. R.E. SUSEP. TX? 1 21 22 0.0C28 0.0239 0.51290 0.51290 F 2 22 23 0.0031 0.0281 0.84650 0.84650 F 3 23 24 0. 0030 0.0410 0.78110 2.00560 F 4 24 25 0.0004 0. 0056 0.19340 0.19340 F . 5 32 109 0.0023 0.0218 0.20660 0.20660 F 6 33 36 0.0067 0.0653 0.63040 0.63040 F 7 36 74 0.0003 0.0031 0. 02710 0.027L0 F 8 35 37 0.0221 0. 0768 0.11510 0.11510 F 9 38 39 C.0C08 0.0048 0.00440 0.00440 F 10 31 46 0.0032 0.0195 0.01890 0.01890 F 1 1 31 90 0.0026 0.0158 0.01540 0.01540 F 12 31 47 C.0055 0.0330 0.03190 0.03190 F 13 37 39 0.0109 0.0651 0.05750 0.05750 F 14 38 40 0.0021 0.0131 0.01290 0.01290 F 15 37 75 0.0030 0. 0190 0.01700 0.01700 F 16 37 97 0.0083 0.0573 0.05560 0.05560 F 17 40 43 0.0035 0.0240 0.02320 0.02320 F 18 41 43 0.0014 0.0087 0.08560 0.08560 F 19 42 43 0.0002 0.0017 0.00140 0.00140 F 21 46 96 0.0018 0.0052 0.36700 0.36700 F 22 31 42 0.0013 0.0079 0.00770 0.00770 F 23 40 41 0.0015 0. 0096 0.08770 0.08770 F 24 39 44 0.0034 0.0028 0. 19730 0. 19730 F 25 39 40 0.0024 0.0155 0.01520 0.01520 F 26 44 45 0.0005 0.0028 0.20620 0.20620 F 27 30 35 0.0102 0.0704 0.06800 0.06800 F 28 30 49 0.0203 0.1401 0.13580 0. 13580 F 29 29 113 0.0122 0.0849 0.08220 0.08220 F ' 30 29 68 0.0077 0. 1046 0.20650 0.20650 F 31 82 83 0.0111 0.0417 0.02380 0.02380 F 32 83 84 0.0107 0. 0394 0.02280 0.02280 F 33 84 85 0.0113 0.0417 0.00140 0.00140 F 34 76 85 0.0967 0.2352 0.00140 0.00140 F 35 79 82 0.0124 0.0481 0.00120 0.00120 F 36 85 87 0.0452 0. 1679 0.00110 0.00110 F 37 79 86 0.0356 0.1255 0.00080 0.00380 F 38 86 87 0.0039 0.0347 0.00020 0.00020 F 39 80 81 0. 1233 0.2051 0.00100 0.00100 F 40 81 82 0.0543 0.0980 0.00050 0.00050 F 41 79 80 0.0632 0.1151 0.00200 0.00200 F 42 76 79 0.0B69 0.2080 0.00130 0.00130 F 43 78 79 0.0535 0. 1697 0.00850 0.00850 F 44 77 78 0.0226 0.0682 0.00040 0.00040 F ALG.=TEST O A T A * S A M P L E ( 5 0 0 l l START=F 0 9 : 2 6 P.M. J U L Y 2 4 . 1977 PAGE 7 «**»»***»**********************************+#+*« L I N E I N F O R M A T I O N : ******************************** L I N E « L I N E NAME S.E. R.E. PER UNIT R PER U N I T X S . E . S U S E P . R . E . S U S E P . T X 7 4 5 76 77 0 . 1 5 3 9 0 . 4 2 3 2 0 . 0 0 2 8 0 0.00 280 F 4 6 72 73 0. 1457 0. 2 5 5 5 0 . 0 0 2 2 0 0 . 0 0 2 2 0 F 4 7 71 73 0 . 2 2 4 8 0 . 6 0 9 9 0 . 0 0 4 8 0 0 . 0 0 4 8 0 F 4 8 61 88 - 1 5 . 3 6 7 C 3 6 . 6 3 4 0 0.0 0.0 F 4 9 4 7 48 0.0C29 0 . 0 1 7 8 0 . 0 0 5 7 0 0 . 0 0 5 7 0 F 5 0 48 6 0 - 0 . 2 6 2 5 0 . 4 7 2 2 0.0 0.0 F 51 6 2 89 - 2 1 . 4 6 8 0 1 6 . 0 6 6 0 0.0 0.0 F 52 6 0 88 - 0 . 0 7 3 2 0. 1962 0.0 0.0 F 53 88 89 - 0 . 8 7 1 8 2 . 4 9 2 0 0.0 0.0 F 5 4 48 59 - 0 . 0 1 7 4 0 . 2 8 1 7 0.0 0.0 . F 5 5 59 88 0.0C38 0. 0 3 4 8 0.0 0.0 F 5 6 4 8 89 - 0 . 0 1 3 1 0 . 1 3 8 9 0.0 0.0 F 5 7 6 2 88 - 0 . 0 2 0 7 0 . 1 3 1 4 0.0 0.0 F 58 59 60 - 0 . 0 0 9 6 0 . 0 3 8 8 0.0 0.0 F 5 9 6 0 62 - 1 . 0 1 6 3 0 . 7 0 5 6 0.0 0.0 F 6 0 59 89 - 0 . 0 0 3 6 0. 0 5 0 9 0.0 0.0 F 6 1 48 61 - 0 . 0 1 8 1 0 . 2 9 6 5 0.0 0.0 F 6 2 61 89 - 0 . 0 3 9 7. 0. 1 7 2 9 0.0 0.0 F 2 2 7 25 89 0.001 7 0 . 0 3 6 3 0 . 8 8 6 3 0 0 . 8 8 6 0 0 F 6 5 59 61 - 0 . 0 6 9 5 0 . 3 6 1 5 0.0 0.0 F 6 6 6 0 89 - 0 . 0 1 4 4 0 . 0 3 0 3 0.0 0.0 F 6 7 6 0 61 - 0 . 3 3 0 6 0. 4 6 4 9 0.0 0.0 F 2 0 1 21 22 0.0028 0 . 0 2 3 9 0 . 5 1 2 9 0 0 . 5 1 2 9 0 F 2 0 2 22 23 0 . 0 0 3 1 C. 0 2 8 1 0 . 8 4 6 5 0 0 . 8 4 6 5 0 F 2 0 3 35 37 0 . 0 1 0 4 0 . 0 5 9 2 0 . 1 5 2 8 0 0 . 1 5 2 8 0 F 2 0 4 31 9 0 O;0C2 7 0 . 0 1 3 7 0 . 0 1 9 5 0 0 . 0 1 9 5 0 F 2 0 5 31 9 0 0 . 0 0 2 6 0 . 0 1 5 8 0 . 0 1 5 2 0 0 . 0 1 5 2 0 F 2 0 6 3 0 35 0 . 0 1 0 0 0 . 0 6 9 0 0 . 0 6 6 7 0 0 . 0 6 6 7 0 F 20 7 82 83 0 . 0 1 1 3 0 . 0 4 2 5 0 . 0 2 4 2 0 0 . 0 2 4 2 0 F 2 0 8 76 77 0 . 1 5 3 7 0 . 4 2 2 6 0 . 0 0 2 8 0 0 . 0 0 2 8 0 F 2 0 9 29 95 O.0C38 0. 0 2 6 7 0 . 0 2 5 9 0 0 . 0 2 5 9 0 F 2 1 0 41 96 0.0012 0 . 0 0 8 0 0 . 6 8 7 0 0 0 . 6 8 7 0 0 F 2 1 1 3 1 45 0 . 0 0 3 3 0. 02 06 0 . 0 7 3 2 0 0 . 0 7 3 2 0 F 2 1 2 38 97 0. 0 0 3 0 0 . 0 1 9 4 0 . 0 1 8 9 0 0 . 0 1 8 9 0 F 2 1 3 23 24 0 . 0 0 2 7 0. 0 3 6 3 0 . 4 8 2 2 0 1. 7067 0 F 2 1 4 99 100 0 . 5 3 0 5 0 . 7 5 2 7 0 . 0 0 3 8 0 0 . 0 0 3 8 0 F 2 1 5 100 1C1 0. 0 7 8 9 0. 1 1 8 3 0 . 0 0 0 6 0 0 . 0 0 0 6 0 F 2 1 6 101 103 0 . 0 0 4 2 0. 0 1 6 4 0 . 0 0 0 1 0 0 . 0 0 0 1 0 F 2 1 7 103 104 0 . 0 1 6 4 0 . 0 6 4 2 0 . 0 0 0 5 0 0 . 0 0 0 5 0 F 2 1 8 101 1 0 6 0 . 0 2 3 6 0. 0 7 8 6 0 . 0 0 0 6 0 0 . 0 0 0 6 0 F 219 104 105 0.0128 0 . 0 4 9 8 0 . 0 0 0 3 0 0 . 0 0 0 3 0 F 2 2 0 105 102 0 . 0 2 5 0 0 . 0 9 2 2 0 . 0 0 0 6 0 0 . 0 0 0 6 0 F 221 106 107 0 . 0 0 9 5 0 . 0 3 5 0 0 . 0 0 0 2 3 0 . 0 0 0 2 0 F A L G . = T E S T C A T A = S A M P L E ( 5 0 0 1 I STARTUP 0 9 : 2 6 P.M. J U L Y 2 4 . 1977 PAGE 8 ************************* *******************«*^ L I N E I N F O R M A T I O N : L I N E » L I N E NAME S . E . R.E. PER UNIT R 2 2 2 107 108 0 . 0 1 4 3 2 2 3 108 102 0.0032 2 2 4 108 102 0 . 0 0 8 8 2 2 5 48 88 - 9 . 7 6 9 3 22 6 59 62 - 2 . 4 8 0 9 6 3 2 5 89 0 . 0 0 1 7 2 2 8 4 9 113 0.0114 2 2 9 30 112 0 . 0 1 1 5 2 3 0 4 6 90 0 . 0 0 2 3 231 36 109 0. 0 0 0 5 232 4 7 114 0 . 0 0 1 2 2 3 3 4 7 114 0.001 1 . 234 6 0 270 0.0 PER UNIT X S . E . S U S E P . R . E . S U S E P . T X ? 0.0529 0. 0 0 0 3 0 0 . 0 0 0 3 0 F 0.0322 0 . 0 0 0 2 0 0 . 0 0 0 2 0 F 0 . 0 3 4 3 0.0002 0 0 . 0 0 0 2 0 F 3 5 . 6 9 9 3 0.0 0.0 F 8.9636 0.0 0.0 F 0 . 0 3 6 3 0 . 8 8 6 0 0 0 . 8 8 6 0 0 F 0.0794 0 . 0 7 7 3 0 0 . 0 7 7 0 0 F 0.08CO 0 . 0 7 7 6 0 0 . 0 7 7 6 0 F 0 . 0 1 4 6 0 . 0 1 4 4 0 0 . 0 1 4 4 0 F 0.0052 0 . 0 4 9 0 0 0 . 04 9 0 0 F 0 . 0 1 0 3 0 . 0 1 0 5 0 0 . 0 1 0 5 0 F 0.0097 0 . 0 0 9 8 0 0 . 0 0 9 8 0 F 0 . 0 1 0 0 0.0 0.0 F CM e a) •u CO CO 4-1 CO OJ H ! - i O 03 4J Cu O 05*91 0S'9T 0*0 0*0 0*0 00*811 51 *</! 08*£I 0*0 0*0 O'O 0*0 OS *ZI 05*21 0*0 O'O 0*0 O'O OS'Zl OS'Zl O'O 0*0 0*0 0*0 09*ZI OE'Zl 0*0 O'O 0*0 O'O 08 *£1 oe'ei 0*0 0*0 O'O 09*S0T 0 W O V V 0*0 O'O 0*0 OS'ZS 08*£1 0 8 ' E l 0*0 0*0 O'O 00*05 S l ' V I 08'EI 0*0 0*0 0*0 O C O V l 08*E 1 08'ET 05*6 Oi ' f a l O'O 00*09 08*£T 08'£T 0*0 0*0 0*0 00" zz 08*£I 08'£T 0*0 O'O O'O oc* zv S V V I 08*£1 O'O 0*0 0*0 00"90E ST **1 08 " ET 0*0 0*0 0*0 O C V V O l 0*0 0 C 0 9 Oi'OZ 0 V Z 9 0*0 O'O 0*0 OO'OEZ O'O 0*0 c*o 0*0 0*0 00*005 O'O 0*0 0*0 O'O O'O OO'OEZ O'O 0*0 0*0 0*0 0*0 00*0£Z 06*59 0Z*9£T 0*0 0*0 O'O OO'OEZ 0i " B 9 0 6 ' I V l O'O 0*0 0*0 OO'OEZ 0Z"1Z 01*99 0*0 0*0 0 "0 00*0£Z O'O 0*0 O'O O'O O'O OO'OEZ 09'6V OS'ZOT 0*0 0*0 O'O 00*0£Z O'O 0*0 C O O'O O'O 00*0£Z 0*0 0*0 0*0 0*0 O'O OO'OEZ O'O 0*0 0*0 0*0 O'O OO'OEZ 09'1V 0Z*59T 0*0 O'O O'O 00*09£ O'O 0*0 O'O 0*0 O'O OO'OEZ 0*0 0*0 0*0 0*0 SI "VI 08*£T 0*0 0*0 0*0 OO'BOZ O'O 00*09E 0*0 0*0 0*0 C O O'O 00*09£ 0*0 0*0 0*0 O'O OO'TVZ OO'OEZ 0*0 0*0 0*0 C O O'O OO'OEZ 0*0 0*0 0*0 O'O O'O 00*0£Z 0*0 0*0 O'O 0*0 S T V T 08'E1 O'O 0*0 0*0 00'19Z O'O 00'8£1 O l ' l V 08*96 O'O 0*0 O'O 00*005 O'O 0*0 0*0 O'O O'O OO'OCS O'O 0*0 O'O 0*0 O'O 00*005 0*0 0*0 0*0 0*0 O'O 00 *00S 0*0 0*0 O'O C O O'O 00*005 0*0 0*0 0*0 0*0 AX AX bVAW MW >JVAW 33V110A 3SV8 avoi N0I1VH3N33 z z z z z z z z z z z z z z 3dAl 9T ma £1 VUd ZDSATX •/DSNS'. NASNSf* ET sna v IdS EI ND8 E l SWD £1 HVM £T r v i £1 NOS E I zaa z SW9 OEZXDS 0EZH3W 00583W 0EZZ1X OEZNVW OEZanw OEZAHM OEZWld 0EZ13N 0EZ i n 8 OEZNdH 0EZ1TM OEZAXD 09ES0S 0£Z1«9 ET i a a 09E1MB 09E3NI OEZONI 0EZA1X OEZNS-. I SH3 8E1SH3 oosaio 00S3NI 00SA1X OOSNSM 005 SH3 3HVN sna 19 99 59 V9 £9 85 IS 95 55 VS ES ZS TS OS 6* BV IV 9* SV VV £V ZV IV OV 6£ 8E IE 9E SE V£ £E ZE TE OE 6Z 8Z LZ SZ *iZ EZ ZZ IZ * sna v******************************************************* i 3 3 v d ii.61 'vz ATOP 'M'a sz*60 j=iavis 8tl*HD9=VlVa 1 S 3 1 « * 3 1 V ALG.=TEST D A T A = B C H . l 3 8 START'F 0 9 : 2 5 P.M. J U L Y 2 4 , 1 9 7 7 PAGE 2 ****************************************** B U S I N F O R M A T I O N : BUS * BUS NAME TYPE GENERATION LOAD MW MVAR MW MVAR 68 GLN138 1 0.0 0.0 1 6 1 . 9 0 5 0 . 9 0 69 t>SN 66 1 0.0 0.0 2 4 9 . 5 0 8 9 . 2 0 70 WSNRX2 1 0.0 0.0 0.0 0.0 71 LA J 66 1 0.0 0.0 3.50 1.70 72 SCN 66 1 0.0 0.0 1 5 . 6 0 7.50 73 BRT 66 1 0.0 0.0 0.40 0.20 74 V.AH360 1 0.0 0.0 0.0 0.0 75 CMS230 1 0.0 0.0 0.0 0.0 76 ING 60 1 0.0 0.0 1 6 4 . 5 0 5 7 . 4 0 77 RUS 60 1 0.0 0.0 3 3 . 1 0 1 2 . 3 0 78 SFL 60 1 0.0 0.0 3 9 . 3 0 1 9 . 1 0 79 BNO 60 1 0.0 0.0 1 8 8 . 0 0 8 7 . 3 0 80 LBN 60 1 0.0 0.0 5.20 2.50 81 SHL 60 1 0.0 0.0 5.70 1.90 ~ 82 HPN 60 I 0 .0 0.0 1 0 7 . 5 0 5 2 . 1 0 83 MUR 60 1 0.0 0.0 1 5 2 . 4 0 7 3 . 8 0 84 SPG 60 1 0.0 0.0 1 1 9 . 4 0 5 7 . 8 0 85 Kt 1 60 I 0.0 0.0 2 1 5 . 1 0 9 4 . 5 0 86 NWR 60 1 0.0 0.0 2 5 . 5 0 1 0 . 8 0 87 RYL 60 1 0.0 0.0 2 5 . 6 0 10.90 90 ARN230 1 0.0 0.0 3 1 2 . 0 0 1 7 0 . 0 0 91 ARN132 1 0.0 0.0 2 0 0 . 0 0 0.0 92 ARN 60 1 0.0 0.0 55.OC 18 . 1 0 95 S V Y 2 3 0 1 0.0 0.0 6 3 . 1 0 2 2 . 5 0 96 CSN230 I 0.0 0.0 5 7 . 5 0 2 7 . 9 0 97 C Y P 2 3 0 1 0.0 0.0 0.0 0.0 98 K L Y RY 1 0.0 0.0 0.0 0.0 99 CKY 60 1 0.0 0.0 5 9 . 8 0 21 .40 100 HSB 60 1 0.0 0.0 1 4 . 5 0 7.00 101 CYP 60 1 0.0 0.0 0.0 0.0 102 WLT 60 1 0.0 0.0 1 3 5 . 5 0 3 3 . 3 0 103 HCT 60 1 0.0 0.0 7.30 3.60 104 GL R 60 1 0.0 0.0 12 . 4 0 6.00 105 CAP 60 1 0.0 0.0 3 2 . 6 0 1 5 . 8 0 106 J L N 60 1 0.0 0.0 18 . 6 0 9.00 107 NOR 60 1 0.0 0.0 31 .90 1 5 . 4 0 108 NVR 60 1 0.0 0.0 6 6 . 1 0 3 0 . 5 0 109 A T Z 3 6 0 1 0.0 0.0 1 0 4 . 2 0 3 4 . 2 0 110 WSNZ73 1 0.0 0.0 0.0 0.0 111 GMS 3 2 8 2 5 . 0 0 0.0 0 .0 0.0 112 HMH230 1 0.0 0.0 2 2 . 7 0 1 0 . 8 0 113 B L H 2 3 0 I 0 .0 0.0 4 2 . 2 0 2 0 . 4 0 BASE VOLTAGE KV KV 1 3 . 8 0 0.0 6 6 . 0 0 0.0 12.00 0.0 6 6 . 0 0 0.0 6 6 . 0 0 0.0 66 .00 0.0 3 6 0 . 0 0 0.0 2 3 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 2 3 0 . 0 0 0.0 1 3 2 . 0 0 0.0 6 0 . 0 0 0.0 2 3 0 . 0 0 0.0 2 3 0 . 0 0 0.0 2 3 0 . 0 0 0.0 12.00 0.0 6 3 . 0 0 0.0 6 0 . 0 0 0. 0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0. 0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 6 0 . 0 0 0.0 3 6 0 . 0 0 0.0 12.00 0.0 13 . 8 0 1 4 . 15 2 3 0 . 0 0 0.0 2 3 0 . 0 0 0.0 LO A L G . " T E S T CATA=BCH.138 START=F 0 9 : 2 5 P.M. J U L Y 2 4 . 1 9 7 7 PAGE B U S I N F C R M A T I O N BUS # BUS NAME T Y P E GENERATION LOAD BASE VOLTAGE MW MVAR MW MVAR KV KV 116 SVA230 t • 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 117 S V A 1 3 8 1 0.0 0.0 7.60 2.50 1 3 8 . 0 0 0.0 118 KW0138 1 0.0 0.0 0.0 0.0 1 3 8 . 0 0 0.0 119 DUG138 1 0.0 0.0 2 9 . 0 0 9.50 1 3 8 . 0 0 0.0 120 VVW138 l 0.0 0.0 1 1 1 . 1 0 3 6 . 5 0 1 3 8 . 0 0 0.0 121 SAK138 1 0.0 0.0 5 1 . 4 0 1 6 . 9 0 1 3 8 . 0 0 0.0 122 VNT 138 I 0.0 0.0 9 1 . 3 0 3 0 . 0 0 1 3 8 . 0 0 0.0 123 WSK138 1 0.0 0.0 1 1 . 4 0 3.80 1 3 8 . 0 0 0.0 124 WSH138 1 0.0 0.0 0.0 0.0 1 3 8 . 0 0 0. 0 125 V.SH 13 5 7 . 6 0 0.0 0.0 0.0 1 3 . 8 0 1 4 . 5 0 126 SLN138 1 0.0 0.0 0.0 0.0 1 3 8 . 0 0 0.0 127 S I N 7 2 1 9 8 . 0 0 0.0 0.0 0.0 7.20 7.20 128 B E L 1 3 8 I 0.0 0.0 0.0 0.0 1 3 8 . 0 0 0.0 i 3 2 HLD138 1 0.0 0.0 2 0 6 . 9 0 4 5 . 9 0 1 3 8 . 0 0 0.0 133 NIC I 38 1 0.0 0.0 7 4 . 1 0 1 9 . 6 0 1 3 8 . 0 0 0.0 134 N I C 2 3 0 I 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 135 N I C 5 0 0 1 0.0 0.0 0.0 0.0 5 0 0 . 0 0 0.0 136 MCA500 1 0.0 0.0 0.0 0.0 5 0 0 . 0 0 0.0 137 MCA 1 3 0 0 . 0 0 0.0 0.0 0.0 1 3 . 8 0 1 3 . 8 0 138 VNT230 1 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0. 0 139 KCN230 1 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 140 KCN 13 375 .00 0.0 0.0 0.0 1 3 . 8 0 1 3 . 8 0 141 S M I 230 1 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 142 BEL 161 1 0.0 0.0 0.0 0.0 1 6 1 . 0 0 0.0 143 BLT 13 1 2 0 . 0 0 0.0 0.0 0.0 1 3 . 8 0 1 3 . 80 144 BL T 69 I 0.0 0.0 3 5 . 0 0 1 5 . 0 0 6 9 . 0 0 0.0 145 C L V 1 6 1 1 0.0 0.0 0.0 0.0 1 6 1 . 0 0 0.0 147 SSL 69 I 0 .0 0.0 1 7 2 . 0 0 31 .00 6 9 . 0 0 0.0 148 T R L 1 6 1 1 0.0 0.0 0.0 0.0 1 6 1 . 0 0 0.0 149 TRL 69 1 0.0 0.0 5 0 0 . 0 0 2 1 0 . 0 0 6 9 . 0 0 0.0 150 WAN 14 3 6 0 . 0 0 0.0 0.0 0.0 1 4 . 4 0 1 4 . 4 0 151 WAN230 I 0.0 0.0 0.0 0.0 2 3 0 . 0 0 0.0 152 WAN 69 1 0 .0 0.0 0.0 0.0 6 9 . 0 0 0.0 153 GLN500 1 0.0 0.0 0.0 0.0 5 0 0 . 0 0 0.0 154 C B K 2 3 0 2 0.0 0.0 2 3 4 . 7 0 8 4 . 7 0 2 3 0 . 0 0 20 7 . 00 155 GMS 9 2 3 0 0 . 0 0 0.0 0.0 0.0 1 3 . 8 0 14. 15 156 MCA 2 2 3 0 0 . 0 0 0.0 0.0 0.0 1 3 . 8 0 1 3 . 8 0 251 C S T 2 3 0 2 12.70 6.20 1 5 0 7 . 1 4 1 3 0 . 6 3 2 3 0 . 0 0 2 3 7 . 6 8 2 52 C S T 5 0 0 2 0.0 0.0 5.56 - 4 2 . 1 9 5 0 0 . 0 0 5 1 2 . 0 0 253 MNR500 2 1 9 2 . 5 0 1 8 4 . 5 0 3 4 6 0 . 7 0 - 7 9 0 . 6 8 5 0 0 . 0 0 5 0 0 . 0 0 2 54 J G C 2 3 0 2 3 4 9 7 . 1 0 5 0 7 . 5 0 2 2 6 6 . 0 2 3 0 . 2 6 2 3 0 . 0 0 2 4 0 . 6 7 2 5 5 B E L 2 3 0 2 104 .60 193.2C 2 1 4 4 . 8 7 - 2 5 0 . 9 8 2 3 0 . 0 0 2 3 6 . 0 0 4> to 8 6 * 0 Z 1 1 8 - 9 1 1 1 9 * 1 0 1 1 6 * 1 0 1 9 V 0 U V 0 * 9 l l 5 8 * 1 1 1 0 8 * 1 0 1 E T O V I 0 1 * 1 1 1 E S ' V l l 9 6 * 1 V Z AX 3 9 V 1 1 0 A V 3 9 V d 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 I 0 0 * 0 0 1 0 0 * 0 0 1 0 0 * 0 0 1 OO'OEZ AX 3 S V 8 O i ' V i O l -1 8 * 5 5 9 -VS * Z Z E -0 V 1 0 0 1 -0 0 * 9 6 £ I -9 8 * 6 1 5 -O V 8 0 Z -U ' V S P -0 0 * Z 1 z-Z V 9 0 9 -Z B * 1 8 -i 6 * 8 Z V S ' S I S l 8 V / 1 0 1 9 0 * 1 5 1 61*0V£1 V i * | 9 9 Z I Z ' V S l l 0 V E E 9 8 6 * 0 V 8 1 E 6 * I B V S 9 * 9 E 8 9E*V0S 0*0 yvAw MH tJVDT O l ' l E O l O B ' E l O l Z N93M0M 19? 0 8 * 0 8 6 0 E * 6 9 1 1 z 3XVNSH 99? 0E"£6S O T 9511 z 3XVNS1 5 9 ? 08*8££1 0 6 * Z S i l z A7Q r V 9 ? 0 V E 0 Z 1 OZ* V69Z z V T 9 0 D 1 £9? OZ'SVS 0V"£Z6 z * 3 / \ 3 N l Z 9? 08*V£V OO'OZl z OddNVH 1 9 ' 01*0991 0 9 * 8 9 1 E £ vaioon 0 9 ? OV "Z BE 0 6 * 9 0 Z Z VW0DV1 6 5 ? 01*Z61 0 T V 6 1 I Z NQXDS 8 5 ? 0 V 8 6 E 0 9 * 9 E 8 Z O 1 8 V I 0 I S ? 09*69 OO'OSE Z 0EZAQ8 957 «VAW MW N 0 U V a 3 N 3 9 3 d A l 3WVN sna * sne : N 0 1 1 V W tl 0 3 N 1 s 1 1 6 1 *VZ Ainr *W*d S Z J 6 0 3 = l b V i S 8 E l * H 3 8 = # i V Q 1 S 3 A = ' 9 1 V O O M O O M B V 9 C 0 0*0 S O M O O M Z £ 1 T 0 O'O S O M O O M Z l l T O 0*0 O O ' l O O M SOEO'O O'O 01 M O O M oezz'o 0*0 O T l O O M 0 8 Z Z ' 0 O'O E O ' l O OM £610'0 0*0 S O M 0 0 * 1 B O I T O O'O 1 0 * I OOM 8 9 1 C 0 0*0 £0"1 0 0 ' 1 V U O ' O O'O Z O M O O M ESZZ'O O'O S O M O O M O'O O'O £6"0 00 * 1 6 S 6 0 ' 0 O'O 86"0 O O M EVIO'O O'O 86 " 0 O O M esso'o O'O E6 " 0 O O M 0 B 9 0 ' 0 O'O 6 6 ' 0 O O M 1 1 1 0 * 0 O'O 9 0 M O O M S U O ' O O'O O O M 0 0 " 1 8*790*0 O'O S C M S O M 60£0*0 O'O S O M OO ' l Z 1 1 T 0 O'O S O M S O M VOEO'O O'O 96"0 1 6 * 0 161£'0 O'O 9 6 * 0 1 6 * 0 LZ*>*/'0 O'O £ 0 M 1 0 M 8 8 1 0 ' 0 O'O O O M 8 6 ' 0 SZSO'O 0*0 S6*0 6 6 " 0 £66Z'0 O'O O O M 86 " 0 0 C 8 C 0 0*0 9 6 ' 0 86"0 8 V 6 T 0 O'O 60 M 9 6 * 0 V E i l ' O 0*0 0 1 M *?6*C 9 0 Z£*0 0*0 S O M 9 6 * 0 0 8 1 T 0 0*0 01 M O O ' l SBEZ'O O'O S O M ZO* 1 £610*0 O'O E U M 9 6 ' 0 8 S 1 0 ' 0 O'O S O M OO ' l 8 0 1 1 * 0 O'O i O M O O ' l 8 9 i 0 * 0 O'O B O M O O M £££1*0 O'O O O M <?0M 1 £ 1 T 0 O'O O O M S O M Z8£0*0 O'O O O M O O ' l S £ 80*0" 0*0 O O M 0 0 * 1 U I O ' O O'O 8 0 M O O M S E E l ' O 0*0 dV l "3"M dVi *3*S 33N»03dWI 33VXV31 I********************* S 39Vd i i b i **>z A W *(j*d sz LZ I Z O I F 6 9 6Z 60E 69 6Z 80E 6Z ZZ 10E ZB 6E 90 E ZB 6E SOE I E *>Z tt)f 91 1 E EOF SB 9<7 ZOE SB 9*/ 10E Z6 0 6 001 16 06 66 £9 6 9 86 OS I Z 16 8Z I Z 96 S9 OE 56 */9 6Z <?6 OL 6Z £6 IZ I Z Z6 0£ EZ . 16 6 9 6Z 06 6Z ZZ 68 ZS ZL 88 ES \ L 18 S£ EE 98 IS EE 58 I L SE */B </£ EE £8 . VS *>L Z8 LL BS 18 SL 15 08 08 9S 61 Z8 6£ 81 I E */Z LL I E Z£ 91 9 i I E 51 S8 9*1 */L £8 *>*i E i 99 Z*i ZL L9 0*1 \L SS S L OL 1SZ SSZ 6 9 £8 *!*> 89 "3*M *3*S 3WVN X i # XI : N Q I i W M D 3 N l M a w a o d S N v a i J=iaviS 8El*H38=VlVa 1S31=*91W ALG.-TEST DATA=BCH.138 START=F 0 9 : 2 5 P.M. J U L Y 2 4 . 1977 PAGE 6 a * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ T R A N S F O R M E R I N F O R M T I O N : IX * TX NAME S.E. R.E. LEAKAGE IMPEDANCE S . E . TAP R . E . TAP 311 9 0 91 0.0 0 . 0 5 0 0 1.00 1.05 312 . 90 91 0.0 0 . 0 5 0 0 1.00 1.05 313 9 0 91 0.0 0 . 9 5 5 0 1.00 1.05 3 1 * 23 3 0 0.0 0.0309 1.00 1.00 315 30 98 0.0 0 . 0 7 2 0 1.00 0.97 31 6 3 7 9 9 0.0 0 . 4 2 8 5 1.00 0.97 3 1 7 3 7 9 9 0.0 0.411 0 1.00 0.97 318 101 97 0.0 0 . 1 1 4 7 1.00 0.91 3 1 9 38 102 0.0 0.0404 1.00 0.97 321 101 97 0.0 0 . 1 1 4 7 1.00 0.91 3 2 3 22 29 0.0 0. 0 3 0 0 1.00 1.00 3 2 4 2 1 111 0.0 0 . 0 1 8 6 1.00 0.98 3 2 6 2 9 110 0.0 0 . 0 7 1 5 1.00 1.06 344 153 68 0.0 0 . 0 3 0 0 1.00 1.03 3 2 8 116 117 0.0 0 . 0 2 3 3 1 .00 1.04 3 2 9 124 125 0.0 0.2 3 4 3 I.00 1.00 3 3 0 14 7 126 0.0 0 . 1 0 1 0 1.00 1.09 343 156 1 3 6 0.0 0 . 0 0 7 3 1.00 1 .02 332 24 31 0.0 0 . 0 1 9 3 1.00 1.03 348 47 48 0.0 0 . 0 1 2 9 1.00 1.03 3 4 9 4 7 4 8 0.0 0 . 0 1 2 9 I . 0 0 1.03 353 21 155 0.0 0 . 0 4 6 5 I . 0 0 0.98 3 33 135 134 \ 0.0 0.0151 I . 0 0 1.03 334 134 133 0.0 0 . 0 4 5 0 1.00 1.00 335 139 140 0.0 0 . 0 3 1 0 1.00 0.97 33 6 138 122 0.0 0 . 0 4 5 0 1.00 1.00 3 3 7 137 136 0.0 0 . 0 0 7 3 1.00 1.02 3 38 142 128 0.0 0 . 1 4 8 0 I . 0 0 0.96 3 3 9 143 144 0.0 0 . 0 4 3 9 1.00 1.05 340 1 2 7 147 0.0 0 . 0 1 6 7 1.00 1.04 341 148 149 0.0 0 . 1 5 4 0 1 .00 0.93 342 150 152 0.0 0.0181 1.00 1.09 A L G . " T E S T DATA=BCH.138 STAR.T=F 0 9 : 2 5 P.M. J U L Y 2 4 . 1 9 7 7 PAGE L I N E I N F O R M A T I O N : L I N E » L I N E NAME S . E . R . E . PER UNIT R PER UNIT X S . E . S U S E P . R.E. S U S E P . T X ? 1 21 22 0. 0 0 2 8 0 . 0 1 7 9 0 . 5 1 2 9 0 0 . 5 1 2 9 0 F 2 22 23 0 . 0 0 3 1 0.0211 0 . 8 4 6 5 0 0 . 8 4 6 5 0 F 3 23 24 0. 0 0 3 0 0 . 0 2 0 5 0 . 7 8 1 1 0 2 . 0 3 5 6 0 F 4 24 25 0.0034 0. 0 0 5 6 0 . 1 9 3 4 0 0 . 1 9 3 4 0 F 5 32 109 0 . 0 0 2 3 0 . 0 2 1 8 0 . 2 0 6 6 0 0 . 2 0 6 6 0 F 6 33 36 O.0C67 0 . 0 6 5 3 0 . 6 3 0 4 0 0 . 6 3 3 4 0 F 7 36 74 0 . 3 0 0 3 0.0031 0 . 0 2 7 1 0 0 . 0 2 7 1 0 F 8 3 5 37 0.0221 0.0768 0 . 1 1 5 1 0 0 . 1 1 5 1 0 F 9 38 39 0 . 0 0 0 8 0.0048 0 . 0 3 4 4 3 0 . 0 3 4 4 0 F 10 31 46 0 . 0 0 3 2 0 . 0 1 9 5 0 . 0 1 8 9 0 0 . 0 1 8 9 0 F 11 31 90 0 . 0 0 2 6 0.0158 0 . 0 1 5 4 0 0 . 0 1 5 4 0 F 12 24 25 0.300 4 0.0047 0 . 2 2 7 0 3 0 . 2 2 7 0 0 F 13 3 7 38 0 . 0 0 9 5 0 . 0 5 7 3 0 . 0 5 6 1 0 0 . 0 5 6 1 0 F 14 38 48 0. J 0 3 7 0. 0 2 3 6 0 . 0 2 3 2 3 0 . 0 2 3 2 0 F 15 37 75 0 . 0 0 3 0 0.0190 0 . 0 1 7 3 0 ' 0 . 0 1 7 0 0 F 1 6 37 97 0 . 0 0 8 3 0 . 0 5 7 3 0 . 0 5 5 6 0 0 . 0 5 5 6 0 F 17 4 2 43 0. 0004 0 . 0 0 2 2 0 . 0 0 2 2 0 0 . 0 0 2 2 0 F 18 4 2 48 0 . 0 0 2 2 0 . 0 1 5 3 0 . 0 1 4 7 0 0 . 0 1 4 7 0 F 19 4 1 48 0 . 0 0 3 5 0.0218 0 . 0 9 8 7 3 0 . 0 9 8 7 0 F 21 4 6 96 0 . 0 0 1 8 0. 0 0 5 2 0 . 3 6 7 0 3 0 . 3 6 7 0 0 F 2 2 31 43 0 . 0 0 0 9 0 . 0 0 5 6 0 . 0 0 5 5 0 0 . 0 0 5 5 0 F 2 3 4 0 41 0 . 0 0 1 5 0. 0 0 9 6 0 . 0 8 7 7 0 0 . 2 4 9 7 0 F 24 4 4 48 0 . 0 0 4 8 0 . 0 3 0 3 0 . 2 5 8 8 0 0 . 2 5 8 8 0 F 2 5 3 9 4 0 0 . 0 0 2 4 0.01 5 5 0 . 0 1 5 2 0 0 . 0 1 5 2 0 F 2 6 44 45 0. 0 0 0 5 0.0028 0 . 2 0 6 2 3 0 . 3 6 8 2 0 F 27 3 0 35 0.0102 0 . 0 7 0 4 0. 0 6 8 0 0 0 . 0 6 8 0 0 F 2 8 3 0 49 0 . 0 2 0 3 0. 1401 0 . 1 3 5 3 0 0 . 1 4 3 0 0 F 2 9 29 113 0 . 0 1 2 2 0 . 0 8 4 9 0 . 0 8 2 2 3 0 . 0 8 2 2 0 F 3 0 22 153 0 . 0 0 1 6 0 . 0 2 1 7 - . 2 0 7 1 0 1 .01740 F 31 82 83 0 . 0 1 1 1 0 . 0 4 1 7 0 . 2 1 5 8 0 0 . 0 2 3 8 0 F 3 2 83 84 0 . 0 1 0 7 0. 0394 0 . 3 0 7 8 3 0 . 0 2 2 3 0 F 3 3 84 85 0 . 0 1 1 3 0 . 0 4 1 7 0 . 1 0 3 4 0 0 . 0 0 1 4 0 F 34 76 85 0. 0 9 6 7 0 . 2 3 5 2 • 0 . 0 0 1 4 0 0 . 0 3 1 4 0 F 3 5 79 82 0.0 124 0. 0481 0 . 0 0 1 2 0 0 . 0 0 1 2 0 F 3 6 8 5 87 0.0452 0 . 1 6 7 9 0 . 0 0 1 1 0 0 . 0 0 1 1 0 F 3 7 79 86 0 . 0 3 5 6 0.1255 0 . 0 0 0 8 3 0 . 0 3 0 8 3 F 38 86 87 0 . 0 0 8 9 0 . 0 3 4 7 0. 0 0 0 2 0 0 . 0 0 0 2 0 F 3 9 80 81 0. 1233 0 . 2 0 5 1 0 . 0 0 1 0 0 0 . 0 0 1 0 0 F 4 0 81 82 0 . 0 5 4 3 0. 0 9 8 0 0 . 0 0 0 5 3 0 . 0 0 0 5 0 F 4 1 7 9 80 0.0632 0 . 1 1 5 1 0 . 0 0 2 0 0 0 . 0 0 2 0 0 F 4 2 76 79 0 . 0 8 6 9 0 . 2 0 8 0 0 . 0 0 1 3 3 0 . 0 3 1 3 0 F 4 3 78 79 0 . 0 5 3 5 0.1697 0 . 0 0 8 5 0 0 . 0 0 8 5 0 F 4 4 77 78 0 . 0 2 2 6 0.0682 0 . 0 0 0 4 0 0 . 0 0 0 4 0 F ALG.=TEST 0 A T A = B C H . l 3 8 START=F 0 9 : 2 5 P.M. J U L Y 2 4 , 1977 PAGE 8 ******* ********************************************** ********************************************************* L I N E I N F O R M A T I O N : L I N E # L I N E NAME S.E. R . E . PER UNIT R PER U N I T X S . E . S U S E P . R . E . S U S E P . 4 5 76 77 0 . 1 5 3 9 0. 4 2 3 2 0.002 80 0 . 0 0 2 8 0 4 6 72 73 0 . 1 4 5 7 0 . 2 5 5 5 0 . 0 0 2 2 0 0 . 0 0 2 2 0 4 7 71 73 0 . 2 2 4 8 0 . 6 0 9 9 0 . 0 0 4 8 0 0 . 0 0 4 8 0 9 0 9 2 6 6 2 6 7 - 2 . 9 0 2 3 2 . 8 0 0 4 0.0 0.0 908 2 6 5 267 - 0 . 5 5 8 8 0 . 8 4 1 1 0.0 0.0 5 0 24 4 7 0 . 0 0 0 2 0 . 0 0 3 0 0 . 1 4 2 6 0 0 . 1 4 2 6 0 5 1 4 0 48 0 . 0 0 1 6 0 . 0 1 0 5 0 . 0 1 0 3 0 0 . 0 1 0 3 0 52 40 48 0 . 0 0 1 6 0 . 0 1 0 5 0 . 0 1 0 3 0 0 . 0 1 0 3 0 9 0 7 2 6 5 2 6 6 - 0 . 6 5 5 0 1.5140 0.0 0.0 9 0 6 2 64 267 - 0 . 1 9 4 3 0 . 3 1 4 7 0.0 0.0 9 0 5 264 2 6 6 - 2 . 2 0 9 4 2 . 3 4 6 4 0.0 0.0 904 2 6 4 265 - 0 . 1 1 2 3 0 . 3 9 6 0 0.0 0.0 903 263 267 - 0 . 1 8 6 3 0 . 2 3 2 6 0.0 0.0 9 0 2 2 6 3 266 - 0 . 1 7 9 5 0 . 4 3 9 8 0.0 0.0 901 263 265 - 0 . 0 8 9 0 0. 2 3 9 0 0.0 0.0 9 0 0 2 6 3 264 - 0 . 0 9 4 1 0 . 1 6 9 7 0.0 0.0 8 9 9 2 62 267 - 0 . 8 8 7 3 0. 8 3 6 2 0.0 0.0 89 8 2 6 2 2 6 6 - 4 . 6 8 9 7 4 . 7 8 2 2 0.0 0.0 897 2 6 2 265 - 1 . 1 3 0 0 1.5223 0.0 0.0 896 2 6 2 264 - 0 . 5 6 5 3 0. 7 0 3 8 0.0 0.0 8 9 5 262 26 3 - 0 . 2 3 2 1 0 . 3 4 3 0 0.0 0.0 894 261 2 6 7 - 0 . 5 9 6 7 0 . 9 3 1 5 0.0 0.0 201 2 1 22 0 . 0 0 2 8 0 . 0 1 7 9 0 . 5 1 2 9 0 0. 5 1 2 9 0 2 0 2 22 23 0 . 0 0 3 1 0 . 0 2 1 1 0 . 8 4 6 5 0 0 . 8 4 6 5 0 20 3 35 37 0.0 134 0. 0 5 9 2 0 . 1 5 2 8 0 0 . 1 5 2 8 0 204 31 9 0 0 . 0 0 2 7 0 . 0 1 3 7 0 . 0 1 9 5 0 0 . 6 8 9 5 0 2 0 5 31 90 0. 0 0 2 6 0. 0 1 5 8 0 . 0 1 5 2 0 0 . 0 1 5 2 0 206 30 35 0 . 0 1 0 0 0 . 0 6 9 0 0 . 0 6 6 7 0 0 . 0 6 6 7 0 2 0 7 82 83 0 . 0 1 1 3 0 . 0 4 2 5 0 . 0 2 4 2 0 0 . 0 2 4 2 0 208 76 77 0.1 537 0 . 4 2 2 6 0 . 0 0 2 8 0 0 . 0 0 2 8 0 2 0 9 29 95 0 . 0 0 3 8 0. 0 2 6 7 0.02 590 0 . 0 2 5 9 0 210 4 1 96 0.0012 0 . 0 0 8 0 0 . 6 8 7 0 0 0 . 6 3 7 0 0 211 31 45 0 . 0 0 3 3 0 . 0 2 0 6 0 . 0 7 3 2 0 0 . 0 7 3 2 0 2 1 2 38 97 0 . 0 0 3 0 0 . 0 1 9 4 0 . 0 1 8 9 0 0 . 0 1 3 9 0 2 1 3 23 47 0.0C26 0. 0 3 4 4 0 . 3 8 9 4 0 1.61390 2 1 4 9 9 100 0 . 5 3 0 5 0. 7 5 2 7 0 . 0 0 3 8 0 0 . 0 0 3 8 0 2 1 5 ICC 1C1 0 . 0 7 3 9 0 . 1 1 8 3 0 . 0 0 0 6 0 0 . 0 0 0 6 0 216 101 103 0. 0 0 4 2 0. 0 1 6 4 0 . 0 0 0 1 3 0 . 0 0 0 1 0 2 1 7 103 104 0.0164 0 . 0 6 4 2 0 . 0 0 0 5 0 0 . 0 0 0 5 0 2 1 8 101 106 0 . 0 2 3 6 0.0786 0 . 0 0 0 6 0 0 . 0 0 0 6 0 219 104 1 0 5 0.0 123 0 . 0 4 9 8 0 . 0 0 0 3 0 0 . 0 0 0 3 0 22 0 105 102 0 . 0 2 5 0 0 . 0 9 2 2 0 . 0 0 0 6 0 0 . 0 0 0 6 0 2 2 1 106 107 0 . 0 0 9 5 0 . 0 3 5 0 0 . 0 0 0 2 0 0 . 0 0 0 2 0 A L G . - T E S T DATA«BCH.138 START*F 0 9 : 2 5 P.M. J U L Y 2 4 . 1977 PAGE 9 «***»*************»***«***£****************»»a**«*«»*******»**»^ L I N E I N F O R M A T I O N : L I N E » L I N E NAME S.E. R.E. PER U M T R PER UNIT X S . E . S U S E P . R . E . S U S E P . T X ? 2 2 2 107 108 0 . 0 1 4 3 0 . 0 5 2 9 0 . 1 9 2 3 0 0 . 0 0 0 3 0 F 2 2 3 108 109 0.0082 0.0322 0 . 1 0 2 2 0 0 . 0 0 0 2 0 F 2 2 4 108 102 0 . 0 0 8 8 0 . 0 3 4 3 0 . 0 0 0 2 0 0 . 0 0 0 2 0 F 893 261 2 6 6 - 2 . 0 2 8 1 4 . 0 0 8 7 0.0 0.0 F 8 9 2 2 6 1 265 - 0 . 0 5 0 1 0 . 4 3 2 0 0.0 0.0 F 891 261 264 - 0 . 0 9 9 1 0 . 3 9 0 6 0.0 0.0 F 2 2 8 49 113 0.0114 0.0794 0 . 0 7 7 0 0 0 . 0 7 7 0 0 F 2 2 9 3 0 112 0 . 0 1 1 5 0.0800 0 . 0 7 7 6 0 0 . 0 7 7 6 0 F 2 3 0 4 6 90 0 . 0 0 2 3 0 . 0 1 4 6 0 . 0 1 4 4 0 0 . 0 1 4 4 0 F 231 36 109 0 . 0 0 3 5 0.0052 0 . 0 4 9 0 3 0 . 0 4 9 0 0 F 8 9 0 261 263 - 0 . 2 2 7 7 0 . 4 4 5 1 0.0 0.0 F 8B9 261 2 6 2 - 1 . 1 9 8 5 1.6585 0.0 0.0 F 888 2 6 0 2 6 7 - 0 . 5 7 8 0 0 . 6 5 2 8 0.0 0.0 F 234 141 154 0 . 0 2 4 8 0 . 1 6 2 3 0 . 1 5 0 0 0 0 . 1 5 0 0 0 F 2 3 5 30 116 0.0119 0 . 0 8 2 2 0 . 0 8 0 0 0 0 . 0 3 0 0 0 F 2 3 6 30 116 0.0 12 1 0.0834 0 . 0 8 1 2 3 0 . 0 8 1 2 0 F 23 7 117 118 0 . 0 2 4 6 0. 0 8 8 6 0 . 0 1 1 3 0 0 . 0 1 1 3 0 F 2 3 8 117 119 0.0276 0.0992 0 . 0 1 2 7 3 0 . 0 1 2 7 0 F 2 3 9 118 120 0 . 0 1 3 9 0. 0 4 9 8 0 . 0 0 6 3 0 0 . 0 0 6 3 0 F 24 0 U 9 120 0 . 0 0 3 6 0 . 0 1 3 1 0 . 1 5 L 7 0 0 . 0 0 1 7 0 F 241 120 121 0. 1118 0 . 2 9 1 8 0 . 0 3 5 2 0 0 . 0 3 5 2 0 F 2 4 2 121 122 0 . 0 5 3 7 0. 1 3 9 7 0 . 0 1 6 7 3 0 . 0 1 6 7 0 F 2 4 3 120 122 0. 1136 0 . 2 9 6 4 0. 03 560 0 . 0 3 5 6 0 F 244 122 123 0 . 1 0 2 0 0.2663 0 . 0 8 2 9 3 0 . 0 3 1 9 0 F 24 5 122 123 0 . 1 0 2 0 0 . 2 6 6 3 0 . 0 3 1 9 0 0 . 0 3 1 9 0 F 2 4 6 123 126 0.0674 0.2048 0 . 0 2 5 0 0 0 . 0 2 5 3 0 F 24 7 123 124 0 . 0 0 5 5 0 . 0 1 6 6 0 . 0 0 2 0 3 0 . 0 0 2 0 0 F 24 8 122 128 0 . 0 4 9 6 0 . 1 5 1 1 0 . 0 1 8 6 0 0 . 0 1 8 6 0 F 8 8 7 260 2 6 6 - 0 . 4 1 3 3 1.1718 0.0 0.0 F 886 2 6 0 265 - 0 . 1 0 6 5 0 . 4 0 1 8 0.0 0.0 F 685 260 264 - 0 . 1 7 4 9 0. 3764 0.0 0.0 F 251 117 132 0 . 0 2 9 5 0. 1062 0 . 0 1 3 5 0 0 . 0 1 3 5 0 F 2 5 2 117 132 0 . 0 5 2 6 0. 1043 0. 0 1 3 7 0 0 . 0 1 3 7 0 F 2 5 3 117 132 0 . 0 1 5 7 0.10 9 1 0 . 0 1 3 7 0 0 . 0 1 3 7 0 F 2 5 4 132 133 0.0374 0. 1348 0 . 0 1 7 1 0 0 . 0 1 7 1 0 F 2 5 5 134 138 0 . 0 1 5 6 0. 1025 0 . 0 9 4 2 0 0 . 0 9 4 2 0 F 2 5 6 138 139 0 . 0 2 7 6 0 . 1 8 1 3 0 . 1 6 6 8 3 0. 1 6 6 3 0 F 2 5 7 139 141 0 . 0 0 7 9 0 . 0 5 1 8 0 . 0 4 7 7 0 0 . 0 4 7 7 0 F 2 5 8 141 256 0.0C19 0 . 0 1 2 5 0 . 0 1 2 2 0 0 . 0 1 2 2 0 F 2 5 9 135 136 0. 002 6 0 . 0 3 5 5 1 . 7 8 6 2 3 0 . 5 6 1 7 0 F 2 6 0 24 135 0 . 0 0 2 5 0 . 0 3 3 2 1. 6 7 2 6 3 0 . 4 4 8 1 0 F 261 122 128 0 . 1 1 9 7 0 . 3 3 9 7 0 . 0 8 9 2 3 0 . 0 8 9 2 0 F 2 6 2 142 145 0.0666 0 . 2 6 8 0 0 . 0 6 2 7 3 0 . 0 6 2 7 0 F ^ I—1 00 o A L G . - T E S T 0 A T A = B C H . l 3 8 STARTUP 0 9 : 2 5 P.M. J U L Y 2 4 , 1977 PAGE 10 ft****************************************** H E I N F O R M A T I O N : L I N E # L I N E NAME S.E. R.E. PER UNIT R 2 6 3 144 149 0 . 0 2 4 4 2 6 4 145 148 0.0364 2 6 5 147 149 0 . 0 2 2 9 26 6 149 152 0 . 0 0 5 5 2 6 7 151 256 0 . 0 0 2 1 271 40 44 0 . 0 0 3 2 801 251 2 5 2 0.0004 802 251 253 - 0 . 0 2 2 7 803 251 254 - 0 . 0 4 2 2 804 251 2 5 5 - 2 0 . 0 6 5 0 8 0 6 2 5 1 257 - 0 . 0 7 0 0 80 7 251 258 - 1 0 2 . 5 9 0 0 808 251 259 - 2 . 8 1 2 5 8 0 9 251 2 6 0 - 0 . 5 6 6 2 8 1 0 2 5 1 261 - 4 . 5 8 8 3 8 1 1 251 262 - 3 . 0 5 8 4 812 251 263 - 4 . 3 8 3 2 8 1 3 2 5 1 264 - 6 . 0 3 9 3 814 251 265 - 6 . 5 0 0 4 8 1 5 251 266 - 3 5 . 8 6 6 0 816 251 2 6 7 - 1 2 . 9 3 5 0 8 1 7 2 5 2 2 53 0.0012 8 1 8 253 2 54 - 0 . 0 0 7 5 8 1 9 2 5 3 255 - 1 . 0 3 0 2 8 2 0 2 5 3 2 5 7 - 0 . 0 4 4 3 8 2 1 2 5 3 2 5 8 - 6 . 3 5 1 9 82 2 2 5 3 259 - 0 . 2 1 8 5 823 2 5 3 2 6 0 - 0 . 0 2 2 0 8 2 4 2 5 3 261 - 0 . 0 9 5 5 82 5 2 5 3 262 - 0 . 1 4 2 4 8 2 6 253 263 - 0 . 1 4 3 6 82 7 2 5 3 264 - 0 . 1 6 6 7 82 8 2 5 3 2 6 5 - 0 . 1 6 6 6 8 2 9 2 5 3 266 - 1 . 3 1 4 7 83 0 2 5 3 267 - 0 . 4 1 5 9 8 3 1 2 5 4 255 0 . 0 0 3 8 832 254 2 5 7 - 0 . 0 8 9 2 8 3 3 2 5 4 258 - 0 . 3 4 5 0 834 254 259 - C . 5 2 1 4 83 5 2 5 4 260 - 0 . 0 0 7 4 836 2 5 4 261 - 0 . 0 9 6 0 8 3 7 254 262 - 0 . 2 5 1 0 8 3 8 2 5 4 263 - 0 . 1 0 7 0 PER U N I T X S . E . S U S E P . R . E . S U S E P . T X ? 0.085 7 0 . 0 0 7 0 0 0 . 0 0 7 0 0 F 0 . 1 4 6 0 0 . 0 3 4 3 0 0 . 0 3 4 3 0 F 0. 0 8 0 4 0.0182 0 0 . 0 1 8 2 0 F 0 . 0 3 2 3 1 . 2 5 5 6 0 0 . 0 0 5 6 0 F 0.0214 0 . 0 2 1 8 0 0 . 0 2 1 8 0 F 0 . 0 2 0 3 0 . 2 2 3 9 0 0 . 2 2 3 9 0 F 0.0098 0.0 0.0 F 0. 1 6 8 3 0.0 0.0 F 0.3900 0.0 0.0 F 5 9 . 5 9 7 4 0.0 0.0 F 0 . 4 5 3 7 0.0 0.0 F 1 8 2 . 2 9 5 0 0.0 0.0 F 5. 7 1 8 0 0.0 0.0 F 1.4469 0.0 0.0 F 8.5837 0.0 0.0 F 4 . 4 0 7 4 0.0 0.0 F 4 . 0 8 9 0 0.0 0.0 F 6.6411 0.0 0.0 F 1 0 . 6 5 4 9 0.0 0.0 F 4 0 . 8 0 9 3 0.0 0.0 F 8.37C6 0.0 0.0 F 0 . 0 2 4 0 0.0 0.0 F 0.0479 0.0 0.0 F 3.0674 0.0 0.0 F 0.1832 0.0 0.0 F 9. 9404 0.0 0.0 F 0.4428 0.0 0.0 F 0.0789 0.0 0.0 F 0 . 3 3 8 0 0.0 0.0 F 0 . 2 5 2 0 0.0 0.0 F 0. 1915 0.0 0.0 F 0. 2 9 2 9 0.0 0.0 F 0 . 4 4 6 8 0.0 0.0 F 1.9227 0.0 0.0 F 0 . 4 1 9 0 0.0 0.0 F 0 . 0 3 5 0 0.0 0.0 F 0 . 4 2 6 3 0.0 0.0 F 3.3338 0.0 0.0 F I . 1 0 6 6 0.0 0.0 F 0 . 0 7 5 2 0.0 0.0 F 0 . 5 2 9 8 0.0 0.0 F 0.5082 0.0 0.0 F 0.2710 0.0 0.0 F ALG.«TEST C A T A = B C H . l 3 8 START=F 0 9 : 2 5 P.M. J U L Y 2 * . 1977 PAGE 11 ******* »«^»******** ******************* ****»****^ L I N E I N F O R M A T I O N : L I N E # L I N E NAME S.E. R.E. PER UNIT R PER UNIT X S . E . S U S E P . R.E. S U S E P . T X ? 8 3 9 2 5 4 2 6 4 - C . 2 2 9 4 0 . 5 1 6 0 0.0 0.0 F 8 4 0 2 54 2 6 5 - 0 . 1 1 6 3 0 . 5 7 1 3 0.0 0.0 F 84 1 254 2 6 6 - 0 . 4 7 3 3 1.7267 0.0 0.0 F 84 2 254 267 - 0 . 6 8 7 3 0 . 8 2 2 4 0.0 0.0 F 84 3 2 5 5 256 0 . 0 0 7 5 0 . 0 6 6 5 0.0 0.0 F 844 2 5 5 2 5 7 - 2 2 . 0 6 6 0 5 0 . 7 0 0 0 0.0 0.0 F 845 2 5 5 258 - 0 . 0 1 4 6 0.0997 0.0 0.0 F 8 4 6 2 5 5 259 - 3 5 . 9 3 7 0 5 8 . 8 1 3 0 0.0 0.0 F 8 4 7 2 5 5 2 6 0 - 0 . 1595 1.4119 0.0 0.0 F 848 2 5 5 261 - 2 . 3 2 4 0 7 . 3 4 3 2 0.0 0.0 F 8 4 9 2 5 5 262 - 7 . 9 5 8 2 1 0. 6 6 8 5 0.0 0.0 F 8 5 0 2 5 5 263 - 0 . 3 5 3 2 1.0663 0.0 0.0 F 851 2 5 5 264 - 3 . 8 1 3 2 5. 5421 0.0 0.0 F 852 2 5 5 2 6 5 - 0 . 5 1 8 8 2 . 4 7 7 8 0.0 0.0 F 853 255 2 6 6 - 0 . 1 7 6 5 0 . 4 4 8 2 0.0 0.0 F 854 2 5 5 267 - 6 . 5 9 8 8 7 . 0 1 4 5 0.0 0.0 F 8 5 5 2 5 7 2 5 8 - 1 0 5 . 6 2 0 0 1 5 2 . 6 3 4 0 0.0 0.0 F 8 5 6 2 5 7 2 5 9 - 2 . 7 5 7 5 4. 7 6 7 0 0.0 0.0 F 8 5 7 2 5 7 260 - 0 . 5 8 0 3 1.2263 0.0 0.0 F 8 5 8 2 5 7 261 - 4 . 4 0 3 0 7.1198 0.0 0.0 F 8 5 9 2 5 7 262 - 2 . 8 6 9 9 3 . 6 1 8 5 0.0 0.0 F 8 6 0 2 5 7 263 - 3 . 9 9 4 9 3 . 2 5 7 9 0.0 0.0 F 86 1 2 5 7 2 64 - 5 . 5 3 7 9 5 . 3 7 0 6 0.0 0.0 F 862 2 5 7 265 - 6 . 1 9 3 0 8. 7 9 6 1 0.0 0.0 F 86 3 2 5 7 2 6 6 - 3 3 . 4 6 7 0 3 3 . 0 6 7 1 0.0 0.0 F 864 2 5 7 267 - 1 1 . 5 4 1 0 6.4312 0.0 0.0 F 86 5 258 259 - 1 6 8 . 3 7 0 0 1 7 6 . 5 5 9 0 0.0 0.0 F 8 6 6 258 2 6 0 - 1 . 5 4 2 0 4 . 3 3 0 6 0.0 0.0 F 867 2 5 8 261 - 2 2 . 0 7 3 0 2 6 . 1 0 8 3 0.0 0.0 F 8 6 8 2 5 8 262 - 4 8 . 4 2 1 0 2 9 . 7 8 9 9 0.0 0.0 F 86 9 2 5 8 263 - 3 . 3 2 3 7 3 . 7 9 3 1 0.0 0.0 F 8 7 0 2 5 8 264 - 2 7 . 7 8 7 0 8 . 6 9 6 7 0.0 0.0 F 8 7 1 2 5 8 265 - 5 . 5 7 4 5 9 . 7 3 8 6 0.0 0.0 F 8 7 2 2 5 8 2 66 - 1 . 1 0 2 7 0.7724 0.0 0.0 F 87 3 2 5 8 ?67 - 4 0 . 7 72 0 7 . 3 7 2 4 0.0 0.0 F 874 259 2 6 0 - 0 . 9 3 7 0 1.5647 0.0 0.0 F 87 5 2 5 9 261 - 5 . 4 7 7 0 7.5895 0.0 0.0 F 8 7 6 259 262 - 2 . 0 1 3 6 2 . 8 6 9 8 0.0 0.0 F 8 7 7 2 5 9 263 - 4 . 1 0 6 2 3.0298 0.0 0.0 F 8 7 8 2 5 9 264 - 5 . 9 5 1 0 5. 1445 0.0 0.0 F 8 7 9 2 5 9 265 - 7 . 5 7 6 8 9 . 0 9 3 7 0.0 0.0 F 8 8 0 2 5 9 266 - 4 0 . 6 0 C 0 3 2 . 8 4 3 8 0.0 0.0 F 881 2 5 9 267 - 1 1. 5520 5.9102 0.0 0.0 F ( — 1 A L G . " T E S T 0ATA=BCH.138 START=F 0 9 : 2 5 P.M. J U L Y 2 4 . 1 9 7 7 PAGE 12 •ft************************************************************************************************************ L I N E I N F O R M A T I O N L I N E # 8 8 2 8 8 3 884 9 9 L I N E NAME S . E . 260 2 6 0 260 9 0 R.E. 261 262 263 91 PER UNIT R - 0 . 0 7 3 0 - 0 . 4 5 1 4 - 0 . 1 0 4 7 0.0 PER UNIT X 0 . 3 2 5 0 0.6506 0 . 2 2 0 8 0 . 0 9 6 8 S . E . S U S E P . R . E . SUSEP. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 . 4 0 6 0 0 T X 7 F F F T oo 00 

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