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Load sharing schemes in multiple induction motor drive applications using volts per hertz control Iyer, Jaishankar 2011

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LOAD SHARING SCHEMES IN MULTIPLE INDUCTION MOTOR DRIVE APPLICATIONS USING VOLTS-PER-HERTZ CONTROL  by Jaishankar Iyer  B.E., The University of Mumbai, India, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCES in THE FACULTY OF GRADUATE STUDIES (Electrical and Computer Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  December 2011  © Jaishankar Iyer, 2011  Abstract Multi induction-motor (IM) drives are commonly used to share a mechanical load in a wide range of industrial applications. In many existing auxiliary applications, the traditional lowcost Volts-per-Hertz (V/F) drives are typically used in speed control mode to simultaneously operate several IMs.  In multi-machine load-sharing applications, it is preferred to have number of identical IMs to share the load equally. Under ideal conditions, the identical IMs would operate with equal loading. However, in practice deviations of the load sharing among the IMs is possible due to many factors including variations in internal or external parameters and operating conditions of each individual IM. Such deviations may result in disproportionate sharing of the mechanical load and even overloading one or several machines while some machines may be under-loaded. The basic low-cost variable frequency drives (VFDs) with traditional open-loop V/F control scheme fail to share the load under such conditions.  In this Thesis, two new methods are proposed to address the load sharing problems under an internal disturbances (such as rotor resistance variations) and external disturbances (such as wheel slippage due to snow/water/oil etc.). The new methods are shown to be effective in sharing the load under disturbances. Moreover, the proposed methodologies may be readily extended to an arbitrary number of motors driving a common mechanical load, and are easy to implement with traditional/existing low-cost VFDs, which may be advantageous for many existing or legacy applications.  ii  Preface A version of Chapter 3 has been published in the following manuscript: Jaishankar Iyer, Kamran Tabarraee, Sina Chiniforoosh, and Juri Jatskevich, “An improved V/F control scheme for symmetric load sharing of multi-machine induction motor drives,” In proc. 24th IEEE Canadian Conference on Electrical and Computer Engineering, Niagara Falls, Ontario, Canada, 2011. I identified the problem, developed the Matlab/Simulink® models, and wrote most of the manuscript, while the conducted research was supervised by Dr. Juri Jatskevich. The manuscript was revised, iterated and discussed among all co-authors, my fellow colleagues Kamran Tabarraee and Sina Chiniforoosh, and my supervisor Dr. Juri Jatskevich.  A version of Chapter 4 has been published in the following manuscript: Jaishankar Iyer, Mehrdad Chapariha, Kamran Tabarraee, Milad Gougani, and Juri Jatskevich, “Load Sharing in V/F Speed Controlled Multi-motor Drives,” In proc. 7th IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, 2011. I identified the problem, developed the Matlab/Simulink® models, devised the solution and wrote most of the manuscript, while the conducted research was supervised by Dr. Juri Jatskevich. The manuscript was revised, iterated and discussed among all co-authors, my fellow colleagues Mehrdad Chapariha, Kamran Tabarraee and Milad Gougani, and my supervisor Dr. Juri Jatskevich.  iii  Table of Contents Abstract .................................................................................................................................... ii Preface ..................................................................................................................................... iii Table of Contents .................................................................................................................... 1 List of Tables ........................................................................................................................... 4 List of Figures .......................................................................................................................... 6 Acknowledgements ............................................................................................................... 10 Dedication .............................................................................................................................. 11 1  2  3  Introduction ................................................................................................................. 12 1.1  Motor Load Applications in Industry ................................................................. 12  1.2  Variable Frequency Drives in Industrial Applications ....................................... 13  1.3  Multi-Motor Load Sharing .................................................................................. 16  1.4  Thesis Composition ............................................................................................ 19  Modeling of Induction Machines and Variable Frequency Drives ............................. 20 2.1  Modeling ............................................................................................................. 20  2.2  Induction Machine Modeling .............................................................................. 20  2.3  Variable Frequency Drive Modeling .................................................................. 24  Load Sharing under Rotor Resistance Variation ........................................................ 26 3.1  Introduction ......................................................................................................... 26  3.2  Induction Machine Steady State Torque ............................................................. 26  3.3  Rotor Resistance Variation and Load Sharing Disparity .................................... 31  3.4  Load Sharing Using Speed Reference Compensation Method Based on Rotor  Resistance ....................................................................................................................... 35  1  3.5  Load Sharing Using Speed Reference Compensation Method Based on Current  Feedback ......................................................................................................................... 40 3.6  4  3.6.1  Physical test bench set-up ............................................................................... 43  3.6.2  Experimental procedure of load sharing and results from VFD interface ...... 48  3.6.3  Steady state measurements and calculations................................................... 52  3.6.4  Verification of model using simulation of the physical set-up ....................... 55  Load Sharing under Wheel Slippage in Vehicular Application.................................. 62 4.1  Motivation ........................................................................................................... 62  4.2  Concept of Torque Transfer and Wheel Slippage............................................... 63  4.3  Adhesion, Tractive Force, and Vehicular Motion .............................................. 64  4.4  Induction Motor Load in a Gantry Crane Application........................................ 70  4.5  System Model and Performance under Wheel Slippage..................................... 73  4.5.1 4.6 4.6.1 5  Experimental Verification of the Proposed Load Sharing Scheme .................... 43  System performance without load sharing ...................................................... 77 Proposed Methodology for Improved Load Sharing under Wheel Slippage ...... 80 Computer studies demonstrating the proposed methodology ......................... 83  Conclusion .................................................................................................................. 86 5.1  Summary ............................................................................................................. 86  5.2  Future Research .................................................................................................. 87  References .............................................................................................................................. 88 Appendices ............................................................................................................................. 94 Appendix A ..................................................................................................................... 94 Appendix B ..................................................................................................................... 96  2  Appendix C ..................................................................................................................... 97 Appendix D ..................................................................................................................... 98  3  List of Tables Table 3-1  Electromagnetic torque developed by IM1 and IM2 under rotor resistance variation using the conventional V/F scheme without compensation. ................................................................................................. 34  Table 3-2  Electromagnetic torque developed by IM1 and IM2 under rotor resistance variation using the proposed load sharing compensation scheme............................................................................................................. 38  Table 3-3  Individual motor torques under different loading conditions for conventional scheme without load sharing compensation scheme. ................ 40  Table 3-4  Individual motor torques under different loading conditions for proposed load sharing compensation scheme. ................................................ 40  Table 3-5  Torque current read from the DriveExplorer® software interface: (a) without compensation; and (b) with proposed compensation for load sharing. ............................................................................................................ 49  Table 3-6  Torque current calculated from the measured data: (a) without compensation; and (b) with proposed compensation. ..................................... 53  Table 3-7  Torque current calculated from the simulated results with and without proposed load sharing compensation. ............................................................. 60  Table 4-1  Sample parameters of the gantry crane used in the simulation. ...................... 73  Table 4-2  Surface adhesion factor parameters for steel wheel on steel rail in dry and slippery conditions. .................................................................................. 74  Table 4-3  Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage without using the proposed load sharing compensation scheme. ................................ 79  4  Table 4-4  Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage using the proposed load sharing compensation scheme. ................................................ 85  5  List of Figures Figure 2.1  Role of machines in different types of industrial loads (a) roller table (©Danieli Centro Combustion) [1]; (b) mill motors (©Eastport trading co. Inc) [2]; (c) processing lines (©Danieli Wean United) [3], (d) crane application (©Thyssenkrup Steel) [4]. ............................................................ 13  Figure 2.2  Torque-speed characteristics for a commanded speed of 188 rad  sec  for  an IM at different loading conditions.............................................................. 16 Figure 2.3  Different load sharing configurations: (a) multiple motors driven by individual drives; and (b) multiple motors driven by a single drive unit........ 17  Figure 2.1  Control schematics for an induction model based on qd reference frame. .............................................................................................................. 23  Figure 2.2  Control schematics for V/F controller. ........................................................... 25  Figure 3.1  Steady state equivalent circuit of an induction machine. ................................ 27  Figure 3.2  Torque-speed characteristics for parameter variation in a 3HP IM: (a) rotor resistance; (b) stator resistance; (c) stator leakage inductance; and (d) magnetizing inductance. ............................................................................ 29  Figure 3.3  Torque-speed characteristics for parameter variation in a 50HP IM: (a) rotor resistance; (b) stator resistance; (c) stator leakage inductance; and (d) magnetizing inductance. ............................................................................ 30  Figure 3.4  Block diagram of Volt / Hertz control scheme. .............................................. 32  Figure 3.5  Block diagram for load sharing between two V/F controlled induction motors under conventional speed referencing. ............................................... 33  Figure 3.6  Torque-speed characteristics of two coupled induction motors, with  6  rotor  resistance  variation,  sharing  a  common  load  without  compensation. ................................................................................................. 34 Figure 3.7  Block diagram of the proposed scheme for load sharing between two V/F controlled induction motors. .................................................................... 37  Figure 3.8  Torque-speed characteristics of two coupled induction motors, with rotor resistance variation, sharing a common load with compensation. ......... 37  Figure 3.9  Load sharing of two coupled IM’s with rotor resistance variation under different loading conditions. ........................................................................... 39  Figure 3.10  Proposed load sharing compensation scheme under rotor resistance variation. ......................................................................................................... 41  Figure 3.11  Mechanical load of 8.1 N.m shared between the coupled IM’s: (a) without compensation; and using proposed speed compensation based on (b) rotor resistances; and (c) current feedback ........................................... 42  Figure 3.12  Physical set-up for verification of the proposed scheme. ............................... 44  Figure 3.13  Load sharing motor test bench used for the practical observations. ............... 45  Figure 3.14  VFD’s used for powering the load sharing motors. ........................................ 46  Figure 3.15  PLC used to control the drives running the load sharing motors. ................... 47  Figure 3.16  Torque and flux component of the motor current. .......................................... 48  Figure 3.17  Screenshots of the DriveExplorer® software interface for the VFD 1 and VFD 2 without load sharing compensation. ............................................. 50  Figure 3.18  Screenshots of the DriveExplorer® software interface for the VFD 1 and VFD 2 with load sharing compensation. .................................................. 51  Figure 3.19  Measured line currents for Motor 1 (1HP) and Motor 2 (5HP): (a)  7  without  compensation;  and  (b)  with  proposed  load  sharing  compensation. ................................................................................................. 52 Figure 3.20  Phasor diagram of voltage and current for Motor 1 (1HP) with and without the proposed load sharing compensation. .......................................... 54  Figure 3.21  Phasor diagram of voltage and current for Motor 2 (5HP) with and without the proposed load sharing compensation. .......................................... 54  Figure 3.22  Measured and simulated line voltages and currents for Motor 1 (1HP) without load sharing compensation. ............................................................... 55  Figure 3.23  Measured and simulated line voltages and currents for Motor 2 (5HP) without load sharing compensation. ............................................................... 56  Figure 3.24  Measured and simulated line voltages and currents for Motor 1 (5HP) with load sharing compensation...................................................................... 57  Figure 3.25  Measured and simulated line voltages and currents for Motor 2 (5HP) with load sharing compensation...................................................................... 58  Figure 3.26  Simulation results for the load sharing without compensation and with the proposed compensation. ............................................................................ 60  Figure 4.1  Gantry crane running on a set of rails with IM driven wheels. ....................... 64  Figure 4.2  Graph depicting general relationship between surface adhesion factor   a and slip-speed for different road conditions. ............................................ 66 Figure 4.3  Graph depicting general relationship between speed correction factor   c and vehicle speed. ...................................................................................... 67 Figure 4.4  Diagram showing different speeds and forces acting on the wheel. ............... 68  Figure 4.5  Slip-stick phenomenon at the contact surface of wheel and rail. .................... 69  8  Figure 4.6  Top view of the gantry crane showing the different speeds and tractive forces. .............................................................................................................. 71  Figure 4.7  Block diagram for conventional load sharing between two V/F controlled induction motors under resilient or stochastic coupling. ............... 72  Figure 4.8  Surface adhesion factor vs. slip speed for parameters listed in Table 4-2. ..... 75  Figure 4.9  Block diagram of the simulation model for the wheel and vehicle dynamics of the gantry crane. ......................................................................... 76  Figure 4.10  Results of wheel slip under conventional V/F control without the proposed load sharing scheme: (a) wheel and vehicle speed; (b) total tractive effort; (c) surface adhesion factor of Wheel 1 and Wheel 2; and (d) load torque on Wheel 1-IM1 and Wheel 2-IM2. ....................................... 78  Figure 4.11  Moment of force vector on the axle under wheel slip with conventional V/F control without the proposed load sharing scheme. ................................ 79  Figure 4.12  Trace of adhesion at different rail conditions vs. slip speed. .......................... 81  Figure 4.13  Proposed change in the speed referencing of the drive powering the wheels of a gantry crane under wheel slippage. ............................................. 82  Figure 4.14  Block diagram of the proposed scheme for improved load sharing between two V/F controlled induction motors under wheel slippage............. 82  Figure 4.15  Results of wheel slip under the proposed load sharing scheme: (a) wheel and vehicle speed; (b) total tractive effort; (c) surface adhesion factor of Wheel 1 and Wheel 2; and (d) load torque on Wheel 1-IM1 and Wheel 2-IM2. ............................................................................................................. 84  9  Acknowledgements I would like to express my deepest appreciation and gratitude to my research supervisor, Dr. Juri Jatskevich, for allowing me to conduct research under him and whose strong academic support and dedication to his students have been the most precious assets. I am also very thankful for the financial support of my thesis project through Dr. Juri Jatskevich’s research grants, which made it both possible and relevant to many practical and industrial applications.  I also would like to thank Dr. Dommel and Dr. Dunford, who have accepted to be on the examining committee and dedicated their time and effort for evaluating my thesis. I owe a huge debt to my mom and dad who have supported and guided me throughout my life. My special thanks also go to my friends and colleagues at the UBC’s Electrical Energy and Power Systems Group who have always supported me and gave their valuable comments and feedback for my research. My previous three-year experience at Siemens Ltd., also helped me to look at the problems from the system level while keeping in mind that a practical solution should be simple and cost effective to find its way into implementation.  Last and but not the least, thanks to all my friends and everyone who intentionally or unintentionally played a part in my life and helped me mold myself into the person I am today.  10  Dedication Mom and Dad,  I Love you, this one is for you.  11  1  1.1  Introduction  Motor Load Applications in Industry  Industrial loads vary in sizes, type of functionality, range of operation, nature of surroundings, etc. The type of motors used varies as per the application. Main-Mill motors, auxiliary motors, pump motors, roller table or conveyor motors, crane motors, high precision / position controlled motors, etc., may be realized using synchronous motors, induction motors, conventional brushed DC motors and permanent magnet brushless DC motors. Figure 1.1 shows different types of industrial applications, wherein multiple motors are used.  Of all the types of motors used in industrial applications, the induction machines (IM) are the most widely used because of their simple but yet rugged construction and low cost. The squirrel cage design is the commonly used type of IMs because of the simple construction of the rotor winding, which makes them robust and requires low maintenance. The squirrel cage induction machines are easy to manufacture as compared to the wound-rotor type. For these reasons, the conventional squirrel cage IMs are generally preferred by the manufacturers and the end-users for many applications.  12  (a)  (c) Figure 1.1  1.2  (b)  (d)  Role of machines in different types of industrial loads (a) roller table (©Danieli Centro Combustion) [1]; (b) mill motors (©Eastport trading co. Inc) [2]; (c) processing lines (©Danieli Wean United) [3], (d) crane application (©Thyssenkrup Steel) [4].  Variable Frequency Drives in Industrial Applications  The IM on its own is difficult to control under the fixed frequency source. The steady state torque-speed characteristic is very nonlinear over the entire speed region and is typically usable only in the region close to the synchronous speed. Hence, an IM cannot be used alone  13  in many industrial applications which require wide range of controlled motion. Several simple power-electronic-based control systems are employed in industry to control the operation of induction machines. The variable frequency drives (VFDs) provide the most efficient and effective way of motor control. The aim of control is usually mechanical speed or output torque of the machine. The VFDs can range from advanced vector-controlled schemes wherein the torque control may be achieved almost instantaneously, to the conventional Volts-per-Hertz (V/F) scalar control which relies on steady-state torque-speed relationship of the machine to deliver the required speed or torque, which may also be used either in open-loop or in a closed-loop with speed regulator.  Vector controlled VFDs are advantageous because of their capability of delivering both speed and torque control with remarkable accuracy which can be used to implement advanced load sharing schemes such as torque-follower or trim control [5]. For example, the Allen Bradley PowerFlex 700 series vector controlled drives from M/s Rockwell Automation have speed regulation of around 0.1% to 0.001% in speed control mode and a torque regulation of ±5% without feedback to ±2% with feedback in torque mode [6]. Hoever, such advanced VFDs are typically very expensive and may not be financially justified for many applications. The choice of the drive is dependent on the type of application. Main mill motors, tension controller, etc., may require high precision torque control and hence would typically need the vector-controlled VFDs.  The advanced control strategies make the vector drive an expensive choice [7] and hence these drives are not popular for normal applications which form a large percentage of  14  industrial processes. It is not financially viable to use vector-controlled VFDs for these applications because it will involve a huge capital investment. The applications such as roller tables, conveyor belts, cooling fans, crane wheel motors, and etc. still make use of traditional volts/hertz control because of its low cost. The basic V/F VFD controllers however only work in speed control mode where the output speed is regulated through a speed feedback, but such VFDs are generally low-cost. The V/F VFD is a speed controller which takes advantage of induction machines torque-speed characteristic in its stable region. In this region, the machine mechanical speed is close to the electrical speed of the voltage which the machine is fed with. The drive control sets the frequency, and then based on that frequency adjust the voltage to prevent the saturation while maintaining flux. The drive varies the voltage and frequency input to alter the torque-speed characteristics such that the torquespeed characteristic intersects the load curve at the commanded speed. Figure 1.2 shows how the torque-speed curve of a 5HP IM (Hyundai® Inverter Shield ™ Premium Efficiency. Specifications are given in Appendix A) is changed to meet the various load requirements at a particular rotor speed of 188 rad  sec  . We can see that the base frequency changes along  with the loading of the IMs. This can be seen by looking at the machine speed at zero torque, i.e. the synchronous speed. As the loading is increased the frequency is increased, however the V/F ratio is maintained.  15  Figure 1.2  Torque-speed characteristics for a commanded speed of 188 rad  sec  for an IM at  different loading conditions.  1.3  Multi-Motor Load Sharing  Some applications need multiple motors to work in tandem or in parallel. The reasons for using multiple motors may vary from lack of space for big motors resulting in the use of several coupled motors of smaller ratings in tandem, to process requirement of parallel motors. Process such as Mills, conveyor belts, roller tables, cranes, etc., cannot work with just one motor. They need more than one motor working in parallel to drive the common mechanical load. In such applications, load sharing is naturally required, and it is important to maintain the speed and the torque of the participating motors the same or in some proportion as required by the process.  16  Load sharing is essentially an arrangement where a common load is shared by multiple motor-drive sets [5], [8]. There are different possible configurations available for powering the load sharing motors. Figure 1.3 shows two such different schemes in multi-motor applications. In Figure 1.3(a), a multiple motor-drive set (motors driven by individual dedicated drive) is used to share the load. In Figure 1.3(b), multiple motors driven by single VFD are used; hence individual control of the motors is not possible and the load sharing occurs naturally and uncontrollable. However, in Figure 1.3(a), it is seen that the motors can be individually controlled by the corresponding VFDs. Hence, only the configuration of Figure 1.3 (a) can be used for effective re-distribution of the load among the motors and achieving effective load sharing under various disturbances. Therefore, this configuration is considered in this thesis. LOAD  LOAD Speed feedback  Speed feedback  VFD1  IM1  VFD2  IM2  IM2  VFDn  IMn  IMn  (a) Figure 1.3  VFD  IM1  (b)  Different load sharing configurations: (a) multiple motors driven by individual drives; and (b) multiple motors driven by a single drive unit.  In multi-motor applications, even if the overall control scheme aims to maintain and control the speed, the internal torque control might be required to share the torque between several 17  motors in order to prevent overloading, over-heating and malfunction of a single motor or the whole system. While the greater part of the drives used in industry are using standard V/F control scheme, it will be required to study the methods to share the torque among such drives in different situation including variations of machine parameters, different motors, or different loading conditions, etc. Thus, this thesis considers the most common type V/F VFDs, unless otherwise explicitly mentioned.  Under load sharing using V/F controller, the torque delivered by the individual participating motor depends on the motor parameters, the command speed and the load on that motor, etc. Without loss of generality, this thesis considers a system with two IMs sharing a common mechanical load. Under ideal conditions, the motor parameters are identical, the commanded speeds are the same, and the loading on each motor would be equal. If the IMs are not identical but are of different rating, then their load may need to be split proportionally to their power rating, which would be a more general scenario. But when the conditions deviate from ideal, e.g. changing rotor resistance or a change in the individual loading, etc., then the torque delivered by the IM will also differ. The machines would become unequally loaded with one motor getting overloaded. The research in my thesis is mainly focused on two such instances where the load sharing is changed due to the following: 1. Variations in the parameters of one of the motors (e.g. rotor resistance) due to temperature variations, use of a replacement motor with different rotor parameters, defective rotor, etc. These variations constitute internal disturbance. 2. The load distribution among the motors may be affected due to changes in external conditions (e.g. wheel slippage). These variations constitute external disturbance.  18  1.4  Thesis Composition  The thesis is comprised of the following Chapters:   Chapter 2 presents the concept of various motor drives and presents the basic model that is used for the studies in this thesis.    Chapter 3 discusses the problem of load sharing between induction motors with different rotor resistances which may be caused by parameter deviations. It provides a solution to improve the load sharing under such variation. The Chapter also shows results from an experimental set-up used to verify the proposed scheme.    Chapter 4 discusses the problem of load sharing among induction motors in vehicular or crane applications, where the wheel slippage may occur. A new methodology is presented to improve the load sharing under the considered disturbances.    Chapter 5 concludes the thesis by summarizing the contributions of conducted research and briefly mentions the future research directions that may be taken beyond my thesis.  The parameters of all induction motors, VFD specifications, software specification and digital power meter specification are all summarized in Appendices in appropriate Sections.  19  2  2.1  Modeling of Induction Machines and Variable Frequency Drives  Modeling  There are various simulation packages available today that can be used very effectively to model the electrical components and networks [9], [10], [11], [12], [13], [14], and many of which can be used for modeling the induction motor drives. The computer simulations, if the models and parameters are correct, should produce results very similar to actual system but at the same time should be fast and simple to execute [15], [16]. The simulation can then be used as a very effective tool for designing and improving the actual physical motor drive systems and their applications. The models developed in this Chapter will be used to analyze the load sharing phenomenon and verify the proposed methodologies presented in the subsequent Chapters.  2.2  Induction Machine Modeling  The classical model for induction machines is the qd model [17], which has been wellknown and used for many years, and is considered sufficient in terms of its assumptions and accuracy for the purpose of this thesis. The model is based on the reference frame theory [18], [19], [20], [21], [22]. In this thesis, a symmetrical squirrel cage induction motor is considered, wherein the zero sequence is neglected due to the assumed Y-connection of the stator winding with floating neutral point. The corresponding voltage equations in qd reference frame can be expressed as  v qds  rs i qds   λ dqs  p λ qds ,  (2.1)  20  vqdr  rr iqdr    r  λdqr  p λ qdr  0 ,  (2.2)  where the voltage, current and flux linkages are represented in vectors such that    f qd  f q  fd    T  , where f can be voltage, current or flux linkages. The stator and rotor  resistance matrix are represented by rs  diagrs    and (2.2), λ dq  d    rs  rs  , and rr  diagrr rr rr. In (2.1)   q and p denotes operator T  d . The remaining variables are dt  defined as follows:  vqs , and vds are the voltages at q axis, and d axis of the stator,  are the voltages at q axis, and d axis of the rotor,  , and vdr vqr rs , and rr are the stator and rotor resistances,  iqs , and ids are the currents at the q axis, d axis of the stator, iqr , and idr are the currents at the q axis, d axis of the rotor,  qs , and ds are the flux linkages at the q axis, d axis of the stator, qr , and dr are the flux linkages at q axis, d axis of the stator,  , and  r are the electrical speeds of the reference frame and rotor speed.  The flux linkages used in the above equations can be expressed as :  λ qds  Lls i qds  LM i qds  iqdr ,  (2.3)  λqd 0r  Llr iqd 0r  LM i qds  iqdr ,  (2.4)  where Lls , Llr , and LM are the stator and rotor leakage inductances and the magnetizing inductance. The leakage inductance and magnetizing inductance are combined to  21  give Ls  Ll  LM . The inductances are converted into the corresponding reactances by X   b L . The flux linkages in the equations (2.1) to (2.4) can be rewritten in flux linkages  per second using variable  and base frequency, b  2  f , as  ψ qd  λ qd b .  (2.5)      where the flux linkages per second are represented in vectors such that ψ qds   qs  ds . T  The developed electromagnetic torque is calculated as   P  3  1  Te         ds iqs  qs ids  .  2   2   b   (2.6)  The real power at the machine terminals is calculated as   3 Pe    vqs iqs  vds ids  . 2  (2.7)  The above equations are realized in the qd model of the induction machine as shown in Figure 2.1  22  Figure 2.1  Control schematics for an induction model based on  qd reference frame.  23  2.3  Variable Frequency Drive Modeling  To study the operation of multi-motor systems with VFDs, modeling is indispensable [17]. The basic VFD with V/F control is used in the industry in most of the cases because to its low cost, and this drive is assumed in this thesis. The control operates under two principles: 1. The rotor speed in the motoring region of an IM is proportional to the input electrical frequency 2. To avoid machine saturation, the voltage-per-frequency ratio input to the motor should be constant (uncompensated approach). These principles result in the following relationships for the voltage and frequency:  V  Vs   b   e* , b  here e*   P * rm , 2  (2.8)  (2.9)  where Vb and b are the rated base voltage and base electrical frequency of the IM; e* and * are the commanded electrical frequency and approximate mechanical speed. The model rm  considered in this thesis is implemented according to the methodology defined in [[17], Chap. 14] and the diagram shown in Figure 2.2.  24  Figure 2.2  Control schematics for V/F controller.  25  3  3.1  Load Sharing under Rotor Resistance Variation  Introduction  The traditional/basic V/F IM drives operate only using speed command signals, and the developed torque is consequently determined according to the torque-speed characteristics of the machine. As the developed torque is a function of rotor resistance, in load-sharing applications, particularly, deviations among the rotor resistance values is probable and will result in disproportionate sharing of the mechanical load and hence overloading of one or several machines. In this thesis, a solution for the above issue is presented in the form of an improved V/F scheme, which compensates for the parameter change by adjusting the command speed reference signals accordingly. The proposed method is shown to be effective and easy to implement, and may be readily extended to an arbitrary number of motors or to the case where dissimilar motors are coupled and the mechanical torque is intentionally distributed unevenly among the machines according to their ratings.  3.2  Induction Machine Steady State Torque  The steady state electromagnetic torque developed by an IM is given by [23] Te  3  P Vth2 rr s ,  2 2 e Rth  rr s    X th  X lr 2  (3.1)  where V th , Rth , and X th are the Thevenin equivalent circuit parameters obtained from the steady state equivalent circuit of Figure 3.1 and s is the rotor slip.  26  Is  rs  Lls  Llr  I'r  Im Vs  Lm  Figure 3.1  Thevenin Equivalent  rr' s  Steady state equivalent circuit of an induction machine.  The stator side of the induction machine can be combined with the magnetizing inductance using Thevenin equivalence. The resulting voltage, resistance and reactance can be calculated as follows: Vth   Vs  j X M  , rs  j  X ls  X M   (3.2)  Rth   rs X M ,  X ls  X M   (3.3)  X th   X ls X M ,  X ls  X M   (3.4)  where V s is the voltage input (per phase) to the IM stator; and  e is the stator electrical frequency.  In the motoring region, where the slip is typically low, (3.1) may be approximated as P Vth2 rr s P Vth2 s . Te  3 3 2  e rr s 2 2  e rr  (3.5)  Equation (3.5) shows that the torque has strong dependence on the rotor resistance and slip and the Thevenin voltage. Changes in these variables will affect the developed torque. Slip is 27  mechanical load dependent. The next step would be to find the sensitivity of the torque toward a change in the remaining electrical parameters V th and rr , the two variables in (3.5).  The Thevenin voltage V th depends on the motor parameters rs , X ls , X M and the source voltage Vs as seen in (3.2). The source voltage Vs is normally regulated by the drive and hence can be considered as constant. Thus to measure the sensitivity dependence of Te on  V th and rr , the effects of variation of the motor parameters rs , rr , X ls , and X M on Te have to be studied. The parameters of 3HP and 500HP IM’s (given in the Appendix A) from [17] and [24] were considered here, and the steady-state torque speed curves were plotted for parameter variations of 130% to 70%. The parameters were changed sequentially and the results are plotted in Figure 3.2 and Figure 3.3.  28  Figure 3.2  Torque-speed characteristics for parameter variation in a 3HP IM: (a) rotor resistance; (b) stator resistance; (c) stator leakage inductance; and (d) magnetizing inductance.  29  Figure 3.3  Torque-speed characteristics for parameter variation in a 50HP IM: (a) rotor resistance; (b) stator resistance; (c) stator leakage inductance; and (d) magnetizing inductance.  30  In Figure 3.2 and Figure 3.3, it is seen that in the motoring region, rotor resistance variation had the most noticeable effect with the operating torque increasing with the decrease in the rotor resistance. This is seen in Figure 3.2 (a) and Figure 3.3 (a). Similar studies were also done on 50HP and 2250HP IMs, which also showed comparable results. Thus, it can be deduced that rotor resistance variation has the most observable impact on the motoring torque and hence this variation was considered for the thesis. The variations in the rotor resistance may naturally occur due to temperature variations, replacement of motors with previously repaired motors, use of non-identical motors, etc.  The sensitivity of the torque also depends on the slope of the torque-speed curve in the motoring region. The IMs with smaller rotor resistance and steeper slopes have higher sensitivity and hence are more vulnerable to large torque fluctuations under small changes in the rotor resistances. Therefore, motors with higher rotor resistance are preferred for load sharing applications as they have higher slip and hence much gentler slope in the motoring region [25]. However, high-slip motors have higher copper loss and are less efficient. Instead, machines with lower rotor resistance are generally preferred to reduce the losses, and such IMs have steeper slopes in the motoring region.  3.3  Rotor Resistance Variation and Load Sharing Disparity  The rotor resistance of the two rigidly-coupled IMs may not be similar. It is highly unlikely that even the motors coming from the same manufacturer will have exactly the same rotor resistances. Moreover, the rotor resistance changes with loading and temperature. The equivalent rotor resistance also changes with the frequency of the rotor currents and slip due  31  to the deep-rotor-bar effect, which depends on the rotor design [23], [26].  The diagram of Figure 2.2 is simplified here and depicted in Figure 3.4. The ramp, PI controller and the speed limit blocks of Figure 2.2 is masked under the “Speed-ControlRegulator” block. The VSI block is the actual hardware of the drive consisting of the switching devices which was shown as “ qd to abc transformation block” in Figure 2.2. Speed feedback  Speed Command  Figure 3.4  Speed Control Regulator  V/F Control  VSI  IM  Block diagram of Volt / Hertz control scheme.  A conventional scheme of multi-motor speed referencing is shown in Figure 3.5. Two motors are rigidly coupled to share the common mechanical load. The input to the V/F control block is the PI controlled difference between the speed feedback and the speed command. In rigidly coupled multi-motor applications, all motors are coupled to each other and hence have a common speed feedback. The PI corrected speed commands for both the VFDs are the same and similar voltages and frequencies are injected into the coupled IMs. Thus, the similarity in the torque developed by the two motors will depend on the rotor resistance of each IM.  32  Speed feedback  Speed Command  Speed Control Regulator  V/F Control  VSI  IM1 LOAD  Speed Control Regulator  Figure 3.5  V/F Control  VSI  IM2  Block diagram for load sharing between two V/F controlled induction motors under conventional speed referencing.  In the following discussion, two IMs rated 1HP each (as per Appendix A) are simulated to share a mechanical load of 8.1 N.m at 188 rad  sec  . The V/F drive and IM are modeled using  (2.1) to (2.9). The inertia of the load is considered to be 0.02 kg.m 2 . The machines (without rotor resistance variation) are both rated to generate a full load torque of 4.05 N.m . Both IMs are identical in all respects, except the rotor resistances which are set to 5.06  and 7.41  for IM1 and IM2, respectively. The resultant torque-speed characteristic of each IM is shown in Figure 3.6. It is observed that, as predicted by (3.5), the motor with the smaller rotor resistance, IM1, carries a higher percentage of the load than the other motor. The values of electromagnetic torque developed by the machines are provided in Table 3-1. It can be seen that IM1 is overloaded to 118% whereas IM2 is operating below the rated torque by 18%. The problem may become more severe from the process point of view, because the overloading may force one or more IMs to operate closer to the breakdown region. In this case, the entire process may become susceptible to breakdown as there is a possibility that the overloaded machine would be isolated either by circuit tripping or by breakdown. The  33  rest of the system might not be able to carry the extra load and leading to stoppage of the production line.  Figure 3.6  Torque-speed characteristics of two coupled induction motors, with rotor resistance variation, sharing a common load without compensation.  Table 3-1  Electromagnetic torque developed by IM1 and IM2 under rotor resistance variation using the conventional V/F scheme without compensation.  IM1 ( rr1  5.06  )  IM2 ( rr 2  7.41  )  Te1  Nm   Te1 Trated 1  Te2  Nm   Te 2 Trated 2  4.77  118%  3.33  82%  34  3.4  Load Sharing Using Speed Reference Compensation Method Based on Rotor  Resistance In the previous Section, it was shown that the electromagnetic torque is sensitive to the rotor resistance, the input voltage and the input frequency. Thus, the participating torques in the load sharing are seldom even or constant. In order to keep the torques of the coupled motors equal under rotor resistance variation, we should change the input voltage and frequency equivalently to compensate the system. This Section describes a methodology of changing the input frequency (the speed reference) so as to vary the torque-speed curve and thus achieve balanced load sharing among the coupled IMs. It is assumed that the rotor resistance variation is known or can be estimated using either temperature-dependent look-up tables or the online estimation methods [23]. Various methods have been proposed in the literature for estimating the rotor resistance, but otherwise such methods are outside of the scope of this thesis.  For two coupled IMs with different rotor resistances, (3.5) can be written as 2  Te1  3  P1 Vth1 s1 , 2 e1 rr1  2 P2 Vth2 s 2 . Te 2  3 2  e2 rr2  (3.6)  (3.7)  Herein, the suffix 1 and 2 correspond to IM1 and IM2, respectively. From (3.6) and (3.7) we can see that when rr1  rr 2 , the operating torques of these IMs are not the same. For these IMs to have the same operating torque, the right hand side of (3.6) and (3.7) should be equal.  35  3  P Vth21 s1 P Vth22 s2 3 . 2 e1 rr1 2 e 2 rr2  (3.8)  Solving (2.8), (3.2) and (3.8) for the electrical frequency of the second drive,  e 2 , we get:    X M 1   rr2   X S 2     X M 2   rr1   X S1  e 2  e1  r        r ,    (3.9)  where r is the rotor electrical frequency, and X S  X M  X ls .  If (3.9) is satisfied then both the IMs will generate the same electromechanical torque and equally share the load. Then, (3.9) is used to generate the corrected reference speed for the second drive in the proposed load sharing scheme. The new scheme is shown in Figure 3.7 where the “Speed reference compensation block” is formed using (3.9). The second drive is now operating without the speed control regulator block and the actual speed feedback is taken to the “Speed reference compensation block”. The speed reference to the second drive is varied as per the change in the rotor resistance. Employing the proposed approach, the improved load sharing is shown in Figure 3.8. Notice that the maximum torque is now different indicating that different voltages and frequencies are injected into the machines. It is also observed that the machines are running with different synchronous speeds unlike the case in Figure 3.6. Most importantly, the torque-speed characteristics of the machines now intersect near the commanded speed which results in almost equal values for torque.  36  Speed feedback  Speed Command  Speed Control Regulator  V/F Control  VSI  IM1  LOAD  Speed Reference compensation block  V/F Control  VSI  IM2  Speed feedback  Figure 3.7  Block diagram of the proposed scheme for load sharing between two V/F controlled induction motors.  Figure 3.8  Torque-speed characteristics of two coupled induction motors, with rotor resistance variation, sharing a common load with compensation.  37  Comparing the torque values in Table 3-2 with those of Table 3-1, it is seen that, using the proposed scheme, the load sharing between the machines has become more symmetrical and the overloading on IM1 is removed. Each of the motors now shares approximately 50% of the load. The proposed scheme can be readily extended to multiple motors (more than two). It can be realized in practice, by implementing the “Speed reference compensation block” in a PLC or similar logical device (assuming that the equivalent rotor resistance may be appropriately estimated online). The first drive is speed referenced as per the required speed and the second drive is speed referenced by the “Speed reference compensation block”.  Table 3-2  Electromagnetic torque developed by IM1 and IM2 under rotor resistance variation using the proposed load sharing compensation scheme.  IM1 ( rr1  5.06  )  IM2 ( rr2  7.41  )  Te1  Nm   Te1 Trated 1  Te2  Nm   Te 2 Trated 2  4.1  101%  4  99%  It is well understood that (3.5) holds true only when the slip is small and the machines operate near the synchronous speed. As load and slip increases, the torque-speed curve gradually loses its linearity. It is then expected that the performance of the proposed load sharing scheme would be very good under lighter loads and will start to deteriorate under heavily loads. In order to investigate the above mentioned characteristic, the IMs considered in this paper are subjected to 25%, 50% and 100% loading. The torque developed by the machines using the conventional and proposed V/F schemes has been superimposed in Figure 3.9.  38  As seen in this figure, using the proposed load sharing scheme, the loading of the machines is essentially equal at 25% load and has a difference of 2% at full load. However, using the conventional/uncompensated method, the load is never shared equally and the difference ranges from 10% at 25% load to 36% at full load. The results are summarized Table 3-3 and Table 3-4. As can be seen in these tables, the proposed compensation scheme significantly improves the load balancing between the considered IMs under light and heavy loads.  Figure 3.9  Load sharing of two coupled IM’s with rotor resistance variation under different loading conditions.  39  Table 3-3  Individual motor torques under different loading conditions for conventional scheme without load sharing compensation scheme.  IM1 ( rr1  5.06  )  Loading  Te1  Nm   Te1 Trated 1  Te2  Nm   Te 2 Trated 2  25%  1.21  30%  0.82  20%  50%  2.40  59%  1.65  41%  100%  4.77  118%  3.33  82%  Table 3-4  Loading  3.5  IM2 ( rr2  7.41  )  Individual motor torques under different loading conditions for proposed load sharing compensation scheme.  IM1 ( rr1  5.06  )  IM2 ( rr2  7.41  )  Te1  Nm   Te1 Trated 1  Te2  Nm   Te 2 Trated 2  25%  1.01  25%  1.01  25%  50%  2.03  50%  2.02  50%  100%  4.10  101%  4.00  99%  Load Sharing Using Speed Reference Compensation Method Based on Current  Feedback The scheme described above provides very good accuracy in torque sharing but requires rotor resistance estimation using various methods [23], which would add to the complexity and cost of the VFDs. A more practical and simpler approach may be required to share the torque under the rotor resistance variations. A simple but practical approach may be derived based equating the real component of the phase current (which sometimes is referred to as the torque current). The torque currents of the individual motors can be taken as a feedback and the signal can be used to alter the speed referencing of the drives. As the generated torque is approximately proportional to the torque current (real component of the phase  40  current), adjusting the torque current can control the generated torque of the IMs. A block diagram depicting this approach is shown in Figure 3.10. Speed feedback Speed Control Regulator  Speed Command  V/F Control  Torque current estimator  VSI  IM1  IM1 current LOAD  PID Torque current estimator Speed Control Regulator  IM2 current  V/F Control  VSI  IM2  Speed feedback  Figure 3.10  Proposed load sharing compensation scheme under rotor resistance variation.  Under normal operation, both motors IM1 and IM2 have equal rotor resistances and take equal torque currents. When the rotor resistance of IM1 drops from the rated rr  7.41  to  rr  5.06  , it starts taking higher percentage of the load. The difference in the currents (error current) are fed back to alter the speed reference of the VFDs such that the error current decreases. The simulation results are plotted in Figure 3.11. Also, in Figure 3.11 we have plotted the results from the speed compensation using resistance block scheme. In the considered study, the motors are assumed to be working with the same rotor resistance till  t  5 sec . At t  5 sec , the rotor resistance of IM1 decreases from rr  7.41  to  rr  5.06  . In practice, this may be a much slower change, but the study is focused on steady state before and after the change. It is seen that when this happens under the traditional method the motor torques start differing away from each other leading to 41  unbalanced loading. However, with the proposed compensation methods, the IMs remain in good balancing throughout the study.  Figure 3.11  Mechanical load of 8.1 N.m shared between the coupled IM’s: (a) without compensation; and using proposed speed compensation based on (b) rotor resistances; and (c) current feedback  42  3.6 3.6.1  Experimental Verification of the Proposed Load Sharing Scheme Physical test bench set-up  To check the validity of the proposed load sharing compensation scheme, we used the following experimental set up available in the Alpha Technology Lab, Kaiser 3075. The overview schematic of the test bench is depicted in Figure 3.12. In the considered motor bench with three machines shown in detail in Figure 3.13, two IMs rated 1HP and rated 5HP were coupled on a common shaft and assumed to be driving a common mechanical load emulated by the remaining third motor. The proposed scheme is implemented by using one of the motors, Motor 3 (1HP), as a load and the other motors (Motor 1 (1HP) and Motor 2 (5HP)) for driving this load. As two identical motors with dissimilar rotor resistances were not available, we used two dissimilar motors, 1HP and rated 5HP, for the experiment. These motors are powered using VFDs which are run in V/F control. The specifications of the VFDs used in the set-up are summarized in the Appendix B. The PLC is used to emulate the control as explained in the previous sections. The details of the PLCs hardware and software are listed in Appendix C. The experimental set up of the VFDs and PLC boxes are shown in Figure 3.14, and Figure 3.15, respectively.  In the considered configuration, Motor 1 (1HP) and Motor 2 (5HP) are speed referenced with 1507.3 rpm anti-clockwise direction; while the Motor 3 (1HP) is torque referenced to run at 100% loading clockwise to emulate a common mechanical load of 4.05 N.m . The excess energy from Motor 3 (1HP) is being dumped through the VFD 3 into an auxiliary breaking resistor box. However, as the PLC was not programmed during the course of the experiment, the above control (changing speed reference) was done manually using a computer  43  (Programming Station) over Ethernet/IP. A customized Rockwell Automation Software DriveExecutive and DriveExplorer were used for online monitoring of the drive parameters.  Figure 3.12  Physical set-up for verification of the proposed scheme.  44  Motor #1  Motor #3 Motor #2  Figure 3.13  Load sharing motor test bench used for the practical observations.  45  Figure 3.14  VFD’s used for powering the load sharing motors.  46  Figure 3.15  PLC used to control the drives running the load sharing motors.  47  3.6.2  Experimental procedure of load sharing and results from VFD interface  The current taken in by an IM comprises of a reactive component and a real component. The reactive component of the current is due to the leakage flux and magnetizing current, whereas the real component of the current is spend on the losses in the resistances and the rotor current which produces the torque (torque current). The real current is in-phase with the supplied voltage as depicted in Figure 3.16. In the following simplified analysis, it is assumed that the IM torque is generated by the real component of the current. Hence, to share the load, the Motor 1 (1HP) and Motor 2 (5HP) should carry the same torque current.  Figure 3.16  Torque and flux component of the motor current.  To emulate the needed conditions, the experimental set-up is run twice: once with identical speed reference for both the drives without the proposed load sharing scheme; and second time with the proposed improved load sharing scheme. To implement the proposed scheme, the speed reference of Motor 2 (5HP) is decreased to a point where the torque currents of both motors are similar. The torque currents are monitored in the DriveExplorer software (see Figure 3.17 and Figure 3.18). Based on results shown in Figure 3.17, we can see that initially both the VFDs were referenced with the same speed, and the individual load torque current for the Motor 1 (1HP) and Motor 2 (5HP) are unequal with second motor taking more load. The results of this study are summarized in Table 3-5, which shows that torque current 48  of Motor 2 (5HP) is 0.9A, whereas the torque current of Motor 1 (1HP) is around 0.2 A. This happens because in the motoring region of the torque speed curve at a shaft speed, the Motor 2 (5HP) has higher electromagnetic torque compared to the Motor 1 (1HP).  In the second study, with the speed reference compensation, these motors run with different operating frequency. The frequency change brings about a change in the torque-speed curve of the IMs. It is seen from Figure 3.18 that the load is now better shared between Motor 1 (1HP) and Motor 2 (5HP) and the torque currents are equalized. The motors now take 0.6 A and 0.7 A of the real currents, respectively. Please note that the total phase current of each motor will be different even with the proposed scheme due to the dissimilar motors that require different flux current. Another interesting observation is that initially the powerfactor of Motor 1 and Motor 2 were 0.16 and 0.29, respectively. With the proposed load sharing, the power-factor of Motor 1 (1HP) has improved to 0.49 due to the increase in the torque current of the motor, and Motor 2 (5HP) power-factor has dropped to 0.21 doe to reduction in load.  Table 3-5  Torque current read from the DriveExplorer® software interface: (a) without compensation; and (b) with proposed compensation for load sharing.  Motor 1 (1HP) Speed Torque Reference Current ( rpm ) (A) Without compensation With compensation  Motor 2 (5HP) Speed Torque Reference Current ( rpm ) (A)  Shaft Speed ( rpm )  1507.3  0.2  1507.3  0.9  1490  1507.3  0.6  1478.0  0.7  1460  49  Figure 3.17  Screenshots of the DriveExplorer® software interface for the VFD 1 and VFD 2 without load sharing compensation.  50  Figure 3.18  Screenshots of the DriveExplorer® software interface for the VFD 1 and VFD 2 with load sharing compensation.  51  3.6.3  Steady state measurements and calculations  The individual motor currents were measured using Yokogawa WT1600 (specification is summarized in the Appendix D). The measured phase currents were captured, saved, and are plotted in Figure 3.19 for the steady state conditions without and with the proposed compensation method. As we can see in Figure 3.19, the currents in the Motor 1 (1HP) increases and the currents in the Motor 2 (5HP) decreases when the proposed speed reference compensation is enabled to improve the load sharing. However, in the given experimental set-up, the currents should not be equal to each other as the machines and their magnetizing currents are different.  Figure 3.19  Measured line currents for Motor 1 (1HP) and Motor 2 (5HP): (a) without compensation; and (b) with proposed load sharing compensation.  52  To further validate the results, we have calculated the real component of the measured currents. This is done by calculating the phase difference between the respective phase voltages and phase currents and then calculating that component of the current which is in phase with the phase voltage. The results are summarized in Table 3-6. These results show that the balance between the torque currents and subsequently the load sharing has improved.  Table 3-6  Torque current calculated from the measured data: (a) without compensation; and (b) with proposed compensation.  Motor 1 (1HP) Speed Torque reference current (A) ( rpm )  Motor 2 (5HP) Speed Torque reference current (A) ( rpm )  Shaft Speed ( rpm )  Without compensation  1507.3  0.3  1507.3  1.4  1490  With compensation  1507.3  0.7  1478.0  1.1  1460  The corresponding voltage and current phasors are also plotted for Motor 1 (1HP) and Motor 2 (5HP) with and without the proposed compensation. The plots are shown in Figure 3.20 and Figure 3.21, respectively. As the torque sharing improves, the load on the previously lightly loaded Motor 1 (1HP) increases. This increases the real current of the machine, improving the power factor of the machine. This can be seen in Figure 3.20, where the angle between the voltage and current phasor corresponding to a particular phase has decreased from 1 to  2 . Thus, the proposed scheme, if used wisely, can improve the sharing and also improve the power factor.  53  Figure 3.20  Phasor diagram of voltage and current for Motor 1 (1HP) with and without the proposed load sharing compensation.  Figure 3.21  Phasor diagram of voltage and current for Motor 2 (5HP) with and without the proposed load sharing compensation.  54  3.6.4  Verification of model using simulation of the physical set-up  In this Section the previously developed model of the multi-motor drive system with verified against the physical set-up for two dissimilar motors. A load of 4.05 Nm equivalent to the load used in the physical set-up is used to load Motor 1 (1HP) and Motor 2 (5HP). The motor parameters are exactly equal to the ones used in the actual set-up. The measured and simulated voltage and current waveforms are shown in Figure 3.22 through Figure 3.25. It is seen that the simulated results match the measured data very well.  Figure 3.22  Measured and simulated line voltages and currents for Motor 1 (1HP) without load sharing compensation. 55  Figure 3.23  Measured and simulated line voltages and currents for Motor 2 (5HP) without load sharing compensation.  56  Figure 3.24  Measured and simulated line voltages and currents for Motor 1 (5HP) with load sharing compensation.  57  Figure 3.25  Measured and simulated line voltages and currents for Motor 2 (5HP) with load sharing compensation.  The simulation results are shown in Figure 3.26 and the corresponding values of the torques and currents are summarized in Table 3-7. Initially, the motors are assumed to run from the VFDs without the proposed compensation. Both the motors’ VFDs are speed referenced with 1507.3 rpm , similar to the physical set-up. It is seen that Motor 2 (5HP) takes most of the load and gets 3.5 N.m ; whereas the Motor 1 (1HP) gets loaded to 0.5 N.m . The torque 58  current of the motors are calculated using the Fourier transform of the current signal and then calculating the component of the current that is in phase with the voltage. These values are close to the ones observed from the test bench tabulated in Table 3-6. At t  2 sec the proposed load sharing scheme is switched on. It is seen that the frequency input for Motor 2 (5HP) decreases until the load torques are matched. The load sharing compensator changes the speed reference of the Motor 2 (5HP) such that the torque speed curve at the motoring region is changed and the motors start sharing the load between them equally. It is seen in Figure 3.26 that with enabled proposed control, the revised speed reference for the second motor has changed to 1484.3 rpm and the torque balancing is improved significantly. The load on the Motor 2 (5HP) reduces whereas the 1HP motor load increases to achieve the desired balance. The revised speed reference is not exactly equal to the ones in the set-up because in the physical model the speed is manually changed using the DriveExecutive software where the speed change is restricted to step size of around 15 rpm .  The motor real power mostly comprise of the resistive losses and the electromagnetic torque. Thus the real power reflects the torque loading of the machines. It is seen that the real power of the machines are different without compensation as seen in Figure 3.26. But when the compensator is switched on, the set-up starts to share the load. The real power of the Motor 2 (5HP) decreases as Motor 1 (1HP) becomes equally loaded.  59  Table 3-7  Torque current calculated from the simulated results with and without proposed load sharing compensation.  Motor 1 (1HP) Speed Torque Reference Current (A) ( rpm ) Without compensation With compensation  Figure 3.26  Motor 2 (5HP) Speed Torque Reference Current (A) ( rpm )  Shaft Speed ( rpm )  1507.3  0.3  1507.3  1.2  1500  1507.3  0.7  1484.3  0.7  1480  Simulation results for the load sharing without compensation and with the proposed compensation.  60  Based on the simulation studies and the experimental results, the proposed method is seen to not only improve the load sharing between similar motors but also dissimilar motors. The scheme also improves the power-factor of the system which is a considerable contribution. The proposed scheme should be wisely used when implementing for dissimilar motors keeping in mind the loading capacity of the individual motors. One way to generalize the proposed scheme is to share the load in relative proportion to the capacity of each participating IMs.  61  4  4.1  Load Sharing under Wheel Slippage in Vehicular Application  Motivation  It was seen in Chapter 3 that load sharing is a function of individual motor parameters, the load distribution among the motors, and the commanded speed of each motor. In this Chapter we extend the concept of load sharing control under the change in the load distribution that may occur in multi-motor systems such as vehicular platforms, rail cranes, etc. due to external factors such as wheel slippage.  IMs driven by basic Volts/Hertz controller are commonly used for driving the wheels of gantry cranes such as the one shown in Figure 1.1(d) and many other industrial applications. The torque developed by the propulsion motors generates the tractive force that moves the vehicular or a crane platform. If the contact between the surface or rail and the driving wheel is not the same among all participating wheels, then the adhesion and the tractive force generated by each wheel will be different leading to unequal loading of the driving IMs. In addition to the degradation of the vehicular/platform/crane performance, the result is undesirable leading to some motors being under loaded and others overloaded. In this Chapter, a method is proposed for sharing the torques equally between the wheels of a gantry crane, driven by IMs with basic VFDs operating in V/F mode. The proposed control strategy is explained for two coupled motors but may be readily extended to a number of coupled motors and other similar applications where the coupling between the motors is not rigid and the torque passed to each IM may vary by the virtue of adhesion.  62  4.2  Concept of Torque Transfer and Wheel Slippage  The torque generated by the IM needs a medium to get transferred from the machine to the load. The medium can be in the form of [27]: 1. Rigid mechanical coupling between the load and the motor, 2. Resilient connection or viscous damping coupling, where the interconnection is either by long shafts, chains or belts, or by the material being processed where twisting and elongation becomes significant, and 3. Friction-based tractive coupling in which changing mechanical surfaces influence the values of the tractive parameters and forces.  The problem discussed in Chapter 3 considered a rigid coupling between the load and the IM. In such coupling, the loss of mechanical torque is minimal as there exists a direct coupling. However, some application makes use of resilient or friction coupling in which the medium of transfer is a contact surface between the machine and the material. Rolling Mill (Steel/Paper/etc.), tube mill, gantry crane wheel motion, roller table application etc. are some of the applications that make use of such coupling. The torque generated by the IM is transferred to the material or the ground/rail by the virtue of contact between the two surfaces. Hence, to have efficient torque transfer, the surfaces should not be slippery and remain always be in contact with each other.  Without loss of generality, in this thesis a gantry crane operation shown in Figure 4.1 is considered. The gantry crane runs on steel rails and typically has multiple wheels driven by IMs. For effective motion of the gantry crane, the torque generated by the wheels should be  63  transferred to the rail to generate the propulsion force. For this to happen there should be active bonding between the wheels and the rail. Such a bonding between the two surfaces is known as adhesion. If the bonding breaks, then the torque does not get transferred and the crane may stop moving in the desired direction with the wheels spinning rapidly (wheel slippage). The bonding can break when the crane is accelerating from standstill or is trying to stop rapidly, for example. The bonding may also break because of wear-out of the wheels and the rails or some external contamination like water or oil spillage, etc.  Trolley hook for lifting loads  Steel Wheel  Induction Motor  Steel Rail  Figure 4.1  4.3  Gantry crane running on a set of rails with IM driven wheels.  Adhesion, Tractive Force, and Vehicular Motion  The total adhesion coefficient  can be considered as a bonding between the wheel and the rail. The bonding is dependent on two factors, namely on the surface adhesion factor  a , and the speed correction factor  c . Both factors changes the total adhesion coefficient  as follows 64    a  c ,  (4.1)  where  a is the surface adhesion factor, and  c is the speed correction factor.  During the normal operation, the gantry (bridge) crane speed is very close but never equal to the linear speed of the wheel. The difference in the speeds is known as the slip-speed  , and is given by    Vw  Vt ,  (4.2)  where V w is the linear circumferential wheel velocity and given by Vw   w rw ; and Vt is the vehicular velocity; and rw is the radius of the wheel.  The slip-speed λ , along with other environmental factors [28], determines the surface adhesion factor  a , between the wheel and the surface. The surface adhesion coefficient determines the amount of tractive force that can be transferred from the wheel onto the rail without sliding [29]. Higher coefficient of surface adhesion factor means better transfer with less energy loss in sliding. Surface adhesion factor points out to the phenomena of bonding between the surfaces in contact. This is a surface phenomenon and is highly dependent on the nature of the surface; such as its roughness, contamination, hardness, chemical and physical composition, etc. The relationship between the surface adhesion factor and the slip-speed is not theoretical and hence there is no standard equation encapsulating this relationship. Significant research has been done to generalize this relationship and today many empirical formulas exist to show this relationship [30], [31]. This relationship is defined for different surfaces in contact and hence there exists more than one equation formulizing this relationship. A sample graph for tire-road adhesion on dry and wet road condition is shown 65  in Figure 4.2. The pattern can be divided into two regions: 1. Stable region (where the adhesion increases with increase in slip also known as Creep Region) 2. Unstable region (where the adhesion decreases with increase in slip know as Slip/Spin Region)  Surface adhesion factor μa  Stable  Dry Condition  Unstable  Wet Condition - 1  Wet Condition - 2  Slip-speed λ (m/s) Figure 4.2  Graph depicting general relationship between surface adhesion factor   a and slip-  speed for different road conditions.  It was also noticed in series of conducted experiments that the total adhesion coefficient decreased with increase in the material speed / vehicle velocity [31]. This is because as the vehicular speed is increased the dwell time is decreased, decreasing the molecular level interlocks and hence decreasing the adhesion energy required to break the interlock. This factor is known as the speed correction factor  c . Similar to the relationship between surface adhesion factor and slip speed, the relationship between the adhesion coefficient and the vehicle speed could only be stated empirically. A sample pattern is as shown in Figure 4.3. This relationship was seen prominent under high velocities.  66  Speed correction factor μc  Vehicle speed - Vt (m/s) Figure 4.3  Graph depicting general relationship between speed correction factor   c and vehicle  speed.  The total adhesion coefficient  defined in (4.1) is responsible for the generation of traction force  FT  N ,  (4.3)  where N is the normal force due to mass on the driving wheel.  For the purpose of further discussion, a wheel with mass M is considered to be rolling on a flat surface as depicted in Figure 4.4. The wheel is rolling with a linear speed of vt and a linear circumferential wheel velocity given by Vw   w rw , under a tractive effort of FT given by (4.3). This tractive effort produces vehicular motion against the rolling resistance R Rolling . This motion can be described by the following differential equation  FT  M  dvt  RRolling . dt  (4.4)  67  If the rail surface were on a slope with respect to the ground, (4.4) would need to include the gravitational component, Mg sin  , which is neglected for our studies as we consider the normal operation where the gantry crane is running on a perfect horizontal rail.  The rolling resistance R Rolling consists of different resistive forces. These forces can be in form of micro-slip (adhesion component), surface deformations (hysteresis component) due to the compressive force of the body [32], [33], [34] and also due to the aerodynamics [35], [36]. The rolling resistance, RRolling in (4.4), is thus a combination of different resistive forces.  RRolling  Radhesion  Rdeformation  Rair .  Figure 4.4  (4.5)  Diagram showing different speeds and forces acting on the wheel.  Adhesion is important in transfer of generated torque to the rail to overcome the surface friction. Adhesion and friction are related and it is helpful to have an overview of the relation between the Adhesion and Friction. Many papers, e.g., [37] and [38], have explained the relationship between adhesion and friction in greater depths. To put it in simpler term, friction can be defined as an undesirable opposition to motion of the body while adhesion can  68  be defined as a force of attraction between the two surfaces [29],[39], [40].  Although (4.4) suggests that increase in tractive effort will result in higher linear velocity of the vehicle, there is an upper limit beyond which the wheel will start spinning and the vehicle will lose its linear velocity. “Spin” is a phenomenon where the vehicle wheel accelerates more than the vehicle; whereas “Slip” is a phenomenon where the vehicle wheel decelerates more than the vehicle [41]. When a wheel moves on a surface, it undergoes micro-slip. Micro-slip, as the name suggests, is a phenomena where the contact surface of the wheel undergoes random slip and stick. The distribution of this slip and stick instances depend on the slip-speed  . A sample slip-stick phenomenon is plotted against the slip-speed in Figure 4.5. When the tractive effort is rapidly increased, the vehicle speed cannot keep up with the wheel speed due to inertia and the slip-speed increases. If the difference is too high, then the slip region in the slip-stick region increases and the vehicle starts slipping [39], [42].  Rolling Direction  SLIP  Low Slip Speed  Figure 4.5  STICK  STICK  Rolling Direction  SLIP  Moderate Slip Speed  Rolling Direction  SLIP  Sliding Motion  Slip-stick phenomenon at the contact surface of wheel and rail.  69  4.4  Induction Motor Load in a Gantry Crane Application  The angular motion of the wheel is generated by the wheel that is driven by IM. In this Section, we discuss the role of an IM in the vehicular motion. The top view of the general case of gantry crane of Figure 4.1 is reproduced in Figure 4.6 for better clarity. For the purpose of this thesis, the gantry crane is assumed to have four wheels, out of which two wheels are driving wheels (Wheel 1 and Wheel 2) coupled to the two separate IMs (IM 1 and IM 2), and the remaining two are passive driven wheels (Wheel 3 and Wheel 4). The total vehicle mass M is considered to be distributed equally amongst the four wheels, with each wheel carrying an equivalent mass of M . Let M1 , and M 2 be the mass acting on the 4 Wheel 1 and Wheel 2. The vehicle is considered to be moving linearly on a perfect plane surface with a linear speed of Vt . The wheels have linear speed of Vw1 (Wheel 1) and V w 2 (Wheel 2) with a total adhesion of 1 and  2 for Wheel 1 and Wheel 2, respectively. Each wheel contributes a tractive force FT 1 (Wheel 1) and FT 2 (Wheel 2), where each force is FT 1  1 M 1 g ,  (4.6)  FT 2   2 M 2 g .  (4.7)  It should be noted that only the driving wheels generates the tractive force. This means that for the gantry crane in the Figure 4.6, the tractive effort of the total vehicle will be 2  FT total  FT 1  FT 2  1 M 1 g   2 M 2 g    i M i g .  (4.8)  i 1  70  Driven Wheel 3  Driving Wheel 1 FT1  IM 1  Vw1  FT total  IM 2  Vt  Driven Wheel 4 Figure 4.6  Vw2  FT2 Driving Wheel 2  Top view of the gantry crane showing the different speeds and tractive forces.  The tractive force FT acts as load torque given by Tload  FT rw . Thus the individual traction loads will be given by the following  Tload1  FT 1 rw ,  (4.9)  Tload 2  FT 2 rw .  (4.10)  The traction loads along with the individual frictional torque T fric1 and T fric2 , and the inertia J 1 and J 2 act as a load on the connected IMs. The torque of IM 1 and IM 2 can be given by  Te1  Tload1  T fric1  J  d rm1 , dt  (4.11)  Te 2  Tload 2  T fric2  J  d rm 2 , dt  (4.12)  where rw is the radius of the driving wheel; and  rm1 , and  rm 2 are the rotational speeds of the IM 1 and IM 2. The motor torques Te1 and Te 2 produces the angular motion of the wheels which helps in generating the micro-slip and further generates the tractive effort as explained  71  in Section 4.3.  Assuming equal mass distribution and an ideal condition where the adhesion under each wheel is the same and neglecting the frictional load, the load on each IM will be equal ((4.11) and (4.12)). However, in reality it is highly unlikely that the adhesion will be the same for both the wheels because of its dependency on various variables. A difference in surface adhesion factor under the wheels (oil/water spillage, snow, surface deformity and abrasion) during the process is also inevitable and will result in a change in tractive effort and thus a change in the loading of the IMs ((4.9) and (4.10)). The loading of the IMs is hence highly susceptible and depends a great deal on the external environmental conditions. The conventional scheme of powering the IMs for the gantry crane application is shown in Figure 4.7. It is seen that similar to Figure 3.5, the speed referencing of both VFDs is the same and hence the input voltage and frequency to both the IMs is the same. Under the conventional scheme, it is impossible to achieve equal load sharing between the wheel motors. In most cases, slip occurs temporarily because of occasional oil slippage or occurrence of water/snow. Though temporarily, such random occurrence of slip can overload the respective IM high enough for circuit tripping and stoppage of the process. Speed feedback  Speed Command  Figure 4.7  Speed Control Regulator  V/F Control  Speed Control Regulator  V/F Control  VSI  IM1  WHEEL-1 RAIL-1  VSI  IM2  WHEEL-2 RAIL-2  Block diagram for conventional load sharing between two V/F controlled induction motors under resilient or stochastic coupling.  72  4.5  System Model and Performance under Wheel Slippage  A slow moving gantry crane is considered for the study in this thesis. The gantry crane is considered to be moving with a speed of 0.5 m  s  or 30 m  min  . The simulation parameters  are listed in Table 4-1. The model used for the simulation is shown in Figure 4.9 and is simulated in Matlab/Simulink® [12], [13]. In the model, the Coriolis-effect of the gantry crane hook and the suspended body, the thermal dependence of adhesion energy and frictional parameters are neglected. For steel wheel on steel rail, the rolling friction is due to the plastic deformation of the contact surfaces and is scarcely affected by lubricants [33]. Hence, the rolling friction is considered constant. Assuming that the gantry crane is moving on planar surface, we can also neglect the effect of gravity. The rolling resistance thus is considered constant at 0.0025/ N.m on each wheel.  Table 4-1  Sample parameters of the gantry crane used in the simulation.  Simulation Parameters Mass (kg)  M  16,000 kg  Moment of inertia  J  0.1 kg m 2  Wheel radius / gear ratio Linear speed of the crane Total number of wheels Number of driving motors (Specifications are given in Appendix A)  rw  G  Vt  0.05 m 0.5 m  s  4 2 x 5HP  73  The surface adhesion factor for the wheel-rail system considered here is modeled as [43]   a  ce  a  de b ,  (4.13)  where a , b , c , and d are the parameters defining the surface adhesion factor depending on the surface condition. For the same considered wheel-rail system, the speed correction factor is modeled as [31]  c  0.24   8 , 100  8v  (4.14)  where v is the vehicle linear speed in km . h  The typical parameters needed for (4.13) to represent the dry and slippery conditions [43] are listed in Table 4-2, and the resultant adhesion is plotted against the slip speed in Figure 4.8.  Table 4-2  Surface adhesion factor parameters for steel wheel on steel rail in dry and slippery conditions.  a  b  c  d  Dry  0.54  1.2  0.29  0.29  Slippery  0.54  1.2  1.0  1.0  Rail Condition  74  Figure 4.8  Surface adhesion factor vs. slip speed for parameters listed in Table 4-2.  75  Figure 4.9  Block diagram of the simulation model for the wheel and vehicle dynamics of the gantry crane.  76  4.5.1  System performance without load sharing  To study the system performance in this Subsection, it is assumed that the driving conditions of one of the wheels, Wheel 1, is changed from dry to slippery for a period of time, and then is changed to dry again. This situation may emulate accidental appearance of ice, oil, etc. on one of the rails, which is passed by the crane platform. The model is run with a speed reference of 10 rad  sec  to have a linear speed of 0.5 m . At time t  8 sec , Wheel 1 s  encounters slippage. This is modeled by changing the surface adhesion factor parameters as shown in Table 4-2 from dry to slippery. This condition prevails for the next 7secs, and at  t  15 sec , the rail condition changes back to dry. The results of such a drop in surface adhesion factor predicted by the model are shown in Figure 4.10. Figure 4.10(a) shows that the vehicle speed decreases when the adhesion on Wheel 1 drops. This is because the tractive effort FT total momentarily falls as shown in Figure 4.10(b) b the driving force is reduced and the vehicle speed drops as per (4.4). The corresponding surface adhesion factor change is shown in Figure 4.10(c). The slip speed of both wheels increases identically as both the IMs are referenced with the same speed command signal. As seen in Figure 4.10(c), the increased slip speed also increases the surface adhesion factor on the Wheel 2. The difference in the adhesion between the wheels gives rise to a variation in the load torque on the motors as seen in Figure 4.10(d). Table 4-3 summarizes the difference in the load torques during this scenario. From Table 4-3, we can see that during the course of disturbance the motor on Wheel 2 becomes overloaded to around 150% while the load on the Wheel 1 motor drops to around 50%, respectively.  77  Figure 4.10  Results of wheel slip under conventional V/F control without the proposed load sharing scheme: (a) wheel and vehicle speed; (b) total tractive effort; (c) surface adhesion factor of Wheel 1 and Wheel 2; and (d) load torque on Wheel 1-IM1 and Wheel 2-IM2.  78  Table 4-3  Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage without using the proposed load sharing compensation scheme.  Adhesion  a  Load torque Te ( Nm )  Time  Wheel 1  Wheel 2  Wheel 1-IM1  Wheel 2-IM2   8 sec 8 sec  15sec  0.01  0.01  19.6  19.6  0.005  0.015  8.82  30.38   15sec  0.01  0.01  19.6  19.6  Moreover, the difference in the tractive force (~431N) between the wheels will generate a deformation torque Tdef around the center of the axle connecting the two wheels given by  Tdef  FT 1  FT 2 l ,  (4.15)  where l is the distance of the wheels from the center of the axle. The formation of deformation torque Tdef is shown in Figure 4.11. This torque will generate a sideward stress on the rail and the wheel, potentially causing faster wear or even blocking of the crane cart in between the rails, which may be catastrophic for the system.  FT1  FT1  FT2 FT1=FT2 Figure 4.11  ℓ  Axle  Tdef > 0 Nm  Tdef = 0 Nm  Axle  FT2 FT1≠FT2  Moment of force vector on the axle under wheel slip with conventional V/F control without the proposed load sharing scheme.  79  4.6  Proposed Methodology for Improved Load Sharing under Wheel Slippage  In a simple V/F control technique, the VFD only has control over the speed of the IM. Thus the reference speed is the only controllable variable that can be taken into consideration. In this Section, a methodology for changing the speed reference of the VFDs to achieve load sharing during wheel slippage is discussed and implemented. The considered adhesion is plotted against the slip speed in Figure 4.12. The adhesions at the different steady state slip speed are indicated with points 1a and 1b , 2a and 2b , and 3a and 3b , respectively. In particular, for the considered points we have: 1. Point 1a and 1b : Steady state operating points of Wheel 1 and Wheel 2 before the slip occurs, 2. Point 2a and 2b : Steady state operating points of Wheel 1 and Wheel 2 after the slip occurred, 3. Point 3a and 3b : Desired steady state operating points for the Wheel 1 and Wheel 2. It is desirable for the wheels to have the same adhesion hence the same torque after the slip occurs.  80  Figure 4.12  Trace of adhesion at different rail conditions vs. slip speed.  When both VFDs have the same speed reference, the slip-speeds of both the wheels are identical. From Figure 4.12, it can be seen that when this happens point 2a and 2b gives different adhesion because of dissimilar characteristics of the rail under each wheel. To have similar adhesion from different road characteristics, we need to alter the wheel speeds differently to give slips (point 3a and 3b ) corresponding to the same adhesion.  From Figure 4.12, it is clear that adhesion from the two rail surfaces can be made equal only by increasing the slip of the Wheel 1 while at the same time decreasing the slip of the Wheel 2. When this is achieved, point 2a moves to 3a while 2b moves to 3b in Figure 4.12. The wheel slip is increased or decreased by increasing or decreasing the wheel speed. The desired speed reference would try to reduce the difference in torque which demonstrates the idea of proposed method for adjusting the speed reference. The resulting proposed control scheme is 81  depicted in Figure 4.13. In this approach, the speed loop alters the reference speed of each wheel to achieve equal torques. In practice, torque may be estimated from measured currents and voltages. The control block diagram of Figure 4.13 is added to Figure 4.9 across the points “A” and “B” to give final proposed control scheme shown in Figure 4.14.  Figure 4.13  Proposed change in the speed referencing of the drive powering the wheels of a gantry crane under wheel slippage.  Speed feedback  Speed Command  Speed Control Regulator  V/F Control  VSI  IM1  WHEEL-1 RAIL-1  Motor Torque-1 controller Motor Torque-2 Speed Control Regulator  V/F Control  VSI  IM2  WHEEL-2 RAIL-2  Speed feedback  Figure 4.14  Block diagram of the proposed scheme for improved load sharing between two V/F controlled induction motors under wheel slippage.  82  4.6.1  Computer studies demonstrating the proposed methodology  The proposed methodology is implemented using the block diagram depicted in Figure 4.14 and the conditions similar to the previous case, wherein the Wheel 1 slipping at time  t  8 sec . The results achieved by the proposed method predicted by the simulation are shown in Figure 4.15. From Figure 4.15(a), it is seen that the slip velocity of the wheels are different unlike in Figure 4.10(a). The slip velocity is automatically adjusted such that the surface adhesion factors [see Figure 4.15(c)] for both the wheels remains the same. Although the wheels are running with different velocities due to the difference in the slip-speed and the road conditions, the adhesion under Wheel 1 and Wheel 2 are the same. Thus, the tractive force for both wheels are equal, which assures that the load torques on both wheels are properly shared as shown in Figure 4.15(d). The results are also summarized in Table 4-4.  83  Figure 4.15  Results of wheel slip under the proposed load sharing scheme: (a) wheel and vehicle speed; (b) total tractive effort; (c) surface adhesion factor of Wheel 1 and Wheel 2; and (d) load torque on Wheel 1-IM1 and Wheel 2-IM2. 84  Table 4-4  Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage using the proposed load sharing compensation scheme.  Adhesion  a  Load torque ( Nm )  Time  Wheel 1  Wheel 2  Wheel 1-IM1  Wheel 2-IM2   8 sec 8 sec  15sec  0.01  0.01  19.6  19.6  0.01 0.01  0.01 0.01  19.6 19.6  19.6 19.6   15sec  To further modify the proposed methodology, the torque signal in Figure 4.13 can be replaced by the real components of the phase current (the torque current). This would be similar to the methodology described in Chapter 3. Also, since the IMs are typically of the same base rating with the same magnetizing current, it may be possible to simply use the rms currents of each motor and use these signals to implement a similar torque balancing approach. It is seen that with the proposed load sharing scheme, the load balancing between the motors has improved significantly even under the wheel slippage. The proposed scheme is simple to implement on existing VFDs with minimal additional hardware.  85  5  Conclusion  In this thesis, two practical cases of load sharing in systems with multiple induction motor drives where studied and their solutions were discussed in detail. The provided solutions have the element of novelty, are simple and cost-effective to implement considering the same existing basic equipment and V/F VFDs, which may be appealing to many industrial applications.  5.1  Summary  Chapter 3 gave analyzes the load sharing among rigidly-coupled induction motors with variations of internal parameters such as rotor resistance, and proposes a solution for load improving sharing under rotor resistance variations. The rigidly-coupled induction motors are common in industrial applications such as roller table, conveyor belts, etc. The proposed solution was designed assuming a basic V/F control VFD which is widely used in the industry and was intended to give a cost effective economical solution to a generic problem.  Chapter 4 extended the problem of load sharing to a practical case of moving vehicular or crane platform with multiple wheels driven by several induction motors and corresponding VFDs. In such common applications, oil / water spillage, occurrence of snow, etc., may cause variations in adhesion and tractive forces. Slipping and/or spinning of wheels are a common phenomenon in such applications leading to uneven distribution of load passed to the individual induction motors. Under traditional V/F divers it was not possible to maintain load balancing under such conditions. A simple solution was provided to improve the load/torque sharing among the participating induction motors, which may be practically realized based  86  on current measurements. Although, the proposed method was developed and presented for a gantry crane application, the proposed methodology with appropriate modifications can be extended to other applications with similar properties, e.g., trains, trolley, vehicles, etc.  5.2  Future Research  Chapter 3 considered knowledge of the rotor resistance variation. In practice, this method may be more difficult to realize effectively. The solution can be suitably modified to include the online parameter identification to identify the rotor resistances and other parameter variations and then change the speed reference accordingly. The online parameter identification is a vast topic of research [44], [45], [46], [47]. A further research would be required to find the most suitable and at the same time simple-to-implement approaches that can be considered together with the existing basic VFDs. The alternative approach proposed in Chapter 3 uses the current measurement which may be more practical for implementation and applicable to larger number of applications with similar problem. This approach can be further generalized to include proportional load sharing among dissimilar motors.  Chapter 4 dealt with load sharing between the motors under wheel slippage. The general idea can be also studied from a point of view of operating the motor at the peak of the adhesion-slip curve (Figure 4.8). This ensures the maximum use of available adhesion resulting in maximizing the tractive effort. 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Kawamura, "Novel Re-adhesion Control for Train Traction System of the “Shinkansen” with the Estimation of Wheel-to-Rail Adhesive Force," in The 27th Annual Conference of the IEEE Industrial Electronics Society (IECON'01), 2001, pp. 1207-1212.  93  Appendices Appendix A Motor Specification A. 5HP Hyundai, 460 V, 60 Hz, 1750 rpm , 4 Pole, Model: HNV413-CC-DBLS, Type: HJS184SR235-HNV413-CC-DBLS, rs  1.503  , rr  1.147  , X ls  3.665  , X lr  4.786  , X m  101.38  , Trated  20.25 N .m , Tmax  60.75 N .m , J  0.105 kg.m 2 .  B. 1HP Baldor Reliance, 460 V, 60 Hz, 1725 rpm , 4 Pole, Catalogue No.: CM3546, Spec No.: 34G795X269, rs  6.98  , rr  7.41  , X ls  11.84  , X lr  11.03  , X m  207.23  ,  Trated  4.05 N .m , Tmax  17.15 N .m , J  0.00261kg.m 2 .  C. 3HP, 220 V, 60 Hz, 1710 rpm , 4 Pole, rs  0.435  , rr  0.816  , X ls  0.754  , X lr  0.754  , X m  26.13  , J  0.089 kg.m 2 .  D. 3HP, 460 V, 60 Hz, 1705 rpm , 4 Pole, rs  0.087  , rr  0.228  , X ls  0.302  , X lr  0.302  , X m  13.08  ,  J  1.662 kg.m 2 .  E. 500HP, 2300 V, 60 Hz, 1773 rpm , 4 Pole, 94  rs  0.262  , rr  0.187  , X ls  1.206  , X lr  1.206  , X m  54.02  ,  J  11.06 kg.m 2 .  F. 2250HP, 2300 V, 60 Hz, 1786 rpm , 4 Pole, rs  0.029  , rr  0.022  , X ls  0.226  , X lr  0.226  , X m  13.04  ,  J  63.87 kg.m 2 .  95  Appendix B Variable Frequency Drive Specification Motor Rating  Drive Rating  1HP  5 HP Normal Duty, 3 HP Heavy Duty  5HP  10 HP Normal Duty, 7.5 HP Heavy Duty  Specifications PowerFlex700 AC Drive, 480 VAC, 3 PH, 8 Amps, 5 HP Normal Duty, 3 HP Heavy Duty, IP20 / Type 1, No HIM (Blank Plate), Brake IGBT Installed, Without Drive Mounted Brake Resistor, Second Environment Filter per CE EMC directive (89/336/EEC), No Communication Module, Vector Control with 120V I/O, No Feedback Input Voltage 480 VAC, 3 PH Current Rating 8 Amps Enclosure IP20 / Type 1 Frame Size Frame Size 0 Output Amps: 8A Cont, Output Current Information 8.8A 1 Min, 12A 3 Sec Vector Control with 120V I/O Options I/O Brake IGBT Brake IGBT Installed Second Environment Filter Options Filter per CE EMC directive (89/336/EEC) PowerFlex700 AC Drive, 480 VAC, 3 PH, 14 Amps, 10 HP Normal Duty, 7.5 HP Heavy Duty, IP20 / Type 1, No HIM (Blank Plate), Brake IGBT Installed, Without Drive Mounted Brake Resistor, Second Environment Filter per CE EMC directive (89/336/EEC), No Communication Module, Vector Control with 24V I/O, No Feedback Input Voltage 480 VAC, 3 PH Current Rating 14 Amps Enclosure IP20 / Type 1 Frame Size Frame Size 1 Output Amps: 14A Cont, Output Current Information 16.5A 1 Min, 22A 3 Sec Vector Control with 24V I/O Options I/O Brake IGBT Brake IGBT Installed Second Environment Filter Options Filter per CE EMC directive (89/336/EEC)  96  Appendix C Software details Name: DriveExecutive Description: This software is an online/offline drive and adapter configuration tool that leverages Windows Explorer-style navigation, built-in html product help, and handy diagnostic and setup wizards. A state-of-the-art comparison tool lets you look at differences and make two devices/files the same. Source: Rockwell Automation Link: http://www.ab.com/en/epub/catalogs/36265/1323285/9616672/9616694/index.html  Name: DriveExplorer Description: DriveExplorer™ Software is an easy-to-use, cost effective application for monitoring and online configuration of your PowerFlex® drives and communication adapters. It makes drive set-up easy and faster than using a Human Interface Module (HIM). Source: Rockwell Automation Link: http://ab.rockwellautomation.com/Drives/Software/9306-DriveExplorer  97  Appendix D Yokogawa WT1600 Digital Power Meter Description: The WT1600 is power meter designed for measurement of extremely small currents in energy-saving equipment, as well as measurement of large currents for evaluating large-sized loads. The WT1600 works with voltages ranging from 1.5 V up to 1000 V, supporting a wide range of applications. Because it can accept signal inputs for up to six phases, a signal WT1600 unit can measure I/O signals on inverters. Source: Yokogawa Link: http://tmi.yokogawa.com/discontinued-products/digital-power-analyzers/digital-poweranalyzers/wt1600-digital-power-meter/  98  

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