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On-line voltage stability assessment and preventive control action recommendations based on artificial… Wang, Zemeng 2016

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ON-LINE VOLTAGE STABILITY ASSESSMENT ANDPREVENTIVE CONTROL ACTIONRECOMMENDATIONS BASED ON ARTIFICIALNEURAL NETWORKbyZemeng WangB. Eng, Huazhong University of Science and Technology, 2013A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Electical and Computer Engineering)The University of British Columbia(Vancouver)July 2016c© Zemeng Wang, 2016AbstractMany power systems are being operated close to their security limits, which makesthe reliable operation more challenging than ever. Voltage instability has been amajor problem faced by many utilities. Many blackouts involved with voltage in-stability have been reported around the world. There is an increasing demand ofaccurate and up-to-date assessment for power system voltage stability and recom-mendations of preventive control actions.On-line voltage stability monitoring tools have been largely matured recently.They are typically integrated with the energy management system (EMS) and as-sess the voltage stability of the present operation condition based on the load-flowsolution generated by state estimator. Preventive control actions to enhance voltagestability against potential contingencies still need to be developed off-line throughextensive studies. They are usually presented to the operators in the form of boundsset of key parameters for voltage security monitoring and control action execution.However, these methods are limited by computation cost, extensive simulations, orconservative operation.This thesis proposes an artificial neural network (ANN) based framework toachieve on-line loading limit assessment and preventive control action recommen-dations for a practical power system. Firstly, an operation knowledge databaseconsisting of interested operation conditions and loading limits is developed off-line. Then an ANN model is trained to map the operation conditions with thecorresponding loading limits. Finally, the proposed framework is applied in BCHydro Vancouver Island system operation for on-line loading limit assessment andpreventive control action recommendations.iiPrefaceThe research work in this thesis is originated from the project entitled “Applicationof Machine Learning Methods in Vancouver Island Supply Capability Determina-tion” sponsored by Mitacs-Accelerate Graduate Research Internship Program andBC Hydro. This work is to the best of my knowledge original and unpublished,except where acknowledgments and references are made to previous work. Myresearch advisor, Dr. Jose´ Martı´, provided the overall supervisory comments andediting during the process of conducting the research and writing the manuscripts.My supervisor at BC Hydro Performance Planning, Mr. Changchun Zuo, proofreadthe manuscript and provided constructive feedback.In Chapter 3, the load-flow base case used was provided by BC Hydro PowerSystem Modeling and Analysis group. The historical hourly load data of ma-jor stations in South Vancouver Island used in Section 3.5 was collected by Mr.Changchun Zuo. The single contingency analysis of Vancouver Island in Sec-tion 3.2 was based on the study conducted by Mr. Changchun Zuo. In Chapter 4,the feature selection method is based on the system operation knowledge and ex-perience shared by Mr. Changchun Zuo.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Power System Reliability . . . . . . . . . . . . . . . . . . 11.1.2 Power System Operating States . . . . . . . . . . . . . . 21.2 Research Motivation . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Research Objective . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . 72 Voltage Stability Assessment . . . . . . . . . . . . . . . . . . . . . . 92.1 Voltage Stability Definition . . . . . . . . . . . . . . . . . . . . . 92.2 Voltage Stability Analysis . . . . . . . . . . . . . . . . . . . . . . 10iv2.2.1 Dynamic and Quasi-Steady-State Analysis: Time-DomainSimulation . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.2 Steady-State Analysis: Load-Flow Method and Modal Anal-ysis Method . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Voltage Stability Index . . . . . . . . . . . . . . . . . . . . . . . 152.4 Voltage Stability Assessment Practice and Tools . . . . . . . . . . 162.4.1 PV Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 162.4.2 QV Curve . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.3 Continuation Power Flow . . . . . . . . . . . . . . . . . 172.5 Voltage Stability Assessment Using Artificial Neural Network . . 182.6 Utility Practice: BC Hydro Planning and Operation Practice onVoltage Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.6.1 Overview of BC Hydro System . . . . . . . . . . . . . . 212.6.2 Preventive Control Action Development: Reliability-Must-Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.6.3 Corrective Control Action Development: Remedial ActionScheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.6.4 Real-Time Voltage Stability Assessment . . . . . . . . . . 262.7 Challenges of Current Practice . . . . . . . . . . . . . . . . . . . 272.7.1 Reliability-Must-Run (RMR) and remedial action scheme(RAS) Development . . . . . . . . . . . . . . . . . . . . 272.7.2 Real-Time Voltage Stability Assessment . . . . . . . . . . 293 Operation Knowledge Database Generation: VI Loading Limit Study 303.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Overview of the BC Hydro VI System . . . . . . . . . . . . . . . 313.2.1 Load and Generation . . . . . . . . . . . . . . . . . . . . 313.2.2 N-1 Contingency Screening Analysis . . . . . . . . . . . 323.3 Base Case Profile . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.1 External System Data . . . . . . . . . . . . . . . . . . . . 333.4 VI System Scenarios Generation Based on Operation and PlanningKnowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5 VI Load Distribution Generation . . . . . . . . . . . . . . . . . . 36v3.5.1 Previously Proposed Approach . . . . . . . . . . . . . . . 363.5.2 Load Uncertainty Analysis of VI System Based on Histor-ical Data . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5.3 Proposed Operation Condition Generation Method . . . . 403.5.4 Verification of the Proposed Method Using Historical HourlyLoad Data . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6 Loading Limit Simulation in VSAT . . . . . . . . . . . . . . . . 453.6.1 Modeling of Control Practice . . . . . . . . . . . . . . . . 453.6.2 Modeling of Overcurrent RAS . . . . . . . . . . . . . . . 473.6.3 Computation Direction of Load and Generation . . . . . . 473.7 Data Verification . . . . . . . . . . . . . . . . . . . . . . . . . . 473.7.1 Base Case Trimming Using Modal Analysis . . . . . . . . 503.8 Visualization of Operation Knowledge Database . . . . . . . . . . 514 Loading Limit Assessment and Preventive Control Action Recom-mendations Using ANN . . . . . . . . . . . . . . . . . . . . . . . . . 544.1 Overview of the Proposed ANN Framework . . . . . . . . . . . . 544.1.1 Off-line Stage . . . . . . . . . . . . . . . . . . . . . . . . 544.1.2 On-line Stage . . . . . . . . . . . . . . . . . . . . . . . . 554.2 Multi-Layer Feed-Forward Neural Network . . . . . . . . . . . . 564.3 Feature Selection and Extraction . . . . . . . . . . . . . . . . . . 574.3.1 Previously Proposed Method . . . . . . . . . . . . . . . . 584.3.2 Feature Selection Based on Engineering Experience andOperation Knowledge . . . . . . . . . . . . . . . . . . . 604.4 ANN Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4.1 Normalization of Input Data . . . . . . . . . . . . . . . . 614.4.2 Performance Measures . . . . . . . . . . . . . . . . . . . 614.4.3 Selection of the Number of Hidden Neurons . . . . . . . . 624.5 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.5.1 ANN Performance and Computational Speed . . . . . . . 634.6 Application for BC Hydro Power System Operation . . . . . . . . 654.6.1 On-Line Loading Limit Assessment . . . . . . . . . . . . 654.6.2 Preventive Measure Recommendations . . . . . . . . . . 66vi5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2.1 Application in Corrective Control Action Development . . 695.2.2 Integration with BC Hydro On-Line Voltage Stability Tool 70Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71viiList of TablesTable 3.1 Load-flow base case information . . . . . . . . . . . . . . . . 34Table 3.2 VI system scenarios definition . . . . . . . . . . . . . . . . . . 36Table 3.3 VI total load level hourly distribution of the year of 2015 . . . 38Table 3.4 VI total load level hourly distribution of the year of 2015 . . . 40Table 3.5 Statistical analysis of VI loading limit generated by hourly load 42Table 3.6 Data samples of operation knowledge database . . . . . . . . . 52Table 4.1 Best MSE performance of MLP models with different size ofhidden layer . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table 4.2 Performance of MLP models with different size of hidden layer 63Table 4.3 ANN structure and training information . . . . . . . . . . . . . 64Table 4.4 ANN average performance of 10 runs with different target MSE 64Table 4.5 ANN average training and prediction time of 10 runs . . . . . . 64viiiList of FiguresFigure 1.1 Power system operating states [6] . . . . . . . . . . . . . . . 3Figure 2.1 Classification of power system stability [17] . . . . . . . . . . 11Figure 2.2 Pre-contingency and post-contingency P-V curve . . . . . . . 16Figure 2.3 Example of a multilayer perceptron neural network . . . . . . 18Figure 2.4 BC Hydro bulk transmission system map [39] . . . . . . . . . 22Figure 2.5 Snapshot of BC Hydro Operating Order 7T41 [40] . . . . . . 24Figure 2.6 Snapshot of BC Hydro Operating Order 7T18 [41] . . . . . . 25Figure 2.7 Real-Time Voltage Stability Assessment Tool (RTVSA) oper-ating procedure . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.8 2-Dimension voltage security region in RTVSA [10] . . . . . 28Figure 2.9 ING to CUS transfer limit versus BCH load and number ofon-line equivalent Burrard synchronous condensers [41] . . . 28Figure 3.1 The flowchart of operation knowledge database generation . . 32Figure 3.2 Transmission map of BC Hydro VI system [39] . . . . . . . . 33Figure 3.3 2015 VI system hourly total load . . . . . . . . . . . . . . . . 39Figure 3.4 Hour-duration versus load level . . . . . . . . . . . . . . . . 40Figure 3.5 Flowchart of operation condition generation . . . . . . . . . . 43Figure 3.6 VI loading limit calculated using assumed load distributionsversus historical hourly load distributions . . . . . . . . . . . 44Figure 3.7 VI loading limit calculation using VSAT . . . . . . . . . . . 46Figure 3.8 Proposed data verification scheme . . . . . . . . . . . . . . . 48Figure 3.9 Modal analysis report of the base case with VLM system . . . 49ixFigure 3.10 Transmission map of BC Hydro VLM system [39] . . . . . . 50Figure 3.11 Heat map of VI loading limit versus operation conditions whenload distribution is all bulk peak . . . . . . . . . . . . . . . . 52Figure 4.1 Overview of the proposed ANN framework . . . . . . . . . . 55Figure 4.2 The structure of a neuron . . . . . . . . . . . . . . . . . . . . 56Figure 4.3 The learning process of MLP . . . . . . . . . . . . . . . . . . 57Figure 4.4 ANN prediction and target regression . . . . . . . . . . . . . 65Figure 4.5 Application of the ANN framework in BC Hydro control center 66Figure 4.6 VI loading limits generated by the trained ANN model of pre-outage 2L123 by enumerating JOR and VIT . . . . . . . . . . 67xGlossarySCADA supervisory control and data acquisitionANN artificial neural networkEMS energy management systemNERC The North American Electric Reliability CorporationRTVSA Real-Time Voltage Stability Assessment ToolCPF continuation power flowFDLF fast decoupled load flowRAS remedial action schemeRMR Reliability-Must-RunQSS quasi-steady-stateMLP Multi-Layer PerceptronBPA Bonneville Power AdministrationWECC The Western Electricity Coordinating CouncilSVC static Volt-Ampere reactive compensatorOLTC on load tap changerMSE Mean Square ErrorxiVAR Volt-Ampere reactivePSAT PowerFlow & Short Circuit Assessment ToolVSAT Transient Security Assessment ToolxiiAcknowledgmentsFirst and foremost, I offer my sincere gratitude to my advisor, Dr. Jose´ Martı´,for his invaluable guidance and strong support during my master study at UBC.Without his encouragement and help for my graduate studies as well as personallife, this thesis would not have been possible. The weekly meetings that haveinspired and motivated me so much will be long missed.Besides my supervisor, I would like to thank the rest members of my exami-nation committee, Dr. Sarbjit Sarkaria and Dr. Hermann Dommel, who dedicatedtheir time to provide insightful comments and constructive feedback. It is such anhonor to have you both in my examination committee.Special gratitude to Mr. Changchun Zuo from BC Hydro for sharing his knowl-edge and experience of power system planning and operation. His expertise inpower system and enthusiasm for smarter power system operation have made thiswork possible.Thanks also go to colleagues in our research group for sharing their knowl-edge and to all my friends who encouraged and supported me during my graduatestudies.I would express my appreciation to BC Hydro and Mitacs for sharing datawith me and financially supporting this research work with the Mitacs AccelerateProject IT06584.Last but not least, my deepest love to my wife Yujie, my daughter Stephanie,my sister Yimeng, my parents and in-laws. Their unconditional love and supportthroughout my life is what I will always be grateful.Adventure is out there!xiiiChapter 1IntroductionScience is but a perversion of itself unless it has as its ultimate goalthe betterment of humanity— Nikola TeslaThis chapter provides brief discussions of power system reliability and operat-ing states. Followed is the motivation of the thesis, which is to develop an on-linevoltage stability assessment system that is able to assess loading limit of the presentoperation condition and recommend preventive control actions. Also included inthis chapter is a description of thesis objective and structure.1.1 Background1.1.1 Power System ReliabilityThe North American Electric Reliability Corporation (NERC) defines power sys-tem reliability as the combination of adequacy and security where [1]:Adequacy: “the ability of the electric system to supply the aggregatedemand and energy requirements of their customers at all times, takinginto account scheduled and reasonably expected unscheduled outagesof system elements/components.”Security: “the ability of the bulk electric system to withstand sudden1disturbances such as electric short circuits, unanticipated loss of sys-tem components or switching operations.”Modern society is very vulnerable of power system blackout. The social andeconomic consequences of big power system blackout are beyond measurement[2, 3]. However, reliable operation of today’s power systems has been more chal-lenging than ever [4]:• Due to the financial pressure, the power systems today are required to beutilized more efficiently. Many existing power systems are required to meetthe increasing electricity consumption without major investment.• Due to the environmental constraints, the generation today often has to bebuilt in far from the load centers. Long distance power transfer brings manypower systems closer to their security limits.• Due to the opening up of the electricity market, the power systems are re-quired to operate under new system loading and generation patterns whichthey are not designed for. The flexible operation of transmission network isthe key for the existence of electricity market but also makes reliable opera-tion challenging.1.1.2 Power System Operating StatesPower system security is characterized as [5]:• The presence of acceptable operating conditions before or after a contin-gency.• The ability of the system to ride through the contingency and to reach thepost-contingency operating condition without becoming unstable.To better analyze power system security and design appropriate control strate-gies, power system operating states are conceptually defined as [6]: normal, alert,emergency, extreme emergency, and restorative. Figure 1.1 shows the five-stateclassification and the transitions among different states.2Restorative AlertNormalExtreme emergencyEmergencyDisturbanceControl actionFigure 1.1: Power system operating states [6]The operation of a power system is in a normal state most of the time, whenvoltages and frequency of the system are in normal range. In this state. the systemis prepared to withstand any considered single contingency without losing stability.In the alert state, all system variables are still in normal range except the se-curity level falls below a certain limit. The state of power system may transit intothe emergency state when subjected to a disturbance. Preventive control actionssuch as generation rescheduling and Volt-Ampere reactive (VAR) support reserveincreasing can restore the system back to normal state.The emergency state arises when system variables are out of the normal rangeor equipment are overloaded. The emergency control actions should be undertakento restore the system to alert state such as fault clearing, excitation control, gener-ation shedding, and load curtailment.The extreme emergency state is a result of ineffective control actions fromemergency state or extreme disturbances from alert state. To avoid a widespreadblackout and save as much of the system as possible, control actions like loadshedding and system separation should be undertaken to restore the system back toemergency state or restorative state.3In the restorative state, power system operators reconnect separated system andrestore system loads. It is regarded as a transition state from extreme emergencystate to normal or alert state.1.2 Research MotivationPower systems become more complicated to manage and are operated in heavilyloaded situations more often. Voltage instability has become a major concern formany power systems [4]. Many blackouts involved with voltage instability havebeen reported in Europe [3, 7], North America [2, 3, 8], and Asia [3]. There is anincreasing interest of accurate and up-to-date assessment of power system voltagestability.The current approach of control action development is a combination of off-linerule development, on-line monitoring, and on-line execution. It requires engineersto conduct a large number of off-line studies for all the possible contingencies toidentify the security limits and develop operation rules. Then the system operatorsneed to monitor several key variables such as power flow of key transmission lines,VAR reserve, and generation patterns based on security limits and operation rulesgenerated off-line.However, the control actions developed by this approach result in power sys-tem conservative operation. The results of off-line studies are typically in the formof bounds set on several key parameters, other parameters have to be set for worstscenario to reduce the number of variables that operators need to monitor. Also,the determination of the operation bounds requires experienced operation plannersconduct extensive simulations and develop operation rules based engineering judg-ment [4]. Furthermore, the control actions have to be redeveloped once the systemchanges, which makes the development a very engineering-intensive task.The on-line security assessment tools have been matured recently, it gathersreal-time information of the power system from the supervisory control and dataacquisition (SCADA) system and assess the security of the system in real-time[5]. A typical on-line security assessment tool integrated with energy managementsystem (EMS) system functions as described below [9, 10]:• A snapshot of the system operation condition is taken from the SCADA4system.• A load-flow or dynamic model is constructed to represent the present opera-tion condition.• The security of the present operation condition regarding to voltage stabilityor transient stability is assessed.• Alarms are raised if violation detected.• The security assessment results are updated on a cyclic base in EMS envi-ronment.As a part of on-line security assessment framework, the on-line voltage sta-bility assessment tool is capable to conduct contingency selection, contingencyscreening, and voltage stability evaluation. It can raise alarm for operators whenany violation appears [9]. For example, BC Hydro uses on-line voltage stabilityassessment tool [10] to monitor the bulk system voltage stability against severalmost extreme contingencies.Although has been used in many power systems, the on-line voltage stabilitytool is still limited in the following perspectives:• The tools for voltage stability assessment such as load-flow based steadystate analysis, continuation power flow, time-domain simulation are timeconsuming for on-line application. It typically takes minutes to update theresults for a set of short-listed contingencies.• The on-line voltage stability tool rely on the load-flow model from state es-timator. Corrupted solution from state estimator will result in failure of thewhole process.• The model generated by state estimator is not consistent with the off-linestudy model. This gap may result in different voltage stability limit for asame operation condition, which makes the result of on-line voltage stabilityassessment incapable to be used as reference for control actions developedoff-line.5• Although the on-line voltage stability tool can assess the voltage security ofthe present operation condition, the preventive and corrective control actiondevelopment still largely relies on off-line studies.The successful application machine learning in control, computer vision andartificial intelligence has attracted considerable research efforts to apply it in volt-age stability assessment.Based on the limitations of the current approaches and the capability of ANN,there are 3 main reasons that why ANN is promising for voltage stability assess-ment and preventive control action recommendations:• On-line voltage stability assessment and preventive control action develop-ment conceptually are to find the loading limit or other voltage stability in-dices for a specified operation condition. It coincides with the basic idea ofmachine learning and data mining.• ANN is powerful for non-linear function approximations. With quantifica-tion of the operation conditions and the loading limits, ANN is ready toapproximate the mapping between operation conditions and loading limits.• The calculation of an output of a trained ANN is very fast, which make itpossible to assess the loading limit and recommend preventive control ac-tions in real-time.Many researchers took advantage of the capability of non-linear function ap-proximations of artificial neural network to approximate the voltage stability mar-gin for a specified operation condition [11–16]. With careful generation of trainingdata and selection of the input feature, the approaches described by the previouswork demonstrate the feasibility of ANN for on-line voltage stability assessment.However, except for reference [14], the ANN approach was only tested forsmall-scale test systems. The ANN approach in [12] was applied for the New Eng-land 39-bus test system. In reference [13], the test systems are IEEE 30-bus testsystem, and the test system in [15] are IEEE 118-bus test system and the Finnish113-bus equivalent transmission system. Although ANN approach for voltage sta-bility margin prediction was reported to applied to a 1844-bus system [14], the6result is not persuasive. The mean error for estimated voltage stability margin isreported as 5% and the maximum error is not reported, which is not acceptable forpractical power system operation.The motivation of this research is to build up an on-line voltage stability as-sessment system for a practical power system which can quickly and accuratelyachieve voltage stability assessment and preventive control action recommenda-tions. The proposed on-line voltage assessment system will be developed for BCHydro Vancouver Island (VI) system operation.1.3 Research ObjectiveThe research objectives of this thesis are:1. Select operation conditions consisting of system scenarios and load distribu-tions which can realistically and completely represent operation conditionsof interested operation period.2. Identify the appropriate method to assess the voltage stability. Calculate theaccurate loading limits of the selected operation conditions.3. Develop an operation knowledge database consisting of interested operationconditions and the corresponding loading limit. Automate the database gen-eration and verification.4. Train an ANN model to approximate the mapping the operation conditionsand the corresponding loading limits based on the operation knowledge database.Implement feature selection, ANN training, validation and testing.5. Implement the proposed framework on a practical system for on-line voltageassessment and preventive control action recommendations.1.4 Organization of the ThesisIn Chapter 2, the definitions, indices, analysis methods, practices, and tools aboutvoltage stability are outlined. The utility planning and operation practice on voltagestability is discussed using BC Hydro as an example.7In Chapter 3, the development of the operation knowledge database is de-scribed. Specifically, the selection of operation conditions based on operation expe-rience and historical load data is discussed. Chapter 3 also presents the calculationof the loading limit using continuation power flow (CPF) method. An automaticdata generation system is proposed in the end of Chapter 3.In Chapter 4, the ANN framework is proposed. ANN model design, featureselection, and ANN training are presented. The application of the proposed frame-work in BC Hydro control center for loading limit assessment and preventive con-trol action recommendations is discussed later.Chapter 5 concludes the work by summarizing the major contributions andhighlighting the future work.8Chapter 2Voltage Stability AssessmentMaybe I can’t define stability, but I know it when I see it!— CARSON W. TAYLORThis chapter starts with a general overview on the definitions, indices, analysismethods, practices, and tools about voltage stability. Then the discussion about theapplication of artificial neural network (ANN) in on-line voltage stability assess-ment is followed. At last, BC Hydro is used as an example to illustrate the utilitypractice on planning and operation of practical power systems against voltage sta-bility problem.2.1 Voltage Stability DefinitionPrior to the discussion of voltage stability, Figure 2.1 shows the classification ofgeneral power system stability and describes how voltage stability is placed withinthe context of general power system stability. The classification scheme is basedon three criteria: phenomenon, time scale, and subjected disturbance.There are two popular definitions about voltage stability across literatures. In[17], voltage stability is defined by IEEE and CIGRE Working Groups as:Voltage stability refers to the ability of a power system to maintainsteady voltages at all buses in the system after being subjected to adisturbance from a given initial operation condition.9Reference [4] defines voltage instability as:Voltage instability stems from the attempt of load dynamics to restorepower consumption beyond the capability of the combined transmis-sion and generation system.Based on the definition above, characteristics and properties of voltage stabilitycan be summarized:• Voltage instability is named by its observed physical phenomenon: low volt-age at buses during or after the disturbance. Load driving is the major char-acteristic of voltage instability.• Voltage stability is not a static but dynamic problem by nature. Althoughlong-term voltage stability or small-disturbance can be assessed by statictools (load-flow or modal analysis), sometimes one has to turn to dynamictools (time-domain simulation) to address the problem.• Small-disturbance instability is also called steady-state or small-signal sta-bility [4]. It can be analyzed by linearization of the dynamic system at theoperating point. Large-disturbance stability is caused by large disturbancesand has to be assessed by time-domain simulation of the system against spec-ified disturbance.2.2 Voltage Stability AnalysisThere are two general types of voltage stability analysis method: dynamic analysisand steady-state analysis. Dynamic analysis typically uses time-domain simula-tions to solve the system differential-algebraic equations, while steady-state analy-sis focuses on the conventional or modified power-flow solution of a system snap-shot.2.2.1 Dynamic and Quasi-Steady-State Analysis: Time-DomainSimulationThe typical description for a power system dynamic response is given by the differential-algebraic equations [18]:10Power System StabilityRotor Angle StabilityFrequency StabilityVoltage StabilitySmall-Disturbance Angle StabilityTransient StabilityLarge-Disturbance Voltage StabilitySmall-Disturbance Voltage StabilityShort Term Short TermShort Term Long TermLong TermFigure 2.1: Classification of power system stability [17]x˙ = f (x,V ) (2.1)I(x,V ) = YbusV (2.2)Where x represents the system state vectors, V represents the bus voltage vec-tor, I represents the current injection vector, and Ybus represents the network nodeadmittance matrix. (2.1) describes the interested dynamics of the system. (2.2)describes the network algebraic constraints. Dynamic analysis solves the systemdifferential-algebraic equations and reveals the system response against subjecteddisturbance in time-domain.Voltage stability is a dynamic problem by nature. Accurate dynamic simula-tion is necessary for post-mortem analysis and the co-ordination of protection andcontrol because the time sequence of the detailed disturbance and the followingcontrol actions can be modeled [19].Due to the variations of the focused type of transient, interested time scale, andavailable model, part or all of (2.1) can be replaced with the corresponding equilib-11rium equations. For example, in transient stability analysis, the fast transients likegenerator stator transient can be eliminated without damaging the accuracy sincethe interested transient if known to be predominantly slow.The same principle also applies in voltage stability simulation. For short-termor large-disturbance voltage instability analysis, conventional transient stabilitysimulation tool can be used with careful modeling of the elements and control ac-tions [19]. For long-term voltage instability analysis, reference [20] firstly broughtup a fast simulation method to achieve balance of efficiency and accuracy. Basedon quasi-steady-state (QSS) concept, all of the differential equations of the tran-sient dynamics are replaced with the equilibrium equations. Instead, the load self-restoration process is modeled by differential equations. The discrete transition ofthe control, protections and limiting devices is also represented in the system equa-tions. The proposed QSS has been [21] validated on the Hydro-Que´bec system.Several commercial softwares are able to simulate wide-spread blackouts based onQSS technique [22].2.2.2 Steady-State Analysis: Load-Flow Method and Modal AnalysisMethodSteady-state analysis only solves the algebraic equations of a specified systemsnapshot. Due to its computational efficiency, steady-state analysis is commonlyused for bulk studies of practical power systems when voltage stability limit ofvarious contingencies and operation conditions needs to be determined [23].Load-Flow MethodLoad-flow method is the most commonly used analytical method for reactive powerresources planning, loading limit determination, and transfer capacity calculationfor practical power systems.Although load-flow method is well known and widely used for voltage stabil-ity analysis, the relationship of between existence of load-flow and existence of asteady-state system equilibrium point should be addressed. Reference [24] firstlyproposed the direct relationship between the singularity of the conventional load-flow full Jacobian matrix and the singularity of the system dynamic state Jacobian12matrix. Reference [25] later examined a linearized system dynamic model and con-cluded that the singularity of the load-flow Jacobian implies operation conditionsclose to maximum loading or power transfer. The rationale can be summarized:• The typical application of load-flow method in voltage stability context is tofind system maximum loading limit or maximum transfer capability.• If the load-flow of a certain level of loading or interchange doesn’t converge,it normally implies that the proposed loading or interchange exceeds loadinglimit or transfer capacity of the system. The maximum loading or inter-change point typically coincides with a zero determinant or singularity forthe load-flow Jacobian.• Case studies in reference [25] shows that the non-singularity of the standardload-flow Jacobian implies the existence of a steady state equilibrium pointfor a specified level of loading or interchange.Load-flow method is valid for a wide range of voltage stability problems andable to calculate the loading limit for a specified operation condition [25]. It isalso necessary to be aware that the load-flow method is limited by the modelingassumptions [23]:• The load in current load-flow software is typically modeled as constant powerfactor load.• The tap changer action and capacitor switching are assumed as instanta-neous.• The generators are voltage controlled buses with fixed real power output.The reactive power outputs are limited by maximum and minimum reactivepower limits.Modal Analysis MethodPrior jumping into the mathematical derivation, intuitively, modal analysis is agradient technique [26]. It examines the changes of the voltage against incremental13changes in reactive power at the nose point of a P-V curve of a system operationcondition. Fundamentally based on gradient concepts, modal analysis calculatesthe smallest eigenvalues and associated eigenvectors of the reduced QV Jacobianmatrix. The eigenvalues and eigenvectors can provide a relative measure of theproximity to voltage instability.For steady-state analysis, the dynamics of the system is assumed to reach equi-librium. Since x˙ = 0 in (2.1), the network constraints in (2.2) can be linearized as(2.3) [6], which is well known as load-flow full Jacobian matrix.[∆P∆Q]=[JPθ JPVJQθ JQV][∆θ∆V](2.3)Jacobian matrix gives the sensitivity between power flow and bus voltage changes.Assuming that P is constant, which is valid at the nose point of the P-V curve, theincremental relationship between Q and V can be derived as:∆Q = JR∆V (2.4)∆V = J−1R ∆Q (2.5)JR =[JQV − JQθJ−1Pθ JPV](2.6)JR is named as reduced Q-V Jacobian matrix and J−1R is the reduced V-Q Jaco-bian matrix. Because the JR is quasi-symmetric and therefore, diagonalizable [23],a set of real eigenvalues and eigenvectors can be obtained by conducting eigenvaluedecomposition.JR = ξΛη (2.7)Where, ξ and η are the right and left eigenvector matrix of JR. Λ is the diagonaleigenvalue matrix. Furthermore, since ξ−1 = η , (2.7) can be written as:∆V = ξΛ−1η∆Q (2.8)v = Λ−1q (2.9)14Where, v = η∆V is referred as vector of modal voltage variations. q = η∆Q isreferred as vector of modal voltage variations. The V-Q relationship is decoupled.The ith mode is:vi =1λiqi (2.10)The magnitude of λi determines the relative degree of stability. At the nosepoint of the P-V curve, the critical mode associated with the smallest eigenvalue,which is typical very close to zero, reveals the cause of stability problems. Theeigenvectors of the critical mode can provide information about voltage stabilitycritical areas.2.3 Voltage Stability IndexOne important question about voltage stability is that how to assess the proximityto voltage instability. A number of voltage stability indices have been brought upto answer this question.Reference [4, 23] have well summarized the indices and corresponding assess-ment methods, including sensitivity factors [27], singular values of full load-flowJacobian [28], eigenvalues of reduced load-flow Jacobian [29], second order per-formance index [30], the energy methods [31], bifurcation theory [32], L-index[33], and Thevenin equivalent impedance based index [34]Among all these indices, the loading limit is the most straightforward and com-monly index used by power system planners and operators. Loading limit tells howmuch additional load can be supplied or transfered under a specified operation con-dition. In utilities, the difference between the actual load and the loading limit istypically referred as voltage stability margin, which is used as an indicator of theproximity to voltage instability.If the system is required to operate safely against a set of contingencies. Theloading limit is defined as the highest load level of the pre-contingency conditionwhere the corresponding post-contingency condition firstly fails to keep voltagestable. As shown in Figure 2.2, Ppost−limit is defined as the loading limit against theapplied contingency.Based on the discussion above, the loading limit is selected as the voltage sta-bility index to the proximity to voltage instability of a specified operation condition15PPre-contingency Post-contingency VPNormal PPost-limit PPre-limitFigure 2.2: Pre-contingency and post-contingency P-V curvein this thesis.2.4 Voltage Stability Assessment Practice and Tools2.4.1 PV CurveP-V curve is a traditional practice to assess the loading limit or transfer capacityof a large power system. To develop a P-V curve, the system load of the interestedarea is increased step by step. At each load level, a specified generation dispatchscheme is used to balance the increased active power demand and stress the inter-ested area or path. The voltage stability critical point is reached when the load-flowsolution last exists. The loading limit of a system or interested area can be foundusing P-V curve. For contingency analysis, P-V curve is used to calculate bothpre-contingency and post-contingency loading limit as shown in Figure 2.2.The conventional Newton-Raphson load-flow can only determine the stablepart of the curve because the Newton iterations tend to become ill-conditioned16near the nose or maximum power point on the curve [23]. This problem has beenwell addressed by continuation method [35], which will be discussed later in thischapter.2.4.2 QV CurveQ-V curve is used to describe the sensitivity relationship between bus voltages andthe reactive power injections. Instead of an area or interface, Q-V curve focuses onthe interested buses. Typically, a fictitious synchronous condenser with unlimitedreactive power is placed at a specified bus to control its voltage. By increasing ordecreasing the reactive power injection in discrete steps, the load-flow is solved ateach reactive injection level. The plot of the reactive power injection versus thebus voltage is referred as Q-V curve. Although useful information can be retrievedfrom Q-V curve, it is also limited in the following perspectives:• The Q-V curve can only study the bus Q-V sensitivity relationship under thegiven operation point. Small changes in the operating point may result in atotally different Q-V curve.• Calculation of a limited number of bus Q-V curves cannot reveal completeinformation for the system voltage stability.2.4.3 Continuation Power FlowThe concept of CPF was firstly brought up in reference [35]. It is a method usedto fully compute the P-V profiles up to the nose point. Conventional load-flowalgorithms like Newton-Raphson suffer from ill-conditioned Jacobian matrix whenthe operating point is close to the nose point of P-V curve. CPF overcomes thisnumerical unstability problem of the conventional load-flow methods.The basic principle of CPF is to use an iterative predictor-corrector scheme totrack the operating point on the P-V curve for the corresponding load level. Thetraditional method to calculate of P-V curve tries to solve the load-flow of eachoperating point along the P-V curve. Instead, CPF regards the voltage collapseproblem as an optimization problem: what is the maximum real power injectionof the system described as non-linear and algebraic load-flow equations [36]. By17InputlayerHiddenlayerOutputlayerInput 1Input 2Input 3Input 4Input 5OuputFigure 2.3: Example of a multilayer perceptron neural networkrestating the problem as an optimization problem, several well-known optimizationtechniques can be applied to compute the collapse point [23]. CPF is regardedequivalent to generalized reduced-gradient [36], which is a well-known nonlinearoptimization method.2.5 Voltage Stability Assessment Using Artificial NeuralNetworkThe basic concept of the ANN stems from the efforts of representing the informa-tion process of human brains using mathematical models as far back as the 1950s[37]. With the maturity of ANN in 1980s, ANN has been applied successfully inmany areas such as artificial intelligence, computer vision, speech recognition, andcontrol.As an example of simple neural network shown in Figure 2.3, ANN is an inter-connected system of elementary non-linear signal processors (referred as neurons)18through adaptive weighted connections. ANN essentially is a non-linear mathe-matical model that maps an input to an output. The training of ANN is the processto minimize the cost criterion (typically the sum of square error function of theprediction) by adapting connection weights for all given input data. Details of theprinciples of ANN architecture are presented in Section 4.4.The assessment of power system voltage stability shares a set of characteristicsthat make it readily to be solved by neural network solutions [15]:• The on-line voltage stability assessment requires the result be updated inreal-time. Conventional on-line voltage stability assessment tools [10] arecomputationally costly and time consuming. It updates voltage stability as-sessment results every a couple of minutes for a limited number of con-tingencies, which is acceptable for voltage stability monitoring but not forremedial action scheme (RAS) and other control actions.• The development of preventive and corrective control actions to operate thesystem is a very engineering-intensive task. Power system planners need tostudy a large number of operation conditions and contingencies to provideguidance for system operation. Moreover, the control schemes have to beredeveloped once the system changes.• The rules and guidance of how to operates the system to achieve voltage sta-bility currently require experienced engineers to summarize from extensivesimulations based on engineering judgment. However, the rules and guid-ance may not be in a functional form, but rather in the form of input andoutput examples directly extracted from the simulation results.The capabilities and properties of ANN make it a great candidate solution toon-line voltage stability assessment:• The ANN provides a powerful and general framework for non-linear func-tion approximations.ANN can set up the mapping between an operation condition with the cor-responding voltage stability index.19• The accuracy and generalization of ANN largely depends on the input data.The accumulated operation data can help improve performance of the ANN.• ANN executes very fast once trained. Most of the calculation occur duringthe initial training.The trained ANN can be integrated into the EMS system and it can achievereal-time voltage stability assessment.• A trained ANN not only can assess the voltage stability of a given opera-tion condition but also provide preventive control action recommendationsto enhance the voltage stability.A trained ANN provides a complete mapping between operation conditionsand the voltage stability index. Given a target voltage stability index, it canbacktrack the corresponding operation conditions, which provide preventivecontrol action recommendations to operate the system.Many the research works used ANN to assess voltage stability of a specifiedoperation condition. An ANN model was trained in [12] to assess the voltagestability margin for the New England 39-bus test system. In reference [13], thetransfer capability of key transmission lines of an IEEE 30-bus test system was pre-dicted using an trained ANN. In reference [38], real and reactive power injectionsof all load buses were used as features to train an ANN model for voltage stabil-ity margin prediction. Using bus voltage magnitudes and angles as input features,an ANN model was trained for voltage stability margin prediction of a 1844-bussystem [14].2.6 Utility Practice: BC Hydro Planning and OperationPractice on Voltage StabilityThe general procedures of voltage stability analysis for utility planning and opera-tion are summarized as [19]:1. Set-up of the base case for interested operation conditions.202. Selection of a list of credible contingencies against which the voltage stabil-ity of the system is to be tested.3. Definition of the voltage stability index (such as an interface transfer or areaload) for voltage stability margin calculation.4. Specification of system voltage stability criterion (such as a 5% security mar-gin of loading limit).5. Determination of system voltage stability index for the base case and allcredible contingency cases.6. Design and validation of and corrective control actions for cases which donot meet the criterion.The planning and operation practice of voltage stability assessment of BC Hy-dro is discussed as an example in the following sections.2.6.1 Overview of BC Hydro SystemAs ranked as third-largest electric utility of Canada, BC Hydro serves over 1.9million residential, commercial and industrial customers covering more than 94%population of British Columbia (BC). It delivers more than 43,000 gigawatt-hoursof electricity annually.As shown in Figure 2.4, the pattern of electricity supply and consumption inBritish Columbia have been largely influenced by the geography of the province.Most of the available sources are located at north interior are distant from thesouth coastal area of the province, where most of the demand for electricity isconcentrated. Over 80% of BC Hydro’s generating capacity is at the facilities in-stalled in the Peace and Columbia river basins. On the other hand, 70%-80% ofthe province’s electricity is consumed in the Lower Mainland and on VancouverIsland. The distance between generation and load center requires long-distancepower transfer.The 500 kV bulk transmission network connects the major generation in thenorthern and southern interior regions with the load centers in heavily populatedsouthwest of the province. BC Hydro’s system is interconnected with the electric21500 KV CIRCUITS230 KV CIRCUITSHYDROELECTRIC GENERATIONTHERMAL GENERATIONINTERCONNECTIONS500 KV SUBSTATION230 KV SUBSTATIONSERIES CAPACITOR STATIONSG.M. SHRUMPEACE CANYONBURRARDSEVEN MILEKOOTENAY CANALREVELSTOKEMICADUNSMUIR MERIDIANINGLEDOWCHEEKYECREEKSIDENICOLACHAPMANSMcLEESEASHTON CREEKSELKIRKCRANBROOKAMERICAN CREEKWILLISTONKENNEDYGLENANNANTELKWASKEENAKELLY LAKEKAMLOOPSVICTORIAPRINCE GEORGEVANCOUVERALBERTAWASHINGTONVASEUXGUICHONNELWAYCLAYBURN TO FORTISBCBC Bulk Transmission SystemAugust 2007Figure 2.4: BC Hydro bulk transmission system map [39]system in Alberta, the FortisBC system in southeastern BC, the Alcan system onthe north coast of the province, and the system of Bonneville Power Administration(BPA) of the USA.2.6.2 Preventive Control Action Development: Reliability-Must-RunSince the operators do not have sufficient time to steer the system manually oncethe contingency occurs, it is necessary to posture the system for voltage stability22by developing preventive control actions.The preventive control actions are constraints and requirements for the pre-contingency operating conditions to ensure the system remaining stable during andafter a contingency. In BC Hydro, the constraints and requirements are namedReliability-Must-Run (RMR), which are pre-outage component restrictions, theminimum level of generating capacity, available VAR support capacity.BC Hydro VI RMR in the operation order 7T-41 [40] is shown in Figure 2.5.For example, the first row of the Table 1.1.1 in Figure 2.5 shows the requirementof JOR generation and VAR support for different level of VI load and C&SVI(central and south VI) load without any contingency. The second row presents theJOR RMR and VAR RMR against a set of contingencies.When requirements for Jordan Generation and VIT-PVO VAR support are vio-lated, the EMS will alarm and the operators have to take actions to Jordan Gener-ation and VIT-PVO to resolve the violations. If the VI load still exceeds the limitwhen all reserves are exhausted, the operators have to shed the load or turn to otherpossible measures.2.6.3 Corrective Control Action Development: Remedial ActionSchemeAccording to [42], RAS is defined as:“An automatic protection system designed to detect abnormal or pre-determined system conditions, and take corrective actions other thanand/or in addition to the isolation of faulted components to maintainsystem reliability.”RAS is classified as corrective control actions, it is widely applied in BC Hydrotransmission system operation. It has greatly secured and extended the operationrange and provided great operation flexibility. RAS typically is to operate forNERC category C (N-1-1) system condition [43, 44] for BC Hydro transmissionoperation. N-1 system conditions appears when one transmission line, transformeror var support device are out of service. N-1-1 system condition appears when N-1system condition is subjected a contingency.23Table 1.1.1 Pre-Outage Restrictions – VI Supply System Normal with VIT PST In Service Notes: VI Supply System Normal means that 5L29, 5L31, 5L30, 5L32, at least one of 5L42 and 5L45, all major equipments in VI shall be in service. CONTINGENCY PRE-OUTAGE RESTRICTIONSWithout  any contingencyLimit: 2L129 ARN <= 590 MWIf TSA alarms “2L129 ARN CONTINUOUS RATING VIOLATION”, the BCHCC Operator must reduce the transfer below the limit by:  Adjusting the tap of the VIT phase shifter transformer, and /or  Bringing HVDC online if it is not in service and increasing HVDC flow, and/or  Bringing JOR online if it is not in service and increasing the output, and/or  Bringing more generation online in north and central VI areas. VI Reliability Must Run (VI RMR) requirements for voltage stability (required for JOR/2L129/2L123/2L128 contingencies): (a) JOR RMR & HVDC Pole 2 Requirements VI Load (MW) 2000<VI Load =<21002100<VILoad=<22002200<VILoad=<23002300<VILoad<=2400JOR GEN (MW) 0 >=50 >=50 >=100 Pole 2 (MW) >= 200 >=200 >=300 336 The South Gulf Island load supplyradially supplied by 1L18 from ARN VI Load must be less than or equal to 2400 MW.If the above condition violates, TSA will alarm “VI RMR VIOLATION: JOR MW < XX” or “VI RMR VIOLATION: HVDC POLE 2 MW < XX” or “VI LOAD MUST BE LESS THAN OR EQUAL TO 2400 MW”, then  BCHCC Operator shall take the following actions:  Bringing JOR online if it is not in service and increasing the output, and/or  Bringing HVDC online if it is not in service and increasing HVDC flow. (b)    VAR Support RMR Define “C & SVI Load” = Pole 2 ARN + 2L129 ARN + (2L123 + 2L128) DMR – (1L115 + 1L116) JPT + JOR MW Define CX_requirement = the total VIT & PVO Var supporting capability available or on-line expressed in % of the maximum Var supporting capability (% MVAR)  VIT SC1 (50 MVAR), SC2 (50 MVAR), SC3 (100 MVAR), SC4 (100 MVAR)  VIT HF1 (67.15 MVAR)  VIT HF2 (96 MVAR)  PVO 1CX1, 1CX2 and 1CX3 (each 46 MVAR at 132 kV)  The maximum Var supporting capability is 601.15 Mvar  The automatic control scheme of PVO CXs must be in service if PVO CXs are considered available “C & SVI Load” (MW) % MVAR 1400 <= “C & SVI Load” < 1485 100 1350 <= “C & SVI Load” < 1400 >= 82 1230 <= “C & SVI Load” < 1350 >= 66 1100 <= “C & SVI Load” < 1230 >= 50 1000 <= “C & SVI Load” < 1100 >= 25  0 0001 <If the above condition violates, TSA will alarm “VI RMR VIOLATION: XX% VIT/PVO VAR SUPPORT”, then  BCHCC Operator shall take the following actions:  Bringing JOR online if it is not in service and increasing the output, and/or  Bringing more generation online in north and central VI areas.  Checking status of 1L18, VIT SCs, VIT HFs, PVO CXs and the automatic control scheme of PVO CXs to meet the requirement.5L29 & 5L31, or5L30 & 5L32, or5L42 & 5L45, orDMR T1 & T2 Note: VI dependable generator output = (JOR+PUN+ASH+SCA+LDR+JHT+ICG) Gen MW VI Reliability Must Run (VI RMR): a. If VI Load > 2350 MW, then  VI dependable generator output shall be greater than 460 MW, and  4 VIT SCs shall be in service. b. If 2200 MW < VI Load <= 2350 MW, then  VI dependable generator output shall be greater than 440 MW, and  At least 3 VIT SCs shall be in service. c. If 1800 MW < VI Load <= 2200 MW,  then   VI dependable generator output shall be greater than 330 MW, and  At least 3 VIT SCs shall be in service. d. If 1400 MW < VI Load <= 1800 MW, then   VI dependable generator output shall be greater than 300MW, and  At least 2 VIT SCs shall be in service. e. If 1200 MW < VI Load <=1400MW, then   VI dependable generator output shall be greater than 260MW, and  At least 2 VIT SCs shall be in service. f. If VI Load <=1200MW, then   VI dependable generator output shall be greater than 100MW, and  At least 2 VIT SCs shall be in service. g.  DMR SVC shall be in service. If the above condition violates, TSA will alarm “VI RMR VIOLATION: 500KV DBL CTGS” and “DMR SVC MUST BE IN SERVICE”, then the BCHCC Operator must reduce the transfer from LM to VI by : Bringing JOR online if it is not in service and increasing the output, and/or  Bringing more generation online in north and central VI areas.  or the BCHCC Operator may need to check the VIT SC’s minimum units on-line or the status of DMR SVC Figure 2.5: Snapshot of BC Hydro Operating Order 7T41 [40]24OO 7T-18Effective Date:  15 December 2015  Page 11 of 446.2 AB TIE RAS Arming for imports from Alcan and US Arm the AB TIE RAS at CBK if:  BCH load < 5260 MW ANDING - Custer transfer  plus NLY - Boundary transfer plus MIN to Kitimat transfer  is less than 0.17 * (3800 - BCH Load) - 1100 MW BCH load >= 5260 MW ANDING - Custer transfer  plus NLY - Boundary transfer plus MIN to Kitimat transfer  is less than 0.38 * (5260 - BCH Load) - 1350 MWOR 5L61 Tripping RAS is armed: ANDING - Custer transfer  plus NLY - Boundary transfer plus WSN to GLN transfer is less than -1.31 * Z – 2000 MW 5L61 Tripping RAS is not armed: ANDING - Custer transfer  plus NLY - Boundary transfer plus MIN to Kitimat transfer  is less than -1.31 * Z – 2000 MWWhere  Z = BC - AB Transfer MW (West to East is: +)Disarm the AB TIE RAS if the arming condition specified above is not met. Example: System condition:  BCH load: 5000 MW   ING - Custer transfer : -1200 MW (BCH is importing 1200 MW on 5L51 and 5L51)  NLY - Boundary transfer: -300 MW (BCH is importing 300 MW on 2L112)  MIN to Kitimat transfer: -280 MW (BCH is importing 280 MW on 2L103)  BC to AB transfer: - 600 MW 5L61 Tripping RAS is not armed Arming condition calculation:   ING - Custer transfer plus NLY - Boundary transfer plus MIN to Kitimat transfer  = -1200 300 280  -1780 0.17 * (3800  BCH Load)  1100 MW = 0.17*(3800  5000) 1100 = -1304 -1.31* (-600) – 2000 MW = -1214 Because (-1780) is less than (-1304), or (-1780) is less than (-1214), arm AB TIE RASFigure 2.6: Snapshot of BC Hydro Operating Order 7T18 [41]25Currently, as one of many utilities, BC Hydro performs off-line studies to de-termine voltage stability limit and RAS to ensure system stability under a certainoperating condition. The interested N-1 system condition is defined, and then eachN-1 condition is expanded by applying a number (10 - 12) contingencies into N-1-1system conditions. Each N-1-1 system condition can cause several system viola-tions, such as voltage stability, transient stability or thermal issues. Planning andoperation engineers study each N-1-1 system conditions and solve each violationby generation shedding, load shedding, or line tripping. The corresponding correc-tive control actions summarized from the off-line study results are then programedinto a computer in control center as a look-up table, which predetermines the con-trol actions for a N-1-1 system conditions. BC Hydro operation center uses thesepredetermined RAS to operate the system under extreme conditions.Figure 2.6 shows the AB-BC tie line RAS arming conditions in BC Hydrooperating order 7T18 [41]. Under certain operation conditions, the AB-BC RASwill trip the tie line connects BC Hydro system and Alberta system to avoid wide-spread blackout.2.6.4 Real-Time Voltage Stability AssessmentWhether or not the present operation condition can maintain voltage stability sub-jected a contingency is always of interest of power system operators. To assess BCHydro bulk system voltage stability in real-time, an application named Real-TimeVoltage Stability Assessment Tool (RTVSA) has been implemented to support op-eration of the power system within voltage stability limit [10]. Based on BC Hydrooperation experience and knowledge of its transmission system, outages involving500 kV lines, particularly the Interior to Lower Mainland lines, are often the mostlimiting conditions which will determine the permissible operating boundaries fora given system condition. The RTVSA is designed to evaluate these most limitingoperation conditions and contingencies.As shown in Figure 2.7, RTVSA runs on a VSAT server and has been imple-mented within the integrated EMS-DSATools environment. RTVSA uses currentsystem conditions as determined by the State Estimator solution and armed gener-ation shedding as recommended by BC Hydro Transient Stability Analysis Pattern26EMS/SCADARTVSAContingenciesVSAT serverVoltage security regionUpdate every 2 minSCADAState EstimatorFigure 2.7: RTVSA operating procedureMatching (TSA-PM) application. The application performs contingency studiesin real-time of a selected number of contingencies (i.e. 5L41, 5L42, 5L44, 5L45,5L81, 5L82 and 5L87) to calculate thermal and voltage stability limits [10].As expected to update every 2 minutes, the results are presented as South Inte-rior (CI-SI) generation plot indicating current operating point, thermal and voltagestability regions, and on-line CI and SI generation capability limits. An example ofthe 2-dimension voltage security region of the present operation condition shownin Figure 2.8.2.7 Challenges of Current Practice2.7.1 RMR and RAS DevelopmentNo matter RMR or RAS, the purpose is to make sure the pre- and post-contingencyoperation conditions remain voltage stable during and after a contingency. The keyis to accurately assess the voltage stability limit of the corresponding operationconditions.Typically, instead of studying all possible operation conditions, power systemplanners focus on worst scenarios and most limiting situations. Tables and nomo-grams are used here to illustrate the relationship between voltage stability limit andthe selected operation conditions. Figure 2.9 is a nomogram indicating the transferlimit versus load and VAR support capability [41].27Figure 2.8: 2-Dimension voltage security region in RTVSA [10]500600700800900100011001200130014001500160017001800190020002100220023002400250026002700280029003400 3600 3800 4000 4200 4400 4600 4800 5000 5200 5400 5600 5800 6000 6200 6400 6600 6800 7000BCH Load (MW))WM( timiL refsnarT SUC ot GNI4 BGS SC3.5 BGS SC3 BGS SC2.5 BGS SC2 BGS SC1.5 BGS SC1 BGS SC0.5 BGS SC0 BGS SC                            Figure 2.9: ING to CUS transfer limit versus BCH load and number of on-line equivalent Burrard synchronous condensers [41]28Thanks to these detailed tables and nomograms, BC Hydro transmission sys-tem operates in a smart way and is able to extend its operation into some extremesystem scenarios. However, along with the expansion of system and RAS ap-plication, the complexity of system operation increases dramatically. The currentpractice leads to challenges for both planning engineers and operators:• With the evolving of system, more and more system scenarios not only needplanning engineers to elaborate but also make operators difficult to under-stand.• To cover all possible system operation scenarios and simplify the study,choosing worst scenarios is typically used, such as applying peak load andheavy transfer for voltage stability related issues. However, only consideringworst scenarios will inevitably result in conservative operation.• The solution of gen-shedding equation or voltage stability security bound-aries usually can take only one or two input variables. Other related variablesare ignored. This makes the system operation further conservative.2.7.2 Real-Time Voltage Stability AssessmentAs shown in Figure 2.7, the input for RTVSA is the load-flow solution reflectingthe current operation condition from the state estimator. Although the load-flowmay be valid from state estimation perspective, it may contain some buses withextreme low voltages. RTVSA relies on high-quality load-flow, bad solution fromstate estimator may cause RTVSA fail to solve security boundaries [10]. Further-more, the model generated by state estimator is not always consistent with modelused in off-line study. It may result in different voltage stability margin for a sameoperation condition, which makes the result of RTVSA invalid to guide the controlactions developed off-line.29Chapter 3Operation Knowledge DatabaseGeneration: VI Loading LimitStudyTo err is human, but to really foul things up requires a computer.— ARTHUR BLOCH (Murphy’s law, Vol. III)In this chapter, the development of an operation knowledge database for VIsystem voltage stability assessment is investigated. The characteristics of BC Hy-dro VI system is firstly overviewed. Then based on the operation experience, theoperation conditions covering VI peak load period system operation is defined.Historical hourly load data is studied to validate the proposed operation condi-tions. The discussion of VI loading limit calculation of each operation conditionis followed, where modal analysis and CPF are applied to ensure the accuracy. Atlast, a data verification scheme is proposed to ensure the quality of the database.3.1 Problem FormulationThe proposed on-line voltage assessment relies on the capability of ANN to mapbetween the operation condition with the VI loading limit. The accuracy of ANNmodel requires a complete and accurate operation knowledge data base, which pro-vide information of interested operations and the corresponding VI loading limit.30To achieve this objective, the sub-tasks includes:• A realistic and complete set of interested operation conditions should be gen-erated for loading limit study. Possible network topology, unit commitment,and load distribution should be taken into consideration.• The post-contingency loading limit should be accurately computed for eachoperation condition. Relevant power system control and operation practicesshould also be appropriately modeled.• A data verification strategy should be develop to ensure the quality of thedatabase.• A automatic data generation system based on available commercial soft-wares should be developed.The flowchart shown in Figure 3.1 presents the process of operation knowledgedatabase generation. In this chapter, an operation condition is the combination ofa specified system scenario and a determined load distribution. System scenario isdefined by the information of the generation status/output, network topology, andcomponent status. And load distribution is defined by the information of status,real power and reactive power of the load.3.2 Overview of the BC Hydro VI System3.2.1 Load and GenerationVI is one of the most populated areas of British Columbia, and along with theLower Mainland, is home to the greatest electricity demand. As shown in Fig-ure 3.2. The VI system consists of 3 subsystems geographically, including North-ern VI system, PAL&LBH system, and Southern VI system. Southern VI systemincludes Southern VIT and Northern VIT subsystems.The generation in Northern VI takes up 76.9%. While in Southern VI, there isonly one generating station named Jordan River generating station (JOR) with 170MW capacity, taking up 17.1%. The rest 6.0% generation is located in PAL&LBHsystem [45].31PSATBase CaseTraining data for neural networkApply system scenariosApply load distributionsVSATSolve loading limitModal analysisOperation conditionsVI loading limitData verificationSolvedload-flowContingencyFigure 3.1: The flowchart of operation knowledge database generationThe total winter peak load of VI is 2046 MW. The load center is located atSouthern VI, taking up 75.4% of the total load. The VI load is also suppliedfrom Lower Mainland system (LM) by two transmission paths, 500 kV double-circuit cables (5L29&5L31) in the north and 230 kV single-circuit cable in thesouth (2L129).3.2.2 N-1 Contingency Screening AnalysisAs a part of VI operating order development, VI N-1 contingency screening hasbeen conducted by BC Hydro Performance Planning group. The purpose of thisstudy is to shortlist and rank the contingencies for further studies. The per-contingencyand post-contingency VI loading limits have been compared under the loss of se-lected line, generation, static Volt-Ampere reactive compensator (SVC) and shunt32North VIL: 16.6%G: 76.9%PAL&LBHL: 8%G: 6.0% South VIL: 75.4%17.1% North VITL: 28.8%South VITL: 46.5%2L129VIT Station5L29 & 5L31Figure 3.2: Transmission map of BC Hydro VI system [39]capacitor. The result has shown that the loss of 2L129 will reduce the VI loadinglimit most significantly [40].The study described in the following sections will focus on exploring the VIloading limit against the loss of 2L129 contingency for VI operation.3.3 Base Case ProfileDocumented in [46], the base cases used in this thesis are prepared by BC Hy-dro Transmission and Station Planning department according to established proce-dures. Base cases include facility models, load forecast data, interchange sched-ules, and external system representation.3.3.1 External System DataThe Western Electricity Coordinating Council (WECC) coordinates the prepara-tion of member system base cases to achieve good representation of the whole ofthe western interconnection system [47, 48]. Each year, WECC produces 11 base33Table 3.1: Load-flow base case informationSystem extentNumber of buses and branchesLoad buses Generator buses BranchesWECC system 16423 3893 16320BC Hydro system 1902 356 1375VI system 244 56 200cases based on the appropriate data submitted by its member [49]. Each case rep-resents a specified conditions which intends to stress some portion of the westerninterconnection for certain typical conditions in a current or future year. For ex-ample, a base case with summer peak loads in California and peak generation inBC, Washington and Oregon is designed to stress the transmission system betweenWashington-Oregon area and California.The accurate representation of external systems is very important in systemtransmission studies. BC Hydro base cases include a representation of externalsystems, normally an equivalent representation based on a current or recent pastyear base case [46].The base case used in this chapter is acquired from BC Hydro Power SystemModeling and Analysis group. The version of base case used here is b16hwp50d,which stands for 2016 heavy winter peak load under bulk load group coincidentwith 1-in-2 probability forecast (Mid-Forecast or P50) [46]. It is customized toreflect the current system topology and operation practice. The basic informationof the base case is shown in Table 3.1.3.4 VI System Scenarios Generation Based on Operationand Planning KnowledgeThe objective of generating a complete and realistic set of operation conditions isto prepare training data for the neural network model described in Chapter 4, whichis designed to be used for VI loading limit calculation for real-time operation con-ditions. Training data provides all the information for the neural network model.It needs to be the representative of the whole operation conditions of concern toensure the generalization of the trained model.34However, practical system like VI system described in Section 3.3 has a largenumber of buses and branches. The combination of possible generation patterns,system topologies, unit commitments, and other operation practices produces agreat number of possible system scenarios, which is impossible to enumerate. Onthe other hand, it is also not necessary to explore all the possible system scenar-ios. Attention should only be given to the key factors that directly determines VIloading limit.As VI system has been well studied and operated BC Hydro transmission plan-ners and operators, key factors are shortlisted into 3 main categories: Jordan RiverGeneration (JOR) availability, Vancouver Island Terminal (VIT) Var support capa-bility, and VI bulk electrical system element N-1 pre-outages.Jordan River Generation AvailabilityAs described in Section 3.2, JOR station is the only major generating station onsouthwest coast of VI. The facility has a generating capacity of 170 MW andcan contribute approximately 17% of the total generation [45]. Its reactive poweroutput limits are -13 MAr to 43 MAr. However, the JOR has relatively smallreservoirs and runs full capacity for a very short period [50]. It is operated foremergency and peak period. As shown in Table 3.2, the status and availability ofJOR are selected from not available, available/synchronous condenser mode, andavailable/Pgen = 30,60,90,120,150,170MW .VIT VAR Support CapabilityVIT has a group of synchronous condensers and shunt capacitors with a total 495MVAR supporting , including 50 MVAR SC2, 100 MVAR SC3 and SC4, 245MVAR switchable shunt capacitors. It is the major VAR support facility for SouthVI system. The availability of VIT VAR capacity is selected from 495 MVAR (allunits available), 445 MVAR (SC2 not available), 395 MVAR (SC3 not available),and 345 MVAR (SC2/SC3 both not available).35Table 3.2: VI system scenarios definitionCategories JOR VITN-1 pre-outagesTotalLine Shunt Cap Transformer SVCCombinations 8 4 15 6 2 2 800VI N-1 Pre-outageThe pre-outages considered include possible outage of transmission line, trans-former, shunt capacitor and SVC out of service (OOS). BC Hydro planners short-listed the pre-outages into the possible outage of 15 major transmission lines, 6load shunt capacitors, 2 major transformers, and 2 SVCs:• Line OOS: {1L10, 1L11, 1L12, 1L14, 2L123, 2L126, 2L143, 2L144, 2L145,2L146, 5L29, 5L30, 5L42, 5L44, 5L45}• Load capacitor OOS: {CLD 25, ESQ 12A, ESQ 12B, GTP 25, HSY 12A,SNY 25}• Transformer OOS: {VIT T6, DMR T1}• SVC OOS: {DMR SVC OOS with 6RX online, DMR SVC OOS with 5RXonline}3.5 VI Load Distribution Generation3.5.1 Previously Proposed ApproachThe importance of load characteristic and distribution has been well discussed in[4, 6]. Many previous works take great efforts to address the variations of loaddistribution. In references [14, 51], 3000 operation conditions were generated fora practical AESO 1844-bus system using the following equations:For 746 load buses,PiL(k) = PiL0(1+2∆PL[0.5− ε iPL(k)]) (3.1)QiL(k) = QiL0(1+2∆QL[0.5− ε iQL(k)]) (3.2)36For 302 generator buses,PiG(k) = PiG0(1+2∆PG[0.5− ε iPG(k)]) (3.3)V iG(k) =ViG0(1+2∆V G[0.5− ε iV G(k)]) (3.4)Where, PiL(k), QiL(k), PiG(k), and ViG(k) are the load active power, load reactivepower, generator active power, and the generator voltage magnitude setting in thegenerated operation conditions. PiL0, QiL0, PiG0, and ViG0 are the base case values ofthe corresponding variables. ∆PG = ∆PL = ∆QL = ±30%, ∆V G = ±3%. ε is theuniform independent random variables between 0 and 1.The same approach was applied for the New England 39-bus test system in[12]. This approach failed to consider the variation of system topology, unit com-mitment, contingencies, and the operation practices of the system, which have greatimpact on power system loading limit. Furthermore, the number of generated op-erations is too few for a 1844 buses system. The generated data set is very likely tobe representative for only part of the operation conditions, leading to poor abilityof generalization.In references [13, 15], variation of system topology, unit commitment, andload distribution were taken into consideration for operation conditions generation.However, this approach was applied for the IEEE 30-bus test system [13], the IEEE118-bus test system and the Finnish 113-bus equivalent transmission system [15].In reference [15], the author discussed the complexity and difficulty in to generaterealistic operation conditions for a practical system. Detailed and accurate models,operation knowledge and robust automation of data generation were required forthe application on a practical system.3.5.2 Load Uncertainty Analysis of VI System Based on HistoricalDataThe study of load uncertainty is very important for load forecasting, which hasattracted a lot of research efforts [52].The historical hourly load data of 10 major South VI distribution stations andVI total load of the period of 2015 was retrieved from BC Hydro PI System. The37Table 3.3: VI total load level hourly distribution of the year of 2015HSY12 HSY25 ESQ KTG KSH SNY GOW GTP CLD SOO VI loadHSY12 1.00HSY25 0.93 1.00ESQ 0.92 0.97 1.00KTG 0.90 0.93 0.94 1.00KSH 0.94 0.92 0.92 0.91 1.00SNY 0.88 0.92 0.93 0.97 0.92 1.00GOW 0.75 0.82 0.80 0.81 0.76 0.80 1.00GTP 0.91 0.97 0.97 0.97 0.90 0.96 0.82 1.00CLD 0.92 0.96 0.96 0.98 0.90 0.95 0.82 0.99 1.00SOO 0.65 0.74 0.74 0.71 0.69 0.73 0.65 0.75 0.74 1.00VI Load 0.91 0.93 0.93 0.95 0.89 0.92 0.79 0.95 0.96 0.73 1.0038Figure 3.3: 2015 VI system hourly total loadnormalized total VI hourly load data is presented as Figure 3.3. The hour-durationversus load level of VI total load is shown as Figure 3.4. Correlation coefficientsare calculated for the 11 hourly load data. The correlation matrix is shown inTable 3.3.The load characteristics in practical power system can be summarized as belowbased on the analysis of the historical data:1. Practical system is heavily loaded for very limited duration.As shown in Figure 3.4 and Table 3.4, the heavy load period of VI system(when the load is larger than 90% of the peak load) is only 64 hours, whichis 0.73% of a year.2. Distribution loads that are geographically close to each other are highly cor-related, namely, they tend to peak at the same time.Most of the correlation coefficients in Table 3.3 are very close to 1, whichdemonstrates the high correlation among the 11 hour load data.390 0.2 0.4 0.6 0.8 1VI total load normalized by peak0100200300400500600Duration (hours)Figure 3.4: Hour-duration versus load levelTable 3.4: VI total load level hourly distribution of the year of 2015Load level Duration (hours) Duration per year90%-100% of peak load 64 0.73%60%-90% of peak load 2720 31.08%30%-60% of peak load 6011 68.67%Less than 30% of peak load 22 0.25%3.5.3 Proposed Operation Condition Generation MethodTaking the load characteristics into consideration, the requirements for generatingrealistic set of load distributions are:• The load distribution generated off-line should be representative of the loaddistributions when VI system is heavily loaded.The general application of the proposed method in this chapter is for VI volt-age stability assessment when the total VI load approaches the loading limit.40Considering the short duration of heavy load period, the load distribution setgenerated off-line is not necessary to cover all possible loading levels, in-stead, it should only match the load distributions when the whole VI systemis heavily loaded.• Assumed load distribution can be used considering the highly correlated loaddistribution among VI stations.As well discussed in [26], virtually all power system transmission planningand operating is practiced using assumed load distributions and growth ratesbased on load forecasts described in Section 3.3.In BC Hydro, the typical assumed load data used by power system plannersand operators are generated by non-coincident station peak load forecasts and co-incidental factor [46]. Non-coincident station peak load forecasts are the predictedpeak load of each substation for a specified year. But not all substations peak atthe same time, or on the same day of any given year. Even among winter peak-ing and summer peaking substations, there is some diversity in the timing of peaknon-coincident loads. Base on the investigation of historical data, the load coinci-dental factor is used to describe the level of load coincidence. Each load in the basecase has 4 coincidental factors: bulk peak, area peak, zone peak, and station peak.For example, the bulk system coincidental factor determines that what should eachload of the system be if the BC Hydro total load reaches its peak. The area of VIcoincidental factor determines what should each load of VI should be when the VItotal load reaches its peak. The base case described in Section 3.3 uses the loadforecasts of the year 2016 and the bulk peak coincidental factor.The proposed load distributions are based on the 2016 load forecasts and thebulk peak coincidental factor. To consider even heavier loaded situation, one of the17 South VI residential loads is set to station peak coincidental load while keepingother loads in VI to bulk peak coincidental load. So for each system scenarios, 18operation conditions are defined by 18 load distributions:• Station peak load: one of {GTP 25, CLD 25, HSY, NFD 25, KTG 25, SNY 25,PVL 25, LTZ 25, HWD 25, GOW 25, PVO 25, KSH 25, ESQ 12, LDY 25,QLC 25, SHA 25, SOO 25}41Table 3.5: Statistical analysis of VI loading limit generated by hourly loadMaximum Minimum Mean Median Standard deviationMW 2129.8 2073.5 2097.4 2098.7 12.345• Bulk peak load: all other loads of BC HydroPowerFlow & Short Circuit Assessment Tool (PSAT) is used to generate op-eration conditions summarized in Figure 3.5. The PSAT software, a part of Pow-ertech’s DSAToolsTM suit, is a full-featured load-flow program with a graphicaluser interface to create, examine and modify power flow data, solve power flow,and view solution reports. The combination of 800 system scenarios and 18 loaddistributions described above produces 14,400 operation conditions in the formof solved load-flow. The operation condition generation process is automated byPSAT scripting feature.3.5.4 Verification of the Proposed Method Using Historical HourlyLoad DataThe discussion above explains the reason to use assumed load distributions to rep-resent the load distributions during the heavy load period. In this section, the load-ing limit of operation conditions defined by historical hourly load data is calculatedto verify the use of assumed load distributions. The process is described as below:• The 64 VI hourly load distributions of 2015 heavy load period (90% - 100%of the peak load) in Table 3.4 are applied to the base case, respectively. Withsetting N-1 pre-outage = 2L123 OOS, VIT = 495 and JOR = 170 for all the64 historical hourly load distributions, 64 operation conditions are generatedin the form of solved load-flow by PSAT.• 18 assumed load distributions described in the previous section are appliedto the base case, receptively. With setting the same N-1 pre-outage, VITcapability, and JOR generation as above for all the 18 assumed load distribu-tions, 18 operation conditions are generated in the form of solved load-flowby PSAT.4218 load distributions800 system scenariosApply JOR status/outputBase caseApply VIT capabilityApply N-1 pre-outageApply load distribution14,400 operation conditionsFigure 3.5: Flowchart of operation condition generation• The VI loading limit of the 64 operation conditions generated by historicaland the 18 assumed load distributions are calculated by Transient SecurityAssessment Tool (VSAT) using the method described in Section 3.6.The statistical analysis of the result is shown in Table 3.5. The comparisonof the loading limit between historical heavy load distribution and assumed loaddistribution is shown in Figure 3.6. The findings can be summarized as:• The variation of the load distribution during the heavy period (when the totalload is more than 90% of the yearly peak) has very limited impact on the432070 2080 2090 2100 2110 2120 2130VI loading limit calculated by VSAT (MW)024681012OccuranceAssumed load distributionHourly load distributionFigure 3.6: VI loading limit calculated using assumed load distributions ver-sus historical hourly load distributionsload limit; the range of the VI loading limit of the hourly load distribution isfrom 2073.5 MW to 2129.8 MW.• VI loading limit of the system conditions generated by assumed load distri-butions is relatively conservative but very close to that of historical hourlyload distributions, which demonstrates the effectiveness of using assumedload distributions.Based on the discussion above, it is reasonable and practical to use assumed loaddistributions to generate system conditions.443.6 Loading Limit Simulation in VSATThe maximum loading point of each operation condition under 2L129 contin-gency is computed by the voltage security assessment tool VSAT. As a key partof DSAToolsTM suite, VSAT helps the system planners and operators determinethe voltage security or power transfer limit of a given system state in off-line or on-line (connected to an operation center EMS environment). The procedure of VIloading limit calculation is summarized in Figure 3.7. The techniques describedbelow are used to ensure accurate and efficient calculation of VI loading limit:• CPF is used for loading limit calculation. As reported in [35], CPF improvesthe accuracy of the voltage collapse point calculation by excluding the pos-sibility of ill-conditioning causing divergence. The principles of CPF hasbeen elaborated in Chapter 2• XB version of fast decoupled load flow (FDLF) is selected for loading limitcalculation by VSAT [53]. FDLF was reported to handle contingency anal-ysis accurately and efficiently [54, 55].3.6.1 Modeling of Control PracticeOn Load Tap ChangerThe on load tap changer (OLTC) positions have been well tuned in the base case toreflect the system voltage control during heavy loading period. During the VSATsimulation, all the OLTCs in VI and Lower Mainland are locked. The reasons are:• Although OLTC action during low voltage conditions is a significant fac-tor contributing to voltage collapse, the scope of this chapter is limited tolong term voltage stability using steady-state method. The voltage collapsemechanism study requires detailed dynamic modeling of load and time do-main simulation.• Unlocking the OLTC sometimes makes the load-flow hard to solve for con-tingency analysis. It is a common practice to lock OLTC to conduct voltagestability studies for transmission planners.45Apply 2L129 contingencySolved load-flowTrip 1L115 and 1L116ConvergedConvergedIncrease VI distribution loadCPF & Modal Analysis1L115 RASConvergedYesLoading limitYesNoNoYesTriggeredNot triggeredNoFigure 3.7: VI loading limit calculation using VSAT46Switchable ShuntsAll the switchable shunts in VI and Lower Mainland are also locked during VSATsimulation. In the base case, which is heavily loaded, all the switchable capacitorsin VI and Lower Mainland at load bus have been switched in. All the shunt reactorsin VI system are fixed as the initial setting in base case.3.6.2 Modeling of Overcurrent RASIn VI system, 1L115 and 1L116 connects DMR 138 kV bus and JPT 138 kV busas shown in Figure 3.2. Under certain circumstances, the current can reach theconductor thermal limit. 1L115 RAS is designed to trip the LTZ to JPT sections of1L115 and 1L116 when 1L115 or 1L116 is over loaded. The logic of 1L115 RASis modeled in VSAT SPS file.3.6.3 Computation Direction of Load and GenerationThe VI loading limit is computed by gradually increasing the distribution load ofVI and the generation of a specified generator group until the post-contingencyload flow diverged. In this study, the distribution load of VI is increased graduallywhile the industrial load of VI remains the same as the base case. At each step,the 2L129 contingency is applied. The generation of 5 major plants at BC Interior(GMS, PCB, MCA, REV, and SEV) is increased gradually to make up the load andloss incremental. The generation of VI remains the same as the base case. TheVI loading limit is reached when the post-contingecency firstly load-flow diverges.The computation procedure of VI loading limit is summarized in Figure 3.7.3.7 Data VerificationAs discussed above, an operation knowledge database of 14,400 operation con-ditions and the corresponding VI loading limit has been generated by PSAT andVSAT. Data verification is a must procedure to ensure high quality data. Two ques-tions need to be answered:• Does the load-flow generated by PSAT represents a practical operation con-dition?47Data verficationTraining data for neural networkCheck key line power flowCheck modal analysis reportCheck the RAS statusCheck key bus voltagePSATBase CaseVSATContingencyFigure 3.8: Proposed data verification schemeLoad-flow problems are expressed as sets of non-linear equations, they haveno unique solutions. Reference [54] also shows that bad initial values outsidethe convergence region lead to load-flow diverged. Transmission plannersand operators rely on experience and knowledge of the system to excludethe infeasible load-flow and tweak the diverged load-flow.• Is maximum loading limit calculated by VSAT accurate?CPF is used for maximum load limit calculation. Yet despite that, inappro-priate modeling of the system may also cause errors in maximum loadinglimit calculation.The data verification procedure is summarized in Figure 3.8, which is pro-gramed in a Python script.48 Modal Analysis Report Continuation Power FLow Called Contingency 2L129                             in Point no.   28                                    =========================================================================    Pre-contg.  VI load         :   2159.9 MW     BCGEN wo VI     :   7269.8 MW      Mode No.  1:     EigenValue =     0.005031    0.000000                          Bus Participations ---------------------------------------------------------------------------------- No.  Bus No., Name             Gen.  Area No., Name  Zone  Part.Fac.  Voltage (Pu) ----------------------------------------------------------------------------------    1   5030  CSL 6G1     6.90    QL    1  BC HYDRO    505   1.00000,        1.1225    2   5000  CSL 6G2     6.90    QL    1  BC HYDRO    505   1.00000,        1.1225    3   5930  CSL 25      25.2          1  BC HYDRO    505   0.89944,        1.1367    4   5966  VLM 52L3    25.2          1  BC HYDRO      5   0.73753,        1.2186    5   5965  VLM 52F     25.2          1  BC HYDRO      5   0.71141,        1.1801    6   5765  VLM 25VR2   25.2          1  BC HYDRO      5   0.71135,        1.1801    7   5709  MIK 25P     25.2          1  BC HYDRO      5   0.69338,        1.2662    8   5909  MIK 25      25.2          1  BC HYDRO      5   0.68960,        1.2685    9   5759  ETC 25P     25.2          1  BC HYDRO      5   0.66756,        1.2958   10   5959  ETC 25      25.2          1  BC HYDRO    505   0.65868,        1.3019   11   5009  MIK 4G1G2   0.48    QL    1  BC HYDRO      5   0.64642,        1.2970   12   5059  ETC .6G     0.60    QL    1  BC HYDRO    505   0.63116,        1.3194   13   5963  VLM 52L4    25.2          1  BC HYDRO      5   0.61131,        1.3795   14   5958  RBV 25      25.2          1  BC HYDRO      5   0.61115,        1.3797   15   5058  RBV 4G3     4.16    QL    1  BC HYDRO    505   0.59584,        1.3955 Mode No.  2:     EigenValue =     0.006349    0.000000                          Bus Participations ---------------------------------------------------------------------------------- No.  Bus No., Name             Gen.  Area No., Name  Zone  Part.Fac.  Voltage (Pu) ----------------------------------------------------------------------------------    1   2960  SOO 25      25.2          1  BC HYDRO      2   1.00000,        0.9145    2   2959  CLD 25      25.2          1  BC HYDRO      2   0.98971,        0.9073    3   2161  JOR 132     132.          1  BC HYDRO      2   0.96575,        0.9636    4   2160  SOO 132     132.          1  BC HYDRO      2   0.94420,        0.9185    5   2061  JOR 13G1    13.8    QL    1  BC HYDRO    402   0.89896,        0.9296    6   2961  JOR 25      25.2          1  BC HYDRO      2   0.89116,        0.9491    7   2461  JOR 25B1    25.2          1  BC HYDRO      2   0.89070,        0.9747    8   2955  GTP 25      25.2          1  BC HYDRO      2   0.87349,        0.8834    9   2948  SNY 25      25.2          1  BC HYDRO      2   0.86186,        0.8804   10   2159  CLD 132     132.          1  BC HYDRO      2   0.83794,        0.9110   11   2648  SNY 60T1    60.0          1  BC HYDRO      2   0.65580,        0.9625   12   2856  GTP  12     12.6          1  BC HYDRO      2   0.63750,        0.8789   13   2748  SNY 60T2    60.0          1  BC HYDRO      2   0.62794,        0.9691   14   2154  GOW 132     132.          1  BC HYDRO      2   0.61334,        0.9245   15   2157  GTP 1T3     132.          1  BC HYDRO      2   0.60298,        0.9208 Mode No.  3:     EigenValue =     0.023157    0.000000                          Bus Participations ---------------------------------------------------------------------------------- No.  Bus No., Name             Gen.  Area No., Name  Zone  Part.Fac.  Voltage (Pu) ----------------------------------------------------------------------------------    1    441  COM 4       4.16          1  BC HYDRO     11   1.00000,        1.0226    2    341  COM 4V51    4.16          1  BC HYDRO     11   0.98190,        1.0227Figure 3.9: Modal analysis report of the base case with VLM system49Figure 3.10: Transmission map of BC Hydro VLM system [39]3.7.1 Base Case Trimming Using Modal AnalysisAs discussed in Chapter 2, the magnitude of the eigenvalues of the reduced Jaco-bian matrix at the nose point of P-V curve can provide a relative measure of theproximity to instability. Bus participation factors of the given mode are used topinpoint the critical areas associated with each mode. Modal analysis is appliedat the maximum loading point for VSAT simulation to reveal the critical areas andbuses causing voltage collapse.The base case described in Section 3.3 is firstly studied by applying 2L129contingency using VSAT. After analyzing the mode and the corresponding busparticipation factors, one mode related to VLM 25 kV area catches the attention,which is always associated with smallest eigenvalue no matter how operation con-ditions vary. The modal analysis report generated by VSAT in Figure 3.9 shows3 typical modes appearing frequently in the studies. The VLM 25 kV area mode50ranks first with the smallest mode while the interested mode associated with VIarea ranks second.VLM 25 kV area is located in BC North Interior, it is known as a weak areawith low reliability. As shown in Figure 3.10, it is connected to BC Hydro 500 kVbackbone system through a more than 300 km single circuit 138 kV transmissionline. Several small run of river hydro generators and loads are connected to VLM138 kV bus through long 25 kV distribution lines, which makes the associatedmode reasonable to rank high in the modal analysis report.Although the characteristics of VLM system well explains the high rankingmode, VLM area is far away the interested area and the voltage stability of VLMarea is out of the study scope. This is a good example that demonstrates the neces-sity of appropriate modeling for voltage stability study. To eliminate the possibilityof VLM area causing voltage instability of the system, the VLM 25 kV system isconverted into an equivalent constant PQ load for all studied cases. The trimmingof the base case ensures that the interested mode associated with VI system alwaysrank first of all studied operation conditions.The data verification summarized in Figure 3.8 checks modal analysis report ofeach operation condition to ensure the voltage stability collapse point is accuratelylocated.3.8 Visualization of Operation Knowledge DatabaseThe operation knowledge database is stored in the form of a table in which eachrow describes an operation condition and its corresponding VI loading limit. Ta-ble 3.6 shows 2 data samples from the database. The first data sample describesan operation conditions when JOR is in synchronous condenser mode, VIT MVARcapability is 345 MVAR, line 1L10 is pre-outage, and the load distribution is CLDpeak. The corresponding VI loading limit is 2220.2 MW. The second data samplecan be interpreted similarly.The visualization of the VI loading limit against the corresponding operationconditions is needed to analyze the voltage stability issue in both planning andoperation stages. The visualization helps the definition of the operation range ,contingency analysis, and pre-outage restriction analysis.51VIT JORVI N-1 pre-outage #1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25345 oos0306090120150170395 oos0306090120150170445 oos0306090120150170495 oos03060901201501701,782.12,461.1VI loading limitFigure 3.11: Heat map of VI loading limit versus operation conditions whenload distribution is all bulk peakTable 3.6: Data samples of operation knowledge databaseOperation Condition Loadinglimit (MW)JOR status JOR MW VIT MVAR Pre-outageLoaddistributionIn service 0 345 1L10 CLD peak 2220.2In service 120 495 2L123 HWD peak 1931.352Figure 3.11 presents the heat map of the VI loading limit subjected 2L129contingency when the load distribution is all bulk peak. For each of the 18 loaddistributions described in Section 3.5, there is a heat map available similar withFigure 3.11.According the VI loading limits shown in Figure 3.11, the worst pre-outageis No. 5, which is corresponding to 2L123 pre-outage. We can also find that theVI loading limit increases with higher JOR output and VIT available VAR supportcapability, which coincides the operation experience.53Chapter 4Loading Limit Assessment andPreventive Control ActionRecommendations Using ANNAll models are wrong but some are useful.— George E. P. BoxIn this chapter, an ANN framework is proposed and implemented for VI load-ing limit assessment and preventive control actions recommendations. The ANNdesign, feature selection, and training are investigated. Finally, how the proposedframework is applied in power system operation is discussed.4.1 Overview of the Proposed ANN FrameworkThe overview of the proposed framework is presented in Figure 4.1. The off-linestage and on-line stage of the framework are discussed in the following sections.4.1.1 Off-line StageIn the off-line stage, a realistic and complete set of VI pre-contingency opera-tion conditions including the variation of N-1 pre-outages, VAR support capability,generation availability and load distribution is generated by PSAT in the form of54Training data generationPSAT:Operation conditionsVSAT:VI loading limitANN model creationANN trainingOff-line stageModelSCADAVI loading limitOn-line stagePreventive control action recommendationsFigure 4.1: Overview of the proposed ANN frameworksolved load-flow. The corresponding loading limits are calculated by VSAT usingCPF. The methodology of data generation and verification has been discussed inChapter 3.Then based on the operation knowledge database, an ANN model is trained bythe selected features representing the operation conditions and loading limits fromthe database. The methodology of the hidden layer size design, feature selection,training, and application of ANN model are discussed later in this chapter.4.1.2 On-line StageIn the on-line stage, the framework is integrated with the SCADA and EMS sys-tem. The information of the system operation conditions received from SCADA isfed into the framework to assess the loading limit. Given a target loading limit, theANN framework can generate the requirements for operation conditions to supplythe specified loading, which can be used as preventive control actions against any55x2 wk2Σ fActivationfunctionykOutputx1 wk1xN wkNWeightsBiaswk0......InputsFigure 4.2: The structure of a neuronpotential contingencies.4.2 Multi-Layer Feed-Forward Neural NetworkAmong various types of ANN have been proposed, the multi-layer feed-forwardneural network, which is commonly referred as Multi-Layer Perceptron (MLP), isthe best and most widely type for function approximations [56]. It is regarded as auniversal approximator, which is capable of non-linear function approximation inmultidimensional space.The fundamental element in MLP is the neuron. The model of a neuron isshown in Figure 4.2 [56]. In mathematical terms, a neuron k can be described as(4.1), where xi is the ith input signal, wki represents the weights of the connectionpath from ith input to kth neuron, yk is the output of the kth neuron. The activationfunction f (x) generally can be any nonlinear, continuously differentiable, mono-tonic and smooth function [56]. The activation function in this thesis is selected asa sigmoid function, given as (4.2).yk = f (N∑i=1wkixi+wk0) (4.1)f (x) =1− e−x1+ e−x(4.2)The architecture of a single hidden layer MLP and its learning process are56InputlayerHiddenlayerOutputlayerInput 1Input 2Input 3Input 4Input 5−Output yio+Target yit∆w =−η ∂J∂wBackpropagationJ := 1M ∑Mi=1(yio− yit)2Error functionWeight addjustmentFigure 4.3: The learning process of MLPshown in Figure 4.3, which is used in this chapter. The MLP consists of one in-put layer, one hidden layer and one output layer. The hidden layer and outputlayer consist of one or more neurons. The learning of a MLP is achieved by itera-tive adjustment of its weights based on the training data and desired outputs. Thederivatives of the defined error function J is applied in a backpropagation algorithmto achieve adaptive weight adjustment. The coefficient η in the backpropagationalgorithm controls the step size of the iterative weight adjustment, which is com-monly referred as learning rate.4.3 Feature Selection and ExtractionIn machine learning problems that involve learning from a finite number of datasamples, a high-dimensional feature will suffer from “the curse of dimensionality”,57namely, an enormous amount of training data are required to ensure that there areseveral samples with each combination of values [57].To reduce the dimension of the input data, feature selection and extraction areused to selected useful features or create new features from the input data set. Theaim of feature selection and extraction are:• To make the model easy to be interpreted by power system engineers• To reduce the training time4.3.1 Previously Proposed MethodFeature Selection Based on the Load-flow VariablesPi =V 2i Gii+Vi∑i 6=kVk(Gik cosθik +Bik sinθik)Qi =−V 2i Bii+Vi∑i 6=kVk(Gik cosθik−Bik sinθik)(4.3)The load-flow network equations shown in (4.3) describe the relationship be-tween bus voltage magnitude V , voltage angle θ , real power P injection and reac-tive power Q injection. A set of these four quantities associated with the load-flowsolution represents and defines an operation condition. Naturally, selection of 2 ormore bus quantities of V , θ , P and Q from the solved load-flow is used as inputfeature in a number of references.In reference [38], real and reactive power injections of all load buses wereused as features to train an ANN model for voltage stability margin prediction.Reference [58] improved the method by adding bus voltage magnitudes into thefeature set. In [59], alongside the voltage magnitudes, real and reactive powerinjections, the tap positions of the OLTCs were placed into the feature set.Reference [14, 51] firstly used voltage angles and magnitudes as input featureset. The ANN model is trained for voltage stability margin prediction for a IEEE39-bus system and an 1844-bus system. Reference [13] placed the topology infor-mation into the input feature set. The generation availability, line status, and loadconditions are formed as the input feature set to calculate the transfer capability fora modified IEEE 30-bus system.58The feature selection methods in the previous works has shown their effec-tiveness for a small-size test system. However, there are challenges to apply to apractical system:• The number of loads, generators, and lines for a practical system is verylarge, which makes the computation and memory cost very high.• The loading limit or voltage stability margin information delivered by the V ,θ , P and Q is masked. Although V , θ , P and Q in (4.3) define and representan operation condition, they do not convey explicit information related toloading limit or voltage stability margin.• The input feature set is not only used for ANN training but also for on-lineloading limit assessment, which requires the input feature set be accuratelymeasured by SCADA system.Feature Extraction Based on Statistical Analysis of the Training DataGeneral dimensionality reduction techniques are used to select features or constructnew features from training data.Reference [12] conducted the parameter sensitivity analysis of the input datausing a second order regression model. Input features were selected based on thesensitivity ranking. The ANN models was applied to the New England 39-bus testsystem.Reference [15] constructed new features from the input load-flow data usingprincipal component analysis and K-means clustering methods. The test systemswere the IEEE 118-bus test system and Finnish 113-bus equivalent transmissionsystem.The methods described above effectively reduce the input data dimension andwork well for the test systems. However, the feature extracted from the trainingdata using statistical methods damages the physical concepts and makes the modelhard to interpret. Moreover, the fact should not be overlooked is that the bestfeature selection and extraction is from the knowledge and operation experience ofthe operators and planners.594.3.2 Feature Selection Based on Engineering Experience andOperation KnowledgeThe ideal feature set is characterized as below:• The feature set should well represent the operation conditions.• The feature set should be the determining factors for the loading limit.• The feature set should be able to be collected from SCADA system with highfidelity.The voltage stability issues of VI system has been well studied by BC Hydroengineers. The determining factors of VI loading limit have been discussed inSection 3.2. Based on the operation knowledge and experience, the VI N-1 pre-outage, the status of JOR, the real power output of JOR, and the VAR supportcapability of VIT are selected as the input feature set X for the ANN model.X =SOOSSJORPJORQV IT28×1(4.4)Where, SOOS is a 25× 1 binary vector representing the status of the possibleVI N-1 pre-outage elements (1 is for the specified element is pre-outage and 0 isfor the specified element is not pre-outage). SJOR is a binary number representingthe JOR availability (1 is for in service and 0 is for out of service). PJOR is areal number representing JOR MW output. QV IT a real number representing VITMVAR capability.The load information is not included in the selected features although it is avery important part to define an operation condition. The reasons are:• The variation of the load distributions in the application context (heavy loadperiod) is very limited. The study of historical hourly load data of VI in Sec-tion 3.5 shows that the peak period is very short and the loads geographicallyclosed to tend to peak at the same time.60• The variation of the load distribution during the heavy load period has lim-ited impact for the variation of the loading limit, shown in Table 3.5.• Using load information as input feature requires massive training data tocover the whole space of possible load distribution, which is not affordabledue to high computation and memory cost.4.4 ANN Design4.4.1 Normalization of Input DataThe selected feature in (4.4) consists of different types of variables which havedifferent orders of magnitude. For example, SOOS and SJOR consist of binary num-bers, PJOR ranges from 0 to 170, and QV IT ranges from 345 to 495. Re-scaling andnormalization is commonly applied to the raw data so that the preprocessed dataall stays in the interval [0,1] or [−1,1]. In theory, it is not strictly necessary tonormalize the raw data because that any re-scaling of the input data can be undoneby the corresponding weights and biases adjustment occurred in the learning pro-cess [37]. But in practice, the normalization can reduce the training time and avoidill-conditioning of the network [37]. The normalization function used in this thesislinearly maps the raw data into [−1,1] interval, given as (4.5).x∗i =2(xi−min(x))max(x)−min(x) −1 (4.5)4.4.2 Performance MeasuresTypically the performance of a MLP is determined by its error function J as shownin Figure 4.3, because it is the objective function to be minimized during the learn-ing process. The error function is defined as J := 1M ∑Mi=1(yio− yit)2, which repre-sents the Mean Square Error (MSE). However, as an application for power system,the Mean Absolute Error (MeanError) in (4.6) and the Maximum Absolute Error(MaxError) in (4.7) are more important for system operator to define the operation61margin.MeanError% =1MM∑i=1|yio− yit |yit×100% (4.6)MaxError% = max1≤i≤M|yio− yit |yit×100% (4.7)Where, yio is the ith output of the trained MLP model, yit is ith loading limit calcu-lated from PSAT and VSAT.4.4.3 Selection of the Number of Hidden NeuronsThe number of hidden neurons determines the complexity of the MLP, whichshould be optimized to match the complexity of the mapping between the inputand the output. Too few hidden neurons may result in under-fitting while too manyhidden neurons may lead to over-fitting. The generalization of the MPL modellargely depends on the appropriate selection of the number of the hidden neurons.The optimal number of the hidden neurons is typically determined by the bestperformance, where is the MSE of the test data. The training, validation, and testdata size is shown in Table 4.3. 11 MLP models with different hidden layer rangingfrom 3 to 13 neurons are compared. The result in Table 4.1 shows that the accu-racy will get higher with more hidden neurons. But even with 3 hidden neurons,the MaxError of the test data is still less than 1%, which is totally acceptable forpractical application. Moreover, due to the limitation of the PV method and pos-sible inaccurate data, the calculated loading limit typically will be added to a fairmargin before used for power system operation.Based on the discussion above and the suggestion from the operation plannersfrom BC Hydro, the target MSE is set as 4. And the optimal number of hiddenlayer neurons is determined by the minimal computation cost.9 MLP models with different hidden layer ranging from 5 to 13 neurons arecompared. The training stopping criteria is set as MSE ≤ 4. The maximum trainingepochs is set as 500. Each model is run for 10 times. The average of training time,total epochs, MSE, MeanError, and MaxError are shown in Table 4.2.As shown in Table 4.2, the MLP with 8 neurons for hidden layer achieves leasttraining time, which is selected for VI loading limit assessment.62Table 4.1: Best MSE performance of MLP models with different size of hid-den layerHiddenNeuron# MSE MaxError% MeanError%3 9.56141 0.616698 0.1111014 7.199555 0.456115 0.0935795 3.876015 0.490066 0.0660136 3.473285 0.42151 0.0622077 3.290587 0.45093 0.0607268 3.136843 0.457118 0.0580719 3.055142 0.425461 0.05420410 2.976155 0.704512 0.05509411 2.947067 0.503209 0.05806712 2.920822 0.478144 0.05703313 2.832558 0.453636 0.054177Table 4.2: Performance of MLP models with different size of hidden layerHiddenNeuron# Epochs Training time MaxError MeanError MSE5 260.2 14.84426 0.658112 0.068269 46 59.7 4.406006 0.618326 0.064231 47 39.8 4.428216 0.49263 0.064082 48 42.9 4.373592 0.577538 0.063823 49 45 5.677716 0.772914 0.064691 410 41.9 7.981438 0.583969 0.064131 411 36.7 7.641469 0.645017 0.062727 412 31.8 6.729378 0.792793 0.064174 413 35.9 8.639795 0.585201 0.063978 44.5 Result4.5.1 ANN Performance and Computational SpeedThe process of generating training data is discussed in Chapter 3. The operationconditions described by selected features and the corresponding VI loading limitare fed into an ANN as training inputs and outputs. As discussed in Section 4.4,the ANN model selected is a MLP with 7 hidden neurons, and 1 output neuron.10,800 out of 14,400 input data are randomly selected to train the ANN. 1,800 input63Table 4.3: ANN structure and training informationANN structure Training data Validation data Test dataSize 28-8-1 10,800 1,800 1,800Table 4.4: ANN average performance of 10 runs with different target MSETarget MSE MaxError% MeanError%3.5 0.791 0.06254.0 0.778 0.06384.2 0.942 0.0652data are randomly selected as validation data to halt training when generalizationstops improving. 1,800 input data are randomly selected as test data to provide anindependent measure of network performance.The ANN output and target regression is shown in Figure 4.4. Table 4.4 showsthe average performance of 20 runs of the ANN model.With setting target MSE as 4, the VI loading limit mean error of the unseenoperation conditions in the test data is 0.0625%, the VI loading limit maximumabsolute error of the unseen operation conditions is 0.778%. For practical opera-tion, utilities typically operate the system with a 5% margin away from the loadinglimit. The result shows that the ANN model is feasible to be applied for a practicaland large size power system, and the accuracy of loading limit estimation is highenough to power system operation.The major advantage of applying ANN for loading limit assessment is that itsfeasibility of real-time operation. Once trained, the ANN model can very quicklylocate the VI loading limit of the specified operation conditions. The training andexecution time of the ANN model is shown in Table 4.5. All the computations areexecuted using a workstation PC with Intel R© CoreTM i5 CPU 760 @ 2.80GHz.As shown in Table 4.5, it only costs less than 0.1 s to predict the loading limits ofTable 4.5: ANN average training and prediction time of 10 runsTarget MSE Training time (s) Epochs 10,000 predictions time (s)4.0 4.4 42.9 0.083641800 1900 2000 2100 2200 2300 2400Target VI loading limit (MW)1800190020002100220023002400Output of the ANN model (MW)DataFitY = TFigure 4.4: ANN prediction and target regression10,000 operation conditions.4.6 Application for BC Hydro Power System OperationThe application of the proposed ANN framework in BC Hydro control center issummarized as Figure 4.5.4.6.1 On-Line Loading Limit AssessmentA trained ANN model is defined by its preprocessing function, activation function,trained weights, and postprocessing function. It can be readily and easily pro-grammed into a computer in control center. As shown in Figure 4.5, once received65ANN modelPresent operation conditionReverse mappingVI loading limitDesired operation conditionsTarget loading limitSCADAPreventive measuresFigure 4.5: Application of the ANN framework in BC Hydro control centerthe information of JOR output, JOR status, VIT MVAR capability and pre-outageinformation from the SCADA system, the ANN model can quickly calculate theVI loading limit of the present operation condition.If the VI total load measured by SCADA exceeds the 95% of the calculated VIloading limit, an alarm will be raised to remind the operators to conduct preventivecontrol actions.4.6.2 Preventive Measure RecommendationsThe preventive control actions to mitigate voltage stability problems used by BCHydro have been briefly discussed in Chapter 2. For VI system, the main pre-ventive control actions to posture the system against potential voltage instabilityare to increase local generation and local VAR support capability. As discussed inSection 3.4 JOR generating station is the only generation in south VI system andoperates for emergency and peak period [50].VIT has a group of synchronous con-densers and shunt capacitors with total 495 MVAR capacity, which are regarded asmost important VAR facilities in south VI system. The preventive control actionsare to increase the generation of JOR or bring VAR facilities in VIT on-line toensure VI voltage stability against potential contingency.661800170185015019004951001950VI Loading Limit When Preoutage =2L1232000JOR (MW)445502050VIT VAr Support (MVAr)395SC ModeOOS 345Figure 4.6: VI loading limits generated by the trained ANN model of pre-outage 2L123 by enumerating JOR and VITThe trained ANN model is able to calculate the VI loading limit of all the possi-ble operation conditions. Figure 4.6 shows the VI loading limit of all possible JORand VIT conditions when 2L123 is pre-outage. With the help of full knowledge ofinput-output mapping, the inverse mapping from VI loading limit to desired JORand VIT conditions can be achieved.When the operators need to conduct preventive control actions to increase theVI loading limit, the ANN model firstly calculates the VI loading limits of all pos-sible JOR and VIT conditions, which can generate the reverse mapping betweentarget loading limits and a set of possible JOR and VIT conditions. Then givena target loading limit from the operators, the desired JOR and VIT conditions arerecommended by the system. Operators can take control actions based the recom-mendations to ensure power system security, as presented in Figure 4.5 .67Chapter 5ConclusionIf you cannot explain it simply, you don’t understand it well enough.— ALBERT EINSTEINIn this concluding chapter, the major contributions of this research project are sum-marized and possible future work is discussed.5.1 ContributionsThis work proposes an ANN-based on-line voltage stability assessment and controlaction recommendation system for BC Hydro Vancouver Island system operation.The contributions of the thesis are:• 14,400 VI operation conditions of VI system are selected for the off-lineoperation knowledge database. The operation conditions are selected basedon the operation experience of BC Hydro, covering the variations interestedsystem scenarios and load distributions. The selected system scenarios aredefined by the key factors limiting VI voltage stability. The selected loaddistributions is based on assumed load generated by load forecasts and co-incidental factors. The effectiveness of using assumed load data is validatedby historical load data.• The loading limit of each operation condition of the operation knowledgedatabase is accurately calculated. Each operation condition is presented in68the form of solved load-flow by PSAT. VSAT uses CPF to accurately solvethe loading limit.• an automatic data generation system is developed based on PSAT and VSAT.PSAT and VSAT scripting feature is used to implement the system. A dataverification scheme using modal analysis and engineering judgment ensuresthe quality of the database.• An ANN model to approximate the mapping the operation conditions andthe corresponding VI loading limit is trained using the operation knowledgedatabase. A feature selection scheme is proposed based on operation ex-perience. The result shows high accuracy for loading limit assessment forunseen operation conditions.• The application of the proposed framework in BC Hydro control center isdiscussed. It is capable to accurately and quickly assess the loading limit ofthe present operation condition as well as recommend control actions whenviolation appears.5.2 Future Work5.2.1 Application in Corrective Control Action DevelopmentCorrective control actions need to be undertaken when a system is in emergencyor extreme emergency state [6]. Currently, it requires the planners study a largenumber of operation conditions and contingencies. And the corresponding to eachcontingencies, corrective control actions is developed to save the system as muchas possible and prevent wide-spread blackout. The operation rules for correctivecontrol actions are summarized by the planners in the form of equations or nomo-grams. For example, BC Hydro sheds the generation against some specified con-tingencies. The shedding amount is defined by the equations involved with tie-linepower transfers.Currently, corrective control actions development and implementation have thechallenges as:69• The equations used for corrective control actions can take only one or twoinput variables. Other related variables are ignored. This makes the systemoperation conservative.• The development of corrective control actions requires the experienced engi-neers summarize the operation rules into equations based on their engineer-ing judgment.• The corrective control actions have to be redeveloped once the system changes,which make it a very engineering-intensive task.Sharing the similar challenges of the loading limit assessment, the correctivemeasure development can be solved using the proposed ANN framework.5.2.2 Integration with BC Hydro On-Line Voltage Stability ToolBC Hydro uses an application named RTVSA to achieve on-line voltage stabilitymonitoring. 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