Transient Stability of Power Systems: A Unified Approach to Assessment and Control

Transient Stability of Power Systems is a monograph devoted to a hybrid-direct temporal method called SIME (for Single Machine Equivalent). SIME processes temporal information about the multimachine system dynamics to assess and control any type of transient instabilities under any type and model of power systems. Two approaches may be distinguished depending upon the source of information used: `Preventative SIME' which relies on a time-domain program to simulate anticipated contingencies, and `Emergency SIME' which uses real-time measurements. Preventative SIME mainly comprises two techniques: contingency filtering, ranking, and assessment; and (simultaneous) stabilization of harmful contingencies. The resulting preventative transient stability assessment and control (TSA&C) software can be used in all application contexts of transient stability studies. In a control center, for instance, its computational performances enable it to cope with very stringent requirements of real-time operation. Besides, interfacing SIME with an OPF algorithm allows combining transient stability constraints with specifics of the liberalized electricity market. Emergency SIME is a novel closed-loop control technique which contains the transient instabilities caused by contingencies' actual occurrence. It relies on real-time measurements to predict (the size of) instability and, accordingly, to design and trigger control actions able to impede system loss of synchronism. Emergency SIME is particularly suitable for protecting important generation sites and can complement preventative SIME. Both approaches rely on the same principles and basic software which yields a comprehensive and unified approach to TSA&C. The design of near optimal control techniques is a major asset of this software. This book provides extensive illustrations on a variety of power systems ranging from a simple 3-machine test system to real-world power systems comprising up to 627 generators and 4112 busses. Transient Stability of Power Systems will be especially helpful to researchers, utility engineers, and software designers and developers who are developing various types of transient stability software packages. Table of Contents Cover TRANSIENT STABILITY OF POWER SYSTEMS - A Unified Approach to Assessment and Control Contents Preface Notation Chapter 1 BACKGROUND 1. INTRODUCTION 2. SECURITY: DEFINITIONS AND STUDY CONTEXTS 2.1 Definitions and classification 2.2 Operating modes 2.3 Preventive TSA&C. Corresponding needs o 2.3.1 Power system planning o 2.3.2 Operation planning o 2.3.3 Real-time operation 2.4 Emergency mode 2.5 Security in a liberalized environment o 2.5.1 Restructured power systems: an introduction o 2.5.2 Congestion management and ATC o 2.5.3 OPF: a comeback 3. MODELS 3.1 General modeling 3.2 Static and dynamic models 3.3 Transient stability models 4. TRANSIENT STABILITY: TIME-DOMAIN APPROACH 5. DIRECT APPROACHES AN OVERVIEW 5.1 Brief introductory notice 5.2 Application of direct methods to transient stability o 5.2.1 Introduction o 5.2.2 Principle o 5.2.3 Discussion 5.3 Past and present status of direct approaches o 5.3.1 Anticipated advantages and dif culties met o 5.3.2 The two families of hybrid solutions o 5.3.3 Concluding remarks 6. AUTOMATIC LEARNING APPROACHES 6.1 Problem statement 6.2 Overview of AL methods o 6.2.1 Decision trees (DTs) o 6.2.2 Arti cial neural networks o 6.2.3 Statistical pattern recognition o 6.2.4 Hybrid AL approaches 6.3 Performances and assets o 6.3.1 Overall comparison o 6.3.2 Main assets of AL methods 6.4 Comparison of methods 7. SCOPE OF THE BOOK 8. SUMMARY Chapter 2 INTRODUCTION TO SIME 1. FOUNDATIONS 1.1 OMIB: concept and variants o 1.1.1 Time-invariant OMIB o 1.1.2 Time-varying and generalized OMIBs 1.2 From EEAC to SIME 1.3 Principle 2. GENERAL FORMULATION 2.1 Critical machines identi cation 2.2 Derivation of OMIB time-varying parameters 2.3 Equal-area criterion revisited 2.4 Stability conditions o 2.4.1 Conditions of unstable OMIB trajectory o 2.4.2 Conditions of stable OMIB trajectory o 2.4.3 Borderline conditions of OMIB trajectory o 2.4.4 Objectivity of the stability criteria 3. STABILITY MARGINS 3.1 Unstable margin 3.2 Stable margin o 3.2.1 Remark o 3.2.2 Triangle approximation o 3.2.3 Weighted least-squares approximation o 3.2.4 Triangle vs WLS approximation o 3.2.5 Note on sensitivity analysis by SIME 3.3 Existence and range of stability margins o 3.3.1 General description o 3.3.2 Illustrations o 3.3.3 Variation of salient parameters with 3.4 A convenient substitute for unstable margins 3.5 Next candidate CMs and margins 3.6 Normalized margins 4. SIME'S TYPICAL REPRESENTATIONS 4.1 Illustrations on the three-machine system o 4.1.1 Stability conditions o 4.1.2 OMIB parameters and numerical results o 4.1.3 SIME's three representations 4.2 Illustrations on the Hydro-Quebec´ system 4.3 SIME as a reduction technique 5. BACK- AND MULTI-SWING PHENOMENA 5.1 Definitions 5.2 Analytical expression of margins 6. DIRECT PRODUCTS AND MAIN BY-PRODUCTS 6.1 Description 6.2 Organization of topics 7. PREVENTIVE vs EMERGENCY SIME 7.1 Preventive transient stability assessment 7.2 Predictive transient stability assessment 7.3 Control 8. SUMMARY Chapter 3 SENSITIVITY ANALYSIS 1. ELEMENTS OF SENSITIVITY ANALYSIS 1.1 Problem statement 1.2 Sensitivity analysis of the linearized system 1.3 Sensitivity analysis of the supplementary motion 1.4 Synthetic sensitivity functions (ssfs) 1.5 Illustrative examples o 1.5.1 Simulation conditions o 1.5.2 Discussion o 1.5.3 Supplementary motion of state variables o 1.5.4 Supplementary motion of time-varying ssf o 1.5.5 Discussion 1.6 Supplementary motion of time-invariant ssfs 2. SIME-BASED SENSITIVITY ANALYSIS 2.1 Specifics and scopes 2.2 On the validity of linearized approximations 3. COMPENSATION SCHEMES (CSs) 3.1 General scope and principle 3.2 CSs appraising critical clearing times o 3.2.1 Description o 3.2.2 Illustrative examples 3.3 CS appraising power limits o 3.3.1 Principle o 3.3.2 Power limit of OMIB o 3.3.3 Power limits of system machines o 3.3.4 Discussion o 3.3.5 Numerical example o 3.3.6 Computing areas of the CS 4. SUMMARY Chapter 4 PREVENTIVE ANALYSIS AND CONTROL 1. PRELIMINARIES 1.1 Chapter overview 1.2 A measure for assessing computing performances 2. STABILITY LIMITS 2.1 Basic concepts 2.2 Critical clearing times o 2.2.1 Basic procedure o 2.2.2 Parameters and technicalities o 2.2.3 Initial clearing time conditions o 2.2.4 Performances Computing requirements. The number of iterations needed for the accurate o 2.2.5 Illustrations on the 3-machine system o 2.2.6 Illustrations on the 627-machine system 2.3 Power limits o 2.3.1 Preliminaries o 2.3.2 "Pragmatic" approach o 2.3.3 SIME-based approaches o 2.3.4 Variants of the SIME-based approach o 2.3.5 Discussion o 2.3.6 Performances o 2.3.7 Illustration of SIME-based computations o 2.3.8 Observations and comparisons o 2.3.9 "Pragmatic" vs SIME-based stabilization o 2.3.10 Concluding remarks 2.4 Stability limits approximate assessment o 2.4.1 Scope and principle o 2.4.2 Two-margin approximation o 2.4.3 Single-margin approximation o 2.4.4 Stopping criteria for rst-swing screening o 2.4.5 Illustrations on the 3-machine system 3. FILTRA 3.1 Scope of contingency ltering, ranking, assessment 3.2 Basic concepts and de nitions 3.3 General design o 3.3.1 Contingency ltering block o 3.3.2 Contingency ranking and assessment block o 3.3.3 Remarks 3.4 A particular realization of FILTRA o 3.4.1 Contingency ltering o 3.4.2 Contingency ranking o 3.4.3 Re ned ranking of harmful contingencies o 3.4.4 Assessment of harmful contingencies o 3.4.5 Computing requirements of FILTRA o 3.4.6 Main properties of FILTRA 3.5 Illustrating FILTRA techniques o 3.5.1 Simulation description o 3.5.2 Zooming in harmful contingencies Filtering block. For the EPRI system, out of the initial list of 252 contingencies, 172 h o 3.5.3 Performances Reliability. Simulations not reported here show that all contingencies discarded by the o 3.5.4 Zooming in classi cation ability of FILTRA 3.6 Variants of the ltering block 3.7 Concluding remarks 4. PREVENTIVE CONTROL 4.1 Generalities 4.2 Single contingency stabilization o 4.2.1 Principle of generation reallocation o 4.2.2 Illustration o 4.2.3 Comparing stabilization patterns 4.3 Multi-contingency simultaneous stabilization o 4.3.1 Principle of generation reallocation o 4.3.2 Illustration on the 3-machine system o 4.3.3 Illustration on the Brazilian system o 4.3.4 Stabilizing inter-area mode oscillations Description. Typically, inter-area oscillations involve a large group of ma- 4. SUMMARY Chapter 5 INTEGRATED TSA&C SOFTWARE 1. INTEGRATED SOFTWARE 1.1 Basic TSA&C software 1.2 Multi-objective TSA&C software 1.3 Adapting the basic OPF algorithm 2. A CASE-STUDY 2.1 Maximum allowable transfer: problem statement 2.2 Plant mode instability constraints o 2.2.1 Problem description o 2.2.2 Contingency ltering, ranking, assessment o 2.2.3 Contingencies' simultaneous stabilization Base case. As stated earlier, the base case aims at achieving the "maximum" o 2.2.4 Logical rule vs OPF-based procedures 2.3 Inter-area mode instability constraints o 2.3.1 Problem description o 2.3.2 Base case conditions o 2.3.3 Contingency ltering, ranking, assessment o 2.3.4 Contingencies' simultaneous stabilization Base case: physical phenomena description. Obviously, the above-identi ed o 2.3.5 NMs' generation rescheduling via OPF Iteration 1. As in the previous case study, the OPF program is run in order to 2.4 Concluding remarks 3. TSA&C IN CONTROL CENTERS 3.1 Introduction 3.2 TSA&C in the EMS o 3.2.1 On-line TSA&C for the TSP o 3.2.2 On-line TSA&C for the ISO 3.3 Congestion management 3.4 TSA&C for the DTS and Study Environments 4. SUMMARY Chapter 6 CLOSED-LOOP EMERGENCY CONTROL 1. OUTLINE OF THE METHOD 1.1 Definitions 1.2 Scope 1.3 Principle 1.4 General organization 1.5 Computational issues o 1.5.1 Involved tasks o 1.5.2 Corresponding durations 1.6 Notation speci c to Emergency SIME 2. PREDICTIVE SIME 2.1 Description 2.2 Procedure 2.3 Remark 2.4 Speci cs 2.5 Salient features 3. EMERGENCY CONTROL 3.1 General principle 3.2 Generation shedding o 3.2.1 Computing stability margins o 3.2.2 Identi cation of the machine(s) to shed o 3.2.3 Straightforward improvements 4. SIMULATIONS 4.1 Description 4.2 Simulation results of Predictive SIME 4.3 Simulation results of Emergency Control 5. DISCUSSION 5.1 Summary of method's features 5.2 Topics for further research work 6. SUMMARY Chapter 7 RETROSPECT AND PROSPECT 1. SIME: HINDSIGHT AND FORESIGHT 1.1 SIME: a unified comprehensive approach 1.2 Preventive SIME 1.3 Emergency SIME 1.4 Preventive vs emergency control o 1.4.1 Description of physical phenomena o 1.4.2 Controlled generation vs control time o 1.4.3 Discussion 1.5 General comparisons o 1.5.1 Description o 1.5.2 Preventive vs emergency control o 1.5.3 Open-loop vs closed-loop EC 2. AN ILLUSTRATION 2.1 Description 2.2 Application 2.3 Simulations results 3. COMPARING CLASSES OF METHODS 3.1 Practical aspects of AL approaches o 3.1.1 Real-world applicability concerns o 3.1.2 SIME as compared with AL approaches 3.2 Synthetic comparison 3.3 The criteria 3.4 Comments 4. POSTFACE Appendix A THE EQUAL-AREA CRITERION 1. GENERAL CONCEPTS 1.1 Introduction 1.2 Principle 1.3 Two-machine system 2. APPLICATION EXAMPLE Appendix B DATA OF SIMULATED SYSTEMS 1. THREE-MACHINE TEST SYSTEM 2. HYDRO-QUEBEC POWER SYSTEM 3. EPRI AMERICAN TEST SYSTEMS 3.1 Test power system C 3.2 Test power system A 4. BRAZILIAN POWER SYSTEM References Index