reading

Cover
About the Author
Preface
1 Basic Theories of Power System Security Defense
1. 1.1 Introduction
2. 1.2 Power System Reliability and Stability
3. 1.3 Three Defense Lines in the Power System
4. 1.4 Summary
5. References
2 Power System Analysis and Control Theory
1. 2.1 Introduction
2. 2.2 Mathematical Model of Power System
3. 2.3 Power System Stability Analysis Method
4. 2.4 Automatic Control Theory
5. 2.5 Summary
6. References
3 Wide‐Area Information Monitoring
1. 3.1 Introduction
2. 3.2 Test System
3. 3.3 Optimal Selection of Wide‐Area Signal
4. 3.4 Optimal Selection of Wide‐Area Controller
5. 3.5 Summary
6. References
4 Stability Analysis of Stochastic System
1. 4.1 Introduction
2. 4.2 Stability Analysis of Stochastic Parameter System
3. 4.3 Stability Analysis of Stochastic Structure System
4. 4.4 Stability Analysis of Stochastic Excitation System
5. 4.5 Summary
6. References
5 Stability Analysis of Time‐Delay System
1. 5.1 Introduction
2. 5.2 Stability Analysis of a Non‐Jump Time‐Delay System
3. 5.3 Stability Analysis of a Jump Time‐Delay System
4. 5.4 Summary
5. Appendix A
6. References
6 Wide‐area Robust Control
1. 6.1 Introduction
2. 6.2 Robust Control for Internal Uncertainties
3. 6.3 Optimal Robust Control
4. 6.4 Error Tracking Robust Control
5. 6.5 Summary
6. References
7 Wide‐Area Adaptive Control
1. 7.1 Introduction
2. 7.2 Adaptive Control Considering Operating Condition Identification
3. 7.3 Adaptive Control Considering Controller Switching
4. 7.4 Summary
5. References
Index
End User License Agreement

List of Tables

Chapter 01
1. Table 1.1 Comparison between two stability classification standards.
Chapter 03
1. Table 3.1 Contribution factors.
2. Table 3.2 Geometric index.
3. Table 3.3 Contribution factors.
4. Table 3.4 Geometric index.
5. Table 3.5 Contribution factors.
6. Table 3.6 Geometric index.
7. Table 3.7 Dominant modes of open‐loop and closed‐loop systems in the test system.
8. Table 3.8 Inter‐area modes of the study system.
9. Table 3.9 Normalized controllability of different generators.
10. Table 3.10 Damping ratios and frequencies of open loop and closed loop.
Chapter 04
1. Table 4.1 Inter‐area modes of the study system.
2. Table 4.2 Changes of the oscillation mode in case 1.
3. Table 4.3 Changes of the oscillation mode in case 2.
4. Table 4.4 Changes of the oscillation mode in case 3.
5. Table 4.5 Changes of the oscillation mode in case 4.
6. Table 4.6 Major parameters of a four‐generator 13‐node system.
7. Table 4.7 Calculation time of two methods applying to the four‐generator 13‐node system.
8. Table 4.8 Corresponding excitation magnification factors of different boundaries in Figure 4.13.
9. Table 4.9 Corresponding excitation system time constants of different boundaries in Figure 4.14.
10. Table 4.10 Calculation times of the two methods applied to the 16‐machine system.
11. Table 4.11 Fault type of a two‐machine system.
12. Table 4.12 Mean square error of the equilibrium point method.
13. Table 4.13 Fault type of a 16‐machine system.
14. Table 4.14 Mean square error of the equilibrium point method.
15. Table 4.15 Comparison of MSE (mean square error) between the trajectory method and the proposed method.
16. Table 4.16 Inter‐area modes of the study system.
17. Table 4.17 State transfer probability of some lines after line 4–14 outage.
18. Table 4.18 System operating condition set after line 4–14 outage.
19. Table 4.19 Minimum damping ratio of different operating conditions.
20. Table 4.20 State transfer probability of some lines after line 1–31 outage.
21. Table 4.21 State transfer probability of some lines after line 1–31 and line 1–30 outage.
22. Table 4.22 System operating condition set after line 1–31 outage
23. Table 4.23 Minimum damping ratio of different operating conditions.
24. Table 4.24 Time cost of the different analyze method.
25. Table 4.25 Different line improvement schemes.
26. Table 4.26 Power flow of different line improvement schemes.
27. Table 4.27 State transfer probability of some lines after applying different line improvement schemes.
28. Table 4.28 The value of μx after applying different line improvement schemes.
29. Table 4.29 Different operation mode adjustment schemes.
30. Table 4.30 State transfer probability of some lines after applying different operation mode adjustment schemes.
31. Table 4.31 The value of μ after applying different operation mode adjustment schemes.
32. Table 4.32 Patterns of conditional wind speed.
33. Table 4.33 Weibull fitting coefficient of conditional wind speed probability density in different wind speed modes.
34. Table 4.34 Inter‐area modes of the study system.
35. Table 4.35 Minimum damping ratio of the 16‐generator system in different operation modes.
Chapter 05
1. Table 5.1 Damping ratio of the power angle difference between G1 and G13 with different time delays when ϑ₀ = 0.03.
2. Table 5.2 Damping ratio of the power angle difference between G8 and G16 with different time delays when ϑ₀ = 0.06.
3. Table 5.3 Damping ratio of the power angle difference between G1 and G16 with different time delays when ϑ₀ = 0.03.
4. Table 5.4 Damping ratio of the power angle difference between G6 and G15 with different time delays when ϑ₀ = 0.06.
5. Table 5.5 Damping ratio of the power angle difference between G9 and G15 with different time delays when ϑ₀ = 0.04.
6. Table 5.6 Damping ratio of the power angle difference between G4 and G13 with different time delays when ϑ₀ = 0.06.
7. Table 5.7 Time‐delay stability upper bound obtained using different methods.
8. Table 5.8 Damping ratio of the power angle difference between G4 and G15 with different time delays.
9. Table 5.9 Damping ratio of the power angle difference between G8 and G15 with different time delays.
10. Table 5.10 Damping ratio of power angle difference between G12 and G16 with different time delays.
11. Table 5.11 Damping ratio of the power angle difference between G3 and G14 with different time delays.
12. Table 5.12 Damping ratio of the power angle difference between G8 and G15 with different time delays.
13. Table 5.13 Damping ratio of the power angle difference between G1 and G16 with different time delays.
14. Table 5.14 Damping ratio of the power angle difference between G4 and G13 with different time delays.
15. Table 5.15 Damping ratio of the power angle difference between G7 and G14 with different time delays.
16. Table 5.16 Time‐delay stability upper bound obtained using different methods.
Chapter 06
1. Table 6.1 Eigenvalue of electromechanical modes in IEEE four‐machine systems without controllers.
2. Table 6.2 Case bank.
3. Table 6.3 Electromechanical modes in four‐machine systems with different controllers under different operating conditions.
4. Table 6.4 Eigenvalues of electromechanical modes in the two‐area four‐machine system.
5. Table 6.5 Dominant modes in a four‐machine system without controllers.
6. Table 6.6 Dominant inter‐area modes of the test system operating in open‐loop and closed‐loop systems.
7. Table 6.7 Dominant oscillation modes of the test system operating in open‐loop and closed‐loop systems.
8. Table 6.8 Dominant modes of the open‐loop system.
9. Table 6.9 Dominant modes of the closed‐loop system.
10. Table 6.10 Generator parameter of the test system.
Chapter 07
1. Table 7.1 Inter‐area modes of the study system.
2. Table 7.2 Case bank.
3. Table 7.3 Damping ratios and frequencies of inter‐area modes with the controllers.
4. Table 7.4 Chi‐square variables for 12 Kalman filters in case 3
5. Table 7.5 Chi‐square variables for 12 Kalman filters in the new case I.
6. Table 7.6 Chi‐square variables for 12 Kalman filters in the new case II.
7. Table 7.7 Inter‐area modes of the test system.
8. Table 7.8 Case bank.
9. Table 7.9 Interarea modes of the study system.
10. Table 7.10 Cases used in the time‐domain simulation.
11. Table 7.11 Operating condition information.
12. Table 7.12 Weighting coefficients of subcontrollers in the 16‐machine system after the wind speed varies to 7.5 m/s
13. Table 7.13 Weighting coefficients of subcontrollers in the 16‐machine system after the wind speed varies to 3.8 m/s.
14. Table 7.14 Operating condition information.
15. Table 7.15 Weighting coefficients of subcontrollers in the 16‐machine system after the load varies to 23.700+j1.180.
16. Table 7.16 Weighting coefficients of subcontrollers in the 16‐machine system after the load varies to 22.500+j1.145.
17. Table 7.17 State transfer probability of some lines after a failure outage of line 1–31.
18. Table 7.18 System state sets after failure outage of line 1–31
19. Table 7.19 Weighted coefficient of the subcontroller after failure outage of line 1–31 of a 16‐machine system.
20. Table 7.20 Weighted coefficient of a subcontroller after failure outage of line 35–34 of a 16‐machine system.
21. Table 7.21 Case bank of different operating conditions.
22. Table 7.22 Time‐delay upper bound and time‐delay varying rate of different jump cases for the 16‐machine system.

List of Illustrations

Chapter 01
1. Figure 1.1 Classification of power system stability by IEEE/CIGRE.
2. Figure 1.2 Classification of power system stability by industry standard DL755‐2001.
3. Figure 1.3 Conversion relationship between power system operation states.
4. Figure 1.4 Three defense lines in power system safety and stability control.
5. Figure 1.5 Power system safety and stability control.
Chapter 02
1. Figure 2.1 Schematic diagram of the ideal generator.
2. Figure 2.2 Block diagram of a typical excitation system.
3. Figure 2.3 Simplified mathematical model of the exciter.
4. Figure 2.4 Mathematical model of the voltage regulator.
5. Figure 2.5 Mathematical model of the excitation system stabilizer.
6. Figure 2.6 Simplified model of hydraulic turbine.
7. Figure 2.7 Simplified model of the hydraulic turbine speed governor.
8. Figure 2.8 Firstorder simplified model of a steam turbine.
9. Figure 2.9 Second‐order simplified model of a steam turbine.
10. Figure 2.10 Third‐order simplified model of a steam turbine.
11. Figure 2.11 Simplified model of a steam turbine hydraulic pressure speed governor.
12. Figure 2.12 Mathematical model of a steam turbine power‐frequency electrohydraulic speed governor.
13. Figure 2.13 Simplified diagram of a feedback control system.
Chapter 03
1. Figure 3.1 Test system of a four‐machine 13‐bus system.
2. Figure 3.2 The 16‐machine, 68 bus test system with tie lines.
3. Figure 3.3 WECC system.
4. Figure 3.4 Open‐ and closed‐loop eigenvalues using different feedback signals.
5. Figure 3.5 Dynamic responses of the angular difference between generators 1 and 4 with a state feedback controller.
6. Figure 3.6 Dynamic responses of angular difference between generators 1 and 4 with a single circuit of line 8–9.
7. Figure 3.7 Dynamic responses of the angular difference between generators 2 and 4 with the output feedback controller.
8. Figure 3.8 Dynamic responses of the 16‐machine system.
9. Figure 3.9 Dynamic responses of the 16‐machine system with a single circuit of line 1–2.
10. Figure 3.10 The and λ planes.
11. Figure 3.11 GPSSs based on a wide‐area controller synthesis configuration.
12. Figure 3.12 Open‐ and closed‐loop eigenvalues for the case of GPSSs: (o) open loop, (·) closed loop.
13. Figure 3.13 The root loci for the case of GPSSs: (o) open loop, (·) root locus.
14. Figure 3.14 The relative angular separations between G13 and G16 on the first simulation: (‐) with GPSSs; (‐‐) without GPSSs.
15. Figure 3.15 The relative angular separations between G14 and G16 on the first simulation: (‐) with GPSSs, (‐‐) without GPSSs.
16. Figure 3.16 The relative angular separations between G15 and G16 on the first simulation: (‐) with GPSSs, (‐‐) without GPSSs.
17. Figure 3.17 The relative angular separations between G13 and G14 on the first simulation: (‐) with GPSSs, (‐‐) without GPSSs.
18. Figure 3.18 The relative angular separations between G13 and G16 on the second simulation: (‐) with GPSSs; (‐‐) without GPSSs.
19. Figure 3.19 The relative angular separations between G14 and G16 on the second simulation: (‐) with GPSSs; (‐‐) without GPSSs.
20. Figure 3.20 The relative angular separations between G15 and G16 on the second simulation: (‐) with GPSSs, (‐‐) without GPSSs.
21. Figure 3.21 The relative angular separations between G13 and G14 on the second simulation: (‐) with GPSSs; (‐‐) without GPSSs.
22. Figure 3.22 Dynamic responses of the system under different time delays.
Chapter 04
1. Figure 4.1 Oscillation modal diagram.
2. Figure 4.2 Improved small‐signal stability region (ISSSR) and its complex plane boundary.
3. Figure 4.3 Decomposition of ISSSR.
4. Figure 4.4 The ISSSR used in the simulation case.
5. Figure 4.5 Stability region corresponding to Region 1.
6. Figure 4.6 Stability region corresponding to Region 2.
7. Figure 4.7 ISSSR of the four‐generator 13‐node system.
8. Figure 4.8 ISSSR compared with SSSR.
9. Figure 4.9 Points inside and outside the ISSSR.
10. Figure 4.10 Time‐domain simulation of point A.
11. Figure 4.11 Time‐domain simulation of point B.
12. Figure 4.12 Time‐domain simulation of point C
13. Figure 4.13 ISSSR under different excitation magnification factors.
14. Figure 4.14 ISSSR under different excitation system time constants.
15. Figure 4.15 ISSSR of the 16‐machine 68‐node system.
16. Figure 4.16 ISSSR compared with SSSR.
17. Figure 4.17 Time‐domain simulation of point A.
18. Figure 4.18 Time‐domain simulation of point B.
19. Figure 4.19 Time‐domain simulation of point C.
20. Figure 4.20 Two‐machine system.
21. Figure 4.21 Two‐machine system after the fault line is removed.
22. Figure 4.22 The system only contains the fault component.
23. Figure 4.23 The simulation results when α is 0.5 and t_c is 0.1 s.
24. Figure 4.24 The simulation results when α is 0.9 and t_c is 0.1 s.
25. Figure 4.25 The simulation results when α is 0.5 and t_c is 0.175 s.
26. Figure 4.26 The simulation results when α is 0.9 and t_c is 0.175 s.
27. Figure 4.27 The simulation results when α is 0.5 and t_c is 0.05 s.
28. Figure 4.28 The simulation results when α is 0.9 and t_c is 0.05 s.
29. Figure 4.29 The simulation results when α is 0.5 and t_c is 0.085 s.
30. Figure 4.30 The simulation results when α is 0.9 and t_c is 0.085 s.
31. Figure 4.31 Multivariable frequency response plots of the input–output characteristics of a power system.
32. Figure 4.32 Dynamic responses of G1–G13 relative power angle in the 16‐machine system.
33. Figure 4.33 Dynamic responses of the relative power angle between generators in the 16‐machine system.
34. Figure 4.34 Dynamic responses of the relative power angle between generators in the 16‐machine system.
35. Figure 4.35 Dynamic responses of the relative power angle between generators in the 16‐machine system.
36. Figure 4.36 Wind generator power curve.
37. Figure 4.37 Dynamic responses of the G2–G3 relative power angle in the four‐generator system when the system operating condition varies from one mode to another mode.
38. Figure 4.38 Dynamic responses of the G2–G3 relative power angle in the four‐generator system when the system operating condition varies between multiple modes.
39. Figure 4.39 Dynamic responses of the G1–G8 relative power angle in the 16‐generator system when the system operating condition varies from one mode to another mode.
40. Figure 4.40 Dynamic responses of the G1–G8 relative power angle in the 16‐generator system when the system operating condition varies between multiple modes.
Chapter 05
1. Figure 5.1 Dynamic responses of the G1–G13 relative power angle with different time delays when ϑ₀ = 0.03.
2. Figure 5.2 Dynamic responses of G8–G16 relative power angle with different time delays when ϑ₀ = 0.06.
3. Figure 5.3 Dynamic responses of the G1–G16 relative power angle with different time delays when ϑ₀ = 0.03.
4. Figure 5.4 Dynamic responses of the G6–G15 relative power angle with different time delays when ϑ₀ = 0.06.
5. Figure 5.5 Dynamic responses of the G9–G15 relative power angle with different time delays when ϑ₀ = 0.03.
6. Figure 5.6 Dynamic responses of the G4–G13 relative power angle with different time delays when ϑ₀ = 0.06.
7. Figure 5.7 Two‐machine infinite‐bus system.
8. Figure 5.8 Power angle of a synchronous generator under different time delays.
9. Figure 5.9 Variation of the time‐delay stability upper bound with ϑ.
10. Figure 5.10 Variation of the synchronous generator power angle with ϑ.
11. Figure 5.11 Variation of the time‐delay stability upper bound with K_a.
12. Figure 5.12 Power angle of a synchronous generator with different values of K_a.
13. Figure 5.13 Variation of the time‐delay stability upper bound with D.
14. Figure 5.14 Power angle of a synchronous generator with different values of D.
15. Figure 5.15 Frequency responses of a Schur‐order reduction.
16. Figure 5.16 Dynamic response of the power angle difference between G4 and G15 with different time delays.
17. Figure 5.17 Time‐delay stability upper bound of the 16‐machine system with different K_a.
18. Figure 5.18 Dynamic response of the power angle difference between G8 and G15 with different time delays.
19. Figure 5.19 Time‐delay stability upper bound of the 16‐machine system with different D values.
20. Figure 5.20 Dynamic response of the power angle difference between G12 and G16 with different time delays.
21. Figure 5.21 Time‐delay stability upper bound of the 16‐machine Markov jump system with different load variations.
22. Figure 5.22 Dynamic response of the power angle difference between G3 and G14 with different time delays.
23. Figure 5.23 Flowchart of the time‐delay stability analysis.
24. Figure 5.24 Dynamic responses of the generator relative power angle with different time delays.
25. Figure 5.25 Dynamic responses of the generator relative power angle with different time delays.
Chapter 06
1. Figure 6.1 The δ₁₃ simulation curves in cases with different controllers under different operating conditions.
2. Figure 6.2 Open‐loop and closed‐loop eigenvalues of the system.
3. Figure 6.3 The relative rotor angle δ₁₄ curves between machine 1 and machine 4 of fault type 1 under given operating conditions.
4. Figure 6.4 The relative rotor angle δ₁₄ curves between machine 1 and machine 4 of fault type 2 under given operating conditions.
5. Figure 6.5 The relative rotor angle δ₁₄ curves between machine 1 and machine 4 of fault type 3 under given operating conditions.
6. Figure 6.6 The mapping of complex planes.
7. Figure 6.7 Structure of the TCSC supplementary controller.
8. Figure 6.8 Eigenvalues of open‐loop and closed‐loop systems.
9. Figure 6.9 System dynamic responses in the first case.
10. Figure 6.10 System dynamic responses in the second case.
11. Figure 6.11 System dynamic responses in the third case.
12. Figure 6.12 System dynamic responses in the fourth case.
13. Figure 6.13 System dynamic responses in case 5.
14. Figure 6.14 System dynamic responses in the case 6.
15. Figure 6.15 The root loci with parameter ρ increasing.
16. Figure 6.16 Speed of G1–G4 without and with the control.
17. Figure 6.17 Speeds of G1–G4 without and with control.
18. Figure 6.18 The real power of the tie line without and with control.
19. Figure 6.19 Speed of G1–G4 without and with control.
20. Figure 6.20 The real power of tie line without and with control.
21. Figure 6.21 System structure
22. Figure 6.22 Control structure of the HVDC supplementary controller.
23. Figure 6.23 System dynamic responses in case 1.
24. Figure 6.24 System dynamic responses in case 2.
25. Figure 6.25 System dynamic responses in case 3.
26. Figure 6.26 System dynamic responses in case 4.
Chapter 07
1. Figure 7.1 D‐stability region.
2. Figure 7.2 Small‐signal model of the ESD unit.
3. Figure 7.3 Control structure for the HVDC small‐signal modulator.
4. Figure 7.4 Construction of the control scheme.
5. Figure 7.5 Eigenvalues of closed‐loop systems for 12 cases shown in Table 7.2.
6. Figure 7.6 Dynamic responses of a power system with different controllers for each case: (‐) with the corresponding controller; (‐‐) with the mismatching controller; (∙∙∙) without controller.
7. Figure 7.7 Dynamic responses of the closed‐loop system using different controllers for the new case.
8. Figure 7.8 Chi‐square variables probabilities under case 3.
9. Figure 7.9 Chi‐square variables probabilities under the new case I.
10. Figure 7.10 Dynamic responses of a closed‐loop system with a combined controller for the new case I.
11. Figure 7.11 Chi‐square variables probabilities under the new case II.
12. Figure 7.12 Dynamic responses of a closed‐loop system with a combined controller for the new case II.
13. Figure 7.13 Parameter space and measurement space.
14. Figure 7.14 The optimum hyperplane for classifying the two different operating classes.
15. Figure 7.15 The structure of the control scheme.
16. Figure 7.16 Maximum singular value plots for different cases.
17. Figure 7.17 Eigenvalues of the closed‐loop system in the 10 cases of Table 7.8.
18. Figure 7.18 Stabilily regions of different controllers under different operating conditions.
19. Figure 7.19 Dynamic responses of power systems with different time delays.
20. Figure 7.20 Dynamic responses of the power system with different controllers for each case: (‐) with the corresponding controller; (‐‐) with the mismatching controller; and (∙∙∙) without the controller.
21. Figure 7.21 Classification and regression trees to distinguish different operating conditions.
22. Figure 7.22 The output trajectory of CART in Situation Ia.
23. Figure 7.23 Relative angular separations of the closed‐loop system with control 5.
24. Figure 7.24 The output trajectory of CART in Situation Ib.
25. Figure 7.25 Relative angular separations of a closed‐loop system with control 9.
26. Figure 7.26 The output trajectory of CART in Situation IIa.
27. Figure 7.27 The combination factors in Situation IIa.
28. Figure 7.28 Dynamic responses of the closed‐loop system with combined control in Situation IIa.
29. Figure 7.29 The output trajectory of CART in Situation IIb.
30. Figure 7.30 The combination factors in Situation IIb.
31. Figure 7.31 Dynamic responses of the closed‐loop system with combined control in Situation IIb.
32. Figure 7.32 Closedloop system with a Youla parameterization‐based control scheme.
33. Figure 7.33 Parameter space and measurement space for the dynamic power system.
34. Figure 7.34 WECC system.
35. Figure 7.35 Multivariable frequency response plots of the input–output characteristics of the power system. (‐) reduced; (∙∙∙) full order.
36. Figure 7.36 The construction of an adaptive control scheme.
37. Figure 7.37 The trajectory of eigenvalues of open loops and closed loops with the changing loads of groups 1 and 2, respectively.
38. Figure 7.38 Dynamic responses of a power system with fixed and adaptive control schemes in the case of multiple disturbances of the load of zone 1.
39. Figure 7.39 Dynamic responses of a power system with fixed and adaptive control schemes in the case of multiple disturbances of the load of zone 2.
40. Figure 7.40 Dynamic responses of a power system with fixed and adaptive control schemes in the case of uniform changes of loads of zones 1 and 2.
41. Figure 7.41 Dynamic responses of a power system with fixed and adaptive control schemes in the case of non‐uniform changes of loads of zones 1 and 2.
42. Figure 7.42 Dynamic responses of a power system with fixed and adaptive control schemes in the case of uniform changes of the load model.
43. Figure 7.43 Dynamic responses of a power system without control and with a fixed control scheme in the case of multiple disturbances of changing topology.
44. Figure 7.44 Dynamic responses of power system without control and with a fixed control scheme in the case of multiple disturbances of changing generation.
45. Figure 7.45 Dynamic responses of the G1–G8 relative power angle and the G1–G13 relative power angle after different controllers are put into operation in the new system operating condition.
46. Figure 7.46 Dynamic responses of the G1–G8 relative power angle and the G1–G13 relative power angle after different controllers are put into operation.
47. Figure 7.47 Dynamic responses of the G1–G10 relative power angle and the G4–G10 relative power angle after different controllers are put into operation in the new system operating condition.
48. Figure 7.48 Dynamic responses of the G1–G10 relative power angle and the G4–G10 relative power angle after different controllers are put into operation.
49. Figure 7.49 Dynamic responses of the relative power angle after different controllers are put into operation when the operating conditions match.
50. Figure 7.50 Dynamic responses of the relative power angle after different controllers are put into operation when operating conditions mismatch.
51. Figure 7.51 Dynamic responses of the power system under different operating conditions: (‐) with the jump controller; (‐ ∙ ‐)without the controller.
52. Figure 7.52 Comparison between the traditional method and the proposed method.