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Cover
1 Introduction
1. 1.1 Importance of Modeling and Understanding Cascading Failures
2. 1.2 Importance of Controlled System Separation
3. 1.3 Constructing Restoration Strategies
4. 1.4 Overview of the Book
5. References
2 Modeling of Cascading Failures
1. 2.1 General Cascading Failure Models
2. 2.2 Power System Cascading Failure Models
3. References
3 Understanding Cascading Failures
1. 3.1 Self‐Organized Criticality
2. 3.2 Branching Processes
3. 3.3 Multitype Branching Processes
4. 3.4 Failure Interaction Analysis
5. References
4 Strategies for Controlled System Separation
1. 4.1 Questions to Answer
2. 4.2 Literature Review
3. 4.3 Constraints on Separation Points
4. 4.4 Graph Models of a Power Network
5. 4.5 Generator Grouping
6. 4.6 Finding Separation Points
7. References
5 Online Decision Support for Controlled System Separation
1. 5.1 Online Decision on the Separation Strategy
2. 5.2 WAMS‐Based Unified Framework for Controlled System Separation
3. References
6 Constraints of System Restoration
1. 6.1 Physical Constraints During Restoration
2. 6.2 Electromagnetic Transients During System Restoration
3. References
7 Restoration Methodology and Implementation Algorithms
1. 7.1 Algorithms for Generating Unit Start‐Up
2. 7.2 Algorithms for Load Restoration
3. 7.3 Case Studies
4. References
8 Renewable and Energy Storage in System Restoration
1. 8.1 Planning of Renewable Generators in System Restoration
2. 8.2 Operation and Control of Renewable Generators in System Restoration
3. 8.3 Energy Storage in System Restoration
4. References
9 Emerging Technologies in System Restoration
1. 9.1 Applications of FACTS and HVDC
2. 9.2 Applications of PMUs
3. 9.3 Microgrid in System Restoration
4. References
10 Black‐Start Capability Assessment and Optimization
1. 10.1 Background of Black Start
2. 10.2 BS Capability Assessment
3. 10.3 Optimal BS Capability
4. References
Index
End User License Agreement

List of Tables

Chapter 02
1. Table 2.1 Analogy between OPA model and sandpile model [34].
2. Table 2.2 Number of line outages in each generation for AC OPA model.
3. Table 2.3 Critical lines identified by AC OPA simulation.
Chapter 03
1. Table 3.1 Estimated parameters for line outage data.
2. Table 3.2 Estimated parameters for load shed data.
3. Table 3.3 Efficiency gain R for load shed data.
4. Table 3.4 Efficiency gain R for line outage data.
5. Table 3.5 Number of cascades needed.
6. Table 3.6 Number of iterations of EM algorithm.
7. Table 3.7 Estimated parameters of branching processes by using M^min cascades.
8. Table 3.8 Estimated parameters of branching processes by using cascades.
9. Table 3.9 Joint entropy of distributions.
10. Table 3.10 Joint entropy of distributions in cross‐validation.
11. Table 3.11 Estimated parameters for three types of outages.
12. Table 3.12 Nonzero elements in B for IEEE 118‐bus system.
13. Table 3.13 Similarity indices for 8000 and 3680 original cascades compared with 41 000 original cascades.
14. Table 3.14 Key links for IEEE 118‐bus system.
15. Table 3.15 Key components for IEEE 118‐bus system.
16. Table 3.16 Average propagation for original and simulated cascades.
17. Table 3.17 Similarity indices for original and simulated cascades.
18. Table 3.18 Link weights for different mitigation strategies.
19. Table 3.19 Average propagation for different mitigation strategies.
20. Table 3.20 Average propagation for AC OPA and interaction model.
21. Table 3.21 Efficiency improvement of the interaction model.
Chapter 04
1. Table 4.1 Decomposition of the graph model of the IEEE 118‐bus system.
Chapter 05
1. Table 5.1 Three stages of the proposed WAMS‐based unified framework for CSS.
2. Table 5.2 Postseparation control strategies for the system load = 60.8 GW.
Chapter 06
1. Table 6.1 Features of selected work related to generating unit start‐up.
2. Table 6.2 Features of selected work related to network reconfiguration.
3. Table 6.3 Features of selected work related to load restoration.
Chapter 07
1. Table 7.1 Parameters of generating units.
2. Table 7.2 Solution steps for the illustrated example.
3. Table 7.3 Component selection at Step 1.
4. Table 7.4 Component selection at Step 2.
5. Table 7.5 Component selection at step 3.
6. Table 7.6 Aggregate characteristics of generators.
7. Table 7.7 Computational complexity of the first stage in load restoration.
8. Table 7.8 Network operation at the beginning of stages.
Chapter 08
1. Table 8.1 Impacts of control parameters on system frequency performances.
2. Table 8.2 PSH units’ characteristics.
3. Table 8.3 Generators’ optimal on‐time for all cases.
4. Table 8.4 Generator characteristics.
5. Table 8.5 Generator and battery characteristics.
6. Table 8.6 Load pickup and frequency dip.
7. Table 8.7 Comparison of load restoration with and without batteries.
8. Table 8.8 Number of total load, houses, vehicles, and PHEVs.
9. Table 8.9 Number of PHEVs in different scenarios.
10. Table 8.10 Total energy served in different cases.
Chapter 09
1. Table 9.1 Optimal placements of PMU of IEEE 14‐bus system.
2. Table 9.2 Optimal placements of PMUs of IEEE 30‐bus and 57‐bus systems.
3. Table 9.3 Restoration‐oriented optimal placements of PMUs in IEEE 118‐bus and 300‐bus systems.
4. Table 9.4 Sequence for restoration of generating units.
Chapter 10
1. Table 10.1 Data of generator characteristics.
2. Table 10.2 Data of transmission system.
3. Table 10.3 Restoration actions.
4. Table 10.4 Comparison of restoration times and system generation capabilities under different installation strategies.
5. Table 10.5 Time to complete generic restoration actions (GRAs).
6. Table 10.6 Data of generator characteristics.
7. Table 10.7 Sequence of restoration actions.
8. Table 10.8 Different sequence of restoration actions compared with base case.
9. Table 10.9 Sequence of restoration actions.
10. Table 10.10 Comparison of restoration time and system generation capability with different BS capabilities.
11. Table 10.11 Performance analysis.

List of Illustrations

Chapter 02
1. Figure 2.1 Probability distribution of cascade size n = 10⁵, n = 10⁷, and ϵ = 0.05.
2. Figure 2.2 Control effect under different parameters. The triangles represent optimal control values ().
3. Figure 2.3 Optimal control and range width of ϵ_act that reduces the total cost for both the 4‐regular and scale‐free case. (a) and (c): The “×” indicates the optimal control values (ϵ), and the vertical range indicates those values of ϵ_act for which the controlled case has lower cost than the uncontrolled case. The triangle is the critical ϵ_dam where the range becomes zero. (a) Optimal control (4‐regular network). (b) Range width of ϵ_act that reduces the total cost (4‐regular network). (c) Optimal control (scale‐free network). (d) Range width of ϵ_act that reduces the total cost (scale‐free network).
4. Figure 2.4 Cascading failure in the western U.S. power grid as triggered by the removal of a single node chosen at random (squares), or among those with largest degrees (asterisks) or highest loads (circles) [16].
5. Figure 2.5 Log‐log plot of the distribution of the number of components failed for three values of average initial load L [24]. L = 0.9 has an isolated point at (1000,0.8), indicating probability 0.8 of all 1000 components failed. The probability of no failures is 0.61 for L = 0.6, 0.37 for L = 0.8, and 0.14 for L = 0.9.
6. Figure 2.6 A process of a cascade of failures [27].
7. Figure 2.7 Distribution of the blackout size under different hidden failure probabilities [24].
8. Figure 2.8 Flow chart of the Manchester model [32].
9. Figure 2.9 CCDs of the normalized load shed from OPA for the WECC 1553‐bus system compared with the data for the western interconnection [37].
10. Figure 2.10 Flow chart of the improved OPA model [39].
11. Figure 2.11 Comparison of the complementary cumulative distributions (CCDs) of the load shed from basic and improved OPA models [39].
12. Figure 2.12 Flow chart of the OPA model with slow process.
13. Figure 2.13 Process of blackout in the Northeast Power Grid of China simulated by the OPA model with slow process.
14. Figure 2.14 CCDs of the line outages and the load shed under different Y. (a) The line outages. (b) The load shed.
15. Figure 2.15 CCDs of the line outages and the load shed under different γ. (a) The line outages. (b) The load shed.
16. Figure 2.16 RTS‐96 three‐area system.
17. Figure 2.17 CCDs of the line outages and the load shed from AC OPA simulation. (a) The line outages. (b) The load shed.
Chapter 03
1. Figure 3.1 Complementary cumulative frequency of the number of customers unserved [24].
2. Figure 3.2 Rescaled probability distribution function (PDF) of energy unserved during blackouts superimposed on the PDF of the avalanche size in sandpile [24].
3. Figure 3.3 Distribution of the load shed from the OPA model with slow process.
4. Figure 3.4 Distribution of line outages from the OPA model with slow process.
5. Figure 3.5 Probability distributions of the number of line outages. (a) Improved OPA on NPGC system at load level 1.3 times the base case. (b) AC OPA on IEEE 118‐bus system at base case load level.
6. Figure 3.6 Probability distribution of the load shed. (a) Improved OPA on NPGC system at load level 1.3 times the base case. (b) AC OPA on IEEE 118‐bus system at base case load level.
7. Figure 3.7 Probability distribution of the blackout size (odd numbered cascades used for estimation). (a) The line outages by improved OPA on NPGC system at load level 1.3 times the base case. (b) The load shed by AC OPA on IEEE 118‐bus system at load level 1.4 times the base case.
8. Figure 3.8 Probability distribution of the blackout size (even numbered cascades used for estimation). (a) The line outages by AC OPA on IEEE 118‐bus system at load level 1.2 times the base case. (b) The load shed by improved OPA on NPGC system at load level 1.6 times the base case.
9. Figure 3.9 Estimated marginal probability distributions of line outages and the load shed by using cascades. (a) The line outages. (b) The load shed.
10. Figure 3.10 Estimated marginal probability distributions of line outages and isolated buses by using cascades. (a) The line outages. (b) The isolated buses.
11. Figure 3.11 Estimated conditional largest possible total outage (CLO) when the total number of line outages is known. (a) The load shed. (b) The isolated buses.
12. Figure 3.12 Estimated marginal probability distributions in cross‐validation when line outages and the load shed are considered. (a) The line outages. (b) The load shed.
13. Figure 3.13 Estimated marginal probability distributions in cross‐validation when line outages and isolated buses are considered. (a) The line outages. (b) The isolated buses.
14. Figure 3.14 Estimated CLO in cross‐validation when the total number of line outages is known. (a) The load shed. (b) The isolated buses.
15. Figure 3.15 Estimated marginal probability distributions assuming there are no load shed or isolated bus data. (a) The load shed. (b) The isolated buses.
16. Figure 3.16 Estimated CLO when the number of line outages is known, assuming there are no load shed or isolated bus data. (a) The load shed. (b) The isolated buses.
17. Figure 3.17 Illustration for determining the cause of component failures.
18. Figure 3.18 Illustration for obtaining the directed acyclic subgraph starting with j.
19. Figure 3.19 Flow chart of the interaction model.
20. Figure 3.20 Number of links for different M. The dash horizontal line indicates card(ℒ(M)) = 419.
21. Figure 3.21 Propagation capacity for different M_u.
22. Figure 3.22 Ratio of completely cause‐indistinguishable components.
23. Figure 3.23 Interaction network for using 41 000 original cascades. The dots denote lines in the IEEE 118‐bus system and the arrows denote the links between lines.
24. Figure 3.24 Interaction network for using 8000 original cascades.
25. Figure 3.25 Interaction network for using 3680 original cascades.
26. Figure 3.26 Key links and key components for IEEE 118‐bus system. Key links shared by the three cases for using 41 000, 8000, and 3680 cascades are denoted by solid arrows; key links only for using 41 000 cascades are denoted by dash arrows; key links only for using 3680 cascades are denoted by dash‐dotted arrows; key components are denoted by thick solid lines and the other lines involved in the key links are denoted by dash lines.
27. Figure 3.27 Probability distributions of the total number of line outages for original and simulated cascades. Triangles indicate the total numbers of line outages of the original cascades; ○, ∇, and ◊ separately indicate total numbers of line outages of simulated cascades for using 41 000, 8000, and 3680 original cascades to quantify interactions; vertical lines indicate standard deviations; squares indicate initial line outages.
28. Figure 3.28 Complementary cumulative distributions (CCD) of the link weight for original and simulated cascades. Triangles indicate CCD of the link weight of original cascades; ○, ∇, and ◊ separately indicate CCD of the link weight of the simulated cascades for using 41 000, 8000, and 3680 original cascades to quantify interactions.
29. Figure 3.29 CCD of the out‐strength for original and simulated cascades.
30. Figure 3.30 CCD of the in‐strength for original and simulated cascades.
31. Figure 3.31 Probability distributions of the total number of line outages under two mitigation strategies. Triangles indicate total numbers of line outages of the original cascades under no mitigation; ○, ∇, and ◊ (•, ▾, and ♦) indicate total numbers of line outages of the simulated cascades under random (intentional) mitigation for using 41 000, 8000, and 3680 original cascades to quantify interactions; vertical lines indicate the standard deviations; squares indicate initial line outages.
32. Figure 3.32 Probability distributions of the total number of line outages under intentional mitigation for AC OPA and interaction model simulations. ○, ∇, and ◊ indicate total numbers of line outages for AC OPA model simulation; •, ▾, and ♦ indicate total number of line outages for simulated cascades using 41 000, 8000, and 3680 original cascades to quantify interactions; vertical lines indicate standard deviations.
33. Figure 3.33 R for different N. Blue, green, and red dots indicate the efficiency improvement R for using 41 000, 8000, and 3680 original cascades. The dashed horizontal line indicates R = 7200.
Chapter 04
1. Figure 4.1 Six‐bus power system.
2. Figure 4.2 Node‐weighted graph model of the six‐bus power system.
3. Figure 4.3 Edge‐weighted graph model of the six‐bus power system.
4. Figure 4.4 Generator grouping with the six‐bus power system.
5. Figure 4.5 A power system with three ECGs.
6. Figure 4.6 Graph model of the six‐bus power system.
7. Figure 4.7 Balanced K‐way graph partition problem converted to a 0–1 KNAPSACK problem.
8. Figure 4.8 Merge a zero‐weight node into its neighbor.
9. Figure 4.9 Merge a one‐degree node into its neighbor.
10. Figure 4.10 Remove a redundant edge.
11. Figure 4.11 Example of which edges can be reduced.
12. Figure 4.12 IEEE 30‐bus network.
13. Figure 4.13 IEEE 118‐bus power system and its graph model.
14. Figure 4.14 Simplification of the IEEE 118‐bus power system. (a) Original network with generation areas each containing a coherent generator group and load areas having clusters of load buses. (b) Reduction generator and load areas to equivalent generator and load buses. (c) Final reduced graph and potential separation strategies.
15. Figure 4.15 Graph‐based network decomposition. (a) Decomposition by one interface graph. (b) Decomposition by two interface graphs.
16. Figure 4.16 Graph‐based network decomposition of the IEEE 118‐bus system. (a) Subgraph G^J ₁. (b) Subgraph G^J ₂. (c) Subgraph G^J ₃.
17. Figure 4.17 Node‐weighted graph model of the six‐bus power system.
18. Figure 4.18 Graph model of the six‐bus system having paths from nodes 1–4 cut off.
19. Figure 4.19 The OBDD of f_GCC⊗f_PBC about the six‐bus power system.
20. Figure 4.20 The OBDD of f_GCC ⊗ f_PBC ⊗ f_MCC about the six‐bus power system.
21. Figure 4.21 Characteristics of N_T and R_T for 500 separation strategies.
22. Figure 4.22 Regions in the “Γ_system–Γ_island” plane indicating the success rate of separation strategies that satisfy the small disruption constraint.
23. Figure 4.23 Relationships between the strategies satisfying the generation coherency constraint (GCC), power balance constraint (PBC), and transmission capacity constraint (TCC); the strategies also satisfying the small disruption constraint (SDC); and the strategies leading to successful system separation.
24. Figure 4.24 Tree structure for checking the small disruption constraint and transmission capacity constraint starting from a minimum‐cut strategy.
25. Figure 4.25 Procedure of checking constraints.
Chapter 05
1. Figure 5.1 Single‐machine‐infinite‐bus system (SMIB).
2. Figure 5.2 Rotor angles of an SMIB system under small (upper) and large (lower) disturbances.
3. Figure 5.3 Gradually damped rotor angle oscillation under a large disturbance.
4. Figure 5.4 F‐A curve on an electromechanical mode.
5. Figure 5.5 PLL algorithm.
6. Figure 5.6 A simple PLL algorithm in the Z‐domain.
7. Figure 5.7 Flowchart of the PLL‐based approach. “LMSE” stands for “least mean square error”.
8. Figure 5.8 “Phase clock” on the mode shape at f_m.
9. Figure 5.9 Graph model of the WECC 179‐bus system with four ECGs respectively merged to equivalent generators.
10. Figure 5.10 Synchrophasor data and modal analysis results on the WECC system. (a) Angle differences between four ECGs. (b) Angle difference between ECGs 1 and 2. (c) Angle difference between ECGs 1 and 4. (d) Angle difference between ECGs 3 and 4. (e) Angle difference between ECGs 2 and 3. (f) Squared‐coherency index for each pair of ECGs. (g) The angle of CSD for each pair of ECGs.
11. Figure 5.11 Angle differences and phase differences on two probable separation boundaries.
12. Figure 5.12 Generator frequencies after separation at 202.5 s.
Chapter 06
1. Figure 6.1 Closing a line. (a) Switching operation. (b) Equivalent circuit.
2. Figure 6.2 Diagram of open‐ended line.
3. Figure 6.3 Diagram of load‐ended model.
4. Figure 6.4 Generator and transformer connected with long no‐load line. (a) A typical system with ferromagnetic overvoltage. (b) Equivalent circuit.
5. Figure 6.5 Odd high‐frequency resonance analysis. (a) Odd high‐frequency current components. (b) N‐order harmonic equivalent diagram.
6. Figure 6.6 Equivalent circuit of an induction motor.
7. Figure 6.7 Curves for voltage and frequency. (a) Motor terminal voltage. (b) System frequency.
8. Figure 6.8 Response curves. (a) Typical response characteristics of the bus frequency. (b) Typical bus voltage waveform.
Chapter 07
1. Figure 7.1 Generic model of generating units.
2. Figure 7.2 The unit step function.
3. Figure 7.3 A bilevel framework for restoring generating units.
4. Figure 7.4 Example for neighborhood searching.
5. Figure 7.5 Flow chart for finding the shortest path from an energized block to a bus.
6. Figure 7.6 An illustrative example of Dijkstra’s algorithm.
7. Figure 7.7 Traceback mechanism for restoring generating units.
8. Figure 7.8 Searching for unenergized buses at Step 0.
9. Figure 7.9 System topology and state of components at Step 1.
10. Figure 7.10 System topology and state of components at Step 2.
11. Figure 7.11 System topology and state of components at Step 3.
12. Figure 7.12 System topology and state of components at Step 4.
13. Figure 7.13 Initial state of an RTS 24‐bus test system.
14. Figure 7.14 Real power output of generation buses. (a) With reserve constraints. (b) Without reserve constraints.
15. Figure 7.15 Reserve levels of an RTS 24‐bus system. (a) With reserve constraints. (b) Without reserve constraints.
16. Figure 7.16 Restored loads in each load bus with reserve constraints.
17. Figure 7.17 Initial state of the IEEE 118‐bus system.
18. Figure 7.18 Reserve level and aggregate restored load level of IEEE 118‐bus system (a) Reserve level. (b) Aggregate restored load level.
19. Figure 7.19 Real power output and restored loads of an IEEE 118‐bus system. (a) Generator output curves. (b) Restored load levels.
Chapter 08
1. Figure 8.1 The offline restoration tool for TSOs to harness renewable energy.
2. Figure 8.2 Total generated power and real and reactive load pickup in the base case.
3. Figure 8.3 Total energy served at different wind farm locations.
4. Figure 8.4 Wind power and load pickup with the 200 MW wind farm at bus 38.
5. Figure 8.5 Wind power and load pickup with the 400 MW wind farm at bus 38.
6. Figure 8.6 Wind power with fluctuations at different restoration times.
7. Figure 8.7 General configuration of an AC system.
8. Figure 8.8 Typical control scheme for a Type 3 WT with stator voltage oriented.
9. Figure 8.9 One‐line circuit model of a Type 3 WT–based islanded system.
10. Figure 8.10 Equivalent form seen from a P‐f relationship.
11. Figure 8.11 Flowchart for Type 3 WTs’ black‐starting action sequence.
12. Figure 8.12 Diagram of the equivalent form of Type 3 WTs with self‐maintained frequency services.
13. Figure 8.13 Black‐starting of Type 3 WTs with sequential actions: (i) t < 30 s, starting up with a synchronous speed command; (ii) t = 30 s, controlled from MPPT [28]; (iii) t = 70 s, cutting off the DC battery; and (iv) t = 100 s, embedding AC voltage control and normal PLL.
14. Figure 8.14 Type 3 WTs’ response in stand‐alone operation: (a) the exported power (p.u.); (b) the rotor speed (p.u.); (c) the system frequency (Hz); and (d) the system frequency response under different parameter settings (Hz).
15. Figure 8.15 Structure of wind‐PSH‐assisted restoration process.
16. Figure 8.16 Forecasted and scheduled wind farm power output without PSH contribution and wind uncertainty.
17. Figure 8.17 Scheduled and forecasted wind farm power output with/without PSH units’ contributions.
18. Figure 8.18 Total load pickup curves with and without PSH units’ contributions.
19. Figure 8.19 Reservoir volume (Hm³) for different PSH locations.
20. Figure 8.20 Impact of budget of uncertainty on total energy served with and without PSH units’ contribution.
21. Figure 8.21 Scheduled and forecasted wind farm power with and without PSH units’ contribution in large fluctuation case.
22. Figure 8.22 Impact of budget of uncertainty on total energy served.
23. Figure 8.23 FRRs of ST, CT, HY, and three batteries.
24. Figure 8.24 Comparison of load pickup under different scenarios.
25. Figure 8.25 SoC of the 450 kWh battery.
26. Figure 8.26 Comparison of load pickup without battery and with one 2.7 MWh battery.
27. Figure 8.27 SoC of the 2.7 MWh battery.
28. Figure 8.28 Comparison of load pickup under different scenarios.
29. Figure 8.29 SOC of the 3.33 and 6.8 MWh battery.
30. Figure 8.30 Illustration of connections between vehicles, aggregator, and upper‐level operators.
31. Figure 8.31 Discrete‐time Markov chain states representation.
32. Figure 8.32 Synthetic driving patterns for a sample vehicle in various parking states.
33. Figure 8.33 Expected mean value of SoC in parking state P_R and driving state D_C.
34. Figure 8.34 Convergence of the expected mean value of SoC for a PHEV in parking state P_R at 6:00 a.m. and 6:00 p.m.
35. Figure 8.35 Number of energized feeders in different case studies.
36. Figure 8.36 State of charge of PHEV batteries in different case studies.
Chapter 09
1. Figure 9.1 LCC‐HVDC configuration.
2. Figure 9.2 DC power controller.
3. Figure 9.3 Controller for the rectifier.
4. Figure 9.4 Controller for inverter.
5. Figure 9.5 LCC‐HVDC with STATCOM for wind power integration (DFIG = doubly fed induction generator).
6. Figure 9.6 Control structures of VSC‐HVDC.
7. Figure 9.7 Active power–DC voltage relationship.
8. Figure 9.8 Auxiliary control in receiving‐end station. (a) V_dc‐ P droop control and f‐P control; (b) Q‐ V_ac droop control.
9. Figure 9.9 Auxiliary P‐V_dc droop control in sending‐end station.
10. Figure 9.10 Configuration of the black‐start study system.
11. Figure 9.11 Inverter output reference voltage.
12. Figure 9.12 Transformer voltage response.
13. Figure 9.13 Voltage response of lump load B.
14. Figure 9.14 Bus 4 voltage response.
15. Figure 9.15 Static var compensator.
16. Figure 9.16 Thyristor‐controlled series capacitor.
17. Figure 9.17 Static synchronous compensator.
18. Figure 9.18 Unified power flow controller static.
19. Figure 9.19 The basic block diagram of PMU.
20. Figure 9.20 An illustrative example.
21. Figure 9.21 Topology of IEEE 14‐bus system.
22. Figure 9.22 A conceptual resilience curve associated with an event.
23. Figure 9.23 Relationships between data sets and task modules.
24. Figure 9.24 Timing of prepositioning and real‐time allocation.
Chapter 10
1. Figure 10.1 Illustration of generation availability connecting three restoration stages.
2. Figure 10.2 Updated restoration plan with additional BS capability.
3. Figure 10.3 Criteria of restoration time and BS capability.
4. Figure 10.4 Restoration tool for updating restoration plans.
5. Figure 10.5 PJM five‐bus system.
6. Figure 10.6 Comparison of different installation strategies.
7. Figure 10.7 Comparison of system generation capability curve under different installation strategies.
8. Figure 10.8 Flow chart of algorithm.
9. Figure 10.9 IEEE RTS 24‐bus test system.
10. Figure 10.10 Comparison of restoration times under different BS capabilities on Bus 22.
11. Figure 10.11 Comparison of restoration times with installation of one new BS unit at different buses.
12. Figure 10.12 Comparison of restoration times at different buses with additional BS capability.
13. Figure 10.13 Comparison of reduced restoration times and installed BS capability at each bus.
14. Figure 10.14 Comparison of increased system generation capability with different BS capabilities.
15. Figure 10.15 Comparison of reduced restoration time and increased system generation capability with installed BS capability at different buses.

Power System Control Under Cascading Failures

Understanding, Mitigation, and System Restoration

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