Advances in Electric Power and Energy

8 Chapter 10TABLE 10.1 Example simulation results with confidence values.TABLE 10.2 Example simulation results (voltages and standard deviations).TABLE 10.3 Example simulation results (accuracy and minimum accuracy values).TABLE 10.4 Compliance ratios.TABLE 10.5 Compliance ratios (case study 2).

9 Chapter 11TABLE 11.1 Correlation factors between voltage estimates with a shared voltage me...TABLE 11.2 Measurement location for Scenario 1.TABLE 11.3 Measurement location for Scenario 2.TABLE 11.4 Measurement location for Scenario 3.

10 Chapter 12TABLE 12.1 Attributes of selected works on multi‐area state estimation.TABLE 12.2 Initialization for boundary state variables.TABLE 12.3 Performance of SFHSE and the comparison with the centralized state est...TABLE 12.4 Comparison between SFHSE, the CSE, and another MASE method for IEEE 11...TABLE 12.5 Distributed bad data identification in the IEEE 118‐bus system test....TABLE 12.6 Comparison between SFHSE and the CSE for real system test.

11 Chapter 13TABLE 13.1 Results for comparison of parallel ASM WLS with centralized WLS.TABLE 13.2 Data sets for simulation.TABLE 13.3 Estimation error for different percentage of PMU installation.TABLE 13.4 Execution time for CPU‐based and GPU‐based DSE.

12 Chapter 14TABLE 14.1 Reported required time [11].

1 Chapter 2 Figure 2.1 One‐line diagram and measurement configuration of a 4‐bus power s... Figure 2.2 Objective function for the WLS estimator as a function of the err... Figure 2.3 Objective function for the LAV estimator as a function of the err... Figure 2.4 Objective function for the QC estimator as a function of the erro... Figure 2.5 Objective function for the QL estimator as a function of the erro... Figure 2.6 Graphical representation of the LMS estimator. Figure 2.7 Problem size comparison for different estimators. Figure 2.8 Example of alternative estimators: four‐bus system. Figure 2.9 Example of alternative estimators: residuals of the WLS solution.... Figure 2.10 Example of alternative estimators: residuals of the LAV solution... Figure 2.11 Example of alternative estimators: residuals of the QC solution.... Figure 2.12 Example of alternative estimators: residuals of the QL solution.... Figure 2.13 Histogram of voltage magnitude estimation accuracy for each meth... Figure 2.14 Histogram of voltage angle estimation accuracy for each method.... Figure 2.15 Histogram of the computation time for each estimator.

2 Chapter 3Figure 3.1 A generic network [24].Figure 3.2 Nine‐branch subsystem of 118‐bus IEEE test system.Figure 3.3 DFAX distribution functions for large and small systems [19].Figure 3.4 DFAX density functions resemble power law functions.Figure 3.5 Degree of vulnerability is affected by interregional transfers.Figure 3.6 Rank of vulnerability for peak, shoulder, and minimum loads.Figure 3.7 Degree of criticality for peak, shoulder, and minimum loads.Figure 3.8 RankV and tipping points as a function of demand, SW WI.

3 Chapter 4Figure 4.1 Intuitive understanding of stealthy false data injection attacks....Figure 4.2 Intuitive understanding of stealthy topology attacks.Figure 4.3 Overview of model‐based anomaly detection approach.Figure 4.4 Detailed workflow of model‐based anomaly detection.Figure 4.5 IEEE 14‐bus system with a measurement configuration.Figure 4.6 Plotting deviation between predicted states and SE outputs over a...Figure 4.7 Variation of FPR with respect to detection thresholds for θ 2Figure 4.8 Variation of TPR with respect to attack magnitude for various det...

4 Chapter 5Figure 5.1 Example microgrid circuit, legacy distance protection.Figure 5.2 Distance relay characteristics.Figure 5.3 Performance of the distance protection, relay I, with a phase A t...Figure 5.4 Example microgrid circuit, legacy line differential protection.Figure 5.5 Line differential relay characteristics (alpha plane method).Figure 5.6 Performance of the line differential protection, relay I, with a ...Figure 5.7 Performance of the line differential protection, relay I, with a ...Figure 5.8 Example topology of a microgrid, adaptive protection scheme.Figure 5.9 An example microgrid system, differential energy‐based protection...Figure 5.10 Phase A current measurement at bus B‐1 of the line DL‐1, grid‐co...Figure 5.11 Phase A current measurement at bus B‐2 of the line DL‐1, grid‐co...Figure 5.12 Phase A current spectral energy at bus B‐1 of the line DL‐1, gri...Figure 5.13 Phase A current spectral energy at bus B‐2 of the line DL‐1, gri...Figure 5.14 Phase A differential energy of the line DL‐1, grid‐connected mod...Figure 5.15 Phase A differential energy of the line DL‐1, islanded mode.Figure 5.16 Control architecture of an example microgrid.Figure 5.17 Two voltage sources and the inductive circuit connecting them.Figure 5.18 Active power/frequency droop and reactive power/voltage droop.Figure 5.19 Active power/frequency droop diagram, method 1.Figure 5.20 Reactive power/voltage droop diagram, method 1.Figure 5.21 Droop control diagram, method 2 [15].Figure 5.22 Secondary control, active power/frequency droop.Figure 5.23 Secondary control, reactive power/voltage droop.Figure 5.24 Two voltage sources and the resistive circuit connecting them.Figure 5.25 Two voltage sources (the inverter and the grid) and the resistiv...Figure 5.26 π‐Equivalent microgrid circuit model.Figure 5.27 Example microgrid system, dynamic state estimation‐based protect...Figure 5.28 Dynamic state estimation‐based protection results: low impedance...Figure 5.29 Dynamic state estimation‐based protection results: high impedanc...Figure 5.30 Adaptive setting‐less protection scheme.Figure 5.31 UMPCU installation and its functions.Figure 5.32 Test case for a distribution feeder. The acronyms WG and L repre...Figure 5.33 Expected errors of states (test case 1).Figure 5.34 Actual absolute errors of states (test case 1).Figure 5.35 Computation time (test case 1).Figure 5.36 Expected errors of states (test case 2).Figure 5.37 Actual absolute errors of states (test case 2).Figure 5.38 Computation time (test case 2).Figure 5.39 Equivalent circuit for a three‐phase induction machine.Figure 5.40 Confidence levels for test cases 3–7.Figure 5.41 Terminal currents for test case 6 (high impedance fault).Figure 5.42 Top: terminal currents for test case 4 (three‐phase‐to‐ground fa...

5 Chapter 6Figure 6.1 Left: Voltage magnitude and angle estimation errors per bus for t...Figure 6.2 Left: The IEEE 14‐bus system partitioned into four areas [25, 31]...Figure 6.3 Average error curves (bottom) and (top) for the LSE and its r...Figure 6.4 (Left) Per area state matrix error and (right) state vector estim...

6 Chapter 7Figure 7.1 Shortest propagation paths from Sensor “ k ” to the fault on Line “...Figure 7.2 Virtual nodes generated at the points “ β k,ℓ D ℓ” ...Figure 7.3 (a) Location of a fault occurring at 99 miles away from Bus 63 th...Figure 7.4 Phasor measurements provided by a PMU.Figure 7.5 7‐Bus system for illustration.Figure 7.6 Placement of 3 two‐channel PMUs in the 7‐bus system.Figure 7.7 Optimal PMU deployment on a 4‐bus system (a) ignoring zero‐inject...Figure 7.8 Configuration of 3 single‐channel PMUs in the 7‐bus system (the d...Figure 7.9 Placement of 5 two‐channel PMUs in the 7‐bus system.

7 Chapter 8Figure 8.1 Schematic of the proposed robust hybrid state estimation framewor...Figure 8.2 The absolute estimation error of the bus voltage magnitude with G...Figure 8.3 The absolute estimation error of the bus voltage angles with Gaus...Figure 8.4 The absolute estimation error of the bus voltage magnitude with G...Figure 8.5 The absolute estimation error of the bus voltage angles with non‐...Figure 8.6 The absolute estimation error of the bus voltage magnitude with L...Figure 8.7 The absolute estimation error of the bus voltage angles with Lapl...Figure 8.8 The estimated states of the proposed method under different bad d...