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USF Tampa Graduate Theses and Dissertations
USF Graduate Theses and Dissertations
June 2023
Enhancing Smart Grid Security and Reliability through Graph
Signal Processing and Energy Data Analytics
Md Abul Hasnat
University of South Florida
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Scholar Commons Citation
Hasnat, Md Abul, "Enhancing Smart Grid Security and Reliability through Graph Signal Processing and
Energy Data Analytics" (2023). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/10118
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List of Tables ................................................................................................................. vi
List of Figures .............................................................................................................. vii
Abstract ......................................................................................................................... xi
Chapter 1: Introduction ................................................................................................ 1
1.1 Research Problems in Situational Awareness . ......................................... 2
1.2 Situational Awareness-Related Problems................................................... 3
1.3 An Introduction to Graph Signal Processing .............................................. 5
1.4 Overview of Energy Data Analytics ............................................................ 6
1.5 Key Contributions of this Dissertation ....................................................... 6
1.5.1 Data Sources ................................................................................. 7
1.5.2 An Overview of Technical Approaches ........................................ 7
1.5.3 Contributions Toward Enhancing Situational
Awareness in Power Grids ................................................................ 8
1.5.3.1 Detection and Location Identification of
Cyber and Physical Stresses ................................................... 8
1.5.3.2 Characterization and Classification of
Cyber and Physical Stresses ................................................... 9
1.5.3.3 Recovery of the Unobservable States and
Optimum Placement of Measurement Devices .................... 10
1.5.3.4 Characterization of Single Bus
Perturbation in Smart Grids ................................................ 11
1.6 Structure of this Dissertation .................................................................. 12
Chapter 2: Fundamentals of Grid-GSP ..................................................................... 15
2.1 GSP Literature Review .............................................................................. 15
2.2 Review of GSP and Energy Graph Signals ............................................... 17
2.2.1 Defining Graph Domain for Power Grids .................................... 17
2.2.2 Representation of Power System Measurements as
Graph Signals: Vertex Domain ........................................................ 19
2.2.3 Spectral Characteristics of Power Grid’s Graph
Signal - Graph-Frequency Domain................................................... 20
2.2.4 Global Smoothness of Graph Signals........................................... 21
2.2.5 Local Smoothness of Graph Signals ............................................. 22
2.2.6 Joint Vertex-Frequency Representations .................................... 22
i
2.2.7 Time-Varying Graph Signals ....................................................... 23
2.2.8 Amount of High Graph-Frequency Components .......................... 23
2.3 Reflection of Smart Grid Stresses on Their Graph Signals ..................... 24
2.3.1 Cyber Attack Models .................................................................... 24
2.3.1.1 Denial-of-service (DoS Attack) ....................................... 24
2.3.1.2 False Data Injection Attack (FDIA) ............................... 25
2.3.1.3 Ramp Attack ................................................................... 26
2.3.1.4 Replay Attack.................................................................. 27
2.3.1.5 Delay Attack ................................................................... 27
2.3.2 Reflection of Cyber Attacks on Graph Spectra............................ 28
2.3.3 Effects of Node-degree of Stressed Buses on
Graph Spectra ................................................................................... 30
2.3.4 Comparative Analyses of Effects of Cyber and
Physical Stresses ............................................................................... 31
2.4 Effects of Cyber Attacks Patterns on Local Smoothness of Graph
Signals .......................................................................................................... 32
2.5 Graph Signal Sampling Overview ............................................................. 35
2.5.1 The Concept of Graph Spectral Bandwidth ................................ 35
2.5.2 Sampling and Reconstruction of Band-limited Graph
Signals ............................................................................................... 36
2.6 Learning of Graph Signals ........................................................................ 39
Chapter 3: Detection and Location Identification of Cyber and Physical
Stresses in the Smart Grid: Part I: State Correlation Approach ......................... 40
3.1 Related Work .............................................................................................. 41
3.2 Effects of Cyber and Physical Stresses on Instantaneous
Correlations .................................................................................................. 44
3.2.1 Instantaneous Correlation Matrix............................................... 44
3.2.2 Visualizing Cyber Stresses Using Instantaneous
Correlation Matrix Image ................................................................. 46
3.2.2.1 DoS Attack ...................................................................... 47
3.2.2.2 Data Replay Attack ........................................................ 48
3.2.2.3 Ramp Attack ................................................................... 50
3.2.2.4 Multiple Cyber Attacks .................................................. 50
3.2.3 Effects of Physical Stresses on Instantaneous
Correlation Matrix Image ................................................................. 51
3.3 Detection and Location Identification Using Image Processing
on Instantaneous State Correlation Matrix Image .................................... 53
3.3.1 Detection and Location Identification Technique ....................... 53
3.3.2 Simulation and Performance Analysis ........................................ 57
3.3.3 Detecting and Locating Physical Stresses................................... 58
3.4 Detection and Location Identification Using the k-Nearest
Neighbor Analysis of Instantaneous State Correlation ............................. 58
3.4.1 Aggregated Instantaneous Correlation Vectors .......................... 59
ii
3.4.2 Feature Extraction and Classification for Stress Detection ....... 62
3.2.2.1 k-NN Method for Classification ..................................... 64
3.4.3 Locating Stresses in the System .................................................. 65
3.4.4 Computational Complexity .......................................................... 66
3.4.5 Simulation and Results ................................................................ 67
3.4.5.1 Generating State Attribute Time Series ....................... 67
3.4.5.2 Detection and Locating Performance ............................. 68
Chapter 4: Detection and Location Identification of Cyber and Physical
Stresses in the Smart Grid: Part II: GSP Approach ............................................. 71
4.1 Related Works ............................................................................................ 73
4.2 Stress Models ............................................................................................. 74
4.2.1 Cyber Attack Models .................................................................... 74
4.2.2 Physical Stress Model .................................................................. 74
4.3 GSP-based Detection and Localization ..................................................... 75
4.3.1 Stresses Detection Using GFT ..................................................... 75
4.3.2 Detecting and Locating Stresses Using VFED ........................... 77
4.3.3 Detecting and Locating Stresses Using Local
Smoothness ....................................................................................... 78
4.4 Performance Evaluation ............................................................................ 81
4.4.1 Simulating Stress Scenarios ........................................................ 81
4.4.2 Performance Metrics .................................................................... 82
4.4.3 Analyses of the Results ................................................................ 83
4.4.4 Comparison with Existing Methods ............................................ 85
4.4.4.1 Candidate Techniques for Comparison .......................... 85
4.4.4.2 Comparison of Detection Accuracy ................................ 86
4.4.4.3 Performance of Location Accuracy ................................. 88
4.4.4.4 Further Discussions ........................................................ 88
4.4.5 Computational Complexity .......................................................... 89
Chapter 5: Classification and Characterization of Cyber and Physical
Stresses in the Smart Grid Using Graph Signal Learning................................... 91
5.1 Related Works ............................................................................................ 92
5.2 Problem Formulations ............................................................................... 93
5.2.1 Classification Problem Formulation ............................................ 93
5.2.1.1 A Short Review of GSP Concepts ................................... 93
5.2.1.2 Classification Models ...................................................... 93
5.2.2 Characterization of Cyber Attacks .............................................. 95
5.2.1.1 Determining the Number of Cyber Attacks................... 95
5.2.1.2 Determining Attack Center and Attack
Radius in Clustered Cyber Attacks........................................ 95
5.3 Feature Extraction Using GSP .................................................................. 96
5.3.1 Different Types of GSP-based Features ...................................... 96
5.3.1.1 Features Extracted from the Moment of
iii
Detection, ............................................................................ 96
5.3.1.2 Features Extracted Using GFT of Temporal
Statistics ................................................................................. 97
5.3.1.3 Features Extracted by Taking Temporal
Statistics of the Time-Varying GFT Values .......................... 98
5.3.2 Dimensionality Reduction of the GFT-based Features .............. 98
5.4 Simulation Details ..................................................................................... 99
5.4.1 Two-stage Classification .............................................................. 99
5.4.2 Characterization ........................................................................... 99
5.5 Performance Evaluation .......................................................................... 100
5.5.1 Performance of the Two-stage Classification ............................ 100
5.5.1.1 Noise Sensitivity of Classification Performance ......... 102
5.5.1.2 Classification Performance with a Reduced
Number of Features .............................................................. 103
5.5.2 Classification Performance for Multiple Random Vs.
Clustered Cyber Attacks................................................................. 104
5.5.3 Determining
and in Clustered Cyber Attacks .................. 105
Chapter 6: Recovery of Missing States and Optimum Meter Placement in
Smart Grid Using Correlation of States and Graph Signal Sampling............... 107
6.1 Related Work ............................................................................................ 109
6.2 State Recovery Using Graph Signal Sampling ....................................... 110
6.2.1 Problem Formulation ................................................................. 110
6.2.2 State Recovery Using Graph Signal Sampling ......................... 112
6.3 State Recovery Using Global and Local Smoothness Graph Signal ...... 112
6.3.1 Recovery Technique.................................................................... 113
6.3.2 Simulation and Results .............................................................. 114
6.3.2.1 Experimental Setup...................................................... 114
6.3.2.2 Estimating the Probability Distributions of the
Local Smoothness ................................................................. 115
6.3.2.3 Solving the Optimization Problem ............................... 115
6.3.2.4 State Recovery Performance Analysis ......................... 116
6.3.2.5 Comparison with Other Reconstruction Methods ....... 117
6.4 Optimum Measurement Device Placement ............................................ 119
6.4.1 Sampling Set Selection in Power System Graph Signal
Sampling ......................................................................................... 119
6.4.1.1 Random Selection of .................................................. 120
6.4.1.2 Degree-based Selection of ......................................... 120
6.4.1.3 Page-rank-based Selection of .................................... 120
6.4.1.4 Load Demand-based Selection of .............................. 121
6.4.1.5 Anti-Aliasing Filter Error-based Selection of ........... 121
6.4.2 Optimum PMU Placement as an Optimization Problem ......... 122
6.4.3 Results ........................................................................................ 123
6.5 State Recovery Using State Correlation .................................................. 124
iv
6.5.1 System and Attack Models......................................................... 124
6.5.1.1 Power System Model .................................................... 124
6.5.1.2 DoS Attack Model ......................................................... 124
6.5.2 Method ........................................................................................ 125
6.5.3 Simulations and Results ............................................................ 127
6.5.3.1 Correlation Among PMU Time Series ......................... 128
6.5.3.2 Estimation of PMU Time Series Under Single
and Multiple DoS Attacks .................................................... 128
6.5.3.3 Most Vulnerable Combination of Attacks.................... 131
6.5.3.4 Parameter Values ..................................................... 132
6.5.3.5 Most Vulnerable Time for the DoS Attack .................. 132
Chapter 7: GSP-based Grid Perturbation Analysis ................................................ 134
7.1 Related Work ............................................................................................ 137
7.2 Mathematical Representation of Perturbation and Associated
Electrical Attributes .................................................................................. 138
7.2.1 Power System Graph Signals .................................................... 138
7.2.2 DC Power Flow Model ................................................................ 140
7.2.3 Smoothness of Graph Signals .................................................... 140
7.2.4 Single Bus Perturbation ............................................................. 142
7.3 Effects of Single Bus Perturbation .......................................................... 144
7.3.1 Spreadability of Single Bus Perturbation ................................. 144
Chapter 8: Conclusion and Future Work ................................................................. 157
8.1 Concluding Remarks ................................................................................. 157
8.2 Future Work ............................................................................................. 160
8.2.1 Detection and Location Identification of Cyber
and Physical Stresses ..................................................................... 161
8.2.2 Characterization and Classification of Cyber
and Physical Stresses ..................................................................... 161
8.2.3 Recovery of the Unobservable States and Optimum
Placement of Measurement Devices .............................................. 161
8.2.4 Characterization of Single Bus Perturbation
in Smart Grids ................................................................................. 162
References .................................................................................................................. 163
Appendix A: Copyright Permissions ......................................................................... 181
v
Replay
Attack
Delay
Attack
FDIA
DoS
Attack
Ramp
Attack
Mean squared Error
Error caused by the Anti-Aliaing Filter
Error caused by the Reconstruction using Matrix Operations
Total Error of Sampling-Reconstruction
Number of Sampled Nodes
Replay
Attack
Delay
Attack
FDIA
DoS
Attack
Ramp
Attack
1
Accuracy
0.8
0.6
0.4
Random Vs. Clustered
Attack Center Locating
Attack Radius Estimation
0.2
0
-0.02
-0.01
0
Amount of change in FDIA
0.01
1
Accuracy
0.95
0.9
0.85
0.8
1
Random Vs. Clustered Classification
Attack Center Locating (Clustered)
Attack Radius Estimation (Clustered)
2
3
Amount of delay (samples)
4
5
Mean Absolute Error of Recovery (in dB)
Clustered Cyber-Attack
Random Cyber-Attack
Number of buses under cyber-attak
Recovery Error (in degree)
1.2
Mean Absolute Error
Maximum Absolute Error
1
0.8
0.6
0.4
0.2
0
5
10
15
Number of Unobservable Buses
20
Mean Absolute Error (in dB)
Random
Degree-based
Pagerank-Based
Load Demand-Based
Proposed Anti-aliasing Filter Error Based
Number of Sampled Vertices
Mean Absolute error (in degree)
Anti-aliasing Filter Error Based Selection
PMU setting
Number of Sampled Vertices / Number of PMUs
Voltage Angle (in Degree)
32.5
Original Voltage Angle
Estimated Voltage Angle
The DoS Attack Moment
32
31.5
31
30.5
30
0
5
10
15
20
25
Time (Hours)
Voltage Angle (in Degree)
-12
Original Voltage Angle
Estimated Voltage Angle
The DoS Attack Moment
-12.5
-13
-13.5
-14
-14.5
0
5
10
15
Time (Hours)
20
25
Original Voltage Magnitude
Estimated Voltage Magnitude
The DoS Attack Moment
0.9895
0.989
0.9885
0.988
0
5
10
15
20
25
Time (Hours)
33
Voltage Angle (in Degree)
Voltage Magnitude (in per unit)
0.99
Estimation for 2 DoS Attacks
Estimation for 8 DoS Attacks
Estimation for 16 DoS Attacks
Estimation for 32 DoS Attacks
Original Bus Voltage Angle
The Moment of DoS Attack
32.5
32
31.5
31
30.5
30
0
5
10
15
Time (Hours)
20
25
Mean squared error
0.25
0.2
Uniform
Clustered
Inhibition
0.15
0.1
0.05
0
0
20
40
60
80
Number of Attackeded PMUs
100
120
Voltage Angle (in Degree)
29.5
a=1
a=5
a=100
a=200
a=500
a=700
Original Bus Voltage Angle
The Moment of DoS Attack
29
28.5
28
27.5
27
26.5
0
5
10
15
Time (Hours)
20
25
0.1
Mean squared error
Day 1
Day 2
0.08
0.06
0.04
0.02
0
0
5
10
15
Time of the day (Hour)
20
25