Advances in Power System Modelling, Control and Stability Analysis

Cover
Contents
About the editors
Preface to the 1st edition
Preface to the 2nd edition
Part I: Modelling
1 Telegrapher's equations for field-to-transmission line interaction
1.1 Transmission line approximation
1.2 Single-wire line above a perfectly conducting ground
1.2.1 Taylor, Satterwhite and Harrison model
1.2.2 Agrawal, Price and Gurbaxani model
1.2.3 Rachidi model
1.3 Contribution of the different electromagnetic field components
1.4 Inclusion of losses
1.5 Case of multi-conductor line
1.6 Time-domain representation of the coupling equations
1.7 Solutions with particular reference to time-domain numerical solutions
1.8 Application of theory to the case of lightning-induced voltages on distribution overhead lines
1.8.1 The LIOV code
1.8.2 The LIOV-EMTP-RV code
1.8.3 LEMP response of electrical distribution systems
1.9 Summary and concluding remarks
Acknowledgements
Bibliography
2 Reliable solutions of uncertain optimal power flow problems by affine arithmetic
2.1 Introduction
2.2 Overview of existing approaches
2.2.1 Sampling methods
2.2.2 Analytical methods
2.2.3 Approximate methods
2.2.4 Non-probabilistic methods
2.2.5 AA-based methods
2.3 Mathematical background
2.3.1 PF analysis
2.3.2 Optimal PF analysis
2.3.3 Self-validated computing
2.3.4 Solving constrained optimization problems by linear AA
2.4 AA-based linear methods for uncertain power system analysis
2.4.1 Uncertain PF problems
2.4.2 Uncertain OPF problems
2.4.3 Numerical results
2.5 Elements of second-order AA
2.5.1 Uncertain power system analysis by second-order AA
2.5.2 Numerical results
2.6 Conclusion
Bibliography
3 DFT-based synchrophasor estimation processes for Phasor Measurement Units applications: algorithms definition and performance analysis
3.1 Literature review
3.2 Definitions
3.2.1 Signal model
3.2.2 Phasor
3.2.3 Synchrophasor
3.2.4 Frequency and rate of change of frequency
3.2.5 Phasor measurement unit
3.3 The discrete Fourier transform
3.3.1 From the Fourier transform to the DFT
3.3.2 DFT interpretation and relevant properties
3.3.3 DFT effects
3.3.4 DFT parameters
3.3.5 DFT calculation in real time
3.4 DFT-based SE algorithms
3.4.1 The Interpolated-DFT technique
3.4.2 The iterative-Interpolated DFT technique
3.5 Performance analysis of SE algorithm
3.5.1 The IEEE Std. C37.118
3.5.2 Performance assessment of the i-IpDFT SE algorithm
3.6 Conclusions
Bibliography
4 Modeling power systems with stochastic processes
4.1 Literature review
4.2 Stochastic differential equations
4.2.1 Method for modeling an SDE with an analytically defined PDF and an exponentially decaying ACF
4.2.2 Method for modeling a SDE with an arbitrary PDF and ACF
4.2.3 Method for modeling SDEs with jumps
4.2.4 Method for modeling correlation
4.3 Modeling power systems as SDAEs
4.3.1 Initialization of stochastic power system models
4.3.2 Modeling stochastic perturbations in power systems
4.3.3 Examples
4.4 Time-domain integration of SDAEs
4.5 Stochastic power system case studies
4.5.1 Initialization of Irish power system models
4.5.2 Irish system with inclusion of wind and solar generation
4.5.3 Irish system with correlated load and wind generation
4.6 Conclusions
Bibliography
5 Detailed modeling of inverter-based resources
5.1 Introduction
5.2 Variable speed WT models
5.2.1 WT aerodynamics
5.2.2 Control of variable speed WTs
5.2.3 Wind parks with variable speed WTs
5.2.4 FSC WTs
5.2.5 DFIG WTs
5.3 Software implementation
5.4 Simulation results
5.4.1 FSC-based WP
5.4.2 DFIG-based WP
5.5 Conclusion
Bibliography
6 Isomorphism-based simulation of modular multilevel converters
6.1 Introduction
6.2 MMC models for EMT simulations: a review
6.2.1 Full physics, full detailed, and bi-value resistor models
6.2.2 Thévenin equivalent model
6.2.3 Switching function model
6.2.4 Average value model
6.3 EMT simulation of MMCs based on isomorphism
6.3.1 Operating principle of the isomorphism-based approach
6.3.2 Dynamic partitioning in the MMC
6.3.3 Key features of the isomorphism-based approach
6.4 Validation
6.4.1 Simulation setting
6.4.2 Simulated scenarios
6.4.3 Analysis of simulation accuracy
6.4.4 Analysis of submodules variables
6.4.5 Analysis of simulation speed
6.5 Conclusions
Bibliography
Part II: Control
7 Optimization methods for preventive/corrective control in transmission systems
7.1 Formulation of a time-continuous dynamic optimization problem for corrective control
7.2 Formulation of a time-discrete static optimization problem for corrective control
7.3 Application to power system DAEs
7.3.1 Control variables
7.3.2 Control effort minimization
7.3.3 Kinetic energy cost function
7.3.4 Voltage penalty functions
7.3.5 Distance relays penalty function
7.4 Application of the proposed methodology for the corrective control of a realistically sized power system (test results)
7.5 Application to preventive control problems
Bibliography
8 Static and recursive PMU-based state estimation processes for transmission and distribution power grids
8.1 State estimation measurement and process model
8.1.1 Measurement model
8.1.2 Network observability
8.1.3 Process model
8.2 Static state estimation: the weighted least squares
8.2.1 Linear weighted least squares state estimator
8.2.2 Non-linear weighted least squares
8.3 Recursive state estimation: the Kalman filter
8.3.1 Discrete Kalman filter
8.3.2 Extended Kalman filter
8.3.3 Kalman Filter sensitivity with respect to the measurement and process noise covariance matrices
8.3.4 Assessment of the process noise covariance matrix
8.4 Assessment of the measurement noise covariance matrix
8.5 Data conditioning and bad data processing in PMU-based state estimators
8.6 Kalman filter vs. weighted least squares
8.7 Numerical validation and performance assessment of the state estimation
8.7.1 Linear state estimation case studies
8.7.2 Non-linear SE case studies
8.8 Kalman filter process model validation
8.9 Numerical validation of Theorem 8.1
Bibliography
9 Real-time applications for electric power generation and voltage control
9.1 Introduction
9.2 Outlines of real-time system concepts
9.2.1 Real-time operating systems
9.2.2 Real-time communications
9.3 Voltage control
9.3.1 Excitation control systems
9.3.2 Secondary voltage control
9.3.3 Voltage control with distributed generation
9.4 Conclusions
Bibliography
10 Optimal control processes in active distribution networks
10.1 Typical architecture of ADN grid controllers
10.1.1 Control architecture
10.1.2 Controller's actions
10.2 Classic computation of sensitivity coefficients in power networks
10.3 Efficient computation of sensitivity coefficients of busvoltages and line currents in unbalanced radial electrical distribution networks
10.3.1 Voltage sensitivity coefficients
10.3.2 Current sensitivity coefficients
10.3.3 Sensitivity coefficients with respect to transformer's ULTC
10.4 Application examples
10.4.1 Distribution network case studies
10.4.2 Numerical validation
10.4.3 Voltage control and lines congestion management examples
10.5 Conclusions
Bibliography
11 Control of converter interfaced generation
11.1 Hardware structure
11.2 Grid-following and grid-forming control
11.3 Implementations for grid-following control
11.4 Implementations for grid-forming control
11.4.1 Internal frequency generation
11.4.2 Synchronization based on power flow
11.4.3 Power-frequency droop control
11.4.4 Emulation of generator swing equation
11.4.5 Single integration of power difference
11.5 Virtual Synchronous Machines
11.6 Virtual Oscillator Control
11.6.1 Power dispatch
11.6.2 Modified Andronov–Hopf oscillator
11.7 Concluding remarks
Bibliography
12 Combined voltage–frequency control with power electronics-based devices
12.1 Introduction
12.2 Voltage-based frequency control through SVC devices
12.2.1 Voltage dependency of loads
12.2.2 Frequency control through SVC
12.3 Frequency control of converter-based resources through modified voltage control reference
12.3.1 Modified voltage control reference
12.3.2 DER and ESS models
12.4 Coupled voltage–frequency control of DERs
12.4.1 Control structure
12.4.2 Assessment metric
12.5 Case study I: VFC through SVC
12.5.1 WSCC 9-bus system
12.5.2 All-island Irish system
12.5.3 Discussion
12.6 Case study II: FC+MRVC scheme for DERs
12.6.1 DERs connected to buses 2 and 3
12.6.2 ESS connected to bus 5
12.7 Case study III: FVP+FVQ control of DERs
12.7.1 FQ and VP control modes
12.7.2 Performance of FVP+FVQ control
12.7.3 Performance of voltage/frequency response metric
12.7.4 Application to aggregated power generation
12.7.5 Impact of resistance/reactance line ratio
12.7.6 Impact of DER penetration level
12.7.7 Impact of system granularity
Bibliography
13 Smart transformer control of the electrical grid
13.1 The smart transformer concept
13.2 ST architectures and control
13.2.1 MVAC/DC converter
13.2.2 DC/DC conversion stage
13.2.3 LV DC/AC converter
13.3 Services provision to AC grids
13.3.1 Disturbance rejection
13.3.2 Load sensitivity identification
13.3.3 Voltage-based load control
13.3.4 Frequency-based load control
13.4 Enabling services for future DC grids
13.5 Conclusions and future outlook
Acknowledgment
Bibliography
14 On the interactions between plug-in electric vehicles and the power grid
14.1 Introduction
14.2 Review of the state-of-the-art
14.2.1 Technological aspects
14.3 Optimized charging of the vehicles
14.3.1 Charging strategies
14.3.2 V2G and vehicle-to-everything (V2X)
14.3.3 Automatic adaptation of charge rates
14.4 Charging strategies
14.4.1 Uncontrolled charging
14.4.2 Controlled charging—centralized solutions
14.4.3 Controlled charging—decentralized solutions
14.4.4 Controlled charging—prioritized decentralized solutions
14.5 Simulations
14.6 Research interests and future trends
14.6.1 Wireless power charging
14.6.2 Peer-to-peer energy exchange
14.6.3 Optimal utilization of electric charge points
14.6.4 Distributed ledger technologies
14.7 Conclusions
Bibliography
Part III: Stability Analysis
15 Time-domain simulation for transient stability analysis
15.1 Introduction
15.2 Time-domain simulations and transient stability
15.3 Transient stability and high-performance computing
15.4 A new class of algorithms: from step-by-step solutions to parallel-in-time computations
15.5 Performances in parallel-in-time computations
15.6 Conclusions
Bibliography
16 Voltage security in modern power systems
16.1 Introduction
16.2 The power flow problem in rectangular coordinated
16.2.1 The power flow with SVC constraints
16.3 The OPF with SVC constraints
16.3.1 The maximum loadability with SVC constraints
16.3.2 Minimisation of the squared deviation of the bus voltage magnitude from a reference value
16.3.3 Constrained maximisation of the loadability with SVC
16.4 Solution of the optimisation problem
16.4.1 Primal-dual interior point method
16.4.2 Reduction of the linear system
16.5 Numerical results
16.5.1 The New England 39 buses network case
16.5.2 The Italian case
16.6 Conclusions
Bibliography
17 Small-signal stability and time-domain analysis of delayed power systems
17.1 Introduction
17.1.1 Time-domain methods
17.1.2 Frequency-domain methods
17.2 A general model for power systems with time delays
17.2.1 Steady-state DDAEs
17.3 Numerical techniques for DDAEs
17.3.1 Padé approximants
17.3.2 Numerical integration of DDAEs
17.3.3 Methods to approximate the characteristic roots of DDAEs
17.4 Impact of delays on power system control
17.4.1 OMIB system with simplified PSS
17.4.2 Numerical example
17.5 Case studies
17.5.1 IEEE 14-bus system
17.5.2 All-island 1479-bus Irish system
Bibliography
18 Shooting-based stability analysis of power system oscillations
18.1 Introduction
18.2 Mathematical background
18.2.1 The time-domain shooting method
18.2.2 The state transition matrix for hybrid dynamical systems
18.2.3 Bordering the Jacobian
18.2.4 The probe-insertion technique
18.3 Revisited power system model
18.3.1 Outlines of standard power system models
18.3.2 From polar to rectangular coordinates
18.3.3 On the unit multipliers of the power system model periodic orbits
18.3.4 Bordering based on the centre of inertia
18.4 Case studies
18.4.1 IEEE 14-bus test system
18.4.2 WSCC 9-bus test system
18.4.3 A switching 2-area PSM
18.4.4 Cascaded ULTC transformers
18.5 Conclusions
Bibliography
19 Stability assessment in advanced DC microgrids
19.1 Introduction
19.2 DC power systems modeling
19.2.1 Radial distribution
19.2.2 Zonal distribution
19.2.3 DC voltage control
19.3 Methodology to assess the DC stability
19.3.1 Stability assessment flowchart
19.3.2 Models for stability study
19.3.3 State-space matrix
19.4 Application on DC microgrids
19.4.1 Power system design
19.4.2 Control design
19.4.3 Average value models
19.4.4 Poles location
19.4.5 Numerical verification
19.4.6 Considerations on stability assessment in zonal distribution
19.5 Conclusions
Acknowledgment
Copyright notice
Bibliography
20 Scanning methods for stability analysis of inverter-based resources
20.1 Introduction
20.2 State-space methods
20.2.1 Development of the state-space models and stability analysis
20.2.2 Advantages and shortcomings of the state-space methods
20.3 Impedance-based methods
20.3.1 Analytical approaches
20.3.2 Measurement-based approaches
20.4 Scanning methods
20.4.1 Positive-sequence scan
20.4.2 dq-frame scan
20.4.3 aß-frame scan
20.4.4 Convergence test
20.4.5 Comparison of the scanning methods
20.5 Simulation results
20.5.1 Scenario I: FSC wind park connected to series-compensated transmission lines
20.5.2 Scenario II: DFIG wind park connected to series compensated transmission lines
20.5.3 Scenario III: interactions of wind parks with large-scale power systems
20.6 Conclusions
Bibliography
Part IV: Appendices
Appendix A Stochastic process fitting procedure
A.1 Find the ACF parameters
A.2 Find the PDF parameters
A.2.1 Analytical PDF
A.2.2 Numerical PDF
Appendix B Modeling correlated stochastic processes
B.1 Two correlatedWiener processes
B.2 Two correlated Poisson jump processes
B.3 Correlated stochastic load model
B.4 Correlated stochastic power flow equations
B.5 Correlated wind fluctuations
Appendix C Data of lines, loads and distributed energy resources
C.1 IEEE 34-bus distribution test feeder data
C.2 IEEE 13-bus distribution test feeder data
C.3 IEEE 39-bus transmission test system data
Bibliography
Appendix D Proofs and tools for DDAEs
D.1 Determination of A0, A1 and A2
D.2 Chebyshev's differentiation matrix
D.3 Kronecker's product
Appendix E Numerical aspects of the probe-insertion technique
E.1 Parameters of the probe-insertion technique
E.2 Integration of (18.34)
Index
Back Cover