Power Distribution System State Estimation

Contents
About the Editors
Preface
1 Introduction
2 Real-time monitoring of distribution systems brazilian experience
2.1 Introduction
2.2 Brazilian distribution system monitoring
2.3 Description of the RTMT implemented in COPEL
2.3.1 Step 1: Data preprocessing
2.3.2 Step 2: Real-time load modeling
2.4 Application results
2.4.1 In-field verification
2.4.2 Application in service restoration
2.4.3 Application in distribution system state estimation
2.4.4 Application for real-time load forecasting
2.5 Concluding remarks
References
3 Practical experiences of distribution state estimation in real life
3.1 Introduction
3.2 Problem settings
3.2.1 Background
3.2.2 Sources of the problems
3.3 Industrial-grade product
3.3.1 Requests for practical implementation in real life
3.3.2 Problems of practical application and how to solve them
3.4 Where are we today?
3.5 Where are we going, and what awaits us?
3.6 Conclusion
3.6.1 Achieved to date
3.6.2 In front of us
Appendix – Schneider Electric DMS Novi Sad LLC
References
4 Three-phase network model for steady-state analysis of distribution systems
4.1 Introduction
4.1.1 Distribution system state estimation
4.1.2 The unbalanced and asymmetrical nature of distribution systems
4.2 Three-phase two-port models
4.2.1 Three-phase two-port admittance model
4.2.2 Polar coordinates
4.2.3 Rectangular coordinates
4.3 Models of the physical components of a distribution system
4.3.1 Distribution lines
4.3.2 Power transformers
4.3.3 Voltage regulators
4.3.4 Loads
4.3.5 Shunt capacitors and reactors
4.3.6 Distributed generation
4.3.7 Energy storage
4.3.8 Electric vehicles
4.3.9 Static compensators (D-FACTS)
4.4 Concluding remarks
References
5 Current-based power flow calculation methods for distribution systems
5.1 Introduction
5.2 Basics of the current-based three-phase power flow
5.2.1 State variables
5.2.2 Specified quantities and bus types
5.2.3 Load modelling
5.3 Branch current–based and admittance matrix–based load flows
5.3.1 State variables
5.3.2 Bus types and equivalent specified quantities
5.3.3 General modelling
5.3.4 Computational aspects and discussion
5.4 Backward/forward sweep load flow
5.4.1 Basic aspects
5.4.2 General modelling
5.4.3 Computational aspects and discussion
5.5 Case studies
5.5.1 Data preparation
5.5.2 Execution of the AMBLF
5.5.3 Execution of the BCBLF
5.5.4 Execution of the BFSLF
5.6 Conclusions and special remarks
References
6 Classical methods applied to distribution system state estimation
6.1 Introduction
6.2 Historical notes
6.3 Basics of BCB and AMB state estimators
6.3.1 State variables
6.3.2 Equivalent measurements
6.3.3 Variances of the equivalent measurements
6.3.4 Reference bus
6.3.5 WLS solution via normal equation
6.4 Jacobian matrix of the AMBSE
6.4.1 Derivatives of the complex current injections
6.4.2 Derivatives of the complex current flows
6.4.3 Derivatives of the equivalent voltages
6.4.4 Derivatives of the complex voltages of the reference bus
6.5 Jacobian matrix of the BCBSE
6.5.1 Derivative of the magnitude of the current flows
6.5.2 Derivative of the complex current injections
6.5.3 Derivative of the complex current flows
6.5.4 Derivative of the equivalent voltages
6.5.5 Derivatives of the complex voltages of the reference bus
6.6 Computational aspects
6.6.1 AMBSE algorithm
6.6.2 BCBSE algorithm
6.7 Case studies
6.7.1 Solving the AMBSE
6.7.2 Solving the BCBSE
6.8 Conclusion
References
7 Fast-decoupled power flow method for active distribution systems
7.1 Introduction
7.1.1 Power flow analysis for active DS
7.2 Basics of Newton–Raphson-based power flow
7.2.1 Fundamentals of the power flow analysis
7.2.2 NRPF formulation
7.2.3 Fast-decoupled approach
7.3 cpu-based fast-decoupled power flow for distribution systems
7.3.1 Fundamentals of the complex per unit normalization
7.3.2 cpu-based power flow algorithm
7.4 Multilevel voltage analyses
7.5 Case studies and performance evaluation
7.5.1 Two-bus test system—convergence example
7.5.2 141-bus distribution feeder
7.6 Final remarks
References
8 Fast-decoupled distribution system state estimation
8.1 Introduction
8.2 Fast-decoupled weighted least-squares state estimation
8.2.1 Conventional weighted least-squares state estimation
8.2.2 Decoupled formulation
8.2.3 Model-decoupled state estimator
8.2.4 Algorithm-decoupled state estimator
8.3 Bus-section level modeling in state estimation
8.3.1 Generalized decoupled formulation
8.4 cpu-based fast-decoupled DSSE
8.4.1 Data and measurement under cpu normalization
8.4.2 Conventional measurement data in cpu system
8.5 Measurement simulator
8.6 cpu-based real-time distribution system network modeling algorithm
8.7 Case studies and performance evaluation
8.8 Final remarks
References
9 Bayesian approach for distribution system state estimation
9.1 Introduction
9.2 Power statistics and pseudo-measurements
9.3 Bayesian approach for state estimation in distribution systems
9.3.1 Measurement model
9.3.2 A Bayes framework for DSSE
9.3.3 Measurement handling
9.3.4 Prior description
9.3.5 Numerical computation of the Bayesian DSSE
9.4 Examples of Bayesian distribution system state estimation
9.5 Concluding remarks
References
10 Multiarea state estimation for distribution systems
10.1 Introduction
10.1.1 Large-scale distribution systems and motivations for MASE
10.2 Multiarea State Estimation
10.2.1 Terminology, definitions, and classifications of multiarea state estimators
10.2.2 Hierarchical architecture
10.2.3 Distributed architecture
10.3 MASE for distribution systems
10.3.1 Two-step method with branch current estimator
10.3.2 Bayesian inference method with nodal voltage estimator
10.4 Application examples of MASE for distribution systems
10.4.1 Example I: Two-step multiarea DSSE
10.4.2 Example II: Bayesian inference multiarea DSSE
10.5 Concluding remarks
References
11 Including synchronized and non-synchronized measurements with different sample rates in distribution system state estimation
11.1 Introduction
11.2 Data sources for DSSE
11.2.1 Measurement data used in DSSE
11.3 Temporal aspects of DSSE
11.3.1 Dynamic state estimation concepts and introduction to Kalman filters
11.3.2 Dynamic, forecasting-aided and tracking state estimation
11.4 Multistages state estimators based on quasi-dynamic techniques
11.4.1 Limitations of Kalman filter-based methods
11.4.2 Consensus DSSE method
11.4.3 Matrix completion-based system state update with granular measurements
11.4.4 Implementations of matrix completion-based DSSE
11.4.5 Numerical results
11.5 Bayesian information fusion approach for multistage DSSE
11.5.1 Bayesian inference concepts and application in DSSE
11.5.2 Posterior inference via orthogonal methods
11.5.3 Bayesian credibility test
11.5.4 Numerical results
11.6 Applications of DSSE and challenges
11.7 Concluding remarks
References
12 State estimation for low voltage distribution grids
12.1 The need for DSSE in LVDGs
12.2 Classical DSSE approach
12.2.1 WLS DSSE
12.2.2 State variables and measurement functions
12.2.3 Kron’s reduction: four wires to three wires
12.3 Challenges for DSSE in LVDGs
12.3.1 Limited sensing
12.3.2 Limited system knowledge
12.3.3 Slow reporting rate – asynchronous measurements
12.3.4 Nonzero neutral voltage
12.4 Enhancing DSSE
12.4.1 Addressing asynchronous measurements using historical data
12.4.2 Addressing the nonzero neutral voltage
12.5 Future directions
12.5.1 State estimation for the whole distribution grid
12.5.2 Leveraging information from PV and EV inverters
12.5.3 Validation in a real-time hardware-in-the-loop framework
12.6 Concluding remarks
References
13 Conclusions
13.1 Historical context
13.2 Alternative modeling and approaches for DSSE
13.3 Future perspectives for the evolution of the DSSE process
13.4 Final remarks
Index
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