Optimal Available Transfer Capability Assessment Strategy for Wind Integrated Transmission Systems Considering Uncertainty of Wind Power Probability Distribution
Abstract
:1. Introduction
2. Optimal Available Transfer Capability (ATC) Assessment Model
2.1. Traditional Chance Constrained Optimal Available Transfer Capability (ATC) Assessment Model
2.1.1. Active and Reactive Power Balance Constraint
2.1.2. Conventional Unit Generating Capacity Constraints
2.1.3. Active and Reactive Wind Power Output Constraints
2.1.4. Chance Constraints of Node Voltage
2.1.5. Chance Constraints of Branch Power
2.2. Distributional Robust Chance Constrained Model
3. Solving Method for Distributional Robust Chance Constrained Optimal Available Transfer Capability (ATC) Assessment Model
3.1. Reformulation of Distributional Robust Chance Constraints
- (1)
- Give the initial value of Q(λ) and V(λ), where λ = 0 at the beginning, it denotes the initial value.
- (2)
- Substitute Q(λ) and V(λ) into the power balance equation [31] to calculate the correction term ΔV(λ) and ΔQ(λ).
- (3)
- Iteration stops when ΔV(λ) = JΔQ(λ), otherwise, go to Step (4).
- (4)
- Use ΔV(λ) and ΔQ(λ) to correct Q(λ) and V(λ), then obtains Q(λ + 1) and V(λ + 1), let λ = λ + 1, go back to Step (2).
3.2. Determination Model for Distributional Robust Chance Constraint
4. Linear Matrix Inequality (LMI)-Based Particle Swarm Optimization (PSO) Algorithm for Available Transfer Capability (ATC) Assessment Problem
- (1)
- Input grid original parameters, the first and second order moments of the wind power, PSO control parameters and control variables. The branch power and node voltage constraints in Equations (10) and (11) can be converted into LMI form as shown in Equations (19) and (20).
- (2)
- Initialization: set the initial solution and , calculate the fitness value, and let the iteration counter K = 0.
- (3)
- Parameter optimization: substitute and into sub-problems in Equations (19) and (20). Solve the resulting LMI problem and obtain the optimal solution , and set .
- (4)
- Optimal decision: substitute into Equation (21), solve the matrix positive condition and power flow calculation to obtain the updated optimal solution and and the corresponding objective value . Vaccine selection and immune selection are defined as shown in Equations (22) and (23), the particle PGi, QG,i with high Prob(PGi, QG,i) value would be selected, and set and
- (5)
- Termination: If the iteration counter K meets the predefined value, then the final optima are obtained, and the algorithm ends. Otherwise, let K = K + 1, and repeat Steps (3) and (4).
5. Numerical Example
5.1. Comparison of the Distributional Robust Chance Constrained ATC (DRCC-ATC) Model and the Traditional Chance Constrained ATC (TCC-ATC) Model
5.2. Available Transfer Capability (ATC) under Different Expectations of Wind Power Probability Distribution, Where Covariance = 0.4 MW2
5.3. Available Transfer Capability (ATC) under Different Covariance of Wind Power Probability Distribution, Where Expectation = 2.0 MW
6. Summary
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Dual Problem of Node Voltage Constraints
Appendix B. Eliminate Random Vector and Convert Matrix Inequalities
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Node | 1 | 2 | 5 | 8 | 11 | 13 |
---|---|---|---|---|---|---|
PG,max (MW) | 139 | 58 | 35 | 21 | 18 | 10 |
PG,min (MW) | 130 | 32 | 30 | 13 | 17 | 10 |
Branch No. | Tmax | Tmin | Tap Ratio | Unit Capacity |
---|---|---|---|---|
11 | 1.1 | 0.9 | 17 | 0.0125 |
12 | 1.1 | 0.9 | 17 | 0.0125 |
15 | 1.1 | 0.9 | 17 | 0.0125 |
36 | 1.1 | 0.9 | 17 | 0.0125 |
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Xie, J.; Wang, L.; Bian, Q.; Zhang, X.; Zeng, D.; Wang, K. Optimal Available Transfer Capability Assessment Strategy for Wind Integrated Transmission Systems Considering Uncertainty of Wind Power Probability Distribution. Energies 2016, 9, 704. https://doi.org/10.3390/en9090704
Xie J, Wang L, Bian Q, Zhang X, Zeng D, Wang K. Optimal Available Transfer Capability Assessment Strategy for Wind Integrated Transmission Systems Considering Uncertainty of Wind Power Probability Distribution. Energies. 2016; 9(9):704. https://doi.org/10.3390/en9090704
Chicago/Turabian StyleXie, Jun, Lu Wang, Qiaoyan Bian, Xiaohua Zhang, Dan Zeng, and Ke Wang. 2016. "Optimal Available Transfer Capability Assessment Strategy for Wind Integrated Transmission Systems Considering Uncertainty of Wind Power Probability Distribution" Energies 9, no. 9: 704. https://doi.org/10.3390/en9090704