An Adaptive Particle Swarm Optimization Algorithm Based on Guiding Strategy and Its Application in Reactive Power Optimization
Abstract
:1. Introduction
2. Original Particle Swarm Optimization (PSO)
3. Adaptive Particle Swarm Algorithm with Guiding Strategy(GSAPSO)
3.1. Strategy for Mixed Particles Update
- (1)
- The central particles were expressed as Equations (3) and (4).
- (2)
- The cooperative particles update formula was as follows
- (3)
- The chaotic particles were determined as follows
3.2. Strategy for Inertia Weight
4. Experiment
4.1. Experimental Setup
- (1)
- Sphere FunctionThe Sphere function is nonlinear and symmetric, it has a single-peak, which can be separated with different dimensions. It is used to test the optimization precision.
- (2)
- Rosenbrock FunctionThe Rosenbrock function is a typical ill-conditioned function that is difficult to minimize. Since this function provides little information for the search, it is difficult to identify the search direction, and the chance of finding the global optimal solution is low. Therefore, it is often used to evaluate the execution performance.
- (3)
- Rastrigin FunctionThe Rastrigin function is a complex multi-peaks function, with large quantity of local optima. It is prone to making the algorithm put local optimum, which will prematurely converge and not get the global optimal solution.
- (4)
- Griewank FunctionThe Griewank function is also a complex multi-peaks function with a large quantity of local minimum.
4.2. Parameter Settings
4.3. Analysis of Test Results
5. Problem Formulations
5.1. Objective Functions
5.2. Constraints
6. GSAPSO Algorithm for RPO
6.1. Treatment of Control Variables
6.2. Treatment of Discrete Variables
6.3. GSAPSO Algorithm for RPO
7. Simulation
8. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Function | Function Expression | Dimension | Range |
---|---|---|---|
Sphere | 30 | ||
Rosenbrock | 10 | ||
Rastrigin | 10 | ||
Griewank | 30 |
Functions | GSAPSO | LDWPSO | WPSO | ||||||
---|---|---|---|---|---|---|---|---|---|
BEST | WORST | MEAN | BEST | WORST | MEAN | BEST | WORST | MEAN | |
Sphere | 9.38 × 10−27 | 2.81 × 10−22 | 4.86 × 10−23 | 7.27 × 10−13 | 1.85 × 10−11 | 9.53 × 10−12 | 1.01 × 10−4 | 1.36 × 10−2 | 2.73 × 10−3 |
Rosenbrock | 1.25 × 10−4 | 2.29 | 1.31 | 0.0837 | 5.795 | 2.975 | 1.81 | 10.187 | 4 |
Rastrigin | 0 | 0 | 0 | 0 | 2.985 | 1.393 | 0 | 3.98 | 1.89 |
Griewank | 0 | 0.0465 | 9.33 × 10−3 | 7.7 × 10−13 | 0.032 | 0.0133 | 6.49 × 10−4 | 0.0623 | 0.0222 |
Functions | GSAPSO | LDWPSO | WPSO | ||||||
---|---|---|---|---|---|---|---|---|---|
AT | BT | SR | AT | BT | SR | AT | BT | SR | |
Sphere | 148 | 119 | 100% | 644 | 623 | 100% | 685 | 571 | 90% |
Rosenbrock | 1626 | 118 | 20% | 2000 | 1090 | - | 2000 | 1944 | - |
Rastrigin | 126 | 84 | 100% | 1762 | 1081 | 20% | 1704 | 513 | 20% |
Griewank | 321 | 125 | 80% | 790 | 622 | 60% | 871 | 620 | 40% |
Variables | Minimum (p.u.) | Maximum (p.u.) | Step |
---|---|---|---|
UG | 0.9 | 1.1 | - |
UPQ | 0.95 | 1.05 | - |
T | 0.9 | 1.1 | 0.025 |
C10 | 0 | 0.05 | 0.2 |
C24 | 0 | 0.02 | 0.2 |
Optimization Results | PSO | LDWPSO | WPSO | GSAPSO |
---|---|---|---|---|
The optimal value/MW | 6.9516 | 6.824 | 6.8242 | 6.8239 |
The worst value/MW | 7.2262 | 6.8667 | 6.8614 | 6.8699 |
The average value/MW | 7.046 | 6.8342 | 6.8354 | 6.8336 |
The variance | 7.034 × 10−3 | 1.31 × 10−4 | 1.21 × 10−4 | 1.17 × 10−4 |
Iterations of the optimal solution | 99 | 92 | 77 | 45 |
Average iterations | 67.3 | 86.8 | 67.2 | 64.6 |
Parameters | PSO | LDWPSO | WPSO | GSAPSO |
---|---|---|---|---|
U1 | 1.0678 | 1.0686 | 1.0686 | 1.0687 |
U2 | 1.0453 | 1.0506 | 1.0506 | 1.0506 |
U5 | 1.0227 | 1.0267 | 1.0267 | 1.0267 |
U8 | 1.0409 | 1.0381 | 1.0381 | 1.0381 |
U11 | 1.0026 | 1.0337 | 1.0099 | 1.0363 |
U13 | 1.0656 | 1.0749 | 1.075 | 1.0749 |
C1 | 40 | 30 | 40 | 30 |
C2 | 10 | 10 | 10 | 10 |
T1 | 1.025 | 1.1 | 1.025 | 1.05 |
T2 | 1.05 | 0.9 | 1 | 0.95 |
T3 | 0.975 | 1 | 1 | 1 |
T4 | 0.975 | 0.975 | 0.975 | 0.975 |
Ploss/MW | 6.9516 | 6.824 | 6.8242 | 6.8239 |
Psave/% | 17.449 | 18.964 | 18.962 | 18.966 |
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Jiang, F.; Zhang, Y.; Zhang, Y.; Liu, X.; Chen, C. An Adaptive Particle Swarm Optimization Algorithm Based on Guiding Strategy and Its Application in Reactive Power Optimization. Energies 2019, 12, 1690. https://doi.org/10.3390/en12091690
Jiang F, Zhang Y, Zhang Y, Liu X, Chen C. An Adaptive Particle Swarm Optimization Algorithm Based on Guiding Strategy and Its Application in Reactive Power Optimization. Energies. 2019; 12(9):1690. https://doi.org/10.3390/en12091690
Chicago/Turabian StyleJiang, Fengli, Yichi Zhang, Yu Zhang, Xiaomeng Liu, and Chunling Chen. 2019. "An Adaptive Particle Swarm Optimization Algorithm Based on Guiding Strategy and Its Application in Reactive Power Optimization" Energies 12, no. 9: 1690. https://doi.org/10.3390/en12091690