Reactive Power Optimization of Large-Scale Power Systems: A Transfer Bees Optimizer Application
Abstract
:1. Introduction
- (1)
- Compared with the traditional mathematic optimization methods, the TBO has a stronger global search ability by employing the scouts and workers for exploitation and exploration. Besides, it can approximate the global optimum more closely via global optimization instead of external equivalent-based local optimization.
- (2)
- Compared with the general AI algorithms, the TBO can effectively avoid a blind search in the initial optimization phase and implement a much faster optimization for a new task by utilizing prior knowledge from the source tasks.
- (3)
- The optimization performance of the TBO was thoroughly tested by RPO of large-scale power systems. Because of its high optimization flexibility and superior optimization efficiency, it can be extended to other complex optimization problems.
2. Transfer Bees Optimizer
2.1. State-Action Chain
2.2. Knowledge Learning and Behavior Transfer
2.2.1. Knowledge learning
2.2.2. Behavior transfer
2.3. Exploration and Feedback
2.3.1. Action policy
2.3.2. Reward function
3. Design of the TBO for RPO
3.1. Mathematical Model of RPO
3.2. Design of the TBO
3.2.1. Design of state and action
3.2.2. Design of the reward function
3.2.3. Behavior transfer for RPO
- Step 1.
- Determine the source tasks according to a typical load curve in a day by Equation (12);
- Step 2.
- Complete the source tasks in the initial study process and store their optimal Q-value matrices;
- Step 3.
- Calculate the comparability between original tasks and new task according to the deviation of power demand according to Equations (13) and (14);
- Step 4.
- Obtain the original Q-value matrices in the new task by Equation (2).
3.2.4. Parameters setting
3.2.5. Execution Procedure of the TBO for RPO
4. Case Studies
4.1. Study of the Pre-Learning Process
4.2. Study of Online Optimization
4.2.1. Study of behavior transfer
4.2.2. Comparative results and discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Parameter | Range | IEEE 118-Bus System | IEEE 300-Bus System | ||
---|---|---|---|---|---|
Pre-Learning | Online Optimization | Pre-Learning | Online Optimization | ||
α | 0 < α < 1 | 0.95 | 0.99 | 0.9 | 0.95 |
γ | 0 < γ < 1 | 0.2 | 0.2 | 0.3 | 0.3 |
J | J ≥ 1 | 15 | 5 | 30 | 10 |
ε0 | 0 < ε0 <1 | 0.9 | 0.98 | 0.95 | 0.98 |
β | 0 < β < 1 | 0.95 | 0.95 | 0.98 | 0.98 |
C | C > 0 | 1 | 1 | 1 | 1 |
η | η > 0 | 10 | 10 | 50 | 50 |
W | W ≥ 0 | — | 50 | — | 100 |
Algorithm Index | ABC | GSO | ACS | PSO | GA | QGA | Ant-Q | TBO |
---|---|---|---|---|---|---|---|---|
Convergence time (s) | 15 | 35.5 | 30.9 | 29.1 | 10.8 | 3.99 | 4.16 | 0.94 |
Ploss (MW) | 1.11 × 104 | 1.11 × 104 | 1.11 × 104 | 1.11 × 104 | 1.11 × 104 | 1.11 × 104 | 1.11 × 104 | 1.10 × 104 |
Vd (%) | 1.51 × 103 | 1.49 × 103 | 1.44 × 103 | 1.48 × 103 | 1.50 × 103 | 1.51 × 103 | 1.50 × 103 | 1.48 × 103 |
f | 6.31 × 103 | 6.30 × 103 | 6.25 × 103 | 6.29 × 103 | 6.31 × 103 | 6.30 × 103 | 6.31 × 103 | 6.25 × 103 |
Best | 6.30 × 103 | 6.30 × 103 | 6.24 × 103 | 6.28 × 103 | 6.31 × 103 | 6.30 × 103 | 6.30 × 103 | 6.24 × 103 |
Worst | 6.31 × 103 | 6.31 × 103 | 6.25 × 103 | 6.30 × 103 | 6.32 × 103 | 6.30 × 103 | 6.31 × 103 | 6.25 × 103 |
Variance | 4.02 | 19.3 | 6.43 | 16.3 | 12 | 6.37 | 8.57 | 2.27 |
Std. Dev. | 2.01 | 4.39 | 2.54 | 4.03 | 3.46 | 2.52 | 2.93 | 1.51 |
Rel. Std. Dev | 3.18 × 10−4 | 6.96 × 10−4 | 4.06 × 10−4 | 6.41 × 10−4 | 5.49 × 10−4 | 4.01 × 10−4 | 4.64 × 10−4 | 2.41 × 10−4 |
Algorithm Index | ABC | GSO | ACS | PSO | GA | QGA | Ant-Q | TBO |
---|---|---|---|---|---|---|---|---|
Convergence time (s) | 72.3 | 63.4 | 228 | 102 | 48.3 | 47.8 | 115 | 3.37 |
Ploss (MW) | 3.82 × 104 | 3.86 × 104 | 3.83 × 104 | 3.81 × 104 | 3.77 × 104 | 3.76 × 104 | 3.74 × 104 | 3.75 × 104 |
Vd (%) | 8.34 × 103 | 8.87 × 103 | 7.36 × 103 | 8.07 × 103 | 7.78 × 103 | 7.56 × 103 | 7.14 × 103 | 6.94 × 103 |
f | 2.33 × 104 | 2.38 × 104 | 2.28 × 104 | 2.31 × 104 | 2.28 × 104 | 2.26 × 104 | 2.23 × 104 | 2.22 × 104 |
Best | 2.32 × 104 | 2.37 × 104 | 2.28 × 104 | 2.30 × 104 | 2.27 × 104 | 2.26 × 104 | 2.23 × 104 | 2.22 × 104 |
Worst | 2.33 × 104 | 2.38 × 104 | 2.28 × 104 | 2.32 × 104 | 2.28 × 104 | 2.26 × 104 | 2.23 × 104 | 2.22 × 104 |
Variance | 381 | 1.29 × 103 | 228 | 2.37× 103 | 178 | 194 | 221 | 66.4 |
Std. Dev. | 19.5 | 36 | 15.1 | 48.7 | 13.4 | 13.9 | 14.9 | 8.15 |
Rel. Std. Dev | 8.39 × 10−4 | 1.51 × 10−3 | 6.61 × 10−4 | 2.11 × 10−3 | 5.87 × 10−4 | 6.16× 10−4 | 6.67 × 10−4 | 3.67 × 10−4 |
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Cao, H.; Yu, T.; Zhang, X.; Yang, B.; Wu, Y. Reactive Power Optimization of Large-Scale Power Systems: A Transfer Bees Optimizer Application. Processes 2019, 7, 321. https://doi.org/10.3390/pr7060321
Cao H, Yu T, Zhang X, Yang B, Wu Y. Reactive Power Optimization of Large-Scale Power Systems: A Transfer Bees Optimizer Application. Processes. 2019; 7(6):321. https://doi.org/10.3390/pr7060321
Chicago/Turabian StyleCao, Huazhen, Tao Yu, Xiaoshun Zhang, Bo Yang, and Yaxiong Wu. 2019. "Reactive Power Optimization of Large-Scale Power Systems: A Transfer Bees Optimizer Application" Processes 7, no. 6: 321. https://doi.org/10.3390/pr7060321