Distributed Integrated Synthetic Adaptive Multi-Objective Reactive Power Optimization
Abstract
:1. Introduction
- A new optimization method (called ISAMOPSO) is proposed based on the MOPSO.
- The proposed ISAMOPSO’s performance is evaluated by testing the selected benchmark functions.
- The active power loss, voltage deviation, and reactive power compensation cost are taken as the optimization objectives, and the multi-objective reactive power optimization mathematical model of the distribution network of a distributed generation is established.
- The new proposed ISAMOPSO approach is applied to solve the reactive power optimization in the distribution networks with DG.
2. Multi-Objective Reactive Power Optimization Model
2.1. Objective Function
2.1.1. Active Power Loss
2.1.2. Voltage Deviation
2.1.3. Reactive Power Compensation Cost
2.2. Constraint Condition
2.2.1. Equality Constraint
2.2.2. Inequality Constraint
3. ISAMOPSO Algorithm
3.1. The Basic Principle of the PSO Algorithm
3.2. Introducing Random Black Hole Strategy
3.3. Adaptive Adjustment of Inertia Weight and Learning Factor
3.4. The Diverse Selection of Leader Particles
3.5. Cyclic Elimination Strategy of Crowding Distance
3.6. ISAMOPSO Algorithm Performance Verification and Analysis
4. Applied ISAMOPSO for Reactive Power Optimization
4.1. Influence of Distributed Generation on Distribution Network
4.1.1. Influence of Distributed Generation Capacity on Distribution Network
4.1.2. Influence of Distributed Generation Position on Distribution Network
4.2. Multi-Objective Reactive Power Optimization Solution Process
- Step 1: Read the system data, set the population size and the maximum iteration number and the related parameters of the improvement strategy, and initialize the population , personal best and global best .
- Step 2: Update the personal best and leader for each particle. Carry out power flow computation and obtain the objective function values of each particle. The non-dominated solutions of the population are confirmed according to the non-dominated ranking strategy, and the positions of the next generation of particles and the individual optimal positions are updated according to Equation (13).
- Step 3: Generate off-spring population according to Equations (11) and (13) based on the current velocity and position of each particle in , and then combine and together and obtain population whose size is .
- Step 4: Identify the non-dominated solutions from , and store them in .
- Step 5: Generate the particle population for the next iteration and the evaluation criterion Formula (17) for the leader particles.
- Step 6: Based on the state of velocity in the population, determine whether it constitutes a perturbation condition, and adjust the population again.
- Step 7: Determine whether the maximum number of iterations is reached; if so, proceed to the next step; otherwise, go to Step 3 for the next iteration.
- Step 8: Output the non-dominated solutions as the final Pareto-optimal solutions.
4.3. Analysis and Discussion Results
4.3.1. Static Reactive Power Optimization
4.3.2. Dynamic Reactive Power Optimization
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Test Function | Index | Algorithm | |||
---|---|---|---|---|---|
NSGAII | MOPSO | SMPSO | ISAMOPSO | ||
DTLZ1 | Mean | 2.6664 × 10−2 | 3.1767 × 10−2 | 3.0328 × 10−2 | 2.6595 × 10−2 |
Std | 1.28 × 10−3 | 1.75 × 10−2 | 1.20 × 10−2 | 1.09 × 10−3 | |
DTLZ2 | Mean | 6.8392 × 10−2 | 7.7528 × 10−2 | 6.6816 × 10−2 | 6.3912 × 10−2 |
Std | 3.38 × 10−3 | 8.42 × 10−3 | 2.30 × 10−3 | 1.79 × 10−3 | |
DTLZ3 | Mean | 6.8458 × 10−2 | 1.2056 × 10−1 | 6.8460 × 10−2 | 9.9426 × 10−2 |
Std | 2.19 × 10−3 | 7.13 × 10−2 | 2.63 × 10−3 | 4.33 × 10−2 | |
DTLZ4 | Mean | 6.6723 × 10−2 | 1.7982 × 10−1 | 1.1460 × 10−1 | 1.5361 × 10−1 |
Std | 3.02 × 10−3 | 1.15 × 10−1 | 1.06 × 10−1 | 1.64 × 10−2 | |
DTLZ5 | Mean | 5.7555 × 10−3 | 7.7760 × 10−3 | 5.3310 × 10−3 | 4.8635 × 10−3 |
Std | 3.61 × 10−4 | 6.66 × 10−4 | 4.20 × 10−4 | 1.35 × 10−4 | |
DTLZ6 | Mean | 5.7767 × 10−3 | 8.5702 × 10−3 | 5.3689 × 10−3 | 4.6755 × 10−3 |
Std | 2.82 × 10−4 | 9.20 × 10−4 | 2.09 × 10−4 | 9.00 × 10−5 | |
DTLZ7 | Mean | 7.9676 × 10−2 | 1.0997 × 10−1 | 1.0327 × 10−1 | 8.2313 × 10−2 |
Std | 6.02 × 10−3 | 9.98 × 10−2 | 3.81 × 10−2 | 6.18 × 10−3 |
Function | NSGAⅡ | MOPSO | SMPSO | ISAMOPSO |
---|---|---|---|---|
DTLZ1 | ||||
DTLZ2 | ||||
DTLZ3 | ||||
DTLZ4 | ||||
DTLZ5 | ||||
DTLZ6 | ||||
DTLZ7 |
Test Function | Index | Algorithm | |||
---|---|---|---|---|---|
NSGAII | MOPSO | SMPSO | ISAMOPSO | ||
DTLZ1 | Mean | 8.2429 × 10−1 | 7.9694 × 10−1 | 8.1700 × 10−1 | 8.1891 × 10−1 |
Std | 3.74 × 10−3 | 4.61 × 10−2 | 5.11 × 10−3 | 3.13 × 10−2 | |
DTLZ2 | Mean | 5.3293 × 10−1 | 5.0980 × 10−1 | 5.3286 × 10−1 | 5.3832 × 10−1 |
Std | 5.53 × 10−3 | 1.29 × 10−2 | 3.90 × 10−3 | 3.56 × 10−3 | |
DTLZ3 | Mean | 5.0795 × 10−1 | 4.6962 × 10−1 | 5.2880 × 10−1 | 5.3488 × 10−1 |
Std | 5.30 × 10−2 | 6.38 × 10−2 | 6.18 × 10−3 | 4.64 × 10−3 | |
DTLZ4 | Mean | 5.4192 × 10−1 | 4.9007 × 10−1 | 5.2322 × 10−1 | 5.2573 × 10−1 |
Std | 3.29 × 10−3 | 4.11 × 10−2 | 3.85 × 10−2 | 6.46 × 10−3 | |
DTLZ5 | Mean | 1.9930 × 10−1 | 1.9691 × 10−1 | 1.9944 × 10−1 | 1.9965 × 10−1 |
Std | 1.70 × 10−4 | 2.61 × 10−3 | 2.09 × 10−4 | 1.25 × 10−4 | |
DTLZ6 | Mean | 1.9958 × 10−1 | 1.9781 × 10−1 | 1.9962 × 10−1 | 2.0015 × 10−1 |
Std | 1.30 × 10−4 | 4.58 × 10−4 | 1.74 × 10−4 | 3.57 × 10−5 | |
DTLZ7 | Mean | 2.7128 × 10−1 | 2.6964 × 10−1 | 2.6817 × 10−1 | 2.7167 × 10−1 |
Std | 1.68 × 10−3 | 1.17 × 10−2 | 2.67 × 10−3 | 2.57 × 10−3 |
Node | 0 | 20% | 40% | 50% | 70% | 90% | 100% |
---|---|---|---|---|---|---|---|
3 | 0.0293 | 0.0228 | 0.022 | 0.0216 | 0.0211 | 0.0208 | 0.0207 |
6 | 0.0239 | 0.0159 | 0.011 | 0.0097 | 0.0089 | 0.0104 | 0.012 |
9 | 0.0239 | 0.0141 | 0.0107 | 0.011 | 0.0148 | 0.0225 | 0.0276 |
12 | 0.0239 | 0.0134 | 0.0118 | 0.0135 | 0.021 | 0.0331 | 0.0405 |
15 | 0.0239 | 0.0134 | 0.015 | 0.0189 | 0.0315 | 0.0491 | 0.0595 |
18 | 0.0239 | 0.0147 | 0.0198 | 0.0258 | 0.043 | 0.0655 | 0.0785 |
19 | 0.0239 | 0.0232 | 0.0229 | 0.0229 | 0.0231 | 0.0237 | 0.0241 |
21 | 0.0239 | 0.0237 | 0.0264 | 0.0286 | 0.035 | 0.0434 | 0.0484 |
23 | 0.0239 | 0.0224 | 0.0217 | 0.0217 | 0.0223 | 0.0236 | 0.0246 |
25 | 0.0239 | 0.0216 | 0.0226 | 0.0243 | 0.0296 | 0.0373 | 0.042 |
26 | 0.0239 | 0.0155 | 0.0107 | 0.0094 | 0.009 | 0.0112 | 0.0132 |
28 | 0.0239 | 0.0135 | 0.009 | 0.0087 | 0.0111 | 0.0173 | 0.0216 |
31 | 0.0239 | 0.0118 | 0.0095 | 0.011 | 0.0185 | 0.0306 | 0.0382 |
33 | 0.0239 | 0.0121 | 0.0108 | 0.0131 | 0.022 | 0.0359 | 0.0444 |
Result | DG1 (Mvar) | DG2 (Mvar) | C1 (Mvar) | C2 (Mvar) | K (pu) | (MW) | (million) | |
---|---|---|---|---|---|---|---|---|
W1 | 0.0335 | 0.2965 | 0.15 | 0.15 | 0.975 | 0.0645 | 0.1581 | 0.0594 |
W2 | 0.1325 | 0.3214 | 0.15 | 0.15 | 0.975 | 0.0663 | 0.1595 | 0.0569 |
W3 | 0.1618 | 0.2933 | 0.3 | 0.45 | 0.975 | 0.0512 | 0.1287 | 0.0701 |
W4 | 0.3187 | 0.3396 | 0.45 | 0.75 | 1 | 0.0547 | 0.2741 | 0.0421 |
W5 | 0.3571 | 0.4163 | 0.45 | 0.3 | 1 | 0.0582 | 0.2803 | 0.0486 |
Comparison Object | Before Optimization | NSGA-II | ISAMOPSO |
---|---|---|---|
(MW) | 0.1885 | 0.0728 | 0.0645 |
1.0435 | 0.1945 | 0.1581 | |
(million) | - | 0.0637 | 0.0594 |
Time | Light Intensity (W/m2) | Temperature (℃) | Wind Speed (m/s) | PV Output (kW) | WT Output (kW) | Time | Light Intensity (W/m2) | Temperature (℃) | Wind Speed (m/s) | PV Output (kW) | WT Output (kW) |
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 0 | 17.33 | 7.15 | 0 | 219.4 | 12 | 494.44 | 27.46 | 5.90 | 287.9 | 134.3 |
1 | 0 | 17.29 | 8.32 | 0 | 313.6 | 13 | 619.44 | 30.10 | 6.72 | 315.1 | 188.1 |
2 | 0 | 17.10 | 7.53 | 0 | 248.4 | 14 | 605.56 | 29.26 | 5.82 | 403.4 | 129.5 |
3 | 0 | 16.73 | 8.16 | 0 | 299.9 | 15 | 565.56 | 29.18 | 5.18 | 392.7 | 93.01 |
4 | 0 | 16.32 | 10.37 | 0 | 513 | 16 | 522.22 | 28.35 | 6.74 | 365.2 | 189.8 |
5 | 91.67 | 16.06 | 9.25 | 0 | 399 | 17 | 394.44 | 26.30 | 5.65 | 334.8 | 119.2 |
6 | 161.11 | 16.11 | 8.86 | 53.78 | 361.6 | 18 | 81.67 | 23.93 | 6.78 | 247.9 | 192.6 |
7 | 245.56 | 16.66 | 9.55 | 95.25 | 428.3 | 19 | 0 | 21.55 | 5.48 | 49.25 | 109.8 |
8 | 333.33 | 17.90 | 8.77 | 146.8 | 353.4 | 20 | 0 | 19.50 | 6.22 | 0 | 154.9 |
9 | 341.67 | 19.91 | 7.43 | 202.1 | 241 | 21 | 0 | 18.03 | 5.96 | 0 | 138.3 |
10 | 391.11 | 22.42 | 5.90 | 208.8 | 134.5 | 22 | 0 | 17.09 | 6.11 | 0 | 147.7 |
11 | 457.22 | 25.05 | 6.34 | 242.4 | 162.4 | 23 | 0 | 16.52 | 6.81 | 0 | 194.9 |
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Song, J.; Lu, C.; Ma, Q.; Zhou, H.; Yue, Q.; Zhu, Q.; Zhao, Y.; Fan, Y.; Huang, Q. Distributed Integrated Synthetic Adaptive Multi-Objective Reactive Power Optimization. Symmetry 2022, 14, 1275. https://doi.org/10.3390/sym14061275
Song J, Lu C, Ma Q, Zhou H, Yue Q, Zhu Q, Zhao Y, Fan Y, Huang Q. Distributed Integrated Synthetic Adaptive Multi-Objective Reactive Power Optimization. Symmetry. 2022; 14(6):1275. https://doi.org/10.3390/sym14061275
Chicago/Turabian StyleSong, Jiayin, Chao Lu, Qiang Ma, Hongwei Zhou, Qi Yue, Qinglin Zhu, Yue Zhao, Yiming Fan, and Qiqi Huang. 2022. "Distributed Integrated Synthetic Adaptive Multi-Objective Reactive Power Optimization" Symmetry 14, no. 6: 1275. https://doi.org/10.3390/sym14061275
APA StyleSong, J., Lu, C., Ma, Q., Zhou, H., Yue, Q., Zhu, Q., Zhao, Y., Fan, Y., & Huang, Q. (2022). Distributed Integrated Synthetic Adaptive Multi-Objective Reactive Power Optimization. Symmetry, 14(6), 1275. https://doi.org/10.3390/sym14061275