Novel Gaussian-Decrement-Based Particle Swarm Optimization with Time-Varying Parameters for Economic Dispatch in Renewable-Integrated Microgrids
Abstract
1. Introduction
2. Methodology
2.1. Microgrid System Modelling
2.1.1. PV Power Generation Modelling
2.1.2. ESS Modelling
- (1)
- Battery capacity (E)
- (2)
- State of Charge (SOC)
2.1.3. Modeling of Disordered Charging of Electric Vehicles
2.1.4. Basic Load Composition
2.2. Modelling of Microgrid Economic Dispatch
2.2.1. Objective Function of the Microgrid Economic Dispatch Model
2.2.2. Constraints of Microgrid Economic Dispatch Model
- (1)
- Total power balance constraints
- (2)
- Power grid interaction constraints
- (3)
- Constraints of energy storage system
- (4)
- PV constraints
2.3. Model Solution
- Parameters of the population size and the initial position and velocity of each particle are initialized.
- The fitness of the particles (the economic cost ) are calculated.
- Value of referring to the historical optimal position information for each particle by the individual optimal position is obtained. The value of referring to a group optimal position from these individual historical optimal positions, is compared with the historical optimal positions to select the best one as the current historical optimal position is obtained.
- The velocity vector is updated as follows:
- When updating the position vector , it is necessary to restrict the position of the particle to be within the boundary range of the search space.
- The number of iterations is checked to determine whether it has reached the maximum number of iterations. If so, the iteration is terminated. Meanwhile, the fitness value is checked to determine whether it meets the convergence condition. If so, the process is terminated and the global optimal solution is obtained.
- The final optimal strategy for microgrid energy dispatching is obtained.
3. Data Analysis and Preprocessing
3.1. Microgrid System Conditions
3.2. Photovoltaic Power Generation Capacity
3.3. Electric Vehicle Charging Power Load
3.4. Sensitivity Analysis of Parameters
4. Results
4.1. Comparative Analysis of the Optimal Economic Costs
4.2. Performance Analyses of Algorithms
4.2.1. Robustness Analysis
4.2.2. Convergence Analysis
4.3. Microgrid Economic Dispatch Strategy
5. Discussion
5.1. Main Findings
5.2. Limitations and Future Directions of Verification
5.3. Application Framework
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameters | Value | Unit |
---|---|---|
Installed Capacity | 631 | kWp |
3155 | m2 | |
0.2 | N/A | |
Cost Coefficient | 0.02 | CNY/kW |
Parameters | Value | Unit |
---|---|---|
Installed Capacity | 945 | kWh |
Cost Coefficient | 0.15 | CNY/kW |
Time period | 23:00~7:00 | 7:00~17:00 | 17:00~23:00 |
Price/CNY | 0.35 | 0.85 | 1.04 |
Parameters | Value | Unit |
---|---|---|
Maximum power | 2500 | kW |
Minimum power | 0 | kW |
Date | Date | Date | |||
---|---|---|---|---|---|
1 June | = 6.06 | 11 June | = 2.49 | 21 June | = 1.25 |
2 June | = 0.79 | 12 June | = 6.87 | 22 June | = 1.70 |
3 June | = 3.59 | 13 June | = 3.42 | 23 June | = 0.27; β = 1.00 |
4 June | = 1.74 | 14 June | = 0.75 | 24 June | = 2.49 |
5 June | = 8.82 | 15 June | = 0.72 | 25 June | = 1.39 |
6 June | = 0.32 | 16 June | = 0.84 | 26 June | = 0.76 |
7 June | = 0.69 | 17 June | = 0.51 | 27 June | = 0.50 |
8 June | = 0.58 | 18 June | = 0.70 | 28 June | = 1.35 |
9 June | = 0.47 | 19 June | = 6.18 | 29 June | = 0.80 |
10 June | = 2.12 | 20 June | = 4.38 | 30 June | = 0.73 |
Parameters | |||||
---|---|---|---|---|---|
Value range |
Algorithms | PSO | PSO-GD | PSO-Linear | PSO-Nonlinear |
---|---|---|---|---|
Parameters | Population size 130. Inertia weighs 0.4. Velocity range [−0.1, 0.1]; Learning factor [0.5, 2.5] | Population size 130. , ; Velocity range [−0.1, 0.1]. , . | Population size 130. Inertia weighs 0.4. Velocity range [−0.1, 0.1] Learning factor [0.5, 2.5] | Population size 130. Inertia weighs 0.4. Velocity range [−0.1, 0.1] Learning factor [0.5, 2.5] |
Algorithms | DE | GA | SA | WOA |
Parameters | Population size 130. Scaling factor 0.5. Crossing probability 0.8 | Population size 130. Probability of crossover 0.8. Probability of variation 0.01 | Initial temperature 100. Cooling rate: 0.95 | Population size 130. Spiral constant b = 1. Coefficient a: 2 to 0. Coefficient a2: −1 to −2. p = rand. |
Algorithms | PSO-GD | PSO | PSO-Linear | PSO-Nonlinear | GA | SA | DE | WOA | |
---|---|---|---|---|---|---|---|---|---|
Mean/CNY | 3526.45 | 3556.86 | 3542.64 | 3542.64 | 3552.99 | 3611.34 | 3545.26 | 3530.62 | |
7.09 | 20.38 | 9.28 | 18.95 | 22.89 | 26.08 | 19.44 | 14.66 |
Date | The Optimal Economic Costs/CNY | Variation/CNY | |
---|---|---|---|
PSO | PSO-GD | ||
1 June | 2279.19 | 2272.76 | 6.42 |
2 June | 2407.40 | 2404.37 | 3.03 |
3 June | 3568.51 | 3566.69 | 1.81 |
4 June | 2128.54 | 2126.68 | 1.86 |
5 June | 2950.32 | 2952.01 | −1.69 |
6 June | 3083.58 | 3081.19 | 2.39 |
7 June | 1984.41 | 1976.40 | 8.01 |
8 June | 2694.03 | 2689.30 | 4.73 |
9 June | 2734.90 | 2720.50 | 14.40 |
10 June | 1579.85 | 1569.72 | 10.13 |
11 June | 2145.23 | 2135.47 | 9.75 |
12 June | 3049.06 | 3048.68 | 0.38 |
13 June | 3007.96 | 3000.21 | 7.76 |
14 June | 1896.05 | 1887.13 | 8.92 |
15 June | 2215.06 | 2214.29 | 0.77 |
16 June | 1960.10 | 1948.06 | 12.04 |
17 June | 2602.04 | 2601.66 | 0.38 |
18 June | 2821.16 | 2832.42 | −11.26 |
19 June | 1807.61 | 1807.38 | 0.23 |
20 June | 2278.43 | 2266.59 | 11.84 |
21 June | 2789.87 | 2754.29 | 35.58 |
22 June | 1560.97 | 1557.78 | 3.19 |
23 June | 2998.08 | 2996.35 | 1.74 |
24 June | 1889.41 | 1874.08 | 15.33 |
25 June | 2313.15 | 2306.91 | 6.24 |
26 June | 1728.59 | 1719.92 | 8.66 |
27 June | 2107.52 | 2110.77 | −3.25 |
28 June | 2124.12 | 2111.63 | 12.48 |
29 June | 3866.65 | 3867.03 | −0.38 |
30 June | 1905.46 | 1898.27 | 7.19 |
50 Vehicles | 200 Vehicles | 400 Vehicles | |
---|---|---|---|
Cost of PSO-GD (CNY) | 2494.1 | 3528.5 | 5036.2 |
Cost of PSO (CNY) | 2506.6 | 3556.8 | 5063.3 |
Cost of PSO-linear (CNY) | 2496.4 | 3542.6 | 5053.1 |
Cost of PSO-nonlinear (CNY) | 2496.1 | 3542.6 | 5052.5 |
Cost of GA (CNY) | 2513.6 | 3552.9 | 5124.7 |
Cost of SA (CNY) | 2548.8 | 3611.3 | 5139.1 |
Cost of DE (CNY) | 2506.7 | 3545.2 | 5054.1 |
Cost of WOA (CNY) | 2520.4 | 3570.6 | 5080.4 |
Low Electricity Price Scenario | Baseline Scenario | High Electricity Price Scenario | |
---|---|---|---|
Cost of PSO-GD (CNY) | 2866.7 | 3528.5 | 4161.4 |
Cost of PSO (CNY) | 2900.1 | 3556.8 | 4197.3 |
Cost of PSO-linear (CNY) | 2869.2 | 3542.6 | 4174.7 |
Cost of PSO-nonlinear (CNY) | 2869.2 | 3542.6 | 4163.1 |
Cost of GA (CNY) | 2884.8 | 3552.9 | 4200.8 |
Cost of SA (CNY) | 3114.3 | 3611.3 | 4576.3 |
Cost of DE (CNY) | 2889.1 | 3545.2 | 4180.7 |
Cost of WOA (CNY) | 2869.2 | 3570.6 | 4162.7 |
PSO | PSO-GD | PSO-Linear | PSO-Nonlinear | GA | SA | DE | WOA | |
---|---|---|---|---|---|---|---|---|
Average number of iterations | 100 | 64 | 100 | 95 | 91 | 81 | 99 | 83 |
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Wang, Y.; Lu, W.; Du, W.; Dong, C. Novel Gaussian-Decrement-Based Particle Swarm Optimization with Time-Varying Parameters for Economic Dispatch in Renewable-Integrated Microgrids. Mathematics 2025, 13, 2440. https://doi.org/10.3390/math13152440
Wang Y, Lu W, Du W, Dong C. Novel Gaussian-Decrement-Based Particle Swarm Optimization with Time-Varying Parameters for Economic Dispatch in Renewable-Integrated Microgrids. Mathematics. 2025; 13(15):2440. https://doi.org/10.3390/math13152440
Chicago/Turabian StyleWang, Yuan, Wangjia Lu, Wenjun Du, and Changyin Dong. 2025. "Novel Gaussian-Decrement-Based Particle Swarm Optimization with Time-Varying Parameters for Economic Dispatch in Renewable-Integrated Microgrids" Mathematics 13, no. 15: 2440. https://doi.org/10.3390/math13152440
APA StyleWang, Y., Lu, W., Du, W., & Dong, C. (2025). Novel Gaussian-Decrement-Based Particle Swarm Optimization with Time-Varying Parameters for Economic Dispatch in Renewable-Integrated Microgrids. Mathematics, 13(15), 2440. https://doi.org/10.3390/math13152440