Assessment of the Renewable Energy Consumption Capacity of Power Systems Considering the Uncertainty of Renewables and Symmetry of Active Power
Abstract
:1. Introduction
2. Probabilistic Modeling of Load and Wind Power
3. Acquisition of Input Variables Sample Space
4. Evaluation of Renewable Energy Consumption Capacity Considering Safety and Stability Constraints
4.1. Assessment Model for Renewable Energy Consumption Capacity
- (1)
- Objective Function
- (2)
- Constraints
4.2. Short-Circuit Ratio Verification
4.3. Assessment Process for Considering Safety and Stability Constraints in the Consumption Capacity Evaluation
5. Case Analysis
5.1. Probabilistic Modeling of Load
5.2. Probabilistic Modeling of Wind Power
5.3. Validity Test of Renewable Energy Consumption Capacity Assessment Method
6. Conclusions
- Through the simulation of the random characteristics of load and wind power and the calculation of probabilistic load flow, the proposed method can comprehensively and accurately reflect the changes in renewable energy integration capacity influenced by the operating state of the power system and its uncertainties.
- A 10-order GMM is used to construct the probabilistic model for load. The research results show that the RMSE and SSE of the 10-order Gaussian distribution load fitting model are 0.000159 and 0.000048, respectively, with a R2 reaching 0.995. Compared to other fitting models, this approach provides more accurate load modeling. Similarly, the 10-order Gaussian distribution wind power fitting model has an RMSE and SSE of 0.000163 and 0.000052, respectively, with an R2 reaching 0.994. Compared to the Weibull distribution, this model offers more precise wind power modeling.
- During the simulation calculations on both the 102 nodes system and IEEE 39-bus system with renewable energy integration, the maximum renewable energy integration capacities were determined to be 1250.91 MW and 1054.87 MW, respectively. The results of different simulation case studies also show that the probability metrics obtained by the M-H algorithm, Gibbs sampling, and the MCS method are basically the same, verifying the accuracy of the proposed method.
- Under the maximum renewable energy integration capacity in different scenarios, it was found through short-circuit ratio and N-1 fault validation that the system can consistently meet stability requirements.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Fit Model | RMSE | SSE | R2 |
---|---|---|---|
normal distribution | 0.000753 | 0.000318 | 0.963 |
5th-order Gaussian distribution | 0.000560 | 0.000127 | 0.988 |
8th-order Gaussian distribution | 0.000382 | 0.000106 | 0.991 |
10th-order Gaussian distribution | 0.000159 | 0.000048 | 0.995 |
12th-order Gaussian distribution | 0.000147 | 0.000027 | 0.993 |
15th-order Gaussian distribution | 0.000132 | 0.000013 | 0.982 |
Fit Model | RMSE | SSE | |
---|---|---|---|
Weibull distribution | 0.000533 | 0.000258 | 0.9677 |
10th-order Gaussian distribution | 0.000163 | 0.000052 | 0.9989 |
Algorithm | Number of Samples | Execution Time/ms | Mean/MW | Standard Deviation/MW | Maximum/MW | Min/MW |
---|---|---|---|---|---|---|
MCS | 10,000 | 0.324 | 801.14 | 79.49 | 1088.94 | 518.04 |
M-H | 2000 | 0.169 | 800.71 | 80.83 | 1054.87 | 535.96 |
Gibbs | 2000 | 0.175 | 798.39 | 75.67 | 1035.28 | 558.37 |
Algorithm | Number of Samples | Execution Time/ms | Mean/MW | Standard Deviation/MW | Maximum/MW | Min/MW |
---|---|---|---|---|---|---|
MCS | 10,000 | 0.379 | 756.58 | 289.31 | 1253.11 | 254.43 |
M-H | 2000 | 0.182 | 757.88 | 286.69 | 1250.91 | 256.38 |
Gibbs | 2000 | 0.237 | 758.39 | 291.67 | 1259.28 | 259.15 |
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Ou, K.; Gao, S.; Wang, Y.; Zhai, B.; Zhang, W. Assessment of the Renewable Energy Consumption Capacity of Power Systems Considering the Uncertainty of Renewables and Symmetry of Active Power. Symmetry 2024, 16, 1184. https://doi.org/10.3390/sym16091184
Ou K, Gao S, Wang Y, Zhai B, Zhang W. Assessment of the Renewable Energy Consumption Capacity of Power Systems Considering the Uncertainty of Renewables and Symmetry of Active Power. Symmetry. 2024; 16(9):1184. https://doi.org/10.3390/sym16091184
Chicago/Turabian StyleOu, Kaijian, Shilin Gao, Yuhong Wang, Bingjie Zhai, and Wei Zhang. 2024. "Assessment of the Renewable Energy Consumption Capacity of Power Systems Considering the Uncertainty of Renewables and Symmetry of Active Power" Symmetry 16, no. 9: 1184. https://doi.org/10.3390/sym16091184