Regional Frequency Measurement Point Selection and System Partitioning Method for High-Renewable-Energy-Penetration Power System
Abstract
:1. Introduction
- (1)
- The FRI index is defined to quantify the comprehensive ability of nodes to dynamically regulate the spatiotemporal dynamics of the power system’s frequency, thereby identifying key frequency regulation nodes in the system, which are then selected as frequency measurement points.
- (2)
- The hierarchical clustering method is used to treat the frequency measurement points as regional cores, progressively merging adjacent nodes with the highest electrical proximity. The modularity indicator is calculated for different partition numbers, ultimately forming a partitioning scheme with strong electrical coupling and frequency synchronization.
2. The Frequency Measurement Point Selection Method
The Node FRI Index
- (1)
- The Linear Impact of Node Power Disturbances Based on a Sensitivity Analysis
- (2)
- The Nonlinear Regulation Capability of Node Oscillation Modes Based on a Modal Analysis
3. The System Partitioning Method Based on Hierarchical Clustering
- (1)
- The FRI values of the nodes in the system are calculated and sorted in descending order. Nodes with higher rankings are selected as the system’s frequency measurement points and initially form their own regions.
- (2)
- The nodes directly connected to the frequency measurement points are first divided into the area to which the frequency measurement points belong.
- (3)
- We calculate the size of the frequency similarity index between the remaining nodes and the frequency measurement points, respectively, and divide the remaining nodes into the area where the frequency measurement point with the largest index is located to complete the initial partitioning.
- (4)
- The modularity index is an important criterion for measuring the quality of network partitioning. The larger the modularity index, the more reasonable the partitioning method [22]. By progressively increasing the number of frequency measurement points and recalculating the modularity K for each partitioning scheme, the optimal partitioning scheme can be determined. The modularity index K is defined as follows:
4. The Simulation Case Analysis
4.1. Frequency Measurement Point Selection and System Partitioning
4.2. The Verification Method for the Validity of the System Partitioning and Frequency Measurement Points
- (1)
- The Primary Frequency Regulation Energy Contribution Index Q%
- (2)
- The Rate of Speed Variation in Unit γ
4.3. Verification of the Validity of the System Partitioning and Frequency Measurement Points
- (1)
- Scheme 1: A fault is set at the Bus17-Bus18 tie-line, which opens at the 100th cycle;
- (2)
- Scheme 2: The load suddenly increases by 300 MW, which opens at the 300th cycle.
- (1)
- Under the conditions of Scheme 1
- (2)
- Under the conditions of Scheme 2
4.4. Validation of the Validity of System Partitioning and Frequency Measurement Points in Extreme Scenarios
5. Conclusions
- (1)
- High penetration of renewable energy exacerbates the spatiotemporal inconsistency in the system’s frequency response, and the unified average frequency of the system can no longer accurately characterize the frequency response variations at each node in the system. For example, using the assessment indicators for the generator’s primary frequency regulation capability, the regional frequency calculation error can reach as high as 7.55%.
- (2)
- Using the frequency of the frequency measurement point as the reference to assess the frequency regulation capability of each generator within the region, the error in the generator’s local speed variation rate is reduced by 2.96%, and the error in the primary frequency regulation energy contribution is reduced by 2.27%. Accurate system partitioning and selection of the regional frequency measurement points can effectively reduce the impact of frequency dispersion.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Region | Nodes Within the Region | Frequency Measurement Point |
---|---|---|
1 | 1, 2, 3, 18, 30, 39 | 2 |
2 | 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 31, 32 | 6 |
3 | 25, 26, 27, 28, 29, 37, 38 | 16 |
4 | 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 33, 34, 35, 36 | 26 |
Region | Speed Variation Rates of Generators Under Different Frequencies as a Benchmark | |||
---|---|---|---|---|
fGi | fkey | fopt | fsys | |
G1 | 5.56 | 5.79 | 5.56 | 5.98 |
G2 | 11.02 | 11.24 | 11.41 | 11.57 |
G3 | 7.26 | 7.42 | 7.51 | 7.64 |
G4 | 6.70 | 6.83 | 6.90 | 7.07 |
G7 | 9.09 | 9.37 | 9.42 | 9.53 |
G8 | 7.91 | 8.15 | 8.29 | 8.38 |
Region | The Primary Frequency Regulation Power Contribution Index Under Different Frequencies as a Benchmark | |||
---|---|---|---|---|
fGi | fkey | fopt | fsys | |
G1 | 62.73 | 62.05 | 62.73 | 60.77 |
G2 | 60.09 | 59.60 | 59.11 | 58.17 |
G3 | 71.42 | 70.12 | 69.74 | 68.21 |
G4 | 59.21 | 58.78 | 57.61 | 57.34 |
G6 | 71.59 | 70.85 | 70.14 | 69.32 |
G9 | 61.82 | 60.95 | 60.14 | 59.75 |
Region | Speed Variation Rates of Generators Under Different Frequencies as a Benchmark | |||
---|---|---|---|---|
fGi | fkey | fopt | fsys | |
G1 | 6.79 | 6.93 | 7.01 | 7.09 |
G2 | 8.64 | 8.89 | 8.94 | 9.06 |
G3 | 6.54 | 6.73 | 6.79 | 6.87 |
G4 | 10.9 | 11.20 | 11.26 | 11.40 |
G7 | 5.48 | 5.67 | 5.70 | 5.72 |
G8 | 7.93 | 8.11 | 8.23 | 8.38 |
Region | The Primary Frequency Regulation Power Contribution Index Under Different Frequencies as a Benchmark | |||
---|---|---|---|---|
fGi | fkey | fopt | fsys | |
G1 | 61.28 | 61.13 | 61.28 | 60.46 |
G2 | 59.11 | 58.75 | 58.57 | 58.23 |
G3 | 62.25 | 61.69 | 61.5 | 61.15 |
G4 | 59.13 | 58.47 | 58.32 | 57.53 |
G6 | 57.39 | 56.7 | 56.04 | 55.62 |
G9 | 64.94 | 64.17 | 63.85 | 63.19 |
Region | The Primary Frequency Regulation Power Contribution Index Under Different Frequencies as a Benchmark | ||
---|---|---|---|
fGi | fkey | fsys | |
G1 | 62.73 | 61.21 | 59.67 |
G2 | 59.21 | 57.98 | 56.54 |
G3 | 66.37 | 64.94 | 63.78 |
G4 | 60.23 | 58.53 | 57.14 |
G6 | 58.52 | 57.69 | 56.93 |
G9 | 71.59 | 70.15 | 69.02 |
Region | The Speed Variation Rates of Generators Under Different Frequencies as a Benchmark | ||
---|---|---|---|
fGi | fkey | fsys | |
G1 | 7.16 | 7.39 | 7.74 |
G2 | 10.89 | 11.23 | 11.71 |
G3 | 7.61 | 7.85 | 8.07 |
G4 | 5.76 | 5.93 | 6.09 |
G7 | 7.26 | 7.49 | 7.69 |
G8 | 9.19 | 9.41 | 9.72 |
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Li, D.; Yao, Z.; Yao, Y.; Xu, B.; Yang, F. Regional Frequency Measurement Point Selection and System Partitioning Method for High-Renewable-Energy-Penetration Power System. Energies 2025, 18, 3040. https://doi.org/10.3390/en18123040
Li D, Yao Z, Yao Y, Xu B, Yang F. Regional Frequency Measurement Point Selection and System Partitioning Method for High-Renewable-Energy-Penetration Power System. Energies. 2025; 18(12):3040. https://doi.org/10.3390/en18123040
Chicago/Turabian StyleLi, Dongdong, Zhenfei Yao, Yin Yao, Bo Xu, and Fan Yang. 2025. "Regional Frequency Measurement Point Selection and System Partitioning Method for High-Renewable-Energy-Penetration Power System" Energies 18, no. 12: 3040. https://doi.org/10.3390/en18123040
APA StyleLi, D., Yao, Z., Yao, Y., Xu, B., & Yang, F. (2025). Regional Frequency Measurement Point Selection and System Partitioning Method for High-Renewable-Energy-Penetration Power System. Energies, 18(12), 3040. https://doi.org/10.3390/en18123040