Distribution System State Estimation Based on Power Flow-Guided GraphSAGE
Abstract
:1. Introduction
- (1)
- By leveraging the generalization ability of GraphSAGE for unknown nodes, inductive learning is performed using measurement information. The simulation results show that even for measurement points not present in the training set, this approach can still qualitatively predict state variables.
- (2)
- The training process is guided by power flow equations, ensuring that the model remains physically meaningful.
- (3)
- The potential application of the proposed approach to real-world distribution systems is explored. Equivalent preprocessing of three-phase voltage measurement data is performed to improve the estimation accuracy at transformer measurement points and simplify the computation involved in DSSE.
2. Methodology
2.1. Traditional Model-Based Method
2.2. GraphSAGE
2.3. Proposed Approach
- The GraphSAGE algorithm estimates the state vector x from the input topological graph and the measurement vector z;
- The state vector x is used to derive the network values through the power flow equations h(x);
- The estimated values h(x) are compared to the actual measurements z using the WLS loss function, with each estimation error weighted by the inverse of its measurement variance;
- The gradient descent method is applied to the loss function L to adjust the GraphSAGE model based on the computed partial derivatives.
Algorithm 1: GraphSAGE Algorithm |
Input: Graph (, ε); depth K; input features zi{Vi, σVi, θi, σθi, Pi, σPi, Qi, σQi}, ∀i ∈ ; weight matrices Wk, ∀k ∈ {1, …, K}; non-linearity ϕ; differentiable aggregator functions AGGREGATEk, ∀k ∈ {1, …, K}; neighborhood function : i→2 |
Output: output features xi {Vi, θi, ∀i ∈ } |
3. Distribution System Three-Phase Data Preprocessing
4. Case Studies
4.1. Test Systems
- Monte Carlo simulation
- Actual power system database
4.2. Simulation Setup
4.3. Analysis
4.3.1. Accuracy and Computation Speed
4.3.2. Generalization and Robustness
4.3.3. Actual Distribution System Testing
5. Conclusions
- (1)
- The approach proposed in this paper effectively fits the state variables under non-Gaussian noise and demonstrates tolerance for faulty data, exhibiting strong adaptability and robustness.
- (2)
- The method does not require true values as labels and has a certain degree of generalization for unseen data.
- (3)
- Through guidance with power flow equations rather than simple numerical analysis, the method becomes more in line with distribution systems’ physical characteristics.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Case (IEEE14, IEEE33) | Actual (CNEDA404) |
---|---|---|
epochs | 500 | 1000 |
batch_size | 64 | 64 |
hidden_layers | 3 | 3 |
internal_dim | 48 | 48 |
sample_nums | 5 | 5 |
training_steps | 20 | 20 |
learning_rate | 0.01 | 0.006 |
dropout_rate | 0.4 | 0.4 |
time_iterations | 30 × 24 | 5 × 96 |
Evaluation Index | WLS | LAV | PF-GraphSAGE |
---|---|---|---|
Voltage RMSE mean | 10.630 | 9.8945 | 3.243 |
(standard deviation) [10−3] | (0.58) | (0.23) | (0.17) |
Voltage RMSE max [10−3] | 17.332 | 12.358 | 4.274 |
Convergence [%] | 100 | 100 | 100 |
Computation time [ms] | 453.049 | 93.738 | 9.764 |
Evaluation Index | WLS | LAV | PF-GraphSAGE |
---|---|---|---|
Voltage RMSE mean | 11.844 | 6.233 | 4.031 |
(standard deviation) [10−3] | (0.76) | (0.28) | (0.19) |
Voltage RMSE max [10−3] | 17.307 | 7.982 | 6.499 |
Convergence [%] | 100 | 87.5 | 100 |
Computation time [ms] | 501.57 | 109.42 | 11.65 |
Evaluation Index | WLS* | LAV | PF-GraphSAGE |
---|---|---|---|
Voltage RMSE mean | 12.14 | 12.36 | 1.653 |
(standard deviation) [10−3] | (0.45) | (0.31) | (0.04) |
Voltage RMSE max [10−3] | 16.12 | 14.72 | 3.628 |
Convergence [%] | 100 | 91.66 | 100 |
Computation time [ms] | 671.74 | 2440.71 | 41.92 |
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Zhai, B.; Yang, D.; Zhou, B.; Li, G. Distribution System State Estimation Based on Power Flow-Guided GraphSAGE. Energies 2024, 17, 4317. https://doi.org/10.3390/en17174317
Zhai B, Yang D, Zhou B, Li G. Distribution System State Estimation Based on Power Flow-Guided GraphSAGE. Energies. 2024; 17(17):4317. https://doi.org/10.3390/en17174317
Chicago/Turabian StyleZhai, Baitong, Dongsheng Yang, Bowen Zhou, and Guangdi Li. 2024. "Distribution System State Estimation Based on Power Flow-Guided GraphSAGE" Energies 17, no. 17: 4317. https://doi.org/10.3390/en17174317