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Sample-Efficient Learning for a Surrogate Model of Three-Phase Distribution System

Hoang Tien Nguyen, Young-Jin Kim, Dae-Hyun Choi

TL;DR

The paper tackles voltage prediction in unbalanced three-phase distribution networks under DER fluctuations by learning a surrogate that maps complex power injections $\mathbf{s}$ to complex voltages $\mathbf{v}$ using a fixed-point load-flow formulation. A fixed-point surrogate $\hat{\mathbf{v}} = \hat{\mathbf{w}} + f_{\hat{\mathbf{X}}}(\hat{\mathbf{v}}, \mathbf{s})$ with learnable $\hat{\mathbf{w}}$ and $\hat{\mathbf{X}}$ is trained by minimizing the RMSE $\mathcal{L} = \sqrt{\frac{1}{3N}\sum_{i=1}^{N} \|\mathbf{v}_i - \hat{\mathbf{v}}_i\|^2}$ via SGD and automatic differentiation. Results on IEEE 13-, 37-, and 123-bus benchmarks show that the proposed approach achieves higher accuracy and sample efficiency than GP and DNN baselines, with fast inference. The work demonstrates the benefit of combining domain physics with data-driven learning for reliable grid planning and operation and suggests future work on learning the full admittance matrix to identify topology and line parameters.

Abstract

A surrogate model that accurately predicts distribution system voltages is crucial for reliable smart grid planning and operation. This letter proposes a fixed-point data-driven surrogate modeling method that employs a limited dataset to learn the power-voltage relationship of an unbalanced three-phase distribution system. The proposed surrogate model is designed using a fixed-point load-flow equation, and the stochastic gradient descent method with an automatic differentiation technique is employed to update the parameters of the surrogate model using complex power and voltage samples. Numerical examples in IEEE 13-bus, 37-bus, and 123-bus systems demonstrate that the proposed surrogate model can outperform surrogate models based on the deep neural network and Gaussian process regarding prediction accuracy and sample efficiency

Sample-Efficient Learning for a Surrogate Model of Three-Phase Distribution System

TL;DR

The paper tackles voltage prediction in unbalanced three-phase distribution networks under DER fluctuations by learning a surrogate that maps complex power injections to complex voltages using a fixed-point load-flow formulation. A fixed-point surrogate with learnable and is trained by minimizing the RMSE via SGD and automatic differentiation. Results on IEEE 13-, 37-, and 123-bus benchmarks show that the proposed approach achieves higher accuracy and sample efficiency than GP and DNN baselines, with fast inference. The work demonstrates the benefit of combining domain physics with data-driven learning for reliable grid planning and operation and suggests future work on learning the full admittance matrix to identify topology and line parameters.

Abstract

A surrogate model that accurately predicts distribution system voltages is crucial for reliable smart grid planning and operation. This letter proposes a fixed-point data-driven surrogate modeling method that employs a limited dataset to learn the power-voltage relationship of an unbalanced three-phase distribution system. The proposed surrogate model is designed using a fixed-point load-flow equation, and the stochastic gradient descent method with an automatic differentiation technique is employed to update the parameters of the surrogate model using complex power and voltage samples. Numerical examples in IEEE 13-bus, 37-bus, and 123-bus systems demonstrate that the proposed surrogate model can outperform surrogate models based on the deep neural network and Gaussian process regarding prediction accuracy and sample efficiency
Paper Structure (7 sections, 8 equations, 3 figures, 6 tables, 1 algorithm)

This paper contains 7 sections, 8 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Load-flow formulation of distribution system
  3. Learning-based surrogate model
  4. Proposed Fixed-Point Surrogate Model
  5. SGD-based Model Training
  6. Simulation results
  7. Conclusion

Figures (3)

  • Figure 1: Illustration of a fixed-point surrogate model.
  • Figure 2: Training curve convergence of the error function $\mathcal{L}$ and no-load voltage error $\Vert \mathbf{\widehat{w}} - \mathbf{w} \Vert_2$.
  • Figure 3: Distributions of voltage magnitude errors of three methods (top) and probabilities of voltage magnitude errors of the proposed method (bottom).

Theorems & Definitions (2)

  • Remark 1
  • Remark 2