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Predicting power grid frequency dynamics with invertible Koopman-based architectures

Eric Lupascu, Xiao Li, Benjamin Schäfer

Abstract

The system frequency is a critical measure of power system stability and understanding, and modeling it are key to ensure reliable power system operations. Koopman-based autoencoders are effective at approximating complex nonlinear data patterns, with potential applications in the frequency dynamics of power systems. However, their non-invertibility can result in a distorted latent representation, leading to significant prediction errors. Invertible neural networks (INNs) in combination with the Koopman operator framework provide a promising approach to address these limitations. In this study, we analyze different INN architectures and train them on simulation datasets. We further apply extensions to the networks to address inherent limitations of INNs and evaluate their impact. We find that coupling-layer INNs achieve the best performance when used in isolation. In addition, we demonstrate that hybrid approaches can improve the performance when combined with suitable INNs, while reducing the generalization capabilities in combination with disadvantageous architectures. Overall, our results provide a clearer overview of how architectural choices influence INN performance, offering guidance for selecting and designing INNs for modeling power system frequency dynamics.

Predicting power grid frequency dynamics with invertible Koopman-based architectures

Abstract

The system frequency is a critical measure of power system stability and understanding, and modeling it are key to ensure reliable power system operations. Koopman-based autoencoders are effective at approximating complex nonlinear data patterns, with potential applications in the frequency dynamics of power systems. However, their non-invertibility can result in a distorted latent representation, leading to significant prediction errors. Invertible neural networks (INNs) in combination with the Koopman operator framework provide a promising approach to address these limitations. In this study, we analyze different INN architectures and train them on simulation datasets. We further apply extensions to the networks to address inherent limitations of INNs and evaluate their impact. We find that coupling-layer INNs achieve the best performance when used in isolation. In addition, we demonstrate that hybrid approaches can improve the performance when combined with suitable INNs, while reducing the generalization capabilities in combination with disadvantageous architectures. Overall, our results provide a clearer overview of how architectural choices influence INN performance, offering guidance for selecting and designing INNs for modeling power system frequency dynamics.
Paper Structure (12 sections, 2 equations, 6 figures, 2 tables)

This paper contains 12 sections, 2 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Architecture of INNs
  3. Categories of INNs
  4. Coupling Layers
  5. Residual blocks
  6. ODE-based approaches
  7. Hybrid INNs
  8. Experiments
  9. Base INNs
  10. Hybrid INNs
  11. Discussion
  12. Conclusion

Figures (6)

  • Figure 1: Schematic representation of a hybrid INN inspired by the architecture introduced by b7. INN $\boldsymbol{i}$ and a non-invertible extension network $\boldsymbol{a}$ are paralleled as an encoder, but only INN $\boldsymbol{i}$ is also used as a decoder. Koopman operator $\mathcal{K}$ is in the middle of the encoder and decoder.
  • Figure 2: Comparison of RRMSE on IEEE (left) and WECC (right) datasets
  • Figure 3: Comparison of modeling performance for different INN structures on the IEEE 14-bus system dataset
  • Figure 4: Comparison of the RRMSE on Training (left) and Test (right) Trajectories on the IEEE-14 bus system
  • Figure 5: Comparison of models on test trajectory 3 on Bus 3 on the WECC dataset
  • ...and 1 more figures