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Selective State-Space Models for Koopman-based Data-driven Distribution System State Estimation

Bader Alabdulrazzaq, Bri-Mathias Hodge

Abstract

Distribution System State Estimation (DSSE) plays an increasingly-important role in modern power grids due to the integration of distributed energy resources (DERs). The inherent characteristics of distribution systems make classical estimation methods struggle, and recent advancements in data-driven learning methods, although promising, exhibit systematic failure in generalization and scalability that limits their applicability. In this work, we propose MambaDSSE, a model-free data-driven framework that incorporates Koopman-theoretic probabilistic filtering with a selective state-space model that learn to infer the underlying time-varying behavior of the system from data. We evaluate the model across a variety of test systems and scenarios, and demonstrate that the proposed method outperforms machine learning baselines on scalability, resilience to DER penetration levels, and robustness to data sampling rate irregularities. We further highlight the Mamba-based SSM's ability to capture long range dependencies from data, improving performance on the DSSE task.

Selective State-Space Models for Koopman-based Data-driven Distribution System State Estimation

Abstract

Distribution System State Estimation (DSSE) plays an increasingly-important role in modern power grids due to the integration of distributed energy resources (DERs). The inherent characteristics of distribution systems make classical estimation methods struggle, and recent advancements in data-driven learning methods, although promising, exhibit systematic failure in generalization and scalability that limits their applicability. In this work, we propose MambaDSSE, a model-free data-driven framework that incorporates Koopman-theoretic probabilistic filtering with a selective state-space model that learn to infer the underlying time-varying behavior of the system from data. We evaluate the model across a variety of test systems and scenarios, and demonstrate that the proposed method outperforms machine learning baselines on scalability, resilience to DER penetration levels, and robustness to data sampling rate irregularities. We further highlight the Mamba-based SSM's ability to capture long range dependencies from data, improving performance on the DSSE task.

Paper Structure

This paper contains 18 sections, 7 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Selective State Space Models
  4. Koopman Theory
  5. Formulation of Distribution System State Estimation
  6. The MambaDSSE Model
  7. Selective SSM as a Matrix Generation Engine
  8. Matrix Structure Constraints
  9. Learning valid approximations of Koopman observables
  10. Probabilistic State Estimator
  11. Experimental setup
  12. Experiments & Ablations Studies
  13. Case studies
  14. Data Preprocessing
  15. Baseline Models
  16. ...and 3 more sections

Figures (5)

  • Figure 1: Overview of the MambaDSSE framework. Historical system data is used to train the model to infer the underlying time-varying behavior of the observed system. The input data is lifted into a high-dimensional latent space via learned Koopman observables, to linearize the complex nonlinear dynamics. The Mamba-based matrix generation engine produces the state transition matrices that drive a probabilistic state estimation filter that's responsible for modeling the measurement noise and process uncertainty. A decoding pipeline, conditioned on the posterior state distribution of the filter, produces the final state predictions.
  • Figure 2: Distribution of state prediction errors across all buses of a 435-bus system, for (a) the voltage magnitude, (b) the voltage angle
  • Figure 3: Comparison of model predictions and tracking during system state transitions. (a)-(b) voltage magnitude transitions, and (c)-(d) phase angle transition
  • Figure 4: Prediction error (MAE) across different DER penetration scenarios for (a) the proposed model, (b) LSTM+SE baseline
  • Figure 5: Impact of the input sequence length on model performance with a Mamba backbone (blue) and LSTM backbone (red)