Sparsity-exploiting Gaussian Process for Robust Transient Learning of Power System Dynamics

TL;DR

The paper addresses learning power-system transient dynamics from limited PMU data in the presence of sparse data corruptions and cyber threats. It introduces a sparsity-exploiting Gaussian Process framework that (i) robustly learns covariances via a MoM-based objective under sparse deviations, and (ii) identifies corrupted PMUs with a sparse weighting/masking scheme to exclude bad data during inference. To scale to large grids, the authors combine k-medoids clustering with dimension reduction and aggregate representations, enabling fast GP inversion without sacrificing accuracy. Empirical results on IEEE test cases, up to a 1354-bus system, demonstrate improved robustness against false data injections, large random errors, and clock drift, as well as substantial inference-time speedups. This approach enhances reliable transient learning in power systems with limited observability and adversarial data, enabling faster and more scalable monitoring and decision-support.

Abstract

Advances in leveraging Gaussian processes (GP) have enabled learning and inferring dynamic grid behavior from scarce PMU measurements. However, real measurements can be corrupted by various random and targeted threats, leading to inaccurate and meaningless results. This paper develops robust transient learning to overcome this challenge by exploiting the sparse corruption patterns in the data flow. Specifically, we integrate sparse optimization with method of moments (MoM) to make learning robust to a sparse distribution of data corruptions; then, we optimize sparse weights to identify corrupted meter locations. To improve inference speed on large-scale systems, we further adopt K-medoid clustering of locations to develop dimension reduction (DR) and aggregate representation (AR) heuristics. Experimental results demonstrate robustness against random large errors, targeted false data injections, and local PMU clock drifts. On a 1354-bus system, inference turns out to be 18x faster using DR and 400x faster when further combined with AR heuristics.

Figures (6)

• Figure 1: 300-bus case with false data injections: Dynamic behavior is predicted for non-metered location in the presence of false data injections. Traditional GP is inaccurate (top), whereas result from our robust method remains accurate (bottom).
• Figure 2: Exploiting sparse data-corruption patterns: The difference between learned and sample correlation matrices is plotted when 5 PMUs are corrupted among a total of 22 meters. Our proposed method (right) 'pushes' large deviations to appear at sparse rows and columns corresponding to bad locations, accurately learning the true covariance in which bad locations are ''correctified''. The classic GP learning (left) cannot capture this structure, and the learned correlation is corrupted almost everywhere by the falsified data.
• Figure 3: 30-bus case with random large errors: dynamic behavior is predicted at non-metered location. Non-robust GP gives very inaccurate results (top), whereas our model retains the true behavior accurately (bottom).
• Figure 4: 300-bus case with local clock drift: Non-metered machine is estimated in the presence of local clock drift. Estimate from least-squares method is distorted (top, bottom left), whereas estimate from sparsity-exploiting method using L1-norm and mask is robust (middle, bottom right).
• Figure 5: 1354-bus case with false data injection: Non-metered locations are predicted with clustering-based dimension reduction. To assess accuracy, 3 locations corresponding to normalized RMSEs at lower-, mid-, and upper-quartile values are displayed.