Contingency Analyses with Warm Starter using Probabilistic Graphical Model

TL;DR

A novel conditional Gaussian Random Field-based data-driven method that performs fast and accurate evaluation of cyberthreats is proposed that achieves speedup of contingency analysis by warm-starting simulations, i.e., improving starting points, for the physical solvers.

Abstract

Cyberthreats are an increasingly common risk to the power grid and can thwart secure grid operations. We propose to extend contingency analysis to include cyberthreat evaluations. However, unlike the traditional N-1 or N-2 contingencies, cyberthreats (e.g., MadIoT) require simulating hard-to-solve N-k (with k >> 2) contingencies in a practical amount of time. Purely physics-based power flow solvers, while being accurate, are slow and may not solve N-k contingencies in a timely manner, whereas the emerging data-driven alternatives are fast but not sufficiently generalizable, interpretable, and scalable. To address these challenges, we propose a novel conditional Gaussian Random Field-based data-driven method that performs fast and accurate evaluation of cyberthreats. It achieves speedup of contingency analysis by warm-starting simulations, i.e., improving starting points, for the physical solvers. To improve the physical interpretability and generalizability, the proposed method incorporates domain knowledge by considering the graphical nature of the grid topology. To improve scalability, the method applies physics-informed regularization that reduces model complexity. Experiments validate that simulating MadIoT-induced attacks with our warm starter becomes approximately 5x faster on a realistic 2000-bus system.

Figures (6)

• Figure 1: A toy instance of MadIoT: a subset of loads is manipulated.
• Figure 2: A power grid can be naturally represented as a graphical model. Each node represents the bus voltage after contingency, each edge represents a branch status after contingency. Now conditioned on an original power grid $G$ and a contingency $c$ that happens on it, we want to know the bus voltages after contingency.
• Figure 3: each node has a NN-node and each edge has a NN-edge, to map the input features to the post-contingency system characteristics.
• Figure 4: Training of the proposed method: forward pass and back-propagation.
• Figure 5: Physical interpretation: This figure visualizes the values in matrices and vectors (the more yellow, the larger the value). Learned model parameters $\Lambda, \eta$ have some similarity with the true post-contingency system admittance matrix $Y_{bus}$ and injection current vector $J$, in terms of the sparse structure and value distribution. This is because the learned parameters $\Lambda, \eta$ aims to form a linear model $\Lambda y= \eta$ which is a linear proxy of the true linearized system model $Y_{bus}y=J$.