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Fast and Reliable $N-k$ Contingency Screening with Input-Convex Neural Networks

Nicolas Christianson, Wenqi Cui, Steven Low, Weiwei Yang, Baosen Zhang

TL;DR

It is shown that ICNN reliability can be determined by solving a convex optimization problem, and by scaling model weights using this problem as a differentiable optimization layer during training, an ICNN classifier is learned that is both data-driven and has provably guaranteed reliability.

Abstract

Power system operators must ensure that dispatch decisions remain feasible in case of grid outages or contingencies to prevent cascading failures and ensure reliable operation. However, checking the feasibility of all $N - k$ contingencies -- every possible simultaneous failure of $k$ grid components -- is computationally intractable for even small $k$, requiring system operators to resort to heuristic screening methods. Because of the increase in uncertainty and changes in system behaviors, heuristic lists might not include all relevant contingencies, generating false negatives in which unsafe scenarios are misclassified as safe. In this work, we propose to use input-convex neural networks (ICNNs) for contingency screening. We show that ICNN reliability can be determined by solving a convex optimization problem, and by scaling model weights using this problem as a differentiable optimization layer during training, we can learn an ICNN classifier that is both data-driven and has provably guaranteed reliability. Namely, our method can ensure a zero false negative rate. We empirically validate this methodology in a case study on the IEEE 39-bus test network, observing that it yields substantial (10-20x) speedups while having excellent classification accuracy.

Fast and Reliable $N-k$ Contingency Screening with Input-Convex Neural Networks

TL;DR

It is shown that ICNN reliability can be determined by solving a convex optimization problem, and by scaling model weights using this problem as a differentiable optimization layer during training, an ICNN classifier is learned that is both data-driven and has provably guaranteed reliability.

Abstract

Power system operators must ensure that dispatch decisions remain feasible in case of grid outages or contingencies to prevent cascading failures and ensure reliable operation. However, checking the feasibility of all contingencies -- every possible simultaneous failure of grid components -- is computationally intractable for even small , requiring system operators to resort to heuristic screening methods. Because of the increase in uncertainty and changes in system behaviors, heuristic lists might not include all relevant contingencies, generating false negatives in which unsafe scenarios are misclassified as safe. In this work, we propose to use input-convex neural networks (ICNNs) for contingency screening. We show that ICNN reliability can be determined by solving a convex optimization problem, and by scaling model weights using this problem as a differentiable optimization layer during training, we can learn an ICNN classifier that is both data-driven and has provably guaranteed reliability. Namely, our method can ensure a zero false negative rate. We empirically validate this methodology in a case study on the IEEE 39-bus test network, observing that it yields substantial (10-20x) speedups while having excellent classification accuracy.
Paper Structure (13 sections, 3 theorems, 20 equations, 4 figures, 1 algorithm)

This paper contains 13 sections, 3 theorems, 20 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Notation
  5. Model and Preliminaries
  6. DC-OPF and Contingency Screening
  7. Input-Convex Neural Networks
  8. Certifying and Enforcing Reliability for ICNN Contingency Classifiers
  9. Training Reliable ICNN Classifiers with Differentiable Convex Optimization Layers
  10. Experimental Results
  11. Contingency Screening Results
  12. Faster Preventive Dispatch via SC-OPF
  13. Discussion and Conclusions

Key Result

Proposition 1

An ICNN classifier for the contingency screening problem is reliable -- i.e., has zero false negative rate -- if and only if for all $j \in \left[2m|{\mathcal{C}}|\right]$, where ${\mathbf{a}}_j$ is the $j$th row of $\mathbf{A}$.

Figures (4)

  • Figure 1: A schematic of our proposed methodology for training reliable classifiers for contingency screening in power systems; see Algorithm \ref{['alg:training']} for a full description. Note that the scaling ratio $r^*$ is computed using a differentiable convex optimization layer, so the gradient $\partial L/\partial f_{\mathrm{ICNN}}$ is aware of this scaling step.
  • Figure 2: 2-dimensional slice of the true feasible region and the predicted feasible region of a trained ICNN with hidden depth 1, with net injections from the test set overlaid.
  • Figure 3: Results for our ICNN-based contingency analysis method, compared against a nonconvex neural network (NN) model and exhaustive checking of contingencies. (Top) Runtime to screen the feasibility of the 2,000 test injections. (Middle) False negative rate. (Bottom) False positive rate.
  • Figure 4: Results for the ICNN-based SC-OPF problem compared to the full SC-OPF problem \ref{['opt:sc_opf']}. (Top) Runtime to solve the SC-OPF problem or ICNN version thereof on 2,000 test injections, disregarding infeasible injections. (Middle) Percent excess cost of the ICNN version of SC-OPF relative to the full SC-OPF problem \ref{['opt:sc_opf']}. (Bottom) Percentage of infeasible demand instances for the ICNN version of SC-OPF compared against the full SC-OPF problem \ref{['opt:sc_opf']}.

Theorems & Definitions (4)

  • Definition 1
  • Proposition 1
  • Theorem 1
  • Theorem 2