Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

TL;DR

This paper introduces a method to train compact neural networks that accurately model AC power flow equations, enabling more efficient and tractable optimization in power system unit commitment problems.

Contribution

It develops a technique for creating optimally compact neural networks that balance accuracy and tractability for modeling nonlinear power flow equations.

Findings

The compact neural network outperforms linearized models in accuracy.

Embedded NN models improve solution quality for AC unit commitment.

The approach reduces the number of binary variables needed for modeling.

Abstract

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural Networks (NNs). These NNs can be exactly transformed into Mixed Integer Linear Programs (MILPs) and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the NN. Accordingly, this paper develops a technique for training an "optimally compact" NN, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We show that the resulting NN model is more expressive than both the DC and linearized power flow approximations when embedded inside of a challenging optimization problem (i.e., the AC unit commitment problem).