On the Choice of Loss Function in Learning-based Optimal Power Flow

TL;DR

This paper compares two training methods for machine learning models in optimal power flow, showing that using decision loss improves feasibility and reduces suboptimality over traditional MSE-based training.

Contribution

It introduces a decision loss function for training ML models in OPF, and develops a neural network with a specialized structure and training algorithm to enhance feasibility.

Findings

Decision loss reduces suboptimality in OPF solutions.

Neural network with Lagrangian duality improves feasibility.

Method outperforms MSE-based training in IEEE 39-bus case study.

Abstract

We analyze and contrast two ways to train machine learning models for solving AC optimal power flow (OPF) problems, distinguished with the loss functions used. The first trains a mapping from the loads to the optimal dispatch decisions, utilizing mean square error (MSE) between predicted and optimal dispatch decisions as the loss function. The other intends to learn the same mapping, but directly uses the OPF cost of the predicted decisions, referred to as decision loss, as the loss function. In addition to better aligning with the OPF cost which results in reduced suboptimality, the use of decision loss can circumvent feasibility issues that arise with MSE when the underlying mapping from loads to optimal dispatch is discontinuous. Since decision loss does not capture the OPF constraints, we further develop a neural network with a specific structure and introduce a modified training algorithm incorporating Lagrangian duality to improve feasibility.} This result in an improved performance measured by feasibility and suboptimality as demonstrated with an IEEE 39-bus case study.