Robust Stochastic Optimal Control via variance penalization: Application to Energy Management Systems

TL;DR

This paper introduces a variance-penalized stochastic optimal control model and algorithm that enhances out-of-sample robustness in energy management systems without increasing computational complexity.

Contribution

It extends stochastic optimal control by incorporating variance penalization and develops a novel VPPHA algorithm for improved robustness and performance.

Findings

VPPHA outperforms standard PHA in robustness.

The approach improves energy management in real-world EMS simulations.

Method maintains computational complexity similar to standard algorithms.

Abstract

This paper addresses a class of robust stochastic optimal control problems. Its main contribution lies in the introduction of a general optimization model with variance penalization and an associated solution algorithm that improves out-of-sample robustness while preserving numerical complexity. The proposed variance-penalized model is inspired by a well-established machine learning practice that aims to limit overfitting and extends this idea to stochastic optimal control. Using the Douglas--Rachford splitting method, the authors develop a Variance-Penalized Progressive Hedging Algorithm (VPPHA) that retains the computational complexity of the standard PHA while achieving superior out-of-sample performance. In addition, the authors propose a three-step control framework comprising (i) a random scenario generation method, (ii) a scenario reduction algorithm, and (iii) a scenario-based optimal control computation using the VPPHA. Finally, the proposed method is validated through simulations of a stationary battery Energy Management System (EMS) using ground-truth electricity consumption and production measurements from a predominantly commercial building in Solaize, France. The results demonstrate that the proposed approach outperforms a classical Model Predictive Control (MPC) strategy, which itself performs better than the standard PHA.