A Sufficient Condition to Guarantee Non-Simultaneous Charging and Discharging of Household Battery Energy Storage

TL;DR

This paper presents a mathematical condition ensuring that household batteries do not charge and discharge simultaneously, simplifying demand response optimization without explicit constraints.

Contribution

It introduces a sufficient condition derived from convex optimization and duality theory to prevent simultaneous charging and discharging in household batteries.

Findings

The condition guarantees non-simultaneous charging/discharging in demand response models.

It simplifies battery management in residential energy systems.

The approach is based on convex optimization and KKT conditions.

Abstract

In this letter, we model the day-ahead price-based demand response of a residential household with battery energy storage and other controllable loads, as a convex optimization problem. Further using duality theory and Karush-Kuhn-Tucker optimality conditions, we derive a sufficient criterion which guarantees non-simultaneous charging and discharging of the battery energy storage, without explicitly modelling it as a constraint