A Reverse Optimization Strategy for Residential Demand Side Management under Linear Pricing

This paper presents a novel algorithmic framework for Demand Side Management (DSM) within grid-connectedresidential microgrids integrated with solar photovoltaic (PV) generation and battery energy storage systems (BESS). Traditional demand response models employ forward-looking heuristic loops that optimize from hour 1 to hour 24, which often introduce optimization delays and valley-filling boundary errors when handling sharp domestic peak load transitions. To mitigate this, we introduce a Reverse Time-Slot Optimization Algorithm that evaluates the system boundaries in reverse chronological order (24 to 1). The mathematical framework isolates domestic appliances into fully-adjustable, semi-adjustable, and non-adjustable categories to evaluate systemic power balance thresholds. Numerical validation using a 24-hour dispatch horizon confirms that backward heuristic load shifting achieves deterministic valley filling, maximizes local PV consumption, and strictly minimizes grid expenditure under non-linear step-pricing constraints with out numerical instability.