Distributionally Robust Scheduling of Electrified Heating Under Heat Demand Forecast Uncertainty

Abstract

Electrified heating systems with thermal storage, such as electric boilers and heat pumps, represent a major source of demand-side flexibility. Under current electricity market designs, balance responsible parties (BRPs) operating such assets are required to submit binding day-ahead electricity consumption schedules, and they typically do it based on forecasts of heat demand and electricity prices. Common scheduling approaches implicitly assume that forecast uncertainty can be well characterized using historical forecast errors. In practice, however, the cumulative effect of uncertainty creates significant exposure to imbalance-price risk when the committed schedule cannot be followed. To address this, we propose a distributionally robust chance-constrained optimization framework for the day-ahead scheduling of a multi-MW electric boiler using only limited residual forecast samples. We derive a tractable convex reformulation of the problem and calibrate the ambiguity set directly from historical forecast-error data through an a priori tunable risk parameter. Numerical results show that enforcing performance guarantees on the heat-demand balance constraint reduces demand violations by 40% compared to a deterministic forecast-based scheduler and up to 10% relative to a nominal chance-constrained model with a fixed error distribution. Further, we show that modeling the real-time rebound cost of demand violations as a second-stage term can reduce the overall daily operating cost by up to 34% by hedging against highly volatile day-ahead electricity prices.