Comfort-Aware Distributionally Robust Chance-Constrained Scheduling of PV-Assisted Heat Pumps under Dynamic Tariffs: A DOE–ANOVA Interaction Analysis

Abstract

Purpose: This paper develops an uncertainty-aware optimisation framework for smart heat pump (HP) operation that minimises electricity cost while maintaining thermal comfort under time-varying tariffs and uncertain PV generation. Design/methodology/approach: A Day-ahead scheduling model is formulated using distributionally robust chanceconstrained programming (DR-CCP) to control the probability of comfort-constraint violation under distributional ambiguity in renewable forecast errors. Thermal comfort is represented using either (i) conventional indoor-temperature (IT) bounds or (ii) Predicted Mean Vote (PMV) constraints. A full-factorial design of experiments (DOE) is conducted across building scale, tariff type, probability of comfort constraint violation (PoCCV) level, and comfort formulation, and ANOVA is applied to quantify statistically significant main and interaction effects on IT, coefficient of performance (COP), and operating cost. Findings: Across the experimental scenarios, dynamic tariffs reduce operating cost relative to fixed tariffs through load shifting, while stricter PoCCV settings increase cost by inducing more conservative schedules. PMV-based comfort constraints achieve lower operating costs than temperature-only bounds, indicating that comfort representation materially changes the feasible operating region for cost-effective flexibility. ANOVA results show that cost outcomes are strongly driven by building scale, tariff type, and comfort formulation, with significant interaction effects demonstrating that tariff benefits and comfort-modelling benefits are context-dependent rather than uniform across settings. Originality/value: The paper contributes an integrated robust optimisation + statistical inference framework for smart HP scheduling: DR-CCP provides tunable protection against distributional misspecification in renewable uncertainty, while DOE/ANOVA yields interpretable and reproducible evidence on which factors and interactions dominate the cost-comfort-efficiency trade-off. The results offer actionable guidance for deploying comfort-aware flexibility strategies for electrified heating.