The flexibility-efficiency nexus in industrial heat electrification: Optimal operation of heat pump-storage systems under variable electricity price

Heat electrification is a key strategy for industrial decarbonisation. However, this transition increases electricity demand, making energy flexibility essential for the reliable integration of electrified systems in the current energy infrastructure. Heat pumps hold significant potential for process heat decarbonisation and flexibility, especially when coupled with thermal energy storage. This study investigates how electricity price-driven operation of heat pump-storage systems impacts both energy flexibility, defined as the ability to adapt operations in response to external signals, and efficiency, defined as the thermodynamic performance of the heat pump. A model is developed to optimise operations over a one-year horizon, minimising energy costs under variable electricity prices, while accounting for the non-linear performance of the heat pump. Multiple configurations, combining different heat pump and storage sizes, are simulated to evaluate performance in terms of energy and cost efficiency, and operational flexibility. To quantify flexibility a new index is introduced: the Flexibility Response Potential (FRP), assessing the flexibility-efficiency nexus of such systems. Results show that optimised operation with thermal storage enables the heat pump to operate more frequently in its high-efficiency range, increasing the COP up to 15%, and reducing CO2 emissions by 1.8–12% compared to a heat-pump-only system, and by 70% compared to a fossil-based heating scenario. Electricity costs decrease by 30% and in some configurations a full load shifting during peak price hours is registered. The study provides practical design guidelines, confirming the techno-economic viability of heat pump-thermal storage systems in industrial decarbonisation strategies, highlighting their role as distributed flexibility resources.