Revealing trade-offs between flexibility and equity in an integrated electricity-heating system

The growing electrification of heating systems enables new opportunities for demand-side flexibility, particularly through residential heat pumps. By utilising building thermal inertia, heat pumps can reduce system costs and support renewable integration. However, such flexibility may be unequally distributed, leading to spatial disparities in indoor thermal comfort. This study developed a mixed-integer linear optimisation model for the short-term operation of an integrated electricity-heating system. A simplified 2050 Great Britain system was used to simulate different flexibility scenarios by varying the allowable indoor temperature deviation. Spatial inequality was assessed using standard deviation (STD), thermal adjustment burden (TAD), and the Gini coefficient. Results show that increasing flexibility reduces system costs and curtailment, but also causes uneven temperature deviations across regions. To address this, Gini-based equity constraints were introduced. These constraints effectively improve fairness but increase system costs—by 10.31 % under the strictest setting (Gini = 0), and only 5.22 % under a moderate constraint (Gini ≤0.3). In addition, the operational patterns of other alternative flexibility sources—such as electrolysers and energy storage systems—were affected under equity constraints, exhibiting increased volatility to compensate for the reduced flexibility from heat pumps. The findings highlight the trade-off between efficiency and equity, offering a modelling framework to support fairer demand-side strategies in future energy systems.