Hierarchical reserve-based distributionally robust chance-constrained optimization for integrated electricity-heat systems during cold waves

Cold waves lead to significant deviations in wind power prediction and load surge of electric-heat systems, which seriously affect the system's power supply and heat supply. In this paper, a distributionally robust chance-constrained optimization model for integrated electricity-heat systems (IEHSs) based on hierarchical reserve is proposed. Firstly, an optimization model for the IEHSs based on hierarchical reserve is constructed. Secondly, a Wasserstein distance-based ambiguity set is formulated to characterize wind power prediction errors during cold wave events, enabling the construction of a distributionally robust optimization model with ambiguous chance constraints for IEHSs. Finally, the proposed methodology employs duality theory and conditional value-at-risk (CVaR) approximation techniques to reformulate the original distributionally robust optimization model as a computationally tractable linear programming problem. The effectiveness of the proposed method is verified using the improved IEEE 24-bus and Barry Island 32-node test system. The results show that compared with the robust optimization (RO), stochastic optimization (SO), and deterministic optimization (DO) models, the proposed method can reduce overall operating costs to mitigate the uncertainty caused by the wind power prediction error during cold waves, and effectively balance economic efficiency and robustness of IEHSs.