Holomorphic Embedding–Based Interval Optimal Electric–Heat Energy Flow Solving Algorithm

With the increase in the proportion of renewable energy and the integration of multiple loads, the uncertainty of the integrated heat and electricity systems (IHESs) has become increasingly prominent. Therefore, it is important to calculate the optimal energy flow while taking into account the uncertainty of IHES. This study proposes an interval optimal electric–heat energy flow solution algorithm based on the holomorphic embedding method (HEM). First, the electric and heat load demands, along with the variable outputs from wind and solar power, are represented in interval forms. Based on HEM, the electric, heat, and coupled unit interval energy flow models are reconstituted into holomorphic series. Second, the analytical expression of the IHES interval energy flow is obtained through recursive solution, resolving the issue of error accumulation and interval expansion. By employing the improved simulated annealing–particle swarm optimization algorithm (SA‐PSO), the optimal set of power series coefficients for the analytical expression of the IHES energy flow is determined. This algorithm combines the global optimization capability of SA with the fast convergence property of PSO, thereby effectively avoiding local optima and enhancing optimization efficiency. Finally, the standard examples of a 51‐node heat network and 14‐node power network are coupled to form an IHES for analysis and calculation. The simulation results show that the proposed method has perfect calculation accuracy and efficiency.