CAO Yuxin, ZHI Menglei, LI Xue
[Objective] Energy flow calculation is fundamental to the planning and operation of integrated energy systems （IES）. The existing holomorphic embedding method requires significant computational effort and long solution times for large-scale IES due to the need for solving coefficient equations of power series and the Padé approximation process. [Methods] This paper proposes an energy flow calculation method for electrical-gas IES based on preconditioned bi-conjugate gradient stabilized （BICGSTAB） restarted holomorphic embedding. The method combines preconditioned BICGSTAB and total multiplication of polynomial （TMP） for grid-side holomorphic embedding power flow calculation， while employing the restarted holomorphic embedding method for gas network energy flow calculation. When solving the power flow at the grid side， the coefficient matrix for solving the power series coefficient equations is first preconditioned； then， the constant value dynamic update mechanism in the Holomorphic Embedding Load Flow Method based on constant values is used to solve the voltage approximation value by using Padé approximation and TMP. When solving the side energy flow of gas network， the restarted holomorphic embedding method is used to calculate the energy flow of gas network， so as to improve the calculation speed and convergence of energy flow. Finally， the proposed method is validated using the E39-G20 and E2383-G60 test systems. [Results] The results demonstrate that the proposed method achieves a maximum relative error of only 0.051 3% compared to the Newton-Raphson method， with a maximum computational speedup ratio of 358.0883. [Conclusions] The proposed method enables accurate and efficient energy flow analysis in the electricity-gas IES， maintains high IES energy flow solution accuracy under various operating conditions， and offers strong robustness， which can provide a new idea for the efficient calculation of IES energy flow.