Abstract：Integrated energy system (IES) is a product of the deep integration between multiple energy networks and the internet. It aims to enhance the comprehensive utilization of various forms of energy, such as electricity, heat, cooling, and gas, by establishing supply, transmission, distribution, and utilization systems. The dynamic simulation calculations of the IES are crucial for subsequent optimization control and energy scheduling research. This paper proposes a dynamic energy flow calculation method for the integrated heat and electricity systems (IHES) based on holomorphic embedding to accurately describe the dynamic characteristics of thermal network pipelines and achieve continuous dynamic simulation of the IHES. Firstly, the study spatially discretizes the dynamic model of thermal network pipelines in the IHES, keeping the differential relationship of temperature concerning time, and the partial differential equation of heat network is transformed into an ordinary differential equation. A thermal network model under mass regulation mode is proposed. Secondly, the energy flow equation is reconstructed with a time-varying holomorphic function, and the dynamic electric-thermal energy flow model is established by holomorphic embedding. Then, using the holomorphic embedding sequence solution (HESS) method to determine the series unfolding sequence, the analytical expressions of node temperature, voltage amplitude, and phase with time can be obtained. Finally, a single thermal pipeline serves as a case study to compare the HESS with the Runge-Kutta method. Simulation results indicate that the HESS can produce a continuous energy flow solution with one recursive calculation (recalculation of holomorphic functions is only necessary when imbalances do not meet the requirements). By inserting time into the current phase of holomorphic functions, the IHES state variable values can be determined without repetitive iterative solutions. In contrast, the Runge-Kutta method requires continuous iteration with a fixed step size to obtain discrete-time energy flow solutions, and its accuracy assurance method involves choosing sufficiently small step sizes, leading to longer computational times. Simulation analysis is conducted on an IEEE 14-node standard case and a 51-node thermal network. By setting scenarios of increased thermal load, simultaneous increase in electrical and thermal loads, and increased generator output, the simulation results are compared with the holomorphic embedding factorization solution (HEFS), fast and flexible holomorphic embedding (FFHE), and Runge-Kutta method. HEFS requires continuous repetitive iterations on subsystems, resulting in longer computation times and lower precision. FFHE, however, models steady-state equations to calculate energy flow solutions at specific time slices, offering better computational speed and precision. The following conclusions are drawn from the simulation analysis. (1) HESS utilizes holomorphic functions to directly calculate the working state of IHES at any moment within the simulation time. The proposed method is more flexible and efficient than the holomorphic embedding decomposition and traditional Runge-Kutta methods. (2) The proposed energy flow calculation method can be used for dynamic simulation of electric- thermal integrated energy systems, especially in load or output fluctuation cases, to continuously analyze the system’s operational state and accurately describe the energy flow process response to disturbances.
李宏仲, 滕佳伦. 基于全纯嵌入的电热综合能源系统动态能流计算方法[J]. 电工技术学报, 2025, 40(4): 1254-1267.
Li Hongzhong, Teng Jialun. Dynamic Energy Flow Calculation Method of Integrated Heat and Electricity Systems Based on Holomorphic Embedding. Transactions of China Electrotechnical Society, 2025, 40(4): 1254-1267.
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2025, Vol. 40 
