Energy Flow Calculation Method for Multi-Energy Systems: A Matrix Approach Considering Alternative Gas Injection and Dynamic Flow Direction

The steady-state energy flow calculation (EFC) of multi-energy systems (MESs) is a fundamental foundation for MES planning and operation. However, most of the existing MES models are designed case-specifically, making them incapable of modelling diverse scenarios. Moreover, since it involves initial value setting, the convergence of the Newton–Raphson (NR) method to solve the EFC problem of MESs is often unsatisfactory. To tackle these problems, a matrix-based EFC method of MESs is proposed in this paper. The universal matrix formulations of heat and gas subnetworks are first constructed, where the injection of alternative gas sources and the effect of gas compressibility factor on the MES state are both considered. Due to the uncertainty of gas flow direction during the NR iteration process, the gas composition tracking equations are modified to avoid ill conditions. The Jacobian matrices for the constructed subnetwork models are then derived and expressed in matrix form. On this basis, the unified NR strategy is adopted to solve the constructed models. Finally, the performance of the proposed method is verified through case studies. The results demonstrate that the proposed models can accurately capture the MES operating state and achieve significant improvements in convergence and computational efficiency compared to traditional models.