Energy flow matrix modeling and optimal operation analysis of multi energy systems based on graph theory

Multi energy system (MES) is considered an efficient pattern to satisfy diverse energy demands of consumers and improve the energy utilization efficiency. A novel matrix modeling method based on graph theory is proposed to model the steady state energy flows of MES. Firstly, a set of new definitions are proposed to build the directed graph of the energy flows of MES including renewable energy, energy storage and demand response. Secondly, the matrices to describe the topology and energy conversion characteristics of MES are presented. Then the energy flow equations matrix modeling processes are demonstrated. Besides, an input data structure of the MES is suggested to facilitate computerized modeling. Based on this, an optimal operation model in matrix form is proposed to minimize the MES daily operation cost. Then optimal operation problems of multi energy systems with different structures are investigated with the novel modeling method. Simulation results show that the modeling method is effective and feasible to describe the energy flows of MESs with different structures including renewable energy, energy storage and demand response. Comparisons of various costs of case 1, case 2 and case 3 indicate that the renewable energy and energy storage can decrease the power cost of case 3 by 17.65% and 6.45%, respectively. Furthermore, comparisons of case 4 and case 3 show that demand response can reduce the power cost of case 4 by 21.91%.