An efficient graph-based power flow algorithm for electrical distribution systems with a comprehensive modeling of distributed generations

Real-time operation, analysis and control of active distribution systems (DSs) mainly rely on accurate power flow (PF) results. Almost all decisions are made considering PF calculations. On the other hand, efficiency of PF algorithm should be updated to comply with new smart grid paradigms which affect traditional management methods of DSs. A new graph theory based PF algorithm is proposed in this paper for active electrical DSs including various distributed generation (DG) models, three phase equipment and meshed topologies. At first, two incidence matrices are proposed for modeling of DSs. These matrices could successfully handle meshed topologies and unbalanced networks. They could also be modified to consider various three phase equipment such as transformers and voltage regulators. Moreover, a comprehensive study of various modeling methods of DGs in PF studies is presented. In order to handle DG models, a new sensitivity matrix is proposed for in-algorithm calculation of reactive power injection of PV buses. Since, the proposed incidence matrices provide a decoupled model of the network, any topology and characteristic change could be simply applied in this PF algorithm. The proposed PF algorithm was tested in several simulations in various test systems. The results of accuracy test, performance test, and robustness test show capability of the proposed PF algorithm for handling various situations in different PF calculations.