A linear programming approach to distribution Power Flow

The modern Distribution Systems (DS) require for accurate and fast Power Flow (PF) algorithms as a basis for other DS applications. Almost all decisions are taken based on accurate PF results and, possibly, they have to be taken in real time. In this paper, a new PF algorithm based on a linear programming approach is proposed. The graph theory is used for modeling the distribution network with some topological matrices. The proposed matrices are then utilized to develop a linear optimization model in rectangular form for PF in DS. Moreover, a linear load model is used for calculating the current injections in each system bus. This leads the PF equations to be linear with acceptable accuracy. In the paper the proposed PF algorithm is implemented on IEEE 18-bus and 33-bus test systems. The results show the accuracy and the performance of the proposed PF model compared to existing models. Since the optimization model is linear, the solution is global optimum. It facilitates the application of the accurate PF results in real-time optimization of DS.