This paper proposes an efficient backward and forward sweep algorithm for the three-phase power flow analysis of weakly meshed distribution system. In the backward sweep, the Kirchhoff's circuit laws are firstly used to calculate each line current and the upstream bus voltage of each line or a transformer branch. Next, the linear proportional principle is applied to find the ratios of the specified (or new) and the calculated bus voltages of the decomposed real and imaginary parts of the network. The compensation method is used to break meshes and to calculate the current injections at each end bus created by breaking the mesh. A useful bus indexing scheme is also proposed to determine the updated voltages at the junction and/or terminal busses for the six decomposed networks in the forward sweep. The procedure repeats and stops after the voltage mismatch of each pair of end busses of the opened mesh and the mismatch of the calculated and specified voltages at the substation bus are less than the predefined threshold value. The proposed method is tested by three IEEE benchmark systems with meshes, and with default system data and different system conditions. Results show that the proposed algorithm is efficient, accurate, and robust in comparing with the commonly used backward/forward sweep method for weakly meshed networks.
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