Unbalanced three-phase distribution system power flow with distributed generation using affine arithmetic

Due to the high penetration of the uncertain distributed generations (DGs), including wind power generators (WTG), photovoltaic (PV) power generation and plug-in hybrid electric vehicle (PHEV), the power flow of the distribution system has become asymmetry and uncertain. Based on the combination of interval and affine arithmetic, this paper establishes the model of three-phase load with uncertain DGs, and proposes a three-phase forward-backward sweep power flow algorithm for the distribution system. Compared with the deterministic power flow, the proposed algorithm can not only analyze the impact of the uncertain load and DGs on the power flow, but also reduce the overestimation of bounds yielded by correlation of variables in interval arithmetic (IA). IEEE 33-bus test systems are used to analyze the influence of the penetration of distributed generations on the distribution system.