Interval Distribution Power Flow with Relative-Distance-Measure Arithmetic

Interval distribution power flow can analyze the uncertainties incurred by the random fluctuations of distributed renewable generation and load demand in distribution networks. The conventional interval arithmetic (IA) and affine arithmetic (AA) cannot fully apply the characteristics of general algebra: associativity, inverse elements, distributive law, so the IA or AA based interval power flows (IPFs) are either very conservative or unreliable. Relative-Distance-Measure (RDM) arithmetic can overcome these defects in the conventional arithmetic for interval analysis and therefore a RDM based IPF is proposed in this paper. Furthermore, a linear programming contractor (LPC) is developed to solve this RDM based IPF, which can iteratively transform the IPF problem into serial linear optimization models and its results are reliable. Simulation results of IEEE 123-bus test systems show that the proposed IPF can obtain much better results than those of baseline methods in terms of accuracy and reliability.