A Mixed Interval Power Flow Analysis Under Rectangular and Polar Coordinate System

A Rectangular Interval Power Flow (RIPF) method is proposed to improve solutions for intervals of power flow problems due to nondeterministic characteristics of demand loads and output of generators. It is based on affine arithmetic which is a self-validated numerical analysis and serves to improve the interval results through optimization method. Since no approximation is presumed, the RIPF method acquires narrower intervals of voltage phase and active power of branches than Polar Interval Power Flow (PIPF), it is an excellent method raised before. However, as RIPF is no better than that of PIPF for estimating intervals of voltage magnitude, because it relaxes restriction of the voltage equations. Therefore, a Mixed Interval Power Flow (MIPF) method is envisaged and developed in the paper to incorporate merits of RIPF for computing the intervals of voltage phase and active power of branches but not giving the advantage of PIPF for evaluating intervals of voltage magnitude. As a validation of our suggested approach, two case studies are carried out, and results conclude that the MIPF method acquires more accurate power flow intervals than the conventional method.