An uncertainty power flow algorithm based on interval and affine arithmetic

The large-scale integration of wind energy causes more and more uncertainties in the power injections and is also a big challenge for the dispatch scheduling. As the basis for the dispatch analysis, traditional power flow calculation is difficult in solving this kind of uncertain power flow problems. The interval and affine arithmetic theory is employed to solve the uncertainty problem. Instead of a single solution, the lower and upper boundaries of solution are obtained in a mathematical sense that the uncertain variables can be expressed as an interval form and the set of nonlinear equations is evaluated by Krawczyk-Moore method. Furthermore, a large overestimation of boundaries in the interval arithmetic yielded by correlation of variables can be improved by affine arithmetic which aims at shortening the gap between the upper and lower boundaries. The algorithm is tested on the standard IEEE 9-bus and IEEE 57-bus systems to validate the applicability.