Determining the active and reactive power range in AC circuits

Abstract

PurposeThe purpose of this paper is to suggest a polynomial complexity method for determining the range of the active and reactive power consumed in AC uncertain parameter circuits whose uncertain parameters are given as intervals.Design/methodology/approachFirst, the original problem is formulated as a corresponding interval quadratic range determination (IQRD) problem. Next, it is shown that the IQRD problem can be transformed equivalently into an interval linear range determination (ILRD) problem.FindingsAn efficient numerical method for solving the associated ILRD problem has been developed, capable of tackling the present active (or reactive) power range problem. It is based on the use of the outer solution y of an associated interval linear system defining the constraints in the ILRD problem.Research limitations/implicationsThe method yields the exact active and reactive power range if the number of the components yi of y containing zero is relatively small (which is most often the case); otherwise, it provides tight outer bounds on the ranges sought.Practical implicationsThe present method can be an alternative to the widely used Monte‐Carlo method since the former method provides exact (within rounding errors) results or tight outer approximations for lesser computation times.Originality/valueTo the best of the author's knowledge, the present paper suggests, for the first time, a simple interval analysis method of polynomial complexity for solving the problem considered which is inherently a NP‐hard problem (of exponential complexity).