A Novel Affine Arithmetic Method With Missed the Triangular Domain With Uncertainties

A novel affine arithmetic (AA) method with missed triangular domain (remaining area is convex polygons) is proposed in this paper for solving interval power flow (IPF) problem with uncertainties. An interval correlation model of random variables is established, and the original correlated interval variables are transformed into the standard space using interval arithmetic (IA) to reduce overestimation problem because of interval operation. To alleviate the errors caused by inaccurate enveloping of different intervals, an interval model with missed triangular domain is proposed and integrated into optimization model of IPF in form of additional constraints, which is developed in this paper through AA. IPF results, i.e., voltage magnitude, voltage angles and line flows are much narrower because it enhances restriction of correlated variables. Case studies on various test systems, i.e., IEEE 33-bus, 69-bus, and 118-bus system, indicate effectiveness of proposed technique compared with the other methods.