Interval Arithmetic in Power Flow Analysis

The power flow is the fundamental tool for the study of power systems. The data for this problem are subject to uncertainty. This paper uses interval withmetic to solve the power flow problem. Interval arithmetic takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object oriented programming techniques make it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval arithmetic computations, the paper describes an iterative method used to obtain the “hull” of the solution set.