Reactive Power Optimization Under Interval Uncertainty by the Linear Approximation Method and Its Modified Method

Abstract

Reactive power optimization is a special kind of optimal power flow for optimizing voltage profile and reactive power flow in the steady state based on deterministic sets of the demand load and generation values, thus minimizing the real power losses or improving the voltage quality of the power grid. However, the input data in power systems have a certain degree of uncertainty that requires the reactive power optimization be solved by means of uncertain nonlinear programming, as advocated in the literature. To address this problem, we represent the uncertain input data as intervals and establish a model of the reactive power optimization that incorporates the interval uncertainties to describe the problem. The linear approximation method is formulated using the interval Taylor extension to help solve this type of problem. To obtain more accurate intervals for the state variables, the affine arithmetic-based power flow calculation is used to solve the interval power flow equation instead of crude computation based on the interval arithmetic, and thus the modified linear approximation method is developed. The proposed methods are presented in detail and the numerical results are analyzed to demonstrate their effectiveness and applicability, especially in comparison to the previously proposed chance constrained programming method.