Interval power flow (IPF) is a special kind of uncertain power flow problem whose demand load and active power generation are regarded as interval uncertainties. A novel optimizing-scenarios method (OSM) is envisaged in this paper to solve this problem to obtain more accurate results. The OSM includes two kinds of approaches, namely the minimum and maximum programming models, in which the interval uncertainties are regarded as variables with varying bounds, and the objective function under study is set to determine these unknown variables. By solving these nonlinear programming models through the interior point method, the changing variables of the IPF problems are determined. Performance of the proposed approach is compared with that of previously established methods, including the affine arithmetic-based method as well as Monte Carlo simulation method, and the overall simulation results demonstrate the effectiveness and robustness of the proposed OSM.

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.

The reactive power optimisation (RPO) is generally used to design an optimal profile of the voltage and reactive power of power systems in the steady state for deterministic sets of demand loads and generation values, and it is a significant procedure in voltage control. However, the input data of a power system is actually uncertain in practise, which makes RPO an uncertain non‐linear programme. To address this problem, the input data were considered as intervals, and the RPO incorporating interval uncertainties model was proposed. To solve this model, the genetic algorithm was employed as the solution algorithm, where the reliable power flow calculation was used to judge the constraints of the model. The Pareto front was established as the solution of the proposed model since it has two objective functions, i.e. the midpoint and radius of real power losses. The application of this technique to the uncertain RPO was explained in detail. Two numerical results were analysed to demonstrate the effectiveness of the proposed method, especially in comparison with the previously proposed chance‐constrained programming method.