A method for evaluating and improving linear power flow models in system with large fluctuations

Linear power flow models are widely used in power system analysis to approximate nonlinear AC power flow equations. A fast and accurate error evaluation for linear power flow models is valuable in predicting error impact on decision-making and selecting appropriate linear power flow models for certain applications. Therefore, this paper focuses on the evaluation of line-form linear power flow models and proposes a novel method that enables a fast and accurate error evaluation for most linear power flow models that have fewer independent variables. In existing studies, linear power flow models are generally evaluated by Monte Carlo simulation method, in which it measures errors by using limited scenarios under certain conditions. Such evaluation method is enough for conventional power systems with low uncertainties. However, in systems with large fluctuations of renewable energy, the conventional Monte Carlo evaluation faces challenges. For example, a system with K uncertain loads requires at least 2^K stochastic scenarios to represent the uncertainty by only considering the upper and the lower bounds of each uncertain load. This system-level scenario enumeration faces dimensionality curse and high computational burdens, especially for large-scale systems with high uncertainties. Given this difficulty, this paper proposes a novel evaluation method that defines the box-set evaluation ranges to avoid the dimensionality curse in system-level scenario enumerations. To achieve a fast evaluation, all algorithms in the proposed evaluation method are analytical. Besides, based on the evaluation method, a formulation for improving the accuracy of linear power flow models is proposed, whose analytical solution is also given. Several typical systems with different load levels are tested, and the results verify the effectiveness of the proposed method.