Uniform Experimental Design-Based Nonparametric Quasi-Monte Carlo for Efficient Probabilistic Power Flow

Probabilistic power system analysis tools like probabilistic power flow (PPF) help system operators in planning and security studies with multiple uncertainties. Sample-based probabilistic approaches like Monte-Carlo and Quasi-Monte Carlo (QMC) methods are preferred for solving PPF, owing to their non-intrusive nature and capability to use the full deterministic model. However, the drawbacks of inconsistent accuracy, variable convergence rate, and lack of a quality measure hinder QMC's wide applicability. To this end, we propose a nonparametric QMC framework to efficiently and accurately solve PPF with non-Gaussian and dependent uncertainties. The proposed framework introduces uniform experimental design (UD) sampling, which is scalable and improves the PPF's accuracy-efficiency balance. Leveraging on the copula viewpoint, the proposed method directly evaluates the desired correlation matrix in standard Gaussian space, reducing the computational burden. In addition, we introduce mixture discrepancy (MD) as a robust sample quality measure, which is helpful to practitioners in identifying the best QMC sample set for PPF without needing any tedious simulation. Results from detailed case studies on the modified 39-bus and 118-bus systems show that the proposed UD-based QMC improves the computational burden and provides accurate PPF results for fewer samples than the existing QMC methods.