A comprehensive power quality confidence evaluation method for microgrid based on Chebyshev inequality

Abstract

A reasonable assessment of microgrid power quality (MGPQ) is essential for ensuring the safe and stable operation of the system. However, due to the complex and variable operating conditions of microgrid (MG), the results of power quality (PQ) assessments are often discrete. Therefore, further research is needed to determine how to accurately estimate the overall PQ of a MG based on these discrete evaluation results. To address this issue, a model for evaluating MGPQ based on confidence estimation using Chebyshev inequality is proposed in this paper. Firstly, Chebyshev inequality is utilized to describe the discreteness of PQ evaluation results in MG. Secondly, the multi-scale adaptive phase number selection CRITIC method and probabilistic statistics method are employed to evaluate the PQ index of the MG under multiple working conditions. Furthermore, sample standard deviation (SD) is used to quantify the dispersion of evaluation results, and a 90% confidence level is used to estimate the confidence interval of multiple evaluation results. Finally, the example presented in this paper demonstrates that at least 90% probability exists for an evaluation result to fall within ±3.16 SDs from its mean. Compared with traditional methods, this paper comprehensively reflects the overall PQ status of MG from three aspects by considering index data characteristics, different time scales, and confidence intervals—providing clear and practical guidance for MG users and managers to ensure safe and stable operation of the MG.