Data-Driven Nonparametric Chance-Constrained Optimization for Microgrid Energy Management

Abstract

In this article, we present a data-driven nonparametric chance-constrained optimization for microgrid energy management. The proposed approach imposes no assumption on probability density and distribution functions of solar generation and load. Adaptive kernel density estimator is utilized to construct a confidence set for each random parameter based on the historical data. The constructed confidence sets encompass the ambiguous true distribution and density functions. The concept of $\phi $ -divergence tolerance is applied to compute the distance between the estimated and true probability distribution functions (PDF)s. The estimated distributions are used to formulate a set of data-driven nonparametric chance constraints and model system/component restrictions. To account for the impact of errors in the forecast distributions on system economics and security, confidence levels of the chance constraints are adjusted with respect to pointwise errors of the estimated PDFs. This adjustment ensures that the microgrid chance constraints are satisfied with a predetermined confidence level even if the true realizations of solar generation and load do not exactly fit on the estimated PDFs. The chance constraints are converted into algebraic constraints. Numerical results show the effectiveness of the proposed approach for microgrid management.