Data-Driven Inverse Optimization for Modeling Intertemporally Responsive Loads
Zhenfei Tan, Zheng Yan, Qing Xia, Yang Wang
Abstract
This letter proposes a novel framework for modeling the response-price relationship of intertemporally responsive loads (IRL) using historical data. This task is cast as a data-driven inverse optimization (DDIO) problem, which trains a surrogate model whose best response to electricity price most closely resembles the observed power trajectory of IRLs. The virtual battery fleet with an adjustable number of elements is used as the surrogate model, which yields a linear modeling result. The DDIO is a bilevel programming problem. To solve it efficiently, a Newton-based algorithm with a grid fitting initialization technique is developed. The accuracy and robustness of the proposed modeling method are validated by numerical tests in comparison with other machine learning regressors.