Gray-box Model

Gray-box model for distribution systems. Inspired by physics-informed machine learning (PINN), we developed a novel gray-box modeling approach for distribution systems with inverter-based resources (IBRs). The proposed gray-box modeling method aims to improve estimation accuracy by taking advantage of both physics-based (white-box) and data-driven (black-box) modeling approaches. To this end, the gray-box modeling framework is constructed by encoding prior physical knowledge of the system in a white-box model and then embedding the output of the white-box model into the input of a black-box model (machine learning approach). Furthermore, case studies demonstrate that our gray-box modeling approach effectively improves estimation accuracy compared to purely physics-based or data-driven methods.