Coordinated Voltage Control and Optimization of Distribution Feeders Using Gaussian Process Regression: Proposing A New Framework

This article proposes a constrained Gaussian process regression (GPR)-based multiobjective distribution optimal power flow (GPR-DOPF) framework to coordinate the voltage-regulating devices [capacitor banks (CBs) and voltage regulators (VRs)] with smart inverter (SI) controls. The GPRs are well suited for the complexity and nonlinearity that characterizes power distribution networks. This work provides a detailed mathematical formulation of the GPR, proposes a scalable GPR-DOPF to address computational inefficiency with large datasets, and models the SI control modes and other voltage-regulating devices for application in the DOPF. The GPR is trained (assuming no significant physical changes in the network) using the extensive power flow data obtained from the power distribution network. To determine the optimal settings of the SIs and the legacy devices using the GPR-DOPF, a multiobjective mixed integer nonlinear problem (MINLP) is formulated. The GPR model is coupled with the Non-Dominated Sorting Genetic Algorithm II (NSGA II) to determine the pareto optimal solutions (POSs) of the proposed MINLP formulation. The mathematical objectives include minimizing the voltage deviation and the overall network active power loss.