This paper proposes a two-path constrained multi-objective framework to determine the optimal volt-VAr droop for grid-connected smart inverters (SI). The first approach formulates a distribution optimal power flow (DOPF) using a heuristic multi-objective optimization algorithm (MOGA) to directly determine the optimal SI volt-VAr droop. In order to eliminate the need for solving the power flow every time to determine the optimal SI volt-VAr droop, (assuming there are no significant changes/update in the network) the second approach develops a multivariate Gaussian process regression (GPR) model for predicting objective functions that are required from solving the DOPF. The GPR is trained using data generated from extensive power flow simulations using the physics of the actual grid. This allows the grid performance values to be predicted model-free. The GPR is also coupled with the MOGA to determine the Pareto Optimal Solution (POS) of the SI's volt-VAr droop. The proposed framework is tested on a standard IEEE 34 distribution network. The objectives considered include minimizing the voltage deviation and the overall network active power loss. The POS of the SI droop obtained from both approaches show that the GPR-based DOPF can achieve a comparable results with the actual physics-based DOPF model. The GPR-based DOPF requires far smaller computational time for determining the SI's optimal volt-VAr droop and also provides effective voltage regulation and control.
