Dynamic Aggregation of Grid-Tied Three-Phase Inverters

The number of grid-tied inverters interfacing renewable resources, energy-storage devices, and flexible loads in distribution networks is steadily increasing. State-space models for inverters are nonlinear and high dimensional which renders the task of modeling large numbers at the edge of the grid to be a difficult undertaking. To address this issue, we develop a distribution-network-cognizant aggregation approach that describes the collective dynamics of grid-tied three-phase inverters. Inverters are clustered based on effective impedances to an infinite bus (modeling the transmission-distribution boundary) and for each cluster, an aggregate dynamical model is developed to preserve the structure and order of each individual inverter state-space model. The K-means algorithm is leveraged for clustering and a suitable linearization of the power-flow equations reduces computational burden involved in determining terminal voltages for the clusters. Numerical simulation results for the IEEE 37-bus feeder system demonstrate the accuracy and computational benefits of the proposed aggregation method.