Dynamic Aggregation of Grid-tied Inverters

Abstract

Power-electronics inverters are being integrated in large numbers in distribution networks with rapid deployment of renewable resources, energy storage, and flexible loads. Since such distributed energy resources will serve a majority of loads in the next- generation power network, it is critical to develop scalable and accurate modeling tools to study the dynamical behavior of systems with large numbers of inverters. Typical dynamical models for grid-tied inverters are nonlinear and composed of a large number of states; therefore it is impractical to study systems with many inverters when their full dynamics are retained. To address this issue, a reduced-order aggregated model for parallel-connected grid-tied three-phase inverters is formulated. A necessary and sufficient set of parametric relationships is derived to ensure that the reduced-order models for an arbitrary number of such paralleled inverters have the same model order and structure as any single inverter. The reduced-order model is extended for photovoltaic (PV) inverters, where a PV array, a maximum power point tracking (MPPT) algorithm, and a dc-link capacitor are incorporated into the three-phase inverter model. Furthermore, a network-cognizant aggregation approach for distribution networks comprising grid-tied inverters is developed. Inverters are clustered based on effective impedances to an infinite bus (modeling the transmission-distribution boundary) and for each cluster, the reduced-order aggregated model is utilized to replace the inverters in the cluster. 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 a benchmark feeder system demonstrate the accuracy and computational benefits of the aggregation method.