The NRPS model and its extension for modeling grids with multiple (virtual) synchronous machines

The increase of the number of inverter-interfaced power sources has made the analysis of the stability for such AC grids an important topic. The complexity of such grids comprising many machines, coupled through a complex transmission network makes the stability analysis challenging. Many models have been proposed, of various complexity, to analyze stability and to derive sufficient conditions for stability for transmission line impedances, inertia and droop constants. A simple and moderately accurate model capable of representing the active power dynamics of grids consisting of virtual synchronous machines (VSMs) and synchronous generators (SGs) is the network reduced power system (NRPS) model. In this paper, we show how active and reactive powers as well as the voltages at the filter capacitors of the VSMs can be obtained from the NRPS model by simple computations. We further introduce a new extension of this model called the reactive active power system (RAPS) model, accounting for reactive power control and internal voltage dynamics, by modeling each generator as a third order (nonlinear) system. We compare the performance of this model, the regular NRPS model and high order simulations for a microgrid with four VSMs and four loads. Finally, we show how to accurately tune the parameters of the NRPS and RAPS models to correctly represent a given grid.