Impact of Harmonics and Unbalance on the Dynamics of Grid-Forming, Frequency-Droop-Controlled Inverters

Due to its multiple advantages, the grid-forming, droop-controlled (GFDC) inverter is a strong contender for large-scale deployment in the future power systems. However, it is still unclear whether higher harmonics can play an important role in the dynamics of GFDC inverter networks. The major objective of this article is to gain insight into whether certain higher harmonics influence or interact with GFDC inverter network dynamics and to characterize this harmonic interaction. For this purpose, a multiple-harmonic dynamic phasor model (DPM) of a representative GFDC network is derived, which can be conveniently extended to hundreds of DPM equations in order to rigorously investigate the effects of dc offsets and/or second-harmonic content, six-step switching harmonics, and unbalance. For a representative network, the results from eigenvalue migration studies show that GFDC dynamics are not strongly influenced by the presence of six-step switching harmonics nor unbalance. For the first time, it is shown that under conditions of high droop slope and high-bandwidth power filtering, dc offsets and second-harmonic content can excite a resonance within the network and even influence the location of the eigenvalues of the linearized DPM. All DPM results are thoroughly validated using Simulink, and the selected results are validated experimentally using the Wisconsin Energy Institute (WEI) microgrid testbed.