Virtual Friction Subjected to Communication Delays in a Microgrid of Virtual Synchronous Machines

Virtual synchronous machines (VSMs) have become popular solutions for grid-tied inverters, suited to work on ac grids with an increasing share of distributed energy sources and storage. However, just like real synchronous machines, VSMs may experience power oscillations. Recently, a new damping concept called virtual friction (VF) has been proposed that makes use of real-time communication between several inverters. VF introduces an additional damping torque in the swing equation of the VSM, proportional to the deviation of the virtual rotor frequency from the center of inertia (COI) frequency. VF can apply high damping without imposing a strong response in the output power of the VSM during frequency transients. However, VF requires the transmission of frequencies over a communication network, which may suffer from transmission delays. We give an experimental proof of concept of VF both in an isolated microgrid and in grid-connected operation of a 45-kVA setup consisting of three VSMs realized by three-phase two-level insulated-gate bipolar transistor (IGBT)-based inverters. We consider continuous constant and discontinuous varying time delays and show theoretically and experimentally under what conditions delays can impact the output powers of the VSMs. Furthermore, we show how to correctly estimate the COI frequency with transmission delays using timestamps to align individual signals.