A Stability Result for Network Reduced Power Systems Using Virtual Friction and Inertia

Florian Reissner*, Hang Yin, George Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove that virtual friction can stabilize a power grid containing several virtual synchronous machines (VSMs), connecting line impedances and loads. Virtual friction is a torque added to the swing equation of each VSM, proportional to the deviation of its frequency from the overall center of inertia (COI) frequency. Our analysis is based on the network reduced power system (NRPS) model. We support our results with simulations for a two-area network of four VSMs, looking at the transients induced by a change of tie-line impedance and an asymmetric load change. We compare the results for the NRPS model with the corresponding results using detailed models of synchronverters and line impedances. We find that virtual friction has a strong stabilizing effect both for the NRPS model and for the detailed model. Furthermore we show simulation results on the influence of time delays in the communication between the inverters. This communication is used to compute the COI frequency. It turns out that communication delays of less than 100ms have practically no effect on the overall system.

Original languageEnglish
Pages (from-to)1668-1678
Number of pages11
JournalIEEE Transactions on Smart Grid
Issue number3
StatePublished - 1 May 2022


  • Kuramoto model
  • NRPS model
  • Power grid
  • exponential stability
  • frequency synchronization
  • inertia
  • virtual friction
  • virtual synchronous machine


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