• Jan Peter Mortensen Christiansen
  • Jonas Lillelund Jørgensen
4. term, Control and Automation, Master (Master Programme)
Grid-forming inverters are becoming increasingly relevant due to an increase of inverter based energy resources. The stability of grids with high penetration of inverter based resources is therefore of great interest. This report aims to show stability of such grids using passivity analysis. An approach that was used to show passivity of grids dominated by synchronous generators by Spanias et al. [1], where the bus dynamics and interconnection of buses are viewed as two separate systems in an interconnection is investigated. A time varying phasor model is used and generators are replaced by inverters. It is shown that such a system cannot be passive. Viewing the complex power as the input to the inverter dynamics and the voltage magnitude and phase angle as the output, passivity of the inverter dynamics can be shown. However, to show stability of the interconnection of inverters using the circle criterion, the interconnection needs to be strictly passive, which it is not. However, using a feedback passivization could in theory remedy this at the cost of accurate time synchronization. Using the invariance principle it is shown that the stability of the system is guaranteed under the assumptions that the system is lossless and the phase angle differences between inverters are small. Simulation models of the Two Area Network from Kundur et al. [2] and the IEEE Reliability Test System [3] are used to investigate the stability of the system without the strict assumptions.
Publication date31 May 2023
Number of pages81
ID: 532395209