State-Space Modeling and C-HIL Validation of a VSM: Virtual-Resistance Effects Across Grid Strengths

Abstract:
This paper develops a full order state space model (SSM) of a grid-connected Virtual Synchronous Machine (VSM) that integrates inner current and voltage/power loops, virtual impedance, the LCL filter, and explicit grid interaction. The unified model is implemented in MATLAB and validated experimentally on a 50 KVA converter via Controller Hardware in the Loop (C-HIL). Reactive power step test under moderate and strong grid conditions shown close agreement between SSM and C-HIL. By sweeping the virtual resistance rv, we quantify a clear trade-off: rv improves low frequency damping in moderate and weak grids but can erode current-loop phase margin and excite LCL - related high frequency dynamics when the bandwidth approaches the resonance (kHz range) in stronger grids. These results provide actionable tuning guidance for rv and highlight the need for co-design with current loop bandwidth and grid strength.