Impedance modeling of permanent magnet synchronous generator with virtual synchronous generator controlled converters based on piecewise affine theory

In recent years, frequent small-signal oscillation incidents have highlighted the urgent need for safety assessment and control optimization of new power systems under dynamic time-varying and high-fluctuation conditions. This paper proposes a grid-forming direct-drive wind turbine impedance modeling method based on piecewise affine theory. First, the active power and reactive power of the converter output, along with the grid-connected point voltage, are selected as partition variables to offline construct a piecewise affine impedance model for grid-connected converters with virtual synchronous generator (VSG) control. During online operation, real-time operating conditions are used to rapidly identify operational sub-regions and dynamically switch linearized models, significantly improving impedance calculation efficiency. Simulation and experimental results demonstrate that the proposed piecewise affine impedance model achieves high consistency with the full-order impedance model, providing an effective tool for stability analysis of new power systems.