Impedance Modelling Mechanisms and Stability Issues of Single Phase Inverter With SISO Structure and Frequency Coupling Effect

Multi-Input and Multi-Output (MIMO) impedance model considering the Mirror Frequency Effect (MFE) has been studied for single phase systems in the past five years. However, the resulting impedance matrix is mathematically intractable without practically physical meaning. Besides, another unique High Frequency Effect (HFE) existed only in single phase systems has received less attention. To tackle these problems, this paper presents a Single-Input and Single-Output (SISO) modeling mechanism for single phase inverter considering both MFE and HFE. Firstly, the accurate response of T/4 delay PLL is derived in this paper. Then, based on the harmonic linearization method, the inverter impedance model is successfully realized in the SISO structure, where MFE and HFE are represented by two additional impedance. And consequently, the influence of HFE on inverter impedance is analysed with varying PLL bandwidth. Applying the Nyquist criteria, the proposed overall impedance model can precisely predict the sub/super-synchronous oscillation that occurs in the weak grid. Finally, all the theoretical analysis results are validated by simulation cases. The proposed work could significantly simplify the traditional MIMO modeling procedure with a more straightforward impedance structure, which might be helpful for solving potential oscillation issues of renewable energy integration.