The mainstream researches focus only on the linearized impedance model and its related coupling effect or stability problems. However, since there also exist various nonlinear components in control loops, their nonlinear dynamics are also needed to be described in some way for improving the modeling accuracy. To fill in this gap, an impedance model with taking the saturation nonlinearity of Pulse-Width Modulation (PWM) into consideration is developed in this paper. It represents this nonlinearity with a series of saturation gains and works out their explicit expressions based on the describing function theory. By incorporating the derived saturation gains into the conventional small-signal impedance expressions, a partly nonlinear impedance model can be achieved to reflect perturbation dynamics. Theoretical results and electromagnetic transient (EMT) simulations have both verified its effectiveness. Quantitative analyses indicate that it is PWM saturation that dominates the overall nonlinearity, but this dominance may be challenged by larger PLL bandwidths or higher perturbation magnitudes.
 

Saturation,impedance model,nonlinear function,grid-connected converters