Using General Synchronous Machine Theory to integrate PLL Controller Dynamics into a Static Power Electronic Converter Model

Many distributed generators generate DC power, which needs to be inverted into AC active power to deliver power to the utility grid. In power electronic inverters the PLL algorithm synchronizes the injected current with the voltage. As a PLL is integrated in to a control loop, a multiplication is integrated in the controller, disabling classical analytical dynamic control theory. There are different types of inverters but in this paper it will be shown that different topologies of inverters can be modeled by one simplified scheme. In order to model the dynamic behavior of the PLL, the synchronous machine theory is applied to integrate the dynamic behavior of any PLL in this basic continuous time model. As a result a dynamic model of the power electronic converter is obtained, and although it does not output actual control values, this model enables the use of classic control theory to analyze the dynamic behavior of power electronic converters.