Using general synchronous machine theory to integrate PLL controller dynamics into a static power electronic converter model

Abstract

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.

Stability Analysis of Large Wind Farms Connected to Weak AC Networks Incorporating PLL Dynamics

“…The converter model represents 10 fully rated wind turbines which are connected to the power grid through voltage source converters. Figures 8 and 9 show the step responses of the d-axis current for the state space model and the time domain model (developed using Simulink) for different SCR values (3)(4)(5)(6)(7)(8)(9)(10) and controller bandwidth (20-100Hz), respectively. As can be seen from Figures 8 and 9, the dynamic performances for the time domain model and the state-space model are very similar which indicates that the state-space model represents the dynamics of the system very well.…”

“…However the d-axis voltage of the converter filter bus is selected as the reference for dq frame and thus, it becomes complicated when studying the dynamics of parallel converters since each converter has its own dq reference. Reference [9] tried to add PLL dynamics to converter dynamic model by using synchronous machines theory though the PLL dynamics was added to the feed forward grid voltage rather than to the converter voltage. In [10], the dynamics of PLL has been studied, but not as a part of the dynamic model of the VSC.…”