Current Proportional-Resonant Control
The proportional-resonant (PR) controller is one of the most popular controllers used for grid-connected inverters to regulate the current injected into the grid. In this chapter, the PR current controller is designed and implemented for three-phase inverters, in the stationary reference frame and in the natural reference frame.
16.1 Proportional-resonant Controller
For inverters, the controller deals with sinusoidal signals, which makes it difficult to design the controller with the correct gain that is able to regulate the performance at the fundamental frequency and also to reject harmonic disturbances. PI controllers, having a pole (with an infinite gain) at the zero frequency, are not able to eliminate the steady-state error at the fundamental frequency (Blaabjerg et al. 2006) unless it is adopted in the dq frame, as done in Chapter 15. Alternatively, PR controllers can be used.
A PR controller is the combination of a proportional term and a resonant term given by
where ω is the resonant frequency. Such a controller has a high gain around the resonant frequency and, thus, is capable of eliminating the steady-state error when tracking or rejecting a sinusoidal signal (Blaabjerg et al. 2006; Sera et al. 2005; Timbus et al. 2006b), according to the internal model principle (Francis and Wonham 1975). As a result, PR controllers ...