Current Proportional-Resonant Control - Control of Power Inverters in Renewable Energy and Smart Grid Integration - page 247

16

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 itdifficult to design
the controller with the correct gain that is able to regulate the performance at the fundamental
frequency and also to reject harmonicdisturbances. 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

s

C PR ( s ) = K p + K i (16.1)

s 2 + ω

2

where 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
asinusoidal 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 are
widely used in inverter control. In order to improve the performance of handling harmonics,
a harmonic compensator given by

ω

s

C HC ( s ) = K ih (16.2)

h ) 2

s 2 + ( ω

h = 3 , 5 , 7 ,..