Current Proportional–Integral Control
Proportional–integral (PI) controllers are so far the most widely applied controllers in industry. In this chapter, a PI controller is applied to grid-connected inverters to track a reference current so that a desired current can be injected into the grid. This is done in the synchronously rotating reference (dq) frame. Its equivalent in the natural (abc) frame is also discussed. Experimental results are provided to demonstrate the performance of the PI control scheme.
15.1 Control Structure
15.1.1 In the Synchronously Rotating Reference (dq) Frame
The transfer function of a PI controller (Aström and Hägglund 1988, 1995, 2006; Tan et al. 1999; Visioli 2006; Yu 1999) is given by
where Kp and Ki are the proportional and integral gains, respectively. As discussed in Chapter 2, three-phase signals in the natural frame can be transformed into DC signals in the synchronously rotating reference (dq) frame. Hence, for inverters, PI controllers are normally designed in the synchronously rotating reference (dq) frame (Teodorescu and Blaabjerg 2004; (Timbus et al. 2006c, 2009).
The block diagram of a current-controlled VSI in the synchronously rotating reference (dq) frame is shown in Figure 15.1. A PLL is adopted to provide the phase information of the grid voltage, which is needed to transform the grid currents into their dq components