Predictive Control of Power Converters and Electrical Drives

13.3 Proportional–Integral Controllers with Pulse Width Modulation

13.3.1 Control Scheme

The use of PI controllers with a pulse width modulator is the method with the greatest development and the most established in the literature [1–3]. Here, the current error is compensated by the PI controllers, which generate the reference voltages that are inputs to the modulator.

This control method can be implemented by considering a stationary or synchronous reference frame for the load current vector [4]. In a stationary reference frame, the controlled currents are sinusoidal signals and the PI controllers are not able to reduce the error to zero. In a synchronous rotating d–q reference frame the load current components are DC quantities and the PI controllers reduce the error to zero at steady state, hence in this work a synchronous frame regulator is used. Considering the synchronous d–q coordinates [5], the load model (13.1) can be expressed as follows:

13.2a

13.2b

where ω is the angular frequency of the rotating frame, v_d and v_q are the components of the voltage vector generated by the inverter in the rotating frame and i_d and i_q are the components of the load current vector in the rotating frame.

The equations (13.2a) and (13.2b) are the mathematical model of the system, which is used ...