3.2 Current Loop Model

To understand the current loop model, first look at the inductor current closely. In Figure 5 the duty cycle D is provided to the PWM modulator, which is connected to the switches Q1 and Q2. With this in mind, see Equation 1:

NOTE

When D is set to 1, all the switches are off, and when D is 0, all switches are on, which connect the inductor to the point to M.

To modulate the current through the inductor, the voltage v_xiN is regulated using the duty cycle control of Q1 and Q2 switches. Assuming the direction of current is positive in the direction from the AC line into the rectifier and using the DC bus feedforward, the input AC voltage feedforward along with the assumption that the grid is fairly stiff. The current loop can be simplified as shown in Figure 5, and the current loop plant model can be written as in Equation 2.

Where:

• K_{v_gain} is the inverse of the maximum voltage sensed that is 1/V_{max_sense} for the bus and the ac input. It is assumed the AC voltage max sense and the DC Bus voltage max sense are equal.
• K_{i_gain} is the inverse of the maximum AC current sensed.
• K_{i_fltr}is the response of the RC filter connected from the current sensor to the ADC pin.
• G_d is the digital delay associated with the PWM update and digital control.
• i_Li^* is the current command, i_Li is the actual inductor current.
• V_bus/2 is the voltage across one of the output bus capacitor.
• Z_i is the impedance of the inductor which includes indictance L_i and resistance R_i .
• H_{p_i} is the current loop plant as seen by the digital controller G_i .
• v _iN is the instantaneous AC voltage at the input.

NOTE

The negative sign on the reference is in place because the current loop is thought to be regulating the voltage v_xiN. To increase the current, v_xiN must be reduced and, thus, the opposite sign for reference and feedback in Figure 5. This current loop model is used to tune the current compensator. A simple proportional controller is used for the current loop. The gain of the proportional gain is adjusted to ensure the system is stable.