# PFC Rectifier Controller (Three-Phase)

**Libraries:**

Simscape /
Electrical /
Control /
Converter Control

## Description

The PFC Rectifier Controller (Three-Phase) block implements a proportional-integral-derivative (PID)-based power factor correction (PFC) rectifier controller. This block converts a three-phase AC supply into the required stable DC-link voltage and controls the reactive power drawn from the supply. To reduce harmonics, the block draws sinusoidal current. The block has an inbuilt phase-locked-loop (PLL) that tracks the angle and magnitude of the supply voltage.

For discrete-time simulation, set **Sample time (-1 for inherited)** to a
positive value or to `-1`

to inherit the sample time. For continuous-time
simulation, set **Sample time (-1 for inherited)** to
`0`

.

This figure shows the circuit configuration of the PFC rectifier.

*V*_{S}is the supply voltage.*I*_{S}is the supply-side current.*X*_{L}is the inductive reactance.*V*_{i}is the inverter-side AC phase voltage.*V*_{dc}is the DC-link voltage.

This equation defines the supply voltage
*V*_{S},

$${V}_{S}(t)={I}_{S}{R}_{L}+L\frac{d{i}_{S}(t)}{dt}+{V}_{i}(t),$$

where:

*R*_{L}is the resistance of the filter inductor.*L*is the filter inductance.*i*_{s}is the inverter-side AC phase current.

### Controller Structure

This diagram shows the structure of the controller.

The inputs to the block are:

The output DC-link voltage reference

*VdcRef*, measured in volts.The per-unit reactive power reference

*QRef*.The measured DC-link voltage

*VdcSens*, in volts.The per-unit measured AC phase voltage

*VabcSens*.The per-unit measured AC phase current

*IabcSens*.

The outputs are the per-unit reference voltage *VabcRef* and
a bus containing signals for visualization.

The DC voltage controller calculates:

The per-unit

*d*-axis reference current*IdRef*.The per-unit error of the DC voltage controller

*VdcCntrlError*.

The PLL calculates:

The phase angle

*pllAngle*, in radians, of the measured AC phase voltage.The per-unit magnitude

*pllVmag*of the measured AC phase voltage.The per-unit

*d*-axis component of the measured AC phase voltage*Vd*.The per-unit

*q*-axis component of the measured AC phase voltage*Vq*.

The reactive power reference calculates the per-unit *q*-axis
reference current *IqRef*.

The current controller calculates:

The per-unit reference voltage

*VabcRef*.The per-unit error of the

*d*-axis current controller*IdCntrlError*.The per-unit error of the

*q*-axis current controller*IqCntrlError*.

### Visualization

The block outputs a bus containing these seven signals for visualization:

The phase angle

*pllAngle*, in radians, of the measured AC phase voltage.The per-unit voltage magnitude

*pllVmag*of the measured AC phase voltage.The per-unit

*d*-axis reference current*IdRef*.The per-unit

*q*-axis reference current*IqRef*.The per-unit error of the DC voltage controller

*VdcCntrlError*.The per-unit error of the

*d*-axis current controller*IdCntrlError*.The per-unit error of the

*q*-axis current controller*IqCntrlError*.

## Examples

## Ports

### Input

### Output

## Parameters

## References

[1] Siva Prasad, J. S., et al. “Vector
Control of Three-Phase AC/DC Front-End Converter.” *Sadhana*,
vol. 33, no. 5, Oct. 2008, pp. 591–613. *Springer Link*,
https://doi.org/10.1007/s12046-008-0045-y.

## Extended Capabilities

## Version History

**Introduced in R2024a**