## Power Factor Correction

Design, tune, and verify power factor correction algorithms using simulation

Power factor for an AC circuit is the ratio of the instantaneous real power used by an electrical load to the apparent power running through the circuit. It is a measure of how effectively power is transmitted and used by loads attached to an electrical grid.

\[Power \; Factor = \frac{Real \; Power \; (kW)}{Apparent \; Power \; (kVA)}\]

In a purely linear circuit,

\[Power \; Factor = cosθ\]

where \(θ\) is the angle between the real power and the apparent power in the vector power triangle below.

A power factor closer to 1 provides the maximum utilization of power drawn from the grid. A low power factor indicates inductive or capacitive elements in the circuit causing the current drawn to lag or lead the voltage, respectively, decreasing the instantaneous real power available to the load and consuming unnecessary current capacity on the cables.

For nonlinear circuits, the power factor is affected by an additional distortion component resulting from the harmonics in the line current.

\[Power \; Factor = cosθ * \frac{1} {\sqrt {1 + Total \; Harmonic \; Distortion^2}}\]

For example, loads like switched-mode power supplies are widely used because of the advantages they offer in the terms of size, cost, and efficiency. However, one disadvantage of a switched-mode power supply without power factor correction is that it introduces these harmonics in the load current due to switching from semiconductor devices such as MOSFETs. This increases the total harmonic distortion of load current, thereby decreasing the power quality.

Engineers use different techniques to improve power quality for such electrical installations. Power factor improvement for linear loads can be brought about by reactive power compensation to compensate for the leading or lagging VARs. However, nonlinear loads generating harmonics require power factor correction techniques like tuned or active harmonic filters to mitigate these harmonics and improve power quality. Such power factor correction techniques rely on the use of power electronics, controlled using analog or digital controllers.

Digital power factor correction control design using Simulink^{®} lets you make use of multirate simulation to design and tune digital control algorithms, enabling you to tailor the input current waveforms, thus keeping losses low while improving the power quality to a desired value. This approach also enables you to test and verify controllers in the presence of varying loads and input voltages before deploying the control algorithms on hardware.

Using Simulink, you can:

- Build accurate simulation models of switched-mode power supplies, AC motors, and other loads in the distribution systems
- Perform harmonic analysis to determine total harmonic distortion present in the circuit
- Size passive components for power converters to ensure desired signal characteristics such as output voltage ripple
- Design digital controllers for these power converters using AC sweeps and automated PID tuning
- Automatically generate ANSI, ISO, or processor-optimized C code and HDL for rapid prototyping and production implementation of the controllers

### Examples and How To

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