- Fundamental Definitions
- AC Circuit Analysis
- Power and Power Triangles in AC Circuits
- Power Factor Correction
- Star-Delta and Delta-Star Conversion in Three-Phase AC Circuits
- Voltage and Currents in Star- and Delta-Connected Loads
- Voltage and Current Phasors in Three-Phase Systems
- Power in Three-Phase AC Circuits
- Three-Phase Power Measurement and Data Logging
- References

## 3.4 Power Factor Correction

When the complex power definition is analyzed, it will be seen that, if a pure inductive or a pure capacitive load is connected to an ac source, the source will be fully loaded while the active power delivered will be zero.

A practical load, however, absorbs both active power and reactive power. As illustrated in Fig. 3-10, the active power does the useful work. On the other hand, the reactive power only represents oscillating energy; however, it is required in many practical loads (for example, in inductive devices, an ac motor or a transformer absorb reactive power to produce the ac magnetic field).

Both the active and the reactive powers place a burden on the conductor (or on the transmission line). Nevertheless, the power company must provide the current to the load whether it is pure inductive or pure capacitive, and this current generates the power losses in the transmission lines. However, customers wish to pay only for the active power since it does the useful work, and the power company wishes to reduce the power losses in the transmission line.

Referring to the power triangle (Fig. 3-11), the hypotenuse *S* is a measure of the loading on the source, and the side *P* is a measure of the useful power delivered. Therefore, it is desirable to have the apparent power as close as possible to
the active power, which makes the power factor approach unity (1.0).

The process of making the power factor approach 1.0 (or below 1.0 but above the existing power factor) is known as power factor correction or power factor compensation.

In practice, power factor correction is performed simply by placing a capacitor or an inductor across the existing load, which itself may be an inductive or a capacitive load, respectively. Although a more complex solution may be employed to shape the nonsinusoidal input current of a load (which mainly occur due to the power electronics converters and arc furnaces in the system), and hence to improve the power factor, this concept will not be covered here.

During the power factor correction process, the voltage across the load remains the same and the active power does not change. However, the current and the apparent power drawn from the supply decrease. This means that the amount of decrease in supply current/power can be utilized somewhere else (may be used by additional loads) without increasing the capacity of the supply.

As an example (Fig. 3-13), if the existing powers and the power factor of a single-phase ac circuit are *P* = 1200 W, *Q* = 1600 *VAR*, *S* = 2000 *VA*, and PF = cos *θ* = 0.6 lagging, and if we wish to correct the power factor to 0.9 lagging, a capacitor must be added across the load. After
the correction is introduced, the active power remains unchanged but the apparent power delivered by the source is reduced
to 1333 *VA*, and the reactive power of the capacitor equals 1015 *VAR* leading, which can be used to determine the ratings of the capacitor for a given voltage and supply frequency.

**Figure 3-13. Representation of the power factor correction concept.**

#### 3.4.1 Virtual Instrument Panel

The front panel of `Power Factor Correction.vi` is given in Fig. 3-14. This VI provides a highly flexible virtual instrument to study the complex power definitions and the power factor correction
concept in single-phase ac circuits.

**Figure 3-14. Front panel and brief user guide of Single Phase Power and Power Factor Correction.vi.**

#### 3.4.2 Self-Study Questions

Although there can be many combinations of settings in the VI, the following studies are sufficient to understand the power
factor correction in single-phase ac circuits. Open and run the custom-written VI named `Single Phase Power and Power Factor Correction.vi` in the `Chapter 3` folder, and investigate the following questions.