 # Introduction to AC Circuits

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This chapter is from the book

## 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.

 1: Set Voltage Amplitude = 339 V, Base Voltage = 339 V, Base Current = 10 A, the value of the impedance to Rload = 0 Ω, Xload = 10 Ω, and observe the waveforms of the voltage, the current, the power, and the power triangle. Then gradually increase the Desired Power Factor to the unity power factor 1.0, and observe the Power Triangle graph. What difference(s) have you noticed? 2: Consider the operating conditions in question 1, and determine the values of the active, the reactive, the apparent power, and the power factor of the load before and after the power factor is corrected. 3: Repeat questions 1 and 2 for new values of the load impedance: Rload = 10 Ω, Xload = −10 Ω. 4: Verify the results of questions 1, 2, and 3 analytically. 5: A single-phase ac motor draws a current of 40 A at a power factor of 0.7 lagging from a 400 V, 50 Hz supply. What value must a parallel capacitor have to raise the power factor to 0.9 lagging? Note that the motor's active power remains unchanged.