Table of Contents

## Introduction to Power Factor

POWER FACTOR of any a.c.load is defined as the ratio of the useful power(also known as active power measured in kiloWatt) to the total power(also known as apparent power measured in kilo Volt-Amps) consumed by that particular load. Basically it is a measurement of how efficiently electrical power is converted into useful output work power. For any load, the ideal power factor is always unity. Any value less than unity mean that extra power is required to complete the particular task. As the power factor is poor or reduces, the effectiveness of usage of electric power reduces in the power system. The poor power factor or power factor reduction is caused by various reasons.

**Power Factor = Average Power (W) / r.m.s.volts X r.m.s. amps**

For a sinusoidal input voltage and a linear load, the current will also be sinusoidal, with a phase-shift of ϕ with respect to the voltage. The power factor is then given by the simple formula

**Power Factor =Vrms.Arms.Cosϕ**

**Here Vrms =Vpeak/√2**

**Irms =Ipeak/√2**

Where V and I are r.m.s. values of voltages and current calculated as above. And so, in this case, the** power factor is** **equal to cos ϕ**. Clearly the maximum possible power-factor is unity. So it can be defined as the cosine of the angle between voltage and current.

**How to Calculate the Power Factor**

As discussed above Power factor is measured as the energy efficiency use in an electrical circuit, and it ranges between 0 and 1. As there are different types of power used in a circuit, and the power factor is the ratio between them. Some of them are defined as follows.

**True power** is defined as the actual power used in the circuit. It is represented as P and measured in watts (W) or kilowatts (kW).

**Reactive power** is defined as the power, absorbed or generated by the circuit to maintain voltage. It usually occurs when the current and voltage are not in phase as the result of inductive or capacitive loads. It is represented as Q and measured in volt-amps reactive (VAR) or kilovolt-amps reactive (kVAR).

**Apparent power** Combining the true power and reactive power results in apparent power. It is represented as S and measured in volt-amps (VA) or kilovolt-amps (kVA).

For improving the power factor there are numerous power factor correction methods. The power factor correction using power factor correction capacitors is the best and efficient method of various power factor correction methods. But, primarily we must know what power factor calculation, and power factor correction.

## Power Factor Calculation

As discussed before that the efficiency of the power system depends on the power factor so that to improve the effective usage of power in an electrical system the power factor is to be improved. But, before that, we have to calculate the power factor of the system. The power factor can be calculated by using the angle between load current and supply voltages given in fig 1.

Fig 1.Angle between Supply Voltage and Load Current

The power factor lies in a fixed interval of -1 to +1. A Power triangle method can be used for the calculation of the power factor. Cosine of the angle between apparent power and active power gives a power factor. It is exactly the same as the angle between the load current and supply voltage.

Fig 2. Active Power and Apparent Power angle

From the figure 2anglebetween active power and apparent power inversely proportional to the cosine of this angle as this reduces, then the cos of this angle increases making the power factor almost unity. Actually unity power factor is practically not possible because the capacitive and inductive loads cause leading or lagging. To improve the power factor for effective use of electrical power there are various power factor correction techniques. First, we will discuss the power factor calculation by considering the power equation.

Here

**S-apparent power**

**Q-reactive power**

**P-active power.**

The power triangle formed by these powers is shown in fig 3

` Fig 3.Power Factor and Power Triangle`

**The real power** that is used for feeding loads is known as active power (P) and is given by the following equation.

**The apparent power** (S) measured in VA or KVA and it can be given as follows

**The reactive power** or energy stored in the power system is directly proportional to each other. It is measured in VAR or KVAR.

Now, **power factor** calculation can be given as

Where D termed as displacement and Power factor (PF) is also termed **displacement power factor (PDF)**.

The single-phase power factor calculation and three-phase power factor calculation can be given as shown below which are deducted from the single-phase and three-phase power calculation equations.

**Single-phase power factor is given as**

Single Phase Power Factor Calculation

Where Power-kW, Voltage-Volts, and Current-Amperes.

**Three-phase power factor derived from three-phase power calculation given by the following equation**

Three-Phase Power Factor Calculation (Line to Line Voltage)

Where Power-kW, Line to Line Voltage-Volts, and Current-Amperes.

Three-Phase Power Factor Calculation (Line to Neutral Voltage)

Where Power-kW, Line to Line Voltage-Volts, and Current-Amperes.

## Power Factor Correction

After calculating the power factor in any power system, it is check for its efficiency, if it is near to unity then it is said that system is doing effective use of power.but if the power factor calculation gives poor results, then the correction method is required to improve the system efficiency. There is the various reason such as inductive loads (induction motors, induction generators, high-intensity discharge lamps, and etc), due to which power factor is being affected. So, the power factor correction technic will improve voltage levels in the power system, minimize losses which will enhance system capacity, removes the power factor penalty, and reduces the demand of peak active power thereby reduces service charges. There are various technics for power factor correction (by reducing the angle between the supply voltage and load current, thereby increasing power factor value tends to unity) such as power factor correction using correction capacitors, filter, and active boost power factor correction.

## Power Factor Correction Capacitors

Fig 4.Power Factor Correction Capacitors

The power factor can be improved by using power factor correction capacitors. By using the capacitor property i.e., a leading power factor can diminish the effect on power factor by inductive loads. Because the inductive reactance of inductive loads can be canceled using the capacitive reactance of the power factor correction capacitors. There are different types of power factor correction capacitors such as ABB power factor correction capacitors, fixed power factor correction capacitors, and automatic power factor correction capacitors, which are normally used for power factor correction.