Power Factor: Calculation, Types and Correction

Power factor of an electrical system is a measurement of how efficiently incoming power is used. A high power factor shows that the power is consumed effectively by the electrical system with minimum power loss. A system with a low power factor wastes energy by inefficiently consuming the incoming power supply. DC circuits have no power factor since their frequency is zero. However, in AC circuits, the power factor is always between 0 and 1. For AC circuits, power factor is the cosine of the phase difference between voltage and current.

The formula for power factor is,

Power Factor = Cos \(\theta\) = \(\frac{Active Power (W)}{Apparent Power(VA)}\)

Key Terms: DC Circuit, AC Circuit, Real Power, Reactive Power, Apparent Power, Unity Power, Capacitive Circuits, Inductive Circuits, Electric Circuit

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What is Power Factor?

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Power factor (PF) of an AC electrical power system is defined as the ratio of working power (measured in kW) absorbed by the load to perceived power (measured in kilovolt amperes, kVA) passing through the electrical circuit. A power factor is a one-dimensional number in the range of -1 to 1.

• One (sometimes known as "unity") is the "ideal" power factor. This occurs when the circuit has no reactive power and hence apparent power (kVA) equals real power (kW). The most efficient loading of the supply is a load with a power factor of one.
• Power factor having value less than one indicates that the voltage and the current are not in phase. 
• When the load generates the real power which flows back to the source, the value of power factor comes negative. 

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How is Power Factor Calculated?

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A power quality analyzer or power analyzer that measures both working power (kW) and apparent power (kVA) and is required to calculate the power factor.

The power factor formula can be written as, 

PF = (True power) / (Apparent power)

Or

PF = W / VA

Here, watts is used to measure the power used by the system and VA measures the power supplied. The ratio of these two powers gives the power factor for an electrical circuit. 

Power factor relates the real power spent to the apparent power, or demand, of the load. Real power is the amount of power accessible to do work. By adjusting for power factor, power factor penalties can be avoided. A load having low power factor draws more current for the same power supplied than the one with high power factor. The flowing of more current increases the loss of energy in the system. Power factor correction increases the power factor of the system, preventing the loss of energy. 

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Types of Power Factor

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In a circuit, the power factor can be leading, lagging or unity depending upon the type of circuit.

Leading Power Factor

A leading power factor is observed when the current in the circuit leads the voltage. This occurs in a purely capacitive circuits. In leading power factor, the phase angle between current and voltage is positive. The value of leading power factor is from -1 to 0. 

Lagging Power Factor

When the current in a circuit is lagging behind the voltage, then the power factor is called lagging power factor. This happens in a purely inductive circuit. In this, the phase angle between the current and the voltage is negative. The value of lagging power factor is from 0 to 1. 

Unity Power Factor

When the current and the voltage are in phase then the power factor is unity. A unity power factor is seen in ideal circuits only. A circuit with unity power factor do not use any reactive power. It has a value of one. 

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Significance of Power Factor

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Significance of power factor stems from the fact that utility companies provide customers with volt-ampere yet charge them in watts.

Watt = Volt × Ampere × Power Factor

A power factor of less than 1.0 necessitates the utility generating more than the minimum volt-ampere required to deliver the power (watts). This raises the cost of generation and transmission. A good power factor is larger than 0.85 or 85 percent.

What Causes Low Power Factor?

Inductive load is the primary reason for low power factor. As in a purely inductive circuit, current lags behind voltage by 90 degrees, resulting in zero power factor due to the significant phase angle difference between current and voltage. Power factor exists in all circuits with capacitance and inductance except resonance circuits or tune circuits where inductive reactance is equal to capacitive reactance (X_L = X_C), making the circuit a resistive circuit). 

Power factor is defined as the ratio of KW to KVA, so when KW is small in comparison to KVA, it results in a low power factor. Large KVA is caused by inductive loads in systems such as-

• Transformer
• Induction motor
• Induction generator (windmill generators)
• High-intensity discharge lighting

These inductive loads account for a significant amount of the power used in industry. The quantity of apparent power (KVA) in the distribution system is increased by the reactive power (KVAR) required by the inductive load. As the reactive and perceived power levels rise, the angle widens, and the cosine (or power factor) increases.

Effects of Low Power Factor

Some major consequences of low power factor are given below: 

• Larger Load Current – The current flowing across a line is inversely proportional to the power factor for a given power and voltage. Thus, a low power factor will result in a larger load current and, as a result, increased losses.
• High Copper Losses – When the power factor is low, line current is high. The line current is directly proportional to the copper losses. So, a low power factor results in higher copper losses. 
• High kVA Rating – Machines like transformers are rated in kVA. kVA is inversely proportional to the power factor. A high kVA rating increases the cost of the equipment. 

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Methods of Power Factor Correction

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There are three primary methods for increasing power factor:

Capacitor Banks

Reducing the phase gap between voltage and current is one way to improve the power factor. Capacitor banks help to close the phase gap between voltage and current. Power factor, in a three-phase system, can be corrected by connecting capacitors in star or delta connection. 

Consider, V_L = Line Voltage

V_P = Phase Voltage

C_y = Capacitance per phase in star connection

C_{\(\triangle\)} = Capacitance per phase in delta connection 

Q_C = V_ar rating of each phase

Delta Connection: 

In delta connection, V_P = V_L 

Capacitance per phase, C_{\(\triangle\)} = \(\frac{Q_c}{wV_{p}^{2}}\)

C_{\(\triangle\)} = \(\frac{Q_c}{wV_{L}^{2}}\)   (eq. 1)

Star Connection: 

V_P = 1/3 V_L

Capacitance per phase, C_Y = \(\frac{Q_c}{wV_{p}^{2}}\)

C_Y = \(\frac{Q_c}{w(\frac{V_{L}}{\sqrt3})^{2}}\)

C_Y = \(\frac{3Q_{C}}{w(V_{L})^{2}}\) (eq. 2)

From eq. 1 and 2, we get

C_Y = 3C_{\(\triangle\)}

This means, capacitance required in a star connection is 3 times capacitance required in delta connection. Hence, in a three-phase system, capacitors are connected in delta for improving power factor. 

Synchronous Condensers

Synchronous condensers are three-phase synchronous motors that have no load on their shaft. The synchronous motor can operate with any power factor, including leading, lagging, and unity, depending on the excitation.

• A synchronous condenser is attached to the load side and is overexcited for inductive loads.
• It acts as a capacitor due to synchronous condensers.
• It either pulls trailing current from the power source or provides reactive power.

Phase Advancers

Phase advancer is an AC exciter that is mostly used to increase the PF of induction motors. They are connected to the rotor circuit of the motor and are installed on the shaft of the motor.

• It raises the power factor by supplying the exciting ampere-turns required to generate the requisite flux at the specified slip frequency.
• It can also be made to function at the leading power factor by increasing ampere-turns.

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Things To Remember

• Power factor is the ratio of real power to the apparent power of a system. 
• The existence of harmonic current lowers the system's power factor.
• An imbalance in the 3-phase electricity develops as a result of poor wiring or electrical mishaps, resulting in a low power factor.
• Induction motors account for 90% of all industrial loads. Such machines draw magnetizing current and create a magnetic field to function properly, and so have a low power factor.
• The machine's kVA rating is inversely related to its power factor.

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