# Power Factor for Electrical Engineers

Power Generation, Transmission and Distribution

Almost at everywhere, the electrical energy is generated, transmitted and distributed in the form of alternating current or AC current. With the name of AC current, the question of power factor immediately comes into picture. Most of the loads (e.g. induction motors, arc lamps) are inductive in nature and hence have low lagging power factor. The low power factor is highly undesirable as it causes an increase in current, resulting in additional losses of active power in all the elements of power system from power station generator down to the utilization devices. In order to ensure most favorable conditions for a supply system from engineering and economic standpoint, it is important to have power factor as close to unity as possible. Therefore, we will discuss about power factor and various methods of power factor improvement.

Power Factor

Briefly, the cosine of angle between voltage and current in an AC circuit is known as power factor. You may surprised, angle between voltage and current ! How it is possible ? In fact, we know that the AC current is like the shape of sinusoidal wave. For that case, when we represent it with sinusoidal wave form, we notice some phase or angle difference between voltage and current. So in an AC circuit, there is generally a phase difference φ between voltage and current. The term cos φ is called the power factor of the circuit. If the circuit is inductive, the current lags behind the voltage and the power factor is referred to as lagging. However, in a capacitive circuit, current leads the voltage and power factor is said to be leading. Consider an inductive circuit taking a lagging current I from supply voltage V. The angle of lag being φ. The circuit current I can be resolved into two perpendicular components, namely ; AC Current and Voltage

1. I cos φ in phase with V

2. I sin φ 90o out of phase with V

The component I cos φ is known as active or wattful component, and component I sin φ is called the reactive or wattless component. The reactive component is a measure of the power factor. If the reactive component is small, the phase angle φ is small and hence power factor cos φ will be high. Therefore, a circuit having small reactive current will have high power factor and vice-versa. That is almost beside unity power factor. It may be noted that value of power factor can never be more than unity. It is a usual practice to attach the word ‘lagging’ or ‘leading’ with the numerical value of power factor to signify whether the current lags or leads the voltage. Thus if the circuit has a p.f. of 0·5 and the current lags the voltage, we generally write p.f. as 0·5 lagging. Sometimes power factor is expressed as a percentage. Thus 0·8 lagging power factor may be expressed as 80% lagging.

Power Triangle

The analysis of power factor can also be made in terms of power drawn by the AC circuit. Power Triangle

If each side of the current triangle OAB of the figure bellow is multiplied by voltage V, then we get the power triangle,

• OA = VI cos φ and represents the active power in watts or kW
• AB = VI sin φ and represents the reactive power in VAR or kVAR
• OB = VI and represents the apparent power in VA or kVA

Thus the power factor of a circuit may also be defined as the ratio of active power to the apparent power. This is a perfectly general definition and can be applied to all cases, whatever be the waveform. The lagging reactive power is responsible for the low power factor. It is clear from the power triangle that smaller the reactive power component, the higher is the power factor of the circuit. For leading currents, the power triangle becomes reversed. This fact provides a key to the power factor improvement. If a device taking leading reactive power (e.g. capacitor) is connected in parallel with the load, then the lagging reactive power of the load will be partly neutralized, thus improving the power factor of the load.

The reactive power is neither consumed in the circuit nor it does any useful work. It merely flows back and forth in both directions in the circuit. A wattmeter does not measure reactive power.

The power factor plays an importance role in AC circuits since power consumed depends upon this factor. It is clear from above that for fixed power and voltage, the load current is inversely proportional to the power factor. Lower the power factor, higher is the load current and vice-versa. A power factor less than unity results in the following disadvantages:

• Large kVA rating of equipment: It is clear that kVA rating of the equipment is inversely proportional to power factor. The smaller the power factor, the larger is the kVA rating. Therefore, at low power factor, the kVA rating of the equipment has to be made more, making the equipment larger and expensive.
• Greater conductor size: To transmit or distribute a fixed amount of power at constant voltage, the conductor will have to carry more current at low power factor. This necessitates large conductor size.
• Large copper losses: The large current at low power factor causes more I 2 R losses in all the elements of the supply system. This results in poor efficiency.
• Poor voltage regulation: The large current at low lagging power factor causes greater voltage drops in alternators, transformers, transmission lines and distributors. This results in the decreased voltage available at the supply end, thus impairing the performance of utilization devices. In order to keep the receiving end voltage within permissible limits, extra equipment is required.
• Reduced handling capacity of system: The lagging power factor reduces the handling capacity of all the elements of the system. It is because the reactive component of current prevents the full utilization of installed capacity.

Causes of Low Power Factor

From economic point of view, low power factor is undesirable. Normally, the power factor of the whole load on the supply system in lower than 0·8. The following are the causes of low power factor:

• Most of the AC motors are of induction type (1φ and 3φ induction motors) which have low lagging power factor. These motors work at a power factor which is extremely small on light load (0·2 to 0·3) and rises to 0·8 or 0·9 at full load.
• Arc lamps, electric discharge lamps and industrial heating furnaces operate at low lagging power factor.
• The load on the power system is varying; being high during morning and evening and low at other times. During low load period, supply voltage is increased which increases the magnetization current. This results in the decreased power factor.

Power Factor Improvement

The low power factor is mainly due to the fact that most of the power loads are inductive and, therefore, take lagging currents. In order to improve the power factor, some device taking leading power should be connected in parallel with the load. One of such devices can be a capacitor. The capacitor draws a leading current and partly or completely neutralizes the lagging reactive component of load current. This raises the power factor of the load. Normally, the power factor of the whole load on a large generating station is in the region of 0·8 to 0·9. However, sometimes it is lower and in such cases it is generally desirable to take special steps to improve the power factor. This can be achieved by the following equipment :

• Static capacitor.
• Synchronous condenser.

Static capacitor: The power factor can be improved by connecting capacitors in parallel with the equipment operating at lagging power factor. The capacitor or static capacitor draws a leading current and partly or completely neutralizes the lagging reactive component of load current. This raises the power factor of the load. For three-phase loads, the capacitors can be connected in delta or star. Static capacitors are invariably used for power factor improvement in factories.

• They have low losses.
• They require little maintenance as there are no rotating parts.
• They can be easily installed as they are light and require no foundation.
• They can work under ordinary atmospheric conditions.

• They have short service life ranging from 8 to 10 years.
• They are easily damaged if the voltage exceeds the rated value.
• Once the capacitors are damaged, their repair is uneconomical.

Synchronous condenser

A synchronous motor takes a leading current when over-excited and, therefore, behaves as a capacitor. An over-excited synchronous motor running on no load is known as synchronous condenser. When such a machine is connected in parallel with the supply, it takes a leading current which partly neutralizes the lagging reactive component of the load. Synchronous condensers are generally used at major bulk supply substations for power factor improvement.

• By varying the field excitation, the magnitude of current drawn by the motor can be changed by any amount. This helps in achieving stepless control of power factor.
• The motor windings have high thermal stability to short circuit currents.
• The faults can be removed easily.

• There are considerable losses in the motor.
• The maintenance cost is high.
• It produces noise.
• Except in sizes above 500 kVA, the cost is greater than that of static capacitors of the same rating.
• As a synchronous motor has not any self-starting torque, therefore, an auxiliary equipment has to be provided for this purpose.

Phase advancers are used to improve the power factor of induction motors. The low power factor of an induction motor is due to the fact that its stator winding draws exciting current which lags behind the supply voltage by 900 . If the exciting ampere turns can be provided from some other AC source, then the stator winding will be relieved of exciting current and the power factor of the motor can be improved. This job is accomplished by the phase advancer which is simply an AC exciter. The phase advancer is mounted on the same shaft as the main motor and is connected in the rotor circuit of the motor. It provides exciting ampere turns to the rotor circuit at slip frequency. By providing more ampere turns than required, the induction motor can be made to operate on leading power factor like an over-excited synchronous motor.

• As the exciting ampere turns are supplied at slip frequency, therefore, lagging kVAR drawn by the motor are considerably reduced.
• Phase advancer can be conveniently used where the use of synchronous motors is inadmissible.

• They are not economical for motors below 200 H.P

With these point of view, though power factor is unwanted, but it is necessary at sometimes. Or the reactive power is unwanted, but is it necessary. But large amount of reactive power is not accepted. To improve this, we can apply any method from these three according is application and following its advantage and disadvantage.

Edited By
Jeion Ahmed
B.Sc. in Electrical & Electronic Engineering (EEE)
Chittagong University of Engineering & Technology (CUET)

Reference