Engineering Economics and Management

• Power Factor
✓ Introduction and definition of power factor
✓ Power triangle
✓ Examples

Engr. Shoaib Ahmed Shaikh

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 Introduction
• The electrical energy is almost exclusively generated, transmitted and distributed in the form
of alternating current. Therefore, 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
economical standpoint, it is important to have power factor as close to unity as possible.

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 Power factor
“The cosine of angle between voltage and current in an a.c. circuit is known as power factor”.
• In an a.c. 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 phasor diagram of
the circuit is shown in Figure. The circuit
current I can be resolved into two
perpendicular components, namely ;
a. I cos φ in phase with V
b. I sin φ 90degree out of phase with V

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 Power factor
• The component I cos φ is known as active or wattful component, whereas component I sin φ is
called the reactive or wattles 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 (i.e., I sin φ) will have high power factor and
vice-versa. It may be noted that value of power factor can never be more than unity.

1. 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.

2. Sometimes power factor is expressed as a percentage. Thus 0·8 lagging power factor may be
expressed as 80% lagging.

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 Power Triangle
• The analysis of power factor can also be made in terms of power drawn by the a.c. circuit. If
each side of the current triangle oab of previous Figure-01 is multiplied by voltage V, then we
get the power triangle OAB shown in Figure-02 where;

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
(i) The apparent power in an a.c. circuit has two components viz., active and reactive power at
right angles to each other.

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 Cont.

*If the current lags behind the voltage, the reactive power drawn is known as lagging reactive
power. However, if the circuit current leads the voltage, the reactive power is known as leading
reactive power.

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 Cont.

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 Cont.
Illustration:

• Let us illustrate the power relations in an a.c. circuit with an example. Suppose a circuit draws
a current of 10 A at a voltage of 200 V and its p.f. is 0·8 lagging. Then,

• The circuit receives an apparent power of 2000 VA and is able to convert only 1600 watts into
active power.
• The reactive power is 1200 VAR and does no useful work. It merely flows into and out of the
circuit periodically.
• In fact, reactive power is a liability on the source because the source has to supply the
additional current (i.e., I sinФ).

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 Disadvantages of low power 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 :
(i) Large kVA rating of equipment.
• The electrical machinery (e.g., alternators, transformers, switchgear) is always rated in kVA.
Now,
kVA = kW/cos φ
• 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.
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 Disadvantages of low power factor
(ii) 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.
• For example, take the case of a single phase a.c. motor having an input of 10 kW on full load,
the terminal voltage being 250 V. At unity p.f., the input full load current would be 10,000/250
= 40 A.
• At 0·8 p.f; the kVA input would be 10/0·8 = 12·5 and the current input 12,500/250 = 50 A.
• If the motor is worked at a low power factor of 0·8, the cross-sectional area of the supply
cables and motor conductors would have to be based upon a current of 50 A instead of 40 A
which would be required at unity power factor.

(iii) Large copper losses.

• The large current at low power factor causes more I^2R losses in all the elements of the supply
system. This results in poor efficiency.

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 Disadvantages of low power factor
(iv) 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 (i.e., voltage regulators) is required.

(v) 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.
• The above discussion leads to the conclusion that low power factor is an objectionable feature
in the supply system

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 Causes of Low Power Factor
• Low power factor is undesirable from economic point of view. 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:

1. Most of the a.c. 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.
2. Arc lamps, electric discharge lamps and industrial heating furnaces operate at low lagging
power factor.
3. 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.

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 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.

Illustration.
• To illustrate the power factor improvement by a capacitor, consider a single-phase load taking
lagging current I at a power factor cos Ф1 as shown in Figure.
• The capacitor C is connected in parallel with the load. The capacitor draws current IC which
leads the supply voltage by 90degree. The resulting line current I’ is the phasor sum of I and IC
and its angle of lag is Ф2 as shown in the phasor diagram of Figure(iii). It is clear that Ф2 is less
than Ф1, so that cos Ф2 is greater than cos Ф1. Hence, the power factor of the load is improved.

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 Power Factor Improvement Methods
• 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 :

1. Static capacitors.
2. Synchronous condenser.
3. Phase advancers.

1. Static capacitor:
• The power factor can be improved by connecting capacitors in parallel with the equipment
operating at lagging power factor. The capacitor (generally known as 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 as shown in Fig. 6.4. Static capacitors are invariably used for power
factor improvement in factories.

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 Cont.

Advantages:
1. They have low losses.
2. They require little maintenance as there are no rotating parts.
3. They can be easily installed as they are light and require no foundation.
4. They can work under ordinary atmospheric conditions.

Disadvantages:
1. They have short service life ranging from 8 to 10 years.
2. They are easily damaged if the voltage exceeds the rated value.
3. Once the capacitors are damaged, their repair is uneconomical
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 Cont.
2. 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. Thus the power
factor is improved.

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 Cont.
Advantages:
1. 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.
2. The motor windings have high thermal stability to short circuit currents.
3. The faults can be removed easily.
Disadvantages:
1. There are considerable losses in the motor.
2. The maintenance cost is high.
3. It produces noise.
4. Except in sizes above 500 kVA, the cost is greater than that of static capacitors of the same
rating.
5. As a synchronous motor has no self-starting torque, therefore, an auxiliary equipment has to
be provided for this purpose.
Note:
The reactive power taken by a synchronous motor depends upon two factors, the d.c field
excitation and the mechanical load delivered by the motor. Maximum leading power is taken by a
synchronous motor with maximum excitation and zero load.

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 Cont.
3. Phase advancers.
• 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 90o.
• If the exciting ampere turns can be provided from some other a.c. 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 a.c. 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.
Advantages:
1. Firstly, as the exciting ampere turns are supplied at slip frequency, therefore, lagging kVAR
drawn by the motor are considerably reduced.
2. Secondly, phase advancer can be conveniently used where the use of synchronous motors is
inadmissible.
Disadvantages:
1. The major disadvantage of phase advancers is that they are not economical for motors below
200 H.P.
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 Importance of Power Factor Improvement
The improvement of power factor is very important for both consumers and generating stations as
discussed below :
(i) For consumers.
• A consumer* has to pay electricity charges for his maximum demand in kVA plus the units
consumed. If the consumer improves the power factor, then there is a reduction† in his maximum
kVA demand and consequently there will be annual saving due to maximum demand charges.
Although power factor improvement involves extra annual expenditure on account of p.f. correction
equipment, yet improvement of p.f. to a proper value results in the net annual saving for the
consumer.
(ii) For generating stations.
• A generating station is as much concerned with power factor improvement as the consumer. The
generators in a power station are rated in kVA but the useful output depends upon kW output. As
station output is kW = kVA × cos φ, therefore, number of units supplied by it depends upon the
power factor.
• The greater the power factor of the generating station, the higher is the kWh it delivers to the
system. This leads to the conclusion that improved power factor increases the earning capacity of
the power station.

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 Most Economical Power Factor
• If a consumer improves the power factor, there is reduction in his maximum kVA demand and
hence there will be annual saving over the maximum demand charges.

• However, when power factor is improved, it involves capital investment on the power factor
correction equipment.

• The consumer will incur expenditure every year in the shape of annual interest and
depreciation on the investment made over the p.f. correction equipment. Therefore, the net
annual saving will be equal to the annual saving in maximum demand charges minus annual
expenditure incurred on p.f. correction equipment.

“The value to which the power factor should be improved so as to have maximum net annual
saving is known as the most economical power factor”.

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Examples
Examples
 SELF TEST
1. Fill in the blanks by inserting appropriate words/figures.
1. The power factor of an a.c. circuit is given by ............... power divided by ............... power.
2. The lagging power factor is due to ............... power drawn by the circuit.
3. Power factor can be improved by installing such a device in parallel with load which takes
........... .
4. The major reason for low lagging power factor of supply system is due to the use of ...............
motors.
5. An over-excited synchronous motor on no load is known as ...............

2. Pick up the correct words/figures from the brackets and fill in the blanks.
1. The smaller the lagging reactive power drawn by a circuit. the ............... is its power factor.
(smaller, greater)
2. The maximum value of power factor can be ............... (1, 0·5, 0·9)
3. KVAR = ............... tan φ (kW, KVA)
4. By improving the power factor of the system, the kilowatts delivered by the generating station
are............... (decreased, increased, not changed)
5. The most economical power factor for a consumer is generally ...............(0·95 lagging, unity,
0·6 lagging)

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 ANSWERS TO SELF TEST
1.
(i) active, apparent,
(ii) lagging reactive
(iii) leading reactive power,
(iv) induction
(v) Synchronous condenser.
2.
(i) greater,
(ii) 1,
(iii) kW,
(iv) increased,
(v) 0·95 lagging.

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References:
Book: Principles of Power system By VK Mehta +Notes
Thank You