POWER FACTOR IMPROVEMENT

1. Introduction

Most utilization devices require two components of current:

1- The power-producing current or active current : is that
current which when converted by the equipment produces useful
work ( in the form of heat, light, or mechanical power).
The unit of measurement is the watt.

2- The magnetizing current also known as the reactive, or

wattless current : is the current required to produce the flux
necessary for the operation of electromagnetic devices ( core of a
transformer, air gap of an induction motor).
The unit of measurement is the var.

and the apparent power is measured by the multiplication of the

readings of the voltmeter and the ammeter.
2. Power Factor Fundamentals:
• Power Factors of loads are important factors in defining power quality and
voltage stability.

• A Load power factor defines the current flowing in lines and those being
produced from generators, voltage drops and losses in feeder, heating of
conductors, loading of switchyards, etc.

• They, thus, contribute to service continuity and power quality.

• Loads’ power factors also define the voltage magnitudes, which are
directly, related to the quantity and direction of reactive power flow
through the whole system.

• These terms are reflected in service continuity, and determine the power
quality for consumers.
2.1 Power Factor & Voltage and Current Waveforms:

• The useful power available from an AC circuit is

given by:
P = V I cos (1)

where
P is the power in watts,
V is the RMS voltage in volts,
I is the total RMS load drawn current in
amperes and
 is the phase angle between the voltage and the
current waveforms.
- In purely resistive AC electrical circuit, the voltage and the current
are in phase, as shown in fig. 1 (a), and the useful power available
from the circuit is maximized since the peaks of voltage and current
occur simultaneously.
- The power is the same as that consumed in a DC circuit having the
same values of voltage and current.

fig. 1 (a)
- When inductive loads are present in the system, the current tends to lag in time
behind the voltage, as seen in fig. 1(b).
- The amount of lag, or phase difference, is measured by the phase angle between
the two waves.
- Since V and I are no longer in phase, the useful power available from the circuit is
reduced from that with the pure resistive load drawing the same current magnitude
under the same voltage.
- The ratio of the useful power available from the inductive circuit to the maximum
useful power, consumed by a resistive load of the same current and voltage , is
called the power factor.
- The value of the power factor is the cosine of the phase angle difference .

fig. 1(b).
2.2 Inductive Loads:

• Inductive or (magnetic) devices are those, which contain coils, where the
current passing through the coil generates lines of flux of a magnetic
field.

• Without this magnetization, energy would not flow through the core of a
transformer, e.g., or across the air gap of a motor or through the choke of
a fluorescent lamp.

• Other examples of inductive loads include lighting chokes or ballasts,

solenoids, induction furnaces, and arc welders.

• Electronic devices forms inductive loads to the 50 Hz components and as

the current passes through these inductive loads, parts of the current is
used for magnetization.

• This gives rise to the phase lag in the current waveform, shown before.
- This results in another way to describe power factor .
- The total current is made up of a magnetizing current and a working
current in a vector sum with the phase angle .
- The power factor is the ratio of the working current to the total
current.
Having the voltage V in kV, the currents Im, Ia, I in amperes, these
relations can be written as:
• Total or apparent power in KVA: S = V I (2)

• Useful or real or active power in KW: P = V Ia (3)

• Reactive or magnetizing power in KVAR: Q= V Im (4)

• Total or apparent power in KVA: S  P2  Q2 (5)

P P
• Power factor : pf  S   cos  (6)
P Q
2 2

• Useful or real or active power = P  S cos   S  pf (7)

• Reactive or magnetizing power = Q  S sin   P tan  (8)

Table (1) gives the power and reactive power delivered from a device rated 100 KVA at
various power factors, as well as the required reactive power and the apparent power for a
load consuming 100 KW useful power at various power factors.
Table 1 Power, reactive power and apparent power at various power factors, for
P=100KW and for S=100KVA
Load Power P = 100 KW S = 100 KVA
Factor
Q(KVAR) S(KVA) P (KW) Q (KVAR)
0 — — 0.0 100.0
0.1 995.0 1000.0 10.0 99.50
0.2 489.90 500.0 20.0 97.98
0.3 317.98 333.3 30.0 95.39
0.4 229.13 250.0 40.0 91.65
0.5 173.20 200.0 50.0 86.60
0.6 133.33 166.7 60.0 80.00
0.707 100.03 141.4 70.7 70.72
0.8 75.00 125.0 80.0 60.00
0.9 48.43 111.1 90.0 43.59
1.0 0.0 100.0 100.0 0.0
Other useful equations include:
• To calculate capacitance from capacitor kVAr rating
C = (kVAr. 109) / (2 f V2)
where C : capacitance in microfarads (F), f : supply
frequency (Hz), V: the line voltage (v)
• To calculate capacitor line current
Single-phase:
Ic = (kVAr. 103) / V
where Ic : line current (A), V : line voltage (v)
Three-phase:
Ic = (kVAr. 103) / (3 V)
where Ic : line current (A), V : line voltage (V)
2.3 Leading and Lagging Power Factor:

• A load is said to have a leading power factor if the

direction of the flow of the KVARs is away from the
load, and a lagging power factor if the direction of the
KVAR flow is towards the load.

• Inductive Loads require KVAR flow towards the load for

magnetization causing a lagging power factor.

• Since the inductive loads are the most common , most

plants power factors are lagging .
2.3 Leading and Lagging Power Factor:
• A lagging power factor is also called "inductive".

• A leading power factor situation could only occur if the

loads were generating KVAR .

• An example could be overexcited synchronous motors or

overcompensated capacitors or excessive cables or with
long over head lines at light loads.

• A leading power factor is also termed "Capacitive".

3. Causes of Low Power Factors & Improvement Opportunities:

• Industrial end-users usually account for most of the power factor

improvement opportunities.

• In general, industrial loads represent between one-third and two-

thirds of the total power consumption.

• In Egypt, industrial consumption is about 50% of the total power

consumption.

• Motors typically account for two-thirds to three-quarters of the

industrial power demand.

• The majority of these industrial motors are AC motors of the

induction type which are characterized by low power factors when
unloaded or lightly loaded as shown in Fig. 3.
Fig. 3 Induction motor power factor at different
loadings
• Low power factor in a plant or facility is attributed to the
presence of a large number of inductive loads, which
contain magnetic circuit or coil and forms the majority of
all known loads.

• Transformers are inductive loads even if they are

unloaded, due to their magnetic circuits.

• Low power factors arise when a plant operates at low

loads.

• Since the magnetizing current which is always necessary,

becomes a greater proportion of the total current.

• The situation is aggravated when loading is further

lowered.
Very common cause of low power factor in a plant are
under loaded motors.
• As shown in fig. (3) , the power factor of an induction
motor decrease rapidly as the mechanical load
decreases.

• Motors suffer from low power factors when working

with light mechanical loads.

• The specified designed power factors are found near full

load condition.

• Motors should be maintained at full load if possible, or

power factor compensation should be installed.
4. Typical Power Factors of Some Industries & Plants :

• Loads may be classified into four main categories:

1. Lighting Lamps (incandescent, fluorescent, mercury vapor,

sodium vapor halogen, low power lamps ),

2. Rotating Motors ( induction motors, linear motors, synchronous

motors, repulsion motors, Single phase commutating
motors…..etc),

3. Heaters ( induction furnaces, microwave ovens, filament

heaters) and

4. Special loads ( arc furnaces, welders, aluminum smelter plants,

soda reduction plants, water analysis plants).
 Table 2 Power factors of some common loads

Load Name Average P.F Load Name Average P.F

filament lamps 1.0 Microwave Ovens 0.7

Fluorescent lamps 0.55 Arc furnaces 0.7 to 0.8

Mercury vapor lamps 0.39 Welders 0.3

Sodium vapor lamps 0.58 Aluminum smelter plants 0.88 to 0.92

Halogens lamps 0.98 Metal coating plants 0.7

Low power lamps 0.8 Soda reduction plants 0.75

Rotating motors 0.6 to 0.8 Water analysis plants 0.8

Filament Heaters 1.0 Unloaded transformer 0.3

Induction furnaces 0.2 to 0.4 Solenoid 0.4

5. Annual Power Factor Penalty:
• An important element of the electricity tariff structure is the cost of
the power factor penalty imposed by the electricity distribution
companies.

• This penalty is applied when the measured power factor is less than
0.9 (in Egypt) and 0.86 (in USA and Europe).

• It is based on the Kilowatt – hour consumption and the average cost

per kilowatt- hour.

• Low power factor can be easily increased to 0.9 or above thus,

eliminating the annual power factor penalty charge.

• In Egypt, the power factor penalty depends on how much the

measured power factor is below 0.9.
• When the power factor is less than 0.9 but higher than 0.6 the
penalty is computed according to the following formula:

Penalty = 0.5x(0.9 – pf)( Yearly KWh)(Average LE per KWh) (9)

• When the power factor is equal to or less than 0.6 but greater than
0.4 the penalty is effectively doubled and computed according to
the following formula:

Penalty = (0.9 – pf)( Yearly KWh)(Average LE per KWh) (10)

• When the power factor is 0.4 or less, the Egyptian electricity

distribution authority refuse to provide electric service to the
consumer.

• Other systems are adopted in USA and Europe and other countries.
6. Low Power Factor Effects:

• Low power Factor has several negative consequences,

which reduce the efficiency and power quality and cost
effectiveness of operating a plant or a facility.

• The most important is the tariff penalty for low power

factor, but other unfavorable or harmful effects will be
introduced into the system itself , such as excessive
voltage drops, excessive currents and losses, more
conductors cross- sections and less available power to
consumers.
7. Benefits of Power Factor Improvement:

Benefits of power factor improvement can be

summarized in the following:
7.1 Elimination of Power Factor Penalty:

• According to the tariff structure in Egypt , large commercial and

industrial consumers are penalized by additional charges on their
electricity bills if the average power factor is less than 0.9 (0.86 in
Europe).

• Penalty can reach considerable amounts of KWhr's with large

industrial firms.
• When there are no wattmeters and VAR meters,
or power factor meters, the utility power factor
may be determined by the reading of the KWh
and KVARh meters.
• An average power factor is then calculated as
follows:
kWh
Average power factor 
(kWh) 2  (kVARh) 2

The improvement of power factor such that the yearly average

exceeds 0.9 will provide savings equivalent to the penalty
on the next electricity bill.
7.2 Reduction of Distribution System Currents:

• A load or a plant consuming power P and reactive power Q under voltage V,

draws a current I given by:

2 2
 P Q
I      (12)
V  V 
• Therefore, low power factor or large amount of reactive power Q will lead to
more drawn current.

• Decreasing Q in the distribution network by improving the load power

factor, will lead to less drawn electric current.

• At unity power factor (or Q = 0), the minimum current consumption will be
reached.

• Excessive current at low power factors require more conductor cross –

sections and lead to more energy losses, and more expenses.
7.3 Reduction of Distribution System losses :

• Low power factor leads to heavy current flowing through

conductors and causes increase in electrical distribution system (
I2R) losses.

• While these losses are small in typical plants ( 2.5-7%), the effect
is much more important and pronounced on national transmission
and distribution networks.

• Losses due to current flowing through conductors are proportional

to the square of the current.

• Since at lower power factor, the total current increases to maintain

a given real power requirement, the distribution losses will increase
as the square of the current increases.
• The losses relation of a load having power P and reactive power Q
and working under voltage V draw a current I through feeders of
resistance R, can be calculated by:

Ploss  RI 2 (13)
2 2
P Q
Ploss  R   R  (14)
V  V 
• Once more, low power factor means high Q flow in distribution
system and the second term is function in the square of Q.
Improving power factor means less Q and less losses.

• The minimum losses occur when Q vanishes at unity power factor

(Q = 0) the reduction in loss is given by:

  Original power factor 
2


% Loss Reduction  1 -     100 (15)

 
Improved power fctor  

7.4 Reduction in Cross Sections of Feeders and Cables:

• Lines or cables cross–sections depend on the flowing current and the

conductor material current density. Having a cable of cross section a1
designed for a load current I1 ,,its current density is i ( A/ mm2 ), then:
I1
a1  (16)
i
• If the power factor is improved to higher value, the load current drops to a
new lower value I2 & required conductor's x–section a2 .

• Using the same conductor material, the new conductor cross section as a
percentage of the original value is given by:
 I2 
a 2  a1   (17)
 I1 
• The reduction in conductors cross section, for the same active power when
power factors are pf1, pf2 is given by:

  Original power factor 
2


% Reduction in feeder cross - section  1 -     100
(18)

 
Improved power fctor  

7.5 Release of System Capacity ( more capacity to Other
Customers):

• System or apparatus or feeders or bus bars or cables or generators or

transformers capacity are defined in KVA or in MVA. The useful
power P provided by these apparatus, when its reactive power is Q, is
given by:

P  kVA  Q
2 2

(19)

•Therefore, at low power factors Q increases and the useful available power
decreases, this was shown earlier in Table (1).
•Improving the power factor decrease the transit Q and increases the
available useful power for other consumers and save the investment required
to feed those consumers
.
• Also, low power factor reduces the capacity of electrical
system, since the system must carry the total current, but
only the active current provides useful power.

• E.g., a transformer bank rated at 1000KVA can only

provide 80 kW of power if the power factor is 0.8.

• If the power factors were improved to 0.9, 900 KW of

power can be provided in this case, by improving the
power factor from 0.8 to 0.9 an additional 100 KW
become available for other consumers.
7.6 Lower voltage drops at Network Nodes:

• Normally, loads are fed from feeding points through feeders or

short transmission lines, which allow in most cases to consider
that the feeding point is an infinite bus with respect to the load
node voltage Vr.

• Having a load consuming useful power P and reactive power Q

through a feeder, of resistance R and reactance X, when the
source voltage is Vs, then the voltage drop is approximately:

XQ  RP
V  Vs  Vr  (20)
Vr
•As P is imposed by the consumer and the feeder is already installed
with its resistance R and reactance X defined , also Vs is assumed to
be constant by control action, the load voltage Vr is the variable with
the variations of the node received reactive power Q.

•Therefore, voltage drops on lines or feeders increase with low

power factor loads or at higher loads reactive power.

•Improvement of power factors means less Q on lines and

consequently less voltage drops.

•The minimum voltage drops occur when power factors become

unity which imply no reactive power transit on lines and voltage
magnitude are all equal.
7.7 Lower Capital Costs for New systems:

• At lower power factor, system capacity for providing power to

consumers decreases.

• Moreover, when installing a system with low power factor,

additional investment in larger conductors, higher KVA rated
transformers, larger bus bar cross- sections, over rated protection
devices and relays, additional switchgears, control of higher
currents, and over rated generators, for the same required useful
power, are needed.
8. Power Factor Correction

• low power factor should be corrected to higher values.

• The lagging power factor occurs as a result of KVAR

flow toward the inductive loads or induction machines.

• To improve power factor, this KVAR flow must be

reduced.

• If some of these KVARs flow can be provided locally at

the load terminals by a separate capacitive reactive power
source ( such as a capacitor), then the inductive load or
device will no longer need reactive power from the
feeding system.
• The net reactive power at the feeding bus bar is reduced
and the power factor is then improved.

• When the net reactive power is zero, the power factor

reaches unity.

• In this case, all the necessary KVAR flow is provided

locally.

• The most common and effective source of this KVAR

flow is the capacitor, which stores negatively charged ions
and compensates for their loss in a system that requires
magnetizing current.

• If applied properly and controlled, capacitors can

significantly improve the performance of distribution
circuits.
• But if not properly applied or controlled, the reactive
power from capacitor banks can create losses and high
voltages.

• The greatest danger of overvoltages occurs under light

load.

• Good planning helps ensure that capacitors are sited

properly.
• Capacitors work their magic by storing energy.

• Capacitors are simple devices: two metal plates

sandwiched around an insulating dielectric.

• When charged to a given voltage, opposing charges fill the

plates on either side of the dielectric.

• The strong attraction of the charges across the very short

distance separating them makes a tank of energy.

• Capacitors oppose changes in voltage; it takes time to fill

up the plates with charge, and once charged, it takes time
to discharge the voltage.
• On ac power systems, capacitors do not store their energy
very long just one-half cycle.

• Each half cycle, a capacitor charges up and then

discharges its stored energy back into the system.

• The net real power transfer is zero.

• Capacitors provide power just when reactive loads need it.

• Just when a motor with low power factor needs power

from the system, the capacitor is there to provide it.

• Then in the next half cycle, the motor releases its excess
energy, and the capacitor is there to absorb it.
• Capacitors and reactive loads exchange this reactive
power back and forth.

• This benefits the system because that reactive power (and

extra current) does not have to be transmitted from the
generators all the way through many transformers and
many miles of lines; the capacitors can provide the
reactive power locally.

• This frees up the lines to carry real power, power that

actually does work.

• Capacitor units are made of series and parallel

combinations of capacitor packs or elements put together
as shown in Figure (3.8).
Figure (3.9) Overhead line capacitor installation
Figure (3.10) Example padmounted capacitor
• This compensation is depicted graphically in fig. (4) in the first
case of the load power factor cos 1 is low with high KVA and
reactive current. Its useful power is P and reactive power is Q1.

• By installing capacitors of rating Qc the reactive component is

reduced to Q2 KVAR and the current is also reduced, the useful
power P does not change.

• The capacitor rating Qc represents the difference (Q1- Q2) .

• Figure (4) shows a phasor diagram of the reactive power triangle

when capacitor for power factor correction, is applied.
• For single-phase loads, this capacitor is shunted directly at the
load terminals.

• For induction motor load with star / delta starter switch, the
correct compensation by shunt capacitors, either fixed or
controlled, is shown in fig. (5)

• For other loads, correcting power factors capacitors are

connected at load nodes or at bus- bars, on star or delta
connections.

• They are usually symmetrical for the three phases and can be used
as elements of the harmonic filters ( fig. 5a).
9. Calculation of the capacitors Rating:

• Capacitor units rated from 50 to over 500 kvar are available; Table
3.5 shows common capacitor unit ratings.

• A capacitor’s rated kvar is the kvar at rated voltage.

• Three-phase capacitor banks are normally referred to by the total

kvar on all three phases.

• Distribution feeder banks normally have one or two or (more

rarely) three units per phase.

• Many common size banks only have one capacitor unit per phase.
Table (3.5) Common capacitor unit ratings
• Capacitors must have an internal resistor that discharges a capacitor
to 50 V or less within 5 min when the capacitor is charged to the
peak of its rated voltage.

• This resistor is the major component of losses within a capacitor.

• The resistor must be low enough such that the RC time constant
causes it to decay in 300 sec.

• Some utilities use a shorting bar across the terminals of capacitors

during shipping and in storage.

• The standard recommends waiting for 5 min to allow the capacitor

to discharge through the internal resistor.

• Capacitors have very low losses, so they run very cool.

• The existing power factor: for the plant or load under question measured
at different loading. Alternately, for a conservative sizing of capacitors,
the lowest power factor over the previous year’s bill can be used.

• The desired power factor: In Egypt where the electricity tariff’s specify a
power factor penalty if the power factor is less than 0.9, the most
economical degree of correction occur is found when the final power
factor is less than 0.9 ( or 0.86 in Europe)

• For safety margin, 0.92-0.95 may be used as the design basic,

alternately, the calculation may be based on a large load. Figure 4 shows
a typical required reactive power Qc with pf correction from cos 1 to
cos 2. The load power is P(KW), through the power triangle.
• Using these information, and regarding the power triangle fig.(4),
the capacitor rating Qc in KVARs required for power factor
correction of a certain load from initial power factor pf1= cos(1) to
a new high power factor pf2= cos(2) for the load
having power P in KW, is given by the formula:

Qc = P ( tan 1 – tan 2) = P Δ tan ( 21)

• The term between brackets represents the ratio of capacitor KVAR/

load KW is called the correction factor.

• It is tabulated in tables such that in table (3) to avoid complications

of calculating tangents of angles.