As we explained before in article “Power Factor Correction Capacitors Sizing Calculations – Part Eleven”, how
to calculate the capacitor KVAR rating for compensation at:
 Transformers,
 Individual motors.
Today, we will explain
how to calculate the capacitor KVAR rating for buildings and power plants
(group compensation).
Calculation Of The Capacitor KVAR
Rating For Buildings And Power Plants

To calculate the capacitor
KVAR rating for buildings and power plants (group compensation), we have (2)
methods:

Method#1: By Using Measuring Devices
This method is used when the old P.F is unknown and there
different methods to measure/calculate this old PF and then calculate the
Capacitor KVAR Rating. These measuring methods are:

Direct
Method: Measurement Of Current And Power Factor
P = √3*V*I*cos
Ø*10^{3} [kW]
After
this, we have (3) options:
1
Calculation by using equation
If
the desired power factor cos Ø was specified, the capacitor power rating can be
calculated from the following formula.
QC = P · (tan Ø1  tan Ø2) in KVAR
2 Calculation
by using Tables published by leading power factor capacitor manufacturers
QC = k.P
For more information about measuring the power
factor, please review our article “Power Factor Correction Capacitors Sizing Calculations – Part Six”.
Table1
Note:
Example#1:
Measured readings in one project are as follows:
Apparent
current: 248 A
Power
factor cos Ø1: 0.86
Desired
cos Ø2: 0.92
Voltage
: 397 V
Calculate
the KVAR rating for the power factor correction capacitors.
Solution:
P = √3*V*I*cos Ø*10^{3} [kW]
P = √3 * 397 * 248 * 0.86 · 10^{3} = 146.6 kW
By using equation:
QC = P* (tan Ø1 
tan Ø2) =
146.6 x (0.59 – 0.43) = 23.456 KVAR
By using Table1 we obtain:
Factor k = 0.17
Required capacitor rating:
QC = 146.6 * 0.17 = 24.9 KVAR
3 Calculation
By Using Nomographs
The Nomograph
shown
in figure1 is used to calculate the capacitor KVAR rating as follows:
Fig.1
Example#2:
An
80 KW load with power factor 0.64, calculate the required KVAR capacitor
rating to get a 0.9 PF by using the nomograph method.
Solution:
First,
trace a line segment from the value of the load 80 KW to the initial cosØ = 0.64 then to the
KVAR line will give Initial KVAR value = 96 KVAR.
Then trace
a line segment from the value of the load 80 KW to the desired cosØ= 0.9 then to the
KVAR line will give final KVAR value = 38.4 KVAR.
Finally,
subtract (Initial KVAR value – final KVAR value) = (96  38.4) = 57.6 KVAR
this will be the desired Capacitor KVAR Rating.
If you apply
the given data to table it will give the same value 57.6 KVAR

Indirect Methods: Measurements With Recording Of Active And
Reactive Power
More
reliable results are obtained with recording instruments. The parameters can
be recorded over a longer period of time, peak values also being included.
Required capacitor power rating is then calculated as follows:
QC = QL – (P · tan Ø2)
Where:
QC = required capacitor rating
QL = measured reactive power
P = measured active power
tan Ø2 =
the corresponding value of tan Ø at the desired cos Ø (can
be obtained from Table1, (e.g. when cos Ø= 0.92 the
corresponding tan Ø= 0.43)

Indirect Methods: Measurement By Reading Meters
The
active and reactive current meters are read at the start of a shift. Eight
hours later both meters are read again. If there has been a break in
operation during this time, the eight hours must be extended by the duration
of this break. Tan Ø can be calculated from the following equation:
tan Ø =
(RM2 – RM1) / (AM2 – AM1)
Where:
RM1 = reactive current meter reading at start
RM2 = reactive current meter reading at finish
AM1 = active current meter reading at start
AM2 = active current meter reading at finish
Using
this calculated value of tan Ø and the desired cos Ø we
can then obtain the factor k from
Table1.
Then,
The required capacitor power rating can thus be derived:
QC = k* f* (AM2 – AM1 ) /8
Where:
The
parameter f is
the ratio of the meter current transformers.
Example#3:
The
following meter readings have been noted:
active
current meter
(AM1)...115.3 KWH
(AM2 )...124.6 KWH
reactive
current meter
(RM1)...311.2 KVAR
(RM2)...321.2 KVAR
The
meters work with 150/5 A current transformers. Calculate the KVAR rating for
the power factor correction capacitors.
Solution:
tan Ø = (RM2 – RM1) / (AM2 – AM1)
tan Ø = (3 2 1 . 2 – 3 1 1 . 2) /(124.6
– 115.3) = 1.08
For a desired cos Ø of 0 .92 a factor k of 0.65 is obtained from Table1.
150/5
A current transformers are used, so here the factor f = 150/5 = 30
The capacitor power rating is thus
QC = k* f* (AM2 – AM1 ) /8
QC =0.65*30*(124.6 – 115.3 )/8 = 22.67 KVAR

Method#2: By Using The Utility Company’s Invoice
First:
In case of using Kilowatthour tariff
the
following procedure can be used to calculate the KVAR rating for the power factor
correction capacitors:
Step#1:
Calculate Tan Ø from the following equation:
tan Ø = reactive energy (regular) /
active energy (regular )
Step#3: Multiply KW by the K multiplier to get the proper Capacitor KVAR Rating.
QC = k.P
Example#4:
The
data derived from the utility company´s invoice are as follows:
Active
power 99 kW
Active
energy (regular tariff) 17820 kWh
Reactive
tariff (offpeak) 19840 kVArh
Calculate
the KVAR rating for the power factor correction capacitors.
Solution:
Step#1:
Calculate Tan Ø from the following equation:
tan Ø= reactive energy (regular) /
active energy (regular )= 19840 KVARH / 17820 kWh =
1.11
Step#2:
The actual value of cos Ø can now be obtained from Table 2, since the
calculated tan Ø of 1.11 corresponds to a cos Ø1
of 0.67.
A
factor k of 0.68 is
then obtained from Table 2 to produce a desired cos Ø2 =
0.92.
Step#3: The
required capacitor power rating is calculated from:
QC = k.P = 0.68 x 99 kW = 67.32 KVAR
In
this case a standard capacitor rating of 75 kVAr must be selected. If a
possible future expansion of the facility is also to be taken into account,
then a somewhat larger capacitor, (e.g. 100 kVAr) could also be selected.
Second:
In case of using Demand tariff
the
following procedure can be used to calculate the KVAR rating for the power
factor correction capacitors:
Step#1:
Use table1 to find the multiplier factor k
Step#2: Multiply KW by the K multiplier to get the proper Capacitor KVAR
Rating.
QC = k.P
Note: In this case the utility company bases its invoice on the maximum amount of power drawn by the user during the given month. It is advisable to select a capacitor power rating that will achieve a cos Ø_{2} of 1.
Example#5:
The
data derived from the utility company´s invoice are as follows:
Maximum
active power = 104 kW
cos
Ø1 =
0.62
Calculate
the KVAR rating for the power factor correction capacitors.
Solution:
Step#1: From
Table1, with an uncorrected cos Ø1 = 0.62 and a
desired cos Ø2 = 1, a factor k of 1.27 is read off.
Step#2: Multiply KW by the K multiplier to get the proper Capacitor KVAR
Rating.
QC = k.P = 1.27 x 104= 132.08 KVAR
For
this duty a reactive power control relay with a capacitor power rating of 150
to 175 KVAR is arranged as a switched variable bank.

Important notes for
sizing Capacitor KVAR Rating For Buildings And Power Plants
Qc_{Y}
= Qc_{Δ}
_{}
C_{Y} = 3 ・ C_{Δ}

In the
next article, we will explain the Effects of
Harmonics on Power Factor Capacitors. Please, keep following.
The
previous and related articles are listed in below table:
Subject Of
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