Today, we will start explaining Different
Methods of Calculations for PF correction capacitor Ratings.
As we explained before in article “Power Factor Correction Capacitors Sizing Calculations – Part Four”, that
the Types of Power Factor Correction Capacitors according to
Location can be categorized to:
 Central Compensation,
 Individual Compensation,
 Group Compensation,
 Hybrid Compensation.
Today, we will start
explaining how to calculate the capacitor KVAR rating for above types of compensation.
Factors Affecting The Rated KVAR For a Capacitor

Before we start explanation of
different methods for Calculation of the Capacitor
KVAR Rating, we must know the (2) factors which affect the Rated KVAR for a
capacitor; the frequency and voltage.
Standard capacitor ratings are designed for 50 or 60Hz
operation. When operated at less than nameplate frequency of 50 or 60Hz, the
actual KVAR attained will be less than rated KVAR.
Also, If the operating voltage is less than the rated voltage, a
reduction in the nameplate KVAR will be realized. The following equation
defines the relation:
C = KVAR / (2Πf E^{2 }X 10^{3 })
Or in another way:
KVAR=2f ΠCE^{2 }X 10^{3}
Where:
C = capacitance in Farads
KVAR= reactive power
Π = 3.1416
E = network voltage in KV
f = network
frequency in Hz

Calculation of the Capacitor KVAR
Rating for Compensation at Transformer

A transformer consumes reactive power to ensure
that its windings are magnetized. We have (3) methods to calculate the capacitor KVAR rating for Compensation at Transformer as
follows:

Method#1:
Using Equation
The capacitor KVAR
rating for Compensation at Transformer can be calculated from the following
equation:
Where:
i_{0}%
: the percentage noload current,
u_{k}%
: the percentage shortcircuit voltage,
P_{fe} : the iron losses,
P_{cu}
: the copper losses.
KL: the
load factor, defined as the ratio between the minimum reference load and the
rated power of the transformer.
The above
data can be derived from the nameplate characteristics of the transformer.
Example#1:
Assume that
the power factor of a 630 kVA oil distribution transformer which supplies a
load equal to 60% of its rated power is to be corrected.
Calculate the capacitor
KVAR rating for Compensation at Transformer.
Solution:
From the
nameplate characteristics of the transformer:
i0% = 1.8%
uk% = 4%
Pcu = 8.9
kW
Pfe = 1.2
kW
The
compensation power of the capacitor bank connected to the transformer shall
be:

Method#2:
Using Tables
Table1 in below
shows the reactive power of the capacitor bank Qc [kvar] to be connected to
the secondary winding of a transformer according to the different foreseen
load level. In particular, the reactive compensation power shall vary
following a quadratic law with respect to the load coefficient of the
transformer.
Table1
Example#2:
From
Table1, For an 630 kVA oil distribution transformer with load factor equal
to 0.5, the necessary compensation power is 17 kvar.

Method#3:
Using Rule Of Thumb
The
below rule of thumb gives Approximate estimates for the required reactive
capacitor rating for compensation at transformer as follows:

Two
important notes must be checked when connecting PFC capacitors to the
transformer terminals:

A
Check for Resonance between Transformer and Capacitor

The resonant frequency can be calculated from the
following formula:
f = f_{p} √(P_{sc}/P_{c})
f = resonant
frequency,
f_{p}
= power frequency,
P_{sc}
= short circuit power of the transformer (kVA),
P_{c}
= power of the capacitor (kVAR).
If the
frequency obtained is too close to that of a harmonic, the value of the
capacitor rating should be modified. Most common harmonic frequencies, 3rd,
5th, 7th, etc...
Example#3:
for the following transformer:
S = 630 KVA
U_{sc}
= 6%
P = 500 KW
Q_{c} =
275
kVAr
Calculate the resonant frequency.
Solution:
The
shortcircuit power is: S_{sc} = S x 100 / U_{sc} = 630 x 100
/ 6 = 10500 KVA
The resonance
frequency will therefore be:
f = f_{p} √(P_{sc}/P_{c}) = 50 x
√(10500/275) = 308.96 Hz
The system will resonate at order n = f/ f_{p} = 6.18

B Checking the
"No Load" Voltage Rise

This step is used to check that if
the Voltage Constraints Met or not. The basic reason why many plants cannot
leave fixed capacitors energized continuously is that the voltage increases
too much when the load is low.
The limit on the steady state voltage is generally about 110%.
Above this limit, the transformers will
saturate and become overheated. Of course, the life of incandescent lamps is
also drastically reduced. If we assume that the normal system voltage could
be a 105%, then the capacitors should cause no more than a 5% rise at no
load.
For simple cases, the percent
voltage rise, ΔV, can be estimated from the kvar of the capacitor and the
percent
impedance, Z, and kVA ratings of the main transformer as follows:
%ΔV = (Kvar x %Z) / KVA
Example#4:
Calculate the voltage rise that will
result from applying a 350 kvar capacitor at the secondary of a 1000 kVA
transformer with an impedance of7%.
Solution:
%ΔV = (Kvar x %Z) / KVA
%ΔV = 350 x 7 / 1000 = 2.45%
Also, from the following curve (fig.1)
you can find the % voltage drop for any power factor improvement.
Fig.1
Example#5:
Improve power
factor from 60 percent to 90 percent, calculate the reduction in voltage
drop.
Solution:
From the above
curve, at PF = 0.6 the, Voltage drop = 5.1%
And at PF =
0.9, the voltage drop = 3.6%
So, the
reduction in voltage drop = 5.13.6 = 1.5%
Fortunately, at many plants where
this could be a problem, the load seldom drops low enough. Or, if the load is
deenergized the capacitors are also deenergized. However, if these
conditions can't be guaranteed, some or all of the capacitors will have to be
switched.

Additional Notes for Capacitor Compensation at Transformer
Fig.2

Calculation of the Capacitor KVAR
Rating for Individual Motors


Methods
of wiring the Individual power factor correction to Motor
Circuits
Figure
shows the common connection diagrams for the power factor correction of motors,
which are (see Fig.4):
Fig.4
For more information
about the above common connections, please review Article ” Power Factor Correction Capacitors Sizing Calculations – Part Four".

Points
to Consider When capacitors connected directly across
the motor terminals
Two
limiting factors must be considered when capacitors are to be switched with a
motor as a unit are as follows:
1
Selfexcitation voltage:
2Transient
torques:
Other
important notes:

Methods For Selecting/Calculation The
Proper Capacitor KVAR Rating For Motors
There are (5) different methods of selecting/calculation the proper
Capacitor KVAR Rating for induction motors. Choose from one of these methods
below based on what information you have available. these methods are:

Method#1: Use motor manufacturer’s
recommendations
Some motors are supplied with maximum KVAR recommendations as in Fig.5
Fig.5

Method#2:
Use Tables published by leading power factor capacitor manufacturers
The total KVAR rating of
capacitors required to improve the power factor to any desired value can be
calculated by using the tables published by leading power factor capacitor
manufacturers. To properly select the
amount of KVAR required to correct the lagging power factor of a 3phase
motor you must follow the steps below:
Step#2: calculate KW – if it’s not given
from the equation KW = √3*V*I*cos Ø*10^{3}
Step#4:
Multiply KW by the K multiplier to get the proper Capacitor KVAR Rating.
Table2
Example#6:
Total KWinput of load from wattmeter reading 100 KW at a power factor
of 65%. Calculate the capacitive KVAR necessary to raise the power factor to
95%.
Solution:
Step#1&2: KW is given = 100 KW
Step#4: Multiply KW by the K multiplier to get the proper Capacitor KVAR
Rating.
100 KW x 0.840 = 84 KVAR. Use 85 KVAR

Method#3: Use NEMA Tables
3, 4, 5 & 6
These Tables lists the recommended sizes of KVAR units needed for
correction of most induction motors to approximately 95% power factor. These
tables show the proper KVAR for a given horsepower and RPM. For motor types
or sizes not listed, please consult the factory.
Table3

Method#4: using rule of thumbs
It is widely
accepted to use a thumb rule that Motor compensation required in KVAR is
equal to:

Method#5: Using Equations
To calculate
required KVAR for energy efficient motors (or any motor) use the following
formula:
PF_{0}
Original Power Factor (supplied by manufacturer)
PF_{1}
desired Power Factor
H.P. Motor
Horsepower from nameplate
% Motor
efficiency from manufacturer nameplate

In the
next article, we will explain the Calculation
methods of the Capacitor KVAR Rating for buildings and power plants. Please,
keep following.
The
previous and related articles are listed in below table:
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