In article” Power Factor Correction Capacitors Sizing Calculations – Part Fifteen”
we indicated that The
Main Components of PFC Panel are as follows:
1 The Main Components of
PFC Panel

A Panel for
power factor correction (PFC Panel) is constituted essentially from the
following main components:

And
we explained how to select the first two items (protective devices and
contactors) in the past article. Today we will explain the following:
 How to select a capacitor for PFC Panel and Capacitors’ rules,
 Capacitor compensation with a detuned reactor,
 How to Select a Detuned Reactor.
Third:
How To Select A Capacitor For PFC Panel

Capacitors’
Selection Rules

Rule#1: Size of capacitor bank
Capacitors are rated in KVAR. Common sizes are 1, 2, 3, 4, 5, 6,
7, 8, 10/12/15/20 and 25 KVAR at 415 or 440V alternating current, 3 phase, 50
Hz. Usually more than one capacitor is required to give the desired degree of
power factor correction. Groups of capacitors are factory assembled in
various configurations. Standard capacitor ratings are designed for 50 or
60Hz operation. The following equation defines the relation:
C= Q_{c} x 10^{9}/ (2πfE^{2})
Where:
C: capacitance in Farads μF
Q_{c}:_{ }reactive power in KVAR
π =3.1416
f: rated frequency in Hz
E: rated voltage in V

Rule#2:
Size of capacitor bank for delta connected 3ph capacitor
For delta connected 3ph capacitor, the capacitance value
of a capacitor can be calculated using following equation Assuming that
capacitance of the three delta connected capacitors are C as shown in the
figure.
C = Q_{c} × 10^{9} / (4πfE^{2})
Where:
C: capacitance in Farads μF
Q_{c}_{ }:_{ }reactive
power in KVAR
π =3.1416
f: rated frequency in Hz
E: rated voltage in V
Example#1:
15 kvar, 3 phases, 415V, 50Hz capacitor, calculate its
capacitance?
Solution:
C = Q_{c}
× 10^{9} / (4πfE^{2})
C = 15 × 10^{9} / (4 x 3.142 × 50 × (415 × 415))
= 138.62μF

Rule#3:
calculation of capacitor KVAR from measured capacitance
For three phase capacitor, KVAR calculation from the measured
capacitance value of a capacitor can be done by using the following equation:
Q_{M} = 2/3 × (C_{a} + C_{b} + C_{c})
× E^{2} × (2πf)/ 10^{9}
Where:
Q_{M}:
capacitor KVAR
C_{a},
C_{b} & C_{c}: capacitances measured between
phases in μF
E: rated
voltage in V
π =3.1416
f: rated
frequency in Hz
Example#2:
Consider you have measured a capacitor rated for
440volts, 50Hz where in measured capacitance value is as follows:
197μf (between R & Y phase)  C_{a}
196μf (between B & Y phase)  C_{b}
200μf (between R & B phase) – C_{c}
Calculate the capacitor KVAR?
Solution:
Q_{M}
= 2/3 × (C_{a} + C_{b} + C_{c}) × E^{2} ×
(2πf)/ 10^{9}
Q_{M} = 2/3 ×(197+196+200)×(440^{2} )×2×3.14×50 / 10^{9}
= 24.04 KVAR
Note:
The
tolerance of capacitance of a capacitor is 5% t0 +10% of capacitor as specified
in the IEC Standards.

Rule#4:
Calculation Of Rated Current For Capacitor With
Rated Supply Voltage And Frequency
The following equation will be used:
I_{N} = KVAR x 10^{3 }/ (√3 x U_{N})
Where:
I_{N}_{: }Rated current_{ }in A
U_{N}: rated
voltage in V
Example#3:
For 50 KVAR, 3 phase, 400V, 50Hz capacitor. Calculate the rated
current?
Solution:
I_{N} = KVAR x 10^{3 }/ (√3 x U_{N})
I_{N} = (50 × 1000) / (1.732 × 400)
I_{N} = 72.16 A

Rule#5:
changing the operating voltage
It is
necessary to note that the reactive power at the service voltage is different
from the rated power given on the nameplate and referred to the rated
voltage; as a general, if the operating voltage is less than the rated voltage, a
reduction in the nameplate KVAR will be realized as follows:
Q
_{supplied} = Q_{c} (U_{e} / U_{n})^{2}
Where:
Q_{c}_{ }is the
reactive power at the rated voltage U_{n};
Q _{supplied} is the
effective power at the service voltage U_{e}.
Example#4:
A capacitor
with 100 KVAR rated reactive power at 500 V, calculate the capacitor KVAR
when the applied voltage is 400 V?
Solution:
Q _{supplied}
= Q_{c} (U_{e} / U_{n})^{2}
Q _{supplied}
= 100 (400/500)^{ 2} = 64 KVAR

Rule#6:
changing the operating voltage and frequency
The KVAR of capacitor will not be same if the measured
voltage and frequency applied to the capacitor changes, and to calculate
capacitor power in KVAR from the measured values at site and name plate data,
the following equation will be used:
Q_{M} = ( f_{M} / f_{N} ) × ( U_{M}
/ U_{N} )^{2} × Q_{N}
Where:
Q_{M}
= Available power in kvar
f_{M}
= Measured frequency in Hz
f_{N}
= Rated Frequency in Hz
U_{M}
= Measured voltage in V
U_{N}
= Rated Voltage in V
Q_{N}
= Rated power in kvar
Example#5:
Name plate details: 15kvar, 3 phases, 440V, 50Hz
capacitor. Measured voltage 425V and measured frequency  48.5Hz, calculate
the change in capacitor KVAR?
Solution:
Q_{M}
= (f_{M} / f_{N} ) × ( U_{M} / U_{N} )^{2}
× Q_{N}
Q_{M} = (48.5/50) × (425 / 440)^{2} × 15
= 13.57kvar.
Also, the current of capacitor will not be same if
voltage applied to the capacitor and frequency changes, and to calculate the
capacitor current from the measured values at site and name plate data, the
following equation will be used:
I_{M }= I_{R} (U_{M x }f_{M}) /
(U_{R} x F_{R})
Where:
I_{M}
= Capacitor Current
I_{R}
= Rated Current
U_{M}
= Measured Voltage
f_{M}
= Measured frequency
U_{R}
= Rated Voltage
F_{R}
= Rated Frequency
Note:
Please
ensure that the measurement at site is done using true RMS clamp meter.
Example#6:
Consider a capacitor of 15 KVAR, 440V, 50 Hz, 3 Phase
Capacitor Rated Current from name plate 19.68A and Measured Values are:
Voltage 425V, Frequency 49.5 Hz, calculate the capacitor current?
Solution:
I_{M
}= I_{R} (U_{M x }f_{M}) / (U_{R} x F_{R})
= 19.68 x(425 x 48.5) / (440 x 50) = 18.43A

Rule#7: Calculating Capacitor KVAR for threephase
capacitor with filter reactors
The
following equation will be used:
Q_{c} = C.3.V^{2}.2. π.f_{n}
/ (1p)
Where:
Q_{c}:
capacitor KVAR
C:
capacitance in μF
V:
rated voltage in V
π =
3.1412
f_{n}:
rated frequency
P: blocking
factor
n: tuning
number, n = f_{r}/f_{n}
_{}
p (as a %):
blocking factor; this is the ratio between the reactor inductance XL compared
to the capacitor inductance XC. It will be calculated from the following
equation:
p
= X_{L}/X_{C} = 1/n^{2 }= (f_{n}/f_{r})^{2}
Where:
f_{n}: fundamental
frequency
f_{r}: Harmonic
frequency
Example#7:
For
3 phase capacitor with detuned reactor , the capacitance equal 3 x 332 μF at
400 V /50 Hz with blocking factor p = 7%. Calculate the capacitor KVAR.
Solution:
Q_{c}
= C.3.V^{2}.2. π.f_{n}
/ (1p)
Q_{c}
= 0.000332 x 3 x 400² x 2 x 3.1416 x 50 / (10.07) = 53.8 KVAR
We can also use
the following equation for Calculating effective Capacitor KVAR for
threephase capacitor with filter reactors:
Where:
Qs: the
effective Capacitor KVAR using detuned reactor
Us: service
voltage
Un: nameplate
voltage of the capacitor
Qn: nameplate
KVAR of the capacitor
P: blocking
factor
In this case, using a reactor creates a voltage surge on the
terminals of the associated capacitor and the capacitor power supply
voltage Uc will be calculated as follows:
Uc = Us / (1p)
Note:
We should choose
a capacitor with nominal voltage Un higher than Uc.
Example#8:
A capacitor with
nominal power of 25 KVAR at 480 V, calculate the effective Capacitor KVAR if
a detuned reactor will be used at 400 V. noting that p =14%.
Solution:
1 Determine the
capacitor power supply voltage:
Uc = Us / (1p)=
400 / (10.14) = 465 V
2 Calculate the
effective Capacitor KVAR at 400 V:

Capacitor
Compensation With A Detuned Reactor

Functions
of Detuned Reactor
On mains
supplies with a high level of harmonic pollution, it is recommended to use
capacitor banks with detuned reactors which have the following functions:
Note:
The serial
frequency (fr) chosen must be below the first harmonic order present in the
circuit.
The most
commonly used reactor tuning frequencies are:
*With network
frequency 50 Hz,
Where:
n: tuning
number, n = f_{r}/f_{n}
p (as a %):
blocking factor; this is the ratio between the reactor inductance XL compared
to the capacitor inductance XC. It will be calculated from the following
equation:
p
= X_{L}/X_{C} = 1/n^{2 }= (f_{n}/f_{r})^{2}
Where:
f_{n}: fundamental
frequency
f_{r}: Harmonic frequency

When/How
to Use Detuned Reactor
To use a detuned
reactor, you need to make a correct assessment of the risks of capacitor bank
resonance in your installation, we recommend the following procedure:

How
to Select a Detuned Reactor

First:
For 3 Phase Capacitors
The reactor
value (inductance per phase) L is calculated from the following equation:
Where:
L: The
reactor value (inductance per phase) in Henry H
Us: service
voltage
P: blocking
factor
Qs: the
effective Capacitor KVAR using detuned reactor
Un: nameplate
voltage of the capacitor
Qn: nameplate
KVAR of the capacitor
ω=2πf
And the current
IL in the reactor will be calculated from the following equation:
I_{L}
= Qs / √3 Us
Example#9:
Use the same data
from Example#8; calculate the reactor inductance value (per phase) and the
reactor current.
Solution:
1 the reactor
inductance value (per phase)
2 the reactor
current
I_{L} =
Qs / √3 Us = 20000 / √3 x 400 = 28.9 A

Second:
For 3 Single Phase Capacitors
The reactor
value (inductance per phase) L is calculated from the following equation:
Where:
L: The
reactor value (inductance per phase) in Henry H
Us: service
voltage
P: blocking
factor
Qs: the
effective Capacitor KVAR using detuned reactor
Un: nameplate
voltage of the capacitor
Qn: nameplate
KVAR of the capacitor
ω=2πf
And the current
IL in the reactor will be calculated from the following equation:
I_{L}
= Qs / 3 Us
Example#10:
A capacitor with
nominal power of 25 KVAR at 480 V, calculate the effective Capacitor KVAR if
a detuned reactor will be used at 400 V. noting that p =14%.
Solution:
1 The reactor
inductance value (per phase)
2 The reactor
current
I_{L} =
Qs / √3 Us = 20000 / 3 x 400 = 16.6 A

In the
next article, we will explain how to choose Resistors, PF Controllers and
Cables for Power Factor Correction Capacitors Calculators. Please, keep
following.
The
previous and related articles are listed in below table:
Subject Of
Previous Article

Article

Glossary of Power Factor Correction Capacitors


Types of Loads,
The Power
Triangle,
What is a power
factor?
Types of power
factor
Why utilities
charge a power factor penalty?
Billing Structure.


What causes
low power factor?
Bad impacts
of low power factor,
Benefits of
Power Factor correction.


How to make
Power Factor Correction?
Types of
Power Factor Correction Capacitors
Individual compensation


Group compensation,
Central compensation,
Hybrid compensation.
Summary for Power Factor Correction
Capacitors Sizing Calculations Steps


Step#1: Collect Monthly Billing Data
Step#2: Make Some Preliminary
Measurements For Current And Voltage


Step#3: Fill the Economic Screening
Worksheet


Step#4: Make Preliminary Measurements
For Harmonics
Step#5: Repeat the Economic Screening
Worksheet
Step#6: Compare the Savings with the
Probable Cost of Capacitors' Installation
Second: Design Phase
Step#1: Performing a Detailed Plant
Survey
Step#1.A:
Review the one line diagram
Step#1.B:
Take into consideration the loads that produce harmonics
Step#1.C:
collect sufficient data Inventory by using measuring instruments


Step#2: Select Economical Capacitor Scheme
Step#3: Checking the "No Load" Voltage Rise
Step#4: Select Capacitor Switching Options
Step#5: Check the Harmonic Distortion and make Harmonic
Mitigation Options
Step#6: Use the Economic Screening Worksheet again


Power Factor Correction
Capacitors Sizing Calculations Steps For New Designs


Factors Affecting The Rated KVAR For a Capacitor
Calculation of the Capacitor KVAR Rating for Compensation at:
1Transformer
2Individual Motors


3 Calculation Of The Capacitor KVAR Rating For Buildings
And Power Plants(Group Compensation)


Harmonics Effects On Power Factor Capacitors
Harmonic Limits in Electric Power Systems (IEEE 5192014)
Options to Reduce Harmonics for PFCC
Power Factor Compensation In Case Of Harmonics


Power
Factor Correction Capacitors Calculators:
1 Arteche Reactive Power and Harmonic Resonance Point
Calculator,
2 Eaton Power Factor Correction Calculator,
3 AccuSine Sizing
Spreadsheet,
4 SquareD (Schneider Electric) Calculator.


The Main Components of PFC Panel
How to select Circuit Breakers for PFC Panel
How to select Fuses for PFC Panel
How to select Contactors for PFC Panel

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