Power Factor Correction Capacitors Sizing Calculations – Part Seventeen



In article” Power Factor CorrectionCapacitors Sizing Calculations – Part Fifteenwe 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:

  1. A protective device;
  2. A switching device (contactor);
  3. One or more capacitors suitably connected;
  4. Resistors for capacitor discharge.
  5. A PF controller is used In case of an automatic PF compensation system to command switching in/off of the capacitors.




And we explained how to select the first three items (protective devices, contactors and capacitors) in the past article. Today we will explain the following:

  • How to Select a Discharge Resistor,
  • How to Calculate the Value of Discharge Resistor,
  • How to Select Power Factor Controller,
  • How to Calculate the Number of Physical Steps, Electrical Steps and Electrical Control.



Fourth: How to Select a Discharge Resistor



IEC Requirements for Discharge of capacitors


  • When installing a capacitor, it is necessary to verify that when it is switched off it can discharge so that the presence of a voltage at its terminals will not be dangerous for people and things.
  • In compliance with the Std. IEC 60252-2 for the power factor correction of motors discharge devices are not often required since the motor windings functioning as discharge resistances.
  • When a discharge device is provided, it shall reduce the voltage at the capacitor terminals from the peak value of the rated voltage to a value of 50 V or less in the time of 1 min from the moment the capacitor is switched off.
  • A discharge device may sometimes be specified, not for safety reasons, but to prevent electrical overstress on the capacitor: this may occur when a disconnected capacitor still charged is reconnected across another capacitor of different polarity.
  • The Std. IEC 60364-5-55, clause 559.8) prescribes the use of discharge resistors for compensation capacitors having a total capacitance exceeding 0.5 μF (75/25 KVAR with star/delta connection at 400 V).
  • Resistors have the purpose of nullifying, within a short time, the residual charge on the plates of the capacitor once it has been disconnected from the network. It is a good rule to provide discharge resistances for all the capacitors with power exceeding 0.5 KVAR, for whatever supply voltage.
  • In compliance with the Std. IEC 60831-1 clause 22 ‘Each capacitor unit and/or bank shall be provided with a means for discharging each unit in 3 min to 75 V or less, from an initial peak voltage of 2 times rated voltage Un.’ Attention is drawn to the fact that in some countries smaller discharge times and voltages are required.




How to Calculate the Value of Discharge Resistor



The discharge resistance in a single-phase unit or in a phase of a poly-phase unit is given by:



Where:

R is the discharge resistance in ohms[Ω];
t is the discharge time from 2 Un to Ur, in seconds [s];
Un is the rated voltage in [V];
Ur is the admitted residual voltage in [V] (At the moment of energizing, the residual voltage must not exceed 10% of the rated voltage);
k is a coefficient depending on the connection modality of resistors to capacitor units, see Fig-1;
C is the capacitance of the capacitor bank in Farads [F].

To comply with the prescriptions of the Std. IEC 60831-1, t = 180 s and Ur = 75 V shall be put in the above formula.

Fig.1




Fifth: How to Select Power Factor Controller



Function Of PF Controllers

ABB RVT PF Controller

  • PF controllers are microprocessor based controllers, which takes real time inputs from the network like the current input signal from the load current transformer and the Voltage tapped from the Bus, then calculate the KVAR required and produce switching commands to control the contactor ON/OFF of the capacitor steps.
  • Intelligent control by PFC controllers ensures an even utilization of capacitor steps, minimized number of switching operations and optimized life cycle.
  • The controller placed inside the panel shall have the reliability to withstand the operating temperature of at least 50 °C or more.




Difference Between Old And Modern PF Controllers

  • C/k value is used in the setting of old generation Power Factor Controllers, however it is found rarely to be used in panels now. C/k value is a threshold value for switching On/Off the capacitor steps by the controller. C/k is the value obtained by dividing first step capacitor power “Q” to the current transformer ratio”K”. This setting shall be automatic or can be set manually. 
  • The main features of the PF controller must include the following:

  1. Automatic C/k- value setting, Connection of different capacitor steps.
  2. Automatic detection and usage of optimum capacitor steps.
  3. Current measuring 10mA-5A, suitable for connecting CT x/1A and x/5A.
  4. Programmable capacitor switching delay
  5. Indication for over current
  6. Indication for low power factor
  7. Fan contact


  • While Modern APFC controllers provide various additional functions like electrical data logging, self diagnostics and system health features and are capable of communication using standard protocols. Additional features can be chosen based on specific requirements of end user which are as follows:

  1. Four Quadrant operation
  2. Automatic phase reversal correction
  3. Various automatic trip conditions can be programmed – over current, over voltage
  4. Single phase measurement
  5. Various metering parameters like V, I, THD-V, Hz, KVAR, temp, PF etc.






PF Controller and Step Combinations

The PF controllers continually measure installation reactive power and monitor on/off of capacitor steps in order to obtain the relevant power factor. Therefore, the capacitor steps are arranged in step combinations, these combinations will give many advantages like:

  1. Enabling accurate control,
  2. Reducing the number of compensation modules,
  3. Reducing Labor,
  4. Reducing financial costs.


Meaning Of The Step Combinations

For example, If we have (7) step PF controller, it will have one of the following step combinations

Step Combination
Meaning
1-1-1-1-1-1 etc.
All steps have the same power as step no. 1
Step no. 1 is always the smallest
1-1-2-2-2-2 etc.
The first two steps have the same power as step no. 1, but from step no. 3 onwards power is double.
1-1-2-3-3-3 etc.
The first two steps have the same power as step no. 1, the 3rd step has twice the power and from step no. 4 onwards power is triple.
1-2-2-2-2-2 etc.
From the 2nd step onwards power is twice that of step no. 1.
1-2-3-3-3-3 etc.
The power of the 2nd step is twice that of step no. 1, and from step no. 3 onwards power is triple.
1-2-3-4-4-4 etc.
The power of the 2nd step is twice that of step no. 1, the 3rd step triples in power, and from step no. 4 onwards power is quadruple.
1-2-4-4-4-4 etc.
The power of the 2nd step is twice that of step no. 1, and from the 3rd step onwards power is quadruple.

There are many other step combinations and in the same manner as above you can know the meaning of each step combinations, for example:
1.2.3.6.6.6 etc.
1.2.4.8.8.8 etc.

The Control Programs Of The Step Combinations

Control Program
Features
normal program (n)

Suitable for all step types.
Commonly used steps: 1.2.4.4.4.4 or 1.1.2.2.2.2
Linear sequence as from the 3rd step, the 1st two steps are used as adjustment steps
(The controller always begins by energizing or tripping the 1st step, then the 2nd step).
Circular program A (CA)

Steps: 1.1.1.1.1.1., circular sequence.
the 1st step energized will be the 1st step tripped
Caution: this program only operates in optimum mode if the number of capacitor bank steps has been properly set.
Circular program B (CB)

Steps: 1.2.2.2.2.2., circular sequence as from the 2nd step, the 1st step is used as an adjustment step.
the 1st step energized will be the 1st step tripped
Caution: this program only operates in optimum mode if the number of capacitor bank steps has been properly set.
Linear program (S)

Steps: 1.1.1.1.1.1., linear sequence
The last step energized is tripped 1st.
Application: harmonic filtering.

The below table shows the possible control programs for each type of step combinations:

Step Combinations
Possible Programs
1.1.1.1.1.1
CA/n/S
1.1.2.2.2.2
n
1.1.2.3.3.3
n
1.2.2.2.2.2
CB/n
1.2.3.3.3.3
n
1.2.3.4.4.4
n
1.2.4.4.4.4
n



Electrical Steps, Physical Steps And Electrical Control



Difference Between Electrical Steps, Physical Steps And Electrical Control


1- Physical Steps:

They represent the Physical/real capacitor units seen by you inside the PFCC panel where their KVAR sum is equal to the total KVAR required for power factor correction and each physical step is tripped individually by a contactor.

2- Electrical Steps:

they represent the KVAR power seen by the electrical installation according to the connected physical steps KVAR at  each time, so their total KVAR is varying according to the load variations of the installation and  their quantity =total KVAR required/smallest physical step KVAR.

3- Electrical Control:

This is equal to the number of electrical step, multiplied by the power of step no. 1 which is always the smallest step.

For example, if we need 100 KVAR for power factor correction of an installation, and we plan to get this 100 KVAR on 10 stages to give 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 KVAR as per the load variations. So, we have two case solutions as follows:

Case solution#1
Using 10 capacitors with 10 KVAR each to get the 100KVAR = 10 x 10 KVAR, in this case we say that the number of physical steps = the number of electrical steps. The step combination in this case will be 1.1.1.1.1.1.1.1.1.1 and this case called the physical steps method.


Case solution#2
Using 4 capacitors with ratings 10, 20, 30 and 40 KVAR to get the 100KVAR = 1 x 10KVAR + 1 x 20KVAR+ 1 x 30KVAR + 1 x 40KVAR, in this case we say that the number of physical steps = 4 and their step combination in this case is 1.2.3.4 and the number of the electrical steps will be 10 steps as follows:

Electrical Steps
Physical Steps
number
Rating (KVAR)
10 KVAR
20 KVAR
30 KVAR
40 KVAR
1
10
1
-
-
-
2
20
-
1
-
-
3
30
-
-
1
-
4
40
-
-
-
1
5
50
1
-
-
1
6
60
-
1
-
1
7
70
-
-
1
1
8
80
1
-
1
1
9
90
-
1
1
1
10
100
1
1
1
1
- = step disconnected & 1 = step in operation

Case# 2 is called the electrical steps method. Comparing the two above case solutions, we will find the following:


Case#1: physical steps method
Case#2: the electrical steps method
Number of used PFC panels
2
1
Number of used contactors
10
4
Number of used fuses
30
12
PF Controller used
10 output
4 output

 So, using the electrical steps method gives the following advantages:

  1. Enabling accurate control,
  2. Reducing the number of compensation modules,
  3. Reducing Labor,
  4. Reducing financial costs.




How to Calculate the Number of Physical Steps, Electrical Steps and Electrical Control



The number of electrical step depends on:
  1. The number of PF controller outputs used,
  2. The chosen step combinations.


Using the below table-1, you can find the number of electrical step.


Table-1

Example#1:

A capacitor bank made up of 7 physical steps:
1 of 30 kvar
6 of 60 kvar

Find the used step combination, calculate the number of electrical steps and calculate the possible power for each electrical step?

Solution:

Steps
unit power
Step#1*
30 kvar = step#1x 1
Step#2
60 kvar = step#1x 2
Step#3
60 kvar = step#1x 2
Step#4
60 kvar = step#1x 2
Step#5
60 kvar = step#1x 2
Step#6
60 kvar = step#1x 2
Step#7
60 kvar = step#1x 2

Then , the Power factor controller step combinations = 1.2.2.2.2.2.2
7 physical steps = 7 contactors = 7 Outputs used
And the Number of electrical step: 1+2+2+2+2+2+2 = 13 electrical steps


* Step no. 1 is always the smallest

Also, you can find the Number of electrical step from table-1 by look up for the column of 7 controller outputs with the row of step combination 1.2.2.2.2.2.2 which will give the Number of electrical step = 13

Electrical control: 13 times the power of step no. 1 = 13 x 30 kvar = 390 kvar


The possible power for each electrical step will be as follows:

possible power step (KVAR)
7 nos. Physical steps
30
60
60
60
60
60
60
30
1
-
-
-
-
-
-
60
-
1
-
-
-
-
-
90
1
1
-
-
-
-
-
120
-
1
1
-
-
-
-
150
1
1
1
-
-
-
-
180
-
1
1
1
-
-
-
210
1
1
1
1
-
-
-
240
-
1
1
1
1
-
-
270
1
1
1
1
1
-
-
300
-
1
1
1
1
1
-
330
1
1
1
1
1
1
-
360
-
1
1
1
1
1
1
390
1
1
1
1
1
1
1


Operating cycle: - = step disconnected & 1 = step in operation


Conclusion: 
  • 13 possible electrical steps, with only 7 physical steps which is the Optimized Solution.



Example#2:

Consider an APFC System of 250 kvar, calculate the number of electrical steps and calculate the possible power for each electrical step and Find the used step combination using the physical steps method and the electrical steps method?

Solution:

Using the physical step method:
10 physical steps will be used each 25 KVAR to get 250 KVAR = 10 steps x 25 KVAR

Using physical steps method
physical step KVAR
25 KVAR
Number of physical steps
10 steps
Total KVAR
25+25+25+25+25+25+25+25+25+25= 250 KVAR
Used step combination
1.1.1.1.1.1.1.1.1.1
Number of used PFC panels
2
Number of used contactors
10
Number of used fuses
30
PF Controller used
12 output(step)


possible power step (KVAR)
10 nos. Physical steps each 25 KVAR
25
25
25
25
25
25
25
25
25
25
25
1
-
-
-
-
-
-
-
-
-
50
1
1
-
-
-
-
-
-
-
-
75
1
1
1
-
-
-
-
-
-
-
100
1
1
1
1
-
-
-
-
-
-
125
1
1
1
1
1
-
-
-
-
-
150
1
1
1
1
1
1
-
-
-
-
175
1
1
1
1
1
1
1
-
-
-
200
1
1
1
1
1
1
1
1
-
-
225
1
1
1
1
1
1
1
1
1
-
250
1
1
1
1
1
1
1
1
1
1

Using the Electrical step method:
4 nos. electrical steps will be used with the following ratings 25, 50, 75, 100 KVAR.

Using electrical steps method
physical step KVAR
25, 50, 75, 100 KVAR
Total KVAR
25+50+75+100= 250 KVAR
Number of electrical steps
total KVAR required/smallest physical step KVAR
250 KVAR / 25 KVAR = 10 steps
Used step combination
1.2.3.4
Number of used PFC panels
1
Number of used contactors
4
Number of used fuses
12
PF Controller used
4 output(step)


possible power step (KVAR)
4 nos. Physical steps
25
50
75
100
25
1
-
-
-
50
-
1
-
-
75
-
-
1
-
100
-
-
-
1
125
1
-
-
1
150
-
1
-
1
175
-
-
1
1
200
1
-
1
1
225
-
1
1
1
250
1
1
1
1

Conclusion
  • High Labor, high cost: non-optimized solution when using the physical step method.
  • Optimized Solution when using the electrical step method.





Notes for designing a capacitor bank with PF controllers

  • When designing a capacitor bank, it is important to break down the total power Qt (KVAR) into several steps so as to ensure the best compromise between the number of steps and suitable regulation.so, first select the required number of electrical steps then Calculate the smallest physical capacitor unit = total KVAR required/ required number of electrical steps.
  • The sum of the physical step power ratings must corresponds to the total reactive power.
  • The maximum switching power of the contactors ≤ 60 kVAr at 400-440 V in order to switch the three-phase capacitors.
  • Don’t exceed the maximum number of relay outputs the controllers can switch.
  • For capacitor banks with few electrical steps, we recommend increasing the step switching times.
  • It is possible to create physical steps > 60 kVAr via simultaneous control of 2 contactors, divided between 2 different capacitors, by the same controller relay output, to which it is essential to add a time delay of 1 second minimum. For Example: To create high-power capacitor banks > 1000 kVAr, a few 100 kVAr physical steps can be created by switching a 50 kVAr contactor-capacitor pairing twice at the same time.
  • For the highest power ratings requiring steps > 18 steps. It is possible to use the same principle of physical steps > 60 kVAr by simultaneously controlling 2 contactors divided between 2 different capacitors using the same controller relay output, to which it is essential to add a long enough time delay (a minimum of several seconds).




In the next article, we will explain how to choose Cables for Power Factor Correction Capacitors. 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:
1-Transformer
2-Individual 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 519-2014)
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- Square-D (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
How to select a capacitor for PFC Panel and Capacitors’ rules
Capacitor compensation with a detuned reactor
How to Select a Detuned Reactor







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