Power Factor Correction Capacitors Sizing Calculations – Part Twelve



As we explained before in article Power Factor Correction Capacitors Sizing Calculations – Part Eleven”, how to calculate the capacitor KVAR rating for compensation at:
  1. Transformers,
  2. 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:
  1. By using measuring devices,
  2. By using The Utility Company’s Invoice.





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:
  1. Direct Measurement method:  Measurement of current and power factor   
  2. Indirect Measurement methods: which includes (2) sub methods:

  • Measurements with recording of active and reactive power
  • Measurement by reading meters





Direct Method: Measurement Of Current And Power Factor

  • Ammeters and power factor meters are often installed in the main low-voltage distribution board, also we can use clamp meters for measuring current. Measurements are made in the main supply line (e.g. transformer) or in the line feeding the equipment whose power factor is to be corrected.
  • Measuring the voltage in the power distribution system at the same time improves the accuracy of the calculation, or the nominal voltage (e.g. 380 or 400 V) may simply be used instead.
  • The active power P is calculated from the measured voltage V, apparent current I 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


  • Step#1: search for Existing Power Factor on Table-1, move across table to Desired Power Factor. The number represented is your multiplier number K.
  • Step#2: Multiply KW by the K multiplier to get the proper Capacitor KVAR Rating.


QC = k.P

For more information about measuring the power factor, please review our article “Power Factor Correction Capacitors Sizing Calculations – Part Six”.



Table-1

Note:
  • Measurements made as described above naturally only give momentary values. The load conditions can, however, vary considerably depending on the time of day and the season of the year. Measurements should therefore be made by someone who is familiar with the installation. Several measurements should be made, ensuring that the consumers whose power factor is to be corrected are actually switched on. The measurements should also be made quickly - if possible reading all instruments simultaneously - so that any sudden change of load does not distort the results.


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 Table-1 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 figure-1 is used to calculate the capacitor KVAR rating as follows:


Fig.1

  1. First, trace a line segment from the value of the load KW to the initial cosϕ then to the KVAR line will give Initial KVAR value.
  2. Then trace a line segment from the value of the load KW to the desired cosϕ then to the KVAR line will give final KVAR value.
  3. Finally, subtract (final KVAR value - Initial KVAR value) this will be the desired Capacitor KVAR Rating.


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 Table-1, (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 Table-1.

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 Table-1.

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

  • The required capacitor power rating can be determined relatively easily and accurately from the power supply company´s monthly invoice.
  • If power consumption is constant throughout the year, the annual electricity consumption or any desired monthly invoice (but not for the month in which the annual shutdown occurs), may be taken as a basis.
  • If seasonal variations are apparent, an invoice from the "high season" must of course be selected.
  • If regular and off-peak tariffs are measured separately, usually the regular tariffs are used for calculation purposes. It can be assumed that the capacitor power rating derived will be adequate to cover the reactive current circulating at night. In special cases, however, where the less expensive off-peak power is used predominantly, the off-peak consumption may not be neglected.


First: In case of using Kilowatt-hour 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#2: Use table-1 to find cos Ø1from the above calculated tan Ø, then find the multiplier factor k

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 (off-peak) 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 table-1 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 Ø2 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 Table-1, 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.




Using Nomographs For Calculation Of Multiplier Factor K

The multiplier factor K can be determined by using the above table-1, and also it can be determined by using the following Nomograph shown in Fig.2.


Fig.2


You can follow the following procedure to determine the multiplier factor K from above nomograph:

  1. first trace a line segment from the value of the initial cosØ to the value of desired cosØ,
  2. Then, the intersection of the line with the middle graduated scale, gives the value of K.





Important notes for sizing Capacitor KVAR Rating For Buildings And Power Plants

  • When selecting automatic bank units, select the closest KVAR rating to the amount of KVAR desired based on present and future applications. If the desired rating is not listed, the next higher KVAR rating should be selected.
  • When selecting fixed bank units, however, select the KVAR rating WITHOUT GOING OVER the desired capacitance level.
  • In a three-phase system, the capacitor bank constituted by three capacitors having the same capacitance, can be delta- or star-connected. When selecting the connection modality, it is necessary to keep into account that with delta connection, each capacitance is subject to the supply line-to-line voltage, but, at the same level of generated reactive power, it has a value equal to 1/3 of the value it will have in case of star-connection:


QcY = QcΔ

CY = 3  CΔ

  • In the low voltage field, where insulation problems are less important, the delta connection is usually preferred for the capacitor bank, since it allows a smaller sizing of the capacitances of each phase.





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 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 Transformer
  • Calculation of the Capacitor KVAR Rating for Compensation at Individual Motors





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