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# Calculate reactive power of the capacitor bank and improve power factor

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## Dimensioning of the capacitor bank

For the dimensioning of the capacitor bank to be installed in order to improve the power factor of a plant, it is necessary to calculate correctly the power factor according to the consumption or to the load cycle of the plant. This in order to avoid the intake of excess reactive energy, which is a condition normally forbidden by power supply authorities.

To carry out distributed or group power factor correction, it is necessary to calculate the cosφ of the single load or of the group of loads (factory areas).

This can be carried out as follows:

1. Directly – through direct measuring by means of a power factor meter
2. Indirectly – through the reading of the active and reactive energy meters
The power factor meter is a measuring instrument able to display the power factor cosφ according to which the load is absorbing energy. The reading of the instrument shall be carried out in different moments of the load cycle, so that an average power factor value can be obtained.

If the readings of the active and reactive energy absorbed by the load or by the whole of the loads constituting the factory areas during a work cycle are available, the average power factor can be calculated as follows:

where:

• EPi and EQi are the values of active and reactive energy read at the beginning of the work cycle
• EPf and EQf are the values of active and reactive energy read at the end of the work cycle

## Calculation of the necessary reactive power

Once the power factor (cosφ1) of the installation and the power factor to be obtained (cosφ2) are known, it is possible to calculate the reactive power of the capacitor bank necessary to improve the power factor.

Indicating by:

• P – the installed active power
• φ1 – the phase displacement angle before power factor correction
• φ2 – the phase displacement angle to be obtained with the power factor correction the power of the capacitor bank Qc is:

Once the initial cosφ is known, Table 1 allows to calculate (in kvar per kW installed) the power of the capacitor bank necessary to obtain a defined power factor.

In a three-phase system, the capacitor bank constituted by three capacitors having the same capacitance, can be delta connected 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:

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.

### Example calculation

In a plant with active power equal to 300 kW at 400 V and cosφ= 0.75, we want to increase the power factor up to 0.90. In the table 1 above, at the intersection between the row “initial cosφ” 0.75 with the column “final cosφ” 0.9, a value of 0.398 for the coefficient K is obtained.

Therefore a capacitor bank is necessary with power Qc equal to:

Qc = K · P = 0.398 · 300 = 119.4 kvar

The factor K can be determined also using the following nomograph:

As shown in the figure, tracing a line segment from the value of the initial cosφ to the value to be obtained, the intersection of the line with the middle graduated scale, gives the value of K which, multiplied by the active power P of the load, defines the necessary reactive power Qc.

Reference // Power factor correction and harmonic filtering in electrical plants by ABB

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### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. Satheesh
May 11, 2020

While desining a power system for industry, how can we design power factor correction unit without installation of load and we know the load value only. How can we calculate the power factor of the loads before installing. Not single load like a single motor. Load that consume for the industry.

• Yunus
May 02, 2021

After calculating the size of your motors, choose the manufacturer/make. Contact the manufacturer. On the name plate, there are usually power factors indicated for full loading. Get the average and that becomes the initial power factor to be used on the table above

2. BHUSHAN
Nov 04, 2019

nice one

3. Ashebir
Oct 30, 2019

thanks a lot, I have learnt more.

4. Alexander Amaglo
Oct 29, 2019

Good to Know

5. Sudarshan
Oct 14, 2019

I have 500kva transformer
How much capacitor bank required please inform with formula

6. Karim
Sep 26, 2019

Is this method wroking also for very high voltage 225KV and 400 KV, for a wind farm of 300 MW?

7. Jabar Rajabi
Oct 11, 2018

Thank you very much

8. Armando Medel Trujillo
May 26, 2018

Excelente información teórica y práctica ya que es un tema muy común en cualquier industria saludos y de favor si me pueden enviar la información en PDF gracias

9. Mina Hanaa
Jan 16, 2018

10. Jamal
Dec 02, 2017

Greetings…Very good information …thanx alot

• Kwabenah Quayson
Oct 29, 2019

Thank you very much

11. hari haran
Nov 21, 2017

Thank for your site. MCCB rating for 200 kVAR capacitor bank. Please guide me.

Aug 26, 2016

Greeting,

thanks for this important article

13. Mallikarjuna Balimidi
Aug 26, 2016

Really it is a good site for electrical engineers. I don’t know the meaning of work cycle? Please explain about work cycle.

• viswanatha reddy
Sep 12, 2016

i am explaining what i know, if any wrong please inform me
work cycle means
in a particular period (ie: 24 hrs or 1 week or month) working condition of the Machine/Equipment
Ex: in one day (ie: 24 hrs)
6am to 9 am – machine running on half load ( power consumption is less)
9 am to 6 pm- machine running on full load ( power consumption also more )
load may be vary from time to time during a period. that may be considered for power factor correction.
other wise if u maintain constant capacitor bank for power factor correction

• K THIRUMAL RAO
Oct 30, 2019

Reply to Mr. Vishwanth Reddy’s query: The site power factor is dynamic to load conditions, varies according to the connected load PF. Generally, an Automatic Power Factor Control relay is introduced in the Mains which constantly monitors and switches On or off set of capacitor banks to compensate the reactive power.
ABB has APFC ( automatic Power factor controller) RVC & RVT and also PLC based soft starter in each capacitor bank circuit, which reduces the high inrush currents encountered during switching ON of the capacitors linked to actual compensation required in plant.

14. ABDULRAHEEM ALLEHIANI
Aug 24, 2016

Greeting,

thanks for this important article,

i have question

the capacitor bank it can be used for power factor correction and voltage regulator (to maintain the drop voltage during start up the high capacity motor)?

15. Martin
Aug 24, 2016

Good day

Through this platform I have learnt really a lot

THANKS