Determining Capacitance of a Three Phase Capacitor Bank 1

[Wfg42438]

Hello,

I have a very basic question on how to determine the capacitance for a 3-Ph capacitor bank.

If I am not mistaken this is done using the following equation:

Where:
Mvar is the power is in Mvar
Vrms is the rms voltage Line to Line Voltage in kV
Freq is the frequency in Hz



Now what I am unclear on is if this capacitance is the total 3-Ph capacitance or the capacitance per phase.

The reason why I am confused about this is that in a paper I was reading which deals with the estimation stored energy of 3-Ph capacitor banks a different approach is taken.

In the paper they use the following equations:

https://files.engineering.com/getfi...a-fb67-4068-b24b-8eb9cc5b7e64&file=TEST22.png

The paper mentions the capacitance calculated is per phase, not the total. However, something seems off since they are calculating this using the total 3Ph MVAR.




Maybe to help understand how this is done the calculation can be done using the sample capacitor bank nameplates below.

I feel Using the actual nameplate data of these banks would help clarify the calculation question above.

Additionally, it would shed some light on how the calculation is affected when multiple capacitors make up a single Cap bank.

Single Cap Case:

https://files.engineering.com/getfi...f-cfa4-4a7d-ab46-78464564a24f&file=Eaton1.jpg

Multi Cap Case:

https://files.engineering.com/getfi...-4e4e-8d6e-3dcab8fe5405&file=Multi_Eaton2.jpg

Any guidance on this mix up would be much appreciated.

 

[magoo2]

Normally you want to work with ohms per phase and then get the capacitance.

Given the 3-phase Mvar and line-to-line kV of the bank, not the nominal p-p voltage

ohms = kV^2/Mvar

You can also take the per phase Mvar and the phase-to-neutral kV rating of the bank and get the same result.

Your second equation for Xc looks OK so just set ohms equal to Xc and solve for capacitance.

I don't recognize your first equation, but this procedure will work.

 

[Wfg42438]

@magoo2

For example, the nameplate data of the example with a single capacitor has the following data:
10 kVar @ 480 Volts for a 3Ph bank.

So Xc= (0.480)^2 / (10kVar/1000) = 23.04 ohms
Therefore Capcitance= 1/ (Xc*2*pi*60) =0.000115129 Farads or 115.129 uF

So based on the results above did I determine the per phase results or total 3-Ph reactance and capacitance?

 

[Wfg42438]

After some research, I was able to find the resources below for the estimation of the capacitor bank capacitance for Y and delta configurations which is listed below.

https://www.se.com/us/en/faqs/FA323640/

 

[che12345]

Dear Mr. Wfg42438
"...I have a very basic question on how to determine the capacitance for a 3-Ph capacitor bank...".
Q1. If I am not mistaken this is done using the following equation
C = [Mvar x 10[sup]6[/sup]]/ [2¶f x (V x 10[sup]3[/sup])[sup]2[/sup]] ......(1)
Where:
Mvar is the reactive power in Mvar
Vrms is the rms voltage Line to Line Voltage in kV
f is the frequency in Hz
C is the capacitance in Farad
A1. Equation (1) is correct.
If you look at it with basic unit, it is C= (var)/ ( 2¶f x V[sup]2[/sup])
Equation (2) X[sub]c[/sub] = 1 / (2¶f C ) ... in Ohm, is also correct.
FYI Equation (1) is derived from (2),
where I[sub]c[/sub] = V / X[sub]c[/sub] = V (2¶f C ) ....in A,
therefore (va)= V x I[sub]c[/sub] = V (V 2¶f C ) = V[sup]2[/sup](2¶f C ) .......(3).

Q2. "... what I am unclear on is this capacitance is the total 3-Ph capacitance or the capacitance per phase.
A2. Eqt (1), (2) and (3) are valid for any [single] (individual) piece of capacitor. The V is the voltage across the capacitor. You may treat it as if for [single-phase]. It is NOT 3ph capacitance. Therefore V is = V[sub]LL[/sub] or V[sub]LN[/sub] does not come into the picture yet, see later when on 3-phase system.
Q3. " The reason why I am confused ...."
A3. Refer the Schneider paper, where for a [3ph bank], the Mvar is the [total 3ph value]. The value of each [ three "equivalent" individual piece of capacitor] is calculated depending on whether it is in Y or D formation.
Q4. "... how the calculation is affected when multiple capacitors make up a single Cap bank.
A4. If a 3ph Bank1 is rated 25 var, when connected in [parallel] to another 3ph Bank2 rated 50 var; the total is (25+50=75) var.
Che Kuan Yau (Singapore)