Convert Capacitor Capacity Between μF and kVAR for Power Factor Correction

How to Convert Capacitor kVAR to μ-Farads & Vice Versa for Power Factor Improvement?

Conversion of kVAR to μ-Farad & μ-Farad to kVAR

The following simple calculation tutorial shows how to calculate and convert the required capacitor bank value in microfarads and then convert to kVAR and vice versa. We will be using three simple methods to convert the capacitor kVAR in μ-Farads and conversion of microfarad in kVAR.

Let’s see the following examples which show how to find and convert the Required Capacitor bank value in both kVAR and Micro-Farads which is applicable in Power Factor improvement Calculation and capacitor bank sizing.

Example 1:

A Single phase 400V, 50Hz, motor takes a supply current of 50A at a P.F (Power factor) of 0.6. The motor power factor has to be improved to 0.9 by connecting a capacitor in parallel with it. Calculate the required capacity of Capacitor in both kVAR and Farads.

Solution:

Calculate and Convert kVAR in Microfarads

(1) To find the required capacity of Capacitance in kVAR and convert it to micro-farad to improve the P.F from 0.6 to 0.9 (Three Methods)

Solution #1 (Simple Method using the Table)

Motor Input = P = V x I x Cosθ

          = 400V x 50A x 0.6

          = 12kW

From Table, Multiplier to improve PF from 0.60 to 0.90 is 0.849

Required Capacitor kVAR to improve P.F from 0.60 to 0.90

Required Capacitor kVAR = kW x Table Multiplier of 0.60 and 0.90

= 12kW x 0.849

= 10.188 kVAR

Solution # 2 (Classic Calculation Method)

Motor Input = P = V x I x Cosθ

          = 400V x 50A x 0.6

          = 12kW

Actual P.F = Cosθ₁ = 0..6

Required P.F = Cosθ₂ = 0.90

θ₁ = Cos^-1 = (0.60) = 53°.13; Tan θ₁ = Tan (53°.13) = 1.3333

θ₂ = Cos^-1 = (0.90) = 25°.84; Tan θ₂ = Tan (25°.50) = 0.4843

Required Capacitor kVAR to improve P.F from 0.60 to 0.90

Required Capacitor kVAR = P in kW (Tan θ₁ – Tan θ₂)

= 12kW (1.3333– 0.4843)

= 10.188 kVAR

Solution # 3 (Using μFarad to kVAR Calculator)

You may directly use the Farad and microfarad to kVAR conversion calculator.

(2) To find the required capacity of Capacitance in Micro-Farads and convert the Capacitor μ-Farads to kVAR to improve the P.F from 0.6 to 0.9 (Three Methods)

Solution #1 (Simple Method using the Table)

We have already calculated the required Capacity of Capacitor in kVAR, so we can easily convert it into Farads by using this simple formula

Required Capacity of Capacitor in Farads/Microfarads

C = kVAR / (2 π f V²) in microfarad

Putting the Values in the above formula

= (10.188kVAR) / (2π x 50Hz x 400²V)

= 2.0268 x 10^-4

= 202.7 x 10^-6

= 202.7μF

Solution # 2 (Classic Calculation Method)

kVAR = 10.188 … (i)

We know that;

I_C = V / X_C

Whereas X_C = 1 / 2π x f x C

I_C = V / (1 / 2π x f x C)

I_C = V x 2π x f x C

= (400V) x 2π x (50Hz) x C

I_C = 125663.7 x C

And,

kVAR = (V x I_C) / 1000     …     [kVAR =( V x I) / 1000 ]

= 400 x 125663.7 x C

I_C = 50265.48 x C … (ii)

Equating Equation (i) & (ii), we get,

50265.48 x C = 10.188C

C = 10.188 / 50265.48

C = 2.0268 x 10^-4

C = 202.7 x 10^-6

C = 202.7μF

Solution # 3 (Using kVAR to μFarad Calculator)

You may use the kVAR to Farad and microfarad conversion calculator.

Capacitor μ-Farad to kVAR and kVAR to μ-Farad Conversion Formula

The following formulas are used to calculate and convert capacitor kVAR into Farads and Vice Versa

Required Capacity of Capacitor in Farads/Microfarads.

Convert Capacitor kVAR in Farads & Microfarads

• C = kVAR x 10³ / 2π x f x V²                         …     in Farad
• C = 159.155 x Q in kVAR / f x V²                 …     in Farad
• C = kVAR x 10⁹ / (2π x f x V²)                       …     in Microfarad
• C = 159.155 x 10⁶ x Q in kVAR / f x V²        …     in Microfarad

Required Capacity of Capacitor in kVAR

Convert Capacitor Farads & Microfarads in VAR, kVAR and MVAR.

• VAR = C x 2π x f x V²x 10^-6                               …     VAR
• VAR = C in μF x f  x V² / (159.155 x 10³)          …     in VAR
• kVAR = C x 2π x f x V²  x 10^-9                           …     in kVAR
• kVAR = C in μF x f x V² ÷ (159.155 x 10⁶)        …     in kVAR
• MVAR = C x 2π x f x V²  x 10^-12                         …     in MVAR
• MVAR = C in μF x f x V² ÷ (159.155 x 10⁹)        …     in MVAR

Where:

• C = Capacitance in Microfarad
• Q = Reactive Power in Volt-Amp-Reactive
• f = Frequency in Hertz
• V = Voltage in Volts