How to Find Capacitor Size in kVAR and Farad for PF Correction?

How to Find Capacitor Size in kVAR and Farad for PF Correction? . Power Factor (PF) correction plays a vital role in improving the efficiency of electrical systems by minimizing energy losses. One of the essential components of this process is the capacitor, used to offset reactive power and enhance the overall power factor. But how do you determine the correct capacitor size in kVAR and Farads? This guide will walk you through the process, providing clear formulas, step-by-step instructions, and practical tips.

Read More : How to Read Capacitor Value?

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Understanding Power Factor and Its Importance

Power factor is the ratio of real power (kW) to apparent power (kVA) in an electrical system. A poor power factor leads to energy inefficiency, resulting in higher energy costs and potential penalties from utility providers.

• Real Power (kW): The actual energy consumed by equipment.
• Reactive Power (kVAR): Power lost due to the phase difference between voltage and current.
• Apparent Power (kVA): The total power supplied by the source.

Correcting the power factor involves adding capacitors to counteract reactive power, reducing the apparent power required.

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How to Calculate the Capacitor Value in kVAR?

Example: 1

A 3 Phase, 5 kW Induction Motor has a P.F (Power factor) of 0.75 lagging. What size of Capacitor in kVAR is required to improve the P.F (Power Factor) to 0.90?

Solution #1 (Simple Method using the Table Multiplier)

Motor Input = 5kW

From Table, Multiplier to improve PF from 0.75 to 0.90 is 0.398

Required Capacitor kVAR to improve P.F from 0.75 to 0.90

Required Capacitor kVAR = kW x Table 1 Multiplier of 0.75 and 0.90

= 5kW x 0.398

= 1.99 kVAR

And Rating of Capacitors connected in each Phase

= 1.99kVAR / 3

= 0.663 kVAR

Solution # 2 (Classic Calculation Method)

Motor input = P = 5 kW

Original P.F = Cosθ₁ = 0.75

Final P.F = Cosθ₂ = 0.90

θ₁ = Cos^-1 = (0.75) = 41°.41; Tan θ₁ = Tan (41°.41) = 0.8819

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

Required Capacitor kVAR to improve P.F from 0.75 to 0.90

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

= 5kW (0.8819 – 0.4843)

= 1.99 kVAR

And Rating of Capacitors connected in each Phase

1.99 kVAR / 3 = 0.663 kVAR

How to Find Capacitor Size in kVAR and Farad for PF Correction?

Read More : Capacitors and Inductors Basics: A Comprehensive Guide

Note: Tables for Capacitor Sizing in kVAr and microfarads for PF Correction

The following tables (given at the end of this post) have been prepared to simplify kVAR calculation for power factor improvement. The size of capacitor in kVAR is the kW multiplied by factor in table to improve from existing power factor to proposed power factor. Check the others solved examples below.

Example 2:

An Alternator is supplying a load of 650 kW at a P.F (Power factor) of 0.65. What size of Capacitor in kVAR is required to raise the P.F (Power Factor) to unity (1)? And how many more kW can the alternator supply for the same kVA loading when P.F improved.

Solution #1 (Simple Table Method using Table Multiple)

Supplying kW = 650 kW

From Table 1, Multiplier to improve PF from 0.65 to unity (1) is 1.169

Required Capacitor kVAR to improve P.F from 0.65 to unity (1).

Required Capacitor kVAR = kW x Table 1 Multiplier of 0.65 and 1.0

= 650kW x 1.169

= 759.85 kVAR

We know that P.F = Cosθ = kW/kVA . . .or

kVA = kW / Cosθ

= 650/0.65 = 1000 kVA

When Power Factor is raised to unity (1)

No of kW = kVA x Cosθ

= 1000 x 1 = 1000kW

Hence increased Power supplied by Alternator

1000kW – 650kW = 350kW

Read More : How to Select the Right Capacitor Value for a Single-Phase Motor

Solution # 2 (Classic Calculation Method)

Supplying kW = 650 kW

Original P.F = Cosθ₁ = 0.65

Final P.F = Cosθ₂ = 1

θ₁ = Cos^-1 = (0.65) = 49°.45; Tan θ₁ = Tan (41°.24) = 1.169

θ₂ = Cos^-1 = (1) = 0°; Tan θ₂ = Tan (0°) = 0

Required Capacitor kVAR to improve P.F from 0.75 to 0.90

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

= 650kW (1.169– 0)

= 759.85 kVAR

How to Calculate the Capacitor Value in Microfarad & kVAR?

The following methods show that how to determine the required capacitor bank value in both kVAR and Micro-Farads. In addition, the solved examples also show that how to convert the capacity of a capacitor in microfarad to kVAR and kVAR to microfarad for P.F. This way, a right size capacitor bank can be installed in parallel to each phase load side to obtain the targeted power factor.

Example: 3

A 500 volts 60 c/s single phase motor takes a full load current of 50 amp at P.F 0.86 lagging. The motor power factor has to be improved to 0.94 by connecting capacitor bank across it. Calculate the required capacity of capacitor in both kVAR and μ-Farads?

Solution:

(1) To find the required capacity of Capacitance in kVAR to improve P.F from 0.86 to 0.94 (Two Methods)

Solution #1 (Table Method)

Motor Input = P = V x I x Cosθ

= 500V x 50A x 0.86

= 21.5kW

From Table, Multiplier to improve PF from 0.86 to 0.94 is 0.230

Required Capacitor kVAR to improve P.F from 0.86 to 0.94

Required Capacitor kVAR = kW x Table Multiplier of 0.86 and 0.94

= 21.5kW x 0.230

= 4.9 kVAR

How to Find Capacitor Size in kVAR and Farad for PF Correction?

Read More : How to Replace a Ceiling Fan Capacitor: The Ultimate Step-by-Step Guide for Beginners

Solution # 2 (Calculation Method)

Motor Input = P = V x I x Cosθ

= 500V x 50A x 0.86

= 21.5kW

Actual or existing P.F = Cosθ₁ = 0.86

Required or target P.F = Cosθ₂ = 0.94

θ₁ = Cos^-1 = (0.86) = 30.68°; Tan θ₁ = Tan (30.68°) = 0.593

θ₂ = Cos^-1 = (0.95) = 19.94°; Tan θ₂ = Tan (19.94°) = 0.363

Required Capacitor kVAR to improve P.F from 0.86 to 0.95

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

= 21.5kW (0.593 – 0.363)

= 4.954 kVAR

(2) To find the required capacity of Capacitance in Farads to improve P.F from 0.86 to 0.97 (Two Methods)

Solution #1 (Table Method)

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 / (2π x f x V²) in Farad
• C = kVAR x 10⁹ / (2π x f x V²) in Microfarad

Putting the Values in the above formula

= (4.954 kVAR) / (2 x π x 60Hz x 500²V)

= 52.56 μF

Solution # 2 (Calculation Method)

kVAR = 4.954 … (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

= (500V) x 2π x (60Hz) x C

I_C = 188495.5 x C

And,

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

= 500V x 188495.5 x C

I_C = 94247750 x C … (ii)

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

94247750 x C = 4.954 kVAR x C

C = 4.954 kVAR / 94247750

C = 78.2 μF

Read More : The Essential Role of a Capacitor in Ceiling Fans: Understanding How it Works

Example 4

What value of Capacitance must be connected in parallel with a load drawing 1kW at 70% lagging power factor from a 208V, 60Hz Source in order to raise the overall power factor to 91%.

Solution:

You can use either Table method or Simple Calculation method to find the required value of Capacitance in Farads or kVAR to improve Power factor from 0.71 to 0.97. So We used the table method in this case.

P = 1000W

Actual Power factor = Cosθ₁ = 0.71

Desired Power factor = Cosθ₂ = 0.97

From Table, Multiplier to improve PF from 0.71 to 0.97 is 0.741

Required Capacitor kVAR to improve P.F from 0.71 to 0.97

Required Capacitor kVAR = kW x Table Multiplier of 0.71 and 0.97

= 1kW x 0.741

= 741 VAR or 0.741 kVAR (required Capacitance Value in kVAR)

Current in the Capacitor =

I_C = Q_C / V

= 741kVAR / 208V

= 3.56A

And

X_C = V / I_C

= 208V / 3.76 = 58.42Ω

C = 1/ (2π x f x X_C)

C = 1 (2π x 60Hz x 58.42Ω)

C = 45.4 μF (required Capacitance Value in Farads)

Key Parameters for Calculating Capacitor Size

To calculate capacitor size, you need the following parameters:

1. System Voltage (V): The operating voltage of your system.
2. Power Factor (Initial and Target): The current and desired power factor.
3. Load (kW): The total active power consumption of the system.

Read More : What Is the Difference Between a Battery and a Capacitor? | Complete Guide

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Capacitor kVAR to μ-Farad & μ-Farad to kVAR Conversion

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

Required Capacitator 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

Required 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

Where:

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

Good to Know:

Following are the important electrical formulas used in Power factor improvement calculation.

Active Power (P) in Watts:

• kW = kVA x Cosθ
• kW = HP x 0.746 or (HP x 0.746) / Efficiency … (HP = Motor Horse Power)
• kW = √ ( kVA² – kVAR²)
• kW = P = V x I Cosθ … (Single Phase)
• kW = P = √3x V x I Cosθ … (Three Phase Line to Line)
• kW = P = 3x V x I Cosθ … (Three Phase Line to Phase)

Apparent Power (S) in VA:

• kVA = √(kW² + kVAR²)
• kVA = kW / Cosθ

Reactive Power (Q) in VA:

• kVAR = √(kVA² – kW²)
• kVAR = C x (2π x f x V²)

Read More : Why Do We Use Capacitor Banks in Power Systems?

Power Factor (from 0.1 to 1)

• Power Factor = Cosθ = P / V I … (Single Phase)
• Power Factor = Cosθ =  P / (√3x V x I) … (Three Phase Line to Line)
• Power Factor = Cosθ =  P / (3x V x I) … (Three Phase Line to Neutral)
• Power Factor = Cosθ = kW / kVA  … (Both Single Phase & Three Phase)
• Power Factor = Cosθ = R/Z … (Resistance / Impedance)

And

• X_C = 1 / (2π x f x C) … (X_C = Capacitive reactance)
• I_C = V / X_C … (I = V / R)

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Causes of Low Power Factor:

The main cause of the low Power factor is Inductive Load. Current lags 90° from the voltage in a purely inductive circuit. This huge difference in phase angle between current and voltage causes zero power factor.

Following are the causes of low Power factor:

• Single phase and three phase induction motors. Usually, Induction motor works at poor power factor i.e. at:
  • Full load, Pf = 0.8 -0.9
  • Small load, Pf = 0.2 -0.3
  • No Load, Pf may drop to Zero (0)
• Varying Load in Power System (when the power system is lightly loaded, the ratio of real power to reactive power is reduced, resulting in a decreased power factor).
• Industrial heating furnaces.
• Electrical discharge lamps (High-intensity discharge lighting) Arc lamps (which operate at a very low power factor).
• Transformers.
• Harmonic Currents.

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Why accurate capacitor bank sizing is required ?

For better efficiency, capacitor bank should be chosen wisely.

• Overly size capacitor bank will cause cable to heat
• Under size capacitor bank will not benefit, as electricity bill will still be high due to high power factor.

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Capacitor Sizing Chart & Table for Power Factor Correction

The following power factor correction chart can be used to easily find the right size of capacitor bank for desired power factor improvement. For example, if you need to improve the existing power factor from 0.6 to 0.98, just look at the multiplier for both figures in the table which is 1.030. Multiply this number with the existing active power in kW. You can find the real power by multiplying the voltage to the current and the existing lagging power factor i.e. P in Watts = Voltage in volts x Current in Amps x Cosθ₁. This easy way, you will find the required value of capacitance in kVAR which is needed to get the desired power factor.

Read More : Why Capacitor Banks Drastically Improve Power Factor in Motor Circuits

Steps for power factor correction calculator:

When power is given in kVA:

For 1 phase AC circuit:

First we have to convert the given power factors into angle using formula:

From the above formula, we can calculate angle of old and new power factor required.

After angle calculation, the required capacitance reactive power is calculated using the formula:

For the capacitance:

For 3 phase AC circuits:

First we have to convert the given power factors into angle using formula:

From the above formula, we can calculate angle of old and new power factor required.

After angle calculation, the required capacitance reactive power is calculated using the formula:

For the capacitance:

If line to line voltage is given, then first it is converted to phase voltage using formula formula (only valid for Y-connected loads, if delta connected load is given then no conversion is required as in delta connected load phase voltage is equal to line voltage):

Note:

In the above formulas:

• Power factor (p.f) is given in form of unit, ranging from 0 to 1 (for example: 0.8, 0.9). If p.f is expressed in terms of percentage then it is first converted into units by dividing percentage power factor by 100 and then its value is given in the formula.
• If load is Y-connected, and line to line voltage is selected then first convert it in to line to neutral voltage (phase voltage) by 1.73

Read More : What Is the Difference Between a Battery and a Capacitor? | Complete Guide

Practical Considerations in Sizing Capacitors

• Overcompensation Risk: Adding excessive capacitance can lead to overcorrection, causing instability and equipment damage.
• Voltage Tolerance: Ensure the capacitor voltage rating matches or exceeds the system voltage.
• Harmonics: High harmonic levels in the system may require special harmonic filters.

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Tools and Software for Capacitor Sizing

To simplify the calculations, you can use tools such as:

• Power Factor Correction Calculators: Many online calculators are available for quick estimations.
• Electrical Simulation Software: Programs like ETAP or MATLAB offer accurate capacitor sizing capabilities.

How to Find Capacitor Size in kVAR and Farad for PF Correction?

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Applications of Power Factor Correction

Capacitor banks are used extensively in:

• Industrial plants to improve machinery efficiency.
• Commercial buildings to lower utility bills.
• Renewable energy systems for grid stability.

Read More : Why Does a Capacitor Block DC But Pass AC?

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Frequently Asked Questions

Q1: Why is power factor correction important?
Power factor correction reduces energy losses, avoids penalties, and enhances the efficiency of electrical systems.

Q2: Can capacitors eliminate all reactive power?
No, capacitors can only compensate for inductive reactive power; they cannot address issues caused by harmonic distortion.

Q3: How do I measure my current power factor?
You can use a power quality analyzer or refer to your utility bill, which often lists the power factor.

Q4: Are there alternatives to capacitors for PF correction?
Yes, synchronous condensers and advanced power electronics like STATCOMs can also correct power factor.

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