Power Factor Correction Capacitors Sizing Calculations – Part Two

Today, we will start explaining the technical part for Power Factor Correction Capacitors Sizing Calculations. We will explain the following topics:

  1. Applicable Standards for Power Factor Correction,
  2. Types of Loads,
  3. The Power Triangle,
  4. What is a power factor?
  5. Types of power factor
  6. Why utilities charge a power factor penalty?
  7. Billing Structure.

1- Applicable Standards for Power Factor Correction

 Applicable Standards for Power Factor Correction will include:

  • IEC: 61921 (Power Capacitors- Low voltage power factor correction banks) this standard is the international standard applicable for Low Voltage Power Factor Correction Banks and Automatic Power Factor Correction (APFC) equipments intended to be used for power factor correction purposes, equipped with built in switch gears and control gears. The guidelines for design, installation, operation and safety of APFC panels are followed based on this international standard.

The design of the Low Voltage Power Factor Correction banks and accessories shall comply with the following standards:

  • IEC60831: Part 1 & 2-Shunt power capacitors of the self healing type for a.c systems having rated voltage up to and including 1kV.
  • IEC 60439-3: Low voltage switchgear and control gear assemblies. Particular requirements for low-voltage switchgear and control gear assemblies intended to be installed in places where unskilled persons have access for their use-Distribution boards.
  • IEC 60947: Low Voltage Switchgear
  • Part 2: Molded Case Circuit Breakers & Air circuit Breakers
  • Part 4: Power Contactors
  • Part 4-3: Thyristor Switch
  • IEC 60269: LV Fuses
  • IEC 60076-6: Reactors
  • IEC 60529: Degree of protection provided by enclosure (IP code)
  • IEC 60044-1: Current transformers.
  • IEC 60664-1 / IEC 61326: Power Factor Controller.

2- Types of Loads

 In our previous article "Electrical Load Classification and Types” in our course “EE-1: Beginners' Electrical design Course”, We explained before that the electrical loads can be classified into various categories according to various factors, here for this course the important electrical loads classified categories will be:

1- According To Load Nature-1

  1. Resistive Electrical Loads.
  2. Capacitive Electrical Loads.
  3. Inductive Electrical Loads.
  4. Combination Electrical Loads.

You can review our explanation for the Linear Electrical Loads in our article “Electrical Load Classification and Types – Part Two

2- According To Load Nature-2
  1. Linear Electrical Load.
  2. None-Linear Electrical Load.

You can review our explanation for the None-Linear Electrical Loads in our article “Electrical Load Classification and Types – Part Three” and also in our article “Generators Sizing Calculations – Part Seven

3- The Power Triangle

 Actually, most loads in modern electrical distribution systems are inductive. Inductive loads are not always easily identifiable, and the most certain way of identifying them is through a power factor survey. The power drawn from the network by inductive loads consists mainly from two different parts; the useful power and reactive power.

1- Useful power P

It is the real power transmitted to loads such as motors, lamps, heaters, computers to achieve the task. The electrical active power is transformed into mechanical power, heat or light. It is measured in kW.

2- Reactive power Q

It is used only to supply the magnetic circuits of machines, motors and transformers. The consumption of reactive power does not contribute to achieving the task.it is measured in KVAR.

The useful power and the reactive power together determine the power drawn from the network, that is, the total power (also known as apparent power),

3- The apparent power S

It is the vector combination of active and reactive power. it is not the linear sum of useful power and reactive power. However, lessening the effects of reactive power will reduce the power needed from the network to complete the same tasks. It is measured in kVA.

A right power triangle is often used to illustrate the relationship between kW, kVAR, and kVA.

Power Triangle

4- What is a power factor?

Power factor is the ratio of active power to apparent power. The Power Factor (P/S) is equal to cos φ.


PF measures how effectively electrical power is being used. A high power factor signals efficient utilization of electrical power, while a low power factor indicates poor utilization of electrical power.

An ideal ratio is 1.0, thatis, a perfect match between power drawn from the network and useful power for the task. This is also known as unity power factor.

5- Types of power factor

 There are two types of power factor should be recognized as follows:

  1. The displacement power factor,
  2. The Total power factor.

5.1 The Displacement Power Factor

Displacement Angle

the above definition of the power factor is used only if there is no harmonics on the network. This is the case when pure sinusoidal (without harmonics) wave forms exist. In this case the power factor angle φ represents a phase shift or displacement between voltage and current. In this case the power factor will be called the displacement power factor and which can be measured with a power factor meter.

5.2 The Total power factor

On some networks and loads harmonics can be found and can be observed by a spectrum analyzer. The Harmonics will make a wave form distortion and a harmonic component will affect the value of the power factor to give what is called The Total power factor.
Comparison between displacement and total power factor:

The Displacement Power Factor
The Total Power Factor

Pure sinusoidal (without harmonics) wave forms exist
Distorted wave forms due to harmonics
Can be measured with a power factor meter
Can’t be measured with a power factor meter, it is observed only by a spectrum analyzer
Can be corrected by adding  capacitors
Can’t be corrected by adding capacitors but can be corrected by using filter circuits.
Commonly specified by the manufactures of equipment
Must be measured with  a power analyzer

Total Power Factor=Displacement Factor×Distortion Factor
Displacement Factor = Cos Φ
Distortion Factor = 1/ (1 + THD2)

Total Power Factor=  Cos Φ / (1 + THD2)

Power Analyzer

Also, you must be able to differentiate between two uses of power factor expression:

  1. Power factor for Equipment,
  2. Power factor for consumer’s network.

5.3 Power Factor For Equipment

This power factor is commonly specified by the manufactures of equipment.

Examples for common Equipment Creating Poor Power Factor are listed in below:

Power Factor%
Incandescent Lamps
The power factor is equal to unity (100%).
Fluorescent Lamps
Usually have a low power factor; for example, 50% power factor would not be unusual. They are sometimes supplied with a compensation device to correct low power factor.
Mercury Vapour Lamps
The power factor of the lamp is low; it can vary from 40% to 60%, but the lamps are often supplied with correction devices.
Distribution Transformer
The power factor varies considerably as a function of the load and the design of the transformer. A completely unloaded transformer would be very inductive and have a very low power factor.
Induction Motors
The power factor varies in accordance with the load. Unloaded or lightly loaded motors exhibit a low power factor. The variation can be 30% to 90%.
Synchronous Motors
Very good power factor when the excitation is properly adjusted. Synchronous motors can be over excited to exhibit a leading power factor and can be used to compensate a low power system.
Industrial Heating

With resistance, as in ovens or dryers, the power factor is often closed to 100%.
Air Compressor & Pumps (external Motors)
Hermetic Motors (compressors)
Arc Welding
Resistance Welding
Arc Furnaces
Induction Furnaces (60Hz)
Standard Stamping
High Speed Stamping
AC DC Converters
DC Drives
AC Drives

Solution for Equipment Creating Poor Power Factor

If a single machine has a poor power factor, capacitors can be connected in parallel with the device, that is, connected to the live and the neutral terminals of the reactive device, so that they compensate for the poor power factor whenever the machine is switched on. This is a form of ‘fixed’ PFC which will be explained in detail later.

5.4 Power Factor For Consumer’s Network

This power factor is representing the efficiency of the consumer’s network for utilizing the utility power. It can be measured by power factor meter or can be calculated using excel sheets or software which will be explained later.

Examples for consumer’s network with poor power factor are listed in below:

Power Factor %
Arc Welding
Resistance Welding
Arc Furnaces
Induction Furnaces (60Hz)
Machine shops
Cement works
Clothing factories
Steel works
Brick works
Cold stores
Plastic moulding
Rolling mills(thyristor drives)
Auto Parts
Coal Mine
Machine Manufacturing
Office Building
Oil field Pumping
Paint Manufacturing
Tool, dies, jigs industry

Solution for Consumer’s Network with Poor Power Factor

  • As a brief, if the power factor at a site is permanently poor and no single item of equipment is solely responsible, fixed PFC can be employed also. In this case, the PFC capacitors will be connected across the main power supply to the premises, that is, the capacitor banks’ terminals are connected to each of the three phase cables as they enter the site. In this case, PFC can be linked with the switchgear.
  • However, there are other circumstances where PFC is not so straightforward. Where many machines are switching on/off at various times, the power factor may be subject to frequent change. In these cases the amount of PFC needs to be controlled automatically — that is, the banks of capacitors need to be selectively switched in and out of the power circuit appropriately. There are various solutions on the market for automatically controlled PFC which will be explained later.

6- Why utilities charge a power factor penalty?

Utility companies as a rule have fixed tariffs for their smaller power consumers, while individual supply contracts are negotiated with the larger consumers.
With most power supply contracts the costs for electrical power comprise:

  • Power [kW] measured with a maximum demand meter, e.g. monthly maximum demand over a 15 minute period.
  • Active energy [kWh] measured with an active current meter usually split into regular and off-peak tariffs.
  • Reactive energy [kVArh] measured with a reactive current meter, sometimes split into regular and off-peak tariffs.

Now, if a facility has low power factor, Utilities must design their systems with oversized equipment to accommodate reactive current. In order to pass along the expense of the larger equipment required and the system losses from the flow of the reactive current, many utilities will charge their customers a penalty for low power factor as one of or combination of, the following:
  • A penalty for power factor below and a credit for power factor above a predetermined value,
  • An increasing penalty for decreasing power factor,
  • A charge on monthly KVAR Hours,
  • KVA demand: A straight charge is made for the maximum value of KVA used during the month. Included in this charge is a charge for KVAR since KVAR increase the amount of KVA. 

There are a variety of means in which this penalty is calculated by the utility, for example:

  • One utility indicated that if the customer’s power factor is less than 90 percent, they are permitted to substitute the kVA reading (apparent power) for the kW reading (true power) for billing purposes.
  • Another utility called for penalties ranging from 1 to 3 percent when power factor drops below 85 percent but not less than 70 percent. Power factors below 70 percent are not permitted, and customers are required to invest in power factor correction equipment to improve the power factor above this level. Until corrections are made, a 25 percent penalty is applied after two consecutive months below 70 percent and continues until corrections are completed.
  • Another utility will invoice the costs of reactive energy only when this exceeds 50% of the active power load. This corresponds to a power factor cos Ø= 0.9. It is not stipulated that the power factor must never dip below this value of 0.9. Invoicing is based on the power factor monthly average. Utility companies in some areas stipulate other power factors, e.g. 0.85 or 0.95.
  • Some utilities will invoice the power not as kW but as kVA. In this case the costs for reactive energy are therefore included in the power price. To minimize operating costs in this case, a power factor cos Ø =1 must be aimed for. In general, it can be assumed that if a power factor correction system is correctly dimensioned, the entire costs for reactive energy can be saved.

7- Billing Structure

Utility Bill

The more common ways utilities calculate electrical bills are as follows:

  1. 90% Billing Structure,
  2. 100% KVA + 100% KW Billing Structure,
  3. kVA billing,
  4. kVA billing + KWH billing,
  5. kW demand billing with power factor adjustment,
  6. kVAR reactive demand charge.

7.1 90% Billing Structure

Where demand billed is based on 90% of the KVA or 100% of the KW, whichever is greater.


The following data for one facility
KVA = 1000, KW = 800, KVAR = 600, PF = .80, calculate the facility billing using 90% Billing Structure.


90% of the KVA 1000 x 0.90 = 900 KVA
100% of the KW = 800 KW
So, the facility will pay demand rates on 900KVA
Thus the facility is paying a penalty on 100 KVA (1000 KVA produced – 900 KVA demand) of unproductive power.
Correcting the facility’s Power Factor to 90% + will eliminate this penalty cost.

7.2 100% KVA + 100% KW Billing Structure


 Where one rate is applied to 100% of the KVA and another rate is applied to 100% of the KW. Both are then added together to determine the total demand charged on the bill.


With the same data from Example#1, calculate the facility billing using 100% KVA + 100% KW Billing Structure.


100% of the KVA 1000 = 1000 KVA
100% of the KW = 800 KW
Thus, Facility will pay demand costs on 1000 KVA + 800 KW = 1800,

7.3 kVA Billing


 The utility measures and bills for kVA demand.


Assume an uncorrected 460 kVA demand, 480V, three-phase at 0.87 power factor, Billing @ $4.75/kVA demand, calculate the facility billing using kVA billing.


Uncorrected original billing:
460 kVA × $4.75 = $2185 / month

7.4 kVA Billing + KWH Billing


Assume the same conditions in Example#3 except that:

kVA demand charge:
$1.91 / kVA / month

Energy charge:
(112,400 kWh / month energy consumed)

$0.0286 / kWh (first 200 kWh / kVA of demand)
$0.0243 / kWh (next 300 kWh / kVA of demand)
$0.021 / kWh (all over 500 kWh / kVA of demand)


kVA billing
460 kVA × $1.91 = $878.60
KWH billing
kWh = 112,400
460 × 200 = 92,000 kWh @ 0.0286 = $2631.20
balance only = 112,400 – 92,000 = 20,400 kWh @ $0.0243 = $495.72
total KWH billing = $2631.20 +$ 495.72 = $3126.92
Total billing = kVA billing + KWH billing = $878.60 + $3126.92 = $4005.52

7.5 KW Demand Billing With Power Factor Adjustment


The utility charges according to the kW demand and adds a surcharge or adjustment for power factor. The adjustment may be a multiplier applied to kW demand. The following formula shows a billing based on 90% power factor:

KW demand = KW × 0.90 / actual power factor

If power factor was 0.84, the utility would require 7% increase in billing, as shown in this formula:

KW demand = kW × 0.90/0.84 = 1.07 kW

Some utilities charge for low power factor but give a credit or bonus for power above a certain level as per the following:

  1. Rates based on power factor of 90% or higher. When power factor is less than 85%, the demand will be increased 1% for each 1% that the power factor is below 90%.
  2. If the power factor is higher than 95%, the demand will be decreased 1% for each 1% that the power factor is above 90%.
  3. There would be no penalty for 87% power factor. However, a bonus could be credited if the power factor were raised to 96%.


Assume a 400 kW load, 87% power factor with the following utility tariff.
Demand charges:
First 40 kW @ $10.00 / kW monthly billing demand
Next 160 kW @ $ 9.50 / kW
Next 800 kW @ $ 9.00 / kW
All over 1000 kW @ $ 8.50 / kW


At 87% power factor, there is no penalty.
So, utility billing will be :
Normal 400 kW billing demand
First 40 kW @ $10.00 = $ 400.00
Next 160 kW @ $ 9.50 = $1520.00
Bal. 200 kW @ $ 9.00 = $1800.00
Total 400 kW @ $3720.00 normal monthly billing


With the same 400 kW load, the power factor is only 81%.


At 81% power factor, there will be a penalty.
In this example, the customer will pay an adjustment on:
kW demand = 400 × 0.90 / 0.81 = 444 billing kW demand
First 40 kW @ $10.00 = $ 400.00
Next 160 kW @ $ 9.50 = $1520.00
Next 244 kW @ $ 9.00 = $2196.00

Total 444 kW $4116.00 – $3495.00 = $621.00 x 12 = $7452.00

7.6 KVAR Reactive Demand Charge


 The utility imposes a direct charge for the use of magnetizing power, usually a waiver of some percentage of kW demand. For example, if this charge were 60 cents per kVAR for everything over 50% of kW, and a 400 kW load existed at the time, the utility would provide 200 kVAR free.


Assume a 400 kW load demand at 81% power factor.

Demand charge is:
$635.00 for the first 200 kW demand
$ 2.80 per kW for all addition

Reactive demand charge is:
$ 0.60 per kVAR in excess of 50% of kW demand


Demand charge:
first 200 kW demand@ $635.00 = $635.00
200 kw addition @ $ 2.80 = $560.00
Total = $635.00 + $560.00 = $1195.00

Reactive demand charge
In this example, kW demand = 400 kW,
therefore 50% = 200 kVAR which will be furnished at no cost.
Cos Ø = PF = kW/kVA = 0.81
Tan Ø = = 0.724 = kvar/kW
kVAR = kW × Tan Ø = 400 × 0.724 = 289.6 kVAR
Because 200 kVAR is allowed, the excess kVAR is 89.6 (round to 90) x $0.60 = $54.00 per month billing for reactive demand.

Total billing = Demand charge + Reactive demand charge = $1195.00 + $54.00 = $1249.00

In the next article, we will continue explaining the technical part for Power Factor Correction Capacitors Sizing Calculations. Please, keep following.

The previous and related articles are listed in the below table:

Subject of Previous Article


Glossary of Power Factor Correction Capacitors

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