Power Factor Correction Capacitors Sizing Calculations – Part Thirteen

Today, we will explain the power factor compensation in case of harmonics distortion.

Linear and Non-Linear Loads

Electrical loads can be categorized to Linear and non-linear loads as follows:

1- Linear loads
  • Linear loads occur when the impedance is constant; which implies the current is proportional to the voltage. a straight-line graph as shown in the figure-1 below.
  • Simple loads, composed of one of the elements (Resistors only or inductors only or capacitors only) do not produce harmonics.

Fig.1: Linear loads

2- Non-linear loads
  • Non-linear loads occur when the impedance is not constant; then the current is not proportional to the voltage. as shown in the figure-2 below. 
  • Combinations of the components normally create non-linear loads and harmonics.

Fig.2: Non-linear loads

  • The non-linear loads (electronic systems) dramatically increase harmonic noise on the line side of the power distribution plant which impacts the whole electrical distribution system. Typical examples of non-linear loads (harmonic sources) are:

1- Electronic Switching Power Converters
Uninterruptible power supplies (UPS)
Solid-state rectifiers
Electronic process control equipment, PLC’s, etc
Electronic lighting ballasts, including light dimmer
Neon SCR controlled equipment
Reduced voltage motor controllers
DC drives
2- Arcing Devices
Discharge lighting, e.g. Fluorescent, Sodium and Mercury vapor
Arc furnaces
Welding equipment
Electrical traction system
3- Ferromagnetic Devices
Transformers operating near saturation level
Magnetic ballasts (Saturated Iron core)
Induction heating equipment
4- Appliances
TV sets, air conditioners, washing machines, microwave ovens & vacuum cleaners
Fax machines, photocopiers, printers

  • Non-linear loads inject non-sinusoidal currents into the network. These currents are formed by a 50 Hz or 60 Hz fundamental component, (as well as a DC component in some cases), plus a series of overlaid currents with frequencies which are multiples of the fundamental frequency which known as harmonics.

Effects Of Harmonics On The Electrical Power System

Harmonics have detrimental effect on the electrical power system in a facility. Examples of Harmonic Distortion Problems are shown in below table-1:uipment Consequences

Current Harmonic Distortion Problems
Blown fuses, reduced capacitor life
Reduced motor life, inability to fully load motor
False/spurious operation, damaged components
Increased copper losses, reduced capacity
Voltage Harmonic Distortion Problems
Increased noise, possible insulation failure
Mechanical fatigue
Electronic loads

Table-1: Negative Consequences of Harmonics on Equipment

If any of these conditions exist in your facility, an analysis of your system must be done.

For more information about harmonics, please review our article” Electrical Load Classification and Types – Part Three

Harmonics Effects On Power Factor Capacitors

  • With non-linear loads it is extremely difficult to correct for poor power factor without increasing existing harmonic distortion.
  • The harmonics lead to a higher capacitor current, because the higher frequencies are attracted to the capacitor. The impedance of the capacitor decreases as the frequency increases. If the frequency of such a resonating circuit is close enough to a harmonic frequency, the resulting circuit amplifies the oscillation and leads to over-currents and over-voltages.
  • Capacitors themselves do not generate harmonics, but under certain conditions they can amplify existing harmonics. Necessary precautions must be undertaken when selecting the capacitors.
  • To minimize the occurrence of harmonic resonance, the resonant harmonic of the system including the capacitor should be estimated.
  • The resonant frequency can be calculated from the following formula:

f = fp √(Psc/Pc)


f = resonant frequency,
fp = power frequency,
Psc = short circuit power of the transformer (kVA),
Pc = power of the capacitor (kVAR).

If the frequency obtained is too close to that of a harmonic, the value of the capacitor rating should be modified. Most common harmonic frequencies, 3rd, 5th, 7th, etc...


for the following transformer:
S = 630 KVA
Usc = 6%
P = 500 KW
Qc = 275 kVAr
Calculate the resonant frequency.


The short-circuit power is: Ssc = S x 100 / Usc = 630 x 100 / 6 = 10500 KVA

The resonance frequency will therefore be:
f = fp √(Psc/Pc) = 50 x √(10500/275) = 308.96 Hz
The system will resonate at order n = f/ fp = 6.18

  • In three-phase, low-voltage systems, harmonic values of 5, 7, 11, 13, 17, 19 etc. should be avoided as they correspond to the characteristic harmonics of non-linear loads. This includes all of the odd harmonics except for the multiples of 3. Examples of such devices are variable-speed and variable-frequency ac drives, dc drives, three-phase power-controlled furnaces and many other types of industrial equipment.
  • In single-phase, low-voltage systems, generally exhibit the following harmonics: 3, 5, 7, 9, 11, 13 etc. Note that this includes all of the odd harmonics. Examples of such devices are those usually powered by ‘switch mode power supplies’, which include personal computers, fluorescent lighting, and a myriad of other equipment found in the modern office. It also includes equipment found in hospitals, TV and radio stations, and control rooms of large processing plants. The harmonics from these devices are generally richest at the third harmonic and continually decrease as the harmonic number increases.

Harmonic Limits in Electric Power Systems (IEEE 519-2014)

Harmonic limitations have been established by IEEE 519 2014 for the following reasons:
  1. To limit the damage to power factor correction capacitors and harmonic filter systems caused by excessive harmonics.
  2. To prevent series or parallel resonance in the electrical system.
  3. To keep the level of harmonics at the PCC (Point of Common Coupling) from being excessive and distorting the system voltage and damaging other equipment on the system.

The PCC is defined as the electrical connecting point or interface between the utility distribution system and the customer's electrical distribution system.

The harmonic voltage limitations set forth by IEEE 519-2014 for Bus voltage V at PCC ≤ 1.0 kV are:

  • Maximum Individual Frequency Voltage Harmonic: 5%
  • Total Harmonic Distortion of the Voltage: 8%

For other voltage ratings, please see below table-2:

Bus voltage V at PCC
Individual harmonic (%)
Total harmonic distortion THD (%)
V ≤ 1.0 kV
1 kV < V ≤ 69 kV
69 kV < V ≤ 161 kV
161 kV < V
Table 2: Voltage distortion limits

Notes to Table-2:
  • aA High-voltage systems can have up to 2.0% THD where the cause is an HVDC terminal whose effects will have attenuated at points in the network where future users may be connected.
  • All values should be in percent of the rated power frequency voltage at the PCC. Table-2 applies to voltage harmonics whose frequencies are integer multiples of the power frequency.

Options to Reduce Harmonics for PFCC

Harmonic levels that exceed the recommended values set forth by IEEE 519-2014 should be addressed through harmonic filtering. Failure to address these harmonic issues may lead to problems on the electrical distribution system, such as those detailed above. For PFCC, the resonant harmonics can be avoided in several ways:

  1. Change the applied KVAR to avoid unwanted harmonics,
  2. Add harmonic filters,
  3. Add blocking inductors (detuned reactors),
  4. Change the method of KVAR compensation (harmonic filter, active filter, etc.).

1- Change the applied KVAR to avoid unwanted harmonics

  • Although this is the least expensive way to avoid resonant harmonics, it is not always successful because typically some portion of the applied KVAR is switched on and off as load conditions require. 
  • The calculation of system harmonics should be repeated for each level of compensation. Adjusting the size of the capacitor(s) may be necessary to avoid the harmonic values.

2- Add Harmonic Filters

  • In order to filter harmonics at a specific site, tuned harmonic filters can be applied. 
  • A capacitor is connected in series with an inductor such that the resonant frequency of the filter equals the harmonic to be eliminated. 
  • Tuned filters should never be applied without a detailed analysis of the system. The currents expected to flow in the filter are difficult to predict and are a complex function of the system and load characteristics.

There are 3 types of filters:

  1. Passive filter,
  2. Active filter,
  3. Hybrid filter.

1- Passive filter

Passive filter

  • This is an LC circuit tuned to a harmonic frequency to be filtered. This filter, mounted on a bypass circuit, absorbs the harmonics and prevents them from flowing in the power supply. However, for a significant reduction of the THD on several harmonic orders, several branch filter circuits will be necessary.
  • Passive filters, which are defined on a case by case basis, according to a particular harmonic to be filtered, are cost-effective and easy to be connected and put into function.

2- Active filter

  • This is an electronic power system designed to compensate either the harmonic voltage or the harmonic currents generated by the load. This filter re-injects, in phase-opposition, the harmonics present on the load's power supply so that the current in the line becomes sinusoidal.
  • The active filter has many advantages as follows:

  1. Filtering simultaneously dozens of harmonics and does not involve design costs for dimensioning.
  2. They continue to guarantee efficient harmonic compensation even when changes are made to the installation.
  3. Auto-configuration to harmonic loads whatever their order of magnitude
  4. Elimination of overload risks
  5. Compatibility with electrical generator sets
  6. Connection to any point of the electrical network
  7. Several conditioners can be used in the same installation to increase depollution efficiency (for example when a new machine is installed)
  8. Active filters may provide also power factor correction.

3- Hybrid filter

  • This involves a combination of the two Passive & Active filters described above for a broad power range.

Hybrid filter

2.1 Choosing The Optimum Filter

Table-3 below shows the criteria that can be taken into account to select the most suitable technology depending on the application.

Passive filter
Active filter
Hybrid filter
Applications with total power of non-linear loads (variable speed drive, UPS, rectifier…)
greater than 200 kVA
lower than 200 kVA
greater than 200 kVA
Power factor correction
Necessity of reducing the harmonic distortion in voltage for sensitive loads
Necessity of reducing the harmonic distortion in current to avoid cable
Necessity of being in accordance with strict
limits of harmonic rejected
Table-3: Choosing the optimum filter

2.2 Where to install your filter?

To choose the most suitable location to connect a filter in an installation, you must take into account:

  1. The type of disturbance present on the installation, which defines the type of filter to be installed.
  2. The configuration of the installation:
  3. Existence of capacitor banks
  4. Existence of major loads causing disturbance
  5. Power and location of the lighting and computer lines.

There are 3 points in an installation where you can connect filtering equipment in order to eliminate disturbances:

1- On the low-voltage general switchboard (LVGS)

  • When the disturbances have been eliminated or attenuated directly at the level of the loads or at the level of the secondary switchboards, the remaining residual disturbances can be eliminated by connecting filtering equipment on the general switchboard. 
  • In this way, it is possible to ensure that the electrical signal is in a satisfactory state at the point of connection with the energy supplier.

2- On the secondary switchboard

  • When there are various low-power loads connected to the secondary distribution switchboard. 
  •  Elimination of the disturbances prevents discharging of the lines connected to the general switchboard.

3- On the terminals of the load generating harmonics

  • This is the best solution for eliminating the disturbance directly at the point where it is generated, thus preventing propagation to all the lines in the electrical installation.

3- Add blocking inductors (detuned reactors)

  • The most common solution, as illustrated in the Std. IEC 61642, consists in connecting in series an inductive reactance with the capacitor (detuning reactance); the inductor shall be sized so that a resonance frequency which is below the lowest frequency of the harmonic voltage in the network is achieved.

Detuned Reactors

  • Inductors added to the lines feeding the capacitor can be sized to block higher than 4th harmonic currents. This method protects the capacitor from the harmonics but does not eliminate the harmonics from the system. A system study is required to determine correct ratings for the capacitor and inductors.

3.1 Choice Of Detuned Reactor Tuning Frequency

The detuned reactor, 400 V, 50 Hz range offers a wide selection of tuning frequencies: 135, 190 or 215 Hz. Tuning frequency of the reactor capacitor must be chosen according to:

  1. The harmonic frequencies present on the installation (tuning frequency must always be lower than the harmonic spectrum)
  2. The remote control frequencies, if any, used by electrical utilities,
  3. Presence of zero-sequence harmonics (3, 9, …),
  4. Need for reduction of the harmonic distortion level,
  5. Optimization of the capacitor and reactor components,
  6. Frequency of ripple control system if any.

Tuning frequency of the reactor capacitor can be selected from the below table-4:

harmonic generators (Gh)
remote control frequency (Ft)

165 < Ft≤ 250 Hz
250 < Ft≤ 350 Hz
Ft > 350 Hz
variable speed drives, rectifiers,
UPS, starters
tuning frequency
135 Hz
190 Hz
215 Hz *
tuning frequency
135 Hz
tuning frequency
190 Hz
tuning frequency
215 Hz
single-phase (Gh 1Ph > 10 % Sn):
discharge lamps, lamps with electronic ballast,
fluorescent lamps, UPS,
variable speed drives, welding machines
tuning frequency
135 Hz

tuning frequency
135 Hz
tuning frequency
135 Hz
tuning frequency
135 Hz

Table-4: DR, 400 V, 50 Hz tuning frequency selection

* Recommended tuning frequency, allowing a greater reduction in 5th order harmonic pollution than the other tuning frequencies.
Gh 1Ph: power of single-phase harmonic generators in kVA.

Relation between tuning frequency, tuning order and relative impedance:

The most common values of relative impedance are 5.7, 7 and 14%. (14% is used with high level of 3rd harmonic voltages).
The tuning frequency can be expressed by the relative impedance of the reactor (in %), or by the tuning order, or directly in Hz.

Relative impedance (%)
Tuning order

Tuning frequency
@50Hz (Hz)
Tuning frequency
@60Hz (Hz)




Power Factor Compensation In Case Of Harmonics

Generally, and from the past articles, we can say that we have 3 general methods of PF compensation according to the level of network harmonic pollution as follows:

  1. Standard compensation,
  2. Overrated compensation,
  3. Detuned compensation.

The selection between the above methods can be made based on the following two criteria:

  1. From the Gh/Gn ratio,
  2. From the THD(I) current total harmonic distortion measured.

1- From the Gh/Gn ratio

Considering the following parameters:

  • Sn : transformer apparent power
  • Gh : apparent power of loads generating harmonics (variable speed motors, static converters, power electronics, etc.)
  • Qc : compensation equipment power
  • U : network voltage

So, the following table can be applied:

Gh/Gn value
Compensation equipment type
< 15%
standard type
15 : 25%
Overrated type
> 25%
detuned type *
> 60%
detuned type + harmonics filtering **

* Please check that the de-tuned capacitor bank does not interfere with telecommunication frequency used by the utilities
** requires a harmonic filtering study.


Select the best compensation method For The following parameters:
U = 400 V
Sn = 800 kVA

In the following cases:
Case#1: P = 450 kW and Gh = 50 kVA
Case#2: P = 300 kW and Gh = 150 kVA
Case#3: P = 100 kW and Gh = 400 kVA


For case#1:
Gh/ Sn  = 6.2 %
Use Standard type equipment

For case#2:
Gh/ Sn  = 18.75 %
Use Overrated type equipment

For case#3:
Gh/ Sn  = 50 %
Use Detuned type equipment

2- From the THD(I) current total harmonic distortion measured

Considering the following parameters:

Sn = transformer apparent power
S = load in kVA at the transformer secondary at the time of measurement

So, the following table can be applied:

THD(I) x S/ Sn < 5 % 
Use Standard type equipment
5 % < THD(I) x S/ Sn < 10 %
Use Overrated type equipment
10 % < THD(I) x S/ Sn < 20 %
Use Detuned type equipment


  • Harmonics must be measured at the transformer secondary, at full load and without capacitors.
  • Apparent power must be taken into account at the time of measurement.

In the next article, we will explain the (3) Famous Power Factor Correction Capacitors Calculators. Please, keep following.

The previous and related articles are listed in below table:

Subject Of Previous Article
  • Glossary of Power Factor Correction Capacitors

  • Types of Loads,
  • The Power Triangle,
  • What is a power factor?
  • Types of power factor
  • Why utilities charge a power factor penalty?
  • Billing Structure.

  • What causes low power factor?
  • Bad impacts of low power factor,
  • Benefits of Power Factor correction.

  • How to make Power Factor Correction?
  • Types of Power Factor Correction Capacitors
  • Individual compensation

  • Group compensation,
  • Central compensation,
  • Hybrid compensation.
  • Summary for Power Factor Correction Capacitors Sizing Calculations Steps

  • Step#1: Collect Monthly Billing Data
  • Step#2: Make Some Preliminary Measurements For Current And Voltage

  • Step#3: Fill the Economic Screening Worksheet

  • Step#4: Make Preliminary Measurements For Harmonics
  • Step#5: Repeat the Economic Screening Worksheet
  • Step#6: Compare the Savings with the Probable Cost of Capacitors' Installation
  • Second: Design Phase
  • Step#1: Performing a Detailed Plant Survey
  • Step#1.A: Review the one line diagram
  • Step#1.B: Take into consideration the loads that produce harmonics
  • Step#1.C: collect sufficient data Inventory by using measuring instruments

  • Step#2: Select Economical Capacitor Scheme
  • Step#3: Checking the "No Load" Voltage Rise
  • Step#4: Select Capacitor Switching Options
  • Step#5: Check the Harmonic Distortion and make Harmonic Mitigation Options
  • Step#6: Use the Economic Screening Worksheet again

  • Power Factor Correction Capacitors Sizing Calculations Steps For New Designs

  • Factors Affecting The Rated KVAR For a Capacitor
  • Calculation of the Capacitor KVAR Rating for Compensation at:

  1. Transformer
  2. Individual Motors

  • 3- Calculation Of The Capacitor KVAR Rating For Buildings And Power Plants(Group Compensation)