Power Factor Correction PFC Capacitors Explained

This post provides deeper look into capacitor based power factor correction circuits and power factor correction (PFC) capacitors.

Power Factor Correction Capacitors: Technical Overview

Power factor correction (PFC) capacitors are used in AC electrical distribution systems to compensate for inductive reactive power. By supplying leading reactive current close to inductive loads, such as motors, transformers, welding equipment and magnetic ballasts, they reduce the reactive-current demand seen by the upstream transformer, cables and utility supply.

ESR of Capacitors, Measurements and Applications

Degradation of Capacitors and its Failure Mechanisms

Backup Capacitors – Supercapacitor

For a given real-power demand in kilowatts (kW), improving power factor reduces apparent power in kilovolt-amperes (kVA) and lowers RMS current. This can release capacity in transformers and cables, reduce voltage drop and reduce resistive losses. Capacitor compensation does not make an inductive machine consume less useful real power; instead, it reduces the reactive current that must be supplied through the electrical distribution system. This article explains the operating principle, kVAr sizing, capacitor-bank architectures, harmonic risks, switching methods, protection requirements and selection criteria for industrial power factor correction capacitors.

Key Takeaways

Power Factor Correction (PFC) reduces reactive power and enhances efficiency in AC loads such as motors and transformers.
Capacitors are key components in PFC circuits, improving the power factor by compensating for lagging current.
Low power factors lead to increased energy costs and penalties from electricity suppliers; PFC systems address these issues.
Various types of PFC capacitors exist, including metallized polypropylene and bi-metallized paper capacitors, each suited for specific applications.
Automatic capacitor banks are recommended for dynamic loads, helping maintain optimal power factor without over- or under-correction.

Some of the AC power consumed by inductive loads is used to maintain magnetic reversals due to phase shift between current and voltage. This energy can be considered as wasted energy since it is not used in performing useful work. Power factor correction circuits are used to minimize reactive power and enhance the efficiency with which inductive loads consume AC power. Capacitors are essential components in power factor compensation circuits, and this article will explore some design considerations when using these components for power factor correction.

Power Factor Correction Circuits

Reactive Power in Inductive Loads

Inductive loads such as chokes, motors, inductive heating equipment, generators, transformers, and arc welding equipment produce an electrical lag that is commonly referred to as inductance. This inductance causes a phase difference between current and voltage. Figure 1 shows current and voltage waveforms for a load with zero lag (purely resistive load).

*Figure 1 Voltage and Current for an ideal load*

As a result of phase shift due to inductance, there are times when current and voltage have different signs. During such times, negative energy is generated and fed back into the power supply network. When the two regain same sign, a similar amount of energy is required to generate the magnetic fields. The energy that is lost due to magnetic reversals in inductive loads is commonly referred to as reactive power. Inductive AC loads are broadly classified into linear and non-linear devices. For linear loads, the current waveform and voltage waveform have matching sinusoidal profiles. Figure 2 shows current and voltage waveforms for a typical linear load. On the other hand, since non-linear loads draw current at different frequencies, the current and voltage waveforms are different. For most non-linear loads, the current waveform is usually non-sinusoidal. Figure 3 shows current and voltage waveforms for a non-linear load.

*Figure 2 Voltage and Current for a linear load*

*Figure 3 Voltage and Current for a non-linear load*

Some examples of linear electrical loads include heating equipment, motors, and incandescent lighting devices. Non-linear devices include variable frequency drives, DC drives, programmable controllers, arc-type lighting devices, induction furnaces, uninterruptible power supplies, and personal computers. Non-linear electrical loads are known to be a major cause of harmonic distortions in power distribution systems.

*Figure 4 and 5, active and reactive power of the total apparent power diagram*

Power Factor

The efficiency with which electrical devices or installations consume AC power varies. Some loads utilize power efficiently, while others waste a significant portion of the power that they consume. Power factor is used to describe the efficiency with which loads consume AC power. This dimensionless quantity ranges between 0 and 1. As shown in Figure 4 and Figure 5, the total AC power, also commonly known as apparent power, consumed by an electrical device or equipment depends on two components: useful power (active power) and reactive power. The useful power refers to the power that a device needs to accomplish a task. On the other hand, reactive power does not produce useful work. The useful power is usually measured in kW while the reactive power is measured in kVAR. As shown in Equation 1, the power factor is equal to the ratio of active power (useful power) to total power (apparent power) drawn by an electrical device or equipment. It can be shown mathematically that the power factor is equal to the cosine of angle θ (Equation 2). The closer this ratio is to 1.0, the higher is the efficiency of the device or equipment.

For an ideal electrical load, the power factor is equal to 1.0 (unity power factor). This means that all the power drawn by a load is used to do useful work. However, it is difficult for an actual electrical load to achieve that. The impedance for the load represented by Figure 5 is given by Equation 3, where XL is the inductive reactance and is given by Equation 4. Why is it difficult for an electrical load to achieve unity power factor? Most electrical loads have inherent reactive properties that make it difficult for them to achieve the ideal power factor. To overcome this limitation, power factor correction circuits are added to a network to compensate for a load’s reactive characteristics.

Power Factor, Displacement Power Factor and True Power Factor

Fundamental power relationships

In a sinusoidal AC system, active power P, reactive power Q and apparent power S form the power triangle:

S^2 = P^2 + Q^2

For a balanced three-phase system:

$P = \sqrt{3}V_{LL}I_L\cos\varphi$

$Q = \sqrt{3}V_{LL}I_L\sin\varphi$

$S = \sqrt{3}V_{LL}I_L$

where V_LL is line-to-line RMS voltage, I_L is line current and $\varphi$ is the phase angle between the fundamental voltage and current components. For a linear sinusoidal load, power factor is:

$\mathrm{PF}=\frac{P}{S}=\cos\varphi$

Why non-linear loads require a different assessment

The expression $mathrm{PF}=\cos\varphi$ applies only when voltage and current are sinusoidal. Variable-frequency drives, rectifiers, UPS systems, switched-mode power supplies and many LED drivers draw non-sinusoidal current containing harmonic components. In such systems, distinguish between displacement power factor, based on the phase shift of the fundamental components, and true power factor:

$\mathrm{True\ PF}=\frac{P}{S}$

Capacitor banks primarily compensate fundamental-frequency inductive reactive power. They do not remove harmonic current and, if poorly selected, can aggravate harmonic resonance. A power-quality measurement should therefore precede the installation or expansion of PFC capacitor banks where significant non-linear loads are present.

Power Factor Compensation

Electrical loads that have a low power factor consume more power that it is needed to perform a task. This can result in a considerable power loss in a network and high transformer losses. Such increases in energy consumption increase the cost of running equipment or installations. Poor power factors also cause a power distribution network to have increased voltage drops. It is common for power suppliers to penalize industries whose power factor is below a specified value.

Electricity suppliers encourage industrial consumers to improve their power factor for various reasons. To start with, improving power factor can help to cut the electricity bill by a significant margin. Secondly, a high power factor helps to minimize efficiency losses in a consumer’s transformers. Thirdly, adding power factor correction system helps to boost the effective capacity of a consumer’s electricity network. Lastly, a high power factor helps to increase the service life of electrical equipment.

A power factor compensation network lessens the power demanded by a load thus improving the overall power factor. The compensation network enables electrical loads to achieve a good power factor, typically between 0.95 and 0.98. A power factor of 0.85 and below is usually considered by utility companies as a poor power factor.

Power Factor Improving Methods and PFC Capacitors

There are various methods of improving the power factor of a load or an installation. One of the commonly used methods involves adding power factor correction capacitors to the network. Figure 6 shows a simple circuit consisting of an AC source and an inductive load.

*Figure 6 and 7 inductive load with and without power factor correction capacitor*

How does a capacitor help in improving the power factor? In an AC circuit, magnetic reversal due to phase difference between current and voltage occurs 50 or 60 times per second. A capacitor helps to improve the power factor by relieving the supply line of the reactive power. The capacitor achieves this by storing the magnetic reversal energy.

Figure 7 shows an inductive load with a power factor correction capacitor. Figure 8 above illustrates the improvement in power factor when the capacitor is added to the circuit. The impedance for a circuit with a power factor compensation capacitor is given by Equation 5, where XC is capacitive reactance and is given by Equation 6.

In most industries, a system of capacitors controlled by a power factor correction controller is installed for reactive power compensation. When designing a power factor correction system, it is important to avoid adding excess capacitance to the network. Adding excess capacitance to a circuit can lead to over-correction as illustrated in Figure 9.

Semiconductor devices are also widely used for power factor correction. Using semiconductor devices to a circuit to improve power factor is commonly referred to as active compensation. Overexcited synchronous machines are also commonly used to improve the power factor of a network.

As mentioned above most electrical loads, including transformers, welding sets, induction motors, and induction furnaces are inductive. Inductive loads require both working power, usually measured in kilowatts (kW), and reactive power, usually measured in kilo-volt-amperes-reactive (kVAR), to operate. The working power is used for performing the actual work, while reactive power is used for sustaining the magnetic field required by inductive loads. When combined, working power and reactive power form apparent power, usually measured in kilovolt-amperes (kVA).

Power factor is a measure of the efficiency with which electrical loads convert electrical power into useful work. It is a ratio of useful power (working power) to the total power (apparent power) supplied. A high power factor is an indicator that the electrical loads are utilising power efficiently, while a low power factor indicates that the connected electrical loads are utilising power inefficiently. A poor power factor results in significant energy wastage, and decreases the capacity of the electrical system. It can be caused by a phase difference between current and voltage at the terminals of an electrical load, or a distorted current waveform.

How to Size Power Factor Correction Capacitors

Calculate the required compensation in kVAr

The required capacitor reactive power is calculated from the real load power and the initial and target power factors:

$Q_C=P\left(\tan\varphi_1-\tan\varphi_2\right)$

where $Q_C$ is the required capacitor rating in kVAr, P is the real load power in kW, $\varphi_1=\cos^{-1}(\mathrm{PF}_1$ ) is the initial phase angle and $\varphi_2=\cos^{-1}(\mathrm{PF}_2)$ is the target phase angle.

Worked PFC capacitor sizing example

Assume a 100 kW industrial load operates at 0.80 power factor and the design target is 0.95 power factor:

$\tan\left(\cos^{-1}(0.80)\right)=0.75$

$\tan\left(\cos^{-1}(0.95)\right)\approx0.329$

$Q_C=100(0.75-0.329)=42.1\ \mathrm{kVAr}$

The initial calculation indicates approximately 42 kVAr of compensation. In practice, the final bank rating and step arrangement must account for the load profile, supply voltage, harmonics, expected future expansion, switching frequency and the utility or facility target. A stepped automatic bank may be preferable if the 100 kW load varies substantially during operation.

Parameter	Example value	Meaning
Real load power, P	100 kW	Useful power delivered to the load
Initial power factor, PF₁	0.80	Existing operating power factor
Target power factor, PF₂	0.95	Selected operating target
Initial tan φ₁	0.750	Initial reactive-to-active-power ratio
Target tan φ₂	0.329	Reactive-to-active-power ratio after correction
Required compensation, Qc	42.1 kVAr	Nominal reactive-power contribution required from the bank

Example calculation of required capacitor-bank reactive-power rating.

Convert a kVAr requirement into capacitance

For a three-phase capacitor bank connected in delta, the approximate capacitance per phase is:

$C_{\Delta}=\frac{Q_C}{3\omega V_{LL}^{2}}$

For a star-connected three-phase bank, the capacitance per phase is:

$C_Y=\frac{Q_C}{\omega V_{LL}^{2}}$

where $\omega=2\pi f$ , f is the line frequency, V_LL is the line-to-line RMS voltage and Q_C is expressed in var. Capacitor reactive output varies approximately with the square of applied voltage:

$Q_C\propto V^2$

Consequently, capacitor voltage rating, normal voltage variation and harmonic overvoltage must be considered during selection. Do not use this simplified calculation as a substitute for a harmonic study and manufacturer-rated bank design.

Power Factor Correction Solutions

Choosing the Right Power Factor Correction Solution

Capacitor-based power factor correction is highly effective for fundamental-frequency inductive reactive power. The correct implementation depends on whether the load is stable or variable, whether non-linear loads are present and whether compensation is installed locally or centrally.

PFC approach	Best suited to	Key design consideration
Individual fixed capacitor	A continuously operating motor or transformer with stable reactive demand	Switch the capacitor with the load; avoid self-excitation and ensure the motor is not overcompensated at light load.
Group fixed capacitor bank	A stable group of inductive loads operating together	Verify the coincident load profile and provide suitable switching and protection.
Automatic stepped capacitor bank	Facilities with variable aggregate load	Use a power factor controller, appropriately sized kVAr steps and capacitor-duty switching devices.
Detuned reactor-capacitor bank	Installations with material harmonic distortion from drives, rectifiers or UPS equipment	Select reactor detuning and capacitor voltage/current ratings from a power-quality study.
Engineered harmonic filter	Sites requiring harmonic mitigation as well as reactive-power compensation	Requires system impedance, harmonic spectrum and resonance assessment by a qualified specialist.
Active PFC power converter	Electronic power supplies and some modern power-electronic equipment	Different from shunt capacitor-bank PFC; typically uses controlled semiconductor switching.

Comparison of common reactive-power compensation and power-quality approaches.

Fixed versus automatic capacitor banks

Fixed compensation is appropriate only where reactive-power demand is predictable. A fixed bank that remains connected while the inductive load is removed can create a leading power factor, overvoltage risk or unsuitable generator operating conditions. Automatic banks divide the total compensation into switched kVAr steps and use a controller to maintain the selected target power factor as the load changes.

Do not confuse capacitor-bank PFC with active PFC

In industrial distribution systems, capacitor-bank PFC generally means shunt-connected capacitors that supply reactive power at the line frequency. In electronic equipment, active PFC usually refers to a controlled semiconductor converter, often a boost topology, that shapes input current to improve true power factor and meet harmonic-current requirements. The two approaches solve different problems and operate at very different power levels and frequencies.

To discourage energy wastage, some electricity distribution companies penalize consumers with a power factor that is below a specified value, and offer an incentive to consumers with a good power factor (usually above 0.95). This encourages consumers to install power factor correction equipment in their electrical systems. Benefits of adding power factor correction capacitors to electricity networks include reduced losses, improved voltage, increased system capacity, and reduced electricity bills. Key variables to consider when selecting capacitors for power factor correction include load type, load constancy, load size, load capacity, method of utility billing, and load starting methods.

Power factor correction capacitors are usually installed as banks of capacitors when substations or large facilities are involved. In the case of sinusoidal or linear loads, they can be installed as individual capacitors that are easy to install or replace, and do not require separate switching. On the other hand, capacitor bank installations have lower cost per kVAR, and provide exact power factor correction capacitance when automatic switching systems are used.

Depending on the needs of a particular substation or facility, fixed or automatically switched capacitor banks can be installed. A fixed power factor capacitor bank can be switched on when the inductive load is on, and off when the individual load is off. Such capacitors are energized only when power factor correction is needed. In facilities with multiple loads, load conditions and power factor correction needs change frequently. Automatic capacitor systems are suitable for such facilities. They prevent over-correction and under-correction.

Large inductive loads such as oil drilling rigs, wind turbines, large motors, arc furnaces and auto crushes have dynamic load characteristics. Such large dynamic loads demand sophisticated automatic capacitor systems with fast response capabilities. Transient-free automatic capacitor banks are used for power factor correction in applications where large inductive loads are involved. Harmonics can significantly reduce the life of capacitor banks. For loads that produce harmonics, a harmonic filter should be added. This filter removes unwanted harmonic frequencies from the electrical system.

Harmonics, Resonance and Detuned Capacitor Banks

Why harmonics can damage PFC capacitor banks

Capacitor impedance decreases as frequency rises:

$X_C=\frac{1}{2\pi fC}$

For this reason, capacitors can draw substantial harmonic current in systems containing variable-frequency drives, rectifier loads, UPS systems, welding equipment, arc furnaces or large concentrations of switched-mode power supplies. Harmonic current raises capacitor RMS current and thermal stress, accelerating dielectric ageing and increasing the risk of fuse operation, case overpressure or premature failure.

Resonance requires system-level assessment

A capacitor bank can interact with the inductance of the upstream transformer and distribution network. Depending on the system impedance and installed kVAr, this interaction can create parallel or series resonance near an existing harmonic frequency. Resonance can amplify harmonic voltage or current rather than reduce it.

Where harmonic distortion is significant, use an engineered detuned reactor-capacitor bank or a purpose-designed harmonic filter. Detuned reactors shift the capacitor-bank resonant frequency away from dominant harmonic orders and limit harmonic current through the capacitors. The required detuning factor, reactor rating, capacitor voltage class and current capability must be based on measured or modelled site conditions rather than selected by rule of thumb.

Design rule: do not add or enlarge a capacitor bank on a harmonic-rich distribution system without reviewing harmonic measurements, transformer impedance, existing capacitor stages, prospective operating configurations and generator or UPS operating modes.

Switching, Protection and Maintenance of PFC Capacitor Banks

Capacitor switching is not ordinary load switching

Capacitor energisation can create high inrush current, particularly when switching a new stage into a bank that already has energized capacitor stages. Select capacitor-duty contactors, pre-insertion resistors, current-limiting reactors or thyristor-switched stages according to the bank configuration and required switching speed. Rapidly changing loads may require transient-free thyristor switching rather than mechanically switched contactors.

Essential protection and installation provisions

Use capacitors specifically rated for AC power factor correction service, with suitable RMS voltage, RMS current, frequency, temperature class and expected harmonic duty.
Provide correctly coordinated branch or stage protection, disconnecting means and fault containment appropriate to the installation.
Use discharge resistors so residual voltage falls to a safe level before re-energisation or maintenance.
Provide adequate panel ventilation and keep capacitors away from persistent external heat sources.
Use capacitor-bank controllers and switching devices designed for the required number of operations and kVAr step sizes.
Inspect periodically for bulging cases, leakage, discoloration, loose connections, abnormal temperature, fuse operation and unequal stage currents.

Modern metallized polypropylene PFC capacitors commonly use self-healing dielectric technology and may incorporate an overpressure disconnector. These features improve fault behaviour but do not eliminate the need for correct protection, thermal design, harmonic derating and planned inspection.

Types of Power Factor Correction Capacitors

Capacitors for power factor correction are manufactured in a variety of types, sizes and designs. The most commonly used types are constructed using a metallized polypropylene film while a few employ metallized polyester film or paper.

Bi-metallized paper capacitors are commonly used in applications that demand robust power factor correction solutions. The special paper used for constructing these capacitors contains a thin layer of metal alloy. Sheets of paper are separated by a polypropylene film. These capacitors are constructed to withstand high temperatures and high harmonic content. Bi-metallized paper capacitors find many applications in power electronics. Metallized polyester film capacitors are compact, light and offer excellent capacitance stability. Although these capacitors are used primarily for DC applications, they are also suitable for AC line filtering and power factor correction.

Standards and Engineering References for PFC Capacitors

Low-voltage PFC capacitor systems should be specified and installed in accordance with the applicable local electrical code, utility requirements and equipment documentation. The following IEC publications are commonly relevant to industrial low-voltage capacitor installations:

IEC 60831-1 and IEC 60831-2 for self-healing shunt power capacitors for AC systems up to 1,000 V.
IEC 61921 for low-voltage power factor correction banks.
IEC 61000 power-quality and electromagnetic-compatibility standards, including the framework used to assess harmonic conditions.
IEC 61439 where the PFC assembly forms part of a low-voltage switchgear and controlgear assembly.

Standards do not replace engineering judgement. Final selection should be based on the site voltage, frequency, load profile, transformer and cable impedance, harmonic spectrum, ambient conditions, switching duty, short-circuit level and local regulatory requirements.

Conclusion

Power factor correction capacitors improve the utilisation of AC electrical distribution systems by supplying leading reactive current locally and reducing the upstream reactive-current demand created by inductive loads. For a fixed kW load, this lowers kVA demand and RMS current, helping to reduce resistive losses, voltage drop and unnecessary loading of transformers, cables and switchgear.

Successful PFC design is more than selecting a capacitor kVAr rating. The designer must distinguish displacement power factor from true power factor, calculate the required compensation, select fixed or automatic switching architecture, evaluate harmonics and resonance, use appropriate switching and protection devices, and maintain the installation throughout its service life. In harmonic-rich facilities, a detuned or filtered solution designed from a power-quality study is often essential.

Metallized polypropylene capacitors remain the dominant technology for low-voltage industrial capacitor banks because of their AC capability, self-healing behaviour and practical volumetric efficiency. However, the capacitor is only one part of the solution: reliable reactive-power compensation depends on the complete electrical system design.