The '''power factor''' of an [[alternating currentAC]] electric power system is defined as the [[ratio]] of the [[AC powerreal power]] to the [[AC powerapparent power]], and is a number between 0 and 1 (frequently expressed as a percentage, e.g. 0.5 pf = 50% pf). Real [[Power (physics)power]] is the capacity of the circuit for performing work in a particular time. [[Apparent power]] is the product of the current and voltage of the circuit. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power can be greater than the real power.
Because the cost of each power line and transformer in a distribution system depends on the peak current it is designed to handle,
a distribution system that is designed to handle the higher currents caused by loads with low power factor will cost more than a distribution system that delivers the same useful energy to loads with a power factor closer to 1.
== Power factor in linear circuit ==
[[Image:Power factor 1.svgrightthumb300pxInstantaneous and average power calculated from AC voltage and current with a unity power factor ({{phisymbol}}=0, cos{{phisymbol}}=1)]]
[[Image:Power factor 0.svgrightthumb300pxInstantaneous and average power calculated from AC voltage and current with a zero power factor ({{phisymbol}}=90, cos{{phisymbol}}=0)]]
[[Image:Power factor 0.7.svgrightthumb300pxInstantaneous and average power calculated from AC voltage and current with a lagging power factor ({{phisymbol}}=45, cos{{phisymbol}}=0.71)]]
In a purely resistive AC circuit, voltage and current waveforms are in step (or in phase), changing polarity at the same instant in each cycle. Where [[Reactance (electronics)reactive]] loads are present, such as with [[capacitor]]s or [[inductor]]s, energy storage in the loads result in a time difference between the current and voltage waveforms. This stored energy returns to the source and is not available to do work at the load. Thus, a circuit with a low power factor will have higher currents to transfer a given quantity of real power than a circuit with a high power factor.
Circuits containing purely resistive heating elements (filament lamps, strip heaters, cooking stoves, etc.) have a power factor of 1.0. Circuits containing inductive or capacitive elements ([[Electrical ballastlamp ballasts]], motors, etc.) often have a power factor below 1.0. For example, in electric lighting circuits, normal power factor ballasts (NPF) typically have a value of (0.4 - 0.6). Ballasts with a power factor greater than (0.9) are considered high power factor ballasts (HPF).
The significance of power factor lies in the fact that utility companies supply customers with [[volt-ampere]]s, but bill them for [[watt]]s. Power factors below 1.0
require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts). This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled (since they are proportional to the square of the current). Alternatively all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current.
Utilities typically charge additional costs to customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.
==Definition and calculation==
[[Alternating currentAC]] power flow has the three components: [[real power]] (P), measured in [[watt]]s (W); [[apparent power]] (S), measured in volt-amperes (VA); and [[reactive power]] (Q), measured in reactive volt-amperes (VAr).
The power factor is defined as:
:.
In the case of a perfectly [[Sine wavesinusoidal]] waveform, P, Q and S can be expressed as vectors that form a [[vector (geometry)vector]] triangle such that:
:
If is the [[phase angle]] between the current and voltage, then the power factor is equal to , and:
:
Since the units are consistent, the power factor is by definition a [[dimensionless number]] between 0 and 1. When power factor is equal to 0, the energy flow is entirely reactive, and stored energy in the load returns to the source on each cycle. When the power factor is 1, all the energy supplied by the source is consumed by the load. Power factors are usually stated as "leading" or "lagging" to show the sign of the phase angle, where leading indicates a negative sign.
If a purely resistive load is connected to a power supply, current and voltage will change polarity in step, the power factor will be unity (1), and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as transformers and motors (any type of wound coil) consume reactive power with current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cable generate reactive power with current phase leading the voltage. Both types of loads will absorb energy during part of the AC cycle, which is stored in the device's magnetic or electric field, only to return this energy back to the source during the rest of the cycle.
For example, to get 1 kW of real power, if the power factor is unity, 1 kVA of apparent power needs to be transferred (1 kW ÷ 1 = 1 kVA). At low values of power factor, more apparent power needs to be transferred to get the same real power. To get 1 kW of real power at 0.2 power factor, 5 kVA of apparent power needs to be transferred (1 kW ÷ 0.2 = 5 kVA). This apparent power must be produced and transmitted to the load in the conventional fashion, and is subject to the usual distributed losses in the production and transmission processes.
== Power factor correction ==
{{mainpower factor correction}}
It is often possible to adjust the power factor of a system to very near unity. This practice is known as ''[[power factor correction]]'' and is achieved by switching in or out banks of [[inductor]]s or [[capacitor]]s. For example the inductive effect of motor loads may be offset by locally connected capacitors. When reactive elements supply or absorb reactive power near the point of reactive loading, the apparent power draw as seen by the source is reduced and efficiency is increased. The reactive elements can create voltage fluctuations and harmonic noise during connection and disconnection procedures, and they will supply or sink reactive power regardless of whether there is a corresponding load operating nearby, increasing the system's no-load losses. In a worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability and severe overvoltage fluctuations. As such, reactive elements cannot simply be applied at will, and power factor correction is normally subject to engineering analysis.
== Non-sinusoidal components ==
In circuits having only sinusoidal currents and voltages, the power factor effect arises only from the difference in phase between the current and voltage. This is narrowly known as "displacement power factor". The concept can be generalized to a total, distortion, or true power factor where the apparent power includes all harmonic components. This is of importance in practical power systems which contain [[non-linear]] loads such as [[rectifiers]], some forms of electric lighting, [[electric arc furnace]]s, welding equipment, [[Switched-mode power supplyswitched-mode power supplies]] and other devices.
A particularly important example is the millions of personal computers that typically incorporate [[Switched-mode power supplyswitched-mode power supplies]] (SMPS) with rated output power ranging from 250 W to 750 W. Historically, these very-low-cost power supplies incorporated a simple full-wave rectifier that conducted only when the mains instantaneous voltage exceeded the voltage on the input capacitors. This leads to very high [[peak-to-average ratioratios of peak-to-average]] input current, which also lead to a low [[distortion power factor]] and potentially serious phase and neutral loading concerns.
Regulatory agencies such as the [[EU]] have set harmonic limits as a method of improving power factor. Declining component cost has hastened acceptance and implementation of two different methods. Normally, this is done by either adding a series inductor (so-called [[Power factor correctionpassive PFC]]) or adding a boost converter that forces a sinusoidal input (so-called [[Active power factor correctionactive PFC]]). For example, [[Switched-mode power supplySMPS]] with passive PFC can achieve power factor of about 0.7–0.75, SMPS with active PFC, up to 0.99 power factor, while a SMPS without any power factor correction has a power factor of only about 0.55–0.65.
To comply with current EU standard EN61000-3-2, all [[Switched-mode power supplyswitched-mode power supplies]] with output power more than 75 W must include passive PFC, at least. [[80 PLUS]] power supply certification requires a power factor of 0.9 or more.[http://www.80plus.org The 80 PLUS Program Home]
A typical [[multimeter]] will give incorrect results when attempting to measure the AC current drawn by a non-sinusoidal load and then calculate the power factor. A true [[Root mean squareRMS]] multimeter must be used to measure the actual RMS currents and voltages (and therefore apparent power). To measure the real power or reactive power, a [[wattmeter]] designed to properly work with non-sinusoidal currents must be used.
==Measuring power factor==
Power factor in a single-phase circuit (or balanced three-phase circuit) can be measured with the wattmeter-ammeter-voltmeter method, where the power in watts is divided by the product of measured voltage and current. The power factor of a balanced polyphase circuit is the same as that of any phase. The power factor of an unbalanced polyphase circuit is not uniquely defined.
A direct reading power factor meter can be made with a [[moving coil meter]] of the electrodynamic type, carrying two perpendicular coils on the moving part of the instrument. The field of the instrument is energized by the circuit current flow. The two moving coils, A and B, are connected in parallel with the circuit load. One coil, A, will be connected through a resistor and the second coil, B, through an inductor, so that the current in coil B is delayed with respect to current in A. At unity power factor, the current in A is in phase with the circuit current, and coil A provides maximum torque,driving the instrument pointer toward the 1.0 mark on the scale. At zero power factor, the current in coil B is in phase with circuit current, and coil B provides torque to drive the pointer towards 0. At intermediate values of power factor, the torques provided by the two coils add and the pointer takes up intermediate positions. Donald G. Fink and H. Wayne Beaty, Standard Handbook for Electrical Engineers, Eleventh Edition,McGraw-Hill, New York, 1978, ISBN 0-07020974-X page 3-29 paragraph 80
Another electromechanical instrument is the polarized-vane type. Meter and Instrument Department, ''Manual of Electric Instruments Construction and Operating Principles, Manual GET-1087A'',General Electric Company, Schenectady, New York, 1949 pp. 66-68 In this instrument a stationary field coil produces a rotating magnetic field (connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application). A second stationary field coil carries a current proportional to current in the circuit. The moving system of the instrument consists of two vanes which are magnetized by the current coil. In operation the moving vanes take up a physical angle equivalent to the electrical angle between the voltage source and the current source. This type of instrument can be made to register for currents in both directions, giving a 4-quadrant display of power factor or phase angle.
Digital instruments can be made that either directly measure the time lag between voltage and current waveforms and so calculate the power factor, or by measuring both true and apparent power in the circuit and calculating the quotient. The first method is only accurate if voltage and current are sinusoidal; loads such as rectifiers distort the waveforms from the sinusoidal shape.
== Mnemonics ==
English-language power engineering students are advised to remember:
"ELI the ICE man" or "ELI on ICE" – the voltage E leads the current I in an inductor L, the current leads the voltage in a capacitor C.
Or even shorter:
CIVIL – in a '''C'''apacitor the '''I''' (current) leads '''V'''oltage, '''V'''oltage leads '''I''' (current) in an inductor '''L'''.
== See also ==
* [[Power Factor Correction]]
==References==
{{Refimprovedate=January 2008}}
[[Category:Electrical parameters]]
[[Category:Electric power]]
[[Category:Electrical engineering]]
[[Category:Power engineering]]
REDUCING POWER FACTOR COST
To understand power factor, visualize a horse pulling a railroad car down a railroad track. Because
the railroad ties are uneven, the horse must pull the car from the side of the track. The horse is
pulling the railroad car at an angle to the direction of the car’s travel. The power required to move the
car down the track is the working (real) power. The effort of the horse is the total (apparent) power.
Because of the angle of the horse’s pull, not all of the horse’s effort is used to move the car down the
track. The car will not move sideways; therefore, the sideways pull of the horse is wasted effort or
nonworking (reactive) power.
The angle of the horse’s pull is related to power factor, which is defined as the ratio of real (working)
power to apparent (total) power. If the horse is led closer to the center of the track, the angle of side
pull decreases and the real power approaches the value of the apparent power. Therefore, the ratio
of real power to apparent power (the power factor) approaches 1. As the power factor approaches 1,
the reactive (nonworking) power approaches 0.
Power Factor =
Working (real) power
Direction of travel
Nonworking
(reactive)
power
Total
(apparent)
power
What is Power Factor?
Real Power
Apparent Power
PB
For example, using the power triangle illustrated below, if
Real power = 100 kW
and
Apparent power = 142 kVA
then
Power Factor = 100/142 = 0.70 or 70%.
Real power = 100 kW
Reactive
power =
100 kVAR
Apparent
power =
142 kVA
This indicates that only 70% of the current provided by the electrical utility is being used to produce useful work.
Cause of Low Power Factor
Low power factor is caused by inductive loads (such as transformers, electric motors, and high-intensity discharge
lighting), which are a major portion of the power consumed in industrial complexes. Unlike resistive loads that
create heat by consuming kilowatts, inductive loads require the current to create a magnetic field, and the magnetic
field produces the desired work. The total or apparent power required by an inductive device is a composite
of the following:
• Real power (measured in kilowatts, kW)
• Reactive power, the nonworking power caused by the magnetizing current, required to operate the device
(measured in kilovars, kVAR)
Reactive power required by inductive loads increases the amount of apparent power (measured in kilovolt
amps, kVA) in your distribution system. The increase in reactive and apparent power causes the power
factor to decrease.
Why Improve Your Power Factor?
Some of the benefits of improving your power factor are as follows:
• Your utility bill will be smaller. Low power factor requires an increase in the electric utility’s generation and
transmission capacity to handle the reactive power component caused by inductive loads. Utilities usually
charge a penalty fee to customers with power factors less than 0.95. You can avoid this additional fee by
increasing your power factor.
• Your electrical system’s branch capacity will increase. Uncorrected power factor will cause power losses in your
distribution system. You may experience voltage drops as power losses increase. Excessive voltage drops can
cause overheating and premature failure of motors and other inductive equipment.
3
Correcting Your Power Factor
Some strategies for correcting your power factor are:
• Minimize operation of idling or lightly loaded motors.
• Avoid operation of equipment above its rated voltage.
• Replace standard motors as they burn out with energy-efficient motors.
Even with energy-efficient motors, however, the power factor is significantly
affected by variations in load. A motor must be operated near its rated capacity
to realize the benefits of a high power factor design.
• Install capacitors in your AC circuit to decrease the magnitude of reactive
power.
As shown in the diagram at right, reactive power (measured in kVARs) caused by inductance always acts at a
90° angle to real power. Capacitors store kVARs and release energy opposing the reactive energy caused by
the inductor. This implies that inductance and capacitance react 180° to each other. The presence of both in
the same circuit results in the continuous alternating transfer of energy between the capacitor and the inductor,
thereby reducing the current flow from the generator to the circuit. When the circuit is balanced, all the
energy released by the inductor is absorbed by the capacitor.
In the diagram below, the power triangle shows an initial 0.70 power factor for a 100-kW (real power) inductive load.
The reactive power required by the load is 100 kW. By installing a 67-kW capacitor, the apparent power is reduced
from 142 to 105 kVA, resulting in a 26% reduction in current. Power factor is improved to 0.95.
In the “horse and railcar” analogy, this is equivalent to decreasing the angle the horse is pulling on the railcar by
leading the horse closer to the center of the railroad track. Because the side pull is minimized, less total effort is
required from the horse to do the same amount of work.
Capacitor suppliers and engineering firms can provide the assistance you may need to determine the optimum
power correction factor and to correctly locate and install capacitors in your electrical distribution system.
Capacitance
Real power 180°
Reactance
Before PF = 100/142 = 0.70 or 70%
After PF = 100/105 = 0.95 or 95%
PB
References:
B.C. Hydro. Power Factor. The GEM Series. October 1989.
Commonwealth Sprague Capacitor, Inc. Power Factor Correction, A Guide for the Plant Engineer. 1987.
Gustafson, R. J. Fundamentals of Electricity for Agriculture. AVI Publishing Co. Inc., pp. 35-58. 1980.
McCoy, G. A; Douglass, J. G. An Energy Management Guide for Motor Driven Systems. Bonneville Power Administration.
Draft, December 1995.
McCoy, G. A; Douglass, J. G. Energy Efficient Electric Motor Selection Handbook. U. S. Department of Energy
and Bonneville Power Administration, DOE/GO-10096-290. Reprint August 1996.
Square D Company. Low Voltage Power Factor Capacitors. 1985.
Turner, W.C. Energy Management Handbook. John Wiley and Sons, pp. 337-345. 1982.
U. S. Department of Energy. Motor Challenge Sourcebook. 1996 Edition.
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