![Power Factor General Case](https://upload.wikimedia.org/wikipedia/commons/f/f1/Power_Factor_General_Case.svg)
In
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, the power factor of an
AC power system is defined as the
ratio
In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
of the ''
real power
Real may refer to:
Currencies
* Brazilian real (R$)
* Central American Republic real
* Mexican real
* Portuguese real
* Spanish real
* Spanish colonial real
Music Albums
* ''Real'' (L'Arc-en-Ciel album) (2000)
* ''Real'' (Bright album) (2010)
...
'' absorbed by the
load
Load or LOAD may refer to:
Aeronautics and transportation
*Load factor (aeronautics), the ratio of the lift of an aircraft to its weight
*Passenger load factor, the ratio of revenue passenger miles to available seat miles of a particular transpo ...
to the ''
apparent power Apparent may refer to:
*Apparent magnitude, a measure of brightness of a celestial body as seen by an observer on Earth
* Apparent places, the actual coordinates of stars as seen from Earth
*Heir apparent, a person who is first in line of successi ...
'' flowing in the circuit. Real power is the average of the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of
RMS current and voltage. 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 may be greater than the real power, so more current flows in the circuit than would be required to transfer real power alone. A power factor magnitude of less than one indicates the voltage and current are not in phase, reducing the average
product
Product may refer to:
Business
* Product (business), an item that serves as a solution to a specific consumer problem.
* Product (project management), a deliverable or set of deliverables that contribute to a business solution
Mathematics
* Produ ...
of the two. A negative power factor occurs when the device (which is normally the load) generates real power, which then flows back towards the source.
In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.
Power-factor correction increases the power factor of a load, improving efficiency for the distribution system to which it is attached. Linear loads with a low power factor (such as
induction motor
An induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor needed to produce torque is obtained by electromagnetic induction from the magnetic field of the stator winding. An induction mot ...
s) can be corrected with a passive network of
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
s or
inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s. Non-linear loads, such as
rectifier
A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation (converting DC to AC) is performed by an Power ...
s, distort the current drawn from the system. In such cases, active or passive power factor correction may be used to counteract the distortion and raise the power factor. The devices for correction of the power factor may be at a central
substation, spread out over a distribution system, or built into power-consuming equipment.
General case
![Power Factor General Case](https://upload.wikimedia.org/wikipedia/commons/f/f1/Power_Factor_General_Case.svg)
The general expression for power factor is given by
:
:
where
is the real power measured by an ideal
wattmeter
The wattmeter is an instrument for measuring the electric active power (or the average of the rate of flow of electrical energy) in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio ...
,
is the rms current measured by an ideal
ammeter
An ammeter (abbreviation of ''Ampere meter'') is an instrument used to measure the current in a circuit. Electric currents are measured in amperes (A), hence the name. For direct measurement, the ammeter is connected in series with the circuit ...
, and
is the rms voltage measured by an ideal
voltmeter
A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit.
Ana ...
. Apparent power,
, is the product of the rms current and the rms voltage.
If the load is sourcing power back toward the generator, then
and
will be negative.
Periodic waveforms
If the waveforms are periodic with the same period which is much shorter than the averaging time of the physical meters, then the power factor can be computed by the following
:
:
:
:
:
where
is the instantaneous current,
is the instantaneous voltage,
is an arbitrary starting time, and
is the period of the waveforms.
Nonperiodic waveforms
If the waveforms are not periodic and the physical meters have the same averaging time, then the equations for the periodic case can be used with the exception that
is the averaging time of the meters instead of the waveform period.
Linear time-invariant circuits
Linear time-invariant circuits (referred to simply as ''linear circuits'' for the rest of this article), for example, circuits consisting of combinations of resistors, inductors and capacitors have a sinusoidal response to the sinusoidal line voltage.
A linear load does not change the shape of the input waveform but may change the relative timing (phase) between voltage and current, due to its inductance or capacitance.
In a purely resistive AC circuit, voltage and current waveforms are in step (or
in phase
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it v ...
), changing polarity at the same instant in each cycle. All the power entering the load is consumed (or dissipated).
Where
reactive
Reactive may refer to:
*Generally, capable of having a reaction (disambiguation)
*An adjective abbreviation denoting a bowling ball coverstock made of reactive resin
*Reactivity (chemistry)
*Reactive mind
*Reactive programming
See also
*Reactanc ...
loads are present, such as with
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
s or
inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s, energy storage in the loads results in a phase difference between the current and voltage waveforms. During each cycle of the AC voltage, extra energy, in addition to any energy consumed in the load, is temporarily stored in the load in
electric
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
or
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
s then returned to the power grid a fraction of the period later.
Electrical circuits containing predominantly resistive loads (incandescent lamps, heating elements) have a power factor of almost 1, but circuits containing inductive or capacitive loads (electric motors,
solenoid
upright=1.20, An illustration of a solenoid
upright=1.20, Magnetic field created by a seven-loop solenoid (cross-sectional view) described using field lines
A solenoid () is a type of electromagnet formed by a helix, helical coil of wire whose ...
valves, transformers,
fluorescent lamp ballasts, and others) can have a power factor well below 1.
In the
electric power grid
An electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of:Kaplan, S. M. (2009). Smart Grid. Electrical Power ...
, reactive loads cause a continuous "ebb and flow" of nonproductive power. A circuit with a low power factor will use a greater amount of current to transfer a given quantity of real power than a circuit with a high power factor thus causing increased losses due to
resistive heating
Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor (material), conductor produces heat.
Joule's first law (also just Joule's law), also known in c ...
in power lines, and requiring the use of higher-rated conductors and transformers.
Definition and calculation
AC power has two components:
*
Real power or active power (
) (sometimes called average power), expressed in
watt
The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s (W)
*
Reactive power
Reactive may refer to:
*Generally, capable of having a reaction (disambiguation)
*An adjective abbreviation denoting a bowling ball coverstock made of reactive resin
*Reactivity (chemistry)
*Reactive mind
*Reactive programming
See also
*Reactanc ...
(
), usually expressed in
reactive volt-amperes (var)
Together, they form the
complex power (
) expressed as
volt-amperes (VA). The magnitude of the complex power is the apparent power (
), also expressed in volt-amperes (VA).
The VA and var are non-SI units mathematically identical to the watt, but are used in engineering practice instead of the watt to state what
quantity
Quantity or amount is a property that can exist as a Counting, multitude or Magnitude (mathematics), magnitude, which illustrate discontinuity (mathematics), discontinuity and continuum (theory), continuity. Quantities can be compared in terms o ...
is being expressed. The
SI explicitly disallows using units for this purpose or as the only source of information about a physical quantity as used.
The power factor is defined as the ratio of real power to apparent power. As power is transferred along a transmission line, it does not consist purely of real power that can do work once transferred to the load, but rather consists of a combination of real and reactive power, called apparent power. The power factor describes the amount of real power transmitted along a transmission line relative to the total apparent power flowing in the line.
The power factor can also be computed as the cosine of the angle θ by which the current waveform lags or leads the voltage waveform,
.
Power triangle
![Power triangle diagram](https://upload.wikimedia.org/wikipedia/commons/b/b8/Power_triangle_diagram.jpg)
One can relate the various components of AC power by using the power triangle in vector space. Real power extends horizontally in the real axis and reactive power extends in the direction of the imaginary axis. Complex power (and its magnitude, apparent power) represents a combination of both real and reactive power, and therefore can be calculated by using the vector sum of these two components. We can conclude that the mathematical relationship between these components is:
:
As the angle θ increases with fixed total apparent power, current and voltage are further out of phase with each other. Real power decreases, and reactive power increases.
Lagging, leading and unity power factors
Power factor is described as ''leading'' if the current waveform is advanced in phase with respect to voltage, or ''lagging'' when the current waveform is behind the voltage waveform. A lagging power factor signifies that the load is inductive, as the load will “consume” reactive power. The reactive component
is positive as reactive power travels through the circuit and is “consumed” by the inductive load. A leading power factor signifies that the load is capacitive, as the load “supplies” reactive power, and therefore the reactive component
is negative as reactive power is being supplied to the circuit.
![Lagging-Leading](https://upload.wikimedia.org/wikipedia/commons/4/40/Lagging-Leading.jpg)
If θ is the
phase angle between the current and voltage, then the power factor is equal to the
cosine of the angle,
:
:
Since the units are consistent, the power factor is by definition a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
between -1 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, referred to as ''unity'' power factor, 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. Capacitive loads are leading (current leads voltage), and inductive loads are lagging (current lags voltage).
If a purely resistive load is connected to a power supply, current and voltage will change polarity in step, the power factor will be 1, and the electrical energy flows in a single direction across the network in each cycle. Inductive loads such as induction motors (any type of wound coil) consume reactive power with the current waveform lagging the voltage. Capacitive loads such as capacitor banks or buried cables generate reactive power with the 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 and is subject to losses in the production and transmission processes.
Electrical loads consuming
alternating current power consume both real power and reactive power. The vector sum of real and reactive power is the complex power, and its magnitude is the apparent power. The presence of reactive power causes the real power to be less than the apparent power, and so, the electric load has a power factor of less than 1.
A negative power factor (0 to −1) can result from returning active power to the source, such as in the case of a building fitted with solar panels when surplus power is fed back into the supply.
Power factor correction of linear loads
![Blindleistungskompensation](https://upload.wikimedia.org/wikipedia/commons/b/b4/Blindleistungskompensation.svg)
A high power factor is generally desirable in a power delivery system to reduce losses and improve voltage regulation at the load. Compensating elements near an electrical load will reduce the apparent power demand on the supply system. Power factor correction may be applied by an
electric power transmission
Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is ...
utility to improve the stability and efficiency of the network. Individual electrical customers who are charged by their utility for low power factor may install correction equipment to increase their power factor so as to reduce costs.
Power factor correction brings the power factor of an AC power circuit closer to 1 by supplying or absorbing reactive power, adding capacitors or inductors that act to cancel the inductive or capacitive effects of the load, respectively. In the case of offsetting the inductive effect of motor loads, capacitors can be locally connected. These capacitors help to generate reactive power to meet the demand of the inductive loads. This will keep that reactive power from having to flow all the way from the utility generator to the load. In the electricity industry, inductors are said to consume reactive power and capacitors are said to supply it, even though reactive power is just energy moving back and forth on each AC cycle.
The reactive elements in power factor correction devices can create voltage fluctuations and harmonic noise when switched on or off. 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 the worst case, reactive elements can interact with the system and with each other to create resonant conditions, resulting in system instability and severe
overvoltage
When the voltage in a circuit or part of it is raised above its upper design limit, this is known as overvoltage. The conditions may be hazardous. Depending on its duration, the overvoltage event can be transient—a voltage spike—or perm ...
fluctuations. As such, reactive elements cannot simply be applied without engineering analysis.
![Condensatorenbatterij](https://upload.wikimedia.org/wikipedia/commons/e/e4/Condensatorenbatterij.jpg)
An automatic power factor correction unit consists of a number of
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
s that are switched by means of
contactor
:''In semiconductor testing, contactors can also be referred to as the specialized socket that connects the device under test.''
:''In process industries, a contactor is a vessel where two streams interact, for example, air and liquid. See Gas- ...
s. These contactors are controlled by a regulator that measures power factor in an electrical network. Depending on the load and power factor of the network, the power factor controller will switch the necessary blocks of capacitors in steps to make sure the power factor stays above a selected value.
In place of a set of switched
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
s, an unloaded
synchronous motor
A synchronous electric motor is an AC electric motor in which, at steady state,
the rotation of the shaft is synchronized with the frequency of the supply current; the rotation period is exactly equal to an integral number of AC cycles. Sync ...
can supply reactive power. The
reactive power
Reactive may refer to:
*Generally, capable of having a reaction (disambiguation)
*An adjective abbreviation denoting a bowling ball coverstock made of reactive resin
*Reactivity (chemistry)
*Reactive mind
*Reactive programming
See also
*Reactanc ...
drawn by the synchronous motor is a function of its field excitation. It is referred to as a
synchronous condenser
In electrical engineering, a synchronous condenser (sometimes called a syncon, synchronous capacitor or synchronous compensator) is a DC-excited synchronous motor, whose shaft is not connected to anything but spins freely.B. M. Weedy, Electric Po ...
. It is started and connected to the
electrical network
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, c ...
. It operates at a leading power factor and puts
vars onto the network as required to support a system's
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
or to maintain the system power factor at a specified level.
The synchronous condenser's installation and operation are identical to those of large
electric motor
An electric motor is an Electric machine, electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a Electromagneti ...
s. Its principal advantage is the ease with which the amount of correction can be adjusted; it behaves like a variable capacitor. Unlike with capacitors, the amount of reactive power supplied is proportional to voltage, not the square of voltage; this improves voltage stability on large networks. Synchronous condensers are often used in connection with
high-voltage direct-current
A high-voltage direct current (HVDC) electric power transmission system (also called a power superhighway or an electrical superhighway) uses direct current (DC) for electric power transmission, in contrast with the more common alternating curre ...
transmission projects or in large industrial plants such as
steel mill
A steel mill or steelworks is an industrial plant for the manufacture of steel. It may be an integrated steel works carrying out all steps of steelmaking from smelting iron ore to rolled product, but may also be a plant where steel semi-finish ...
s.
For power factor correction of high-voltage power systems or large, fluctuating industrial loads, power electronic devices such as the
static VAR compensator
A static VAR compensator (SVC) is a set of electrical devices for providing fast-acting reactive power on high-voltage electricity transmission networks. SVCs are part of the flexible AC transmission system device family, regulating voltage, power ...
or
STATCOM A static synchronous compensator (STATCOM), originally known as a static synchronous condenser (STATCON), is a regulating device shunt-connected to alternating current electricity transmission network. It is based on a power electronics voltage-sou ...
are increasingly used. These systems are able to compensate sudden changes of power factor much more rapidly than contactor-switched capacitor banks and, being solid-state, require less maintenance than synchronous condensers.
Non-linear loads
Examples of non-linear loads on a power system are rectifiers (such as used in a power supply), and arc discharge devices such as
fluorescent lamp
A fluorescent lamp, or fluorescent tube, is a low-pressure mercury-vapor gas-discharge lamp that uses fluorescence to produce visible light. An electric current in the gas excites mercury vapor, which produces short-wave ultraviolet lig ...
s, electric
welding
Welding is a fabrication (metal), fabrication process that joins materials, usually metals or thermoplastics, by using high heat to melt the parts together and allowing them to cool, causing Fusion welding, fusion. Welding is distinct from lower ...
machines, or
arc furnace
An electric arc furnace (EAF) is a Industrial furnace, furnace that heats material by means of an electric arc.
Industrial arc furnaces range in size from small units of approximately one-tonne capacity (used in foundry, foundries for producing ...
s. Because current in these systems is interrupted by a switching action, the current contains frequency components that are multiples of the power system frequency. ''Distortion power factor'' is a measure of how much the harmonic distortion of a load current decreases the average power transferred to the load.
Non-sinusoidal components
In linear circuits having only sinusoidal currents and voltages of one frequency, the power factor arises only from the difference in phase between the current and voltage. This is "displacement power factor".
Non-linear loads change the shape of the current waveform from a
sine wave
A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth p ...
to some other form. Non-linear loads create
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
currents in addition to the original (fundamental frequency) AC current. This is of importance in practical power systems that contain
non-linear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
loads such as
rectifiers
A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation (converting DC to AC) is performed by an inver ...
, some forms of electric lighting,
electric arc furnace
An electric arc furnace (EAF) is a furnace that heats material by means of an electric arc.
Industrial arc furnaces range in size from small units of approximately one-tonne capacity (used in foundries for producing cast iron products) up to ab ...
s, welding equipment,
switched-mode power supplies
A switched-mode power supply (switching-mode power supply, switch-mode power supply, switched power supply, SMPS, or switcher) is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently.
Lik ...
, variable speed drives and other devices. Filters consisting of linear capacitors and inductors can prevent harmonic currents from entering the supplying system.
To measure the real power or reactive power, a
wattmeter
The wattmeter is an instrument for measuring the electric active power (or the average of the rate of flow of electrical energy) in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio ...
designed to work properly with non-sinusoidal currents must be used.
Distortion power factor
The distortion power factor is the distortion component associated with the harmonic voltages and currents present in the system.
:
is the
total harmonic distortion
The total harmonic distortion (THD or THDi) is a measurement of the harmonic distortion present in a signal and is defined as the ratio of the sum of the powers of all harmonic components to the power of the fundamental frequency. Distortion facto ...
of the load current.
:
is the fundamental component of the current and
is the total current – both are
root mean square
In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...
-values (distortion power factor can also be used to describe individual order harmonics, using the corresponding current in place of total current). This definition with respect to total harmonic distortion assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation for stiff voltage sources (not being affected by changes in load downstream in the distribution network). Total harmonic distortion of typical generators from current distortion in the network is on the order of 1–2%, which can have larger scale implications but can be ignored in common practice.
The result when multiplied with the displacement power factor (DPF) is the overall, true power factor or just power factor (PF):
:
Distortion in three-phase networks
In practice, the local effects of distortion current on devices in a
three-phase distribution network rely on the magnitude of certain order harmonics rather than the total harmonic distortion.
For example, the triplen, or zero-sequence, harmonics (3rd, 9th, 15th, etc.) have the property of being in-phase when compared line-to-line. In a
delta-wye transformer
A delta-wye transformer is a type of three-phase electric power transformer design that employs delta-connected windings on its primary and wye/star connected windings on its secondary. A neutral wire can be provided on wye output side. It can ...
, these harmonics can result in circulating currents in the delta windings and result in greater
resistive heating
Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor (material), conductor produces heat.
Joule's first law (also just Joule's law), also known in c ...
. In a wye-configuration of a transformer, triplen harmonics will not create these currents, but they will result in a non-zero current in the
neutral wire
Ground and neutral are circuit conductors used in alternating current electrical systems. The ground circuit is connected to earth, and neutral circuit is usually connected to ground. As the neutral point of an electrical supply system is often ...
. This could overload the neutral wire in some cases
and create error in kilowatt-hour metering systems and billing revenue. The presence of current harmonics in a transformer also result in larger
eddy currents
Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magn ...
in the magnetic core of the transformer. Eddy current losses generally increase as the square of the frequency, lowering the transformer's efficiency, dissipating additional heat, and reducing its service life.
Negative-sequence harmonics (5th, 11th, 17th, etc.) combine 120 degrees out of phase, similarly to the fundamental harmonic but in a reversed sequence. In generators and motors, these currents produce magnetic fields which oppose the rotation of the shaft and sometimes result in damaging mechanical vibrations.
Switched-mode power supplies
A particularly important class of non-linear loads is the millions of personal computers that typically incorporate
switched-mode power supplies
A switched-mode power supply (switching-mode power supply, switch-mode power supply, switched power supply, SMPS, or switcher) is an electronic power supply that incorporates a switching regulator to convert electrical power efficiently.
Lik ...
(SMPS) with rated output power ranging from a few watts to more than 1 kW. 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
ratios of peak-to-average input current, which also lead to a low distortion power factor and potentially serious phase and neutral loading concerns.
A typical switched-mode power supply first converts the AC mains to a DC bus by means of a
bridge rectifier
A diode bridge is a bridge rectifier circuit of four diodes that is used in the process of converting alternating current (AC) from the input terminals to direct current (DC, i.e. fixed polarity) on the output terminals. Its function is to conv ...
. The output voltage is then derived from this DC bus. The problem with this is that the
rectifier
A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction. The reverse operation (converting DC to AC) is performed by an Power ...
is a non-linear device, so the input current is highly non-linear. That means that the input current has energy at
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
s of the frequency of the voltage. This presents a problem for power companies, because they cannot compensate for the harmonic current by adding simple capacitors or inductors, as they could for the reactive power drawn by a linear load. Many jurisdictions are beginning to require power factor correction for all power supplies above a certain power level.
Regulatory agencies such as the
EU have set harmonic limits as a method of improving power factor. Declining component cost has hastened implementation of two different methods. To comply with current EU standard EN61000-3-2, all switched-mode power supplies with output power more than 75 W must at least include passive power factor correction.
80 Plus
80 Plus (trademarked 80 PLUS) is a voluntary certification program launched in 2004, intended to promote efficient energy use in computer Power supply unit (computer), power supply units (PSUs).
Certification is acquirable for products that hav ...
power supply certification requires a power factor of 0.9 or more.
Power factor correction (PFC) in non-linear loads
Passive PFC
The simplest way to control the
harmonic
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
current is to use a
filter
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
that passes current only at
line frequency
The utility frequency, (power) line frequency (American English) or mains frequency (British English) is the nominal frequency of the oscillations of alternating current (AC) in a wide area synchronous grid transmitted from a power station to th ...
(50 or 60 Hz). The filter consists of capacitors or inductors and makes a non-linear device look more like a
linear
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
load. An example of passive PFC is a
valley-fill circuit
A valley-fill circuit is a type of passive power-factor correction (PFC) circuit.
For purposes of illustration, a basic full-wave diode-bridge rectifier is shown in the first stage, which converts the AC input voltage to a DC voltage.
Operati ...
.
A disadvantage of passive PFC is that it requires larger inductors or capacitors than an equivalent power active PFC circuit. Also, in practice, passive PFC is often less effective at improving the power factor.
Active PFC
![Active pfc PSU packaging](https://upload.wikimedia.org/wikipedia/commons/e/e8/Active_pfc_PSU_packaging.png)
Active PFC is the use of
power electronics
Power electronics is the application of electronics to the control and conversion of electric power.
The first high-power electronic devices were made using mercury-arc valves. In modern systems, the conversion is performed with semiconducto ...
to change the waveform of current drawn by a load to improve the power factor. Some types of the active PFC are
buck
Buck may refer to:
Common meanings
* A colloquialism for a dollar or similar currency
* An adult male in some animal species - see List of animal names
* Derby shoes, nicknamed "bucks" for the common use of buckskin in their making
People
*Buck ...
,
boost,
buck-boost and
synchronous condenser
In electrical engineering, a synchronous condenser (sometimes called a syncon, synchronous capacitor or synchronous compensator) is a DC-excited synchronous motor, whose shaft is not connected to anything but spins freely.B. M. Weedy, Electric Po ...
. Active power factor correction can be single-stage or multi-stage.
In the case of a switched-mode power supply, a
boost converter
A boost converter (step-up converter) is a DC-to-DC power converter that steps up voltage (while stepping down current) from its input (supply) to its output (load). It is a class of switched-mode power supply (SMPS) containing at least two semi ...
is inserted between the bridge rectifier and the main input capacitors. The boost converter attempts to maintain a constant voltage at its output while drawing a current that is always in phase with and at the same frequency as the line voltage. Another switched-mode converter inside the power supply produces the desired output voltage from the DC bus. This approach requires additional semiconductor switches and control electronics but permits cheaper and smaller passive components. It is frequently used in practice.
For a three-phase SMPS, the
Vienna rectifier
The Vienna Rectifier is a pulse-width modulation rectifier, invented in 1993 by Johann W. Kolar.
Features
Vienna Rectifier provides following features:
* Three-phase three-level three-switch PWM rectifier with controlled output voltage.
* Thr ...
configuration may be used to substantially improve the power factor.
SMPSs with passive PFC can achieve power factor of about 0.7–0.75, SMPSs with active PFC, up to 0.99 power factor, while a SMPS without any power factor correction have a power factor of only about 0.55–0.65.
Due to their very wide input voltage range, many power supplies with active PFC can automatically adjust to operate on AC power from about 100 V (Japan) to 240 V (Europe). That feature is particularly welcome in power supplies for laptops.
Dynamic PFC
Dynamic power factor correction (DPFC), sometimes referred to as "real-time power factor correction," is used for electrical stabilization in cases of rapid load changes (e.g. at large manufacturing sites). DPFC is useful when standard power factor correction would cause over or under correction. DPFC uses semiconductor switches, typically
thyristor
A thyristor () is a solid-state semiconductor device with four layers of alternating P- and N-type materials used for high-power applications. It acts exclusively as a bistable switch (or a latch), conducting when the gate receives a current ...
s, to quickly connect and disconnect capacitors or inductors to improve power factor.
Importance in distribution systems
![Condensor bank 150kV - 75MVAR](https://upload.wikimedia.org/wikipedia/commons/e/ed/Condensor_bank_150kV_-_75MVAR.jpg)
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. When the power factor is close to unity, for the same kVA rating of the transformer more load current can be supplied.
Utilities typically charge additional costs to commercial 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.
With the rising cost of energy and concerns over the efficient delivery of power, active PFC has become more common in consumer electronics. Current
Energy Star
Energy Star (trademarked ''ENERGY STAR'') is a program run by the U.S. Environmental Protection Agency (EPA) and U.S. Department of Energy (DOE) that promotes energy efficiency. The program provides information on the energy consumption of pro ...
guidelines for computers call for a power factor of ≥ 0.9 at 100% of rated output in the
PC's power supply. According to a white paper authored by Intel and the
U.S. Environmental Protection Agency
The Environmental Protection Agency (EPA) is an independent executive agency of the United States federal government tasked with environmental protection matters. President Richard Nixon proposed the establishment of EPA on July 9, 1970; it be ...
, PCs with internal power supplies will require the use of active power factor correction to meet the ENERGY STAR 5.0 Program Requirements for Computers.
In Europe,
EN 61000-3-2 requires power factor correction be incorporated into consumer products.
Small customers, such as households, are not usually charged for reactive power and so power factor metering equipment for such customers will not be installed.
Measurement techniques
The 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
An ammeter (abbreviation of ''Ampere meter'') is an instrument used to measure the current in a circuit. Electric currents are measured in amperes (A), hence the name. For direct measurement, the ammeter is connected in series with the circuit ...
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.
Another electromechanical instrument is the polarized-vane type.
In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor. The field coils are connected either directly to polyphase voltage sources or to a phase-shifting reactor if a single-phase application. A second stationary field coil, perpendicular to the voltage coils, carries a current proportional to current in one phase of the circuit. The moving system of the instrument consists of two vanes that 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 four-quadrant display of power factor or phase angle.
Digital instruments exist that directly measure the time lag between voltage and current waveforms. Low-cost instruments of this type measure the peak of the waveforms. More sophisticated versions measure the peak of the fundamental harmonic only, thus giving a more accurate reading for phase angle on distorted waveforms. Calculating power factor from voltage and current phases is only accurate if both waveforms are sinusoidal.
Power Quality Analyzers, often referred to as Power Analyzers, make a digital recording of the voltage and current waveform (typically either one phase or three phase) and accurately calculate true power (watts), apparent power (VA) power factor, AC voltage, AC current, DC voltage, DC current, frequency, IEC61000-3-2/3-12 Harmonic measurement, IEC61000-3-3/3-11 flicker measurement, individual phase voltages in delta applications where there is no neutral line, total harmonic distortion, phase and amplitude of individual voltage or current harmonics, etc.
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 I leads the voltage E in a capacitor C.
Another common mnemonic is "CIVIL" – in a capacitor (C) the current (I) leads voltage (V), voltage (V) leads current (I) in an inductor (L).
References
External links
* .
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