View source for Electric power

{{Short description|Rate at which electrical energy is transferred by an electric circuit}}
{{Infobox physical quantity
  | name = Power
  | unit = [[watt]] (W)
  | symbols = ℘ or P
  | baseunits = [[kilogram|kg]]⋅[[metre|m]]{{sup|2}}⋅[[second|s]]{{sup|−3}}
  | dimension = wikidata
  | derivations =
    {{ublist
      | {{math|1=''℘'' = [[Energy|''E'']]/[[Time|''t'']]}}
      | {{math|1=''℘'' = [[Force|''F'']]·[[Velocity|''v'']]}}
      | {{math|1=''℘'' = [[Voltage|''U'']]·[[Electric current|''I'']] }}
      | {{math|1=''℘'' = [[Torque|''τ'']]·[[Angular velocity|''ω'']] }}
    }}
}}

[[File:NIGU Strain tower.JPG|thumb|upright|Electric power is transmitted by [[Overhead power line|overhead lines]] like these, and also through underground [[high-voltage cable]]s.]]

{{Electromagnetism |Network}}

'''Electric power''' is the rate of transfer of [[electrical energy]] within a [[electric circuit|circuit]]. Its [[SI]] unit is the [[watt]], the general unit of [[power (physics)|power]], defined as one [[joule]] per [[second]]. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively.

In common parlance, electric power is the production and delivery of electrical energy, an essential [[public utility]] in much of the world. Electric power is usually produced by [[electric generator]]s, but can also be supplied by sources such as [[Electric battery|electric batteries]]. It is usually supplied to businesses and homes (as domestic [[mains electricity]]) by the [[electric power industry]] through an [[electrical grid]].

Electric power can be delivered over long distances by [[electric power transmission|transmission lines]] and used for applications such as [[Electric motor|motion]], [[Electric light|light]] or [[Electric heat|heat]] with high [[Electrical efficiency|efficiency]].<ref name="smith-2001">
{{cite book | last = Smith | first = Clare | title = Environmental Physics | date = 2001 | publisher = [[Routledge]] | location = London | isbn = 0-415-20191-8}}</ref>

==Definition==
Electric power, like [[Power (physics)|mechanical power]], is the rate of doing [[Work (electrical)|work]], measured in [[watt]]s, and represented by the letter ''P''. The term ''wattage'' is used colloquially to mean "electric power in watts". The electric power in [[watt]]s produced by an [[electric current]] ''I'' consisting of a [[electric charge|charge]] of ''Q'' coulombs every ''t'' seconds passing through an [[electric potential]] ([[voltage]]) difference of ''V'' is:<ref name="Manglik" /><ref name="Glisson" />
<math display="block">\text{Work done per unit time} = P = \frac{W}{t} = \frac{W}{Q} \frac{Q}{t} = VI </math>
where:
*''W'' is work in [[joule]]s
*''t'' is time in [[second]]s
*''Q'' is electric charge in [[coulomb]]s
*''V'' is electric potential or voltage in [[volt]]s
*''I'' is electric current in [[ampere]]s

I.e., 

:watts = volts times amps.

==Explanation==
[[File:Electric power source animation 2.gif|thumb|upright=0.6|Animation showing power source]]
[[File:Electric load animation 2.gif|thumb|upright=0.6|Animation showing electric load]]
Electric power is transformed to other forms of energy when [[electric charge]]s move through an [[electric potential]] difference ([[voltage]]), which occurs in [[electrical component]]s in electric circuits. 

An often confusing aspect of the terminology is that the direction of electric current (''conventional current'') is defined as the direction that positive charge flows, but the actual mobile [[charge carrier]]s in circuits are [[electron]]s, which have a negative charge.  But a flow of positive charge in one direction is equivalent to an equal flow of negative charge in the other direction.  So the electrons in the circuit flow in the opposite direction to the direction of ''conventional current''.  

=== Sources and loads ===
From the standpoint of electric power, components in an electric circuit can be divided into two categories:<ref name="Manglik">{{cite book
  | last = Manglik
  | first = Rohit 
  | title = Fundamentals of Mechatronics
  | publisher = 9789369069576
  | date = 2024
  | pages = ch. 11
  | url = https://books.google.com/books?id=Mn89EQAAQBAJ&q=circuits++power+voltage++current+active+passive+%22potential+energy%22
  | archive-url= 
  | archive-date=
  | doi = 
  | id = 
  | isbn = 9789369069576
  | mr = 
  | zbl = 
  | jfm =}}</ref><ref name="Glisson">{{cite book  
  | last = Glisson
  | first = Tildon H.
  | title = Introduction to Circuit Analysis and Design
  | publisher = Springer
  | year = 2011
  | location = USA
  | pages = 113–115
  | url = https://books.google.com/books?id=7nNjaH9B0_0C&dq=%22passive+sign+convention%22++power+%22negative+resistance%22&pg=PA116
  | doi =
  | id =
  | isbn = 978-9048194421}}</ref>
*'''<span lang="en" dir="ltr">Active</span> devices (power sources):'''  If conventional [[electric current]] (positive charge) is forced to flow through the device in the direction from the lower electric potential to the higher, ''against'' the opposing force of the [[electric field]] (''E'') between the terminals, (this is equivalent to the negatively charged electrons moving from the positive terminal to the negative terminal),  work will be done ''on'' the charges.  So energy is being converted to electric [[potential energy]] from some other type of energy, such as [[mechanical energy]] or [[chemical energy]]. Devices in which this occurs are called ''[[Passivity (engineering)|active]]'' devices or ''power sources''; such as [[electric generator]]s and [[electric battery|batteries]]. 
*'''Passive devices (loads):''' If [[conventional current]] flows through the device in a direction from higher potential to lower potential (equivalent to the negative electrons moving from the negative terminal to the positive terminal), in the same direction as the force of the [[electric field]], work is done by the charges on the device. The [[potential energy]] of the charges due to the voltage between the terminals is converted to [[kinetic energy]] in the device. These devices are called ''[[Passivity (engineering)|passive]]'' components or ''loads''; they 'consume' electric power from the circuit, converting it to other forms of energy such as [[mechanical work]], heat, light, etc. Examples are [[electrical appliance]]s, such as [[light bulb]]s, [[electric motor]]s, and [[electric heater]]s. 
Some devices can be either a source or a load, depending on the voltage and current through them. For example, a [[rechargeable battery]] acts as a source when it provides power to a circuit, but as a load when it is connected to a battery charger and is being recharged.  

In [[alternating current]] (AC) circuits the direction of the voltage and current periodically reverses, but the definition of sources and loads is the same; in a source at any instant the current flows from the lower potential to the higher potential, while in a load the instantaneous current flows from the higher to lower potential.

===Passive sign convention===
{{main|Passive sign convention}}
[[File:Electric source and load animation 2.gif|thumb|upright=1.2|Transmission of power through an electric circuit]]
Since electric power can flow either into or out of a component, a convention is needed for which direction represents positive power flow.<ref name="Manglik" /><ref name="Glisson" /> Electric power flowing ''out'' of a circuit ''into'' a component is arbitrarily defined to have a positive sign, while power flowing ''into'' a circuit from a component is defined to have a negative sign. Thus passive components have positive power consumption, while power sources have negative power consumption. This is called the ''[[passive sign convention]]''.

===Resistive circuits===
In the case of [[resistive]] (Ohmic, or linear) loads, the power formula (''P'' = ''I·V'') and [[Joule heating|Joule's first law]] (''P'' = ''I^2·R'') can be combined with [[Ohm's law]] (''V'' = ''I·R'') to produce alternative expressions for the amount of power that is dissipated:
<math display="block">\wp = I V = I^2 R = \frac{V^2}{R}</math>
where ''R'' is the [[electrical resistance]].

===Alternating current===
{{Main|AC power}}

In [[AC power|alternating current]] (AC) circuits, the polarity of the voltage and the direction of current flow reverses twice each cycle. In resistive circuits, with no [[electrical reactance|reactance]], in which the current reverses at the same instant as the voltage reverses, the circuit behaves the same as a DC circuit described above, with power flowing out of sources and consumed by loads.  

However in circuits with energy storage elements such as [[inductance]] and [[capacitance]], in addition to the energy being consumed by resistances, some of the energy flowing into passive components is stored temporarily and returned to the circuit each cycle.  This may result in periodic reversals of the direction of energy flow. The portion of energy flow (power) that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as [[real power]] (also referred to as active power).<ref name="ThomasRosaToussaint_2016">{{cite book | title = The Analysis and Design of Linear Circuits | edition = 8 | first1 = Roland E. | last1 = Thomas | first2 = Albert J. | last2 = Rosa | first3 = Gregory J. | last3 = Toussaint | publisher = Wiley | year = 2016 | pages = 812–813 | isbn = 978-1-119-23538-5}}</ref> The amplitude of that portion of energy flow (power) that results in no net transfer of energy but instead oscillates between the source and load in each cycle due to stored energy, is known as the absolute value of [[reactive power]].<ref name="ThomasRosaToussaint_2016" /><ref name="FraileMora_2012">{{cite book | title = Circuitos eléctricos | language = Spanish | first = Jesús | last = Fraile Mora | publisher = Pearson | year = 2012 | pages = 193–196 | isbn = 978-8-48-322795-4}}</ref><ref name="IEEE_1459">{{cite book | title = IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions | publisher = IEEE | year = 2010 | pages = 4 | isbn = 978-0-7381-6058-0 | doi = 10.1109/IEEESTD.2010.5439063}}</ref> The product of the RMS value of the voltage wave and the RMS value of the current wave is known as [[apparent power]]. The real power '''''P''''' in watts consumed by a device is given by
<math display="block">\wp = {1 \over 2} V_p I_p \cos \theta = V_{\rm rms}I_{\rm rms} \cos \theta </math>
where
*''V''<sub>p</sub> is the peak voltage in volts
*''I''<sub>p</sub> is the peak current in amperes
*''V''<sub>rms</sub> is the [[root-mean-square]] voltage in volts
*''I''<sub>rms</sub> is the [[root-mean-square]] current in amperes
*''θ'' = ''θ''<sub>v</sub> − ''θ''<sub>i</sub> is the [[phase (waves)|phase angle]] by which the voltage sine wave leads the current sine wave, or equivalently the phase angle by which the current sine wave lags the voltage sine wave

[[File:Power Triangle 01.svg|thumb|Power triangle: The components of [[AC power]]]]

The relationship between real power, reactive power and apparent power can be expressed by representing the quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the hypotenuse of a right triangle formed by connecting the real and reactive power vectors. This representation is often called the ''power triangle''. Using the [[Pythagorean Theorem]], the relationship among real, reactive and apparent power is:
<math display="block">\text{(apparent power)}^2 = \text{(real power)}^2 + \text{(reactive power)}^2</math>

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both [[Sine wave|sinusoids]] with a known phase angle θ between them:
<math display="block">\text{(real power)} = \text {(apparent power)}\cos \theta</math>
<math display="block">\text{(reactive power)} = \text {(apparent power)}\sin \theta</math>

The ratio of real power to apparent power is called [[power factor]] and is a number always between −1 and 1. Where the currents and voltages have non-sinusoidal forms, power factor is generalized to include the effects of distortion.

===Electromagnetic fields===
Electrical energy flows wherever electric and magnetic fields exist together and fluctuate in the same place. The simplest example of this is in electrical circuits, as the preceding section showed. In the general case, however, the simple equation ''P'' = ''IV'' may be replaced by a more complex calculation. The closed [[surface integral]] of the [[cross product|cross-product]] of the electric field intensity and magnetic field intensity [[vector (geometric)|vectors]] gives the total instantaneous power (in watts) ''out of'' the volume: <ref name="HaytBuck_2012">{{cite book |title=Engineering Electromagnetics |edition=8 |first1=William H. |last1=Hayt |first2=John A. |last2=Buck |publisher=McGraw-Hill |year=2012 |pages=385 |isbn=978-0-07-338066-7}}</ref>
<math display="block">\wp = \oint_\text{area} (\mathbf{E} \times \mathbf{H}) \cdot d \mathbf{A}.</math>

The result is a scalar since it is the ''[[surface integral]]'' of the ''[[Poynting vector]]''.

==Production==

===Generation===
{{Latest pie chart of world power by source}}
{{main|Electricity generation}}

The fundamental principles of much electricity generation were discovered during the 1820s and early 1830s by the British scientist [[Michael Faraday]]. His basic method is still used today: electric current is generated by the movement of a loop of wire, or disc of copper between the poles of a [[magnet]].

For [[Electric utility|electric utilities]], it is the first process in the delivery of electricity to consumers. The other processes, electricity [[Electric power transmission|transmission]], [[Electric power distribution|distribution]], and electrical energy storage and recovery using [[Pumped-storage hydroelectricity|pumped-storage]] methods are normally carried out by the [[electric power industry]].

Electricity is mostly generated at a [[power station]] by electromechanical [[electrical generator|generators]], driven by [[heat engine]]s heated by [[combustion]], [[geothermal power]] or [[nuclear fission]]. Other generators are driven by the [[kinetic energy]] of flowing water and wind. There are many other technologies that are used to generate electricity such as [[photovoltaic]] solar panels.

A [[Battery (electricity)|battery]] is a device consisting of one or more [[electrochemical cell]]s that convert stored chemical energy into electrical energy.<ref name="Webster">[http://www.merriam-webster.com/dictionary/battery "battery" (def. 4b)], ''Merriam-Webster Online Dictionary'' (2009). Retrieved 25 May 2009.</ref> Since the invention of the first battery (or "[[voltaic pile]]") in 1800 by [[Alessandro Volta]] and especially since the technically improved [[Daniell cell]] in 1836, batteries have become a common power source for many household and industrial applications. According to a 2005 estimate, the worldwide battery industry generates [[United States dollar|US$]]48 [[1000000000 (number)|billion]] in sales each year,<ref>[http://www.dfj.com/cgi-bin/artman/publish/article_141.shtml Power Shift: DFJ on the lookout for more power source investments] {{webarchive|url=https://web.archive.org/web/20051201015849/http://www.dfj.com/cgi-bin/artman/publish/article_141.shtml |date=2005-12-01 }}. ''Draper Fisher Jurvetson''. Retrieved 20 November 2005.</ref> with 6% annual growth. There are two types of batteries: [[Primary battery|primary batteries]] (disposable batteries), which are designed to be used once and discarded, and [[Secondary battery|secondary batteries]] (rechargeable batteries), which are designed to be recharged and used multiple times. Batteries are available in many sizes; from miniature [[button cell]]s used to power [[hearing aid]]s and wristwatches to battery banks the size of rooms that provide standby power for [[telephone exchange]]s and computer [[data center]]s.

===Electric power industry===
{{main|Electric power industry}}

The electric power industry provides the production and delivery of power, in sufficient quantities to areas that need [[electricity]], through a [[grid connection]]. The grid distributes electrical energy to customers. Electric power is generated by central [[power station]]s or by [[distributed generation]]. The electric power industry has gradually been trending towards deregulation – with emerging players offering consumers competition to the traditional public utility companies.<ref>[https://www.en-powered.com/blog/the-opportunity-of-energy-group-buying The Opportunity of Energy Group-Buying] {{Webarchive|url=https://web.archive.org/web/20170525165435/https://www.en-powered.com/blog/the-opportunity-of-energy-group-buying |date=2017-05-25 }} ''EnPowered'', April 18, 2016,</ref>

==Uses ==
Electric power, produced from central generating stations and distributed over an electrical transmission grid, is widely used in industrial, commercial, and consumer applications. A country's per capita electric power consumption correlates with its industrial development. <ref>Ignacio J. Pérez-Arriaga (ed), ''Regulation of the Power Sector'', Springer Science & Business Media, 2014 {{ISBN|1447150341}}, p. 8.</ref> Electric motors power manufacturing machinery and propel subways and railway trains. Electric lighting is the most important form of artificial light. Electrical energy is used directly in processes such as extraction of aluminum from its ores and in production of steel in [[electric arc furnace]]s. Reliable electric power is essential to telecommunications and broadcasting. Electric power is used to provide air conditioning in hot climates, and in some places, electric power is an economically competitive energy source for building space heating. The use of electric power for pumping water ranges from individual household wells to irrigation and energy storage projects.

==See also==
{{Portal|Energy}}
* [[EGRID]]
* [[Electric energy consumption]]
* [[Electric power system]]
* [[High-voltage cable]]
* [[Power engineering]]
* [[Rural electrification]]

==References==
{{Reflist}}

==Bibliography==
* [https://web.archive.org/web/20060616214056/http://www.nerc.com/~filez/blackout.html Reports on August 2003 Blackout, North American Electric Reliability Council website]
* {{cite book
 | last = Croft
 | first = Terrell
 |author2=Summers, Wilford I.
 | title = American Electricians' Handbook
 | edition = Eleventh
 | date = 1987
 | publisher = [[McGraw Hill]]
 | location = New York
 | isbn = 0-07-013932-6
}}
* {{cite book
 | last = Fink
 | first = Donald G.
 | author-link = Donald G. Fink
 |author2=Beaty, H. Wayne
 | title = Standard Handbook for Electrical Engineers
 | edition = Eleventh
 | date = 1978
 | publisher = McGraw Hill
 | location = New York
 | isbn = 0-07-020974-X
}}

==External links==
{{Commons category|Electrical power}}
* [https://www.energy.gov/energysources/electricpower.htm U.S. Department of Energy: Electric Power]

{{Electricity generation}}
{{Authority control}}

[[Category:Electric power| ]]
[[Category:Electromagnetic quantities|Power]]
[[Category:Temporal rates]]