# Electric power

Last updated
Power
Common symbols
P
SI unit watt (W)
In SI base units kgm 2s −3
Derivations from
other quantities
Dimension ${\displaystyle {\mathsf {L}}^{2}{\mathsf {M}}{\mathsf {T}}^{-3}}$

Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard suffixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively.

## Contents

A common misconception is that electric power is bought and sold, but actually electrical energy is bought and sold. For example, electricity is sold to consumers in kilowatt-hours (kilowatts multiplied by hours), because energy is power multiplied by time.

Electric power is usually produced by electric generators, but can also be supplied by sources such as 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 transmission lines and used for applications such as motion, light or heat with high efficiency. [1]

## Definition

Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts." The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential (voltage) difference of V is

${\displaystyle P={\text{work done per unit time}}={\frac {W}{t}}={\frac {W}{Q}}{\frac {Q}{t}}=VI}$

where

## Explanation

Electric power is transformed to other forms of energy when electric charges move through an electric potential difference (voltage), which occurs in electrical components in electric circuits. From the standpoint of electric power, components in an electric circuit can be divided into two categories:

### Active devices (power sources)

If the charges are moved by an 'exterior force' through the device in the direction from the lower electric potential to the higher, (so positive charge moves from the negative to the positive terminal), work will be done on the charges, and 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 active devices or power sources; such as electric generators and batteries. 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.

When electric charges move through a potential difference from a higher to a lower voltage, that is when conventional current (positive charge) moves from the positive (+) terminal to the negative (−) terminal, 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 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 appliances, such as light bulbs, electric motors, and electric heaters. In alternating current (AC) circuits the direction of the voltage periodically reverses, but the current always flows from the higher potential to the lower potential side.

### Passive sign convention

Since electric power can flow either into or out of a component, a convention is needed for which direction represents positive power flow. 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, Joule's law can be combined with Ohm's law (V = I·R) to produce alternative expressions for the amount of power that is dissipated:

${\displaystyle P=IV=I^{2}R={\frac {V^{2}}{R}}}$

where R is the electrical resistance.

### Alternating current without harmonics

In alternating current circuits, energy storage elements such as inductance and capacitance 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). [2] 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. [2] [3] [4] 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

${\displaystyle P={1 \over 2}V_{p}I_{p}\cos \theta =V_{\rm {rms}}I_{\rm {rms}}\cos \theta }$

where

• Vp is the peak voltage in volts
• Ip is the peak current in amperes
• Vrms is the root-mean-square voltage in volts
• Irms is the root-mean-square current in amperes
• θ = θvθi is the 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

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:

${\displaystyle {\text{(apparent power)}}^{2}={\text{(real power)}}^{2}+{\text{(reactive power)}}^{2}}$

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both sinusoids with a known phase angle θ between them:

${\displaystyle {\text{(real power)}}={\text{(apparent power)}}\cos \theta }$
${\displaystyle {\text{(reactive power)}}={\text{(apparent power)}}\sin \theta }$

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 of the electric field intensity and magnetic field intensity vectors gives the total instantaneous power (in watts) out of the volume: [5]

${\displaystyle P=\oint _{\text{area}}(\mathbf {E} \times \mathbf {H} )\cdot d\mathbf {A} .}$

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

## Production

### Generation

2019 world electricity generation by source (total generation was 27 petawatt-hours) [6] [7]

Coal (37%)
Natural gas (24%)
Hydro (16%)
Nuclear (10%)
Wind (5%)
Solar (3%)
Other (5%)

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

Electricity is mostly generated at a power station by electromechanical generators, driven by heat engines 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 is a device consisting of one or more electrochemical cells that convert stored chemical energy into electrical energy. [8] 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 US\$48 billion in sales each year, [9] with 6% annual growth. There are two types of batteries: primary batteries (disposable batteries), which are designed to be used once and discarded, and secondary batteries (rechargeable batteries), which are designed to be recharged and used multiple times. Batteries are available in many sizes; from miniature button cells used to power hearing aids and wristwatches to battery banks the size of rooms that provide standby power for telephone exchanges and computer data centers.

### 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 stations 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. [10]

## Use

Electric power, produced from central generating stations and distributed over an electrical transmission grid, is widely used in industrial, commercial and consumer applications. The per capita electric power consumption of a country correlates with its industrial development. [11] 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 furnaces. 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 source of energy for building space heating. Use of electric power for pumping water ranges from individual household wells to irrigation projects and energy storage projects.

## Related Research Articles

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 Maxwell's equations. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions. The electrochemical cells which generate an electric current are called voltaic or galvanic cells and those that generate chemical reactions, via electrolysis for example, are called electrolytic cells. A common example of a galvanic cell is a standard 1.5 volt cell meant for consumer use. A battery consists of one or more cells, connected in parallel, series or series-and-parallel pattern.

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points, which is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The old SI definition for volt used power and current; starting in 1990, the quantum Hall and Josephson effect were used, and recently (2019) fundamental physical constants have been introduced for the definition of all SI units and derived units. Voltage or electric potential difference is denoted symbolically by , simplified V, especially in English-speaking countries or international U, for instance in the context of Ohm's or Kirchhoff's circuit laws.

The volt is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).

In electrical engineering, the power factor of an AC power system is defined as the ratio of the real power absorbed by the load to the apparent power 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 of the two. A negative power factor occurs when the device generates real power, which then flows back towards the source.

In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit.

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

In electromagnetism and electronics, electromotive force is the electrical action produced by a non-electrical source, measured in volts. Devices provide an emf by converting other forms of energy into electrical energy, such as batteries or generators. Sometimes an analogy to water pressure is used to describe electromotive force..

In electrical circuits, reactance is the opposition presented to alternating current by inductance or capacitance. Greater reactance gives smaller current for the same applied voltage. Reactance is similar to resistance in this respect, but differs in that reactance does not lead to dissipation of electrical energy as heat. Instead, energy is momentarily stored in the reactance, and a quarter-cycle later returned to the circuit, whereas a resistance continuously loses energy.

Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor produces heat.

In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation.

In physics and engineering, a phasor is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor depending on time and frequency. The complex constant, which depends on amplitude and phase, is known as a phasor, or complex amplitude, and sinor or even complexor.

In an electric circuit, instantaneous power is the time rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of the direction of energy flow. Its SI unit is the watt.

The wattmeter is an instrument for measuring the electric active power in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio frequency power; other types are required for radio frequency measurements.

A volt-ampere is the unit for the apparent power in an electrical circuit. The apparent power equals the product of root mean square voltage and root mean square current. In direct current (DC) circuits, this product is equal to the real power in watts. Volt-amperes are usually used for analyzing alternating current (AC) circuits. The volt-ampere is dimensionally equivalent to the watt. VA rating is most used for generators and transformers where loads may be reactive.

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.

A permanent magnet synchronous generator is a generator where the excitation field is provided by a permanent magnet instead of a coil. The term synchronous refers here to the fact that the rotor and magnetic field rotate with the same speed, because the magnetic field is generated through a shaft mounted permanent magnet mechanism and current is induced into the stationary armature.

Leading and lagging current are phenomena that occur as a result of alternating current. In a circuit with alternating current, the value of voltage and current vary sinusoidally. In this type of circuit, the terms lead, lag, and in phase are used to describe current with reference to voltage. Current is in phase with voltage when there is no phase shift between the sinusoids describing their time varying behavior. This generally occurs when the load drawing the current is resistive.

In electrical engineering, the passive sign convention (PSC) is a sign convention or arbitrary standard rule adopted universally by the electrical engineering community for defining the sign of electric power in an electric circuit. The convention defines electric power flowing out of the circuit into an electrical component as positive, and power flowing into the circuit out of a component as negative. So a passive component which consumes power, such as an appliance or light bulb, will have positive power dissipation, while an active component, a source of power such as an electric generator or battery, will have negative power dissipation. This is the standard definition of power in electric circuits; it is used for example in computer circuit simulation programs such as SPICE.

This glossary of electrical and electronics engineering is a list of definitions of terms and concepts related specifically to electrical engineering and electronics engineering. For terms related to engineering in general, see Glossary of engineering.

## References

1. Smith, Clare (2001). Environmental Physics. London: Routledge. ISBN   0-415-20191-8.
2. Thomas, Roland E.; Rosa, Albert J.; Toussaint, Gregory J. (2016). The Analysis and Design of Linear Circuits (8 ed.). Wiley. pp. 812–813. ISBN   978-1-119-23538-5.
3. Fraile Mora, Jesús (2012). Circuitos eléctricos (in Spanish). Pearson. pp. 193–196. ISBN   978-8-48-322795-4.
4. IEEE Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions. IEEE. 2010. p. 4. doi:10.1109/IEEESTD.2010.5439063. ISBN   978-0-7381-6058-0.
5. Hayt, William H.; Buck, John A. (2012). Engineering Electromagnetics (8 ed.). McGraw-Hill. p. 385. ISBN   978-0-07-338066-7.
6. "Data & Statistics". International Energy Agency . Retrieved 2021-11-25.
7. "World gross electricity production by source, 2019 – Charts – Data & Statistics". International Energy Agency . Retrieved 2021-11-25.
8. "battery" (def. 4b), Merriam-Webster Online Dictionary (2009). Retrieved 25 May 2009.
9. Power Shift: DFJ on the lookout for more power source investments Archived 2005-12-01 at the Wayback Machine . Draper Fisher Jurvetson. Retrieved 20 November 2005.
10. The Opportunity of Energy Group-Buying EnPowered, April 18, 2016,
11. Ignacio J. Pérez-Arriaga (ed), Regulation of the Power Sector, Springer Science & Business Media, 2014 ISBN   1447150341, page 8