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Kilowatt-hour

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"KWH" redirects here. For other uses, see KWH (disambiguation).
Residential electricity meter located in Canada

The kilowatt hour, or kilowatt-hour, (symbol kW·h, kW h or kWh) is a unit of energy equal to 1000 watt hours or 3.6 megajoules.[1][2] For constant power, energy in watt hours is the product of power in watts and time in hours. The kilowatt hour is most commonly known as a billing unit for energy delivered to consumers by electric utilities.

Definition

The kilowatt-hour (symbolized kWh) is a unit of energy equivalent to one kilowatt (1 kW) of power expended for one hour (1 h) of time.

Inversely, one watt is equal to 1 J/s. One kilowatt hour is 3.6 megajoules, which is the amount of energy converted if work is done at an average rate of one thousand watts for one hour.

Examples

A heater rated at 1000 watts (1 kilowatt), operating for one hour uses one kilowatt hour (equivalent to 3.6 megajoules) of energy.

Using a 60-watt light bulb for one hour consumes 0.06 kilowatt hours of energy. Using a 60-watt light bulb for 1000 hours consumes 60 kilowatt hours of energy.

Using a 100-watt light bulb for one hour consumes 0.10 kilowatt hours (100 W / 1000 W/kW) × 1 h = 0.10 kW·h. If the rate being charged for electricity is 10 cents[3] per kilowatt hour, then running the 100-watt bulb for one hour would cost 0.10 kW·h × $0.10/kW·h = $0.01, or one cent. Running a typical space heater rated at 1500 watts would cost 15 cents per hour (1.5 kW × 1 h x $0.10/kW·h = $0.15). Indeed one can determine how much any electrical device will cost to run by multiplying the amount of kilowatts consumed by the device by the rate per kilowatt hour by the time it will be run for (kilowatts × hours × rate-per-kilowatt-hour = cost-to-run), being mindful of the fact that different rates may exist even within one tariff.

Symbol and abbreviation for kilowatt hour

The international standard for SI[4] states that in a forming a compound unit symbol, "Multiplication must be indicated by a space or a half-high (centered) dot (·), since otherwise some prefixes could be misinterpreted as a unit symbol" (i.e., kW h or kW·h). This is supported by a voluntary standard[5] issued jointly by an international (IEEE) and national (ASTM) organization. However, at least one major usage guide[6] and the IEEE/ASTM standard allow "kWh" (but do not mention other multiples of the watt hour). One guide published by NIST specifically recommends avoiding "kWh" "to avoid possible confusion".[7] Nonetheless, it is commonly used in commercial, educational, scientific and media publications.[8]

Conversions

Further information: Conversion of units of energy

To convert a quantity measured in a unit in the left column to the units in the top row, multiply by the factor in the cell where the row and column intersect.

joule watt hour electronvolt calorie
1 J = 1 kg·m2 s−2 = 1 2.77778 × 10−4 6.241 × 1018 0.239
1 W·h = 3600 1 2.247 × 1022 859.8
1 eV = 1.602 × 10−19 4.45 × 10−23 1 3.827 × 10−20
1 cal = 4.1868 1.163 × 10−3 2.613 × 1019 1

Watt-hour multiples and billing units

The kilowatt hour is commonly used by electrical distribution providers for purposes of billing, since the monthly energy consumption of a typical residential customer ranges from a few hundred to a few thousand kilowatt hours. Megawatt hours, gigawatt hours, and terawatt hours are often used for metering larger amounts of electrical energy to industrial customers and in power generation. The terawatt hour and petawatt hour are large enough to conveniently express annual electricity generation for whole countries.

Template:SI multiples 2

In India, the kilowatt hour is often simply called a Unit of energy. A million units, designated MU, is a gigawatt hour and a BU (billion units) is a terawatt hour.[9][10]

Several other units are commonly used to indicate power or energy capacity or use in specific application areas. All the SI prefixes may be applied to the watt-hour: a megawatt hour is 1 million W·h, (symbols MW·h, MW h) a milliwatt hour is 1/1000 W·h, and has the symbol mW·h or mW h, and so on.

Average annual power production or consumption can be expressed in kilowatt hours per year; for example, when comparing the energy efficiency of household appliances whose power consumption varies with time or the season of the year, or the energy produced by a distributed power source. One kilowatt hour per year equals about 114.08 milliwatts applied constantly during one year.

The energy content of a battery is usually expressed indirectly by its capacity in ampere-hours; to convert watt hours (W·h) to ampere hour (A·h), the watt hour value must be divided by the voltage of the power source. This value is approximate since the voltage is not constant during discharge of a battery.

The Board of Trade unit (BOTU) is an obsolete UK synonym for kilowatt hour. The term derives from the name of the Board of Trade that regulated the electricity industry until 1942 when the Ministry of Power took over.[11] The B.O.T.U. should not be confused with the British thermal unit or BTU, which is a much smaller quantity of thermal energy. To further the confusion, at least as late as 1937, Board of Trade unit was simply abbreviated BTU.[citation needed]

Burnup of nuclear fuel is normally quoted in megawatt-days per tonne (MW·d/MTU), where tonne refers to a metric ton of uranium metal or its equivalent, and megawatt refers to the entire thermal output, not the fraction which is converted to electricity.[citation needed]

Confusion of kilowatt hours and kilowatts

The terms power and energy are frequently confused. Power is the rate at which energy is generated or consumed. Power therefore has the unit watts, which is joules per second. A unit of energy is kilowatt hour.

For example, when a light bulb with a power rating of 100W is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt hour, or 360 kJ. This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 50-watt bulb for 2 hours. A power station would be rated in multiples of watts, but its annual energy sales would be in multiples of watt hours. A kilowatt hour is the amount of energy equivalent to a steady power of 1 kilowatt running for 1 hour, or 3.6 MJ.

Power units measure the rate of energy per unit time. Many compound units for rates explicitly mention units of time, for example, miles per hour, kilometers per hour, dollars per hour. Kilowatt hours are a product of power and time, not a rate of change of power with time. Terms such as watts per hour are often misused.[12] Watts per hour (W/h) is a unit of a change of power per hour. It might be used to characterize the ramp-up behavior of power plants. For example, a power plant that reaches a power output of 1 MW from 0 MW in 15 minutes has a ramp-up rate of 4 MW/h. Hydroelectric power plants have a very high ramp-up rate, which makes them particularly useful in peak load and emergency situations.

Major energy production or consumption is often expressed as terawatt hours(TWh) for a given period that is often a calendar year or financial year. One terawatt hour is equal to a sustained power of approximately 114 megawatts for a period of one year.

See also

References

  1. ^ Thompson, Ambler and Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) (Special publication 811). Gaithersburg, MD: National Institute of Standards and Technology. 12.
  2. ^ "Half-high dots or spaces are used to express a derived unit formed from two or more other units by multiplication." Barry N. Taylor. (2001 ed.) The International System of Units. (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
  3. ^ A reasonable approximation for simple calculations; Electric Power Monthly (Oct. 2011) states that "The average [US] retail price of electricity for July 2011 was 10.58 cents per kilowatthour (kWh)"
  4. ^ The International System of Units (SI). (2006, 8th ed.) Paris: International Bureau of Weights and Measures. 130.
  5. ^ Standard for the Use of the International System of Units (SI): The Modern Metric System. (1997). (IEEE/ASTM SI 10-1997). New York and West Conshohocken, PA: Institute of Electrical and Electronics Engineers and ASTM. 15.
  6. ^ Chicago Manual of Style. (14th ed., 1993) University of Chicago Press. 482.
  7. ^ Taylor, Barry N. (1995). 13
  8. ^ See for example: Wind Energy Reference Manual Part 2: Energy and Power Definitions Danish Wind Energy Association. Retrieved 9 January 2008; "Kilowatt-Hour (kWh)" BusinessDictionary.com. Retrieved 9 January 2008; "US Nuclear Power Industry" www.world-nuclear.org. Retrieved 9 January 2008; "Energy. A Beginners Guide: Making Sense of Units" Renew On Line (UK). The Open University. Retrieved 9 January 2008.
  9. ^ "Get enlightened about electricity". The Financial Express. December 20, 2004. Retrieved 29 November 2009.
  10. ^ "BHEL manufactured units generate record power". The Hindu. Press Trust of India. July 24, 2008. Retrieved 29 November 2009.
  11. ^ "The Board of Trade 1621-1970". http://webarchive.nationalarchives.gov.uk/+/http://www.berr.gov.uk/aboutus/corporate/history/outlines/BT-1621-1970/page13919.html. {{cite web}}: External link in |work= (help); Missing or empty |url= (help)
  12. ^ "Inverter Selection". Northern Arizona Wind and Sun. Retrieved 27 March 2009.
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