# Capacity factor

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Definition of Capacity factory presented by United State Nuclear Regularoty Commission says that^{[1]}:

*Capacity factory is the ratio of the net electricity generated, for the time considered, to the energy that could have been generated at continuous full-power operation during the same period*.

The capacity factor is every electricity producing installation. Using renewable energy (e.g. wind or sun) or a fuel consuming power plant defines the issue that the capacy factory is. It also can be used to confront various types of electricity production.

The Way to calculate the capacity factor is **to take the total amount of energy produced by plant in some period of time and divide by the whole energy the plant would have produced at full capacity.** Capacity factors differ with every type of fuel.

The maximum possible output power of an installation assumes its continuous operation at full rated output over a given period of time. The current energy production in this period and the capacity factor vary considerably depending on a number of factors. The capacity factor must never exceed the availability factor or the operating time during this period. Operating times can be reduced, for example, due to reliability and maintenance problems, whether planned or unplanned.

Other factors include the design of the installation, its location, the type of electricity production and, with it, the fuel used or, in the case of renewable energy, local weather conditions. In addition, the efficiency ratio may be subject to regulatory constraints and market forces.

The capacity ratio is often calculated over a period of one year, averaging the most temporary fluctuations. However, it can also be calculated over a month to gain insight into seasonal variations. Alternatively, it is calculated over the lifetime of the power source, both during operation and after decommissioning.

## Sample calculations

**Nuclear power plant**

Nuclear power plants are at the top of the range of performance factors, ideally reduced only by the availability of factors, i.e. maintenance and refuelling
The largest nuclear power plant in the US, the Palo Verde nuclear power station, has a nominal capacity of 3942 MW between three reactors. In 2010 Its annual production amounted to 31 200 000 MWh^{[2]}, which led to a coefficient of performance\[\frac{31,200,000 MW × h}{(365 days) × (24hours/day) × (3942 MW)}= 0.904 = 90.4%\]

Each of the three Palo Verde reactors is refuelled every 18 months, with one refuelling every spring and autumn. In 2014. The refuelling was completed in a record 28 days compared to 35 days of downtime, which corresponds to the efficiency ratio in 2010^{[3]} .

**Wind farm**

The Danish offshore wind farm Horns Rev 2, at its inauguration in 2009,^{[4]} has a rated output of 209.3 MW. From January 2017 onwards. It has produced 6416 GWh since its launch 7.3 years ago, i.e. an average annual production of 875 GWh/year and an efficiency ratio^{[5]}\[\frac{875,000 MW × h}{(365 days) × (24hours/day) × (209,3 MW)}= 0.477 = 47,7%\]

Areas with lower coefficients of yield may be considered feasible for wind farms, for example on land 1 GW Fosen Vind from 2017. It is under construction in Norway and is expected to have a capacity factor of 39%. Some onshore wind farms may have efficiency ratios above 60%, for example, the 44 MW Eolo power plant in Nicaragua had 232.132 GWh net in 2015, which corresponds to an efficiency ratio of 60.2%, while the US annual capacity ratios from 2013 to 2016 range from 32.2% to 34.7%.

Since the wind turbine power factor measures current production in relation to potential production, it is not related to a Betz factor of 16/27 of about 59.3%, which limits production compared to wind power.

**Hydroelectric dam**

From 2017 onwards The Three Gorges dam in China is the largest power plant in the world in terms of installed capacity with a capacity of 22,500 MW. In 2015 It generated 87 TWh for the capacity factor\[\frac{87,000,000 MW × h}{(365 days) × (24hours/day) × (22,500 MW)}= 0.45 = 45%\]

The Hoover dam has a power rating of 2080 MW [8] and an annual generation of an average of 4.2 TW-hour. (The annual generation ranged from 10,344 TW - hw 1984 to 2648 TW - hw 1956^{[6]}). Taking the average value for the annual generation gives the coefficient of capacity\[\frac{4,200,000 MW × h}{(365 days) × (24hours/day) × (2,080 MW)}= 0.23 = 23%\]

## Footnotes

## References

*Arizona Nuclear Profile 2010*, (2010), "U.S. EIA"*Capacity factors at Danish offshore wind farms*, (2019), "Energy Numbers"*Capacity factor (net)*, (2019), "U.S. NRC"*Hoover Dam Frequently Asked Questions and Answers*, (2009), "United States Bureau of Reclamation"- McDermott M. (2009),
*Denmark Inaugurates World's Largest Offshore Wind Farm - 209 MW Horns Rev 2*, "Treehugger" *Palo verde unit 2 ranked as top u.s. generator for 2013*, (2013), "Aps"

**Author:** Anna Syjud