# 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:

${\displaystyle {\frac {31,200,000MWh}{(365days)\cdot (24hours/day)\cdot (3942MW)}}=0.904=90.4\%}$

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]:

${\displaystyle {\frac {875,000MWh}{(365days)\cdot (24hours/day)\cdot (209,3MW)}}=0.477=47,7\%}$

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:

${\displaystyle {\frac {87,000,000MWh}{(365days)\cdot (24hours/day)\cdot (22,500MW)}}=0.45=45\%}$

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:

${\displaystyle {\frac {4,200,000MWh}{(365days)\cdot (24hours/day)\cdot (2,080MW)}}=0.23=23\%}$

## Examples of Capacity factor

• The capacity factor of a nuclear power plant is the amount of electricity produced by the plant over a period of time, divided by the maximum amount of electricity it could produce. For example, if a nuclear plant produces 100 megawatts of electricity over a period of one month, and its maximum capacity is 200 megawatts, then its capacity factor would be 50%.
• The capacity factor of a wind turbine is the amount of electricity produced by the turbine over a period of time, divided by the maximum amount of electricity it could produce. For example, if a wind turbine produces 5 megawatts of electricity over a period of one month, and its maximum capacity is 10 megawatts, then its capacity factor would be 50%.
• The capacity factor of a solar panel is the amount of electricity produced by the panel over a period of time, divided by the maximum amount of electricity it could produce. For example, if a solar panel produces 1 megawatt of electricity over a period of one month, and its maximum capacity is 2 megawatts, then its capacity factor would be 50%.

A Capacity Factor is a measure of the performance of a nuclear power plant over a period of time. It is defined as the ratio of the actual energy produced to the maximum possible energy that could have been produced during the same period. The Capacity Factor is a useful tool for assessing a nuclear power plant's efficiency and performance. Below are some of the advantages of Capacity Factor:

• It provides a snapshot of how well a nuclear power plant is running, allowing for comparison between plants and over time.
• It helps to identify areas for improvement, allowing for more efficient operation of the plant.
• It can be used to monitor plant safety, as higher Capacity Factors tend to indicate better safety measures are being taken.
• It can be used to assess the economic viability of a nuclear power plant, as higher Capacity Factors tend to be associated with higher revenues.
• It can be used to assess the environmental impact of a nuclear power plant, as higher Capacity Factors tend to be associated with lower emissions.

## Limitations of Capacity factor

A Capacity factor is defined by the United States Nuclear Regulatory Commission as a measure of the actual output of a nuclear generating plant compared to its potential output over a period of time. However, there are several limitations associated with the use of a capacity factor to evaluate a nuclear generating plant's performance. These include:

• The capacity factor does not take into account the quality of the output produced by the plant. For example, it will not distinguish between the amount of energy produced through fission and the amount of energy lost through waste heat.
• Capacity factors can be affected by the amount of time a plant is out of service. If a plant is offline for a significant period of time, its capacity factor will be lower than a plant that is consistently operational over the same period of time.
• Capacity factors do not take into account the cost of running the plant. The cost of electricity produced by a nuclear plant can be much higher than the cost of electricity produced by other sources.
• Capacity factors do not account for the cost of the fuel used in the plant. This can be an important factor when evaluating the overall cost of electricity produced by a nuclear plant.
• Capacity factors do not take into account the environmental impacts of nuclear power production. The emissions of radioactive material into the atmosphere, the risks associated with nuclear waste disposal, and the potential for a nuclear accident can all be important considerations when assessing the performance of a nuclear generating plant.

## Other approaches related to Capacity factor

A Capacity factor is a measure of the efficiency of production in a nuclear power plant, calculated by dividing the total energy produced by the power plant over a period of time by the energy that could have been produced if the plant had operated continuously during that period. There are other approaches related to Capacity factor such as:

• Capacity Credit - This approach uses the plant's reliable operating performance over the past year to estimate the amount of energy the plant will produce in the future.
• Plant Performance Data - This approach uses the historical data collected from the plant's operations over a period of time to calculate a Capacity factor.
• Load Factor - This approach is based on the total energy produced by a plant over a period of time, divided by the total energy that could have been produced if the plant had operated at its maximum capacity for the entire period.

In summary, Capacity factor is a measure of the efficiency of production in a nuclear power plant, and there are several other approaches related to it, such as Capacity Credit, Plant Performance Data, and Load Factor.

## Footnotes

1. U.S. NRC, 2019
2. U.S. EIA, 2010
3. asp.com, 2013
4. Matthew McDermott, 2009
5. energynumbers.com, 2019
6. United States Bureau of Reclamation, 2009

 Capacity factor — recommended articles Structural productivity — Life-cycle cost analysis (LCCA) — Shadow Pricing — Overall equipment effectiveness — Capture rate — Capacity analysis — Project evaluation methods — Tooling costs — Hidden cost

## References

Author: Anna Syjud