### Abstract

This paper describes a new probability theory of the capacity value of additional generation in electrical power systems. A closed-form expression for the effective load carrying capability or equivalent firm capacity of a small additional capacity is derived. This depends on the mean and variance of the distribution of available additional generation capacity, and the shape of the distribution of the difference between available existing capacity and demand, near zero margin. The theory extends naturally to the case where the pre-existing background and additional resource are not statistically independent.

The theory may be used to explain and confirm the generality of various well-known properties of capacity value results, as is illustrated using Great Britain examples. Of particular note is the common observation that if the distribution for demand is shifted so as to increase the calculated risk, then the capacity value of additional generation increases. The new theory demonstrates that this is not true in general, but rather is a consequence of the shape near zero margin of the probability distribution of the margin of existing generating capacity over demand.

The theory may be used to explain and confirm the generality of various well-known properties of capacity value results, as is illustrated using Great Britain examples. Of particular note is the common observation that if the distribution for demand is shifted so as to increase the calculated risk, then the capacity value of additional generation increases. The new theory demonstrates that this is not true in general, but rather is a consequence of the shape near zero margin of the probability distribution of the margin of existing generating capacity over demand.

Original language | English |
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Pages (from-to) | 33-43 |

Journal | Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability |

Volume | 226 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Feb 2012 |

### Keywords

- capacity credit
- capacity value
- wind power
- power system reliability evaluation
- intermittent generation
- variable generation

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## Cite this

Zachary, S., & Dent, C. J. (2012). Probability theory of capacity value of additional generation.

*Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability*,*226*(1), 33-43. https://doi.org/10.1177/1748006X11418288