Loss of load

Not to be confused with Load loss.

Loss of load in an electrical grid is a term used to describe the situation when the available generation capacity is less than the system load. ^[1] Multiple probabilistic reliability indices for the generation systems are using loss of load in their definitions, with the more popular ^[2] being Loss of Load Probability (LOLP) that characterizes a probability of a loss of load occurring within a year. ^[1] Loss of load events are calculated before the mitigating actions (purchasing electricity from other systems, load shedding) are taken, so a loss of load does not necessarily cause a blackout.

Loss-of-load-based reliability indices

Multiple reliability indices for the electrical generation are based on the loss of load being observed/calculated over a long interval (one or multiple years) in relatively small increments (an hour or a day). The total number of increments inside the long interval is designated as ${\displaystyle N}$ (e.g., for a yearlong interval ${\displaystyle N=365}$ if the increment is a day, ${\displaystyle N=8760}$ if the increment is an hour): ^[3]

• Loss of load probability (LOLP) is a probability of an occurrence of an increment with a loss of load condition. LOLP can also be considered as a probability of involuntary load shedding; ^[4]
• Loss of load expectation (LOLE) is the total duration of increments when the loss of load is expected to occur, ${\displaystyle {LOLE}={LOLP}\cdot N}$. Frequently LOLE is specified in days, if the increment is an hour, not a day, a term loss of load hours (LOLH) is sometimes used. ^[5] Since LOLE uses the daily peak value for the whole day, LOLH (that uses different peak values for each hour) cannot be obtained by simply multiplying LOLE by 24; ^[6] although in practice the relationship is close to linear, the coefficients vary from network to network; ^[7]
• Loss of load events (LOLEV) a.k.a. loss of load frequency (LOLF) is the number of loss of load events within the interval (an event can occupy several contiguous increments); ^[8]
• Loss of load duration (LOLD) characterizes the average duration of a loss of load event: ^[9] ${\displaystyle {LOLD}={\frac {LOLE}{LOLF}}}$

One-day-in-ten-years criterion

A typically accepted design goal for ${\displaystyle LOLE}$ is 0.1 day per year ^[10] ("one-day-in-ten-years criterion" ^[10] a.k.a. "1 in 10" ^[11] ), corresponding to ${\displaystyle {LOLP}={\frac {1}{10\cdot 365}}\approx 0.000274}$. In the US, the threshold is set by the regional entities, like Northeast Power Coordinating Council: ^[11]

resources will be planned in such a manner that ... the probability of disconnecting non-interruptible customers will be no more than once in ten years

— NPCC criteria on generation adequacy

See also

• Value of lost load

References

1. Ascend Analytics 2019.
2. Elmakias 2008, p. 174.
3. Duarte & Serpa 2016, p. 157.
4. Wang, Song & Irving 2010, p. 151.
5. Ela et al. 2018, p. 134.
6. Billinton & Huang 2006, p. 1.
7. Ibanez & Milligan 2014, p. 4.
8. NERC 2018, p. 13.
9. Arteconi & Bruninx 2018, p. 140.
10. Meier 2006, p. 230.
11. Tezak 2005, p. 2.

Sources

• "Loss of Load Probability: Application to Montana" (PDF). Ascend Analytics. 2019.
• David Elmakias, ed. (7 July 2008). New Computational Methods in Power System Reliability. Springer Science & Business Media. p. 174. ISBN   978-3-540-77810-3. OCLC   1050955963.
• Arteconi, Alessia; Bruninx, Kenneth (7 February 2018). "Energy Reliability and Management". Comprehensive Energy Systems. Vol. 5. Elsevier. p. 140. ISBN   978-0-12-814925-6. OCLC   1027476919.
• Meier, Alexandra von (30 June 2006). Electric Power Systems: A Conceptual Introduction. John Wiley & Sons. p. 230. ISBN   978-0-470-03640-2. OCLC   1039149555.
• Wang, Xi-Fan; Song, Yonghua; Irving, Malcolm (7 June 2010). Modern Power Systems Analysis. Springer Science & Business Media. p. 151. ISBN   978-0-387-72853-7. OCLC   1012499302.
• Ela, Erik; Milligan, Michael; Bloom, Aaron; Botterud, Audun; Townsend, Aaron; Levin, Todd (2018). "Long-Term Resource Adequacy, Long-Term Flexibility Requirements, and Revenue Sufficiency". Studies in Systems, Decision and Control. Vol. 144. Springer International Publishing. pp. 129–164. doi:10.1007/978-3-319-74263-2_6. eISSN   2198-4190. ISBN   978-3-319-74261-8. ISSN   2198-4182.
• "Probabilistic Adequacy and Measures: Technical Reference Report" (PDF). NERC. February 2018. p. 13.
• Ibanez, Eduardo; Milligan, Michael (July 2014), "Comparing resource adequacy metrics and their influence on capacity value" (PDF), 2014 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), IEEE, pp. 1–6, doi:10.1109/PMAPS.2014.6960610, ISBN   978-1-4799-3561-1, OSTI   1127287, S2CID   3135204
• Billinton, Roy; Huang, Dange (June 2006), "Basic Concepts in Generating Capacity Adequacy Evaluation", 2006 International Conference on Probabilistic Methods Applied to Power Systems, IEEE, pp. 1–6, doi:10.1109/PMAPS.2006.360431, ISBN   978-91-7178-585-5, S2CID   25841586
• Tezak, Christine (June 24, 2005). Resource Adequacy - Alphabet Soup! (PDF). Stanford Washington Research Group.
• Duarte, Yorlandys Salgado; Serpa, Alfredo del Castillo (2016). "Assessment of the Reliability of Electrical Power Systems". In Antônio José da Silva Neto; Orestes Llanes Santiago; Geraldo Nunes Silva (eds.). Mathematical Modeling and Computational Intelligence in Engineering Applications. Springer. doi:10.1007/978-3-319-38869-4_11. ISBN   978-3-319-38868-7.