Loss of load

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] ${\displaystyle {LOLD}={\frac {LOLE}{LOLF}}}$

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

• Value of lost load

• "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.