Loss of load

Term for when the available generation capacity in an electrical grid is less than the system load

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 $N$ (e.g., for a yearlong interval $N=365$ if the increment is a day, $N=8760$ 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, ${LOLE}={LOLP}\cdot N$ . 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] ${LOLD}={\frac {LOLE}{LOLF}}$

One-day-in-ten-years criterion

A typically accepted design goal for $LOLE$ is 0.1 day per year^[10] ("one-day-in-ten-years criterion"^[10] a.k.a. "1 in 10"^[11]), corresponding to ${LOLP}={\frac {1}{10\cdot 365}}\approx 0.000274$ . 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

References

^ ^a ^b Ascend Analytics 2019.
^ Elmakias 2008, p. 174.
^ Duarte & Serpa 2016, p. 157.
^ Wang, Song & Irving 2010, p. 151.
^ Ela et al. 2018, p. 134.
^ Billinton & Huang 2006, p. 1.
^ Ibanez & Milligan 2014, p. 4.
^ NERC 2018, p. 13.
^ Arteconi & Bruninx 2018, p. 140.
^ ^a ^b Meier 2006, p. 230.
^ ^a ^b 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.