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{{distinguish|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 [[electrical load|system load]].{{sfn|Ascend Analytics|2019}} Multiple probabilistic [[reliability index|reliability indices]] for the [[Electricity generation|generation systems]] are using loss of load in their definitions, with the more popular{{sfn|Elmakias|2008|p=174}} being '''Loss of Load Probability''' ('''LOLP''') that characterizes a probability of a loss of load occurring within a year.{{sfn|Ascend Analytics|2019}} 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 [[Power outage|blackout]].

== Loss-of-load-based reliability indices ==
Multiple [[reliability index|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 <math>N</math> (e.g., for a yearlong interval <math>N=365</math> if the increment is a day, <math>N=8760</math> if the increment is an hour):{{sfn|Duarte|Serpa|2016|p=157}}
* '''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]];{{sfn|Wang|Song|Irving|2010|p=151}}
* '''Loss of load expectation (LOLE)''' is the total duration of increments when the loss of load is expected to occur, <math>{LOLE} = {LOLP} \cdot N</math>. 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.{{sfn|Ela|Milligan|Bloom|Botterud|2018|p=134}} 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;{{sfn|Billinton|Huang|2006|p=1}} although in practice the relationship is close to [[Linear function (calculus)|linear]], the coefficients vary from network to network;{{sfn|Ibanez|Milligan|2014|p=4}}
* '''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);{{sfn|NERC|2018|p=13}}
* '''Loss of load duration (LOLD)''' characterizes the average duration of a loss of load event:{{sfn|Arteconi|Bruninx|2018|p=140}} <math>{LOLD} = \frac {LOLE} {LOLF}</math>

== One-day-in-ten-years criterion ==
A typically accepted design goal for <math>LOLE</math> is 0.1 day per year{{sfn|Meier|2006|p=230}} ("'''one-day-in-ten-years criterion'''"{{sfn|Meier|2006|p=230}} a.k.a. "1 in 10"{{sfn|Tezak|2005|p=2}}), corresponding to <math>{LOLP} = \frac {1} {10 \cdot 365} \approx 0.000274</math>. In the US, the threshold is set by the [[regional entity|regional entities]], like [[Northeast Power Coordinating Council]]:{{sfn|Tezak|2005|p=2}} {{quote|resources will be planned in such a manner that ... the probability of disconnecting [[Firm service|non-interruptible customers]] will be no more than once in ten years|NPCC criteria on [[Resource adequacy|generation adequacy]]}}

== See also ==
* [[Value of lost load]]

== References ==
{{RefList}}

== Sources ==
* {{cite web | last =  |title=Loss of Load Probability: Application to Montana |url=https://www.northwesternenergy.com/docs/default-source/default-document-library/about-us/regulatory/2019-plan/montana-lolp-memo-v2019.07.15.pdf?sfvrsn=34c85ca5_5#:~:text=A%20loss%20of%20load%20occurs,point%20in%20a%20given%20year. |publisher=Ascend Analytics |ref={{SfnRef|Ascend Analytics|2019}} | date = 2019}}
* {{cite book | editor = David Elmakias | date = 7 July 2008 | title = New Computational Methods in Power System Reliability | publisher = Springer Science & Business Media | page = 174 | isbn = 978-3-540-77810-3 | oclc = 1050955963 | url = https://books.google.com/books?id=NHEChBndy8AC&pg=PA174 | ref={{SfnRef|Elmakias|2008}}}}
* {{cite book | first1 = Alessia | last1 = Arteconi | first2=Kenneth | last2=Bruninx | date = 7 February 2018 | title = Comprehensive Energy Systems | publisher = Elsevier | page = 140| isbn = 978-0-12-814925-6 | chapter = Energy Reliability and Management | oclc = 1027476919 | url = https://books.google.com/books?id=foxODwAAQBAJ | chapter-url=https://books.google.com/books?id=foxODwAAQBAJ&pg=RA4-PA140 |volume=5}}
* {{cite book | first = Alexandra von | last=Meier | date = 30 June 2006 | title = Electric Power Systems: A Conceptual Introduction | publisher = John Wiley & Sons | page = 230 | isbn = 978-0-470-03640-2 | oclc = 1039149555 | url = https://books.google.com/books?id=bWAi22IB3lkC&pg=PA230}}
* {{cite book | first1 = Xi-Fan | last1 = Wang | first2 = Yonghua | last2 = Song | first3 = Malcolm | last3 = Irving | date = 7 June 2010 | title = Modern Power Systems Analysis | publisher = Springer Science & Business Media | page = 151 | isbn = 978-0-387-72853-7 | oclc = 1012499302 | url = https://books.google.com/books?id=JSg5F_ma-20C&pg=PA151}}
* {{cite book | title = Studies in Systems, Decision and Control | last1 = Ela | first1 = Erik | last2 = Milligan | first2 = Michael | last3 = Bloom | first3 = Aaron | last4 = Botterud | first4 = Audun | last5 = Townsend | first5 = Aaron | last6 = Levin | first6 = Todd | chapter = Long-Term Resource Adequacy, Long-Term Flexibility Requirements, and Revenue Sufficiency | date = 2018 | volume = 144 | pages = 129–164 | publisher = Springer International Publishing | issn = 2198-4182 | eissn = 2198-4190 | doi = 10.1007/978-3-319-74263-2_6 | isbn = 978-3-319-74261-8 | chapter-url = https://books.google.com/books?id=5TtMDwAAQBAJ&pg=PA134}}
* {{cite web |title=Probabilistic Adequacy and Measures: Technical Reference Report |url=https://www.nerc.com/comm/PC/Agenda%20Highlights%20and%20Minutes%202013/Draft_PC_Meeting_Agenda_March_6-7_2018_Jacksonville_FL.pdf |publisher=[[North American Electric Reliability Corporation|NERC]] |ref={{SfnRef|NERC|2018}} |page=13 |date=February 2018}}
* {{citation | last1 = Ibanez | first1 = Eduardo | last2 = Milligan | first2 = Michael | title = 2014 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS) | chapter = Comparing resource adequacy metrics and their influence on capacity value | date = July 2014 | pages = 1–6 | publisher = IEEE | doi = 10.1109/PMAPS.2014.6960610 | osti = 1127287 | isbn = 978-1-4799-3561-1 | s2cid = 3135204 | chapter-url = https://www.nrel.gov/docs/fy14osti/62847.pdf }}
* {{citation | last1 = Billinton | first1 = Roy | last2 = Huang | first2 = Dange | title = 2006 International Conference on Probabilistic Methods Applied to Power Systems | chapter = Basic Concepts in Generating Capacity Adequacy Evaluation | date = June 2006 | pages = 1–6 | publisher = IEEE | doi = 10.1109/PMAPS.2006.360431| isbn = 978-91-7178-585-5 | s2cid = 25841586 | chapter-url = https://ieeexplore.ieee.org/document/4202394 }}
* {{cite book |last1=Tezak |first1=Christine |title=Resource Adequacy - Alphabet Soup! |date=June 24, 2005 |publisher=Stanford Washington Research Group |url=https://hepg.hks.harvard.edu/files/hepg/files/stanford.washington.resource.adequacy.pdf}}
* {{cite book |last1=Duarte |first1=Yorlandys Salgado |first2=Alfredo del Castillo |last2=Serpa |chapter=Assessment of the Reliability of Electrical Power Systems |editor1= Antônio José da Silva Neto |editor2=Orestes Llanes Santiago |editor3=Geraldo Nunes Silva |title=Mathematical Modeling and Computational Intelligence in Engineering Applications |date=2016 |publisher=Springer |isbn=978-3-319-38868-7 |doi=10.1007/978-3-319-38869-4_11 |chapter-url=https://link.springer.com/chapter/10.1007/978-3-319-38869-4_11 }}

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[[Category:Electrical engineering]]
[[Category:Reliability indices]]