Will there be enough power when it matters? Resource adequacy and capacity accreditation

Simulate 500 years of weather and plant outages, count the days that run short, then rate what each new resource is worth

Analyst lesson A5 of Energy Systems, Step by Step: simulate 500 resampled weather years with random plant outages, estimate the loss-of-load expectation, and accredit wind, solar, a battery, demand response and peakers.
  • Analyst · L2
  • 30 min guided · about 30 min practice
  • After lesson 3 and lesson 6 and K5

The Plains Grid over 500 simulated years (seed 2025; illustrative fleet, resampled weather)

  1. 4,000 MW of coal and gas units, 3,000 MW of wind and 1,200 MW of solar serve a 4,000 MW peak. Units fail at random.
  2. Over 500 simulated years the loss-of-load expectation is 0.228 days a year (± 0.049 from sampling alone), above the 1-in-10 criterion of 0.1. In 410 years nothing went short.
  3. Shortfalls bunch on summer evenings: 81% of the shortfall hours fall in June to September.
  4. Each 500 MW added, demand response counted as supply, lifts a nameplate reserve margin from 105.0% to 117.5%, yet LOLE ends anywhere from 0.012 to 0.200.
  5. Rated by the perfect MW that cut unserved energy as much, the five resources range from 89% (peakers) to 15% (solar) of their 500 MW (table below).
  6. Three blocks of solar in a row: 15%, then 6%, then 3%. Beside a 500 MW battery, solar's first block rates 31%.
500 MW of What it is LOLE (days a year) Firm MW at equal unserved energy Accreditation
Nothing added – 0.228 – –
Gas peakers 5 units of 100 MW, each out 7% of the time 0.012 447 MW 89%
Wind farm 500 MW, the same shape as the grid's wind 0.160 79 MW 16%
Solar farm 500 MW, the same shape as the grid's solar 0.200 75 MW 15%
4-hour battery 500 MW, 2,000 MWh, 85% round trip 0.014 276 MW 55%
Demand response 500 MW of load that can be cut, at most 4 hours a day 0.048 132 MW 26%

With JavaScript on, you roll simulated years, run 500 of them with a seed you can change, and rate each resource yourself.

  • A teaching simulation: the Plains Grid, its units, their outage rates and the resources added are illustrative, set so that the grid misses the criterion before anything is added.
  • Weather is resampled, not observed: each week of a simulated year is a real week of 2024 or 2025, shifted by up to a week. The extremes are days that happened then.
  • Real shapes: demand, wind and sun of the Southwest Power Pool (EIA-930, 2024 and 2025); wind and solar scaled to EIA's 2025 monthly capacity factors, as in M3.
  • Units fail independently of each other and of the weather. Planned maintenance, the network and imports are left out.
  • A simulated year is not a forecast; LOLE, LOLH and EUE are averages over the 500 years. LOLE is shown with its Monte Carlo error, which leaves out uncertainty in the weather history and the assumptions.

Need a refresher? Lesson 3 (reserves), lesson 6 (firm capacity) and toolbox K5 (Monte Carlo and standard error).

What you just did, as diagrams

Resource adequacy
Enough supply in nearly every hour, judged over many weather years and plant outages.
Loss-of-load expectation (LOLE)
Shortfall days a year, averaged over the simulated years; the common criterion is 0.1, one day in ten years.
Expected unserved energy (EUE)
Unserved MWh a year: how deep and long the shortfalls are, which LOLE does not say.
Reserve-margin screen
MW installed over the peak, demand response counted as supply: quick, but blind to when the MW show up.
Accreditation
The smallest perfect MW that would cut unserved energy as much, as a share of the MW added; it changes with the mix.
Go deeper · AnalystDays or megawatt-hours: which reliability to match
  • Two measures, two answers. LOLE counts days of any shortfall; EUE weighs each by its MWh. Demand response here removes many short, shallow days but less energy, so its rating depends on which is matched.
  • This lesson matches EUE. In 500 years a count of days moves in steps of 0.002, too coarse to rate one block. PJM rates its classes by EUE too (Manual 20A, sections 2.4 and 2.6).
  • Marginal, not average. Each block is rated against the mix already present. An average can hide how the contribution of the next block differs.
Go deeper · ModelerThe simulation in five lines, and its symbols
  • Outages. Each unit is up or out, in spells of random length: out for \(r\) hours on average, up for \(r(1-f)/f\), so out a share \(f\) of the time.
  • Margin. \(M_t = \text{units}_t + 3{,}000\,w_t + 1{,}200\,s_t - 4{,}000\,d_t\) MW. A battery discharges only when \(M_t < 0\) and charges from any surplus.
  • Accreditation. The smallest \(C\) with \(\text{EUE}(\text{grid} + C) \le \text{EUE}(\text{grid} + \text{resource})\), by bisection: halve the range of MW again and again until the two match.
  • Unique, or a boundary. EUE falls strictly while above zero, so \(C\) is unique. If the resource leaves no shortfall in the sample, the smallest \(C\) is a limit of 500 years, not zero risk.
  • Correlated outages. Real studies tie outage rates to temperature (PJM’s Manual 20A, section 2.3); open tools such as PRAS do this at scale. A9 adds hazards.
Symbol Meaning Unit
\(f\) forced outage rate: the share of time a unit is out share
\(r\) average length of one outage, the repair time hours
\(t\) hour of the simulated year hour
\(\text{units}_t\) coal and gas units not out in hour \(t\) MW
\(w_t\), \(s_t\) wind and solar output per MW installed share
\(d_t\) demand over its own yearly peak share
\(C\) perfect capacity: always available, never out MW

Check yourself

Myth or fact? “An LOLE of 0.1 days a year means 2.4 hours without power each year.”

  • Myth
  • Fact
Answer

Myth. LOLE counts days with any shortfall, of any size or length. Here 0.228 days a year came with 0.70 shortfall hours a year, mostly short evening events.

Myth or fact? “500 MW of solar adds as much reliability as 500 MW of peakers.”

  • Myth
  • Fact
Answer

Myth. In this grid the peakers rate 89% of their 500 MW and solar 15%: shortfalls come after sunset.

Myth or fact? “A resource's accreditation is a fixed property of its technology.”

  • Myth
  • Fact
Answer

Myth. It depends on the grid and its mix: solar's third block rates 3% here, and its first block 31% beside a battery.

Myth or fact? “Two plans with the same reserve margin at nameplate can have very different LOLE.”

  • Myth
  • Fact
Answer

Fact. Each 500 MW added gives 117.5% at nameplate, yet LOLE ends at 0.012 with peakers and 0.200 with solar.

In 500 simulated years, 114 days had at least one hour of shortfall. What is the LOLE?

  • 114 days a year
  • 0.228 days a year
  • 0.1 days a year
  • 2.28 days a year
Answer

114 ÷ 500 = 0.228 shortfall days a year, above the 1-in-10 criterion of 0.1.

500 MW of wind cuts unserved energy as much as 79 MW of perfect capacity would. What is its accreditation?

  • 79%
  • 34%
  • 16%
  • 100%
Answer

79 ÷ 500 ≈ 16%. PJM's 34% for onshore wind is another grid's rating, from another model.

Numbers, sources and what’s next

Numbers to remember

Number What it means Source
0.1 days a year PJM's adequacy criterion: a loss-of-load expectation of one day in ten years. PJM Manual 20A, section 1.3 · Rev. 3, effective 24 June 2026
67% and 59% PJM's class ratings for gas combustion turbines and 4-hour storage in its 2028/29 auction. PJM ELCC class ratings, 2028/2029
34%, 10% and 7% The same for onshore wind, tracking solar and fixed-tilt solar. PJM ELCC class ratings, 2028/2029
0.228 days a year This lesson's Plains Grid before anything is added (seed 2025, 500 resampled years). This lesson's simulation (illustrative fleet)

Keep going

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Sources and further reading

Spotted an error, or stuck? Write to hlli@ksu.edu. Corrections are made in place and dated here.

Text licensed CC BY 4.0, code MIT: teachers and students may reuse and adapt it, with credit to Honglin Li.