LOLD Implementation

[akrivi]

This PR:

• Implements the Loss of Load Days (LOLD) metric as defined in [1]
• Adds a new documentation page: "Interpreting Resource Adequacy Metrics"

Mathematical formulation

We define the Loss of Load Days (LOLD) metric as:

$$ \mathrm{LOLD} = \mathbb{E}\left[\sum_{d} I_{d,s}\right] $$

where:

$$ I_{d,s} = \begin{cases} 1 & \text{if } \exists t \in {T}(d) \text{ such that } \sum_r S_{r,t,s} > 0 \\ 0 & \text{otherwise} \end{cases} $$

and

• $r$ indexes regions in the system
• $t$ indexes timestamps
• $d$ indexes calendar days
• $s$ indexes Monte Carlo samples
• $S_{r,t,s}$ is the shortfall in region $r$, time $t$, sample $s$
• ${T}(d)$ is the set of all time periods belonging to day $d$

We note that LOLD is not naturally defined at a single timestamp, since it aggregates over all time periods within a day. As a result, additional computation is needed compared to LOLE, namely:

1. grouping time periods by calendar day
2. aggregating within each day

Benchmarks

Complexity wise, the system wide and full-horizon LOLD scales with total simulation size, while the day-specifc queries scale only with the size of the selected day.

We also provide below a comparison of the benchmarks between LOLD and LOLE:

References:
[1] G. Stephen et al., "Clarifying the Interpretation and Use of the LOLE Resource Adequacy Metric," 2022 17th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), Manchester, United Kingdom, 2022, pp. 1-4, doi: 10.1109/PMAPS53380.2022.9810615.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 94.05941% with 6 lines in your changes missing coverage. Please review.
✅ Project coverage is 84.52%. Comparing base (f49c56e) to head (30ae683).

Files with missing lines	Patch %	Lines
PRASCore.jl/src/Results/ShortfallSamples.jl	92.30%	3 Missing ⚠️
PRASCore.jl/src/Results/utils.jl	90.32%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #108      +/-   ##
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+ Coverage   84.14%   84.52%   +0.38%     
==========================================
  Files          45       45              
  Lines        2491     2592     +101     
==========================================
+ Hits         2096     2191      +95     
- Misses        395      401       +6     

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[abdelrahman-ayad]

Excellent work Akrivi! I left a couple of very minor comments. Can we also include metrics tests in the test/Results/metrics.jl ?

[sriharisundar]

Why do we need this?

[sriharisundar]

Why do we need this?

[sriharisundar]

I'm unsure if we need this here, and would favor the results db/event viewer which will come soon, mainly because we don't expose how this can be read back in or develop tools for down stream analysis with this output.

[sriharisundar]

I'm wondering if this is an extension to PRAS walkthrough, please give me your thoughts! Can you also include the CVAR here if we go ahead with this? Also will be nice to link this to the docs/resourceadequacy.md page.

[sriharisundar]

Actually let's keep this here, bring CVAR in. Call this "Multi metric resource adequacy analyses with PRAS"

[sriharisundar]

Is it appropriate to cite ESIG report as well - https://www.esig.energy/reports-briefs/new-resource-adequacy-criteria/?

[sriharisundar]

Let's move this to below NEUE please

[sriharisundar]

Could you split this into separate lines like the other imports here?

[sriharisundar]

I think I'd rather have this passed in as a variable to get_lold_result from the write() function and being tracked there, than this global variable for the function, as this will be set to true once, and then won't be displayed if used in loop (like in the REPL)