Differentiable Reliability, live

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Race two ways to compute capacity accreditation, how much each resource counts toward reliability, for eight resources of the RTS-GMLC test system. Infinitesimal perturbation analysis (IPA) needs one Monte Carlo simulation for all of them; the perturbation method re-runs the simulation for each resource.

Resources

Simulated years

IPA our method1 simulation

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Perturbation10 simulations

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Accreditation factor share of nameplate that counts toward adequacy

Resource IPA Perturb. Paper

Gas combined cycle355 MW — — 0.84

Gas turbine55 MW — — 0.96

Coal155 MW — — 0.91

Nuclear400 MW — — 0.49

Oil turbine20 MW — — 0.89

Hydro50 MW — — 0.75

Wind714 MW — — 0.08

Solar115 MW — — 0.09

About these numbers baseline reliability, the paper’s timings, sources, caveats

Baseline reliability

Measure	This run	Paper
Expected unserved energy	—	394 MWh/yr
Loss-of-load hours	—	2.1 h/yr

The paper ran one million simulated years.

In the paper, Table I

Resource	IPA	Perturbation
Gas combined cycle	0.84	0.84
Gas turbine	0.96	0.96
Coal	0.91	0.91
Nuclear	0.49	0.48
Oil turbine	0.89	0.89
Hydro	0.75	0.76
Wind	0.08	0.09
Solar	0.09	0.09

In the paper, Table II

Method	Seconds per generator	Runs per resource	Runs for the system
ELCC (Bisection)	452.8	≈ 7	1 + N_gN_p
ELCC (Secant)	307.5	≈ 3.7	1 + N_gN_p
MRI (Perturb)	65.7	1	1 + N_gN_p
MRI (IPA)	0.4^*	0	1

^* One IPA run divided by N_g = 153 generators, since one run gives all their gradients. The scripts also run the perfect resource, so this page counts N_g + 2 = 155.

Caveats

The random numbers differ from PRAS’s, so the factors agree with the paper’s statistically, not digit for digit; ± is one standard error.
Wind: both methods settle near 0.08 here, as in Table I’s IPA column and the paper’s Table VII (0.080). Table I’s perturbation column prints 0.09.
Hydro: the perturbation lane reads about 0.005 high. That is the 10 MW step; a 1 MW step closes the gap.
Solar: IPA counts solar only in shortfall hours, while the finite difference also credits solar that charged the battery beforehand, so it reads about 0.007 higher.
Both lanes run at once on this device, one thread each, with identical seeds and samples, so the speedup is about K + 2 by construction for K resources.
The battery and the 200 MW concentrating-solar plant are simulated but not accredited; storage has no IPA factor in the paper either.

Sources

Q. Zhang, F. Zhao, G. Stephen, C. Singh, L. Xie, ‘A Gradient-Based Capacity Accreditation Framework in Resource Adequacy: Formulation, Computation, and Practical Implications’, arXiv:2601.22087, Tables I and II. Model: RTS-GMLC as packaged for NREL’s PRAS, one copperplate region, prepared as the paper’s scripts prepare it; one sample is one simulated year of 8,784 hours.