Battery reserve autonomy and diesel generator mission reliability

Overview

The study questions an assumption common in data-centre design: that a short battery autonomy, because it bridges to generator operation, markedly improves generator reliability. The author builds a no-repair mission-survival model. The generator must be available at onset (availability a), start successfully (failure-to-start probability p) and survive the mission duration minus battery autonomy (mean time to failure m). The battery is modelled as a reserve held only for generator failure, able to carry the full critical load and not cycled for fuel optimisation.

Inputs come from two generator populations in NREL report TP-5C00-76553: the Fehr population (availability 0.9998, start-failure probability 0.0013, mean MTTF 1662 h) and the Hong Kong population (0.9984, 0.0165, 61 h). The formulas are R = a(1−p)exp(−t/m) for a single generator and R = a(1−p)exp(−(t−b)/m) with a b-hour reserve, and the minimum reserve for a target reliability is also given in closed form. Results are checked with one million Monte Carlo missions per case.

The finding shows the structural limit of short reserve. For a 72 h mission with Fehr parameters, reliability is 0.95617 for one generator, 0.95847 with an ideal 4 h battery and 0.99808 with two independent generators. With the lower-MTTF Hong Kong parameters the values are 0.30163, 0.32207 and 0.51227, and a 2% common-cause probability lowers the last to about 0.502. Autonomy covering the full mission, in contrast, changes the success event and also covers failure to start and onset unavailability.

The author states the limits openly: published aggregate parameters are used and no new field measurements were taken; the model assumes constant load, no repair and a fully usable reserve; and parameter uncertainty is propagated as scenario corners rather than a joint confidence interval. The results are conditional checks, not a maintenance-effect estimate or a site design validation. The author discloses using generative AI in drafting and analysis.

Key points

1. Fehr population: availability 0.9998, start-failure probability 0.0013, mean MTTF 1662 h; Hong Kong population: 0.9984, 0.0165, 61 h (NREL TP-5C00-76553).
2. Single-generator mission reliability is R = a(1−p)exp(−t/m); with a reserve b < t it is R = a(1−p)exp(−(t−b)/m); the minimum reserve for target r is b = t + m ln[r/(a(1−p))], valid only if r < a(1−p).
3. For a 72 h mission with Fehr parameters: 0.95617 with one generator, 0.95847 with an ideal 4 h battery reserve, 0.99808 with two independent generators.
4. With the lower-MTTF Hong Kong parameters at 72 h: 0.30163 for one generator, 0.32207 with a 4 h reserve, 0.51227 with two independent generators; a 0.02 common-cause probability reduces the last to about 0.502.
5. To meet a 0.95 target over 72 h with Hong Kong parameters an ideal reserve of about 69.98 h is needed; for 168 h the reserve thresholds are about 85.24 h (Fehr) and 165.98 h (Hong Kong).
6. Partial autonomy only reduces running exposure and cannot remove the failure-to-start ceiling; full-mission autonomy changes the success event.
7. A battery cycled daily for fuel or energy savings may not hold its reserve at outage onset, so reserved usable energy must be separated from economic cycling.

Using it in design

• When presenting UPS battery autonomy as a way to improve generator reliability, compute the reserve threshold against the mission duration and report that autonomy of minutes adds little to long-outage generator reliability.
• For long-outage scenarios (72 h, 168 h), compare a single generator with two independent generators or full-mission autonomy, and make the common-cause probability an explicit input.
• Separate reserve energy from economic cycling: model the reserved usable capacity at outage onset apart from any battery cycling for fuel or energy optimisation.
• Use the results as conditional checks and replace them with site-specific generator data and field validation.

Who should read it

Design engineers weighing backup power architecture, generator fuel storage and battery autonomy decisions in reliability terms.

Document contents

1. 1 Introduction
2. 2 Materials and methods (2.1 Computational verification, 2.2 Use of generative artificial intelligence)
3. 3 Results (3.1 Computational verification)
4. 4 Discussion
5. 5 Conclusions
6. 6 Nomenclature
7. 7 Data availability
8. 8 Statements and Declarations

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Publication details

Authors

Mahmoud Abdelfattah Abbas Mahmoud

Publisher

Springer Science and Business Media LLC (preprint)

Year

2026

Document language

English

Source type

Scientific

Access

Open licence — downloadable

DOI

10.21203/rs.3.rs-11224866/v1

Licence

CC BY 4.0 — share with attribution

Licence evidence

www.researchsquare.com

Citation