---
id: VOLT-HOME-WP-023
title: "Can a charging plan survive uncertain arrival times?"
slug: can-a-charging-plan-survive-uncertain-arrival-times
description: "A robust-scheduling wholesale scenario that measures the opportunity cost of planning for uncertain evening EV arrival."
published: 2026-08-30
cluster: "Smart EV charging"
status: measured
evidence_url: /research-data/home-papers/can-a-charging-plan-survive-uncertain-arrival-times.json
figure_url: /research-media/home-papers/can-a-charging-plan-survive-uncertain-arrival-times.webp
figure_alt: "Chart for Can a charging plan survive uncertain arrival times?: mean robust-schedule regret under uncertain 17:00–20:00 arrival, shown as P10, Median, P90."
source_ids:
  - nature-v1g-v2g-2026
  - applied-energy-smart-charging
  - acer-retail-2025
  - iea-demand-flexibility
  - ec-sdac-15m
peer_reviewed: false
---

## Abstract

An EV cannot charge before it arrives, so a plan made for an uncertain evening arrival can either risk infeasibility or reserve a schedule that works even under the latest declared arrival. This paper measures the wholesale scenario opportunity cost of the second approach. The frozen simulation assumes an 18 kWh event, wholesale energy only, perfect charger efficiency, and an outer local availability window of 17:00–07:00. Arrival is sampled uniformly from 17:00, 18:00, 19:00, and 20:00, while the robust schedule reserves feasibility from 20:00 onward. Across 3,338 observations, mean robust-schedule regret is a wholesale scenario value of €0.07968277786099462 per event. The evidence records a bootstrap field from €0.07357852528125 to €0.09669403245625001. The result quantifies the price of conservatism in this scenario, not a failure rate or observed customer behavior. It does not establish that a robust schedule is preferable to an adaptive one.

## Plain-language answer

Yes, a plan can be made feasible for every arrival time in the declared 17:00–20:00 set by acting as though the vehicle arrives at 20:00. That conservative choice removes earlier charging opportunities even when the simulated vehicle actually arrives sooner. In the frozen evidence, the mean lost wholesale scenario opportunity is €0.07968277786099462 per event, with a recorded bootstrap field from €0.07357852528125 to €0.09669403245625001.

This is the cost of one robust rule, not the cost of uncertainty in all charging systems. A controller that can observe arrival and re-optimize may use the actual available window. A controller that must publish an immutable plan in advance faces a different tradeoff. The paper therefore distinguishes “survives uncertainty” from “is optimal after uncertainty resolves.” The robust plan survives the declared arrival set, but it pays for that guarantee by declining intervals that would have been feasible after an earlier arrival.

## Research question

The research question is: what wholesale scenario regret is created by reserving an EV schedule that remains feasible under a latest arrival of 20:00 when actual arrival is sampled uniformly from 17:00, 18:00, 19:00, and 20:00?

Regret is defined relative to information available after the sampled arrival is known. The adaptive comparison may select any eligible interval from actual arrival until 07:00. The robust schedule may select only intervals from 20:00 until 07:00. Both must deliver the same 18 kWh under the same charger-power rule and recorded price curve. The difference measures optionality given up to guarantee feasibility.

The question does not estimate arrival probabilities from telemetry, forecast an individual driver, or test non-completion. Uniform sampling is an explicit scenario assumption. The result is therefore conditional on the declared set and sampling rule.

## Data and provenance

The registered contract includes `day_ahead_prices`, `forecasts`, `forecast_accuracy`, `generation_mix`, and `zones`. Recorded interval prices and zone timezones directly support the schedule comparison. No behavioral or vehicle telemetry enters the evidence.

The evidence declares daily prices from 2021-01-01 through 2026-08-29, detailed intervals from 2025-10-01 through 2026-08-29, and long history from 2015-01-01 through 2026-08-29. Its publication cutoff is 2026-08-30T00:00:00Z. Extraction used a read-only transaction and a 180-second statement timeout.

The snapshot SHA-256 is `7e97489fc8528c8cc8c38830e05b48d949ce1f67b98575dff26f5d7c321e4c67`. Protocol, registry, source-registry, and analysis-code SHA-256 values are respectively `adb36bf6b447af9f96339249b8becaefc20422499cca1977242866347a97bd4b`, `7bcb91d7476d0a69fe9fa75a5c7782f8117e0153f82f9112b7e1d307d3943717`, `07949550ac443ff673fda5c0209b99f137544f3ffecf6775f109bb9d09663bd6`, and `57c57de79cdab2b5b6d6c54c485cb5162598c5ba0b0bfe995da40d75e6c52ba9`. These identifiers bind the public result to the frozen evidence rather than a mutable serving state.

## Method

For each eligible zone-day, the analysis uses the zone’s local timezone. A deterministic random process samples one arrival from 17:00, 18:00, 19:00, or 20:00 with uniform probability. The adaptive candidate set begins at that sampled arrival and extends to 07:00. The robust candidate set always begins at 20:00 and extends to 07:00.

Within each candidate set, intervals are sorted by day-ahead price. Energy is allocated from cheapest upward subject to an 18 kWh requirement, 7.4 kW charger power, and recorded interval duration. A final interval may be partially used to finish the event. Perfect efficiency is assumed, and wholesale scenario cost is computed from allocated energy and the recorded EUR/MWh price.

Only cases in which both allocations are feasible contribute a paired regret. Robust-schedule regret equals robust wholesale scenario cost minus adaptive wholesale scenario cost. Because the robust candidate set is contained within the actual-arrival candidate set, the regret cannot be negative under a correct implementation. The primary result is the mean across paired observations.

The method family is constraint-aware charging simulation with paired schedule regret and scenario sensitivity. The evidence declares within-family Holm control for inferential claims and labels this result descriptive, with no unadjusted significance claim.

## Results

Mean robust-schedule regret is a wholesale scenario value of €0.07968277786099462 per event across 3,338 observations. The recorded bootstrap field spans €0.07357852528125 to €0.09669403245625001. Positive regret means that reserving feasibility for the latest declared arrival costs more than optimizing after the sampled earlier arrival is known.

The result captures the value of arrival information under the frozen scenario. It does not imply that the robust schedule wastes energy or fails to complete charging. Its defining purpose is feasibility. The monetary contrast arises because some low-priced intervals between sampled arrival and 20:00 are unavailable to the conservative plan.

The figure values are published in the JSON: P10 = 0.0, median = 0.0, and P90 = 0.1773102500000002 EUR per event. They describe the outcome distribution and are distinct from the day/row-block mean bootstrap interval of €0.07357852528125 to €0.09669403245625001.

## Robustness and placebo checks

The same-curve paired comparison holds prices, energy, power, efficiency, timezone, and departure boundary constant. Only the start boundary differs. Feasible-set nesting supplies a directional implementation check: the robust schedule cannot be cheaper than an optimum that has all robust intervals plus additional eligible intervals.

Uniform sampling over the four declared arrival times prevents the scenario from silently favoring one time. It is a design assumption rather than an empirically estimated distribution. The fixed random process makes the panel reproducible when the same ordered inputs are used.

No alternative arrival distribution, immutable-plan benchmark, behavioral placebo, or forecast model is reported in the evidence. Nor is there a causal experiment. Within-family Holm control would govern inferential claims across related papers, but this paper makes a descriptive scenario statement. Its robustness is computational and constraint-based, not proof of external validity.

## Limitations

Every euro amount is a wholesale scenario value. Taxes, network charges, supplier margin, battery losses, and charger losses are excluded. Perfect efficiency, an 18 kWh event, a 7.4 kW charger, and 07:00 completion are simplifying assumptions.

Actual arrivals are not uniformly distributed merely because the scenario samples them that way. Arrival may be correlated with weekday, season, travel demand, price conditions, and required energy. None of those relationships is identified here. The scenario also assumes arrival is known immediately and that charging can be dispatched without communication delay.

The robust policy is deliberately conservative: it acts as if every arrival is 20:00. Other policies could hold a reserve, update after arrival, or optimize against an explicit probability distribution. Their reliability and wholesale scenario values are not measured. This result therefore cannot rank robust control against adaptive stochastic control.

The aggregate does not expose zone-level heterogeneity. The published distribution quantiles show a zero median and a positive upper tail, while the bootstrap interval describes sampling variation in the mean under the implemented day/row-block procedure, not uncertainty about real driver behavior.

## Practical implication

Automation should separate hard feasibility from expected-value optimization. If a charger must commit before arrival and cannot revise, planning from the latest credible arrival is transparent and safe within the declared set, but it gives up wholesale scenario optionality. If the system can detect connection and re-optimize, it may recover some of that optionality.

The input should be surfaced to users and evaluators: a schedule guaranteed from 20:00 is not comparable to one that assumes 17:00 arrival. Reliability claims should state the arrival set they cover. Wholesale scenario values should state whether they are calculated before or after arrival is observed.

The measured €0.07968277786099462 does not justify a device, tariff, or behavioral recommendation. It demonstrates a measurable tradeoff and motivates explicit policy selection: conservative fixed plan, adaptive plan, or another declared rule.

## Reproducibility

Verify the frontmatter against the public evidence JSON, including paper ID, title, slug, measured status, exact assumptions, figure metadata, source tables, windows, primary result, sample size, and provenance hashes. Confirm each reference against the source registry; no empirical result is imported from those citations.

Use snapshot `7e97489fc8528c8cc8c38830e05b48d949ce1f67b98575dff26f5d7c321e4c67` and analysis code `57c57de79cdab2b5b6d6c54c485cb5162598c5ba0b0bfe995da40d75e6c52ba9`. Recreate local-time price panels, sample uniformly from 17:00, 18:00, 19:00, and 20:00 using the frozen process, solve the actual-arrival and 20:00-robust 18 kWh schedules at 7.4 kW, and subtract their wholesale scenario costs.

The reproduced panel should have 3,338 paired observations and return €0.07968277786099462 per event, with the day/row-block mean bootstrap interval €0.07357852528125 to €0.09669403245625001. Infeasible cases must not be converted to zero, and timestamps must remain zone-local for window membership. The current evidence and figure SHA-256 hashes are `34a305d87eebd5521f7346fd71ebffc2a5c8e43b437ed10cf9d6b8e101b0d635` and `728752ef6bb8779970eb499b55928ae46c5d700654daf70f0822a5bc47dcfdf1`.

## Disclosure

Analysis and drafting were model-assisted. Sources, code identity, assumptions, evidence, and hashes are disclosed. This working paper is not peer reviewed.

It is not trading advice, investment advice, tariff advice, or evidence of logged customer behavior. Every monetary amount is a wholesale scenario value. References use exact registry metadata, and no external finding was invented or used as a measurement.

## References

- `nature-v1g-v2g-2026` — Nature Energy. [Coordinated planning of European charging infrastructure and energy system for optimal V1G and V2G deployment](https://doi.org/10.1038/s41560-026-02107-5). Kind: peer-reviewed.
- `applied-energy-smart-charging` — Applied Energy. [The value of smart charging at home and its impact on EV market shares](https://doi.org/10.1016/j.apenergy.2024.124997). Kind: peer-reviewed.
- `acer-retail-2025` — ACER and CEER. [Rewarding flexibility: How retail contract choice can help unlock consumer flexibility](https://www.ceer.eu/wp-content/uploads/2025/11/ACER-CEER-2025-Retail-monitoring.pdf). Kind: official.
- `iea-demand-flexibility` — International Energy Agency. [Scaling Up Demand Flexibility](https://www.iea.org/reports/scaling-up-demand-flexibility). Kind: official.
- `ec-sdac-15m` — European Commission. [EU electricity trading in the day-ahead markets becomes more dynamic](https://energy.ec.europa.eu/news/eu-electricity-trading-day-ahead-markets-becomes-more-dynamic-2025-10-01_en). Kind: official.