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On long-duration storage, weather uncertainty and limited foresight

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Pith's one-line read Limited weather foresight changes long-duration storage from arbitrageur to defensive hedge.

desk verdict Solid first application of full multi-stage SDDP to capacity expansion with LDES; the limited-foresight vs perfect-foresight comparison is well-designed, but the storage-target terminal penalty contaminates the headline stockpiling and bidding-curve results, so the magnitudes need a continuation-value treatment before they can be taken at face value. read the letter →

arxiv 2505.12538 v3 pith:JANVHKMH submitted 2025-05-18 econ.GN math.OCq-fin.EC

Felix Schmidt This is my paper · ORCID
classification econ.GNmath.OCq-fin.EC
keywords long-durationenergystorageweatheruncertaintylimitedforesightstochasticprogrammingcapacityexpansionmarginalvaluepriceformationrenewableelectricitymarkets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether capacity-expansion models that assume perfect weather foresight misrepresent the role of long-duration energy storage (LDES). It argues they do: when operators cannot see months ahead, LDES stops acting as an arbitrageur and instead stockpiles energy in autumn and early winter as a defensive hedge against extreme weather states. A stochastic limited-foresight model of fully renewable systems in Germany, Spain, and the UK is compared with a perfect-foresight benchmark, and the paper finds that solar PV gains system value (roughly 25% more capacity in the UK) while onshore wind loses some, and that LDES bids smooth electricity price duration curves. If the claim is right, planning studies that assume perfect foresight overstate wind and understate solar, and extreme price disparity in energy-only markets is partly an artifact of that assumption.

What carries the argument

The load-bearing object is the marginal storage value (MSV), the derivative of the expected future cost-to-go with respect to the storage level at the end of a dispatch stage. The recursive identity $\lambda^{\mathrm{MSV}}_{s,t,h} = \sum_{j=h}^{H(t)}(\mu^e_{s,t,j}-\bar\mu^e_{s,t,j}) + \mathbb{E}[\lambda^{\mathrm{MSV}}_{s,t+1,1}]$ expresses the MSV in a given month and hour as current-period storage-bound effects plus the conditional expectation of next month's MSV, so today's value of stored energy already contains the weather-dependent probability of all future scarcity events. At the margin, discharging sets the electricity price at $\lambda_{t,h}=(\eta^f_s)^{-1}\lambda^{\mathrm{MSV}}_{s,t,h}$ and charging at $\lambda_{t,h}=\eta^h_s\lambda^{\mathrm{MSV}}_{s,t,h}$. The model approximates the expected cost-to-go functions with a cutting-plane algorithm, then evaluates their slopes over the storage domain in steps of 10 GWh to produce monthly bidding curves; those curves are concave in autumn, convex in spring, and their height is set by the cost of the outside option (load shedding or hydrogen imports).

What would settle it

Re-solve the UK No-Imports case with a discounted infinite-horizon stochastic formulation (or with two linked weather years) and compare the storage-level distributions and bidding curves. If the October-to-full stockpiling and the convex spring bidding curves persist, the limited-foresight mechanism is robust; if they flatten or shift, the paper's headline results are driven by the terminal target rather than by weather uncertainty.

Watch

Extended reading notes

Core claim

The central claim is that weather uncertainty changes both the operation and the system value of long-duration storage. In a fully renewable, sector-coupled system with limited foresight, the optimal LDES policy is defensive: the storage builds toward full capacity by October, holds high levels through winter, and only then returns to its target level, so that the distribution of storage trajectories lies well above the perfect-foresight distribution. The bidding logic that produces this behavior is the marginal storage value: a storage unit at the margin bids the efficiency-adjusted expected value of stored energy, and that expectation is the probability of future extreme scarcity (when storage would be empty and load must be shed or hydrogen imported) times the cost of that state. Perfect foresight removes the probability term, allowing aggressive, year-specific dispatch that perfect-foresight models mistake for optimal operation. The paper's quantitative claims include up to 25% higher solar PV capacity and 20% lower onshore wind in the United Kingdom under limited foresight, little change in LDES capacities, and smoother price duration curves because LDES bids vary continuously with storage level and season.

Load-bearing premise

The load-bearing premise is that the value of storage beyond the modeled year can be represented by a single end-of-June target level chosen by the planner, with any shortfall penalized at the value of lost load; if that artificial target is replaced by a proper continuation value, the stockpiling pattern and the spring and summer bidding curves could change, and with them the headline capacity results.

Editorial extensions

If this is right

  • Capacity-expansion studies that assume perfect foresight likely overestimate onshore wind and underestimate solar PV; in the wind-dominated UK case, limited foresight raises solar capacity by about 25% and cuts onshore wind by about 20%.
  • Limited-foresight LDES trajectories are systematically higher in autumn and early winter than perfect-foresight trajectories, and the stockpiling difference is largest in wind-dominated systems and nearly disappears when cheap hydrogen imports provide backup.
  • When LDES sets the electricity price, its bid is the efficiency-adjusted expected marginal storage value, so prices embed the weather-dependent probability of extreme states and price duration curves are smoother than in perfect-foresight models.
  • LDES capacities themselves change little between the two models; the main adjustments are more solar, less onshore wind, and more battery energy capacity (about 86% more in the UK).
  • The derived monthly bidding curves give a concrete starting point for heuristic LDES bidding rules in large-scale planning models that cannot solve a full stochastic program.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: because the paper's operator minimizes expected cost and is risk-neutral, the smoothing of price duration curves is a central-case result; a risk-averse operator would weight tail states more heavily, so the hedging and price-smoothing effects would likely be stronger, not weaker.
  • Editorial extension: the results imply that the system value of a generation technology under limited foresight depends on the predictability of its output in the storage-filling season, not only on its annual energy; technologies with narrow weather variance should command a premium in planning models.
  • Editorial extension: the bidding-curve framework could be reused to value interconnectors, demand response, or firm low-carbon backup, since each lowers the effective cost of the outside option and should flatten the autumn bidding curves.
  • Editorial extension: a testable prediction is that systems with higher wind variance and weaker interconnection will show larger solar-for-wind substitution and higher optimal autumn storage levels; comparing weather-year variances across countries would give a direct check.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper develops a multi-stage stochastic capacity expansion model of a fully renewable, sector-coupled energy system with long-duration hydrogen storage, solved with Stochastic Dual Dynamic Programming (SDDP), and compares it against a two-stage perfect-foresight benchmark. The central methodological contribution is a KKT-based derivation that represents LDES dispatch as bidding the efficiency-adjusted expected marginal storage value (MSV), conditional on storage level and time of year. The case study covers Germany, Spain, and the UK under three backup-availability scenarios. The headline findings are that, under limited weather foresight, LDES operates defensively and stockpiles to hedge extreme future states; solar PV gains capacity (up to about 25% in the UK) at the expense of onshore wind; and energy-only price duration curves become smoother because LDES bids reflect the weather-dependent probability of scarce states. The paper is transparent about its simplifications and provides code and data.

Significance. If the results hold, the paper makes a significant contribution to capacity expansion modeling for very high renewable shares: it moves from weather variability to weather uncertainty, gives a clean analytical bridge between stochastic dynamic programming and storage bidding behavior, and produces concrete, testable claims about capacity mixtures and price formation. The derivation in Section 2.4 (Equations 2a-2e) is a genuine strength, and the comparison of model types C and D is a well-designed natural experiment for isolating the role of foresight. The availability of open-source code and data is another positive element. The main residual risk is that the headline stockpiling and bidding-curve results are partly generated by the artificial terminal storage target, a limitation the paper itself identifies.

major comments (2)
  1. [Section 2.3, SI.1p-q, Section 4.3] The storage-target terminal condition is load-bearing for the central claims, not a neutral modeling detail. Under Eq. SI.1p-q, any end-of-June storage shortfall relative to the endogenously chosen initial level is penalized at the value of lost load (100,000 EUR/MWh). Section 4.3 states that in June the MSV is 100,000 EUR/MWh below the target and 0 above it, and that even in earlier months MSVs 'increase rapidly as a shortfall against the storage target becomes more likely.' This means the spring/summer shape of the bidding curves in Figure 6 and the stockpiling trajectories in Figure 4 are driven in part by an artificial terminal cliff, not purely by limited foresight about winter scarcity. The paper itself concedes in Section 5.3 that under an infinite-horizon or continuation-value treatment 'seasonal differences between bidding curves would likely be less pronounced.' Because the perfect-foresight model can meet the same target without the same precautionary margin, the LF-PF differences in storage behavior and the resulting capacity shifts (up to +25% solar, -20% wind in the UK) are inflated by the terminal penalty. A sensitivity analysis with a reduced terminal penalty, or better a continuation-value/infinite-horizon treatment along the lines of the cited Hole et al. work [37], is needed before the headline effects can be attributed to limited foresight itself rather than to the end-of-horizon construction.
  2. [Section 3.4 and SI.3, Table SI.1] The SDDP runs are stopped by iteration (15,000) or wall-clock (54 h) limits, with only an ex-post inspection of the lower bound and of capacity trajectories as a convergence guarantee. Table SI.1 shows that two specifications actually stop on the time limit, and SI.3 reports a rolling mean of forward-pass simulations rather than a confidence interval for the upper bound. The paper presents the resulting capacity differences as model outputs, so the absence of a quantitative convergence diagnostic is a concern for the magnitude of the headline shifts. The statement that capacity decisions stabilize after about 3,000 iterations is encouraging, but the refining of the policy for another 12,000 iterations could still change the marginal storage values used in the bidding curves of Section 4.3. At minimum, please report the lower-bound/upper-bound gap or a sensitivity check showing that the capacity results and bidding curves do not materially change if training is extended or restarted with a different random seed.
minor comments (5)
  1. [Section 2.4, Eq. (2c)] The notation H(t)\{H} in Equation (2c) is confusing: H(t) is a set of periods, and writing '\{H}' suggests a single period. Please write H(t)\setminus\{H(t)\}, or define H as the last period of the stage.
  2. [SI.2, Eq. (SI.3c)] The phrase 'fishing constraint' appears to be a typo for 'fixing constraint' or 'coupling constraint'. Please correct it.
  3. [Figure 6 and Section 4.3] The example of '127 EUR/MWh at 80% storage in August' should state explicitly that it refers to the No Imports scenario in Germany and to the MSV in EUR/MWh_H2. The y-axis break makes cross-scenario comparison difficult; consider a log-scale inset for the high-MSV range.
  4. [Section 2.2 and Section 5.3] The claim that one-month foresight likely produces a lower bound on the effect of limited foresight is plausible but not demonstrated. A short-horizon sensitivity (e.g., two-week stages for one country) would substantially strengthen this argument, even if only for a subset of scenarios.
  5. [Section 4.1] The statement that under perfect foresight 'the maximum dispatch event across all weather years defines the storage size' is a useful intuition but is stated more strongly than the evidence shown. Consider phrasing it as a tendency observed in the simulations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LDES bidding curves are derived from the model's KKT conditions, and the storage-target caveat is a stated modeling limitation rather than a circular input.

full rationale

I walked the derivation chain from the multi-stage stochastic capacity expansion program (Eq. 1) through the SDDP solution method to the KKT-based derivation of marginal storage values and LDES bidding curves (Eqs. 2a-2e). The bidding curves are derived, not fitted: Eq. 2e defines the MSV recursively as the sum of current-period storage-bound duals plus the expected next-stage MSV, and the paper explicitly frames this as a derivation ('We derive the LDES bidding behavior in the Limited foresight model') rather than as an independent empirical prediction. No parameter is fitted to reproduce the headline stockpiling behavior or the capacity shifts; the storage target level e_ini is an endogenous optimization variable, and the terminal penalty is an exogenous modeling device that is present in both the Limited Foresight and Perfect Foresight models. Thus the LF-PF difference in storage trajectories is not enforced by the input. The paper candidly admits in Section 5.3 that the storage target creates an end-of-horizon effect and that seasonal bidding-curve differences would be less pronounced under an infinite horizon; this is a clearly disclosed limitation affecting the interpretation of magnitudes, but it does not make the derivation circular because the storage target is not defined in terms of the predicted stockpiling. The self-citations ([26] for trust-region stabilization, [81] for a limitation about thermal storage) are not load-bearing for the central claim, and no uniqueness theorem or ansatz is smuggled in via self-citation. Overall, the central results are consequences of the model's stated assumptions and derivations, not equivalences to the inputs by construction.

Assumptions & free parameters 5 free parameters · 8 assumptions · 0 invented entities

All free quantities are inputs from prior literature or explicit modeling choices; the central claims are model outputs, not fitted constants. The most influential choices are VOLL, the import price and limit, the monthly stage length, and the storage-target penalty. No invented physical or economic entities are introduced.

free parameters (5)
  • Value of lost load (VOLL) = 100,000 EUR/MWh_el
    Set very high in the No Imports scenario; it drives LDES bids and stockpiling through the penalty for unmet load. Chosen from prior literature, not fitted to data.
  • H2 spot import price = 250 EUR/MWh_H2
    Cost of the outside option in the Constrained and Unlimited Imports scenarios; it caps the marginal storage value bids. This is an assumed input.
  • H2 spot import limit = 5.5 GWh_H2/h
    Maximum hourly hydrogen import in the Constrained Imports scenario, derived from a back-of-the-envelope ammonia ship calculation; an assumption that affects scarcity pricing.
  • Monthly stage length = 1 month, 168 to 186 four-hourly periods
    Chosen to balance stagewise independence and forecast realism; the paper concedes it is likely an overestimate of foresight and that shorter horizons would amplify effects.
  • Storage target penalty = VOLL applied to any deviation below the endogenous target level
    Terminal condition approximating interannual steady state; the paper admits it creates an end-of-horizon effect that may bias dispatch and capacity decisions.
assumptions (8)
  • domain assumption Stagewise independence of monthly weather vectors
    Section 2.2 assumes the distribution of the next month's weather is independent of past months; tested via autocorrelation but cross-dependencies are not tested. Load-bearing for SDDP tractability and for the limited-foresight policy.
  • domain assumption Risk neutrality of the system operator
    Section 2.5 minimizes expected system costs; risk aversion is not modeled directly. Varying VOLL and import options is used as a proxy for risk preferences.
  • standard math Relatively complete recourse
    SI.2 assumption 1: a feasible dispatch exists for every incoming state and weather realization, a requirement for SDDP cuts.
  • standard math Finite weather sample space and sample average approximation
    SI.2 assumption 3: 35 historical monthly samples per stage stand in for the true weather distribution; this is a sample average approximation.
  • ad hoc to paper Storage target terminal condition approximates steady-state marginal storage value
    Section 2.3 introduces an endogenous initial storage level and a VOLL penalty for missing it; the paper admits this is a coarse approximation with end-of-horizon effects.
  • domain assumption No electricity or hydrogen trade with neighboring countries
    Section 3.1 uses isolated single-node systems, which the paper notes is likely to exaggerate LDES requirements and extreme-state prices.
  • domain assumption Technology costs and potentials are taken from external projections
    Section 3.2 uses Danish Energy Agency technology data, TYNDP 2024 limits, and ERAA 2021 potentials; the results depend on these projections.
  • domain assumption Perfect foresight within each monthly stage
    Section 2.2 assumes the operator sees the full current month ahead; monthly stage length is an explicit assumption about forecast reliability.

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Pith. "Pith review of On long-duration storage, weather uncertainty and limited foresight." pith.science (2026). https://pith.science/paper/JANVHKMH

@misc{pith2026250512538,
  author       = {Pith},
  title        = {Pith review of: On long-duration storage, weather uncertainty and limited foresight},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JANVHKMH}},
  note         = {Machine review of arXiv:2505.12538}
}
read the original abstract

Long-duration energy storage (LDES) is a key component for fully renewable, sector-coupled energy systems based on wind and solar. While capacity expansion planning has begun to take into account interannual weather variability, it often ignores weather uncertainty and limited foresight in capacity and operational decisions. We build a stochastic capacity expansion model for fully decarbonized energy systems with LDES in Europe accounting for weather uncertainty - isolating the effect of limited foresight by comparing it to a perfect foresight benchmark. Under limited foresight, LDES acts as a hedge against extreme system states operating defensively and exhibiting a stockpiling effect absent under perfect foresight. Solar PV gains in system value for its higher predictability with up to 25% higher capacities versus the benchmark while onshore wind capacities are lower. We shed light on the underlying mechanisms by deriving implicit LDES bidding curves. We show that LDES bids reflect the costs and the weather-dependent probability of extreme system states conditional on the current system state. This has important implications for the price formation on renewable electricity markets, as a wide and continuous range of probabilistic LDES bids alleviates concerns of extreme price disparity at high renewable shares.

Figures

Figures reproduced from arXiv: 2505.12538 by the authors.

Figure 1
Figure 1. Model setups to deal with weather variability and uncertainty: Panel A represents single-year deterministic models. Panel B is a deterministic model that includes a (long) sequence of weather years in the dispatch stage. Panel C is a two-stage stochastic setup in which the capacity decision is taken under uncertainty. There is perfect foresight in the dispatch stage. Lastly, Panel D represents the multi-stage stocha… view at source ↗
Figure 2
Figure 2. Autocorrelation functions of weather variables at monthly stage length. Monthly autocorrelation for solar photovoltaic, wind onshore, wind offshore, run of river, hydro reservoirs, pumped hydro storage (PHS) with inflows, residential and commercial aggregate heat demand and heat pump efficiencies. In the face of weather uncertainty, this is directly related to the system planner’s ability to produce or procure reli￾… view at source ↗
Figure 3
Figure 3. System representation and sampling lattice: Panel A shows a stylized representation of the considered system. Electricity generation is confined to renewable sources. In the case of Spain and the UK, existing nuclear capacities are also considered. Electrified heat demand is served by a single type of heat pump. Hydrogen is produced via electrolysis or imported by ship, either under long-term contracts or, depending… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: shows the distribution (5th-95th, 25th-75th percentile and mean trajectories as well as the actual paths) of storage trajectories when simulating the Perfect Foresight case (blue; PF) and the Limited Foresight case (red; LF) over the 35 historical weather years between…
Figure 5
Figure 5. Figure 5: Comparison of capacity choices: Assuming No Imports; Left panels show generation capacities; middle panels show Li-Ion capacities; right panels show capacities for LDES components. In addition to Limited Foresight (red) and Perfect Foresight (blue), gray crosses repres…
Figure 6
Figure 6. Figure 6: LDES bidding curves: Monthly LDES marginal values of storage derived from trained SDDP model differentiated by alternative H2 import options for Germany. In summary, it is the probability of extreme weather realizations in which the LDES cannot cover all the load and t…
Figure 7
Figure 7. Figure 7: Electricity price duration curves over 35 simulated weather years 5. Discussion and conclusion 5.1. Summary In this work, we use a method developed for the optimization of hydro-dominated electricity systems to optimize a simplified capacity expansion model for fully r…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.