Nutzung von Massespeichern zur Flexibilisierung des Energieverbrauchs: Kosteneffizienter Anlagenbetrieb durch Anpassung an Marktpreise

Alexander Fay; Christian Derksen; Felix Gehlhoff; Julian Jepsen; Lasse Matthias Reinpold; Lukas Peter Wagner; Maximilian Kilthau; Nils Loose

REVIEW 3 major objections 5 minor 12 references

Nutzung von Massespeichern zur Flexibilisierung des Energieverbrauchs: Kosteneffizienter Anlagenbetrieb durch Anpassung an Marktpreise

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A mixed-integer linear program schedules a wastewater plant's decanters to follow cheap intraday power prices, and a 26-hour field trial matched the plan within 3–7 percent error while cutting energy cost by roughly 56 percent.

desk verdict A genuine 26-hour field trial of MILP-based decanter scheduling, whose headline 56% savings rests on an infeasible constant-power baseline. read the letter →

arxiv 2412.02708 v1 pith:PUOYF2VP submitted 2024-11-27 eess.SY cs.SY

Lukas Peter Wagner , Lasse Matthias Reinpold , Maximilian Kilthau , Felix Gehlhoff , Christian Derksen , Nils Loose , Julian Jepsen , Alexander Fay This is my paper · ORCID

classification eess.SYcs.SY

keywords energyflexibilitymassstorageMILPoptimizationoperationalplanningwastewatertreatmentplantintradaymarketfieldtrialdemand-side

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

This paper tries to show that the buffer tanks and sludge storages of a wastewater treatment plant can act as mass storage for shifting electricity consumption toward cheap hours on the continuous intraday market. The authors build a mixed-integer linear program (MILP) that schedules two decanters under operating states, hold times, startup constraints, and storage mass balances, minimizing electricity cost over a roughly 26-hour horizon. The resulting plan was handed to plant operators as recommendations and executed in a real field trial. Measured power and sludge flows followed the plan with normalized RMSE between 2.8 and 7.1 percent, and the flexible schedule cost about 56 percent less than constant-power operation over the same horizon. If this transfers, existing buffer capacity can make industrial plants price-responsive without new hardware.

What carries the argument

The load-bearing object is the MILP model built from a generic constraint structure for flexible energy resources: the operating point $OP$ in $[0,1]$ linearly determines electric power and sludge flows; binary state variables enforce exactly one active state per time step, feasible state transitions, and minimum/maximum dwell times; and a storage balance $SOC_t = SOC_{t-1} + (P_{\text{in},t} - P_{\text{out},t})\Delta t$ with fixed bounds tracks sludge inventory. A no-simultaneous-start constraint avoids startup peak loads. The objective is minimizing total energy cost over the horizon at quarter-hourly intraday prices. This model is embedded in a dedicated modeling environment that generates the constraints automatically and hands the problem to a commercial MILP solver.

What would settle it

Run the same optimization-and-execution protocol for several weeks with continuous measurement of tank level and inflow: if the realized tank level leaves its bounds or the measured saving against constant-power operation falls close to zero whenever inflow deviates from the assumed 10 m³/h, the paper's central claim would be contradicted.

Watch

Extended reading notes

Core claim

The paper's central claim is that a linear scheduling model of decanters and mass storages is accurate enough to guide real plant operation and that shifting operation to low intraday prices yields large cost savings. The model maps each decanter's operating point to electric power, thin-sludge throughput, and, via a fixed dry-solids density, dry-sludge throughput, and couples the decanters to a sludge tank and dry-sludge containers through mass balances with 100 percent storage efficiency. Binary states Off/Start/Run, minimum hold times, and a constraint preventing simultaneous starts reproduce real operating rules. In the 26-hour field trial the optimized plan raised power use in low-price periods, met the operator's target of returning the sludge tank to its starting level, and cut energy cost from €42.28 to €18.57 compared with steady operation at the same average power, a 56 percent reduction.

Load-bearing premise

The planning model treats the thin-sludge inflow into the storage tank as constant at 10 m³/h and the dry-solids density as constant at 30 g/l for the whole horizon, while the plant only records the tank level manually every eight hours; if those values drift, the optimized schedule, the final tank level, and the 56 percent saving estimate all shift.

Editorial extensions

If this is right

The normalized RMSE values of 2.8 to 7.1 percent for power, thin-sludge flow, and dry-sludge mass flow show the model predicts real plant behavior closely enough for operator guidance.
The sludge tank returns to its 350 m³ starting level by the end of the horizon, so the cost reduction does not come from violating the operator's boundary condition.
Both decanters follow the same state-machine rules (Off/Start/Run, minimum hold times, no simultaneous start), preventing the frequent switching and startup load peaks that would otherwise erode savings.
The optimization solves in about five to six seconds, so revised schedules can be recomputed within the same day when newer intraday prices are published.
Because the constraint set is generic and the only storage-specific part is a mass balance, the same model structure transfers to other buffer-equipped production plants.

Reading between the lines

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

The 56 percent figure is a single-horizon estimate; extension beyond the paper suggests the realized saving tracks the size of the day's intraday price spread, so repeat trials on flat-price days would bound the likely annual saving.
Continuously measuring tank level and inflow, which the paper recommends as future hardware, would let the optimizer re-run whenever the assumed 10 m³/h inflow and 30 g/l solids density drift; the field trial does not test that regime.
The same MILP shell could co-optimize decanter operation with on-site renewable generation or battery storage, since the objective already sums power times price and the constraints are linear.
Deviations between plan and measurement, such as the degradation traced to fouling in one decanter, could serve as a low-cost diagnostic: a persistently worse nRMSE on one unit flags maintenance needs.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things worth knowing. The paper does contain a real field trial: 26 hours, two decanters and a sludge tank, operators following a MILP schedule derived from a model built in their EOM environment. Power tracking is believable (nRMSE 2.8% and 4.5% for the two decanters), the integral deviations converge near zero, and all operator-set production goals were met. That is a genuine and useful data point for the energy-flexible operations community, and the authors are candid about the simplifications (constant inflow, manual tank-level readings, no code or data).

The second thing is that the headline 56% cost saving is not well-defined. The baseline is a static operation with constant power draw of 26.09 kW, equal to the average power of the flexible plan. Under the paper's own equations, that baseline cannot process the assumed 10 m3/h sludge inflow. One decanter at 26.09 kW runs at OP ≈ 0.377, giving 4.52 m3/h of thin sludge — about 118 m3 over 26 h, versus 260 m3 of inflow. The minimum feasible constant-power operation is roughly 30 kW with one decanter at OP ≈ 0.833, or about 53 kW with both decanters running. So the baseline under-processes sludge, and the 56% figure is computed against a strawman. A feasible static schedule (e.g., one decanter cycling at full load most of the time) would have a different cost and a different saving.

Also worth flagging: the sludge-flow agreement is partly tautological. Thin-sludge flow is fixed at e·OP with e = 12 m3/h, and dry-sludge flow is that times an assumed density of 30 g/l, so the 4.8–7.1% nRMSE for those variables is not independent validation. The power agreement is the real validation.

The bottom line: this is a worthwhile demonstration study for readers interested in field validation of energy-flexible scheduling, not a methodological advance. The field execution and the plan-following evidence merit publication after the baseline is fixed and the savings claim is reframed as a scenario comparison against a feasible static policy. The flaws are fixable, and the paper deserves a serious referee.

Referee Report

3 major / 5 minor

Summary. The paper presents a mixed-integer linear programming (MILP) model for the energy-flexible operation of a wastewater treatment plant with decanters and mass storage (a sludge tank and containers). The model is embedded in the 'Energie-Options-Modell' (EOM) optimization environment, uses continuous intraday electricity prices, and is tested in a real field trial lasting about 26 hours. The authors report good agreement between the optimized plan and measurements, with nRMSE values ranging from 2.8% to 7.1% for electrical power and sludge flows, and claim roughly 56% energy cost savings compared to a constant-power baseline. The manuscript also describes the assistance system used to convey operating recommendations to plant operators and discusses limitations such as the absence of continuous fill-level measurement and the difficulty of predicting sludge inflow and solids content.

Significance. If the claims are sound, the paper would be a valuable real-world demonstration of energy-flexible operation of an industrial plant using mass storage, a topic that is often treated only in simulation. The field trial, the use of actual market prices, and the integration of optimization with an operator-facing assistance system are concrete strengths. The strategy evaluation plots provide a useful way to visualize plan execution. However, the central quantitative claims need scrutiny: the sludge-flow validation is partly tautological because the model fixes thin-sludge flow to a constant parameter, and the 56% savings estimate rests on a baseline that appears infeasible under the model's own equations. These issues currently prevent the paper's headline claims from being accepted as they stand.

major comments (3)

[Sec. 3.2.1 and Eqs. (3)-(4)] The constant-power baseline used to compute the 56% savings is infeasible under the model's own mass balance. A constant electrical draw of 26.09 kW from one decanter implies OP ≈ (26.09 - 22.356 - 0.0182·30)/8.464 ≈ 0.377 in Eq. (2). By Eq. (3), the thin-sludge throughput is then e·OP ≈ 4.52 m³/h, which over 26 h processes only about 118 m³, far less than the 260 m³ of inflow that the tank balance (Eqs. 13–14) requires with the assumed 10 m³/h inflow. With both decanters operating continuously to process the inflow, the minimum power is about 52.9 kW, not 26.09 kW. Thus the static baseline either under-processes sludge and violates the tank constraints, or it is not a constant-power operation. The cost comparison should be re-run against a feasible non-flexible schedule (e.g., one decanter at full load for the necessary duration), which would change the reported savings figure.
[Sec. 3.2.1, Eqs. (3)-(4)] The reported agreement for sludge flows is partly by construction. Because P_DS,t = e·OP_t with e fixed at 12 m³/h, the model's predicted thin-sludge flow is exactly 12 m³/h whenever a decanter is on, so the nRMSE values of 4.8–7.1% essentially test whether the real flow equals that assumed constant, not whether the model captures a variable relationship. Similarly, P_TS,t = P_DS,t·Trockenschlammdichte with the density fixed at 30 g/l makes the dry-sludge flow a scaled version of the same constant. The authors acknowledge in Section 3.2.2 that the inflow and density vary in reality, but the abstract and Section 4 claim 'good agreement with real measurements' without making this caveat explicit. Please qualify the validation claim to reflect that the sludge-flow comparison is primarily a check of the constancy assumptions.
[Sec. 3.2.3] The 56% savings figure is a point estimate from a single 26-hour trial with no uncertainty or sensitivity analysis. The authors note that the thin-sludge inflow (set to 10 m³/h) and the dry-solids content (set to 30 g/l) are variable and hard to predict; both parameters directly affect the optimized schedule, the terminal tank level (Eqs. 13–14), and the resulting electricity cost (Eq. 15). Given the baseline infeasibility identified above, the savings estimate should be recomputed for a feasible baseline and, ideally, reported as a range over plausible parameter variations, or at minimum with explicit caveats that it is a single-trial point estimate.

minor comments (5)

[Eq. (2)] The parameter 'Trockenschlammdichte_t' is written with a time subscript in Eq. (2) even though it is a constant (30 g/l) in the model; the subscript is misleading and should be removed or explained.
[Table 1] The term 'Trockenschlammdichte' is technically a solids concentration (g/l), not a density. Consider using 'Trockensubstanzgehalt' or 'solids concentration' in the English version to avoid terminological confusion.
[Fig. 8] Figure 8 includes a measured fill level at 16:00, which lies outside the optimization horizon; the caption should state that this point is for context only and was not used in the optimization.
[Eqs. (10)-(11)] The Haltedauern constraints use a set T_h that is not formally introduced; please define the window explicitly.
[Abstract] The abstract reports 'average errors between 3% to 7%', while the text gives individual nRMSE values from 2.8% to 7.1%; the abstract should match the reported range or note the rounding.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the MILP is fully specified and the field measurements are external checks; the mass-flow comparisons test stated constant assumptions rather than reducing to fitted data.

full rationale

The optimization model is explicitly stated (Eqs. 1-15) and parameterized from Table 1. The field measurements of electrical power, volume flow, and tank level are external to the model, so the reported nRMSE values are genuine comparisons rather than identities. The thin-sludge flow prediction in Eq. (3) is the constant e = 12 m3/h whenever the decanter is operating; this is a testable constant-throughput assumption, not a fitted input called a prediction, because the paper does not claim that e was fitted to the field-trial measurements. The dry-sludge flow in Eq. (4) is the product of thin-sludge flow and dry-solids density in both the model and the process control system; the paper explicitly notes that the real density varies and attributes the small deviations to this, so the comparison is not forced to unity by construction. Self-citations [4]-[6] are used for model-structure provenance and evaluation methodology, but the constraints, parameters, and results are presented and tested in this paper, so they are not load-bearing circular justification. The constant-power baseline in Sec. 3.2.3 raises a separate feasibility/correctness concern (26.09 kW at OP about 0.377 would not process the assumed 10 m3/h inflow under Eq. (3)), but that is a benchmarking flaw rather than a circular reduction of the model's outputs to its inputs.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claims rest on calibrated model coefficients and assumed constant process conditions rather than on first-principles physics. The validation of sludge-flow variables is partly tautological because the model fixes those flows as constants. No new physical entities are introduced.

free parameters (7)

a = 22.356 kW
Power model coefficient in Eq. (2); source or identification procedure not documented.
b = 8.464 kW
Power model coefficient in Eq. (2); source or identification procedure not documented.
c = 0.0182 (kW*l)/g
Power model coefficient in Eq. (2); source or identification procedure not documented.
d = 21.366 kW
Start power coefficient in Eq. (2); source or identification procedure not documented.
e = 12 m3/h
Thin-sludge flow per operating point in Eq. (3); constant by assumption, so validation of Dünnschlamm flow is partly by construction.
Expected thin-sludge inflow = 10 m3/h
Assumed constant inflow to the sludge tank (Section 2.3); used in the tank mass balance.
Expected dry solids density = 30 g/l
Assumed constant density in Eq. (4); used to compute dry-sludge flow and affects power via Eq. (2).

assumptions (6)

standard math MILP solver (CPLEX) finds a solution within optimality gap 10^-3
Relies on solver correctness and gap tolerance; stated in Section 3.1.
domain assumption Mass storage tanks have 100% efficiency and no losses (Eq. 13)
The energy and mass balance for the sludge tank and containers ignores losses, leakage, and sedimentation effects.
domain assumption Thin-sludge inflow is constant at 10 m3/h over the horizon
Used in the tank balance; authors acknowledge the real inflow is variable and hard to predict (Section 3.2.2).
domain assumption Dry solids density is constant at 30 g/l over the horizon
Used in Eq. (4); authors note it fluctuates slightly in reality (Section 3.2.1).
domain assumption Plant operators execute the recommended setpoints from the assistance system
The field results assume human operators follow the schedule; deviations are discussed around starts and stops (Section 3.2.1).
domain assumption Intraday electricity prices for the optimization horizon are known or forecastable
The schedule is computed from price data shown in Figure 1; the authors split the horizon into two stages after prices for the next day are known (Section 3.1).

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Cite this review

Pith. "Pith review of Nutzung von Massespeichern zur Flexibilisierung des Energieverbrauchs: Kosteneffizienter Anlagenbetrieb durch Anpassung an Marktpreise." pith.science (2026). https://pith.science/paper/PUOYF2VP

@misc{pith2026241202708,
  author       = {Pith},
  title        = {Pith review of: Nutzung von Massespeichern zur Flexibilisierung des Energieverbrauchs: Kosteneffizienter Anlagenbetrieb durch Anpassung an Marktpreise},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PUOYF2VP}},
  note         = {Machine review of arXiv:2412.02708}
}

read the original abstract

The increasing share of renewable energy sources and necessitate new concepts for energy flexible operation of industrial production resources. In this paper, we demonstrate the potential of mass storage to increase energy flexibility in industrial operations through the application of optimized operational planning based on market prices. A wastewater treatment plant equipped with decanters and storages is examined to optimally utilize its energy-flexibility. An MILP model was created for energy-flexible production facilities. The resulting operation plan was transmitted to the plant operators and executed over a period of more than 24 hours. The model shows good agreement with real measurements (average errors between 3% to 7%). The results demonstrate significant potential for cost savings of roughly 56% for the investigated time horizon. -- Der zunehmende Anteil erneuerbarer Energien erfordert neue Konzepte zur energieflexiblen Steuerung industrieller Produktionsanlagen. In diesem Beitrag wird demonstriert, wie das Potenzial von Massespeichern zur Steigerung der Energieflexibilit\"at in industriellen Prozessen durch die Anwendung optimierter Betriebsplanung basierend auf Marktpreisen, genutzt werden kann. Es wird eine Abwasseraufbereitungsanlage mit Dekantern und zugeh\"origen Massespeichersystemen betrachtet, um deren Energieflexibilit\"at optimiert zu nutzen. Der resultierende Betriebsplan wurde in einem Assistenzsystem an die Anlagenbetreiber \"ubermittelt und \"uber einen Zeitraum von \"uber 24 Stunden ausgef\"uhrt. Das Modell zeigt eine gute \"Ubereinstimmung mit den realen Messwerten (Fehlern zwischen 3% und 7%). Alle von den Betreibern gesetzten Betriebsziele wurden erreicht, was die Anwendbarkeit des Modells in industriellen Umgebungen best\"atigt. Die Ergebnisse zeigen ein erhebliches Einsparpotenzial von etwa 56% f\"ur den untersuchten Zeitraum.

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Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Kuhlmann, I

T. Kuhlmann, I. Bianchini, D. Umgelter, C. Schneider und V . Lampret, „Die Energieversorgung der Zukunft: Flexibel, intelligent, effizient,“ atp maga- zin, Jg. 66, Nr. 4, S. 24–30, 2024

work page 2024

[2] [2]

L. M. Reinpold, L. P. Wagner, M. Kilthau, A. Karmann und A. Fay, „Pla- nungsfunktionen für (Energie-)Speicher,“ atp magazin, Jg. 65, Nr. 3, S. 60– 69, 2023. DOI: 10.17560/atp.v65i3.2652

work page doi:10.17560/atp.v65i3.2652 2023

[3] [3]

Adresse: www.epexspot.com (besucht am 08

EPEX SPOT SE, Hrsg., Continuous intra-day prices for Germany , 2024. Adresse: www.epexspot.com (besucht am 08. 08. 2024)

work page 2024

[4] [4]

L. P. Wagner, L. M. Reinpold, M. Kilthau und A. Fay, „A Systematic Review of Modeling Approaches for Flexible Energy Resources,“ Renewable and Sustainable Energy Reviews , Jg. 184, 113541, 2023. DOI: 10.1016/j. rser.2023.113541

arXiv 2023

[5] [5]

L. M. Reinpold, L. P. Wagner, L.-T. Reiche und A. Fay, „Experimental Se- tup for the Evaluation of Optimization Strategies for Flexible Energy Re- sources,“ in 2nd IEEE Industrial Electronics Society Annual Online Confe- rence (ONCON), online, 2023, S. 1–6. DOI: 10 . 1109 / ONCON60463 . 2023.10430717

arXiv 2023

[6] [6]

L. P. Wagner, L. M. Reinpold und A. Fay, „Design Patterns for Optimization Models of Flexible Energy Resources,“ in 2nd IEEE Industrial Electronics Society Annual Online Conference (ONCON) , online, 2023, S. 1–6. DOI: 10.1109/ONCON60463.2023.10430916

work page arXiv 2023

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Baumann, G

C. Baumann, G. Huber, J. Alavanja, M. Preißinger und P. Kepplinger, „Ex- perimental validation of a state-of-the-art model predictive control approach for demand side management with a hot water heat pump,“Energy and Buil- dings, Jg. 285, 112923, 2023. DOI: 10 . 1016 / j . enbuild . 2023 . 112923

work page 2023

[8] [8]

Kasper, P

L. Kasper, P. Schwarzmayr, F. Birkelbach, F. Javernik, M. Schwaiger und R. Hofmann, „A digital twin-based adaptive optimization approach applied to waste heat recovery in green steel production: Development and experimen- tal investigation,“ Applied Energy , Jg. 353, 122192, 2024. DOI: https : //doi.org/10.1016/j.apenergy.2023.122192

work page arXiv 2024