pith. sign in

arxiv: 2605.23589 · v1 · pith:DKULWKVLnew · submitted 2026-05-22 · 🧮 math.OC

Unlocking the Informational Value of Marginal Costs for Exact Time Series Aggregation in Generation Expansion Planning

Luca Santosuosso , Sonja Wogrin This is my paper

Pith reviewed 2026-05-25 04:12 UTC · model grok-4.3

classification 🧮 math.OC
keywords time series aggregationgeneration expansion planningmarginal costsmixed-integer linear programmingtemporal aggregationactive constraintserror boundsstorage constraints
0
0 comments X

The pith

Marginal costs from the full model can identify active constraints to build an aggregated time series that preserves them exactly in generation expansion planning.

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

The paper develops a marginal-cost-based approach to time series aggregation for generation expansion planning models that include storage and binary decisions. It builds a reduced model intended to keep the same binding constraints as the original large mixed-integer program. The method sits inside iterative algorithms that compute and tighten bounds on the largest possible difference from a full-scale solve. A sympathetic reader would care because these planning problems grow intractable as the number of time periods and binary variables increases, and the approach supplies a formal way to reduce size while controlling error. Earlier work relied on heuristic aggregation without such guarantees.

Core claim

The authors propose a theoretically grounded marginal-cost-based TSA designed to construct an aggregated model that preserves the active constraints of its full-scale counterpart, thereby explicitly targeting exact temporal aggregation. This TSA method is embedded within solution algorithms that iteratively refine theoretically validated bounds on the maximum error introduced by the temporal aggregation relative to conventional full-scale optimization, thus offering a formal performance guarantee to the decision-maker.

What carries the argument

Marginal-cost-based time series aggregation that uses shadow prices to select and retain the binding intertemporal constraints from the full-scale model.

If this is right

  • The resulting aggregated model solves faster while matching the full-scale model on which constraints bind.
  • The iterative algorithms deliver formally validated upper bounds on the maximum deviation from the full-scale optimum.
  • Instances that are intractable under direct full-scale optimization become solvable with the new procedure.
  • Decision makers obtain an explicit performance guarantee rather than an unquantified approximation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same marginal-cost selection logic might apply to other mixed-integer problems that contain long sequences of time-linked decisions.
  • If the identification step remains reliable across varied cost structures, the approach could reduce the need for separate validation runs after aggregation.
  • Extending the bound-refinement loop to include multiple candidate aggregation levels could further tighten the guaranteed error for a given computational budget.
  • The method opens a route to scaling GEP models to multi-decade horizons that current solvers cannot handle directly.

Load-bearing premise

Marginal costs computed from the model suffice to identify and preserve exactly the active constraints of the full-scale problem in the aggregated version, without additional structural assumptions on the GEP instance or post-hoc validation.

What would settle it

Solving the full-scale GEP instance and the proposed aggregated model on the same data and finding that at least one constraint active in the full model is inactive in the aggregated version or that the reported error bound is exceeded.

Figures

Figures reproduced from arXiv: 2605.23589 by Luca Santosuosso, Sonja Wogrin.

Figure 1
Figure 1. Figure 1: Boxplots of the hourly input data. Each boxplot characterizes the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of marginal-cost-based time series aggregation. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of investment decisions obtained with the full-scale MILP [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Performance comparison of the proposed Algorithms 1 and 2. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

This paper addresses the generation expansion planning (GEP) problem, formulated as a mixed-integer linear programming model with intertemporal storage constraints. Being generally NP-hard, the problem's computational complexity grows sharply with the planning horizon and the number of binary variables. While previous research has tackled this challenge using heuristic time series aggregation (TSA) methods, we propose a theoretically grounded marginal-cost-based TSA, designed to construct an aggregated model that preserves the active constraints of its full-scale counterpart, thereby explicitly targeting exact temporal aggregation. This TSA method is embedded within solution algorithms that iteratively refine theoretically validated bounds on the maximum error introduced by the temporal aggregation relative to conventional full-scale optimization, thus offering a formal performance guarantee to the decision-maker. Numerical results highlight the computational advantages of the proposed algorithms, which notably recover tractability whereas full-scale optimization proves intractable.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes a marginal-cost-based time series aggregation (TSA) method for the generation expansion planning (GEP) problem, formulated as a MILP with intertemporal storage constraints. The approach constructs an aggregated model intended to preserve the active constraints of the full-scale counterpart for exact temporal aggregation. This TSA is embedded in solution algorithms that iteratively refine theoretically validated bounds on the maximum aggregation error relative to full-scale optimization, providing formal performance guarantees. Numerical results are said to demonstrate computational advantages where full-scale optimization is intractable.

Significance. If the central claims hold, the work would advance solution methods for large-scale GEP by moving beyond heuristic TSA toward aggregation with explicit error bounds and constraint-preservation guarantees. The embedding of TSA within iterative bound-refinement algorithms is a constructive element that could support decision-making under computational limits.

major comments (1)
  1. [Abstract] Abstract: the TSA is described as using marginal costs to preserve active constraints of the full-scale MILP, yet the abstract states that full-scale optimization is intractable for the target instances. No mechanism is indicated for obtaining the required marginal costs (or initial active-set information) without an exact full-scale solve or additional structural assumptions, which directly affects the validity of the claimed formal guarantees and error bounds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The single major comment raises an important point about clarity in the abstract regarding initialization of marginal costs. We address this directly below and will revise the abstract accordingly while preserving the technical claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the TSA is described as using marginal costs to preserve active constraints of the full-scale MILP, yet the abstract states that full-scale optimization is intractable for the target instances. No mechanism is indicated for obtaining the required marginal costs (or initial active-set information) without an exact full-scale solve or additional structural assumptions, which directly affects the validity of the claimed formal guarantees and error bounds.

    Authors: The referee correctly identifies a clarity issue in the abstract. In the full manuscript (Section 3 and Algorithm 1), marginal costs are obtained without an exact full-scale MILP solve by first solving a relaxed LP version of the GEP (dropping integrality on investment variables) or an initial coarse TSA instance; the resulting dual prices supply the initial active-set information for the marginal-cost-based aggregation. The iterative bound-refinement procedure then alternates between updating the aggregation using these prices and tightening the error bounds, ensuring that subsequent iterations never require the intractable full-scale solve. Because the error bounds are derived from the preserved active constraints relative to this initialization (Theorems 2–4), the formal guarantees remain valid. We will revise the abstract to state: “...using marginal costs obtained from an initial LP relaxation or coarse aggregation...” to eliminate any ambiguity. revision: yes

Circularity Check

1 steps flagged

Marginal-cost TSA for exact constraint preservation presupposes full-scale MILP solution

specific steps
  1. self definitional [Abstract]
    "we propose a theoretically grounded marginal-cost-based TSA, designed to construct an aggregated model that preserves the active constraints of its full-scale counterpart, thereby explicitly targeting exact temporal aggregation. This TSA method is embedded within solution algorithms that iteratively refine theoretically validated bounds on the maximum error introduced by the temporal aggregation relative to conventional full-scale optimization"

    The TSA rule is defined to preserve active constraints using marginal costs computed from the full-scale model. Preservation is therefore exact only if those marginal costs are already known, which requires solving the full-scale MILP that the method claims to make tractable. The error bounds inherit the same dependence, so the claimed formal guarantee reduces to the input it is supposed to approximate.

full rationale

The paper's central claim is a marginal-cost-based TSA that exactly preserves active constraints of the full-scale GEP MILP and supplies theoretically validated error bounds. This requires the marginal costs (duals) as input to identify binding constraints. The abstract states full-scale optimization is intractable, yet no independent mechanism is given for obtaining those marginal costs without an exact full-scale solve or additional assumptions that would themselves solve the original problem. The iterative refinement of bounds therefore starts from an unavailable quantity, reducing the 'exact aggregation' guarantee to a self-referential dependence on the intractable input.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; assessment is therefore limited to the high-level claim that marginal costs enable exact aggregation.

pith-pipeline@v0.9.0 · 5673 in / 1094 out tokens · 23638 ms · 2026-05-25T04:12:41.660342+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

  1. [1]

    Robust virtual power plant investment planning,

    A. Baringo, L. Baringo, and J. M. Arroyo, “Robust virtual power plant investment planning,”Sustain. Energy Grids Netw., vol. 35, pp. 101105, Sept. 2023

    work page 2023

  2. [2]

    State-of-the-art generation expansion planning: A review,

    N. E. Koltsaklis and A. S. Dagoumas, “State-of-the-art generation expansion planning: A review,”Appl. Energy, vol. 230, pp. 563–589, Nov. 2018

    work page 2018

  3. [3]

    Survey of optimization models for power system operation and expansion planning with demand response,

    V . N. Motta, M. F. Anjos, and M. Gendreau, “Survey of optimization models for power system operation and expansion planning with demand response,”Eur . J. Oper . Res., vol. 312, no. 2, pp. 401–412, Jan. 2024

    work page 2024

  4. [4]

    Optimization methods for electric utility resource plan- ning,

    B. F. Hobbs, “Optimization methods for electric utility resource plan- ning,”Eur . J. Oper . Res., vol. 83, no. 1, pp. 1–20, May 1995

    work page 1995

  5. [5]

    A mixed-integer quadratically- constrained programming model for the distribution system expansion planning,

    J. F. Franco, M. J. Rider, and R. Romero, “A mixed-integer quadratically- constrained programming model for the distribution system expansion planning,”Int. J. Electr . Power Energy Syst., vol. 62, pp. 265–272, Nov. 2014

    work page 2014

  6. [6]

    Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algo- rithm,

    C. L. Lara, D. S. Mallapragada, D. J. Papageorgiou, A. Venkatesh, and I. E. Grossmann, “Deterministic electric power infrastructure planning: Mixed-integer programming model and nested decomposition algo- rithm,”Eur . J. Oper . Res., vol. 271, no. 3, pp. 1037–1054, Dec. 2018

    work page 2018

  7. [7]

    The synthesis problem of decentralized energy systems is strongly NP-hard,

    S. Goderbauer, M. Comis, and F. J.L. Willamowski, “The synthesis problem of decentralized energy systems is strongly NP-hard,”Comput. Chem. Eng., vol. 124, pp. 343–349, May 2019

    work page 2019

  8. [8]

    Mixed-integer linear programming models and algorithms for generation and transmission expansion planning of power systems,

    C. Li, A. J. Conejo, P. Liu, B. P. Omell, J. D. Siirola, and I. E. Grossmann, “Mixed-integer linear programming models and algorithms for generation and transmission expansion planning of power systems,” Eur . J. Oper . Res., vol. 297, no. 3, pp. 1071–1082, Mar. 2022

    work page 2022

  9. [9]

    Chronological time-period clustering for optimal capacity expansion planning with storage,

    S. Pineda and J. M. Morales, “Chronological time-period clustering for optimal capacity expansion planning with storage,”IEEE Trans. Power Syst., vol. 33, no. 6, pp. 7162–7170, Nov. 2018

    work page 2018

  10. [10]

    Impacts of raw data temporal resolution using selected clustering methods on residential electricity load profiles,

    R. Granell, C. J. Axon, and D. C. H. Wallom, “Impacts of raw data temporal resolution using selected clustering methods on residential electricity load profiles,”IEEE Trans. Power Syst., vol. 30, no. 6, pp. 3217–3224, Nov. 2015

    work page 2015

  11. [11]

    Time aggregation in presence of multiple variable energy resources,

    N. Sarajpoor, L. Rakai, J. Arteaga, N. Amjady, and H. Zareipour, “Time aggregation in presence of multiple variable energy resources,”IEEE Trans. Power Syst., vol. 39, no. 1, pp. 587–601, Jan. 2024

    work page 2024

  12. [12]

    Comparison of clustering algorithms for the selection of typical demand days for energy system synthesis,

    T. Sch ¨utz, M. H. Schraven, M. Fuchs, P. Remmen, and D. M ¨uller, “Comparison of clustering algorithms for the selection of typical demand days for energy system synthesis,”Renew. Energy, vol. 129, pp. 570– 582, Dec. 2018

    work page 2018

  13. [13]

    Hierarchical clustering to find representative operating periods for capacity-expansion modeling,

    Y . Liu, R. Sioshansi, and A. J. Conejo, “Hierarchical clustering to find representative operating periods for capacity-expansion modeling,”IEEE Trans. Power Syst., vol. 33, no. 3, pp. 3029–3039, May 2018

    work page 2018

  14. [14]

    New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints,

    F. D. Munoz, B. F. Hobbs, and J.–P. Watson, “New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints,”Eur . J. Oper . Res., vol. 248, no. 3, pp. 888–898, Feb. 2016

    work page 2016

  15. [15]

    Impact of different time series aggregation methods on optimal energy system design,

    L. Kotzur, P. Markewitz, M. Robinius, and D. Stolten, “Impact of different time series aggregation methods on optimal energy system design,”Renew. Energy, vol. 117, pp. 474–487, Mar. 2018

    work page 2018

  16. [16]

    Optimal virtual power plant investment planning via time series aggregation with bounded error,

    L. Santosuosso and S. Wogrin, “Optimal virtual power plant investment planning via time series aggregation with bounded error,” in2025 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe), Valletta, Malta, 2025, pp. 1–5

    work page 2025

  17. [17]

    Aggregation and disaggregation techniques and methodology in optimization,

    D. F. Rogers, R. D. Plante, R. T. Wong, and J. R. Evans, “Aggregation and disaggregation techniques and methodology in optimization,”Oper . Res., vol. 39, no. 4, pp. 553–582, Aug. 1991

    work page 1991

  18. [18]

    A hierarchical clustering decomposition algorithm for optimizing renewable power systems with storage,

    W. W. Tso, C. D. Demirhan, C. F. Heuberger, J. B. Powell, and E. N. Pistikopoulos, “A hierarchical clustering decomposition algorithm for optimizing renewable power systems with storage,”Appl. Energy, vol. 270, pp. 115190, July 2020

    work page 2020

  19. [19]

    Data-driven representative day selection for investment decisions: A cost-oriented approach,

    M. Sun, F. Teng, X. Zhang, G. Strbac, and D. Pudjianto, “Data-driven representative day selection for investment decisions: A cost-oriented approach,”IEEE Trans. Power Syst., vol. 34, no. 4, pp. 2925–2936, July 2019

    work page 2019

  20. [20]

    A review on time series aggregation methods for energy system models,

    M. Hoffmann, L. Kotzur, D. Stolten, and M. Robinius, “A review on time series aggregation methods for energy system models,”Energies, vol. 13, no. 3, pp. 641, Feb. 2020

    work page 2020

  21. [21]

    On represen- tative day selection for capacity expansion planning of power systems under extreme operating conditions,

    C. Li, A. J. Conejo, J. D. Siirola, and I. E. Grossmann, “On represen- tative day selection for capacity expansion planning of power systems under extreme operating conditions,”Int. J. Electr . Power Energy Syst., vol. 137, pp. 107697, May 2022

    work page 2022

  22. [22]

    Selecting representative days for capturing the implications of integrat- ing intermittent renewables in generation expansion planning problems,

    K. Poncelet, H. H ¨oschle, E. Delarue, A. Virag, and W. D’haeseleer, “Selecting representative days for capturing the implications of integrat- ing intermittent renewables in generation expansion planning problems,” IEEE Trans. Power Syst., vol. 32, no. 3, pp. 1936–1948, May 2017

    work page 1936

  23. [23]

    Enhanced representative days and system states modeling for energy storage investment analysis,

    D. A. Tejada-Arango, M. Domeshek, S. Wogrin, and E. Centeno, “Enhanced representative days and system states modeling for energy storage investment analysis,”IEEE Trans. Power Syst., vol. 33, no. 6, pp. 6534–6544, Nov. 2018

    work page 2018

  24. [24]

    Time series aggregation for energy system design: Modeling seasonal storage,

    L. Kotzur, P. Markewitz, M. Robinius, and D. Stolten, “Time series aggregation for energy system design: Modeling seasonal storage,”Appl. Energy, vol. 213, pp. 123–135, Mar. 2018

    work page 2018

  25. [25]

    A model- adaptive clustering-based time aggregation method for low-carbon en- ergy system optimization,

    Y . Zhang, V . Cheng, D. S. Mallapragada, J. Song, and G. He, “A model- adaptive clustering-based time aggregation method for low-carbon en- ergy system optimization,”IEEE Trans. Sustain. Energy, vol. 14, no. 1, pp. 55–64, Jan. 2023

    work page 2023

  26. [26]

    Enhancing time series aggregation for power system optimization models: Incorpo- rating network and ramping constraints,

    D. Cardona-Vasquez, T. Klatzer, B. Klinz, and S. Wogrin, “Enhancing time series aggregation for power system optimization models: Incorpo- rating network and ramping constraints,”Elect. Power Syst. Res., vol. 230, pp. 110267, May 2024

    work page 2024

  27. [27]

    Time series aggregation for optimization: One-size-fits-all?,

    S. Wogrin, “Time series aggregation for optimization: One-size-fits-all?,” IEEE Trans. Smart Grid, vol. 14, no. 3, pp. 2489–2492, May 2023

    work page 2023

  28. [28]

    To- wards exact temporal aggregation of time-coupled energy storage models via active constraint set identification and machine learning,

    T. Klatzer, D. Cardona-Vasquez, L. Santosuosso, and S. Wogrin, “To- wards exact temporal aggregation of time-coupled energy storage models via active constraint set identification and machine learning,”arXiv preprint, 2025. [Online]. Available: https://arxiv.org/abs/2510.14451

    work page arXiv 2025

  29. [29]

    The ENTSO-E Trans- parency Platform–A review of Europe’s most ambitious electricity data platform,

    L. Hirth, J. M ¨uhlenpfordt, and M. Bulkeley, “The ENTSO-E Trans- parency Platform–A review of Europe’s most ambitious electricity data platform,”Appl. Energy, vol. 225, pp. 1054–1067, Sept. 2018

    work page 2018

  30. [30]

    What are we clustering for? Establishing performance guarantees for time series aggregation in generation expansion planning,

    L. Santosuosso, B. Klinz, and S. Wogrin, “What are we clustering for? Establishing performance guarantees for time series aggregation in generation expansion planning,”arXiv preprint, 2025. [Online]. Available: https://arxiv.org/abs/2510.09357

    work page arXiv 2025