A Causation-Based Framework for Pricing and Cost Allocation of Energy, Reserves, and Transmission in Modern Power Systems

Alexandre Street; Jose Manuel Arroyo; Luiza Ribeiro; Rodrigo Moreno

REVIEW 2 major objections 3 minor 35 references

A Causation-Based Framework for Pricing and Cost Allocation of Energy, Reserves, and Transmission in Modern Power Systems

T0 review · 2 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A security charge levied on the generators whose outages drive reserve needs makes consumer payments exactly match generation and transmission revenues in contingency-constrained electricity markets.

desk verdict A clean and correct dual-based extension of the Arroyo-Galiana pricing scheme; the security charge is new and the accounting is right, but the causal story needs a dual-selection rule and the efficiency claims outrun the proofs. read the letter →

arxiv 2505.24159 v2 pith:OIIVQ2AB submitted 2025-05-30 eess.SY cs.SYecon.THmath.OCq-fin.CPq-fin.PR

Luiza Ribeiro , Alexandre Street , Jose Manuel Arroyo , Rodrigo Moreno This is my paper

classification eess.SYcs.SYecon.THmath.OCq-fin.CPq-fin.PR MSC 90C0590C4691B24

keywords causation-basedpricingsecuritychargesoperatingreservescontingency-constrainedschedulingrevenueadequacyneutralitytransmissionLagrangianduality

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 proposes a pricing scheme for electricity markets that co-optimize energy, operating reserves, and transmission under contingency constraints. The central claim is that the Lagrange multipliers of the post-contingency power-balance constraints can be re-attributed so that each generator pays a security charge for the contingency states in which that generator's own outage creates the need for reserves; the generator whose possible failure actually binds the system pays, and the others pay nothing. With that charge in place, the settlement becomes revenue-adequate (no participant is forced to a loss) and revenue-neutral (total consumer payment equals total generation revenue, or generation plus transmission revenue in the network model), eliminating the missing-money imbalance shown by the earlier Arroyo and Galiana pricing. The scheme also prices up- and down-spinning reserves separately and pays transmission lines for the capacity dedicated to delivering reserves in every contingency state. If correct, the framework gives markets a way to allocate reliability costs to the agents that cause them without ad hoc out-of-market compensation.

What carries the argument

The load-bearing object is the Lagrangian dual function of the clearing LP. The authors build the dual by relaxing the power-balance constraints (and, in the network model, the line-flow limits) and then read each term as a settlement account: consumer payment, generator profit, consumer profit, and, for the network model, transmission congestion rent. The decisive algebraic step is rewriting the contingency-state revenue $\psi^g_{ik}(\pi_k, x_i) = \pi_k a^g_{ik}(g_{i0} + r_i^{up})$ as $\pi_k(g_{i0} + r_i^{up})$ over all states minus $\pi_k(g_{i0} + r_i^{up})$ over the states $k \in K^{OFF}_i$ in which the generator is unavailable; that subtracted term is the security charge. Strong duality then turns the equality between primal cost and dual value into the revenue-neutrality identity, and the fact that each agent's term in the dual is a linear program over non-negative variables gives non-negative profits. Splitting each contingency price as $\pi_{bk} = \pi^+_{bk} - \pi^-_{bk}$ yields separate up- and down-reserve prices, and the absolute values of the line-flow bound multipliers form the transmission price.

What would settle it

Take the paper's two-bus example and tighten the line so the line-outage contingency also binds, making a second flow multiplier nonzero at the same time as the generator-1 outage, then recompute the proposed settlement and check whether consumer payments still equal generation plus transmission revenue; alternatively, add a single binary unit-commitment variable with a startup cost and observe whether the balance fails, which would show the LP strong-duality premise is doing the work.

Watch

Extended reading notes

Core claim

The paper's central claim is that the dual of a contingency-constrained energy-and-reserve market-clearing LP contains a complete, self-balancing settlement, provided the revenue that each generator would collect in contingency states is first reduced by a security charge for the states in which that generator is out of service. In the single-bus model the charge is $C_i^s = \sum_{k \in K^{OFF}_i} \pi_k^*(g_{i0} + r_i^{up})$, the product of the contingency power-balance prices and the generator's pre-contingency output plus up-reserve. Because $\pi_k^*$ is positive only for the contingencies that actually constrain the system, the charge falls on the generator whose potential outage drives the reserve requirement, exactly implementing cost causation. The same rearrangement applied to the network model splits the contingency prices into positive and negative parts to price up- and down-spinning reserves separately, and adds a transmission price $p_l^f = |\pi^{f*}_{l0}| + \sum_k |\pi^{f*}_{lk}|$ per MW of line capacity. Theorems 1 and 2, with network extensions in Appendices D and E, prove via strong duality that generator and consumer profits stay non-negative and that consumer payments exactly equal generation revenue, or generation plus transmission revenue in the network case. The two worked examples show the previously reported scheme leaving shortfalls of $5,200 and $6,900 that the new settlement closes.

Load-bearing premise

The entire construction assumes the market-clearing problem is a linear program with continuous variables, so the primal and dual optima coincide; the revenue adequacy and neutrality guarantees can break down once binary unit-commitment decisions, startup costs, or other nonconvexities enter the model.

Editorial extensions

If this is right

In the single-bus model the proposed settlement makes total generator revenue exactly equal the consumer payment, closing the $5,200 gap left by the Arroyo-Galiana pricing on the paper's example.
In the network model consumer payments exactly match the sum of generation revenue and transmission revenue, closing the $6,900 gap and removing the need for out-of-market compensation.
Generators whose outages bind the contingency constraints pay security charges while others pay nothing, so reserve costs follow the cost-causation principle while all profits remain non-negative.
Up- and down-spinning reserves receive distinct nodal prices, so a unit that deploys downward reserve in a contingency with a negative price is paid according to that separate price rather than a blended security price.
Transmission lines are remunerated for the capacity they dedicate to reserve deliverability across all contingency states, giving line owners an economic incentive tied to reserve provision.

Reading between the lines

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

Because the neutrality identity is a bookkeeping consequence of strong duality, it should hold in every LP instance of the paper's class; a cheap stress test is to generate many random cost, capacity, and contingency instances and verify that consumer payment minus generation and transmission revenue is identically zero in each.
The same dual-rearrangement logic should carry over to probabilistic security criteria, where each contingency's price would be weighted by its probability when computing the security charge, yielding causation-based charges under stochastic reserve requirements.
The paper notes that over-frequency events are the demand-side mirror of generator outages; a symmetric construction would levy security charges on loads whose sudden disconnection forces downward-reserve purchases, completing the causation story on both sides of the market.
If implemented, the security charge would give the paying generator a direct financial incentive to lower its forced-outage rate, turning what looks like a penalty into a reliability investment signal, a behavior the paper motivates but does not model.

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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 to know up front. The actual contribution is a settlement rule — a security charge, separated up- and down-reserve prices, and a transmission rent term — all derived from the Lagrangian dual of a contingency-constrained LP. And the two headline theorems, revenue adequacy and neutrality, are correct but close to strong duality restated as a bookkeeping identity. They validate the construction; the interesting load is carried by the causal story, which is argued by example rather than proven.

It does several things well. The security charge is clean: generator i pays the dual price of the contingency in which it is out, applied to its pre-contingency output plus reserves. In the single-bus example it deletes the $5,200 missing-money gap in the Arroyo-Galiana settlement while leaving every profit non-negative. Separating the contingency multipliers into positive and negative parts to price up- and down-reserve distinctly is a nice touch, and the transmission term fixes a real gap in the 2005 scheme. The two cases reconcile numerically, and the appendix proofs are correct within the declared LP scope.

The soft spots, in proportion. First, the abstract and conclusion claim efficient operations and reliability incentives. Nothing in the paper derives those; what is proven is non-negative profit and an accounting identity. Second, the dual-degeneracy concern lands: when the dual optimal face has more than one point, different optimal multipliers give different security charges, all revenue-neutral. The paper gives no selection rule, so the causal attribution is underdetermined in exactly those cases. I would not call this fatal — the same is true of LMP schemes generally — but the cost-causation language should be softened or a tie-break rule provided. Third, the LP assumption: add unit-commitment binaries and strong duality fails, taking neutrality with it. The paper is honest that the models are linear, but the practical claims outrun that scope. Fourth, the Shapley/nucleolus literature is cited as motivation and never compared against. The paper flags multi-period and renewable extensions as future work, but it never notes the nonconvexity or degeneracy issues, which are the ones a referee would want addressed.

This is for market-design people working on joint energy-reserve clearing who want a concrete, provably revenue-neutral alternative to ad hoc uplift. It deserves a serious referee. I would send it out, with a request for a dual-selection rule or a scaling-back of the causal claims.

Referee Report

2 major / 3 minor

Summary. This paper proposes a pricing and cost-allocation framework for contingency-constrained, co-optimized energy and reserve markets. It introduces a security charge that is subtracted from each generator's revenue, defined from the Lagrangian dual of an LP market-clearing model, and it derives separate nodal prices for up-spinning reserves, down-spinning reserves, and transmission services. In a single-bus model and a two-bus network model, the paper compares its settlement with that of Arroyo and Galiana (2005), shows that the proposed scheme removes the revenue imbalance, and states two theorems: revenue adequacy (nonnegative profits for generators and consumers) and revenue neutrality (consumer payments equal generation plus transmission revenue). Proofs are given in Appendices B-E, and two numerical examples illustrate exact settlement balance.

Significance. If the results stand, the framework offers a clean, dual-based method to repair the revenue mismatch of a well-known pricing scheme while preserving nonnegative profits. The paper's strengths are its explicit, checkable price definitions, its complete proofs of revenue adequacy and neutrality for the stated LP models, and its exact numerical reconciliation in both examples. The separation of up- and down-reserve prices and the explicit transmission remuneration are useful contributions. However, the central 'causation-based' interpretation is not fully supported unless the optimal dual solution is unique or a selection rule is provided; the same physical dispatch can in principle support multiple dual-based settlements. The paper is also silent on the scope limitation that the guarantees rely on strong duality and therefore do not extend to nonconvex market-clearing models.

major comments (2)

[Sections 2.3 and 3.3 (Eq. (46)-(47), Tables 22-27)] The security charge C_i^g, the up/down reserve prices, and the transmission price are all defined as functions of one optimal dual solution Pi*. The paper does not prove that the optimal dual solution of (1)-(6) or (15)-(31) is unique, and in LP degeneracy it generally is not. Different optimal dual extreme points can yield different security charges and different reserve/transmission prices while leaving the primal dispatch and the total settlement balance unchanged. The numerical results were obtained with CPLEX's simplex algorithm, which selects one basis without economic justification. Because the paper's central claim is that these charges 'reflect the different contributions of generators' and provide reliability incentives, the absence of a uniqueness result or a selection rule leaves the cost-causation attribution underdetermined. Theorems 1 and 2 remain correct for any optimal dual, but the causation narrative needs either a uniqueness argument, an explicit selection rule, or a reformulation of the result as a family of admissible revenue-neutral settlements.
[Abstract and Appendix E (Eq. (E.1))] The abstract and conclusion state revenue neutrality and adequacy without qualification, but the proofs in Appendices B-E rely essentially on strong duality for the LP models (1)-(6) and (15)-(31). If the market-clearing model includes binary unit-commitment variables, startup costs, or other nonconvexities, the strong-duality identity can fail, and the neutrality and adequacy guarantees may fail as well. The paper does not mention this limitation in the conclusion or in the discussion of future work. Please add an explicit scope statement clarifying that the proposed settlement is guaranteed only for the continuous linear-programming formulation, and temper the unqualified 'no missing money' claim in the abstract.

minor comments (3)

[Section 3.3, Eq. (32)-(34)] The sign convention for the line-flow multipliers is nonstandard: pi^{f-} is described as nonpositive even though it multiplies (F - H\theta). Since pi^{f-} is apparently the negative of the usual upper-bound multiplier, please state this explicitly to avoid confusion.
[Section 2.2, Table 7] The term 'missing money' is used to describe a situation where generation revenue exceeds consumer payments by $5,200. That is a revenue surplus, not the usual meaning of 'missing money' (insufficient revenue). Please use a different term, such as 'settlement surplus' or 'revenue imbalance'.
[Conclusion, Section 4] The future-work paragraph lists multi-period settings and renewable uncertainty but does not mention nonconvex market clearing (binary unit commitment, startup costs). Adding that direction would be a natural and relevant extension, given the LP-only scope of the current proofs.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the revenue-neutrality and revenue-adequacy theorems are explicit consequences of LP strong duality and the chosen settlement definitions, and the self-citations are not load-bearing.

full rationale

The paper's central theorems are not circular. Revenue neutrality is proven in Appendices C and E by writing the Lagrangian dual identity and then canceling identical terms; this is a direct consequence of strong duality for the stated linear programs, not a hidden restatement of an assumed conclusion. The security charge is introduced in Equation (14) as the negative dual term associated with generator outages, and the settlement definitions in Tables 8 and 22-24 are then shown to satisfy the balance identity. This is a mechanism-construction check rather than an empirical prediction, but the derivation is explicit, self-contained, and does not presuppose the theorem. The paper also relies on the pricing definitions of Arroyo and Galiana (2005), a work coauthored by one of the present authors, but it re-derives those price components from the same Lagrangian decomposition instead of importing them as an unverified premise, so the self-citation is not load-bearing. The dual-multiplier non-uniqueness raised in the skeptic brief is a legitimate robustness and interpretation concern for the cost-causation narrative, but it does not make the arguments circular: revenue adequacy and neutrality hold for any optimal dual solution. Overall, the mathematical derivation chain is sound and not equivalent to its inputs by definition.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

The framework depends on standard LP duality, a DC network model, and an exogenous deterministic contingency set with binary unit availability. No free parameters are fitted to external data; the two case studies are illustrative.

assumptions (5)

standard math Strong duality holds for the market-clearing LP, with zero duality gap and existence of optimal dual prices.
Appendices C and E use strong duality to equate primal cost and dual value; this is standard LP theory, but it is a load-bearing assumption for the settlement identity.
domain assumption DC load-flow approximation for the network.
Section 3.1 constraints (16)-(19) use a dc load flow model, ignoring losses, reactive power, and voltage constraints.
domain assumption Deterministic credible contingency set K with binary generator availability a_ik, without probabilistic outage modeling.
Section 2.1 invokes a practical deterministic security criterion; causation is defined only over this fixed set of contingencies.
domain assumption Offer-based linear cost functions and no nonconvexities such as startup costs or unit commitment.
Objectives (1) and (15) are linear, and constraints (5)-(6) and (22)-(25) are convex without integer variables, which is needed for strong duality.
domain assumption Zero lower bounds and feasible zero-output choices for every generator and load.
The revenue adequacy proofs in Appendices B and D rely on x_i=0 and y_j=0 being feasible, so the maximized profit is non-negative.

invented entities (1)

Security charge C_i^g = sum_{k in K_OFF_i} pi_k^*(g_i0 + r_i^up)
purpose: New settlement charge that allocates reserve costs to generators whose outages create reserve needs and ensures revenue neutrality.
Introduced in Section 2.3 and Table 8; it is an accounting term defined to balance consumer payments and generation revenue, not an independently observable physical quantity.

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Cite this review

Pith. "Pith review of A Causation-Based Framework for Pricing and Cost Allocation of Energy, Reserves, and Transmission in Modern Power Systems." pith.science (2026). https://pith.science/paper/OIIVQ2AB

@misc{pith2026250524159,
  author       = {Pith},
  title        = {Pith review of: A Causation-Based Framework for Pricing and Cost Allocation of Energy, Reserves, and Transmission in Modern Power Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OIIVQ2AB}},
  note         = {Machine review of arXiv:2505.24159}
}

read the original abstract

The increasing vulnerability of power systems has heightened the need for operating reserves to manage contingencies such as generator outages, line failures, and sudden load variations. Unlike energy costs, driven by consumer demand, operating reserve costs arise from addressing the most critical credible contingencies - prompting the question: how should these costs be allocated through efficient pricing mechanisms? As an alternative to previously reported schemes, this paper presents a new causation-based pricing framework for electricity markets based on contingency-constrained energy and reserve scheduling models. Major salient features include a novel security charge mechanism along with the explicit definition of prices for up-spinning reserves, down-spinning reserves, and transmission services. These features ensure more comprehensive and efficient cost-reflective market operations. Moreover, the proposed nodal pricing scheme yields revenue adequacy and neutrality while promoting reliability incentives for generators based on the cost-causation principle. An additional salient aspect of the proposed framework is the economic incentive for transmission assets, which are remunerated based on their use to deliver energy and reserves across all contingency states. Numerical results from two case studies illustrate the performance of the proposed pricing scheme.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

H., and Waight, J

Aganagic, M., Abdul-Rahman, K. H., and Waight, J. G. (1998). Spot pricing of capacities for generation and transmission of reserve in an extended Poolco model . IEEE Transactions on Power Systems , 13(3):1128--1135

work page 1998

[2] [2]

Arroyo, J. M. and Galiana, F. D. (2005). Energy and reserve pricing in security and network-constrained electricity markets. IEEE Transactions on Power Systems , 20(2):634--643

work page 2005

[3] [3]

Wholesale electricity market design summary

Australian Energy Market Operator (AEMO) (2023). Wholesale electricity market design summary. https://aemo.com.au/-/media/files/initiatives/wem-reform-program/wem-reform-market-design-summary.pdf. 2025-01-20

work page 2023

[4] [4]

Badesa, L., Matamala, C., and Strbac, G. (2025). Who should pay for frequency-containment ancillary services? Making responsible units bear the cost to shape investment in generation and loads . Energy Policy , 196(Article 114379)

work page 2025

[5] [5]

Badesa, L., Matamala, C., Zhou, Y., and Strbac, G. (2023). Assigning shadow prices to synthetic inertia and frequency response reserves from renewable energy sources. IEEE Transactions on Sustainable Energy , 14(1):12--26

work page 2023

[6] [6]

and Tsitsiklis, J

Bertsimas, D. and Tsitsiklis, J. N. (1997). Introduction to Linear Optimization . Athena Scientific, Belmont, MA, USA

work page 1997

[7] [7]

Billimoria, F., Mancarella, P., and Poudineh, R. (2020). Market design for system security in low-carbon electricity grids: From the physics to the economics. The Oxford Institute for Energy Studies , (Article EL 41)

work page 2020

[8] [8]

D., and Conejo, A

Bouffard, F., Galiana, F. D., and Conejo, A. J. (2005). Market-clearing with stochastic security--Part II: Case studies . IEEE Transactions on Power Systems , 20(4):1827--1835

work page 2005