Optimal Pricing in Markets with Nonconvex Costs

Azizan, Navid; Su, Yanqing; Dvijotham, Krishnamurthy; Wierman, Adam

doi:10.1287/opre.2019.1900

Cited by 12 publications

(14 citation statements)

References 16 publications

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“…Figure 1d shows that RP requires zero make-whole payment, which is also consistent with the results in Azizan et al (2020). RCDP ensures revenue adequacy and thus also needs no make-whole payment.…”

Section: Pricing In Scarf's Examplesupporting

confidence: 83%

Copositive Duality for Discrete Markets and Games

Guo¹,

Bodur²,

Taylor³

2021

Preprint

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Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer (2009) that mixedbinary quadratic programs can be written as completely positive programs, which are convex. Completely positive reformulations of discrete optimization problems therefore have strong duality if a constraint qualification is satisfied. We apply this perspective in two ways. First, we write unit commitment in power systems as a completely positive program, and use the dual copositive program to design a new pricing mechanism.Second, we reformulate integer programming games in terms of completely positive programming, and use the KKT conditions to solve for pure strategy Nash equilibria. To facilitate implementation, we also design a cutting plane algorithm for solving copositive programs exactly.

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Section: Pricing In Scarf's Examplesupporting

confidence: 83%

Copositive Duality for Discrete Markets and Games

Guo¹,

Bodur²,

Taylor³

2021

Preprint

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“…In [35], a non‐negative amendment function is constructed through certain redundant constraints and their associated multipliers to directly obtain the total payment. In [36], an equilibrium‐constrained pricing scheme is proposed to simultaneously determine the payment function and optimal schedule, which is applicable to general non‐convex costs and allows different forms of parametric payment functions. The extension to networked conditions and a computationally efficient approximation algorithm are also studied.…”

Section: Pricing With Non‐convexitymentioning

confidence: 99%

Extensions of the locational marginal price theory in evolving power systems: A review

Tan

Cheng

Liu

et al. 2022

IET Generation Trans & Dist

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The locational marginal price (LMP) theory is the foundation of nowadays electricity markets. With the rapid growth of intermittent renewable generation, new features are emerging in power systems, such as the uncertainty of power supply, the scarcity of flexibility, and the increase of distributed generation. In this situation, the electricity pricing scheme needs to be augmented with new features to meet requirements of incentive compatibility, cost causation-awareness, revenue adequacy, and transparency in a new market environment. Though a broad spectrum of literature has investigated extensions of the LMP addressing different challenges, a panorama of these extension directions is absent. To this end, this paper provides a systematic review of existing LMP extension research from four aspects, including pricing with non-convexity, pricing with multiple intervals, pricing with uncertainty, and pricing in distribution systems. These extension directions are derived from the impacts of the power system evolution on dispatch and pricing models. For each extension direction, the motivation and basic problem setup are introduced, followed by a critical survey of related research progress. Future directions and research gaps of the LMP extension are also indicated in this paper.

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“…We solve (8) for ∈ [0, 1] and compute demand utility (d ′ ; ). Since parameterizes the "amount" of flexibility demand offers, increasing values of correspond to greater demand flexibility (looser bounds on min/max consumption in each interval).…”

Section: Participation Incentives For Loadsmentioning

confidence: 99%

“…Analysis of incentive and participation constraints in market mechanisms was pioneered by Hurwicz, Groves, and Ledyard, among others [25,34]. The study of incentives in electricity markets has a rich history beginning with the seminal work of Schweppe [44] and has strongly influenced subsequent research on congestion pricing [15,28] and non-convex pricing [8,24,30,36]. In addition there has been research on market manipulation by generators, e.g., through market power and/or strategic curtailment of renewable generation.…”

mentioning

confidence: 99%

Pricing flexibility of shiftable demand in electricity markets

Werner

Wierman

Low

2021

Proceedings of the Twelfth ACM International Conference on Future Energy Systems

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Enabling participation of demand-side flexibility in electricity markets is key to improving power system resilience and increasing the penetration of renewable generation. In this work we are motivated by the curtailment of near-zero-marginal-cost renewable resources during periods of oversupply, a particularly important cause of inefficient generation dispatch. Focusing on shiftable load in a multi-interval economic dispatch setting, we show that incompatible incentives arise for loads in the standard market formulation. While the system's overall efficiency increases from dispatching flexible demand, the overall welfare of loads can decrease as a result of higher spot prices. We propose a market design to address this incentive issue. Specifically, by imposing a small number of additional constraints on the economic dispatch problem, we obtain a mechanism that guarantees individual rationality for all market participants while simultaneously obtaining a more efficient dispatch. Our formulation leads to a natural definition of a uniform, time-varying flexibility price that is paid to loads to incentivize flexible bidding. We provide theoretical guarantees and empirically validate our model with simulations on real-world generation data from California Independent System Operator (CAISO). CCS CONCEPTS• Hardware → Renewable energy; • Mathematics of computing → Mathematical analysis.

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Optimal Pricing in Markets with Nonconvex Costs

Cited by 12 publications

References 16 publications

Copositive Duality for Discrete Markets and Games

Copositive Duality for Discrete Markets and Games

Extensions of the locational marginal price theory in evolving power systems: A review

Pricing flexibility of shiftable demand in electricity markets

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