The Subgradient Simplex Cutting Plane Method for Extended Locational Marginal Prices

Wang, Congcong; Peng, Tengshun; Luh, Peter B.; Gribik, Paul R.; Zhang, Li

doi:10.1109/tpwrs.2013.2243173

Cited by 32 publications

(12 citation statements)

References 26 publications

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“…CHP-Primal is an LP through which the exact convex hull prices can be obtained. CHP-Primal solves in 0.02 seconds, resulting in the same convex hull prices as reported in [15]. The duality gap between the UCED problem and its Lagrangian dual problem is $1 148, which equals the total lost opportunity cost.…”

Section: Examplementioning

confidence: 99%

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A Convex Primal Formulation for Convex Hull Pricing

Hua

Baldick

2017

IEEE Trans. Power Syst.

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In certain electricity markets, because of non-convexities that arise from their operating characteristics, generators that follow the independent system operator's (ISO's) decisions may fail to recover their cost through sales of energy at locational marginal prices. The ISO makes discriminatory side payments to incentivize the compliance of generators. Convex hull pricing is a uniform pricing scheme that minimizes these side payments. The Lagrangian dual problem of the unit commitment problem has been solved in the dual space to determine convex hull prices. However, this approach is computationally expensive. We propose a polynomially-solvable primal formulation for the Lagrangian dual problem. This formulation explicitly describes for each generating unit the convex hull of its feasible set and the convex envelope of its cost function. We cast our formulation as a second-order cone program when the cost functions are quadratic, and a linear program when the cost functions are piecewise linear. A 96period 76-unit transmission-constrained example is solved in less than fifteen seconds on a personal computer.

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Section: Examplementioning

confidence: 99%

“…In addition to the T active constraints of type (16), 2T − 1 other linearly independent constraints must be active at (p g ,x g ,û g ). These 2T −1 constraints can only be of type (13)- (15) or (19). Because the projection of the set (21)…”

Section: Characterization Of the Convex Hullsmentioning

confidence: 99%

A Convex Primal Formulation for Convex Hull Pricing

Hua

Baldick

2017

IEEE Trans. Power Syst.

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“…The resulting prices and payments only minimize the combination of make-whole payments and lost opportunity costs (i.e., they do not minimize make-whole payments alone) and are not guaranteed to be revenue adequate. After originally implementing an approximation to Convex Hull Pricing, Midcontinent ISO (MISO) has updated the formulation to include better approximations (Wang et al 2013;Hua and Baldick 2017). Implementation of full Convex Hull Pricing is immensely computationally difficult (Schiro et al 2016;Zheng et al 2018), which is why ISOs have approximated the method for implementation.…”

Section: Methods and Proposals In Literaturementioning

confidence: 99%

“…Many ISOs have also presented or written extensively on price formation efforts. MISO staff produced technical and academic reports on their Extended LMP formulation (Gribik 2011;Wang et al 2013). ISO-NE created a series of technical sessions on pricing (Schiro and White 2015), and PJM produced a similar set of detailed presentations as they explore an alternative pricing mechanism for their market (PJM 2018).…”

Section: Iso Implementationmentioning

confidence: 99%

Impacts of Price Formation Efforts Considering High Renewable Penetration Levels and System Resource Adequacy Targets

Hytowitz

Frew

Stephen

et al. 2020

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“…The convex hull forms a dual problem with the power balance and flow constraints in the objective function, so a set of limiting constraints must be found first, to enable the solution of the already complicated model. Indeed, all numerical attempts made to solve the problem instances ignore transmission capacity constraints [17], [18]. There is a lack of studies on minimum-uplift prices in network-constrained environment.…”

Section: A Literature Reviewmentioning

confidence: 99%

Direct Minimum-Uplift Model for Pricing Pool-Based Auction With Network Constraints

Żółtowska

2016

IEEE Trans. Power Syst.

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Auctions with non-convexities, as considered in this paper, use a multi-period optimal power flow (OPF) model based on generators' offers to calculate efficient schedules. The standard locational marginal prices (LMPs) may not support these schedules and uplifts are needed to help the generators break even. This paper presents a direct minimum-uplift (DMU) pricing model, which is formulated as a mixed integer linear programming problem with uplift minimization objective. New DMU prices are major variables constrained with decomposition formula based on shift factors, similar to the actual practice of developing LMPs. The remaining constraints reflect the generators' profits and uplifts modeled as functions of the DMU prices. The main feature of the DMU model is individual rationality attained in pool-based auction, under prices properly reflecting network constraints, complemented with minimum uplifts. The model is validated on several cases, including the IEEE 24-node system.

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The Subgradient Simplex Cutting Plane Method for Extended Locational Marginal Prices

Cited by 32 publications

References 26 publications

A Convex Primal Formulation for Convex Hull Pricing

A Convex Primal Formulation for Convex Hull Pricing

Impacts of Price Formation Efforts Considering High Renewable Penetration Levels and System Resource Adequacy Targets

Direct Minimum-Uplift Model for Pricing Pool-Based Auction With Network Constraints

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