Uniqueness and multiplicity of market equilibria on DC power flow networks

Krebs, Vanessa; Schewe, Lars; Schmidt, Martin

doi:10.1016/j.ejor.2018.05.016

Cited by 25 publications

(5 citation statements)

References 22 publications

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“…Moreover, uniqueness of the solution of a short-run model, again without DC power flow constraints is proven in [42] for the case of transport costs. However, the most related study is given in [41]. There, a short-run market equilibrium model is analyzed that also incorporates DC power flow constraints.…”

Section: An Equivalent Variational Inequalitymentioning

confidence: 99%

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

2021

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We consider uncertain robust electricity market equilibrium problems including transmission and generation investments. Electricity market equilibrium modeling has a long tradition but is, in most of the cases, applied in a deterministic setting in which all data of the model are known. Whereas there exist some literature on stochastic equilibrium problems, the field of robust equilibrium models is still in its infancy. We contribute to this new field of research by considering $$\Gamma $$ Γ -robust electricity market equilibrium models on lossless DC networks with transmission and generation investments. We state the nominal market equilibrium problem as a mixed complementarity problem as well as its variational inequality and welfare optimization counterparts. For the latter, we then derive a $$\Gamma $$ Γ -robust formulation and show that it is indeed the counterpart of a market equilibrium problem with robustified player problems. Finally, we present two case studies to gain insights into the general effects of robustification on electricity market models. In particular, our case studies reveal that the transmission system operator tends to act more risk-neutral in the robust setting, whereas generating firms clearly behave more risk-averse.

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Section: An Equivalent Variational Inequalitymentioning

confidence: 99%

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

2021

Self Cite

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“…These conditions can be guaranteed, for example, by enforcing individual bids to have compact feasible regions and continuous cost functions, and to admit an empty injection profile as a feasible dispatch, i.e., [0, ..., 0] ∈ F s , ∀s. Uniqueness of the optimal dispatch and payments to market participants are also important concerns, which can be guaranteed under conditions on the cost functions; see, e.g., Krebs et al (2018). When the uniqueness conditions are not met, markets implement rules to choose among multiple solutions; see, e.g., Feng et al (2012) and Alguacil et al (2013).…”

Section: From Bids To Market Clearingmentioning

confidence: 99%

Price-region bids in electricity markets

Bobo

Mitridati

Taylor

et al. 2021

European Journal of Operational Research

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“…These profiles in conjunction with the parameters of the grid allow the identification of all technical indexes that represent the behavior of the electrical network, such as the power loss, voltage stability, power flow on the branches, and power factor [7]. The PF has been widely studied in the past decades on AC networks [8][9][10]. However, concerning power-flow analysis in DC grids, the exploration of this problem started recently due to the paradigm shift regarding energy distribution with renewable energy and batteries, which typically operate with DC technologies [11][12][13][14][15][16].…”

Section: General Contextmentioning

confidence: 99%

A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors

et al. 2020

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This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures.

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Uniqueness and multiplicity of market equilibria on DC power flow networks

Cited by 25 publications

References 22 publications

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

$$\Gamma $$-Robust electricity market equilibrium models with transmission and generation investments

Price-region bids in electricity markets

A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors

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