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General metaheuristic-based methodology for computation and decomposition of LMPs

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Abstract

Locational marginal prices (LMPs) are economic signals paramount to the deliberations, policy designs, and planning judgments of most electricity markets. This paper presents a general metaheuristic-based methodology applied in the scope of two subproblems to compute and decompose the LMPs considering the incorporation of a distributed slack bus model in the power flow formulation. The deterministic core of the methodology is governed by a process of sequential setting of maximum number of metaheuristic iterations based on load disharmony indices (LDIs) in the context of the initial subproblem. The metaheuristic crux of the methodology is anchored in a random initialization strategy based on time-traveling parameters in the environment of both subproblems. In the introductory arrangement of the optimization sequence, the chain order of the operating horizon periods is defined based on the LDIs. Due to its notorious merits and the breadth of its applications in power system problems, a particle swarm optimization (PSO) algorithm model is used to solve the mentioned subproblems. For the practical purposes of this paper, in the PSO algorithm model instance the particle coordinates are adopted as time-traveling metaheuristic parameters. Numerical simulations on a 3-bus system and on the IEEE 30-bus test system corroborate the efficiency and adequacy of the proposed methodology.

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Availability of data and material

All data pertinent to theoretical foundations, mathematical corroborations, and computational simulations concerning the present work are extracted from sources duly cited in the scope of this manuscript. In addition, the data defined by the authors are also adequately described throughout the body of the aforementioned manuscript.

Abbreviations

\(\varvec{\theta}^{t}\) :

Vector of voltage angles at all buses at period \(t\) excluding the angular reference bus

\(p_{ds}^{t}\) :

Active power injection at the distributed slack bus at period \(t\)

\(\varvec{p}^{t}\) :

Vector of net active power injections at all buses at period t

\(\varvec{f}^{t}\) :

Active power flow functions at all buses at period \(t\)

\(\varvec{fl}^{t}\) :

Vector of active power flow at all branches at period \(t\)

\(\lambda_{ds}^{t}\) :

LMP at the distributed slack bus at period \(t\)

\(\varvec{\lambda}^{t}\) :

Vector of LMPs at all buses at period \(t\)

\(\varvec{\lambda}_{e}^{t} ,\varvec{\lambda}_{l}^{t} ,\varvec{\lambda}_{c}^{t}\) :

Vectors of energy, loss, and congestion components of LMPs at period \(t\)

\(\varvec{\mu}^{t}\) :

Vector of Lagrange multipliers associated with the inequality constraints of active power flows at all branches at period \(t\)

\(\varvec{\pi}^{\hbox{max} t} ,\varvec{\pi}^{\hbox{min} t}\) :

Vectors of Lagrange multipliers associated with the inequality constraints of upper and lower limits of generator outputs at period \(t\)

\(\varvec{\eta}^{t}\) :

Vector of participation factors at period \(t\)

\(0_{i} ,1_{i}\) :

\(i \times 1\) vectors fully integrated by zeros and ones

\(\sigma_{i}^{t}\) :

Load disharmony index at time slot \(t\) with respect to total load at period \(i\)

\(\varvec{X}_{j,t}^{ite} ,\varvec{V}_{j,t}^{ite}\) :

Vector of position and velocity coordinates of a particle \(j\) at iteration \(ite\) of the PSO algorithm at period \(t\) of the time horizon

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Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

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Authors and Affiliations

  1. Department of Electrical Engineering, Federal University of Maranhão (UFMA), São Luis, MA, 65085-580, Brazil

    Felipe Oliveira Silva Saraiva & Vicente Leonardo Paucar

Authors
  1. Felipe Oliveira Silva Saraiva
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  2. Vicente Leonardo Paucar
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Contributions

All authors made indispensable contributions to the conception and elaboration of the present work. The literature review, code implementations, and data acquisition were performed by Felipe Oliveira Silva Saraiva. The analysis and interpretation of the simulation results were performed by Felipe Oliveira Silva Saraiva and Vicente Leonardo Paucar. Finally, the definitive critical survey of the work was carried out by Vicente Leonardo Paucar. It is worth mentioning that all authors endorse the final version of this manuscript by mutual agreement.

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Correspondence to Felipe Oliveira Silva Saraiva.

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Saraiva, F.O.S., Paucar, V.L. General metaheuristic-based methodology for computation and decomposition of LMPs. Electr Eng 103, 793–811 (2021). https://doi.org/10.1007/s00202-020-01112-5

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  • DOI: https://doi.org/10.1007/s00202-020-01112-5

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