A Stochastic Programming Model for the Optimal Operation of Unbalanced Three-Phase Islanded Microgrids

Pedro Pablo Vergara Barrios*, Juan Camilo Lopez, Marcos J. Rider, Hamid Reza Shaker, Luiz Carlos Pereira da Silva, Bo Nørregaard Jørgensen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

This paper presents a stochastic mixed-integer nonlinear programming (MINLP) model for the optimal operation of islanded microgrids in the presence of stochastic demands and renewable resources. In the proposed formulation, the microgrid is modeled as an unbalanced three-phase electrical distribution system comprising distributed generation (DG) units with droop control, battery systems (BSs) and wind turbines (WTs). The stochastic nature of the consumption and the renewable generation is considered through a scenario-based approach, which determines the optimal values of the decision variables that minimize the average operational cost of the microgrid. A set of efficient linearizations are used to transform the proposed MINLP model into an approximated convex model that can be solved via commercial solvers. In order to assess the effectiveness of the obtained solution, Monte Carlo simulations (MCS) are carried out. Results show that the proposed model considers the uncertainty while reducing the average operational costs and load curtailments, when compared with a deterministic model.

Original languageEnglish
Article number105446
JournalInternational Journal of Electrical Power & Energy Systems
Volume115
ISSN0142-0615
DOIs
Publication statusPublished - 1. Feb 2020

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Stochastic programming
Nonlinear programming
Distributed power generation
Linearization
Wind turbines
Costs

Keywords

  • Droop control
  • Islanded mode
  • Microgrids
  • Optimal power flow
  • Stochastic optimization

Cite this

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title = "A Stochastic Programming Model for the Optimal Operation of Unbalanced Three-Phase Islanded Microgrids",
abstract = "This paper presents a stochastic mixed-integer nonlinear programming (MINLP) model for the optimal operation of islanded microgrids in the presence of stochastic demands and renewable resources. In the proposed formulation, the microgrid is modeled as an unbalanced three-phase electrical distribution system comprising distributed generation (DG) units with droop control, battery systems (BSs) and wind turbines (WTs). The stochastic nature of the consumption and the renewable generation is considered through a scenario-based approach, which determines the optimal values of the decision variables that minimize the average operational cost of the microgrid. A set of efficient linearizations are used to transform the proposed MINLP model into an approximated convex model that can be solved via commercial solvers. In order to assess the effectiveness of the obtained solution, Monte Carlo simulations (MCS) are carried out. Results show that the proposed model considers the uncertainty while reducing the average operational costs and load curtailments, when compared with a deterministic model.",
keywords = "Droop control, Islanded mode, Microgrids, Optimal power flow, Stochastic optimization",
author = "{Vergara Barrios}, {Pedro Pablo} and Lopez, {Juan Camilo} and Rider, {Marcos J.} and Shaker, {Hamid Reza} and {da Silva}, {Luiz Carlos Pereira} and J{\o}rgensen, {Bo N{\o}rregaard}",
year = "2020",
month = "2",
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doi = "10.1016/j.ijepes.2019.105446",
language = "English",
volume = "115",
journal = "International Journal of Electrical Power & Energy Systems",
issn = "0142-0615",
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A Stochastic Programming Model for the Optimal Operation of Unbalanced Three-Phase Islanded Microgrids. / Vergara Barrios, Pedro Pablo; Lopez, Juan Camilo; Rider, Marcos J.; Shaker, Hamid Reza; da Silva, Luiz Carlos Pereira ; Jørgensen, Bo Nørregaard.

In: International Journal of Electrical Power & Energy Systems, Vol. 115, 105446, 01.02.2020.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A Stochastic Programming Model for the Optimal Operation of Unbalanced Three-Phase Islanded Microgrids

AU - Vergara Barrios, Pedro Pablo

AU - Lopez, Juan Camilo

AU - Rider, Marcos J.

AU - Shaker, Hamid Reza

AU - da Silva, Luiz Carlos Pereira

AU - Jørgensen, Bo Nørregaard

PY - 2020/2/1

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AB - This paper presents a stochastic mixed-integer nonlinear programming (MINLP) model for the optimal operation of islanded microgrids in the presence of stochastic demands and renewable resources. In the proposed formulation, the microgrid is modeled as an unbalanced three-phase electrical distribution system comprising distributed generation (DG) units with droop control, battery systems (BSs) and wind turbines (WTs). The stochastic nature of the consumption and the renewable generation is considered through a scenario-based approach, which determines the optimal values of the decision variables that minimize the average operational cost of the microgrid. A set of efficient linearizations are used to transform the proposed MINLP model into an approximated convex model that can be solved via commercial solvers. In order to assess the effectiveness of the obtained solution, Monte Carlo simulations (MCS) are carried out. Results show that the proposed model considers the uncertainty while reducing the average operational costs and load curtailments, when compared with a deterministic model.

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KW - Stochastic optimization

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