New Iterative Method Based Jacobian Matrix and λ<sub>opt</sub> to Solve Power Flow Equation for Islanded MGs

Ali Ghorbani Dehaghani; Rohallah Pourbagher; Heidar Mozafari Vanani

doi:doi:10.11648/j.mcs.20210604.12

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New Iterative Method Based Jacobian Matrix and λ_opt to Solve Power Flow Equation for Islanded MGs

Ali Ghorbani Dehaghani, Rohallah Pourbagher, Heidar Mozafari Vanani

Published in Mathematics and Computer Science (Volume 6, Issue 4)

Received: 16 July 2021 Accepted: 28 July 2021 Published: 6 September 2021

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Abstract

Power flow analysis and calculation play an essential role in analysis of electrical power system. Solving the load flow equations of an electrical power system are very sensitive to the value of the right-hand side constant vector or to the value of the coefficients of the Jacobian matrix, the equations of the electrical power system are called to be ill-conditioned. In an ill-conditioned case study, the determinant of the Jacobian matrix is close to singular or singular. Computing the set of load flow equations of an electrical power system may sometimes lead to the incidence of the ill-conditioned equations. The ill-conditioning mood in MGs power system is due to several reasons such as the situation of the reference bus, high value of r/x ratio of power system's lines, connections of very low and very high impedance power system's lines at a bus and heavy loading condition of an electrical power system. In an islanded MG, the use of traditional PFA is not effective as the voltage of the swing or slack bus and the frequency of the MG are assumed to be constant. This paper proposes a simple and effective iterative method based on the Jacobian matrix λ_opt to solve the PF equation for islanded MGs. The new proposed technique prepares a simple, straightforward for implementation, and precise technique to calculate the PF equations for MGs. The new suggested technique is exerted to the 38-bus case study electrical power system. The outcomes are compared against simulation outcomes that accredit the efficiency of the new technique.

Published in	Mathematics and Computer Science (Volume 6, Issue 4)
DOI	10.11648/j.mcs.20210604.12
Page(s)	65-70
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Power Flow Analysis, Microgrids, Iterative Method

References

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APA Style

Ali Ghorbani Dehaghani, Rohallah Pourbagher, Heidar Mozafari Vanani. (2021). New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs. Mathematics and Computer Science, 6(4), 65-70. https://doi.org/10.11648/j.mcs.20210604.12

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ACS Style

Ali Ghorbani Dehaghani; Rohallah Pourbagher; Heidar Mozafari Vanani. New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs. Math. Comput. Sci. 2021, 6(4), 65-70. doi: 10.11648/j.mcs.20210604.12

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AMA Style

Ali Ghorbani Dehaghani, Rohallah Pourbagher, Heidar Mozafari Vanani. New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs. Math Comput Sci. 2021;6(4):65-70. doi: 10.11648/j.mcs.20210604.12

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@article{10.11648/j.mcs.20210604.12,
  author = {Ali Ghorbani Dehaghani and Rohallah Pourbagher and Heidar Mozafari Vanani},
  title = {New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.mcs.20210604.12},
  url = {https://doi.org/10.11648/j.mcs.20210604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210604.12},
  abstract = {Power flow analysis and calculation play an essential role in analysis of electrical power system. Solving the load flow equations of an electrical power system are very sensitive to the value of the right-hand side constant vector or to the value of the coefficients of the Jacobian matrix, the equations of the electrical power system are called to be ill-conditioned. In an ill-conditioned case study, the determinant of the Jacobian matrix is close to singular or singular. Computing the set of load flow equations of an electrical power system may sometimes lead to the incidence of the ill-conditioned equations. The ill-conditioning mood in MGs power system is due to several reasons such as the situation of the reference bus, high value of r/x ratio of power system's lines, connections of very low and very high impedance power system's lines at a bus and heavy loading condition of an electrical power system. In an islanded MG, the use of traditional PFA is not effective as the voltage of the swing or slack bus and the frequency of the MG are assumed to be constant. This paper proposes a simple and effective iterative method based on the Jacobian matrix λopt to solve the PF equation for islanded MGs. The new proposed technique prepares a simple, straightforward for implementation, and precise technique to calculate the PF equations for MGs. The new suggested technique is exerted to the 38-bus case study electrical power system. The outcomes are compared against simulation outcomes that accredit the efficiency of the new technique.},
 year = {2021}
}

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TY  - JOUR
T1  - New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs
AU  - Ali Ghorbani Dehaghani
AU  - Rohallah Pourbagher
AU  - Heidar Mozafari Vanani
Y1  - 2021/09/06
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210604.12
DO  - 10.11648/j.mcs.20210604.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210604.12
AB  - Power flow analysis and calculation play an essential role in analysis of electrical power system. Solving the load flow equations of an electrical power system are very sensitive to the value of the right-hand side constant vector or to the value of the coefficients of the Jacobian matrix, the equations of the electrical power system are called to be ill-conditioned. In an ill-conditioned case study, the determinant of the Jacobian matrix is close to singular or singular. Computing the set of load flow equations of an electrical power system may sometimes lead to the incidence of the ill-conditioned equations. The ill-conditioning mood in MGs power system is due to several reasons such as the situation of the reference bus, high value of r/x ratio of power system's lines, connections of very low and very high impedance power system's lines at a bus and heavy loading condition of an electrical power system. In an islanded MG, the use of traditional PFA is not effective as the voltage of the swing or slack bus and the frequency of the MG are assumed to be constant. This paper proposes a simple and effective iterative method based on the Jacobian matrix λopt to solve the PF equation for islanded MGs. The new proposed technique prepares a simple, straightforward for implementation, and precise technique to calculate the PF equations for MGs. The new suggested technique is exerted to the 38-bus case study electrical power system. The outcomes are compared against simulation outcomes that accredit the efficiency of the new technique.
VL  - 6
IS  - 4
ER  -

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Author Information

Ali Ghorbani Dehaghani

Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Technical and Vocational University (TVU), Shahre-Kord, Iran
Rohallah Pourbagher

Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Technical and Vocational University (TVU), Shahre-Kord, Iran
Heidar Mozafari Vanani

Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Technical and Vocational University (TVU), Shahre-Kord, Iran

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APA Style

Ali Ghorbani Dehaghani, Rohallah Pourbagher, Heidar Mozafari Vanani. (2021). New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs. Mathematics and Computer Science, 6(4), 65-70. https://doi.org/10.11648/j.mcs.20210604.12

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ACS Style

Ali Ghorbani Dehaghani; Rohallah Pourbagher; Heidar Mozafari Vanani. New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs. Math. Comput. Sci. 2021, 6(4), 65-70. doi: 10.11648/j.mcs.20210604.12

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AMA Style

Ali Ghorbani Dehaghani, Rohallah Pourbagher, Heidar Mozafari Vanani. New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs. Math Comput Sci. 2021;6(4):65-70. doi: 10.11648/j.mcs.20210604.12

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@article{10.11648/j.mcs.20210604.12,
  author = {Ali Ghorbani Dehaghani and Rohallah Pourbagher and Heidar Mozafari Vanani},
  title = {New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.mcs.20210604.12},
  url = {https://doi.org/10.11648/j.mcs.20210604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210604.12},
  abstract = {Power flow analysis and calculation play an essential role in analysis of electrical power system. Solving the load flow equations of an electrical power system are very sensitive to the value of the right-hand side constant vector or to the value of the coefficients of the Jacobian matrix, the equations of the electrical power system are called to be ill-conditioned. In an ill-conditioned case study, the determinant of the Jacobian matrix is close to singular or singular. Computing the set of load flow equations of an electrical power system may sometimes lead to the incidence of the ill-conditioned equations. The ill-conditioning mood in MGs power system is due to several reasons such as the situation of the reference bus, high value of r/x ratio of power system's lines, connections of very low and very high impedance power system's lines at a bus and heavy loading condition of an electrical power system. In an islanded MG, the use of traditional PFA is not effective as the voltage of the swing or slack bus and the frequency of the MG are assumed to be constant. This paper proposes a simple and effective iterative method based on the Jacobian matrix λopt to solve the PF equation for islanded MGs. The new proposed technique prepares a simple, straightforward for implementation, and precise technique to calculate the PF equations for MGs. The new suggested technique is exerted to the 38-bus case study electrical power system. The outcomes are compared against simulation outcomes that accredit the efficiency of the new technique.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - New Iterative Method Based Jacobian Matrix and λopt to Solve Power Flow Equation for Islanded MGs
AU  - Ali Ghorbani Dehaghani
AU  - Rohallah Pourbagher
AU  - Heidar Mozafari Vanani
Y1  - 2021/09/06
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210604.12
DO  - 10.11648/j.mcs.20210604.12
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210604.12
AB  - Power flow analysis and calculation play an essential role in analysis of electrical power system. Solving the load flow equations of an electrical power system are very sensitive to the value of the right-hand side constant vector or to the value of the coefficients of the Jacobian matrix, the equations of the electrical power system are called to be ill-conditioned. In an ill-conditioned case study, the determinant of the Jacobian matrix is close to singular or singular. Computing the set of load flow equations of an electrical power system may sometimes lead to the incidence of the ill-conditioned equations. The ill-conditioning mood in MGs power system is due to several reasons such as the situation of the reference bus, high value of r/x ratio of power system's lines, connections of very low and very high impedance power system's lines at a bus and heavy loading condition of an electrical power system. In an islanded MG, the use of traditional PFA is not effective as the voltage of the swing or slack bus and the frequency of the MG are assumed to be constant. This paper proposes a simple and effective iterative method based on the Jacobian matrix λopt to solve the PF equation for islanded MGs. The new proposed technique prepares a simple, straightforward for implementation, and precise technique to calculate the PF equations for MGs. The new suggested technique is exerted to the 38-bus case study electrical power system. The outcomes are compared against simulation outcomes that accredit the efficiency of the new technique.
VL  - 6
IS  - 4
ER  -

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