Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation
The minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select...
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MDPI AG
2022-05-01
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1600 |
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| author | Oscar Danilo Montoya Francisco David Moya Arul Rajagopalan |
| author_facet | Oscar Danilo Montoya Francisco David Moya Arul Rajagopalan |
| author_sort | Oscar Danilo Montoya |
| collection | DOAJ |
| description | The minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select the nodes where the capacitor banks must be installed. In the second stage, a recursive power flow method is employed to make an exhaustive evaluation of the solution space. The main contribution of this research is the use of the expected load curve to estimate the equivalent annual grid operating costs. Numerical simulations in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness of the proposed methodology in comparison with the solution of the exact optimization model in the General Algebraic Modeling System software. Reductions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.04</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>34.29</mn><mo>%</mo></mrow></semantics></math></inline-formula> with respect to the benchmark case are obtained with the proposed two-stage approach, with minimum investments in capacitor banks. All numerical implementations are performed in the MATLAB software using the convex tool known as CVX and the Gurobi solver. The main advantage of the proposed hybrid optimization method lies in the possibility of dealing with radial and meshed distribution system topologies without any modification on the MIQC model and the recursive power flow approach. |
| first_indexed | 2024-03-10T03:55:39Z |
| format | Article |
| id | doaj.art-74d570c79816480dabe9f85e7e6b24ae |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:55:39Z |
| publishDate | 2022-05-01 |
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| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-74d570c79816480dabe9f85e7e6b24ae2023-11-23T08:46:44ZengMDPI AGMathematics2227-73902022-05-01109160010.3390/math10091600Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical FormulationOscar Danilo Montoya0Francisco David Moya1Arul Rajagopalan2Grupo de Compatibilidad e Interferencia Electromágnetica, Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogota 110231, ColombiaGESETIC Research Group, School of Electrical Engineering, Universidad Distrital Francisco José de Caldas, Bogota 110231, ColombiaSchool of Electrical Engineering, Vellore Institute of Technology, Chennai 600127, IndiaThe minimization of annual operating costs in radial distribution networks with the optimal selection and siting of fixed-step capacitor banks is addressed in this research by means of a two-stage optimization approach. The first stage proposes an approximated mixed-integer quadratic model to select the nodes where the capacitor banks must be installed. In the second stage, a recursive power flow method is employed to make an exhaustive evaluation of the solution space. The main contribution of this research is the use of the expected load curve to estimate the equivalent annual grid operating costs. Numerical simulations in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness of the proposed methodology in comparison with the solution of the exact optimization model in the General Algebraic Modeling System software. Reductions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>33.04</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>34.29</mn><mo>%</mo></mrow></semantics></math></inline-formula> with respect to the benchmark case are obtained with the proposed two-stage approach, with minimum investments in capacitor banks. All numerical implementations are performed in the MATLAB software using the convex tool known as CVX and the Gurobi solver. The main advantage of the proposed hybrid optimization method lies in the possibility of dealing with radial and meshed distribution system topologies without any modification on the MIQC model and the recursive power flow approach.https://www.mdpi.com/2227-7390/10/9/1600fixed-step capacitor banksdaily load variationsannual operating costs minimizationtwo-stage optimization approachsuccessive approximation power flow method |
| spellingShingle | Oscar Danilo Montoya Francisco David Moya Arul Rajagopalan Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation Mathematics fixed-step capacitor banks daily load variations annual operating costs minimization two-stage optimization approach successive approximation power flow method |
| title | Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation |
| title_full | Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation |
| title_fullStr | Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation |
| title_full_unstemmed | Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation |
| title_short | Annual Operating Costs Minimization in Electrical Distribution Networks via the Optimal Selection and Location of Fixed-Step Capacitor Banks Using a Hybrid Mathematical Formulation |
| title_sort | annual operating costs minimization in electrical distribution networks via the optimal selection and location of fixed step capacitor banks using a hybrid mathematical formulation |
| topic | fixed-step capacitor banks daily load variations annual operating costs minimization two-stage optimization approach successive approximation power flow method |
| url | https://www.mdpi.com/2227-7390/10/9/1600 |
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