On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks
The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes wh...
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| Format: | Article |
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MDPI AG
2022-02-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/10/2/32 |
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| author | Oscar Danilo Montoya Walter Gil-González Alejandro Garcés |
| author_facet | Oscar Danilo Montoya Walter Gil-González Alejandro Garcés |
| author_sort | Oscar Danilo Montoya |
| collection | DOAJ |
| description | The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>138.416</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>kW and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>145.397</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>kW, which improves the best literature results reached with the flower pollination algorithm, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>139.075</mn></mrow></semantics></math></inline-formula> kW, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>145.860</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver. |
| first_indexed | 2024-03-09T22:15:58Z |
| format | Article |
| id | doaj.art-1d000d7710c243baaa97fdb1b68231ca |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T22:15:58Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
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| series | Computation |
| spelling | doaj.art-1d000d7710c243baaa97fdb1b68231ca2023-11-23T19:22:37ZengMDPI AGComputation2079-31972022-02-011023210.3390/computation10020032On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution NetworksOscar Danilo Montoya0Walter Gil-González1Alejandro Garcés2Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, ColombiaFacultad de Ingeniería, Institución Universitaria Pascual Bravo, Medellín 050036, ColombiaPrograma de Ingeniería Eléctrica, Universidad Tecnológica de Pereira, Pereira 660003, ColombiaThe problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>138.416</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>kW and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>145.397</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>kW, which improves the best literature results reached with the flower pollination algorithm, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>139.075</mn></mrow></semantics></math></inline-formula> kW, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>145.860</mn><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula>kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.https://www.mdpi.com/2079-3197/10/2/32capacitor banksdistribution networkssecond-order cone programming modelpower losses minimization |
| spellingShingle | Oscar Danilo Montoya Walter Gil-González Alejandro Garcés On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks Computation capacitor banks distribution networks second-order cone programming model power losses minimization |
| title | On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_full | On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_fullStr | On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_full_unstemmed | On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_short | On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks |
| title_sort | on the conic convex approximation to locate and size fixed step capacitor banks in distribution networks |
| topic | capacitor banks distribution networks second-order cone programming model power losses minimization |
| url | https://www.mdpi.com/2079-3197/10/2/32 |
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