{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T12:19:21Z","timestamp":1766578761739,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,24]],"date-time":"2022-09-24T00:00:00Z","timestamp":1663977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>This paper deals with the problem regarding the optimal placement and sizing of distribution static compensators (D-STATCOMs) in radial and meshed distribution networks. These grids consider industrial, residential, and commercial loads within a daily operation scenario. The optimal reactive power flow compensation problem is formulated through a mixed-integer nonlinear programming (MINLP) model. The objective function is associated with the minimization of the expected energy losses costs for a year of operation by considering the investment costs of D-STATCOMs. To solve the MINLP model, the application of a master\u2013slave optimization approach is proposed, which combines the salp swarm algorithm (SSA) in the master stage and the matricial backward\/forward power flow method in the slave stage. The master stage is entrusted with defining the optimal nodal location and sizes of the D-STATCOMs, while the slave stage deals with the power flow solution to determine the expected annual energy losses costs for each combination of nodes and sizes for the D-STATCOMs as provided by the SSA. To validate the effectiveness of the proposed master\u2013slave optimizer, the IEEE 33-bus grid was selected as a test feeder. Numerical comparisons were made against the exact solution of the MINLP model with different solvers in the general algebraic modeling system (GAMS) software. All the simulations of the master\u2013slave approach were implemented in the MATLAB programming environment (version 2021b). Numerical results showed that the SSA can provide multiple possible solutions for the studied problem, with small variations in the final objective function, which makes the proposed approach an efficient tool for decision-making in distribution companies.<\/jats:p>","DOI":"10.3390\/a15100345","type":"journal-article","created":{"date-parts":[[2022,9,25]],"date-time":"2022-09-25T21:14:28Z","timestamp":1664140468000},"page":"345","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Application of the SSA for Optimal Reactive Power Compensation in Radial and Meshed Distribution Using D-STATCOMs"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7530-0011","authenticated-orcid":false,"given":"Javier Andr\u00e9s","family":"Mora-Burbano","sequence":"first","affiliation":[{"name":"Grupo de Compatibilidad e Interferencia Electromagn\u00e9tica, Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 110231, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8211-425X","authenticated-orcid":false,"given":"Cristian David","family":"Fonseca-D\u00edaz","sequence":"additional","affiliation":[{"name":"Grupo de Compatibilidad e Interferencia Electromagn\u00e9tica, Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 110231, Colombia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6051-4925","authenticated-orcid":false,"given":"Oscar Danilo","family":"Montoya","sequence":"additional","affiliation":[{"name":"Grupo de Compatibilidad e Interferencia Electromagn\u00e9tica, Facultad de Ingenier\u00eda, Universidad Distrital Francisco Jos\u00e9 de Caldas, Bogot\u00e1 110231, Colombia"},{"name":"Laboratorio Inteligente de Energ\u00eda, Facultad de Ingenier\u00eda, Universidad Tecnol\u00f3gica de Bol\u00edvar, Cartagena 131001, Colombia"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.ijepes.2018.11.012","article-title":"Power transmission and distribution losses\u2014A model based on available empirical data and future trends for all countries globally","volume":"107","author":"Sadovskaia","year":"2019","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5927","DOI":"10.1016\/j.enpol.2010.05.046","article-title":"Developing electricity distribution networks and their regulation to support sustainable energy","volume":"38","author":"Shaw","year":"2010","journal-title":"Energy Policy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s40031-018-0344-6","article-title":"Optimal Reconfiguration of Distribution Network Using Modified Culture Algorithm","volume":"99","author":"Verma","year":"2018","journal-title":"J. Inst. Eng. (India) Ser. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.ijepes.2013.07.011","article-title":"Optimal capacitor placement in radial distribution systems using teaching learning based optimization","volume":"54","author":"Sultana","year":"2014","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"108346","DOI":"10.1016\/j.epsr.2022.108346","article-title":"Minimization of the distribution operating costs with D-STATCOMS: A mixed-integer conic model","volume":"212","author":"Montoya","year":"2022","journal-title":"Electr. Power Syst. Res."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Martin, O., Terry, S., and Bottrell, N. (2021, January 7\u20138). Application of a Distribution STATCOM to Manage Network Voltages. Proceedings of the 17th International Conference on AC and DC Power Transmission (ACDC 2021), Glasgow, UK.","DOI":"10.1049\/icp.2021.2450"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1016\/j.rser.2017.04.035","article-title":"Optimal placement and sizing of distribution static compensator (D-STATCOM) in electric distribution networks: A review","volume":"77","author":"Sirjani","year":"2017","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e2723","DOI":"10.1002\/etep.2723","article-title":"Optimal allocation of D-STATCOM and reconfiguration in radial distribution network using MOPSO algorithm in TOPSIS framework","volume":"29","author":"Marjani","year":"2018","journal-title":"Int. Trans. Electr. Energy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Montoya, O.D., Chamorro, H.R., Alvarado-Barrios, L., Gil-Gonz\u00e1lez, W., and Orozco-Henao, C. (2021). Genetic-Convex Model for Dynamic Reactive Power Compensation in Distribution Networks Using D-STATCOMs. Appl. Sci., 11.","DOI":"10.3390\/app11083353"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Castiblanco-P\u00e9rez, C.M., Toro-Rodr\u00edguez, D.E., Montoya, O.D., and Giral-Ram\u00edrez, D.A. (2021). Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm. Electronics, 10.","DOI":"10.3390\/electronics10121452"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.epsr.2011.11.016","article-title":"Optimization of distributed generation systems using a new discrete PSO and OPF","volume":"84","author":"Jurado","year":"2012","journal-title":"Electr. Power Syst. Res."},{"key":"ref_12","first-page":"360","article-title":"Optimal Allocation of DG and D-STATCOM in a Distribution System using Evolutionary based Bat Algorithm","volume":"12","author":"Salkuti","year":"2021","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1407","DOI":"10.1109\/TPWRS.2012.2184307","article-title":"Convex Models of Distribution System Reconfiguration","volume":"27","author":"Taylor","year":"2012","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_14","first-page":"267","article-title":"Optimal Placement of Custom Power Devices in Power System Network to Mitigate Voltage Sag under Faults","volume":"2","author":"Tanti","year":"2012","journal-title":"Int. J. Power Electron. Drive Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.ijepes.2014.02.020","article-title":"Optimal location and sizing of DSTATCOM in distribution systems by immune algorithm","volume":"60","author":"Taher","year":"2014","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/j.ijepes.2014.05.021","article-title":"Optimal location and sizing of Distribution Static Synchronous Series Compensator using Particle Swarm Optimization","volume":"62","author":"Devi","year":"2014","journal-title":"Int. J. Electr. Power Energy Syst."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gupta, A.R., and Kumar, A. (2015, January 21\u201322). Optimal placement of D-STATCOM in distribution network using new sensitivity index with probabilistic load models. Proceedings of the 2015 2nd International Conference on Recent Advances in Engineering & Computational Sciences (RAECS), Chandigarh, India.","DOI":"10.1109\/RAECS.2015.7453316"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Faris, H., Mirjalili, S., Aljarah, I., Mafarja, M., and Heidari, A.A. (2019). Salp Swarm Algorithm: Theory, Literature Review, and Application in Extreme Learning Machines. Nature-Inspired Optimizers, Springer International Publishing.","DOI":"10.1007\/978-3-030-12127-3_11"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"106414","DOI":"10.1016\/j.epsr.2020.106414","article-title":"Properties of convex optimal power flow model based on power loss relaxation","volume":"186","author":"Yuan","year":"2020","journal-title":"Electr. Power Syst. Res."},{"key":"ref_20","first-page":"289","article-title":"Optimal Placement of SVC Incorporating Installation Cost","volume":"9","author":"Sharma","year":"2016","journal-title":"Int. J. Hybrid Inf. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"123959","DOI":"10.1016\/j.jhydrol.2019.123959","article-title":"A novel Master\u2013Slave optimization algorithm for generating an optimal release policy in case of reservoir operation","volume":"577","author":"Turgut","year":"2019","journal-title":"J. Hydrol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.asoc.2016.12.011","article-title":"A cooperative-competitive master\u2013slave global-best harmony search for ANN optimization and water-quality prediction","volume":"51","author":"Jaddi","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1109\/TLA.2020.9099675","article-title":"A New Approach for PV Nodes Using an Efficient Backward\/Forward Sweep Power Flow Technique","volume":"18","year":"2020","journal-title":"IEEE Lat. Am. Trans."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Shen, T., Li, Y., and Xiang, J. (2018). A Graph-Based Power Flow Method for Balanced Distribution Systems. Energies, 11.","DOI":"10.3390\/en11030511"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1109\/TPWRS.2015.2394296","article-title":"A Linear Three-Phase Load Flow for Power Distribution Systems","volume":"31","author":"Garces","year":"2016","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_26","first-page":"335","article-title":"Improved salp swarm algorithm for feature selection","volume":"32","author":"Hegazy","year":"2020","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/j.advengsoft.2017.07.002","article-title":"Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems","volume":"114","author":"Mirjalili","year":"2017","journal-title":"Adv. Eng. Softw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.procs.2015.10.100","article-title":"Energy Savings Using D-STATCOM Placement in Radial Distribution System","volume":"70","author":"Gupta","year":"2015","journal-title":"Procedia Comput. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Montano, J., Tob\u00f3n-Mejia, A.F., Rosales-Mu\u00f1oz, A.A., Andrade, F., Garz\u00f3n-Rivera, O.D., and Mena-Palomeque, J. (2021). Salp Swarm Optimization Algorithm for Estimating the Parameters of Photovoltaic Panels Based on the Three-Diode Model. Electronics, 10.","DOI":"10.3390\/electronics10243123"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"106250","DOI":"10.1016\/j.compstruc.2020.106250","article-title":"A new Newton metaheuristic algorithm for discrete performance-based design optimization of steel moment frames","volume":"234","author":"Gholizadeh","year":"2020","journal-title":"Comput. Struct."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/10\/345\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:57Z","timestamp":1760143137000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/10\/345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,24]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["a15100345"],"URL":"https:\/\/doi.org\/10.3390\/a15100345","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2022,9,24]]}}}