Evaluation of convex optimization models for minimizing losses in distribution systems
DOI:
https://doi.org/10.37431/conectividad.v5i3.152Keywords:
Convexity, Distribution, Optimization, Losses, WirtingerAbstract
This paper proposes the evaluation of convex models for short-term energy dispatch, optimizing the location of generators and minimizing losses in distribution networks. For this purpose, convex models are used in a 12-hour period with an hourly variation of the demand, using the IEEE system of 15 radial type nodes. Due to the nodal injection active and reactive power equations, the problem becomes non-convex and requires more computational resources to find local optimal solutions. To address the nonlinearity problem. The Wirtinger calculus and the second-order conic approximation are analyzed. The first model solves in 8.12 seconds with voltage errors of 0.63% and angle of 1.40%, and the second model in 17.8 seconds with errors of 0.61% and 1.38%, respectively. The optimal location of the generating units are nodes 7, 8 and 10. The objective function value for each model is 0.00731149 p.u. for the nonlinear model, 0.00734619 p.u, for the Wirtinger model 0.00744715 p.u, and for the second order conic approximation model (SOC), with a base of 100 kVA.
References
Anwar, A., & Pota, H. R. (2011). Loss reduction of power distribution network using optimum size and location of distributed generation. AUPEC 2011, 1–6.
Cabezas Soldevilla, F. R., & Alfredo Cabezas Huerta, F. (2019). Minimization of Losses in Power Systems by Reactive Power Dispatch using Particle Swarm Optimization. 2019 54th International Universities Power Engineering Conference, UPEC 2019 - Proceedings. https://doi.org/10.1109/UPEC.2019.8893527
Caiza, C. Q., & Toaza, J. X. (2021). Un modelo de optimización convexo para minimizar las pérdidas de energía en los sistemas de distribución A convex optimization model for energy losses minimization in distribution systems . Ciencias de La Ingeniería y Aplicadas, 5(2), 114–124.
Dias Tamayo, D. A., & Garcés Ruiz, A. (2017). Despacho económico en sistemas de potencia considerando estabilidad transitoria. Revista Tecnura, 21(51), 27. https://doi.org/10.14483/udistrital.jour.tecnura.2017.1.a02
Garcés-Ruiz, A. (2022). Mathematical programming for power systems operation: from theory to applications in Python. https://doi.org/10.1002/9781119747291.fmatter
Gopi, A., & Raj, P. A.-D.-V. (2012). Distributed generation for line loss reduction in radial distribution system. 2012 International Conference on Emerging Trends in Electrical Engineering and Energy Management (ICETEEEM), 29–32. https://doi.org/10.1109/ICETEEEM.2012.6494439
Javier Martínez-Peralta, A. I., & Eugenia Llosas-Albuerne, Y. I. (2022). Técnicas para la ubicación óptima de generación distribuida en redes de distribución de energía eléctrica. Dominiodelasciencias.Com, 8(1), 503–520. https://dominiodelasciencias.com/ojs/index.php/es/article/view/2506
Le, A. D. T., & Kashem, M. A. (2007). Optimal distributed generation parameters for reducing losses with economic consideration. 2007 IEEE Power Engineering Society General Meeting, PES, 1–8. https://doi.org/10.1109/PES.2007.386058
Leeton, U., & Uthitsunthorn, D. (2010). Power loss minimization using optimal power flow based on particle swarm optimization. ECTI-CON2010: The 2010 ECTI International Confernce on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology, 440–444.
Low, S. H. (2014a). Convex relaxation of optimal power flow-part II: Exactness. IEEE Transactions on Control of Network Systems, 1(2), 177–189. https://doi.org/10.1109/TCNS.2014.2323634
Low, S. H. (2014b). Convex Relaxation of Optimal Power Flow—Part I: Formulations and Equivalence. IEEE Transactions on Control of Network Systems, 1(1), 15–27. https://doi.org/10.1109/TCNS.2014.2309732
María, J., & Luis Alfonso. (2008). Flujo de potencia óptimo usando el método del gradiente para reducción de pérdidas en sistemas de potencia. Ingeniería y Ciencia, 4, 71–85. https://www.redalyc.org/articulo.oa?id=83540704
Martínez-Peralta, A. J. (2018). Wirtinger’s Calculus for the Load Flow in Power Distribution Grids. 2018 IEEE ANDESCON, ANDESCON 2018 - Conference Proceedings. https://doi.org/10.1109/ANDESCON.2018.8564691
Molzahn, D. K., & Hiskens, I. A. (2019). A Survey of Relaxations and Approximations of the Power Flow Equations. Foundations and Trends® in Electric Energy Systems, 4(1–2), 1–221. https://doi.org/10.1561/3100000012
Muttaqi, K., & Negnevitsky, M. (2006). Distributed generation for minimization of power losses in distribution systems. IEEE Power Engineering Society General Meeting, 8 pp. https://doi.org/10.1109/PES.2006.1709179
Oñate Y, P. E., & Ramírez A, J. M. (2009). SOLUCIÓN AL PROBLEMA DE COORDINACIÓN HIDROTÉRMICA DE CORTO PLAZO POR ALGORITMOS GENÉTICOS. Revista Técnica “Energía,” 5(1). https://doi.org/10.37116/revistaenergia.v5.n1.2009.239
Ramirez, D. A., & Garcés, A. (2019). A Wirtinger Linearization for the Power Flow in Microgrids. 2019 IEEE Power & Energy Society General Meeting (PESGM), 1–5. https://doi.org/10.1109/PESGM40551.2019.8973647
Stephen Lieven. (2013). Convex Optimization. United States of America by Cambridge University Press, New York.
Yuan, Z., & Hesamzadeh, M. R. (2019). Second-order cone AC optimal power flow: convex relaxations and feasible solutions. Journal of Modern Power Systems and Clean Energy, 7(2), 268–280. https://doi.org/10.1007/s40565-018-0456-7
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