Application of the quasi-newton in interior point methods for solving the predispatch problem
Tipo de documento
Lista de autores
Simões de Carvalho, Silvia, Oliveira, Aurelio
Resumen
Brazilian energy matrix is essentially based on hydroelectricity with long transmission lines, allowing the exchange of energy produced in all regions of the country, the increased demand for energy and the search for lower costs, the application of more efficient and robust methods to minimize generation and transmission losses is necessary, since these are functions of generated and transmitted power, respectively. The purpose of this work is to implement primal dual interior point method for the predispatch of a hydroelectric system, with partial replacement of the Newton method with the quasi-Newton method in order to compute the system Jacobian matrix and reduce the computational costs of the iterations arising from approximations of the inverses of the Hessian matrix. This means that, in order to obtain a search direction, only a matrix vector product is necessary, which is much more efficient, for example, than the Newton method, in which a linear system has to be solved at each iteration. Computational results prove the efficiency of the approach used.
Fecha
2023
Tipo de fecha
Estado publicación
Términos clave
Contextos o situaciones | Ecuaciones e inecuaciones | Resolución de problemas | Sistemas de ecuaciones | Teoremas | Tipos de metodología
Enfoque
Idioma
Revisado por pares
Formato del archivo
Usuario
Volumen
8
Número
1
Rango páginas (artículo)
63-80
ISSN
25255444
Referencias
S. Bocanegra, F. F. Campos, and A. R. L. Oliveira. Using a hybrid precondi-tioner for solving large-scale linear systems arising from interior point methods.Computational Optimization and Applications, pages 149–164, 2007.[2] S. M. S. Carvalho and A. R. L. Oliveira. Interior point methods applied to the pre-dispatch hydroelectric system with simulated modification in the network topology.Magazine IEEE Latin America, 13:143–149, 2015.[3] S. M. S. Carvalho, A. R. L. Oliveira, and M. V. Coelho. M ́etodos de pontosinteriores aplicados ao problema de pr ́e-despacho do sistema hidroel ́etrico commanobras e reserva girante.Trends in Applied and Computational Mathematics,18:55–67, 2017.[4] S.M.S. Carvalho, C. Lyra, and A. R. L. Oliveira. Predispatch of hydroelectricpower systems with modifications in network topologies.Annals of OperationsResearch - Springer, 2:1 – 19, 2018.[5] S.M.S. Carvalho and A. R. L Oliveira. Interior point method applied to the pre-dispatch problem of a hydroelectric with scheduled line manipulations.AmericanJournal of Operations Research, 1:266 – 271, 2012.[6] S.M.S. Carvalho, A.R.L. Oliveira, and M.V. Coelho. Predispatch linear systemsolution with preconditioned iterative methods.Control Autom. Electrical System,32:145–152, 2021.[7] John E. Dennis and Robert B. Schnabel.Numerical Methods for UnconstrainedOptimization and Nonlinear Equations. SIAM, Philadelphia, PA, 1996.[8] I. I. Dikin. Iterative solution of problems of linear and quadratic programming.Soviets Math. Doklady, 8:674–675, 1967.[9] I. S. Duff, A. M. Erisman, and J. K. Reid.Direct Methods for Sparse Matrices.Clarendon Press, Oxford, 1986.ReviSeM, Ano 2023, No.1, 63–8078 Carvalho, S.; Oliveira, A.[10] P. Franco, M. F. Carvalho, and S. Soares. A network flow model for short-termhydro-dominated hydrothermal scheduling problem.IEEE Transactions on PowerSystems, 9(2):1016–1021, 1994.[11] J. Gondzio and F. N. C. Sobral. Quasi-newton approaches to interior point methodsfor quadratic problems.Computational Optimization and Applications., 74:93–120,2019.[12] Dennis J.E. and R.B. Schnabel. Least change secant updates for quasi-newtonmethods.SIAM., 4:443–459, 1979.[13] T. Manteuffel. An incomplete factorization technique for positive definite linearsystems.Math. Comp., 34:473–497, 1980.[14] J.M. Martinez. Practical quasi-newton methods for solving nonlinear systems.Comput. Appl. Math., 124 (1-2):97–121, 2000.[15] S. Mehrotra. On the implementation of a primal-dual interior point method.SIAMJournal on Optimization, 2(4):575–601, 1992.[16] J. A. Momoh, M. E. El-Hawary, and R. Adapa. A review of selected optimalpower flow literature to 1993, part II Newton, linear programming and interiorpoint methods.IEEE Transactions on Power Systems, 14(1):105–111, 1999.[17] J. Nocedal and S.J. Wright.Numerical Optimization. Springer, New York, secondedition, 2006.[18] T. Ohishi, S. Soares, and M. F. Carvalho. Short term hydrothermal schedulingapproach for dominantly hydro systems.IEEE Transactions on Power Systems,6(2):637–643, 1991.[19] A. R. L. Oliveira, S. Soares, and L. Nepomuceno. Optimal active power dispatchcombining network flow and interior point approaches.IEEE Transactions onPower Systems, 18(4):1235–1240, November 2003.[20] A. R. L. Oliveira, S. Soares, and L. Nepomuceno. Short term hydroelectric sche-duling combining network flow and interior point approaches.Electrical Power &Energy Systems, 27(2):91–99, 2005.[21] A. R. L. Oliveira and D. C. Sorensen. A new class of preconditioners for large-scalelinear systems from interior point methods for linear programming.Linear Algebraand Its Applications, 394:1–24, 2005.ReviSeM, Ano 2023, No.1, 63–8079 Carvalho, S.; Oliveira, A.[22] G. Santos, E. Barbosa, J. Silva, and R. Abreu. Propostas para o setor eletricobrasileiro.Revista do BNDES, Rio de Janeiro, RJ, 14:435 – 474, 2008.[23] S. Soares and C. T. Salmazo. Minimum loss predispatch model for hydroelectricsystems.IEEE Transactions on Power Systems, 12(3):1220–1228, 1997.[24] R. J. Vanderbei.Linear Programming – Foundations and Extensions. KluwerAcademics Publishers - fourth edition, Boston, USA, 2017.[25] S. J. Wright.Primal–Dual Interior–Point Methods. SIAM Publications, SIAM-second edition, Philadelphia, PA, USA, 2010.
Proyectos
Cantidad de páginas
80