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A nonlinear programming approach to a very large hydroelectric system optimization

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Abstract

A large scale hydroelectric system optimization is considered and solved by using a non-linear programming method. The largest numerical case involves approximately 6 000 variables, 4 000 linear equations, 11 000 linear and nonlinear inequality constraints and a nonlinear objective function. The solution method is based on

  1. (i)

    partial elimination of independent variables by solving linear equations,

  2. (ii)

    essentially unconstrained optimization of a compound function that consists of the objective function, nonlinear inequality constraints and part of the linear inequality constraints. The compound function is obtained via penalty formulation.

The algorithm takes full advantage of the problem's structure and provides useful solutions for real life problems that, in general, are defined over empty feasible regions.

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References

  1. J. Abadie and J. Carpentier, “Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints”, in:Optimization, Ed. R. Fletcher (Academic Press, New York, 1969) pp. 37–47.

    Google Scholar 

  2. R. Fletcher, “A FORTRAN subroutine for minimization by the method of conjugate gradients”, Rept. AERE-R 7073, Harwell (1972).

  3. R. Fletcher and C.M. Reeves, “Function minimization by conjugate gradients”,Computer Journal 7 (1964) 149–154.

    Google Scholar 

  4. C.R. Gagnon, R.H. Hicks, S.L.S. Jacoby and J.S. Kowalik, “A mathematical model and a digital computer program for automatic hydroelectric power system critical period analysis”, Rept. BCS-G0216, Boeing Computer Services, Inc. (1973).

  5. S.L.S. Jacoby, J.S. Kowalik and J.T. Pizzo,Iterative Methods for Nonlinear Optimization Methods, Prentice—Hall series in automatic computation (Prentice—Hall, Englewood Cliffs, N.J., 1972).

    Google Scholar 

  6. J. Peschon, D.W. Bree, Jr. and L.P. Hajdu, “Optimal power-flow solutions for power system planning”,Proceedings of the IEEE 60 (1972) pp. 64–70.

    Google Scholar 

  7. E. Polak and G. Ribiere, “Note sur la convergence de methodes de directiones conjugees”,Revue Francaise d'Informatique et de Recherche Opérationnelle, 16-R1 (1969).

  8. P. Wolfe, “Methods for linear constraints”, in:Nonlinear Programming Ed. J. Abadie (North-Holland, Amsterdam, 1967) pp. 99–131.

    Google Scholar 

  9. P. Wolfe, “On the convergence of gradient methods under constraint”,IBM Journal of Research and Development 16 (1972) 407–411.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Boeing Computer Services, Inc., Seattle, Washington, USA

    C. R. Gagnon

  2. Bonneville Power Administration, Portland, Oregon, USA

    R. H. Hicks

  3. Boeing Computer Services, Inc., Seattle, Washington, USA

    S. L. S. Jacoby

  4. Sir George Williams University, Montreal, Canada

    J. S. Kowalik

Authors
  1. C. R. Gagnon
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  2. R. H. Hicks
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  3. S. L. S. Jacoby
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  4. J. S. Kowalik
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Gagnon, C.R., Hicks, R.H., Jacoby, S.L.S. et al. A nonlinear programming approach to a very large hydroelectric system optimization. Mathematical Programming 6, 28–41 (1974). https://doi.org/10.1007/BF01580220

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  • DOI: https://doi.org/10.1007/BF01580220

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