Abstract
Load duration curves play an important role in the planning practice of electric power systems. In the paper, we consider the problem of approximating a load duration curve by a polynomial under monotonicity and some other constraints. We show that semi-infinite programming techniques can be applied for solving this problem. A convergent inner-outer method and a finite ε-optimal algorithm is proposed.
Zusammenfassung
Lastdauerlinien spielen eine wichtige Rolle in der Planungspraxis der elektrischen Energiesysteme. In der Arbeit betrachten wir das Problem der Approximation einer Lastdauerlinie durch ein Polynom unter Monotonie und einigen anderen Nebendedingungen. Es wird gezeigt, daß die Verfahren der semi-infiniten Programmierung zur Lösung dieses Problems anwendbar sind. Eine konvergente innere-äußere Methode und ein endlicher ε-optimaler Algorithmus werden vorgeschlagen.
Similar content being viewed by others
References
Bernau, H.: An exact penalty function method for strictly convex quadratic programs. In: Guddat, J. et al. (eds.) Advances in mathematical optimization. Berlin: Akademie-Verlag 1988, pp. 35–43.
Dörfner, P., Fülöp, J., Hoffer, J.: LDC Module, User's Guide, Version 2.0. Budapest: Hungarian Electricity Board, Argonne: Argonne National Laboratory (March 1991).
Energy and Power Evaluation Program (ENPEP), Documentation and Users Manual. Argonne: Argonne National Laboratory (August 1987).
Expansion Planning for Electrical Generating Systems, A Guidebook. Technical Reports Series No. 241, International Atomic Energy Agency, Vienna (1984).
Fülöp, J.: A semi-infinite programming method for approximating load duration curves by polynomials. Working Paper 92-2, Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Budapest (1992).
Gustafson, S. A., Kortanek, K. O.: Numerical treatment of a class of semi-infinite programming problems. Naval Research Logistics Quarterly20, 477–504 (1973).
Hansen, P., Jaumard, B., Lu, S.-H.: Global minimization of univariate functions by sequential polynomial approximation. International Journal of Computer Mathematics28, 183–193 (1988).
Hettich, R., Zencke, P.: Numerische Methoden der Approximation und semi-infiniten Optimierung. Stuttgart: Teubner 1982.
Hettich, R.: A review of numerical methods for semi-infinite optimization. In: Fiacco, A. V., Kortanek, K. O. (eds.) Semi-infinite Programming and Applications. New York: Springer 1983, pp. 158–178.
Hettich, R.: An implementation of a discretization method for semi-infinite programming. Mathematical Programming34, 354–361 (1986).
Hettich, R., Gramlich, G.: A note on an implementation of a method for quadratic semi-infinite programming. Mathematical Programming46, 249–254 (1990).
Hu, H.: A one-phase algorithm for semi-infinite linear programming. Mathematical Programming46, 85–103 (1990).
Tichatschke, R., Nebeling, V.: A cutting plane method for quadratic semi-infinite programming problems. Optimization19, 803–817 (1988).
van der Waerden, B. L.: Algebra. Berlin: Springer 1966.
WASP-III (Wien Automatic System Planning Package, a Computer Code for Power Generating System Expansion Planning), User's Manual, International Atomic Energy Agency (IAEA), Vienna, Austria (1980).
Author information
Authors and Affiliations
Additional information
Dedicated to the memory of Hansjör Wacker
This research was supported in part by Hungarian National Research Foundation, OTKA No. 2568.
Rights and permissions
About this article
Cite this article
Fülöp, J. A semi-infinite programming method for approximating load duration curves by polynomials. Computing 49, 201–212 (1992). https://doi.org/10.1007/BF02238929
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02238929