Abstract
The problem of generation planning is studied with particular reference to the modelling of forced outages of power plants in the operation submodel (that is to say, in the section of the planning model which evaluates the production costs of the system over the period of study). Using a partitioning method developed by Benders the planning problem is decomposed into a sequence of investment selection and operation costing problems. It is shown how the operation costing problem can be formulated as a linear model when forced outages are considered explicity. A modified version of a closed-form subroutine known in the literature as a stochastic production costing algorithm is used to solve this operation subproblem. The result is a highly efficient planning algorithm which has interesting convergence properties.
This work was jointly supported by Hydro-Québec and by the Social Sciences and Humanities Research Council of Canada.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D. Anderson, “Models for determining least-cost investments in electricity supply” The Bell Journal of Economics and Management Science 3 (1972) 267–299.
R. Billinton, Power system reliability evaluation (Gordon and Breach, New York, 1970).
R. Billinton, “Bibliography on the application of probability methods in power system reliability evaluation”, IEEE Transactions on Power Apparatus and Systems PAS-91 (1972) 649–660.
R.R. Booth, “Power system simulation model based on probability analysis”, IEEE Transactions on Power Apparatus and Systems PAS-91 (1972) 62–69.
R.R. Booth, “Optimal generation planning considering uncertainty”, IEEE Transactions on Power Apparatus and Systems PAS-91 (1972) 70–77.
G. Côté and M.A. Laughton, “Decomposition techniques in power system planning: The Benders’ partitioning method”, International Journal of Electrical Power and Energy Systems 1 (1979) 57–64.
G. Côté, “Reliability aspects of optimal generation planning models for power systems”, Ph.D. Thesis, Univesity of London (1979).
G. Côté and M.A. Laughton, “Large-scale mixed integer programming: Benders-type heuristics”, presented at the Tenth International Symposium on Mathematical Programming, Montréal, August 27–31 (1979).
P.N. Fernando, A.S. Induruwa, B.J. Cory and A. McKechnie, “Further developments in generation planning using integer programming”, Proceedings of the Sixth Power Systems Computation Conference, Darmstadt, August 21–25 (1978) 12–21.
A.M. Geoffrion, “Elements of large-scale mathematical programming Part II: synthesis of algorithms and bibliography”, Management Science 16 (1970) 676–691.
P.G. Harrington and R. Billinton, “Reliability evaluation in energy limited generating capacity studies”, IEEE Transactions on Power Apparatus and Systems PAS-97 (1978) 2076–2085.
R.T. Jenkins and D.S. Joy, “WIEN automatic system planning package (WASP)—An electric utility optimal generation expansion planning computer code”, Oak Ridge National Laboratory Report ORNL-4945 (1974).
R. Juseret, “Long term optimisation of electrical system generation by convex programming”, Mathematical Programming Study 9 (1978) 186–195.
H.M. Khatib, “Economics of reliability of electrical power systems”, Ph.D. Thesis, University of London (1974).
A.S. Manne, “A mixed integer algorithm for project evaluation”, Development Research Centre, International Bank for Reconstruction and Development, Memorandum 71-3 (1971).
F. Noonan and R. Giglio, “Planning electric power generation: A non-linear mixed integer model employing Benders’ decomposition”, Management Science 23 (1977) 946–956.
M.A. Sager, R.J. Ringlee and A.J. Wood, “A new generation cost program to recognise forced outages”, IEEE Transactions on Power Apparatus and Systems PAS-91 (1972) 2114–2124.
D.M. Simmons, Linear programming for operations research, (Holden-Day, San Francisco, (1972).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1982 The Mathematical Programming Society, Inc.
About this chapter
Cite this chapter
Côté, G., Laughton, M.A. (1982). Stochastic production costing in generation planning: A large-scale mixed integer model. In: Goffin, JL., Rousseau, JM. (eds) Applications. Mathematical Programming Studies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121226
Download citation
DOI: https://doi.org/10.1007/BFb0121226
Received:
Revised:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00851-1
Online ISBN: 978-3-642-00852-8
eBook Packages: Springer Book Archive