Management of dam systems via optimal price control

Boris M. Miller, Daniel McInnes

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

7 Citations (Scopus)

Abstract

This paper considers an optimal management strategy for a system of linked dams. The level of each dam is approximated by N discrete levels and each dam is then modeled as a continuous-time controlled Markov chain on a finite control period. The inflow processes for each dam are non-stationary as are the customer demands. We also consider non-stationary losses from each dam due to evaporation. The controls are a time and state dependent price control, the bounds of which are prescribed by regulators, and time and state dependent flow controls between dams. The innovation in this model is that the price control is a feedback control that takes into account the active sectoral demands of customers. The general approach to the solution is to consider the solution of this stochastic optimization problem in the average sense and solve it using the dynamic programming method. We consider some issues of the numerical procedures involved in this method and parallelization as a means to deal with higher dimension problems in reasonable time. We show that we can obtain optimal price controls for each joint state of the dam system using numerical methods. The result is illustrated by a numerical example.
Original languageEnglish
Title of host publicationProcedia Computer Science
Subtitle of host publicationInternational Conference on Computational Science (ICCS 2011)
EditorsMitsuhisa Sato, Satoshi Matsuoka, G. Dick van Albada, Jack Dongarra, Peter M A Sloot
Place of PublicationAmsterdam, Netherlands
PublisherElsevier
Pages1373-1382
Number of pages10
Volume4
DOIs
Publication statusPublished - 2011
EventInternational Conference on Computational Science 2011: The Ascent of Computational Excellence - Nanyang, Singapore
Duration: 1 Jun 20113 Jun 2011
Conference number: 11th
http://www.iccs-meeting.org/iccs2011/index.html

Conference

ConferenceInternational Conference on Computational Science 2011
Abbreviated titleICCS 2011
CountrySingapore
CityNanyang
Period1/06/113/06/11
OtherThe International Conference on Computational Science aims to bring together annually researchers and scientists from mathematics and computer science as basic computing disciplines, researchers from various application areas who are pioneering advanced application of computational methods to sciences such as physics, chemistry, life sciences, and engineering, arts and humanitarian fields, along with software developers and vendors, to discuss problems and solutions in the area, to identify new issues, and to shape future directions for research, as well as to help industrial users apply various advanced computational techniques.
Internet address

Keywords

  • Stochastic control
  • Optimal control
  • Optimization problems
  • Dynamic programming
  • Markov decision problems
  • Parallelization

Cite this

Miller, B. M., & McInnes, D. (2011). Management of dam systems via optimal price control. In M. Sato, S. Matsuoka, G. D. van Albada, J. Dongarra, & P. M. A. Sloot (Eds.), Procedia Computer Science: International Conference on Computational Science (ICCS 2011) (Vol. 4, pp. 1373-1382). Amsterdam, Netherlands: Elsevier. https://doi.org/10.1016/j.procs.2011.04.148
Miller, Boris M. ; McInnes, Daniel. / Management of dam systems via optimal price control. Procedia Computer Science: International Conference on Computational Science (ICCS 2011). editor / Mitsuhisa Sato ; Satoshi Matsuoka ; G. Dick van Albada ; Jack Dongarra ; Peter M A Sloot. Vol. 4 Amsterdam, Netherlands : Elsevier, 2011. pp. 1373-1382
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Miller, BM & McInnes, D 2011, Management of dam systems via optimal price control. in M Sato, S Matsuoka, GD van Albada, J Dongarra & PMA Sloot (eds), Procedia Computer Science: International Conference on Computational Science (ICCS 2011). vol. 4, Elsevier, Amsterdam, Netherlands, pp. 1373-1382, International Conference on Computational Science 2011, Nanyang, Singapore, 1/06/11. https://doi.org/10.1016/j.procs.2011.04.148

Management of dam systems via optimal price control. / Miller, Boris M.; McInnes, Daniel.

Procedia Computer Science: International Conference on Computational Science (ICCS 2011). ed. / Mitsuhisa Sato; Satoshi Matsuoka; G. Dick van Albada; Jack Dongarra; Peter M A Sloot. Vol. 4 Amsterdam, Netherlands : Elsevier, 2011. p. 1373-1382.

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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AB - This paper considers an optimal management strategy for a system of linked dams. The level of each dam is approximated by N discrete levels and each dam is then modeled as a continuous-time controlled Markov chain on a finite control period. The inflow processes for each dam are non-stationary as are the customer demands. We also consider non-stationary losses from each dam due to evaporation. The controls are a time and state dependent price control, the bounds of which are prescribed by regulators, and time and state dependent flow controls between dams. The innovation in this model is that the price control is a feedback control that takes into account the active sectoral demands of customers. The general approach to the solution is to consider the solution of this stochastic optimization problem in the average sense and solve it using the dynamic programming method. We consider some issues of the numerical procedures involved in this method and parallelization as a means to deal with higher dimension problems in reasonable time. We show that we can obtain optimal price controls for each joint state of the dam system using numerical methods. The result is illustrated by a numerical example.

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Miller BM, McInnes D. Management of dam systems via optimal price control. In Sato M, Matsuoka S, van Albada GD, Dongarra J, Sloot PMA, editors, Procedia Computer Science: International Conference on Computational Science (ICCS 2011). Vol. 4. Amsterdam, Netherlands: Elsevier. 2011. p. 1373-1382 https://doi.org/10.1016/j.procs.2011.04.148