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Calculation of the equilibrium distribution for a solar energy storage model

Published online by Cambridge University Press:  14 July 2016

G. Hooghiemstra  and
M. Keane
G. Hooghiemstra*
Affiliation:
Delft University of Technology
M. Keane*
Affiliation:
Delft University of Technology
*
∗ Postal address: Department of Mathematics and Informatics, Delft University of Technology, P.O. Box 365, 2600 AJ Delft, The Netherlands.
∗ Postal address: Department of Mathematics and Informatics, Delft University of Technology, P.O. Box 365, 2600 AJ Delft, The Netherlands.
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Abstract

The study of simple solar energy storage models leads to the question of analyzing the equilibrium distribution of Markov chains (Harris chains), for which the state at epoch (n + 1) (i.e. the temperature of the storage tank) depends on the state at epoch n and on a controlled input, acceptance of which entails a further decrease of the temperature level. Here we study the model where the input is exponentially distributed. For all values of the parameters involved an explicit expression for the equilibrium distribution of the Markov chain is derived, and from this we calculate, as one of the possible applications, the exact values of the mean of this equilibrium distribution.

Keywords

CONTROLLED INPUT STORAGE MODEL
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 852 - 864
Copyright
Copyright © Applied Probability Trust 1985 

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References

[1] Daley, D. J. and Haslett, J. (1982) A thermal energy storage process with controlled input. Adv. Appl. Prob. 14, 257–271.Google Scholar
[2] Haslett, J. (1980) Problems in the storage of solar thermal energy. In Analysis and Optimization of Stochastic Systems , ed. Jacobs, O. L. R. et al., Academic Press, London.Google Scholar
[3] Haslett, J. (1982) New bounds for the thermal energy storage process with stationary input. J. Appl. Prob. 19, 894–899.CrossRefGoogle Scholar
[4] Lang, S. (1968) Analysis I. Addison-Wesley, New York.Google Scholar
[5] Tweedie, R. L. (1976) Criteria for classifying general Markov chains. Adv. Appl. Prob. 8, 737–771.CrossRefGoogle Scholar