Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-10T21:17:38.450Z Has data issue: false hasContentIssue false
  • English
  • Français

A jump-driven Markovian electric load model

Published online by Cambridge University Press:  01 July 2016

Roland Malhamé
Roland Malhamé*
Affiliation:
École Polytechnique de Montréal
*
∗Postal address: École Polytechnique de Montréal, Département de Génie Électrique, Montréal, Québec H3C 3A7, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

Electric water heating loads, in power systems, can be adequately modeled by Markov processes comprising a mix of continuous and discrete states. A physically-based characterization of the dynamic behavior of large aggregates of electric water heating loads is obtained by deriving the forward Kolmogorov equations associated with the individual hybrid-state processes. In addition, by focusing on the discrete part of the state, a Markov renewal viewpoint of the processes is developed. Both viewpoints are used to analyze and predict the transient and steady-state behavior of these loads, of great importance in load management applications.

Keywords

LOAD MODELINGMARKOV RENEWAL PROCESSESFIRST-PASSAGE TIMES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 564 - 586
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bischke, R. F. (1985) Design and control of use on water heater load management. IEEE Trans. Power App. Systems. 104, 1290–1293.Google Scholar
Chong, C. Y. and Malhame, R. (1983) Statistical approach to physically based load modeling. Georgia Institute of Technology, DE-AS01–77 and 29116.Google Scholar
Çinlar, E. (1975) Markov renewal theory: a survey. Management Sci. 21, 727–751.Google Scholar
Davis, M. H. A. (1984) Piecewise-deterministic Markov processes. A general class of non-diffusion models. J. R. Statist. Soc. B 46, 353–388.Google Scholar
Doetsch, G. (1971) Guide to the Application of Laplace and Z Transforms. Van Nostrand Reinhold, London.Google Scholar
Galiana, F. D., Handschin, E. and Fiechter, A. R. (1974) Identification of stochastic electric load models from physical data. IEEE Trans. Autom. Control 19, 887–893.Google Scholar
Kailath, T. (1980) Linear Systems. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Malhamé, R. and Chong, C. Y. (1983) Stochastic hybrid-state systems for electric load modelling. Proc. IEEE CDC, San Antonio, Texas, 1143–1149.Google Scholar
Malhamé, R. and Chong, C. Y. (1985) Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system. IEEE Trans. Autom. Control. 30, 854–860.Google Scholar
Malhamé, R. and Chong, C. Y. (1988) On the statistical properties of a cyclic diffusion process arising in the modeling of thermostat-controlled power system loads. SIAM J. Appl. Math. 48, 465–480.CrossRefGoogle Scholar
Schick, C. I., Usoro, P. B., Ruane, M. F. and Schweppe, F. C. (1988) Modeling and weather-normalization of whole-house metered data for residential end-use load shape estimation. IEEE Trans. Power Systems 3, 213–219.Google Scholar
Silvestrov, D. S. and Rezhnikov, G. (1983) Explicit estimates for the rate of convergence in ergodic theorems for random processes with semi-Markov switchings. 17th School Colloquium on Prob. Theory and Math. Statist., Bajuriani, ed. Shevarshidze, I. L., 72–78.Google Scholar
Vermes, D. (1985) Optimal control of piecewise deterministic processes. Stochastics 14, 165–208.Google Scholar