On the role of renewal theory in the analysis of a class of cyclic hybrid-state stochastic systems

TLDR: In this paper, a class of cyclic hybrid-state stochastic processes arising in the modeling of thermostat-controlled electric power system loads, and particularly important in load management applications, are discussed.

Abstract: Summary form only given. The author reviews a class of cyclic hybrid-state stochastic processes arising in the modeling of thermostat-controlled electric power system loads, and particularly important in load management applications. He shows that there are two distinct viewpoints for analyzing the statistical properties of these processes: an internal viewpoint and an external one. The internal viewpoint, where the full state is considered, yields the complete statistical picture. It is possible to establish an associated system of coupled forward Kolmogorov equations, together with appropriate boundary conditions. In general, this system of equations is difficult to analyze. By contrast, in the external viewpoint the focus is on the discrete part of the process only. It is then possible to uncover an underlying renewal structure. This renewal structure is useful in a rapid establishment of the existence of a statistical steady state as well as its precise determination. Partial transient results can also be obtained in this manner. The two analytical viewpoints usefully complement one another. >