A Semi-Markov Model of the Variability of Power Generation from Renewable Sources

Abstract

This paper presents a new approach to modeling the variability of power generation from a renewable source such as wind or flowing water. The force of the power generating agent is assumed to change according to a semi-Markov process with finite state space. For the purpose of its construction, the range of possible values expressing the agent’s force is divided into a finite number of subintervals. It is natural to assume that the length of time during which the agent’s force remains within one such interval, and the probabilities of transitions to neighboring intervals depend to some extent on the agent’s earlier behavior. The model’s accuracy is determined by the number of subintervals used and the assumed degree to which the agent’s force depends on its history (the number of the most recently entered subintervals relevant to predicting the agent’s future behavior). According to the presupposed accuracy level, an appropriately complex state-space and diagram of the inter-state transitions for the modeled process are constructed. Subsequently, it is demonstrated how certain parameters of this process, related to forecasting power generation, can be calculated by means of the calculus of Laplace transforms.