Stochastic study of hourly total solar radiation in Corsica using a Markov model

Capacity and fairness of the multiple access channel in energy harvesting wireless networks

“…Stochastic models are typically used to describe the unpredictable nature of energy harvesters. In [23] solar energy is modeled as a Markov process after analysis of years of observed data. In this work, we use a 10-state model with transition probabilty matrix as given in [24] and a similar energy profile.…”

Stochastic Modeling and Analysis for Environmentally Powered Wireless Sensor Nodes

“…Therefore, finding a representative model able to capture the uncertainty of the energy source requires attentive thinking. For example, the performance of solar energetic systems is dependent on the variable levels of solar radiation, which are neither completely random, nor fully deterministic [23]. For the stochastic energy model, no classical probability law could be suitably fitted to solar radiation empirical probabilities.…”

“…For the stochastic energy model, no classical probability law could be suitably fitted to solar radiation empirical probabilities. On the other hand, the literature on climatology and renewable energy is already well established, using historical data, descriptive Markov chain models for various forms of environmental energy, such as solar radiation [9], [18], [23], wind speed [17] and ambient temperature, or autoregressive process models [22]. More exactly, [23] proposes a firstorder stationary discrete time Markov chain model for each month of the year, due to the big monthly variations, built from traces taken over a period of 20 years.…”

“…We accomplish this by equally dividing the interval of possible energy quantities generated in the (predefined) time step of 10 seconds and associate each of the 10 subintervals, in our case, to one of the states of the Markov chain. We build the transitional frequency matrix and the transitional probability matrix the standard way, as in [23], by using a simple home built script that analyzes the collected time series, as depicted in Figure 1. More exactly, to assign probabilities on the transitions originating in a state of the DTMC, we go over the solar panel current trace and count the occurrences of each transition from that state (by transition in the trace we understand the jump from one energy level to the next, 10 seconds later).…”

“…Using the same technique, statistical models for different periods of the year can be generated. We advocate the creation of a library of different models associated, for example, with each month, from which the designer can choose, as in [23]. Therefore, the model in Figure 4 is a possible item from the library.…”