Stochastic Models for Solar Power

Abstract

In this work we develop a stochastic model for the solar power at the surface of the earth. We combine a deterministic model of the clear sky irradiance with a stochastic model for the so-called clear sky index to obtain a stochastic model for the actual irradiance hitting the surface of the earth. Our clear sky index model is a 4-state semi-Markov process where state durations and clear sky index values in each state have phase-type distributions. We use per-minute solar irradiance data to tune the model, hence we are able to capture small time scales fluctuations. We compare our model with the on-off power source model developed by Miozzo et al. (2014) for the power generated by photovoltaic panels, and to a modified version that we propose. In our on-off model the output current is frequently resampled instead of being a constant during the duration of the "on" state. Computing the autocorrelation functions for all proposed models, we find that the irradiance model surpasses the on-off models and it is able to capture the multiscale correlations that are inherently present in the solar irradiance. The power spectrum density of generated trajectories matches closely that of measurements. We believe our irradiance model can be used not only in the mathematical analysis of energy harvesting systems but also in their simulation. keywords: Solar power · Semi-Markov process · Photovoltaic panel

Short-Scale Stochastic Solar Energy Models: A Datacenter Use Case

“…Second, we believe that a correct way to assess the quality of a solar source model is through a "queuing evaluation". We mean by this that instead of focusing on the arrival process of energy with methods of the signal processing literature (as we have ourselves done in [5]), it is necessary to evaluate the quality of a source through its performance in a finite queue. We believe this is relevant for several reasons.…”

“…Despite this global understanding of the phenomenon, no model seems to emerge for generating synthetic traces of it, at the minute level. In [5], we proposed such a model as a semi-Markov process with a finite number of states, to which some random noise is added. Although promising, this approach lacked the dependency on seasons and weather, and also produced trajectories with excessive variations.…”

“…In addition to the global irradiance, the data [20,21] report predictions of the clear sky irradiance using Bird's model [11]. We rely on these predictions of I CS (d, m) to compute the clear sky index α(τ(d), m) according to (5). The subsequent step is to identify which features of days will be used for the classification.…”

“…Table 7 lists the top 10 configurations according to the sum of all three criteria. Configuration (5,11) is ranked first according to both the maximum/mean relative distance and the sum of three criteria, and ranked eightth according to the root mean square distance. The fact that this configuration yields small errors according to the three criteria is confirmed visually in Figure 14, although the neighboring configurations are not as good.…”

Softwarization and Optimization for Sustainable Future Mobile Networks: A Survey

“…The model is based on extensive database of solar irradiation for many years and it gives a reasonable estimate of expected energy arrival considering time of the day, month and status of the day. In addition, the authors in [78] also propose a solar irradiance model that can capture the small t ime-scale (in order of minutes) fluctuations. However, both papers exp loit only the temporal variation of solar energy arrival.…”