[eng] Nowadays the climatic change due to the excess of carbon dioxide in the air is a clear problem we
have on our planet earth. Consequently, the use of renewable energies has intensified considerably
in the last decades while at the same time has aroused motivation for the study of the power grid
frequency stability control. In fact, this control is a demanding task which requires expensive power
plants to adjust the supply to the fluctuating demand. With renewable energies in the system, in
addition on the fluctuations of the demand, there are also much more fluctuations on the production
side due to meteorological conditions, for instance when there are clouds passing over photo-voltaic
panels, causing a harder problem in the frequency control theory. Then, the big question at this
moment is if it could be possible to acquire all the energy of the planet from renewable energies. But
before facing this dilemma, we should analyze and study the stability of the power grid fluctuations
in detail in the current configurations.
The aim of this work is to study the stability of the power grid frequency fluctuations for small
networks, proposing a simple power plant model. As a matter of fact, first of all we have analyzed
the actual frequency fluctuations from Grand Canary Island (Spain) measured during six consecutive
days. Moreover, a stochastic demand model is applied by just adjusting a simple parameter in order
to reproduce the statistical properties of the demand fluctuations. We have computed the mean,
the standard deviation and the skewness of the experimental probability density function of the
frequency fluctuations finding an asymmetry with positive skewness. However, once we perform
the numerical simulations using the standard power plant model together with the calibrated
stochastic demand model, we see that the experimental and numerical results do not match on
the tails of the distributions, finding a symmetric numerical distribution. Therefore, we introduce
and explain the physical interpretation of several new hypotheses such as the non-linear control
regulation and the non-stationary demand model in order to adjust more accurately the probability
density function. We have analyzed the changes in the response of the system under these new
conditions. Finally, we have shown that combining both hypotheses the statistical properties of the
frequency fluctuations given by the model are in good agreement with the experimental ones. The
results of our study could be a very powerful framework to explain correctly many more frequency
fluctuations of small power grids, with the possibility to expand them to large larger power grids if
we would introduce the network interaction between several power plants.