Effects of control limitations on the power grid fluctuations

Abstract

[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.