Smart meters density effects on the number of collectors in a Smart Grid

The conventional power grids are not efficient today due to their aged infrastructure, requiring a more effective management of their functions. This goal is at the base of the Smart Grid (SG) concept that aim at introducing intelligence in the energy grid. Among several SG devices, smart meters (SMs) work in the demand side of the power grids and their number is increasing massively in the last years. A SM is a SG electronic device which records electric energy consumption in certain time intervals for communicating such information to the utility and SG Control Station through the collectors for monitoring, demanding response and billing services. The wireless communication systems have an important role in the SG functions. However, the spectrum scarcity due to growing number of users is becoming an important problem. The number of SMs is a function of area size and SM density. The inter arrival rate in a single collector which supports a certain number of SMs, follows Poisson distribution. Moreover, the amount of data that a single collector receives from SMs, increase exponentially by increasing the number of SMs. Thus, introducing an algorithm to avoid the exponential data increasing by defining the minimum number of collectors for a certain number of SMs can be a suitable solution to manage SG communication infrastructure. The definition of the threshold number of SMs and its relation with SMs density which should be supported by a single collector is a primary step to reach the goal. This paper focuses on definition of an algorithm aiming to obtain the minimum number of collectors respect to the number of SMs as a function of SM density and to maximize the spectrum efficiency of the collectors.