The latest wireless network, 3GPP Long Term Evolution (LTE), is considered to be a promising solution for smart grids because it provides both low latency and large bandwidth. However, LTE was not originally intended for smart grids applications, where data generated by the grid have specific delay requirements that are different from traditional data or voice communications. In this paper, the specific requirements imposed by a smart grids on the LTE communication infrastructure is first determined. The latency offered by the LTE network to smart grids components is investigated and an empirical mathematical model of the distribution of the latency is established. It is shown by experimental results that with the current LTE up-link scheduler, smart grid latency requirements are not always satisfied and that only a limited number of components can be accommodated. To overcome such a deficiency, a new scheduler of the LTE medium access control is proposed for smart grids. The scheduler is based on a mathematical linear optimization problem that considers simultaneously both the smart grid components and common user equipments. An algorithm for the solution to such a problem is derived based on a theoretical analysis. Simulation results based on this new scheduler illustrate the analysis. It is concluded that LTE can be effectively used in smart grids if new schedulers are employed for improving latency.