Photovoltaic (PV) systems are used to generate electricity and they are considered less aggressive in their environmental impact. These systems require no further maintenance once they are installed, they do not pollute the environment and their average lifespan is high. These are the reasons why they are considered a good alternative for electricity generation. However, PV systems have different challenges to solve when they are connected to low voltage distribution grids and one of them is related to the power quality when there is a high penetration of PV systems, when voltage variations usually appear. In this paper, a central energy storage system (ESS) is considered to alleviate grid voltage variations under a high penetration scenario of PV systems instead of using multiples ESS. The proposal controls the energy injected into the grid to maintain the voltage variation within the standard, no limitations are imposed on the PV systems, and then as an advantage of the proposal, the PVs’ available energy is fully delivered to the grid. In addition, in the absence of sunlight the ESS may provide power to the grid. An analysis and experimental setup were built to validate the proposed scheme.