For reasons of the intermittent nature of electricity produced by renewable power plants, the analysis and design of an efficient energy storage system (ESS) are becoming a point of interest. The current paper presents a simulation-based analysis to find the best dimensions of the gravity ESS. The considered system is the piston in cylinder pumped hydro-electric storage. Five design parameters are considered, namely, chamber height, piston height, piston diameter, return pipe length, and diameter. First, the system was modeled by the governing mathematical equations. The mathematical model is then simulated and validated by comparing its results with experimental benchmarking from literature with different cases. To find the best design parameters in function of the uncertain energy input, a Fuzzy logic controller is designed with three membership functions: triangular, trapezoidal, and Gaussian. The uncertainty of the energy produced by the renewable power plant is modeled by Fuzzy inputs for the energy and rate of energy change. The developed Fuzzy interface model is a Mamdani one. The ARMAX method was used to select the most suitable membership function to represent the Fuzzy simulation of the storage system. Results showed that the Gaussian membership function is the most suitable membership function to represent the Fuzzy model of the storage system. Using the Gaussian membership function and Centroid defuzzification, the best design parameters of the different size power plants are determined using MATLAB-Simulink.