The system according to the invention comprises a weighted piston (30), which has the role of accumulating gravitational potential energy by lifting it vertically inside a cylinder (10) with the reinforced concrete wall, filled with water, the piston (30) being provided in the center with a high pressure pipe (20) which conducts pressurized water from the base of the cylinder to an electricity generating system (50) using impulse turbines, the water machined in the cycle of electricity production (50) being discharged back into the cylinder (10), above the piston. For the cycle of absorption and storage of energy from an electrical network, the system also comprises an electrical energy absorption system (60) which takes over the water above the piston (30) and inserts it into the high pressure channel (20), under the piston (30).