In terms of encouraging the use of more environmentally friendly forms of energy, renewable energy sources (RES) are incorporated into the power system (EES). One of the solutions to unpredictability and changeability in OIE production is the use of a large capacity energy tank such as a battery. During the peak consumption in the system, the electricity price is the highest. To reduce the total cost of energy procurement, battery storage is charged in a period with small consumption in the system (lower energy price), while in the period of peak consumption, the battery is discharged. The advantage of the battery is that it is an independent source of power but the investment costs are great. Following the mathematical formulation of the model studied in this Final paper, with the help of the programming language Python solved the optimization problem using the solver for the optimization problems Gurobi. Analyzing the modified Garver system with 6 buses without and with the battery tank concludes that it is profitable to invest in a battery tank. Analyzes have shown that the lowest wind generation scenario gives the highest savings, while one with the highest gives the lowest savings. Despite a large investment cost over a 10-year period, the difference in running costs without and with a battery pack is big enough to get profit. Future work or continuation of this paper should include the addition of new battery roles to the power system, such as a reserve, as studied in this Final Paper only theoretically.