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The present paper proposes a new approach to optimize the sizing of a multi-source PV/Wind with Hybrid Energy Storage System (HESS). Hence, a developed modeling of all sub-systems composing the integral system has been designed to establish the proposed optimization algorithm. Besides, a frequency management based on Discrete Fourier Transform (DFT) algorithm has been also used to distribute the power provided by the power supply system into different dynamics. Thus, many frequency channels have been obtained in order to divide the roles of each storage device and show the impact of integrating fast dynamics into renewable energies based applications. The reformulation of our optimization problem is considered by the minimization of the Total Cost of Electricity (TCE) and the Loss of Power Supply Probability (LPSP) of the load, simultaneously. In this respect, a multi-objective based Genetic …