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Batteries and supercapacitors (SC) complement one another; a battery has a relatively high energy density but a low power density, whereas an SC has a relatively high power density but a low energy density. In order to offset their opposing limitations, an active battery/SC hybrid energy storage system (HESS) using a dc/dc converter has been proposed. The major problem concerning an active HESS is in how to control the current flow in order to achieve two objectives: the minimization of the magnitude/fluctuation of the current flowing in and out of the battery and the energy loss seen by the SCs. This problem has not been analytically investigated for an optimal solution regarding these two goals. In this paper, we present an optimal energy management scheme for active HESS. In order to obtain the optimal solution, we formulate the problem as an optimization problem concerning these two objectives. Observing that the feasibility and optimality of the solution critically depends on the boundary parameters of the problem, we present an algorithm that effectively adjusts the parameter values. The proposed algorithm is based on the multiplicative-increase- additive-decrease principle, which guarantees a feasible optimal solution. Through MATLAB simulations, we demonstrate that the proposed scheme can optimally minimize the magnitude/fluctuation of the battery current and the SC energy loss.