Power storage devices are shown to increase their efficiency if they are designed by using quantum systems. We show that the average power output of a quantum battery based on a quantum interacting spin model, charged via a local magnetic field, can be enhanced with the increase of spin quantum number. In particular, we demonstrate such increment in the power output when the initial state of the battery is prepared as the ground or canonical equilibrium state of the spin-j XY model and the bilinear-biquadratic spin-j Heisenberg chain (BBH) in presence of the transverse magnetic field. Interestingly, we observe that in the case of the XY model, a trade-off relation exists between the range of interactions in which the power increases and the dimension while for the BBH model, the improvements depend on the phase in which the initial state is prepared. Moreover, we exhibit that such dimensional advantages persist even when the battery-Hamiltonian has some defects or when the initial battery-state is prepared at finite temperature.
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