  In general, quantum systems most likely undergo open system dynamics due to
their smallness and sensitivity. Energy storage devices, so-called quantum
batteries, are not excluded from this phenomenon. Here, we study fundamental
bounds on the power of open quantum batteries from the geometric point of view.
By defining an \emph{activity operator}, a tight upper bound on the charging
power is derived for the open quantum batteries in terms of the fluctuations of
the activity operator and the quantum Fisher information. The variance of the
activity operator may be interpreted as a generalized thermodynamic force,
while the quantum Fisher information describes the speed of evolution in the
state space of the battery. The thermodynamic interpretation of the upper bound
is discussed in detail. As an example, a model for the battery, taking into
account the environmental effects, is proposed, and the effect of dissipation
and decoherence during the charging process on both the stored work and the
charging power is investigated. Our results show that the upper bound is
saturated in some time intervals. Also, the maximum value of both the stored
work and the corresponding power is achieved in the non-Markovian underdamped
regime.
