Today it is common practice to use simplified equivalent circuit models for predicting the short term behaviour of the voltage and current during charging and discharging battery cells. If the circuit parameters are assumed to be unchanged the response for a given open circuit voltage (OCV) will be the solution to a linear ordinary differential equation. This means that for given voltage limits the maximum charge and discharge powers can be analytically derived. In advanced battery management units, such as those used for hybrid electric vehicles, it is central to know how much that can be charged or discharged within a certain range of time, which is one definition of state of power (SoP). Using the linearizing assumption we derive a method for an adaptive estimation of the state of power based on incremental analysis. The method is easy to implement and have two tuning parameters that are straightforward to relate to. Using frequency analysis the method is analytically proven to have very strong robustness properties. The risk of exceeding voltage limits by effectively applying the maximum charge or discharge currents is marginal in spite of large circuit parameter errors, unmodelled hysteresis, unknown OCV and static nonlinearities.