In recent years, lithium-ion batteries have often been proposed as part of various hybrid energy systems. Examples of such applications are hybrid vehicles, photovoltaic-battery or wind-battery systems and power distribution grids. One of the key functions of a battery is to be source of an additional power when the main power source in the system cannot cover the power demands. The power capability of the battery is described by its impedance characteristic. It depends significantly on the battery state-of-charge (SoC), the temperature, the current and the previous history. In this paper, these dependencies and their variations over the battery lifetime are investigated on a 40 Ah lithium-ion cell produced by Kokam (Type SLPB100216216H) with nickel manganese cobalt oxide (NMC) cathode material as an example. For this purpose, a full characterisation of the battery impedance is performed in the new and aged states using electrochemical impedance spectroscopy (EIS) and the current-pulse technique. The results obtained for the new and aged states are compared. The results show, for example, that the SoC range, in which the battery operates with high efficiency, decreases due to significant aging. For the first time, the nonlinearity (current dependency) of the battery resistance is investigated extensively. It varies slightly with the SoC and considerably with the temperature, and it also changes during the battery lifetime. Furthermore, the dependency of the lithium-ion battery impedance on the short-time previous history is shown for the first time for a new and aged cell. The influence of the measured dependencies of the battery impedance on potential applications is discussed.