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The number of fluctuating energy sources in the power grid increases continuously. Simultaneously the importance of electrical energy storage increases. Batteries are one promising possibility for short-term storage. In this work a mathematical impedance model of a Lithium-ion battery with high dynamics for simulation of loads due to driving cycles and battery-to-grid applications as well as parameterization and validation of the model are presented. The model approach is based on an equivalent circuit. Parameterization of the model is done at many different operating points to assess the dependencies of the parameters on different battery states and model inputs. Both for high dynamic impacts and static periods simulation of terminal voltage shows good results in the considered operational range. The model is real time capable and suitable for robust control. Hence a useful tool for battery-to-grid and electric mobility applications is introduced.