Lithium-ion cells, especially when used in electric vehicles at varying operation conditions, require a sophisticated battery management to ensure an optimal operation regarding operation limits, performance, and maximum lifetime. In some cases, the best trade-off between these conflictive goals can only be reached by considering internal, non-measurable cell characteristics. This article presents a data-driven model-reduction method for a strict electrochemical model. The model describes the charging process of a lithium-ion cell and possibly occurring degradation effects in a large temperature range and is presented in Part I of this contribution. The model-reduction process is explained in detail, and the gained model is compared to the original electrochemical model showing a very high approximation quality. This reduced model offers a very low computation complexity and is therefore suitable for the implementation in a battery management system (BMS). Based on this model, an advanced charging strategy is presented and evaluated for possible reductions in charging times especially at low temperatures.