Advanced battery management systems rely on mathematical models to guarantee optimal functioning of Lithium-ion batteries. The Pseudo-Two Dimensional (P2D) model is a very detailed electrochemical model suitable for simulations. On the other side, its complexity prevents its usage in control and state estimation. Therefore, it is more appropriate the use of simplified electrochemical models such as the Single Particle Model with electrolyte dynamics (SPMe), which exhibits good adherence to real data when suitably calibrated. This work focuses on a Fisher-based optimal experimental design for identifying the SPMe parameters. The proposed approach relies on a nonlinear optimization to minimize the covariance parameters matrix. At first, the parameters are estimated by considering the SPMe as the real plant. Subsequently, a more realistic scenario is considered where the P2D model is used to reproduce a real battery behavior. Results show the effectiveness of the optimal experimental design when compared to standard strategies.