Unified State-Space Modelling of EV Powertrain Dynamics Integrating Thevenin Battery and PMSM Subsystem

This study presents a unified state-space model of an electric vehicle (EV) powertrain that explicitly captures the dynamic coupling between electrochemical battery behaviour, energy depletion, and electromechanical drivetrain dynamics. A Thevenin battery model, augmented with a State-of-Charge (SOC) state, is algebraically combined with a Permanent Magnet Synchronous Motor (PMSM) drivetrain to form a single fourth-order linear timeinvariant system, eliminating algebraic loops and enabling system-level eigenstructure analysis. Beyond subsystem integration, the proposed formulation reveals how battery internal dynamics introduce additional slow modes that reshape the damping and transient response of the drivetrain, even in open-loop operation. Eigenvalue analysis and time-domain simulations demonstrate that battery parameters and energy dynamics directly influence motor current overshoot, voltage sag, and long-term energy behaviour during load disturbances and regenerative operation. The results show that battery dynamics are not passive energy elements but active contributors to EV powertrain behaviour, highlighting the necessity of unified modelling for accurate transient analysis and for future motor control and battery management system co-design.