State of power (SOP) reflects the peak power capability of a lithium-ion battery (LIB). Constant power (CP) operation (e.g., discharge or charge) is more representative of actual battery loadings in electric vehicle (EV) applications (e.g., EV acceleration, gradient climbing and regenerative braking) than constant current or constant voltage operation. However, relevant research on CP-based SOP estimation for LIBs in EVs is still rare. In this article, a novel model switching-based iterative algorithm is proposed for multi-constraint SOP estimation under a CP operation scenario. Two state-space models with implicit representations are constructed to describe the indirect relationships between a given CP over a prediction window and the maximum look-ahead current/voltage at the end of this window. An unscented Kalman filter-based correction strategy is applied to determine the dominant limitation factor so as to pinpoint battery SOP in high fidelity. Moreover, a SOP testing approach is designed to calibrate reference SOPs in high precision for validations. Experimental results have demonstrated that the proposed method achieves promising accuracy with a mean absolute error of less than 0.26 W under both static and dynamic conditions.