<p>Trajectory smoothing for connected and autonomous vehicles (CAVs) offers opportunities to improve traffic efficiency and reduce energy consumption, especially at intersections. Most previous studies in this research area only considered trajectory smoothing for a single CAV or assumed a homogenous CAV platoon. This paper proposes a trajectory-smoothing method for power-heterogeneous CAV platoons at signalized intersections. A Distributed Model Predictive Control (DMPC) algorithm was used to maintain a constant time headway for power-heterogeneous CAVs, considering the differences in capabilities between electric- and fuel-powered vehicles in terms of the inertial time lag to minimize speed fluctuations within the platoon. Additionally, a trajectory smoothing method was proposed that used CAV platoons as the minimum control unit, thus enabling well-formed platoons to pass through signalized intersections without stopping. Simulation experiments on the SUMO platform validated the effectiveness of the proposed methods compared to benchmark cases without trajectory smoothing for CAV platoons. This strategy can improve the traffic efficiency by reducing the total delay and waiting time, especially with high traffic demand. The results also indicate that this method can lead to substantial energy savings, highlighting the potential of advanced CAV technologies to contribute to more sustainable urban transportation systems.</p>