In response to the challenges posed by the low energy utilization of single-power pure electric vehicles and the limited lifespan of power batteries, this study focuses on the development of a compound power system. This study constructs a composite power system, analyzes the coupling characteristics of multiple systems, and investigates the energy management and optimal control mechanisms. Firstly, a power transmission scheme is designed for a hybrid electric vehicle. Then, a multi-state model is established to assess the electric vehicle’s performance under complex working conditions and explore how these conditions impact system coupling. Next, load power is redistributed using the Haar wavelet theory. The super capacitor is employed to stabilize chaotic and transient components in the required power, with low-frequency components serving as input variables for the controller. Further, power distribution is determined through the application of fuzzy logic theory. Input parameters include the system’s power requirements, power battery status, and super capacitor state of charge. The result is the output of a composite power supply distribution factor. To fully exploit the composite power supply’s potential and optimize the overall system performance, a global optimization control strategy using the dynamic programming algorithm is explored. The optimization objective is to minimize power loss within the composite power system, and the optimal control is calculated through interpolation using the interp function. Finally, a comparative simulation experiment is conducted under UDDS cycle conditions. The results show that the composite power system improved the battery discharge efficiency and reduced the number of discharge cycles and discharge current of the power battery. Under the cyclic working condition of 1369 s, the state of charge of the power battery in the hybrid power system decreases from 0.9 to 0.69, representing a 12.5% increase compared to the single power system. The peak current of the power battery in the hybrid power system decreases by approximately 20 A compared with that in the single power system. Based on dynamic programming optimization, the state of charge of the power battery decreases from 0.9 to 0.724. Compared with that of the single power system, the power consumption of the proposed system increases by 25%, that of the hybrid power fuzzy control system increases by 14.2%, and that of the vehicle decreases by 14.7% after dynamic programming optimization. The multimode energy shunt relationship is solved through efficient and reasonable energy management and optimization strategies. The performance and advantages of the composite energy storage system are fully utilized. This approach provides a new idea for the energy storage scheme of new energy vehicles.