Range-extended electric vehicles (REEVs) are becoming a development trend of new vehicles. Energy management is one of the core problems in REEVs. The structure and control method of the auxiliary power unit (APU) is determined based on the configuration analysis in this paper. An energy management optimization problem is proposed to solve the power distributions of APUs and batteries in the charge-sustaining (CS) stage of REEVs, which are determined by dynamic programming and pseudo-spectral optimal control, respectively. The results show that different limits of the APU power changing rate significantly influence fuel consumption. To obtain the power changing rate of APUs and to evaluate the energy management optimization method of REEVs, a model of the APU control system is built and verified by a platform test; the dynamic response characteristics and control parameters of the APU are obtained by step-changing conditions. Two types of strategies for tracking APU power are proposed for different power changing rates, and the fuel consumption of REEVs is analyzed in four types of driving cycles. The effect on fuel consumption caused by the power changing rate of the APU is verified.