Compound power-split configurations exhibit better fuel consumption than input and output power split configurations. However, there is a need to understand how to design the best compound power split configuration. In this paper, potential compound power-split configurations with two planetary gear sets are explored. Based on the planetary connection, there are 18 possible compound power-split configurations, but only 17 of those are applicable because of the lever length limitation. According to one-dimensional Equivalent Consumption Minimization Strategy and battery degradation model, the impact of compound power-split configuration design and control on fuel consumption and battery degradation are investigated. The results show the one-dimensional Equivalent Consumption Minimization Strategy based on Direct Transmit Points can further decrease the fuel consumption and battery degradation in compound power-split configurations. Similarly, the design parameters with lever length beta close to -0.5 and lever length alpha close to -1.5 also lead to fuel consumption and battery degradation decreasing. The advantage of fuel consumption is observed because the system efficiency operation points are closer to the maximum efficiency line in optimized compound power-split design and control. Moreover, the compound power-split configuration can further decrease battery degradation in optimized design and control is because the current through the battery is less. (C) 2018 Elsevier Ltd. All rights reserved.