## 1 Introduction  
With the increasingly stringent emission and fuel consumption regulations, major automobile manufacturers have stepped up the research and development of hybrid electric vehicle (HEV), which is a key technology for energy saving and emission reduction. Compared with a conventional fuel vehicle, the HEV can adopt electric energy to replace fossil fuels wholly or partially for driving when the engine is in the condition of low efficiency and high fuel consumption, which can improve fuel economy and reduce emissions [1; 2; 3]. In recent years, the HEV market has been dominated by the power-split hybrid electric vehicle with the function of an electric continuously variable transmission (ECVT) [4; 5]. Both Toyota Hybrid System (THS) and GM (General Motors Corporation) Advanced Hybrid System (AHS) adopt the power-split hybrid powertrain configuration scheme [6; 7; 8; 9]. By introducing clutch to change the way of combination and connection between PG nodes and power resource components, the power-split hybrid powertrain configuration possesses multiple operating modes, which greatly increases the probability of high-efficient operation for the vehicle. Therefore, the multi-mode power-split hybrid powertrain configuration based on planetary gear (PG) has enormous potential in improving fuel economy [10; 11]. However, the flexible combination and connection of PG lead to a large number of configuration candidates, which make it difficult to simultaneously express the topology and functional characteristics and judge the feasibility and applicability of configurations. Therefore, it is a challenging task to search out excellent configurations in a large number of configuration candidates [12]. To overcome this issue, many scholars have carried out relevant research on the optimization of and screening for configuration schemes. [PERSON] et al. optimized the all power-split configuration with single PG (PSC-1 PG) by applying the lever method [13]. Similarly, [PERSON] et al. screened the PSC-1 PG by adopting the method of increasing/decreasing clutch, and optimized the parameters of components [14]. Literatures [13; 14] mainly use the simple model of lever mechanics to replace complex and changeable PG systems, which can intuitively express the connection between PG and power resource components. However, the lever method mainly extracts the dynamic equation of configuration by a manual approach. Therefore, it is almost impossible to employ the lever method to seriatim analyze the complex multi-PG configuration and obtain the optimal configuration. In view of this issue, literature [15] proposed a general matrix search method based on the internal connection relationship of PG and the state sequence of clutch. By employing this method, the power-split configuration with dual PGs (PSC-2 PG) was searched completely, and the PSC-2 PG with greater advantages in fuel economy was obtained. On the basis of literature [15], [PERSON] et al. added the acceleration constraints to the above search method, searched the power-split configuration with three PGs (PSC-3 PG) with the optimization objectives of fuel economy and dynamic performance, and pointed out that compared with the PSC-2 PG, the PSC-3 PG has an obvious advantage only in traction performance [16]. Therefore, in hybrid powertrain configuration based on PG, the introduction of dual PGs can maximize the improvement potential of configuration in fuel economy and other performances. Based on the idea of mode combination and superposition in the search process of configuration, literatures [15; 16] provide a variety of operating modes for the hybrid powertrain configuration with multi-PG, which increases the probability of high-efficient operation for the vehicle. However, due to the discrete characteristics of the state sequence of clutch, it is necessary to seriatim analyze and classify the operating modes in the search process. In addition, literature [17] optimized the hybrid powertrain configuration by adopting a bond graph.