###### Abstract  
The power-split architecture is the most promising hybrid electric powertrain. However, a real advantage in energy saving while maintaining high performance can be achieved only by the implementation of a proper energy management strategy. This requires an optimized functional design before and a comprehensive analysis of the powertrain losses after, which could be rather challenging owing to the constructive complexity of the power-split transmission, especially for multi-mode architecture with multiple planetary gearing. This difficulty was overcome by a dimensionless model, already available in the literature, that enables the analysis of any power-split transmission, even in full electric operation. This paper relies on this approach to find the operating points of the internal combustion engine and both electric machines which minimize the total power losses. This optimization is carried out for given vehicle speed and demanded torque, by supposing different scenarios in respect of the battery capability of providing or gathering power. The efficiency of the thermal engine and the electric machines is considered, as well as the transmission mechanical power losses. The aim is to provide a global efficiency map that can be exploited to extract data for the implementation of the most suitable real-time control strategy. As a case study, the procedure is applied to the multi-mode power-split system of the Chevrolet Volt. hybrid electric vehicles; power-split powertrain; global efficiency; multi-mode transmission; Voltec analysis 2021  
analysis, their calculation is far from trivial [18; 19; 20; 21]. Thus, mechanical power losses are considered in very simple one-PG transmission [22; 23] or evaluated by using simplified approaches that avoid the analysis of the transmission power flows [24; 25] or even more often neglected [26; 27; 28; 29; 30; 31; 32]. The focus of this paper is to provide the global efficiency map of the multi-mode Chevrolet Volt hybrid electric powertrain by assessing all powertrain losses, not only those occurring in the propulsors but also the transmission mechanical power losses. This can be achieved by applying a unified parametric model [33; 34; 35; 36] without convoluted or case-specific formulations. All the relationships of the model are ruled by few basic functional parameters which can be swiftly derived from any PS-CVT constructive arrangement, even multi-PG or multi-mode [34; 36]. These enable the calculation of speed, torque, and power ratios in real conditions, by using a fast black-box method [35; 36] to assess the PSU mechanical losses and then the actual power that the electric machines should provide to the PSU for given ICE power and required output. The whole procedure applies also to the FEV operation [36]. This unified parametric model was first applied to the transmission of the Chevrolet Volt in [34], where an alternative design was proposed but any power losses were neglected. Then, the mechanical losses occurring in the PSU were considered in the Chevrolet Volt dimensionless analysis carried out in [35]. This article aims to consider also the power losses occurring in the propulsors, by moving from the dimensionless variables to those expressed in physical units of measurement. In addition, the analysis of the Chevrolet Volt in FEV operation is presented for the first time. The utilization of dimensionless independent and dependent variables expressed as speeds, torques, or powers ratios results in utmost generality, which makes the model suitable for analyzing any PS-CVT. Nonetheless, the loss factors of the propulsors are strictly related to their operating point, therefore the brake specific fuel consumption (BSFC) map of the engine and the efficiency maps of the electric machines have to be introduced.