Multi-objective optimization design and performance evaluation for plug-in hybrid electric vehicle powertrains

Highlights

• Different PHEV powertrain configurations are comparative analyzed.

• Configuration-sizing-control integrated multi-objective optimization is developed.

• PHEV powertrain configuration evaluation methodology is proposed.

• Pareto optimal selection of PHEV powertrain configuration is provide.

Abstract

This study provides an optimal selection methodology for plug-in hybrid electric vehicle (PHEV) powertrain configuration by means of optimization and comprehensive evaluation of powertrain design schemes. The challenge of this study is to reveal each powertrain configuration performance potential in different situations of object trade-off and solve the control-physical integrated optimization problem of the PHEV powertrain design. To determine performance potential, a configuration-sizing-control strategy integrated multi-objective powertrain optimization design is proposed and applied to series, parallel pre-transmission (P2), output power-split, and multi-mode power-split powertrain configurations. Firstly, considering simultaneous optimization of fuel economy, electric energy consumption, and acceleration capacity, the parameters of the powertrain components and vehicle performance of each configuration are optimized based on global optimal control in different situations of object trade-off. Then, the Pareto optimal selection of powertrain configuration and its corresponding optimal component parameters are obtained by performance comparison and non-domination sorting. The results suggest that the P2 configuration and its optimal sizing can be selected when the goal is to optimize acceleration capacity, the multi-mode power-split configuration and its optimal sizing can be selected when the goal is to optimize electric energy efficiency, and the output power-split configuration and its optimal sizing can be selected when the fuel economy needs to be optimized.

Introduction

As an important solution to the more strict regulations on fuel economy and pollutant emission [1], [2], [3], [4], vehicle powertrain electrification has received considerable attention from researchers and engineers. Compared with pure electric vehicles (PEVs), hybrid electric vehicles (HEVs) can be propelled by energy from either the battery or fuel. This implies that there is no range constraint due to battery capacity. Thus, HEVs have proven to be the most available powertrain alternative [5], [6], [7]. Due to the adoption of the external charger, plug-in hybrid electric vehicles (PHEVs) can utilize grid electric energy, which is a significant fuel replacement, making the PHEVs the dominant choice for new HEV development [8], [9], [10], [11]. Although PHEVs have distinct advantages, realizing their improved or optimal performance through elaborate design is not a trivial task owing to the adoption of more complex powertrain configurations and control.

Immediate performance improvement can be achieved by means of control strategy modification. It was verified that significant fuel savings could be achieved by employing optimal control strategies designed by dynamic programming (DP) [12], [13], Pontryagin’s minimum principle (PMP) [14], [15], and convex programming (CP) [16], [17], [18]. Moreover, powertrain control algorithms considering different driving conditions (urban, extra-urban, and off-road) was also developed [19]. However, the physical characteristics of the powertrain, in terms of power flow, power coupling, and transmission patterns, cannot be changed by control strategies. To further enhance fuel economy, the sizing of the powertrain components was optimized [20], [21]. From studies in [21], it is clear that control strategies directly influence powertrain performance, while the powertrain physical system determines the feasible domain of control variables. However, a powertrain physical system is constructed with various components, and the powertrain configuration determines the powertrain component selection and connection scheme, which is a more important and complex issue for powertrain physical system design, more so than powertrain sizing. A reasonable methodology for selection of powertrain configurations must be developed to complete the powertrain physical system optimization design.

The performance of a powertrain can be greatly influenced by the configuration. It was observed that slight changes in the connection of planetary gear set nodes (ring gear, sun gear, and carrier) could result in apparent fuel economy improvement [22]. Furthermore, by enumerating all possible connections between planetary gear nodes, an exhaustive search and filter methodology was proposed for multi-mode power-split HEV powertrain optimal design [23], [24]. Besides, fuel economy variations were observed when changes were made in the power coupling pattern and motor position in parallel configuration HEV powertrain [25]. In addition, powertrain configuration selection may vary according to different vehicle mass or loading conditions [26]. Although the optimal control strategy was applied in [22], [23], [24], [25], [26], the proposed powertrain configuration optimization and evaluation methodologies ignored component sizing. The optimal sizing results demonstrated that different configurations of power-split HEV powertrains possessed different component parameter selection preferences [27], [28]. However, power plant (engine, motor/generators) parameters were not included in the analyses [27], [28], which essentially changed the full-load profile and feasible working domain, rather than transforming the working points by gear ratio. As a summary of the studies described above, in order to make a proper powertrain configuration design, the configuration selection should be based on the optimal performance of each configuration, which should be evaluated considering component parameters, and control strategies should be integrated according to the configuration. For PHEV powertrains, as the utilization of electric energy increases, the excellent designs of non-plug-in HEV powertrains may not result in brilliant fuel economy performance [29], [30], as the part of the PHEV powertrain that experiences major energy loss gradually switches from the engine to the electric drive system. Powertrain configuration optimization design considering different structural features is needed but has not been extensively studied. Instead of only focusing on the planetary gear power-split configuration mentioned above, a comparison of fuel economy between general configurations (for example, the series and parallel configurations) should be conducted in order to identify more fuel-saving powertrain designs, especially for PHEVs.

Although most studies have focused on fuel economy, there are other concerns associated with powertrains that result in a multi-objective optimization problem (MOOP), such as acceleration capacity [31], [32], battery capacity degradation [33], and system construction cost [34]. To fully utilize the powertrain configuration and component working capacity, simultaneous optimization of all the objects with a certain trade-off is commonly desired. However, objects do not always respond consistently to the same change in a design variable, and there are a set of non-dominated solutions, namely the Pareto optimal solutions, that are based on the different situations of object trade-off [35], [36], [37], [38]. It is impossible to take the interaction between the objects into consideration in a single-objective optimization problem (SOOP). It was demonstrated that the fuel economy and acceleration capacity had conflicting performances in terms of final drive gear ratio design for single planetary gear set power-split powertrains, and through the multi-objective optimization of the two ratios, some configurations of the single planetary gear set power-split powertrain still existed that possessed almost the same fuel economy but better acceleration performance than the benchmark powertrain [31], [32]. Considering multiple design objectives, different powertrain configuration schemes may possess special advantage in a certain design objective or performance. This special advantage of a powertrain configuration should be captured in optimization design results. In addition, objects of HEV powertrains with conflicting performances may also be compromised by operation mode synthesis and operation mode selection control, for example, pure electric launch and engine-only cruise. The effect of different situations of design objects trade-off on control strategy should still be included in the optimization methodology.

As a summary of the entire literature review, to complete the optimization design methodology of powertrains, configuration, component parameters, and control strategy design should be taken into account and solved integrated. However, for current state-of-the-art, there is still a large shortage of PHEV powertrain optimization methodologies. Firstly, it is challenging to reveal and evaluate the optimal performance of different configurations in a systematic way. Due to the limited optimal performance evaluations of power-split and general configurations, a guarantee of optimality focusing on power-split configuration only does not exist. Secondly, there is still the open question for us to select an optimal design scheme according to different situations of design object trade-off.

From the perspective of the comprehensive performance of a PHEV, in this study, a configuration-sizing-control integrated multi-objective optimization to simultaneously optimize the fuel consumption in the charge sustain (CS) driving process, acceleration capacity, and electric energy consumption within the full electric driving condition was proposed and applied to PHEV powertrains with different configurations. In order to fully exploit the PHEV powertrain inherited multi-mode operation capacity, the mode decision was integrated into the control strategy for all simulation analyses. Furthermore, the motor parameters, namely maximum torque and maximum speed were also considered in the optimization. In this manner, instead of considering final drive gear and planetary gear set ratios, the contribution of motor parameters in terms of object performance can be examined.

This study makes three main contributions: (1) optimal performance evaluations of power-split and general configurations were conducted; (2) for each configuration, the extreme performance in each design object under the constraint of other design objects was obtained based on optimal powertrain sizing and optimal control strategies; and (3) the Pareto optimal selection of powertrain configuration and its corresponding optimal sizing were obtained by performance evaluation and non-domination sorting to adapt to different situations of object trade-off.

The remainder of the paper is organized as follows. Section 2 depicts the powertrain configurations with their corresponding mathematical models. Section 3 presents optimal control strategies based on DP. Section 4 illustrates the integrated multi-objective optimization scheme. Optimal results and performance comparison are discussed in Section 5. Finally, the conclusions are summarized in Section 6.