Electric Vehicle Powertrain Architecture and Control Global Optimization

The design of a full electric vehicle (or battery electric vehicle (BEV)) requires the development and optimization of a complete electric powertrain, including battery, power electronics, electric machine, sensors and control system.When designing an electrical platform, from the very beginning of the V-cycle, it is mandatory to rely on modelling and simulation tools in order to drive the main choices and then to optimize the system. This paper presents an electric powertrain simulation platform developed with Matlab-Simulink, dedicated to multiphysic optimization of the system.As an example, the basic electrical powertrain architecture first considered in this paper includes a battery, an inverter, a dc-dc buck converter supplying motor inductor and a wound rotor synchronous machine (WRSM). The purpose is to show how simulation tools can help in comparing different powertrain control strategies.The present simulation platform is also useful to study physics architecture. To illustrate this point, another electrical architecture is also presented, including a dc-dc boost converter between battery and inverter. This structure must be considered here as an example only in order to show how to optimize control laws taking into account various criteria, including architecture ones. Simulation results are compared for both architectures in terms of powertrain performances and range.


Introduction
When designing an electrical platform, from the very beginning of the V-cycle, it is mandatory to rely on modeling and simulation tools in order to drive the main choices and then to optimize the system. The paper is organised as follows. The section 2 presents an electrical powertrain simulation platform developed with Matlab-Simulink. Main models and equations are described in order to introduce different optimization strategies with criteria on performances and on powertrain losses in section 3. Optimization is performed with a powertrain architecture with three degrees of freedom. As the aim is to expose methodologies and to show typical results, the results presented in this paper are related to typical study cases, and not to an industrial one. Section 4 presents an architecture optimization introducing a fourth degree of freedom, specially used when battery is partially discharged. Finally, we draw concluding remarks in section 5.

Simulation Platform of an
Electric Vehicle Powertrain

Power system
An electric powertrain is a closed-loop system, mainly constituted by battery, converters, motor and control structure (Fig.1). High-voltage battery has to supply with energy not only traction motor, but also high power loads like air-conditioning or heating as well as the low-voltage network.

Simulation platform
The powertrain simulation platform used for optimization includes the following models ( Fig.2

) [1] [2]:
• A dynamic battery model • Two three-phase AC-DC converter models supplying WRSM stator: one model for fast transients including switch models and one model for quasi-static transients (first harmonic only) with voltage and current average signals. These models make it possible to simulate fast phenomena over short times (dynamic behaviour of the powertrain) and driving cycles lasting many minutes (e.g. NEDC) as it is explained at the end of this section. • Two dc-dc converter models supplying WRSM rotor (fast transient / quasi-static transient). • A WRSM model with consideration of magnetic saturation, using Park (d,q) transformation. • Sensor models (currents, rotor position …). The first category implements analytical expressions of losses, range, cost, etc. used in a global approach, for example for the synthesis of control laws. The second category deals with "average" models dedicated to driving cycle simulations (e.g. NEDC) on wider time horizons. Finally, the third category deals with short time switching and fast variation of currents, voltages, torque, etc. For example, it is possible to observe electric resonances on the network and torque oscillations on the drive shaft.
In order to understand powertrain control methods presented in section 3, it is important to detail converters and motor models.

Electric motor model
The three-phase Motor considered in this paper is a Wound Rotor Synchronous Machine (WRSM), represented in Park coordinate (a,b,c) → (d,q). Indeed, WRSM presents more degrees of freedom than Permanent Magnet Machine, as it will be explained in section 3.1. It is why it has been chosen for the work described in this paper. However, the methodology is quite versatile and can also be applied to any other type of motor (Permanent Magnet, Induction, etc.) Motor notations and symbols: Magnetic saturations are taken into account: depend on stator and rotor currents through non-linear complex equations. Each inductance parameter is function of three To determine these relations, we use steady-state maps of magnetic fields To include magnetic saturation in Park equations, we proceed as follows: • a map of ( ) The methodology is the same for rotor field In addition to electrical equations, the mechanical part can be modelled by the following equation To determine l C expression, we solve the following equation with steady state relations:

Three-phase inverter
The inverter converts DC-voltage from battery to AC-voltage in order to supply stator of electric motor. This converter is made of six switches. Our model considers simplified IGBT/diode switches (Fig.4). To simulate complete driving cycles, we use a slow-transient model of inverter (or "first harmonic" model). Inputs are three-phased voltage references, AC current and DC voltage. Outputs are AC voltage and DC current. To take into account converter losses, output DC current is modified according to losses map inside Simulink model.

DC-DC converters
A classical buck converter is used between highvoltage battery and machine rotor. Both fasttransient and slow-transient models are realized in the same way as AC-DC converter.   Two control strategies with criteria on performances ("torque maximization strategy") and range ("losses minimization strategy") are explained and compared in following sections.

Torque maximization
In a first time, we consider motor inductance parameters as constant. According to torque equation ( . . To illustrate these results, we plot e C for different values of I (Fig.7). Optimal operating points corresponding to torque maximum values are represented with stars (see Figure 7).   Optimization problem: • cost function to minimize: • variables : We use a classical SQP (Successive Quadratic Procedure) to solve this optimization. Results are plotted on Figures 9 and 10.

Losses minimization
The difficulty of a losses minimization strategy depends on the chosen approach: • approach 1 : to use a fine and complex model of motor losses (e.g. through losses maps from tests). Advantage is a high correlation between tests and simulation results. Major drawback concerns optimization method complexity: when the cost function to minimize is not an explicit function of optimization variables, simple and fast gradient-based methods can not be applied.
More complex methods (such as heuristic algorithms) are required, with longer computation times.
• approach 2 : to use simplified losses model, with explicit expressions of optimization variables. There are two advantages of this approach : first, the use of fast optimization methods is possible; secondly, it allows studying losses variations with motor parameters. Drawback is advantage of first approach (classical compromise between precision and computation times).
Approach 2 is used in this paper. For that purpose, simplified losses expressions are required.
The cost function to minimize represents global losses in powertrain (apart from battery losses).
Converters losses: • Conduction losses: • Switching losses: (9) where the parameters are: • Core losses:  B  A  B  A  ,  ,  , coefficients for stator and rotor converters, we apply linear regression to data maps. These maps represent converters global losses and motor current measures according to torque and speed. Linear regression consists in approximating a linear equation Modelling error on converters losses is quasiinexistent. Concerning motor, in low torque area, there is up to 20% error, certainly due to losses simplified model (e.g. stray losses are neglected).
To achieve computation, we use as previously a SQP procedure.
To understand the importance of taking into account both losses in motor and converters for optimization (instead of motor losses only for example), we compare global efficiency with two control strategies (Fig.16) [11]: a. motor losses minimization (Fig.14 Efficiency gain does not exceed 5%. Indeed, in this study case, converter efficiency is much higher then motor efficiency. Figure 17 shows a global efficiency map obtained with torque maximization strategy (previously presented and frequently used in literature [6]). This strategy is compared with losses minimization strategy (Fig.18). Losses minimization strategy allows increasing efficiency, especially for low torques area, where a maximal rotor current is not necessary.

Architecture Optimization
When dealing with powertrain performances, it is mandatory to take into account the way battery voltage changes with respect to the state of charge. This voltage value has a direct impact on optimization. As well as global efficiency differences, we observe variations of operating points limit due to optimization constraints (Fig.20). Battery voltage has an impact on both efficiency and performances.

DC-DC Boost converter
The electrical architecture of the powertrain may have a great influence on battery voltage variations impact. For example, introducing a dc-dc converter between the battery and the inverter can change the behaviour of the system. The function of this converter is to stabilize as much as possible the inverter dc voltage whatever the battery state of charge is [12].
To study the efficiency of this architecture, a dc-dc boost converter model with IGBT has been integrated in the simulation platform (Fig. 21).

Low-level control with four degrees of freedom
With this new powertrain architecture, four degrees of freedom are now potentially available: currents as previously presented and dc-dc voltage reference. When optimizing powertrain control, output battery voltage constraints can thus be partly relaxed (especially when the battery state of charge is low). Figure 22 shows various results with and without dc/dc converter.

Conclusion
A platform for Electric Vehicle Powertrain has been presented in this paper. Battery, converters and traction motor are modelled with the intention of optimizing performances and powertrain efficiency (highly linked with vehicle range). Consequently, models are as much simplified as possible. Further, explicit formulations depending on degrees of freedom are preferred. In a second step, we have presented two powertrain control strategies resulting from a "software" optimization: we have used a classic electric powertrain architecture and shown how performances and efficiencies can be different depending on control laws. Finally, we have studied an example of "hardware" optimization by introducing an additional degree of freedom with a dc-dc boost converter between battery and inverter. Comparison results have been obtained with the simulation platform. This platform has proven its efficiency and has brought much than satisfactory results for the deep understanding of proposed optimized control laws and architectures.