1. Introduction

2. Digital Twin Powertrain System Framework

3. Technical Scheme of Digital Twin Test Bench

Figure 2. Schematic diagram of the multi-cabinet intermodulation program.

Figure 2. Schematic diagram of the multi-cabinet intermodulation program.

Figure 3. Schematic diagram of DT bench technology scheme.

Figure 3. Schematic diagram of DT bench technology scheme.

4. Testing Platform for Sandian Digital Twin System

4.2. Software Modelling

The software component of the digital twin testing platform is primarily responsible for translating the computational logic and intrinsic relationships between the signals of various controllers into unified mathematical expression models for testing purposes [22]. This section discusses typical components of the three-in-one system: the vehicle paramodel, motor paramodel, and battery paramodel. According to the project database, the vehicle characteristics are summarized in Table 2.

4.2.1. Vehicle Longitudinal Dynamics Para Model

The vehicle longitudinal dynamics model plays a critical role in automotive engineering by simulating the dynamic behavior of the vehicle under various driving conditions, particularly during acceleration and braking, thus assisting engineers in analyzing vehicle handling and safety [23]. According to automotive theory:

$${\mathrm{F}}_{\mathrm{t}}={\mathrm{F}}_{\mathrm{f}}+{\mathrm{F}}_{\mathrm{w}}+{\mathrm{F}}_{\mathrm{i}}+{\mathrm{F}}_{\mathrm{a}}$$

(1)

where Ft is the driving force of the whole vehicle; Ff is the rolling friction resistance; Fw is the air resistance when the vehicle is travelling; Fi is the ramp resistance of the vehicle on an uneven road; and Fa is the resistance due to acceleration of the vehicle.

$${\mathrm{F}}_{\mathrm{t}}=\mathrm{mgf}\cos \beta +0.5{\mathsf{\rho }\mathrm{AC}}_{\mathrm{d}}{\mathrm{V}}^2+\mathrm{mgf}\sin \beta +\mathsf{\delta }\mathrm{m}{\displaystyle \frac{\mathrm{dv}}{\mathrm{dt}}}$$

(2)

where $\beta$ is the road slope; m is the vehicle’s overall mass, g is the gravitational acceleration; ρ is the air density at room temperature; and δ is the vehicle’s rotational mass factor.

4.2.2. Vehicle Controller Unit Para Model

In the Sandian simulation testing, the vehicle controller VCU simulation model typically consists of several key components, each playing a crucial role in ensuring the system meets the expected performance and functionality [24]. The main functions of the VCU model components are as follows:

Sensor Simulation Module: This module is responsible for simulating the input signals from various sensors within the vehicle system, such as speed and steering sensors. It provides real-time environmental data and ensures coordination between the sensors and the VCU.Actuator Simulation Module: This module simulates the actuators of the vehicle’s powertrain, such as the engine and brake actuators. It receives control commands from the VCU and simulates the actual behavior of these actuators. Communication Interface Module: This module simulates the communication process between the VCU and other vehicle systems, including the reception of sensor data and the transmission of control commands. It ensures normal communication between the VCU and the entire vehicle system.

The VCU digital twin simulation model is constructed as illustrated in Figure 5.

By coordinating these components and implementing their functions, the VCU simulation model effectively simulates the behavior and performance of the entire vehicle system during HiL testing, thereby supporting system integration validation.

4.2.3. Motor Controller Unit Para Model

The main components and their functions of the MCU simulation model in the Sandian test are: a communication interface module to achieve data transmission, command exchange; a signal acquisition module to simulate the signal acquisition function in the MCU of the motor controller, including receiving feedback signals from sensors, such as speed, temperature, etc.; a control algorithm module to achieve speed control, torque control, position control, etc.; a PWM generator module to simulate PWM signal generation function for driving power semiconductor devices in the motor controller; a protection logic module: to achieve overcurrent protection, voltage protection, temperature protection, etc. of the controller to avoid damage to the controller. The PWM generation module simulates the PWM signal generation function, which is used to drive the power semiconductor devices in the motor controller; the Protection logic module: realises the controller’s over-current protection, over-voltage protection, over-temperature protection, etc., to avoid the controller from suffering from potential damages [25].

The primary parameters of the motor model are determined by the slope of the operating environment, the vehicle’s mass, and the transmission efficiency of the power system [26], as expressed by Equation:

$${\mathrm{T}}_{\mathrm{m}}={\displaystyle \frac{\mathrm{mgfcos}\left(\mathrm{arctg}\right(\mathrm{grade}/100\left)\right)\mathrm{r}}{{\mathrm{i}}_0\mathsf{\eta }}}+{\displaystyle \frac{\mathrm{mgsin}\left(\mathrm{arctg}\right(\mathrm{grade}/100\left)\right)\mathrm{r}}{{\mathrm{i}}_0\mathsf{\eta }}}$$

(3)

where: Tm is the peak torque of the motor; grade is the climbing parameter set for the vehicle; i0 is the powertrain transmission ratio; $\mathsf{\eta }$ is the system efficiency.

The voltage equation of the permanent magnet motor based on rotor field orientation is obtained as follows:

$$\left\{\begin{array}{l}{u}_d=R_s{i}_d+L_d{\displaystyle \frac{d{i}_d}{dt}}-{\omega }_r{L}_q{i}_q\\ u_q=R_s{i}_q+L_q{\displaystyle \frac{d{i}_q}{dt}}+{\omega }_r(L_d{i}_d+{\psi }_f)\end{array}\right.$$

(4)

where Rs, Ld, and Lq are the stator winding resistance, stator d-axis inductance, and stator q-axis inductance. Ψf is the magnetic chain of permanent magnets. ωr is the rotor electric angular velocity; id and iq are the d-axis and q-axis currents; and ud and uq are the d-axis and q-axis voltages, respectively.

The motor torque formula is given by:

(5)

where p is the number of motor pole pairs.

Accordingly, the MCU digital twin simulation model is built as shown below.

Figure 6. The simulation pare model of MCU.

Figure 6. The simulation pare model of MCU.

4.2.4. Battery Management System Para Model

The main components and their functions of the battery management system simulation model in the hardware-in-the-loop test are listed: the communication interface module is responsible for simulating the communication process between the battery controller BMS and other vehicle systems; the data acquisition module realises the collection and monitoring of battery parameters such as voltage, current, temperature, etc.; the state estimation module simulates the state estimation algorithms in the battery controller BMS, which is used to estimate the battery’s residual capacity and health status, etc.; the protection control module simulates the protection functions in the battery controller BMS, including over-capacity protection, over-discharge protection, short-term protection, etc. information; the protection control module simulates the protection functions in the battery controller BMS, including overcharge protection, over-discharge protection, short circuit protection, etc. [27].

The model of the battery addresses the mathematical relationship between the state of charge SOC of the battery and the characteristic parameters of the battery [28]. This is shown in the following equation:

$$\mathrm{SOC}={\mathrm{SOC}}_{\mathrm{int}}-{\displaystyle \frac{1}{\mathrm{Q}}}\eta {\displaystyle \int {\mathrm{I}}_{\mathrm{t}}}\mathrm{dt}$$

(6)

$${\mathrm{I}}_{\mathrm{t}}={\displaystyle \frac{（{\mathrm{U}}_{\mathrm{t}}-\sqrt{{{\mathrm{U}}_{\mathrm{t}}}^2-4{\mathrm{R}}_{\mathrm{t}}{\mathrm{P}}_{\mathrm{bat}}}）}{2{\mathrm{R}}_{\mathrm{t}}}}$$

(7)

In these equations, SOC_int is the initial state of charge; η is the Coulombic efficiency of the battery; Q is the capacity of the battery. U_t is the open-circuit voltage of the battery; R_t is the internal resistance of the battery; and P_bat is the output power of the battery.

The BMS digital twin simulation model is constructed as illustrated in the following figure.

Figure 7. The simulation para model of BMS.

Figure 7. The simulation para model of BMS.

5. Test Case Design of Sandian Platform

6. Test Results

Figure 8. The physical drawing of the powertrain digital twin bench.

Figure 8. The physical drawing of the powertrain digital twin bench.

6.1. Functional Simulation Test

In the 13 sub-projects of the functional test, they all follow the five major steps of initialisation, power detection, start-up process, charge/discharge status, and test completion.

Figure 9. Logical flow diagram of functional testing for the real vehicle.

Figure 9. Logical flow diagram of functional testing for the real vehicle.

Based on the principles of multi-controller participation, typical power up/down conditions of the powertrain system are tested using the digital twin platform.

Figure 10. Key signal timing diagram of power Up/Down conditions.

Figure 10. Key signal timing diagram of power Up/Down conditions.

As shown in the figure, during the power-up process of the powertrain system, the status flag signals of the BMS and MCU, specifically BMS_BattReadySts and RMCUWorkingModSts, transition from their initial default states (1 and 5, respectively) to the high-voltage standby state (0) at the 3.5-second mark. After 1.8 seconds in the high-voltage standby state, the BMS indicates the statuses of the main negative relay (BMS_BattRelay_Neg) and main positive relay (BMS_BattRelay_Pos), which switch from open (0) to closed (1), marking the completion of high-voltage power supply to the system. Once the VCU confirms the high-voltage power supply completion feedback from the BMS and MCU, it issues a command (VCU_HV_PowerOnSts = 1), which changes the motor status signal (RMCUWorkingModSts) from the high-voltage standby state (value 1) to the operational state (value 2). Subsequently, provided that there are no faults in the feedback from each controller, the VCU transitions the powertrain system to the ready state (VCU_PowertrainReady = 1).

At the power-down moment, the powertrain system first changes from the ready state to power down (VCU_PowertrainReady = 0). Then, at the 22-second mark, the VCU issues a high-voltage power down command (VCU_HV_PowerOnSts = 0), resulting in the disconnection of the main positive and negative relays of the battery. The status flag signals of the BMS and MCU (BMS_BattReadySts and RMCUWorkingModSts) revert to their initial default states. The three-electric testing platform successfully completes the testing of power up/down conditions.

Figure 11. Key signal timing diagram of driving and braking conditions.

Figure 11. Key signal timing diagram of driving and braking conditions.

The above diagram illustrates the signal timing for the driving and braking conditions of the powertrain system. As seen in the figure, at the 11-second mark, when the VCU-related signals indicate that the accelerator pedal position (VCU_AccelPedalPosition = 0) and brake pedal switch (VCU_BrakePedalSts = 0) are released, the vehicle begins to accelerate due to the creep functionality, causing the vehicle speed signal (VCU_VehSpd) to gradually increase. At the 13-second and 15.5-second marks, the driver operates the accelerator pedal position, increasing it from 0 to 10% and then to 20%. Consequently, the torque feedback from the MCU (RMCU_ActTorq) begins to increase non-linearly, with the BMS working current (BMS_HV_BattCurr) peaking at 60A.

At the 27.8-second mark in the figure, the driver depresses the brake pedal, resulting in (VCU_BrakePedalSts = 1). The vehicle speed signal (VCU_VehSpd) decreases from 42 km/h as the system initiates energy recovery, with the MCU feedback torque (RMCU_ActTorq) becoming negative and outputting negative torque. The BMS working current (BMS_HV_BattCurr) also becomes negative, with a peak negative value of -46A, ultimately reducing the vehicle speed to zero. Thus, the testing of the driving and braking conditions of the three-electric system is completed.

In summary, the recorded parameters from the above tests indicate that the functional logic processes of the digital twin simulation technology and the actual vehicle testing align effectively, demonstrating the validity of the digital twin model. Multiple condition parameters are set as required, enhancing the efficiency of functional testing.

6.2. Functional Requirements Test Cases Design

To achieve comprehensive testing of the powertrain system within the scope of fault injection, it is necessary to inject signals that surpass predefined system setpoints. By observing the responses of various controllers to these disturbances, the fault response mechanisms of the powertrain system can be evaluated. However, during actual vehicle testing, the voltage levels at which the drive motor and battery pack operate normally range from 320 to 425 V, significantly exceeding the human safety voltage range of 0 to 36 V. Executing such test cases on actual vehicles poses uncertainties, such as high voltage leakage, which could endanger the safety of testing personnel.

As a result, this chapter employs a digital twin testing platform to execute the test cases, injecting over-voltage faults into the motor bus voltage during the execution of environmental test cases. The variations in the test result signals are illustrated in the following figure.

As shown in the figure, when the driver presses the accelerator pedal (VCU_AccelPedalPosition = 10), the vehicle speed signal (VCU_VehSpd) begins to increase from zero. At the 36.6-second mark, the software ControlDesk is used to forcibly alter the MCU bus voltage signal (RMCU_HV_DClinkVolt) from the normal range of 375 V to an abnormal range of 525 V. This action prompts the MCU to report a level 8 fault at the 39.1-second mark (RMCU_SystemFault_Level_8 = 1). Consequently, the VCU_Fault_Level_8 also transitions to 1, causing the system to command the vehicle to decelerate to zero. The BMS working current (BMS_HV_BattCurr) gradually decreases to zero. The changes in signal behavior align with the predefined fault response mechanisms.

Figure 12. Key signals Timing diagram of typical fault injection working condition.

Figure 12. Key signals Timing diagram of typical fault injection working condition.

7. Conclusions

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