# Investigating Effects of Non-Idealities of Current Sensors and Powertrain on the Performance of an EV System using PLECS Simulation Software

## This article highlights Plexim Incorporated PLECS is a simulation tool developed for drives engineers for very efficient and robust modeling of such system.

*Drive system applications experience a significant coupling between the controls, electrical and mechanical domains. To fully understand the behavior of the entire electromechanical system, the characteristics of the individual domains and their effects on the overall system must be taken into account. PLECS is a simulation tool developed for drives engineers that allows for very efficient and robust modeling of such systems with multi-physical domains and their associated controls. In this study, an electric vehicle has been modeled and the effects of non-ideal components have been investigated in detail using PLECS.*

*Figure 1: Schematic of the EV drive model in PLECS*

## Introduction

The turn of the century has seen a push towards vehicle electrification to improve fuel economy and reduce dependence on conventional transportation fuels. Major car manufacturers have added plug-in hybrid electric vehicles (PHEVs) and electric vehicles (EVs) to their fleets. The field of power electronics is becoming increasingly important in the auto industry with applications from motor drives for vehicle propulsion to battery charging. With drive applications, a significant coupling exists between the controls, electrical and mechanical aspects. It is important for drive system engineers to model the influence of the different areas on overall electromechanical system performance. System simulations using computer tools are crucial to understanding these interactions.

PLECS is a simulation platform developed for engineers designing power electronics and motor drive systems. It provides an easy-to-use interface for modeling such systems and examining their behavior. In this study, the effects of non-idealities of the rotor shaft and the current sensor on the performance of an EV system are investigated. Further, a possible control solution to mitigate the observed issue is proposed and the overall system performance is compared before and after a damping algorithm is added.

## Electric vehicle system modeling in PLECS

Figure 1 shows a schematic of a front-wheel drive EV system, developed in PLECS using its control, electrical and mechanical modeling domains. The EV implementation consists of two slip-based wheel models. This two-wheel model incorporates the effect of speed and acceleration on the front and rear axle weight distribution, and thus, the effect on the front and rear wheel traction forces. The wheels are modeled using the advanced slip-based tire models proposed in [1]. The two-wheel vehicle model is shown in Figure 2.

*Figure 2: Two-wheel vehicle modeled in the PLECS mechanical domain*

The EV is propelled by a wye-connected permanent magnet synchronous machine (PMSM) attached to a single-speed gearbox. The damping and stiffness properties of the half-shafts connecting the gearbox and differential to the EV’s front wheels are incorporated in the system model. A backlash component is used to model the mechanical play in the gearbox (engagement and disengagement of gears). A simple field-oriented controller is used to regulate a two-level voltage source inverter that drives the PMSM.

## Excitation of powertrain natural frequency

A sudden step-change in motor torque leads to oscillation of the motor inertia. This windup effect occurs due to excitation of a natural frequency (f0) of the powertrain, given by:

where Ks is the shaft stiffness coefficient, G is the gear ratio and Jm is the rotor inertia. The inertia of the wheel/vehicle system is neglected because it is assumed to be significantly larger than the motor inertia.

When modeling electric drives it is often assumed that all measurements are ideal and accurate. However, in reality, some amount of offset and gain errors are present in all sensors. It can be shown that gain errors of the current measurement may lead to torque oscillation at twice the fundamental frequency of the phase currents. This torque ripple can excite the natural frequency of the mechanical system (at low speeds) as described above, and reduce vehicle driveability.

## Mechanical damping

A possible solution to reducing the windup and torque ripple effect is to change the natural frequency and damping factor of the rotor shaft, by adding an additional inertia onto the rotating shaft. However, this is not practical as it requires increasing overall vehicle weight and cost, and would adversely affect performance.

## Active damping

A more realistic solution to minimize drivetrain oscillations is to actively control the torque demand on the PMSM [2]. In this model, a basic damping algorithm has been implemented based on the measured rotor speed using a digital PI controller with an anti-windup mechanism that generates a correction torque. This correction torque, along with the torque demand of the driver, is used to modify the torque setpoint that is fed into the torque controller.

## Simulation results

In the simulation, an EV is modeled to start from standstill on a steep slope and accelerate to steady-state speed over the course of 6 seconds. A gain error in the measurement of two of the phase currents has been modeled, with one phase current overestimated by 5% and another underestimated by 5%. The simulation results in Figure 3 show the vehicular system response to a torque demand of 100 Nm. The simulation is first run for an EV system without an active damping algorithm. The system is then simulated with the simple active damping algorithm enabled and the results are overlaid on top of the previous results. The blue trace corresponds to the undamped system, while the red trace corresponds to the actively damped system.

As seen in Figure 3, for the undamped system, the step change in torque results in the rotor speed quickly increasing from standstill to 790 rpm. The rotor then reverses its motion with a maximum speed of 230 rpm in the opposite direction. Additionally, the gain error of two of the phase current measurements results in a low-frequency oscillation of the generated motor torque that translates to a sustained low-frequency oscillation in the motor speed. The peak-to-peak amplitude of the low-frequency motor speed oscillation is 81% of the average motor speed.

*Figure 3: Simulation results for an undamped (blue trace) and actively damped (red trace) system*

The active damping controller adjusts the torque demand signal that is fed into the torque controller. This results in a signifi cant reduction of the windup effects that occur without any damping. The low frequency oscillation of the motor speed arising from the current sensor measurement error is also mitigated through active damping. The feedback of the motor speed results in a low frequency adjustment in the steady-state torque demand setpoint. This translates to a reduction in the amplitude of the motor’s peak-to-peak low frequency speed oscillation to 7.5% of the average motor speed at steady state.

The maximum steady-state powertrain oscillation due to current sensor error occurs when the vehicle is traveling at a velocity v0 where the motor torque excites the natural frequency f0 of the system. The steady-state speed oscillation is reduced by deviating from this velocity, as can be seen in the undamped system in Figure 4. In practice, EV drivetrain oscillations are most prevalent at low speeds and high torque commands. The red trace corresponds to a vehicle moving at a steady speed v0, while the blue trace is for a vehicle moving at 2v0.

*Figure 4: Motor speed oscillation for undamped and damped systems at multiple steady-state speeds*

For a system regulated with the active damping algorithm described above, the magnitude of the peak-to-peak steady-state oscillation is significantly reduced (81% vs. 13%), as shown in Figure 4. The algorithm reduces motor speed oscillations to 7.5% for the vehicle moving at v0, while the oscillation is reduced to 5% for the vehicle moving at 2v0.

## Conclusion

In a real vehicle, the windup effect due to the powertrain resonance excitation and the low-frequency speed oscillation may significantly reduce vehicle driveability. It is important for drive systems engineers to model overall system performance issues that may arise due to mechanical components and measurement devices, and develop possible solutions to mitigate these concerns. With PLECS, these multi-domain effects can be evaluated in a single system model without excessive simulation times, providing an effective and accurate means to investigate and address issues related to real-world system non-idealities. Such fully integrated models provide power electronic designers and engineers with more insight into a system before components (such as sensors) are selected and hardware is built, reducing time and cost. The model discussed in this article is provided as a PLECS demo model and can be further explored using the Demo Mode of PLECS Standalone.

#### About the Authors

**Munadir Ahmed **received his Bachelor of Arts in Mathematics, Physics, and Statistics at Macalester College, then Master of Science in Electrical Engineering at Purdue University. At UCSC Silicon Valley Extension, he studied Digital Design with Verilog, and using FPGA. He worked as an application engineer at Plexim, a global leader company in simulation software for power electronic systems.

**Beat Arnet** received his Doctor of Philosophy (Ph.D.) in Electrical Engineering at the Federal Institute of Technology in Lausanne. He worked as a general manager in North America at Plexim, a global leader company in simulation software for power electronic systems.

**Kristofer Eberle** received his Bachelor of Science in Electrical Engineering summa cum laude at Northeastern University, then Master of Science in Electrical Engineering at the University of Wisconsin-Madison. He worked as a director of business development in America at Plexim, a global leader company in simulation software for power electronic systems.

#### References

- Pacejka, H.B.: Tire and Vehicle Dynamics, 3rd Edition, Butterworth-Heinemann, Oxford, 2012, Chapters: 1, 4, 7, and 8.
- Menne, M.: Drehschwingungen im Antriebsstrang von Elektrostraßenfahrzeugen, 2001, Aachen University of Technology

This article originally appeared in the Bodo’s Power Systems magazine.

1 CommentI had the pleasure and relief of witnessing Dr. Arnet solve large and frustrating EV drivetrain backlash, with just the 16Kx16 20MHz ‘F240, induction motor, and no damper: Using his wide and detailed knowledge of control, dynamics, embedded programming, and elegant tight software. It was an honor and pleasure working with him, and seeing the success he has brought to Solectria and Azure, and all his endeavors.