This article presents a spatial harmonics model of a permanent magnet synchronous machine implemented on a field-programmable gate array (FPGA). The real-time model is parameterized by finite element analysis (FEA) and is suitable for model-based development and hardware-in-the-loop (HIL) applications. Since the quality of the real-time model depends on the parameterization, the accuracy of three FE models of different fidelity levels is evaluated by test bench measurements. It was found that a priori assessment can be realized with good precision by virtual prototypes. In addition to the selection of a suitable FE model for parameterization, a surrogate model to describe the machine effects is mandatory to achieve real-time capability. Using an inverse current-flux correlation in the dq reference frame and a parallel resistor in the equivalent circuit for iron loss consideration, a high-fidelity model is developed. Moreover, the temperature effect is solved by a highly sophisticated shifting strategy of the reference currents to affect the nonlinearity and harmonics of the electromagnetic behavior. The temperature correction approach yields a maximum deviation of 0.3 Nm. This corresponds to a percentage error of less than 1%.

In order to reduce automotive development times and costs, particular development tasks are rescheduled to earlier program phases (frontloading) by applying hardware-in-the-loop (HiL) tests. However, there is a shortage of studies considering HiL tests for function developments considering the thermal behavior of electric drives. This article shall be a first step toward closing this gap. A real-time co-simulation of a battery electric vehicle and a driver model are developed and connected to an electric traction machine at a laboratory test bench. A thermal derating function is designed and calibrated at this test setup. In particular, linear derating functions with different gradients are implemented and tested for high load performances during a track race, and the trade-off between energy demand and the lap time is determined. Larger gradients of thermal derating functions lead to shorter lap times and higher energy demands. Thus, for this case study, an increase of the gradient of the thermal derating function by a factor of two results in a lap time improvement of 2.3% and a higher energy demand of 4.7%. The test results demonstrate how HiL setups offer a favorable testing scenario to calibrate thermal derating functions of electrified powertrains in early development phases.

This paper presents a comprehensive evaluation of system interactions in a battery electric vehicle caused by temperature sensitivity of permanent magnet synchronous machines (PMSM). An analytical model of a PMSM considering iron losses and thermal impact is implemented on a field programmable gate array suitable for hardware-in-the-loop testing. By the presented virtual prototyping approach, different machine characteristics defined by the design are used to parameterize the analytical model. The investigated temperature effect is understood as an interacting influence between machine characteristics and control, which are investigated in terms of torque generation, voltage utilization and efficiency under closed-loop condition in a vehicle environment. In particular, using a surface permanent magnet rotor and an interior permanent magnet rotor, the performance of both machine designs is analyzed by varying temperature-adjusted feedforward control strategies on the basis of a driving cycle from a racetrack. The comparison shows that the machine design with surface-mounted magnets is associated with higher temperature sensitivity. In this case, the temperature consideration in the feedforward control provides a $$14\,\%$$14 % loss reduction in closed-loop vehicle test operation. It can be summarized that the electromagnetic torque is less sensitive to a temperature variation with increasing reluctance. The presented development approach demonstrates the impact of interactions in electric powertrains without the need of real prototypes.

Externally excited synchronous machines (EESMs) are a rare-earth-free solution for traction applications. However, variable field excitation and magnetic coupling increase control complexity. Efficient validation of the resulting control functionalities can be carried out using hardware-in-the-loop (HIL) testing, which requires high-fidelity real-time simulation models. This paper presents a semi-analytical, discrete-time EESM model tailored for HIL applications. Nonlinear magnetic saturation and magnetic coupling are captured using an inverted flux–current characteristic combined with a rotating coordinate transformation, which improves resource utilization. Spatial harmonics are included through a Fourier decomposition of the angle-dependent inverse characteristics. Additionally, different loss mechanisms are considered to accurately represent the physical behavior of the machine. The model is parameterized using finite element analysis (FEA) results from a 100$\mathrm{k}$$\mathrm{W}$ salient-pole EESM. It is implemented on a field-programmable gate array to achieve real-time capability at a simulation frequency of $2.5$$\mathrm{M}$$\mathrm{Hz}$. Validation results for the typical operating range show deviations below $0.1$% compared to detailed FEA results, demonstrating accurate real-time simulation of the electromagnetic behavior.