# Drivetrain Loss Analysis for Various Switching Frequencies and Modulation Strategies Applied to IPMSMs

Philipp Tillmann, Daniel Rodriguez Pinto, Martin Nell, Rolf Loewenherz, Rik

W de Doncker

► To cite this version:

Philipp Tillmann, Daniel Rodriguez Pinto, Martin Nell, Rolf Loewenherz, Rik W de Doncker. Drivetrain Loss Analysis for Various Switching Frequencies and Modulation Strategies Applied to IPMSMs. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0084. hal-05088691

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Submitted on 28 May 2025

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# Drivetrain Loss Analysis for Various Switching Frequencies and Modulation Strategies Applied to IPMSMs

Philipp Tillmann*†, Daniel Rodriguez Pinto*, Martin Nell†, Rolf Loewenherz†, Rik W. De Doncker*

*Institute for Power Electronics and Electrical Drives
RWTH Aachen University
Campus-Boulevard 89
52074 Aachen, Germany

URL: https://www.isea.rwth-aachen.de

Tel.: +49 241 80-96920

†ENGIRO GmbH

Avantisallee 51

52072 Aachen, Germany

URL: https://www.engiro.de

Tel.: +49 241 99798-0

**Index Terms**—Finite-element analysis (FEA), Pulse Width Modulation (PWM), Modulation strategy, Test bench, Permanent Magnet Synchronous Machine (PMSM)

**Abstract**—This paper presents holistic loss simulations for round wire interior permanent magnet synchronous machines (IPMSMs) influenced by switching frequency and modulation strategy. Pulse width modulation (PWM) current waveforms, calculated with a precise nonlinear machine model, serve as input to a current-based finite element analysis (FEA) loss simulation in a two-step approach. Simulation and measurements align closely in test bench validations.

## I. INTRODUCTION

Modern electric drives are typically composed of an IPMSM powered by a voltage source inverter (VSI). The PWM voltage results in additional losses in the machine. To increase the system efficiency and therefore the range of an electric vehicle, an optimisation of the switching frequency and the modulation scheme can be performed to balance the inverter and the machine losses.

Furthermore, the machine components respond differently to the losses caused by PWM. This can lead to local temperature increases, which depend not only on the operating point (OP), but also on the switching parameters. For the determination of these losses an analysis employing a FEA with sinusoidal currents is insufficient. To calculate the phase currents which are influenced by the PWM-modulated voltage, a system simulation that models the machine as well as the inverter is necessary.

In this work, a tool is developed to efficiently simulate OP-dependent losses in an electric drive system

consisting of an inverter and an IPMSM taking into account the influence of the pulsating voltage on the machine loss behaviour.

## A. Key Aspects

Key aspects about the loss analysis in this work are the following:

* An accurate lumped parameter model (LPM) of the IPMSM employing 3D lookup tables (LUTs) for the inductances and the magnet flux linkage, which are calculated by means of FEA to retain the geometry information

* A system simulation that allows a faster phase current simulation compared to FEA-based co-simulations while taking phase coupling, saturation and the effect of PWM into account by combining the machine LPM with an inverter model that allows manipulation of the PWM parameters

* An accurate loss calculation utilising the FEA approach to allow for spatial loss separation taking into account the effect of PWM, stranded wires and the machine geometry

* Proximity and skin effect as well as parallel current sharing effect on copper losses by using a single wire machine model

* Accurate hysteresis loss calculation by employing a vector hysteresis model and accurate eddy current losses using a one dimensional eddy current simulation in axial direction

* Fast FEA calculation by following a 2D approach with an analytical factor for the end winding effect
## B. Similar Work

A similar simulation toolchain (STC) was implemented in [1], where the LPM parameters are analytically estimated and, unlike the STC implemented in this work, show no dependence on the OP. Iron losses are determined using LUTs based on the magnetic flux density at frequency sampling points. Copper losses are modelled using single wires. Accurate LPM parameterisation improves current ripple simulation, and the quality of the loss calculation depends on the accuracy of the LUT. In [2], a stator with hairpin winding is studied using a 3D model for FEA-based loss calculation. Phase current ripple is calculated by solving IPMSM state equations with OP-dependent parameters. By contrast, the STC presented here uses a system simulation for time-resolved phase current calculation and a 2D FEA for an IPMSM with round wires, which have a PWM loss dependency that is different from hairpin windings. The authors in [3] also conduct a 2D current-based FEA simulation and the phase current ripple is determined by an analytical PWM voltage calculation based on an unspecified LPM. In [4], the OP is simulated without PWM influence. The simulated flux linkages and sinusoidal currents solve the IPMSM voltage equation. These are then used to analytically calculate the inverter voltage which are used in a voltage-based 3D FEA simulation, focusing on iron and magnet losses with the winding modelled as a copper block. The same approach is applied in [5]. In [6], a 2D voltage-based FEA determines the phase current profile, but only copper losses are analytically examined. A purely analytical approach to calculate PWM-induced losses is employed in [7].

# II. EQUATIONS

# III. MACHINE MODEL

## A. Machine Equations

The electric model of an IPMSM with $m$ phases can be described by (1), where the stator flux linkage $\vec{\psi}_s$ depends on the matrix of absolute inductances in stator system reference frame $\mathbf{L}_s^{\text{abs}}$, the phase current $\vec{i}_s$ and the permanent magnet flux linkage $\vec{\psi}_M$ [8]. Both $\mathbf{L}_s^{\text{abs}}$ and $\vec{\psi}_M$ are a function of the phase current $\vec{i}_s$ and the rotor angle $\theta_m$. The stator voltage $\vec{u}_s$ is described in (2) with the phase resistance $R_s$. The equations are combined in (3).

$$ \vec{\psi}_s(\vec{i}_s, \theta_m) = \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m) \cdot \vec{i}_s + \vec{\psi}_M(\vec{i}_s, \theta_m). \quad (1) $$

$$ \vec{u}_s(\vec{i}_s, \theta_m) = R_s \cdot \vec{i}_s + \frac{d\vec{\psi}_s(\vec{i}_s, \theta_m)}{dt}. \quad (2) $$

$$ \begin{aligned} \vec{u}_s(\vec{i}_s, \theta_m) = R_s \cdot \vec{i}_s &+ \frac{d\mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m)}{dt} \cdot \vec{i}_s \\ &+ \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m) \cdot \frac{d\vec{i}_s}{dt} + \frac{d\vec{\psi}_M(\vec{i}_s, \theta_m)}{dt}. \end{aligned} \quad (3) $$

Reformulating the derivative terms as presented in [9] and introducing the mechanical angular velocity $\omega_m = \frac{d\theta_m}{dt}$, eq. (3) can be expressed as

$$ \begin{aligned} \vec{u}_s(\vec{i}_s, \theta_m) ={}& R_s \cdot \vec{i}_s \\ &+ \sum_{j=1}^{m} \left( \frac{\partial \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m)}{\partial i_{s,j}} \frac{d i_{s,j}}{dt} \right) \cdot \vec{i}_s \\ &+ \frac{\partial \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m)}{\partial \theta_m} \cdot \omega_m \cdot \vec{i}_s \\ &+ \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m) \cdot \frac{d\vec{i}_s}{dt} + \sum_{j=1}^{m} \left( \frac{\partial \vec{\psi}_M(\vec{i}_s, \theta_m)}{\partial i_{s,j}} \frac{d i_{s,j}}{dt} \right) \\ &+ \frac{\partial \vec{\psi}_M(\vec{i}_s, \theta_m)}{\partial \theta_m} \cdot \omega_m. \end{aligned} \quad (4) $$

The differential inductance

$$ \mathbf{L}_s^{\text{diff}} = \mathbf{L}_s^{\text{abs}}(\vec{i}_s) + \frac{d\mathbf{L}_s^{\text{abs}}(\vec{i}_s)}{dt} \cdot \vec{i}_s. \quad (5) $$

can be used to combine the terms of the inductance that are influenced by the change of the current. Hence, (4) can be simplified to (6). In a second step, the influence of the changing current can be combined in an inductive voltage term and an equivalent incremental inductance $\mathbf{L}_s^{\text{inc}}$ can be introduced for practical purposes as described below.

$$ \begin{aligned} \vec{u}_s(\vec{i}_s, \theta_m) ={}& \underbrace{R_s \cdot \vec{i}_s}_{\text{ohmic}} \\ &+ \underbrace{\left( \mathbf{L}_s^{\text{diff}}(\vec{i}_s, \theta_m) \cdot \frac{d\vec{i}_s}{dt} + \sum_{j=1}^{m} \left( \frac{\partial \vec{\psi}_M(\vec{i}_s, \theta_m)}{\partial i_{s,j}} \frac{d i_{s,j}}{dt} \right) \right)}_{\text{inductive}} \\ &+ \underbrace{\left( \frac{\partial \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m)}{\partial \theta_m} \cdot \vec{i}_s + \frac{\partial \vec{\psi}_M(\vec{i}_s, \theta_m)}{\partial \theta_m} \right)}_{\text{back-EMF}} \cdot \omega_m \\ ={}& \underbrace{R_s \cdot \vec{i}_s}_{\text{ohmic}} + \underbrace{\mathbf{L}_s^{\text{inc}}(\vec{i}_s, \theta_m) \cdot \frac{d\vec{i}_s}{dt}}_{\text{inductive}} \\ &+ \underbrace{\left( \frac{\partial \mathbf{L}_s^{\text{abs}}(\vec{i}_s, \theta_m)}{\partial \theta_m} \cdot \vec{i}_s + \frac{\partial \vec{\psi}_M(\vec{i}_s, \theta_m)}{\partial \theta_m} \right)}_{\text{back-EMF}} \cdot \omega_m. \end{aligned} \quad (6) $$
<table><caption>TABLE I: Machine parameters DUT motor.</caption><thead><tr><th>Parameter</th><th>Value</th><th>Unit</th></tr></thead><tbody><tr><td>Number of phases</td><td>3</td><td></td></tr><tr><td>Number of pole pairs</td><td>4</td><td></td></tr><tr><td>Stator diameter</td><td>205</td><td>mm</td></tr><tr><td>Number of windings</td><td>43</td><td></td></tr><tr><td>Number of parallel conductors</td><td>2</td><td></td></tr></tbody></table>

<table><caption>TABLE II: Operating points for the simulation.</caption><thead><tr><th>OP</th><th>n<br>rpm</th><th>I<sub>ph</sub><br>A</th><th>T<br>Nm</th><th>U<sub>DC</sub><br>V</th></tr></thead><tbody><tr><td>1</td><td>500</td><td>354</td><td>275</td><td>700</td></tr><tr><td>2</td><td>5000</td><td>141</td><td>114</td><td>700</td></tr><tr><td>3</td><td>7000</td><td>70.7</td><td>50.7</td><td>700</td></tr></tbody></table>

This expression is sufficient to model the electrical behaviour of the IPMSM without simplifications. It comprises the ohmic voltage drop, the inductive voltage drop resulting from a current change, and the back-EMF voltage drop that originates from the flux change with respect to time as the machine rotates. Using expressions for $L_s^{abs}$, $L_s^{inc}$ and $\vec{\psi}_M$ that depend on the phase currents $i_s$ and the mechanical angle $\theta_m$, the voltage equation can be used to model the electrical behaviour of the IPMSM in a system simulation. The LUTs for $L_s^{abs}$, $L_s^{inc}$ and $\vec{\psi}_M$ are calculated using FEA simulations and the Frozen Permeability method described in [10].

## B. Simulation Parameters

In order to test the STC, an exemplary machine model is employed. The machine model is based on the device under test (DUT) motor (cf. Sec. V-A) whose parameters are provided in Table I. The simulation is performed for an operating point OP1 characterized by low speed and high torque and two operating points OP2 and OP3 characterized by high speed and low torque. They are compared in Table II.

## C. Loss Modelling

The time-resolved phase currents calculated during the system simulation serve as input to a FEA loss simulation which determines the copper losses $P_{Cu}$, iron losses $P_{Fe} = P_{Eddy} + P_{Hys}$ consisting of eddy current losses and hysteresis losses in stator ($P_{Eddy,S}$, $P_{Hys,S}$) and rotor ($P_{Eddy,R}$, $P_{Hys,R}$), and magnet losses $P_{Mag}$. For the calculation of $P_{Cu}$, a 2D model including single conductors in the stator slots is conceived, which is capable of modelling the AC copper losses including skin and proximity effect, as well as unequal current sharing [11]. The eddy current losses $P_{Eddy}$ are calculated using a one-dimensional FEA-approach along the thickness of a

single iron sheet. To calculate $P_{Hys}$, a vector hysteresis model is employed.

## IV. SIMULATION RESULTS

The modelling approach using the machine LPM described in Sec. III-A and the loss model described in Sec. III-C is used to analyse the impact of several PWM parameters on the losses of the IPMSM. The parameters analysed in this work are

* the switching frequency $f_{sw}$,

* the modulation scheme and

* the DC-link voltage $U_{DC}$.

### A. Influence of the Switching Frequency

The influence of the switching frequency $f_{sw}$ on the machine loss components in OP1 is shown in Figs. 1 to 3. Loss components are normalized with respect to the loss values that occur when the phase currents are assumed to be purely sinusoidal. It can be seen that all loss components are higher with the influence of PWM. Furthermore, the losses decrease with increasing switching frequency. This is because the total harmonic distortion (THD) is decreasing. The exact behaviour of the losses is specific to every loss component. For example, the magnet losses rise sharply when the switching frequency is low and this can lead to losses several times greater than the losses with purely sinusoidal currents. The copper losses, on the other hand, are only a few percent higher than with purely sinusoidal currents. At the high torque operating point OP1, the copper losses constitute the largest part of the total losses. Therefore, PWM has a significant effect on the efficiency by increasing copper losses. Other components like the magnet losses are less significant in terms of their effect on the system efficiency. However, they may lead to significant temperature increases in the magnets which can result in a torque reduction for a given current amplitude and carry a higher risk of demagnetisation.

### B. Influence of the Modulation Strategy

Using discontinuous pulse width modulation (DPWM) instead of space vector pulse width modulation (SVPWM) generally increases machine losses due to a higher harmonic content in the phase currents. At the same time, the inverter losses are reduced because there are less switching actions. Depending on the OP and the switching frequency, the overall system losses may be reduced. The results for an operating point at $n = 5000$ rpm, $i_d = -45.1$ A
<figure><img src="image_2.png" /><figcaption>Fig. 1: Magnet loss variation with $f_{sw}$ in three OPs relative to analysis with purely sinusoidal currents.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2: Copper losses variation with $f_{sw}$ in OP1 relative to analysis with purely sinusoidal currents.</figcaption></figure>

and $i_q = 108.6$ A resulting in a torque of $T = 100$ Nm are shown in Table III and Table IV for switching frequencies $f_{sw} = 8$ kHz and $f_{sw} = 12$ kHz. The OP as well as the switching frequency influence the loss reduction potential of the DPWM modulation. For $f_{sw} = 8$ kHz the losses are reduced by 4.23% when employing the DPWM1 modulation strategy. For $f_{sw} = 12$ kHz the losses are reduced by 9.91% with DPWM2. The most efficient DPWM method for each OP and switching frequency also coincides with the smallest increase in magnet losses $P_{Mag}$ in the examples provided. This is an interesting finding because it allows for an optimization of the PWM parameters for efficiency without a significant temperature rise in the rotor. As shown in Tables III and IV, the increase in magnet losses utilizing DPWM2 is low compared

<figure><img src="image_4.png" /><figcaption>Fig. 3: Iron loss variation with $f_{sw}$ in OP1 relative to analysis with purely sinusoidal currents.</figcaption></figure>

<table><caption>TABLE III: Increase in losses depending on the modulation strategy in % for $n = 5000$ rpm and $f_{sw} = 8$ kHz compared to SVPWM.</caption><thead><tr><th>Modulation</th><th>P<sub>Cu</sub></th><th>P<sub>Mag</sub></th><th>P<sub>Eddy,S</sub></th><th>P<sub>Eddy,R</sub></th></tr></thead><tbody><tr><td>DPWMMIN</td><td>2.42</td><td>65.0</td><td>7.33</td><td>4.30</td></tr><tr><td>DPWMMAX</td><td>3.30</td><td>67.5</td><td>5.48</td><td>3.00</td></tr><tr><td>DPWM0</td><td>2.41</td><td>87.5</td><td>3.59</td><td>1.93</td></tr><tr><td>DPWM1</td><td>2.90</td><td>36.2</td><td>5.97</td><td>2.65</td></tr><tr><td>DPWM2</td><td>8.37</td><td>40.2</td><td>7.29</td><td>3.80</td></tr><tr><td>DPWM3</td><td>2.13</td><td>85.7</td><td>2.51</td><td>0.735</td></tr></tbody></table>

<table><thead><tr><th>Modulation</th><th>P<sub>Hys,S</sub></th><th>P<sub>Hys,R</sub></th><th>P<sub>Mot</sub></th><th>P<sub>Inv</sub></th><th>P<sub>Total</sub></th></tr></thead><tbody><tr><td>DPWMMIN</td><td>6.40</td><td>7.54</td><td>6.27</td><td>-20.8</td><td>-2.35</td></tr><tr><td>DPWMMAX</td><td>4.19</td><td>3.45</td><td>6.25</td><td>-22.7</td><td>-3.00</td></tr><tr><td>DPWM0</td><td>3.61</td><td>2.93</td><td>6.03</td><td>-16.5</td><td>-1.14</td></tr><tr><td>DPWM1</td><td>4.58</td><td>3.65</td><td>4.91</td><td>-23.8</td><td>-4.23</td></tr><tr><td>DPWM2</td><td>4.75</td><td>6.98</td><td>8.80</td><td>-23.8</td><td>-1.58</td></tr><tr><td>DPWM3</td><td>3.43</td><td>2.45</td><td>5.54</td><td>-16.5</td><td>-1.47</td></tr></tbody></table>

to other DPWM methods. The authors in [2] come to a similar conclusion, which is that the magnet loss increase is the lowest for DPWM2 because the current ripple amplitude is the lowest out of all DPWM strategies.

## V. TEST BENCH RESULTS

### A. Test Bench Setup

The investigated drivetrain consists of an IPMSM, whose performance data is given in Table V and a Semikron Danfoss SKiiP® 603 GD123-3DUW V3 inverter [12]. The DUT motor is controlled via a MATLAB®-Simulink® model running in real-time on a dSPACE DS1103 controller board [13].
<table><caption>TABLE IV: Increase in losses depending on the modulation strategy in % for $n = 5000$ rpm and $f_{sw} = 12$ kHz compared to SVPWM.</caption><thead><tr><th>Modulation</th><th>P<sub>Cu</sub></th><th>P<sub>Mag</sub></th><th>P<sub>Eddy,S</sub></th><th>P<sub>Eddy,R</sub></th></tr></thead><tbody><tr><td>DPWMMIN</td><td>1.83</td><td>27.8</td><td>1.45</td><td>1.04</td></tr><tr><td>DPWMMAX</td><td>2.02</td><td>32.2</td><td>1.62</td><td>1.42</td></tr><tr><td>DPWM0</td><td>1.72</td><td>50.6</td><td>-0.275</td><td>0.069</td></tr><tr><td>DPWM1</td><td>2.49</td><td>29.6</td><td>2.96</td><td>2.14</td></tr><tr><td>DPWM2</td><td>1.80</td><td>7.18</td><td>3.08</td><td>2.31</td></tr><tr><td>DPWM3</td><td>1.30</td><td>30.0</td><td>0.038</td><td>0.284</td></tr></tbody></table>

<table><caption>TABLE V: Performance data of the DUT motor.</caption><thead><tr><th>Modulation</th><th>P<sub>Hys,S</sub></th><th>P<sub>Hys,R</sub></th><th>P<sub>Mot</sub></th><th>P<sub>Inv</sub></th><th>P<sub>Total</sub></th></tr></thead><tbody><tr><td>DPWMMIN</td><td>-0.003</td><td>0.625</td><td>2.28</td><td>-25.5</td><td>-8.54</td></tr><tr><td>DPWMMAX</td><td>0.240</td><td>1.20</td><td>2.62</td><td>-27.1</td><td>-8.93</td></tr><tr><td>DPWM0</td><td>-0.395</td><td>-0.683</td><td>2.51</td><td>-21.5</td><td>-6.82</td></tr><tr><td>DPWM1</td><td>0.638</td><td>2.18</td><td>3.16</td><td>-29.2</td><td>-9.42</td></tr><tr><td>DPWM2</td><td>0.313</td><td>2.39</td><td>2.03</td><td>-28.7</td><td>-9.91</td></tr><tr><td>DPWM3</td><td>-0.453</td><td>-0.355</td><td>1.67</td><td>-18.7</td><td>-6.25</td></tr></tbody></table>

<table><thead><tr><th rowspan="2">Quantity</th><th colspan="2">Magnitude</th><th rowspan="2">Unit</th></tr><tr><th>Nominal</th><th>Maximum</th></tr></thead><tbody><tr><td>P<sub>M</sub></td><td>59</td><td>115</td><td>kW</td></tr><tr><td>T</td><td>112</td><td>298</td><td>Nm</td></tr><tr><td>n</td><td>5000</td><td>8000</td><td>min<sup>-1</sup></td></tr><tr><td>U<sub>DC</sub></td><td>700</td><td>850</td><td>V</td></tr><tr><td>I<sub>ph</sub></td><td>108</td><td>298</td><td>A</td></tr><tr><td>η</td><td>-</td><td>96</td><td>%</td></tr></tbody></table>

By measuring the DC-link voltage $U_{DC}$ and current $I_{DC}$, the input power $P_{DC,meas}$ can be compared to the inverter output power $P_{AC,meas}$. Furthermore, by measuring speed $n_{meas}$ and torque $T_{meas}$, the mechanical output power $P_{M,meas}$ can be calculated. This enables a calculation of the inverter losses $P_{Inv,meas}$ and the machine losses $P_{Mot,meas}$.

The machine losses $P_{Mot,meas}$ can be separated further but only into copper losses $P_{Cu,meas}$ and iron losses $P_{Fe,meas}$. This is done by measuring the stator resistance $R_s$ and the stator current $\vec{i}_s$, which allows the calculation of the stator copper losses $P_{Cu,meas}$. The iron losses $P_{Fe,meas}$ are calculated by subtracting the copper losses $P_{Cu,meas}$ as well as the friction losses from the total machine losses $P_{Mot,meas}$. The friction losses are measured separately in a no-load test.

To demonstrate the accuracy of the electromagnetic machine model, a comparison of the simulated and measured phase current waveforms is shown in Fig. 4.

The test involves an OP at $n = 3000$ rpm, $i_d = -45.1$ A and $i_q = 108.6$ A, which corresponds to $T = 100$ Nm using the maximum torque per ampere (MTPA) method. The selected PWM strategy is

<figure><img src="image_5.png" /><figcaption>Fig. 4: Comparison of simulated and measured phase current.</figcaption></figure>

SVPWM, with a switching frequency of $f_{sw} = 10$ kHz and a DC-link voltage of $U_{DC} = 750$ V. A second-order Butterworth filter is applied both forward and backward to the measured signal in Fig. 4 to avoid phase distortion, with a cutoff frequency of 40 kHz.

## B. Loss Measurement

The machine loss is measured in the same OP in terms of torque as described in Sec. V-A for three different speeds and four different switching frequencies. The deviation of the measured losses from the simulation is given in Fig. 5. The error between the measured losses and simulated losses is below 15%. However, with increasing switching frequency, the error decreases to under 7% for frequencies above $f_{sw} = 10$ kHz. This behaviour can be explained with an inaccuracy in the loss model used in the simulations. It is impossible to match the modelling of the distribution of single strands in the winding system to the winding system of the DUT. However, the influence of the wire distribution on the AC phase resistance and therefore on the copper losses is significant. As the simulated and measured phase currents exhibit a very good agreement as shown in Fig. 5, they can be ruled out as source of the error. However, phase resistance measurements with an LCR meter confirm that the AC phase resistance of the machine deviates from simulations. While the measured DC phase resistance of the machine is only 4.71% higher than the simulated value, the AC phase resistance at $f = 10$ kHz is already 27.8% higher. In [11], the distribution of parallel conductors is also stated as one of the main sources for error in the loss simulation due to PWM influence.
<figure><img src="image_6.png" /><figcaption>Fig. 5: Error between measured machine losses and simulated losses at $U_{DC} = 750$ V.</figcaption></figure>

<table><caption>TABLE VI: Rotor temperature rise and simulated magnet losses for different PWM parameters.</caption><thead><tr><th>Quantity Unit</th><th>f<sub>sw</sub> kHz</th><th>U<sub>DC</sub> V</th><th>Δϑ<sub>R</sub>/t °C/min</th><th>P<sub>Mag</sub> W</th></tr></thead><tbody><tr><td>M1</td><td>8</td><td>750</td><td>1.29</td><td>35.8</td></tr><tr><td>M2</td><td>12</td><td>750</td><td>0.896</td><td>20.6</td></tr><tr><td>M3</td><td>6</td><td>375</td><td>0.850</td><td>26.4</td></tr><tr><td>M4</td><td>8</td><td>375</td><td>0.516</td><td>18.0</td></tr></tbody></table>

### C. Magnet Losses

The influence of PWM on the magnet losses is significant, not because they are a large contributor to the overall losses, but because the rotor temperature $ϑ_R$ rises significantly at high magnet losses. Table VI shows that PWM parameters that lead to a high THD and high magnet losses, i.e. M1, lead to higher rotor temperatures than for example M4. This experiment is repeated for two different levels of $U_{DC}$ and two different switching frequencies for each voltage level. The temperature rise is the highest for $U_{DC} = 750$ V and for low switching frequencies. M2 and M3, whose voltage-time area is comparable, also result in similar temperature profiles. The correlation between magnet losses and rotor temperature rise, which can be seen in Table VI will have to be confirmed by a thermal model of the machine in further work.

## VI. CONCLUSION

This work describes a method to simulate the loss components in an IPMSM that takes into account the impact of the PWM parameters. Special focus is put on the magnet losses, which the simulations show are highly dependent on the switching frequency and can lead to overheating of the rotor. The test bench results prove a

<figure><img src="image_7.png" /><figcaption>Fig. 6: Rotor temperature profile.</figcaption></figure>

good agreement between simulations and measurements. The magnet loss behaviour shows the same trend in both simulation and measurement. Further work will focus on a thermal model to predict the temperature rise in the respective machine components based on calculated losses. To address the challenge of accurately calculating the AC copper losses due to randomly distributed conductors, further work on the loss model is necessary. Methods of statistical modelling of the conductors as well as test bench measurements with a variety of distributions will be performed in future work.

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[13] dSPACE, "DS1103." [Online]. Available: https://www.dspace.com/en/pub/home.cfm