# Impact of PWM Modulation Strategies on Bearing Currents in Electrically Excited Synchronous Motors

Yuyang Li, Nicolas Patin, Vincent Lanfranchi, Nicolas Buiron, Rachid Missoum, Clemence Huet, Patrice Mercay

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Yuyang Li, Nicolas Patin, Vincent Lanfranchi, Nicolas Buiron, Rachid Missoum, et al. Impact of PWM Modulation Strategies on Bearing Currents in Electrically Excited Synchronous Motors. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0269. hal-05085106

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# Impact of PWM Modulation Strategies on Bearing Currents in Electrically Excited Synchronous Motors

Yuyang LI¹, Nicolas PATIN¹, Vincent LANFRANCHI¹, Nicolas BUIRON¹, Rachid MISSOUM², Clemence HUET², Patrice MERCAY²

¹ROBERVAL, UNIVERSITY OF TECHNOLOGY OF COMPIEGNE
Centre de recherche Royallieu - CS 60 319 - 60 203 Compiègne Cedex, France

²AMPERE, RENAULT GROUP

1 Av. du Golf, 78280 Guyancourt, France

Tel.: +33 6 65 57 08 84

E-Mail: yuyang.li@utc.fr

yuyang.li@ampere.cars

***Index Terms***—EESM, Converter control, Common-mode current, Bearing currents, Pulse Width Modulation (PWM).

***Abstract***—Bearing failures are a critical issue in electrically excited synchronous machines (EESMs), particularly due to electrical erosion caused by high-frequency converters in modern electric and hybrid electric Vehicles. This phenomenon, driven by common-mode currents and parasitic capacitances, significantly impacts the reliability and performance of rotating machinery. This paper investigates the impact of various converter control strategies in mitigating bearing erosion. Through comprehensive modeling of the complete drive system—including motor components and power electronics—simulations are performed to evaluate the effectiveness of different PWM approaches and their combinations on reducing bearing voltage and current. The results provide valuable insights into the optimal control strategies that minimize electrical corrosion, offering a pathway to enhanced durability and performance for EESM-based systems.

## I. INTRODUCTION

Electrically excited synchronous machines (EESMs) are electric motors that offer controllable excitation fields, making them suitable for vehicle applications. Compared to permanent magnet (PM) and induction motors (IM), EESMs' ability to regulate rotor excitation current is a key advantage. Typically, EESMs are powered by an inverter and chopper circuit, utilizing pulse width modulation (PWM) to control voltage supply to the stator and rotor windings.

While PWM inverters improve the dynamic performance and output waveform of motors, they introduce

undesirable effects such as shaft voltages, bearing currents, insulation breakdown, and electromagnetic interference (EMI), which can reduce motor lifespan and reliability [1]. Common methods to mitigate common-mode phenomena, such as bearing currents, can be categorized into two primary types based on their functionality [2]. The first category aims to change the impedance of the bearing circuit, using devices such as hybrid or ceramic bearings and external brushes to modify the path of bearing currents. The second category focuses on the sources of bearing currents, emphasizing the converter modulation strategies and the implementation of common-mode filters [2].

This paper examines the impact of different modulation strategies and combinations on bearing voltages and currents in EESMs. Section II models common-mode voltage and current pathways, focusing on the model of parasitic capacitances and detailed electrics models of bearing in different operational conditions. Section III explores various modulation strategies, comparing several PWM and chopper techniques, and discusses their effectiveness in reducing common-mode voltages and currents. Section IV presents simulation results that demonstrate the advantages of specific control strategies in reducing bearing voltage and current. These results provide clear insights into optimal control strategies to minimize electrical bearing erosion and enhance EESM reliability. Finally, Section V concludes with a discussion on how adaptive PWM control and broader impedance spectrum analysis can further improve bearing protection in future research.
## II. ANALYSIS AND MODELING OF COMMON MODE PHENOMENA

### A. Common-Mode Voltage and Current Pathways in EESM Systems

The EESM is powered by both an inverter and a chopper. The pathways of common-mode current (CMC) and associated components are illustrated in Figure 1. Within the EESM system, elements contributing to common-mode phenomena include the battery, inverter, chopper, motor, bearing and gearbox.

The inverter supplies power to the stator through PWM technology. However, the rapid switching actions of the inverter induce high-frequency voltage fluctuations, causing an imbalance in the output phase voltage, which results in the generation of Non-zero common mode voltage (CMV) at stator side. The voltage between ground and the neutral point of the stator windings, referred to as the stator common-mode voltage, can be described as :

$$V_{\text{com, stator}} = \frac{V_{U} + V_{V} + V_{W}}{3} \quad (1)$$

where $V_U$, $V_V$, and $V_W$ denote the phase voltages of the U, V, and W phases, respectively.

The CMV produced by the inverter is coupled to ground through parasitic capacitances within the machine, such as the capacitance between the stator windings and the stator frame, which provides a path for CMC. Similarly, the chopper, which supplies excitation voltage to the rotor windings, introduces rotor common-mode voltage and rotor common-mode current due to its rapid switching behavior. The rotor common-mode voltage can be defined as:

$$V_{\text{com, rotor}} = \frac{V_{\text{rotor1}} + V_{\text{rotor2}}}{2} \quad (2)$$

where $V_{\text{rotor1}}$ and $V_{\text{rotor2}}$ represent the voltages between ground and each terminal of the rotor windings, respectively.

### B. Parasitic Capacitances in Electric Machines and Capacitive Bearing Current

Under normal operating conditions, the motor's internal capacitances have minimal influence. However, when exposed to high-frequency common-mode voltages, these parasitic capacitances play a significant role in the electrical behavior of the system [3]. The key parasitic capacitances are shown in Figure 2:

* Stator Winding to Frame Capacitance ($C_{sw,f}$): The capacitance between the stator winding and grounded stator frame, governed by insulation between the copper windings and the stator iron.

* Stator Winding to Rotor Capacitance ($C_{sw,r}$): The capacitance between the stator winding and rotor, influenced by the air gap, slot wedges, and insulation between stator windings and rotor surface.

* Rotor Core to Stator Core Capacitance ($C_{rf}$): Capacitance across the air gap between the rotor and stator iron, determined by the air gap and the surfaces of both the rotor and stator iron, particularly at the stator teeth tips.

* Rotor Winding to Frame Capacitance ($C_{rw,f}$): Capacitance between rotor windings and rotor frame insulation.

* Rotor Winding to Shaft Capacitance ($C_{rw,sh}$): Capacitance between rotor windings and the rotor shaft.

* Gear Capacitance ($C_{gear}$): Capacitance formed between conductive surfaces of gears, affected by the mechanical and material properties of the gears, particularly their conductive surfaces and the air gap between them.

* Bearing Capacitance ($C_b$): When the lubricating film in the bearings remains intact, the bearings exhibit capacitive behavior. This capacitance can be commonly categorized based on the bearing's location: the drive-end bearing capacitance ($C_{b,DE}$) and the non-drive-end bearing capacitance ($C_{b,NDE}$). It is important to be noted that this capacitance is significantly influenced by key operational parameters, including the rotational speed, bearing's temperature, and the applied load.

These motor capacitances form a high-frequency capacitive network, which acts as a voltage divider that transfers the common-mode voltage from the winding terminals to the bearing voltage. In the absence of coupling from the gear system, the bearing voltage, $V_b$, is influenced by the distribution of parasitic capacitances within the motor, including those between the stator, rotor, frame, and bearings. It can be expressed as follows:

$$V_b = \frac{V_{\text{com, stator}} \cdot C_{\text{sw,r}} + V_{\text{com, rotor}} \cdot C_{\text{rw,sh}}}{C_{\text{sw,f}} + C_{\text{rw,sh}} + C_{\text{rf}} + C_{b,DE} + C_{b,NDE}} \quad (3)$$

### C. Bearing model

In real motor operations, bearings exhibit variable impedance, with their electrical properties being strongly influenced by lubrication conditions [4]. These lubrication conditions, in turn, are affected by motor operating parameters, including speed, temperature, and load.
<figure><img src="image_2.png" /><figcaption>Fig. 1: EESM System with Common-Mode Current Paths.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2: High-Frequency Parasitic Capacitance Model in EESMs.</figcaption></figure>

For rolling bearings, under low-speed, high-load, and high-temperature conditions, the lubrication film is generally thin. The contact between the rolling elements and raceways occurs through surface asperities, allowing current to flow through contact points, modeled as electrical contact resistance. In contrast, under high-speed and low-load conditions, the lubrication film becomes thick enough to separate contact surfaces, entering the elastohydrodynamic lubrication (EHL) regime.

In the EHL state, when the external electric field is weak, the contact can be described by a parallel capacitance-resistance model, where the lubrication film offers high resistance. However, once the electric field exceeds a threshold, film breakdown occurs, and the contact remains in the parallel capacitance-resistance model, but the resistance decreases significantly to represent conduction.

When the lubrication film is thin, these two states (capacitive and resistive) can alternate rapidly, allowing the contact to be modeled as a switch. Based on this electrical model, the impedance and breakdown voltage

of rolling bearings can be calculated under various operating conditions [4].

In the following simulations, appropriate motor operating parameters were selected to ensure that lubrication film operates consistently within the same regime, such as in the EHL lubrication regime.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Electrical Model of Bearings.</figcaption></figure>

### III. CONTROL STRATEGIES AND COMBINATIONS

#### A. Inverter Modulation Strategies

Several pulse width modulation strategies based on space vector techniques have been documented in the literature for reducing CMV [5]. Key methods include Active Zero State PWM (AZSPWM), Remote State PWM (RSPWM), and Near State PWM (NSPWM). This study compares the effects of these PWM strategies, combined with chopper modulation strategies, on bearing voltage and currents.

Space Vector PWM utilizes two zero vectors per cycle. It provides good harmonic performance and is simple to use. However, it suffers significant switching losses and has common mode voltage problems.
<figure><img src="image_5.png" /><figcaption>Fig. 4: Inverter Modulation Strategies and Corresponding Voltage Linearity Regions (a) SVPWM, GDPWM. (b) AZSPWM. (c) NSPWM. [6]</figcaption></figure>

Generalized Discontinuous PWM minimizes switching losses by keeping one branch continuously open or closed during the switching cycle, but still faces CMV issues.

Next, several modulation strategies focus on reducing the amplitude of CMV by decreasing the use of zero vectors. Active Zero State PWM replaces zero vectors with two opposite active vectors and then generates the reference output voltage together with two adjacent active vectors, theoretically reducing high CMV amplitudes. However, it suffers from simultaneous switching in different branches.

Near State PWM employs three adjacent active vectors to reduce high CMV amplitudes and it minimizes switching losses, but its linear modulation range is limited ($\frac{\pi}{3\sqrt{3}} < M < \frac{\pi}{2\sqrt{3}}$), with similar branch-switching issues as AZSPWM.

## B. Chopper Modulation Strategies for EESM Motors

In contrast to PM and IM motors, EESM motors exhibit the issue of rotor common-mode voltage due to the chopper, which requires special attention to the chopper control strategy. Signals $C_1$ and $C_2$ control the switching states of the chopper bridge arms. There are three possible switching states:

* $C_1 = 1$ and $C_2 = 1$: Both switches are closed, and the output voltage is $+V_{dc}$.

* $C_1 = 0$ and $C_2 = 0$: Both switches are open, resulting in an output voltage of $-V_{dc}$.

* $C_1 \neq C_2$: The output voltage is 0.

We introduce three different modulation strategies:

In bipolar PWM control, signals $C_1$ and $C_2$ are the same. The chopper output voltage switches between positive voltage $+V_{dc}$ and negative voltage $-V_{dc}$. The duty cycle $\alpha$ is calculated as:

$$ \alpha = \frac{1}{2} \left( \frac{V_{out}}{V_{dc}} + 1 \right) \quad (4) $$

<figure><img src="image_6.png" /><figcaption>Fig. 5: Chopper Modulation Strategies: (a) Bipolar PWM Control. (b) Unipolar PWM Control with Single-Switch. (c) Unipolar PWM Control with Dual-Switch.</figcaption></figure>

This modulation ensures faster transitions between positive and negative states.

Next, we analyze unipolar PWM control, where the modulation signals satisfy $C_1 \neq C_2$. This control scheme can be implemented in two distinct approaches. In the first approach, one switch remains constant (either high or low) while the other bridge arm is modulated. For example, $C_1$ is held at 0 or 1 during the entire modulation cycle, while $C_2$ is modulated. This results in the chopper output voltage switching between positive voltage $+V_{dc}$ and zero voltage. The duty cycles for this mode are calculated as:

$$ \alpha_1 = 1, \quad \alpha_2 = \frac{V_{out}}{V_{dc}} \quad (5) $$

This modulation reduces switching losses and the variation of voltage.

In the second unipolar PWM control approach, both bridge arms are actively switched. As shown in Figure 5, a phase shift $\delta$ is introduced between $C_1$ and $C_2$. This allows the output voltage to switch between positive voltage $+V_{dc}$ and zero voltage, providing finer control over the output waveform. The duty cycle is given by:

$$ \alpha_{1,2} = \frac{1}{2} \pm \delta, \quad \delta = \frac{1}{2} \left( \frac{V_{out}}{V_{dc}} \right) \quad (6) $$

## IV. SIMULATION AND DISCUSSION

The simulation is carried out under the same motor operating conditions and a elastohydrodynamic lubrication state. We applied four inverter PWM strategies and three chopper modulation strategies to obtain capacitive bearing voltages and bearing currents. Measured values of motor parasitic capacitances at 1 MHz were used, and bearing capacitances were calculated under the specified motor operating conditions, as presented in Table I.
<table><caption>TABLE I: Electrical Parameters Used in Simulation</caption><thead><tr><td>Parameter</td><td>Value</td><td>Unit</td></tr></thead><tbody><tr><td>Rotation speed</td><td>3000</td><td>rpm</td></tr><tr><td>Temperature</td><td>30</td><td>°C</td></tr><tr><td>Radial load</td><td>100</td><td>N</td></tr><tr><td>DC voltage</td><td>400</td><td>V</td></tr><tr><td>Pole pairs</td><td>4</td><td>-</td></tr><tr><td>Stator switching frequency</td><td>10</td><td>kHz</td></tr><tr><td>Rotor switching frequency</td><td>5</td><td>kHz</td></tr><tr><td>Stator phase resistance</td><td>8</td><td>mΩ</td></tr><tr><td>Stator phase inductance</td><td>1</td><td>mH</td></tr><tr><td>Excitation winding resistance (Rf)</td><td>6</td><td>Ω</td></tr><tr><td>Excitation winding inductance (Lf)</td><td>0.26</td><td>H</td></tr></tbody></table>

The simulation results and FFT analysis of the CMV at the stator terminal (see Figure 6) indicate that:

1) The stator common-mode voltage exhibits a dominant frequency of approximately 10 kHz, which corresponds to the inverter's switching frequency.

2) Compared to SVPWM, GDPWM strategies, such as DPWM1, show limited effectiveness in reducing the stator CMV amplitude at the dominant frequency. On the other hand, AZSPWM and NSPWM effectively reduce the CMV amplitude at the stator terminals, demonstrating suppression effects on both the dominant and high-frequency components. Despite NSPWM providing the lowest stator CMV amplitude at 10 kHz, its application must remain within the linear modulation range, as the use of zero-voltage vectors becomes unavoidable when the modulation index drops below 0.61.

Similarly, the rotor CMV simulation results and FFT analysis (see Figure 7) provide the following observations:

1) With unipolar PWM, the primary frequency of the rotor common-mode voltage is around 5 kHz, matching the chopper's switching frequency.

2) Bipolar PWM control generates the lowest rotor CMV with almost no high-frequency harmonics, except for a minor raie at 400 kHz. This is due to the symmetrical motor configuration applied in the simulation, as shown in 1, where the rotor common-mode voltages on both sides compensate each other. Thus, the symmetrical nature of bipolar PWM control effectively minimizes the total rotor-side CMV.

3) For asymmetric control strategies, the amplitude of the variation of rotor CMV equals the multiple of the DC bus voltage. Compared to unipolar PWM with dual-switch modulation, unipolar PWM with single-switch modulation more effectively reduces

the rotor CMV amplitude at 5 kHz. This is because only one switch operates during each switching cycle, resulting in smoother voltage variations.

Figures 8 and 9 present the simulation results for bearing voltage and bearing current obtained by applying different control strategy combinations under identical operating conditions.

According to the time-domain and frequency-domain simulation results of bearing voltage:

1) The bearing voltage is significantly influenced by the rotor-side control strategy. Among them, the Unipolar PWM with Dual-Switch strategy exhibits higher high-frequency components in bearing voltage.

2) In contrast, the Unipolar PWM with Single-Switch mode demonstrates a noticeable reduction in high-frequency components and time-domain oscillations. However, compared to the Bipolar PWM mode, the high-frequency components remain more pronounced.

3) The Bipolar PWM mode proves to be the most robust, effectively minimizing high-frequency components and ensuring a smoother time-domain waveform.

From the time-domain and frequency-domain simulation results of bearing current:

1) The behavior of the bearing current exhibits a strong correlation with bearing voltage in terms of high-frequency characteristics and sensitivity to PWM strategies, but its high-frequency phenomena are more pronounced. In the time domain, the bipolar PWM mode yields the lowest amplitude of bearing current, ensuring the smoothest waveform. In contrast, the single-switch unipolar PWM mode shows moderate improvement but remains affected by significant oscillations and spikes, whereas the dual-switch unipolar PWM mode performs the worst, exhibiting the highest levels of high-frequency oscillations and spikes. The overall ranking in the time domain is as follows: Bipolar PWM > Single-Switch Unipolar PWM > Dual-Switch Unipolar PWM.

2) Similarly, in the frequency domain, bipolar PWM once again demonstrates the best performance, with NSPWM and AZSPWM strategies significantly reducing high-frequency noise. In contrast, the single-switch unipolar PWM mode exhibits relatively high high-frequency components, while the dual-switch unipolar PWM mode presents the highest high-frequency energy distribution, ranking
<figure><img src="image_7.png" /><figcaption>(a) SVPWM</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(b) GDPWM</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>(c) AZSPWM</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>(d) NSPWM</figcaption></figure>

<caption>Fig. 6: Stator Terminal Common Mode Voltage with Different PWM Strategies</caption>

second in performance. This ordering remains con-
sistent with the time-domain evaluation.

3) Considering both time-domain and frequency-domain performance, the NSPWM + Bipolar PWM combination emerges as the most optimal solution, producing smooth waveforms with minimal high-frequency components. This combination effectively suppresses oscillations and spikes, reducing the risk of bearing capacitance breakdown and mitigating electrical and mechanical damage. The next best configurations is AZSPWM + Bipolar

PWM, which closely approximate the optimal con-
figuration.

V. CONCLUSION

As more high-frequency switching converters are
increasingly applied in electric vehicles, the influence of
parasitic capacitances within the motor has significantly
increased, providing pathways for common-mode cur-
rent. These pathways, not originally designed for motor
power supply, lead to electrical degradation of bearing
balls and raceways, reducing their operational lifetime.
<figure><img src="image_11.png" /><figcaption>(a) Bipolar PWM Control</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>(b) Unipolar PWM Control with Single-Switch</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>(c) Unipolar PWM Control with Dual-Switch</figcaption></figure>

<caption>Fig. 7: Rotor Terminal Common Mode Voltage with Different PWM Strategies</caption>

Among the mitigation measures for reducing bearing current, the most cost-effective method is directly reducing its source, that is, decreasing CMV and CMC through software-based solutions. To this end, we developed a EESM model with converters and bearings model, controlled different PWM strategies, and performed a comparison of different approaches and combination. Finally, simulations were conducted to demonstrate the effectiveness of various control strategy combinations in mitigating the influence of common-mode effects on the bearings. The results indicate that certain strategies show advantages in reducing both bearing voltage and bearing current, allowing us to find optimal and non-optimal PWM strategies at fixed operational points.

In future research, hardware solutions can also be combined, and simulations can be conducted under different operating conditions. The present results are based on parasitic capacitance measurements around 1 MHz and bearing capacitance under specific lubrication conditions, which introduces certain limitations. Consequently, future studies should consider a wider range of bearing impedance variations arising from broader motor operating conditions. Additionally, a more extensive impedance spectrum analysis can be achieved by simulating and measuring voltage and current spectra across a broader frequency range.

Furthermore, adaptive adjustments in the time domain are necessary, such as adjusting PWM strategies and switching frequency ($f_d$) based on the motor's operational point. Ultimately, this will lead to the development of adaptive PWM control strategies with tunable parameters.
<figure><img src="image_14.png" /><figcaption>(a) SVPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(c) AZSPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(e) SVPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>(g) AZSPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>(i) SVPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>(k) AZSPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>(b) GDPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>(d) NSPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>(f) GDPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>(h) NSPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>(g) GDPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>(l) NSPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<caption>Fig. 8: Simulated Bearing Voltage Results for Various PWM Strategy Combinations</caption>
<figure><img src="image_26.png" /><figcaption>(a) SVPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>(c) AZSPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>(e) SVPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>(g) AZSPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>(i) SVPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>(k) AZSPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>(b) GDPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>(d) NSPWM + Bipolar PWM</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>(f) GDPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_35.png" /><figcaption>(h) NSPWM + Unipolar PWM with Single-Switch</figcaption></figure>

<figure><img src="image_36.png" /><figcaption>(g) GDPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>(l) NSPWM + Unipolar PWM with Dual-Switch</figcaption></figure>

<caption>Fig. 9: Simulated Bearing Current Results for Various PWM Strategy Combinations</caption>
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