Research on Analysis and Suppression Methods of the Bearing Current for Electric Vehicle Motor Driven by SiC Inverter ^†

Abstract

The silicon carbide (SiC) inverter brings great advantages to the motor drive systems of new energy vehicles; however, severe challenges to the bearings also happen. The high dc bus voltage and switching frequency of SiC inverter can increase the discharge frequency and energy when the bearing grease film collapses. As a result, the bearing suffers severe electric corrosion, and the service life of the motor drive system can be shortened. In this paper, the characteristics of common-mode voltage and bearing voltage are analyzed, firstly under space vector pulse width modulation (SVPWM). After that, the common-mode equivalent circuit model of the motor drive system is established. The frequency characteristics of bearing voltage are revealed, and the safe working area is determined. Then, the frequency characteristics of bearing voltage and current are verified based on IGBT and SiC inverters in experiments. After that, by designing a common-mode filter, the bearing voltage and current are significantly attenuated. Furthermore, the active zero state PWM (AZSPWM) is adopted to reduce the common-mode voltage from the inverter. At the same time, combined with the common-mode filter, the bearing voltage and current are further reduced. The experimental results show that the switching frequency has a decisive effect on the amplitude of bearing voltage and current. The bearing voltage can be attenuated to around half of the reference bearing voltage by using the common-mode filter and AZSPWM strategy, respectively. The combination of the common-mode filter and AZSPWM strategy can reduce the bearing voltage to around one-fourth of the reference bearing voltage, which can effectively reduce the breakdown time and discharge energy of the grease oil film.

1. Introduction

The bearing is the key component which determines the life and reliability of the motor drive system. Motor failures are largely attributed to damage to the bearing, and electric corrosion is one of the main factors [1,2]. Considering the complexity and cost, the three-phase, two-level voltage source inverter is mainly adopted in the electric vehicle drive system. The common-mode voltage of the inverter couples through the parasitic capacitances of the motor, resulting in bearing voltage on both sides of the bearing lubricating grease oil film. When the bearing voltage exceeds the breakdown threshold of the lubricating grease oil film, the discharge phenomenon occurs, leading to the electric discharge machining (EDM) bearing current. The energy released during the discharge can cause concave pits on the surface of inner and outer rings as well as on the rolling balls of the bearing. A large number of breakdown discharges can cause great damage to the bearing, posing a serious threat to the life of the motor drive system [3,4,5].

The 800 V dc bus voltage and SiC power devices are becoming the development direction for electric vehicle drive systems [6,7]. The high voltage and high frequency are conducive to the reduction in the volume and the improvement of the power density of motor drive systems [8]. For example, in 2022, Marelli Europe S.p.A., a well-known auto parts supplier, developed a high power density SiC inverter with a dc bus voltage of 900 V and a switching frequency of 65 kHz. Compared with the traditional IGBT inverters, its volume and weight were reduced by 30%, the loss was reduced by 50%, and the efficiency reached 99.5% [9]. The National New Energy Vehicle Technology Innovation Center also developed an SiC inverter with a dc bus voltage 900 V in 2022, with the capacity of 550 kVA and a switching frequency of 25 kHz. Compared with the traditional design, the volume was reduced by 6.6 times, and the weight was reduced by 3.3 times [10]. However, the increase in dc bus voltage and switching frequency could exacerbate the bearing electric corrosion. Bearing electric corrosion has become a pain point problem that needs to be solved urgently in the field of electric vehicles.

From current research, it could be summarized that the suppression of the motor bearing current can be addressed from three aspects, including the bearing reinforcement, the capacitive coupling paths within the motor, and the source of common-mode voltage. Conductive grease bearings and ceramic bearings have been applied to suppress bearing current [11]. Conductive grease bearings create a conductive channel inside the bearing, bypassing the bearing oil film, making it difficult to establish a stable bearing voltage, which prevents the discharge of the bearing oil film. However, the metallic particles in the lubricating grease can increase its mechanical wear. Additionally, designing a lubricating grease that balances both lubrication and conductivity poses a technical challenge [12]. Ceramic bearings employ the insulating method to block the current path, increasing the bearing impedance to suppress the bearing current. However, the ceramic bearing can impact the rotor heat dissipation. Additionally, the accumulated bearing voltage on the shaft still exists, which can create a coupling loop through the non-insulated bearing or gear system of the reducer, still leading to electric corrosion. Ceramic bearings are generally used with the conductive brush to obtain better suppression effect. The conductive brush can release the bearing voltage as much as possible to the housing through a low-impedance path. However, ceramic bearings are relatively expensive, and the conductive brushes require regular maintenance and replacement.

From the perspective of the capacitive coupling paths, it can diminish the capacitive coupling effect to reduce bearing voltage by optimizing the motor design [13]. Additionally, a grounded electromagnetic shielding layer is installed at the end of the stator windings to alter the parasitic capacitive coupling path, thereby suppressing the bearing currents [14]. However, the suppression effect of bearing currents is relatively small through optimizing windings and slot shapes. Moreover, the electromagnetic shielding layer increases the manufacturing difficulty and the motor cost. The eddy current effect inside the shielding layer leads to an increased temperature, thus reducing its practical application in the industrial field.

The root cause of bearing current lies in the common-mode voltage of the inverter. The amplitude and frequency of the common-mode voltage directly determine the severity of bearing currents. Therefore, by reducing the amplitude of the common-mode voltage at its source, the pressure on bearing design can be significantly alleviated. The suppression of common-mode voltage can be achieved through both software and hardware methods. Software methods involve the utilization of non-zero vectors modulation strategies, such as AZSPWM, remote-state PWM (RSPWM), near-state PWM (NSPWM), etc. [15]. Non-zero vector modulation strategies can reduce the amplitude of common-mode voltage to one-third of that in traditional SVPWM. The hardware suppression methods mainly include innovative inverter structures, such as multi-level and multi-phase topology circuits, etc. These topologies provide a higher degree of design freedom and can effectively reduce the common-mode voltage when combined with specific modulation strategies. However, considering all factors, including the cost, the power density, and the complexity, the multi-phase and multi-level topologies are less commonly applied in electric vehicles [16,17]. In addition, the passive filters can also be used to suppress bearing currents thanks to the simple structure [18,19].

Unlike IGBT inverters, the SiC inverters have a unique impact on bearing voltage and bearing current. Currently, few studies on motor bearing current under an SiC inverter are available. The high-frequency characteristics of the SiC inverter are more likely to excite parasitic capacitances within the motor, causing complex effects on bearing voltage and bearing current. Moreover, the mechanisms of the bearing voltage and bearing current are not clear, and urgent studies are needed.

This paper aims to reveal the frequency characteristics of bearing voltage and bearing current, and to propose an effective suppression method. In this paper, the characteristics of bearing voltage and bearing current are studied by using IGBT and SiC inverters. The common-mode equivalent circuit of a motor drive system is established, and the frequency–characteristic curve of bearing voltage is obtained. The principle of dividing the anger zone and safe operating zone of bearing voltage is obtained. The common-mode filter and AZSPWM strategy are adopted to suppress the bearing voltage. This paper is organized as follows. Section 2 presents the generation mechanism and coupling path of bearing voltage and bearing current. Section 3 presents the high-frequency common-mode equivalent circuit of the motor drive system and the concept of the safe operating zone for bearing voltage. Section 4 describes the experimental platform and test results based on IGBT and SiC inverters. Section 5 presents a suppression method of a common-mode filter to suppress the bearing current. Section 6 presents a suppression method of combining the AZSPWM strategy with the common-mode filter. Section 7 concludes the paper.

2. Bearing Voltage and Bearing Current in Motor Drive System

2.1. Generation Mechanism and Coupling Path

The source of the bearing voltage and bearing current is the high-frequency common-mode voltage output by the inverter. As shown in Figure 1, a three-phase, two-level voltage source inverter comprises of six switch devices, and the common-mode voltage of the inverter V_cm is shown as Equation (1). V_ag, V_bg, and V_cg are the three-phase voltages of the inverter to the reference ground g (the inverter heatsink and the motor housing). There are eight switch states for the inverter under the SVPWM strategy. The numbers 0 and 1 are utilized to denote the switch states of a bridge arm in an inverter. The state of 1 indicates that the upper device is closed while the lower device is open. The state of 0 indicates that the upper device is open while the lower device is closed. Consequently, the V_cm values of eight switch states are shown in

Table 1. Common-mode voltage of the inverter under 8 switch states by using the SVPWM strategy.

States	S0	S1	S2	S3	S4	S5	S6	S7
	000	100	110	010	011	001	101	111
Values	$-\frac{U_{\mathrm{dc}}}{2}$	$-\frac{U_{\mathrm{dc}}}{6}$	$\frac{U_{\mathrm{dc}}}{6}$	$-\frac{U_{\mathrm{dc}}}{6}$	$\frac{U_{\mathrm{dc}}}{6}$	$-\frac{U_{\mathrm{dc}}}{6}$	$\frac{U_{\mathrm{dc}}}{6}$	$\frac{U_{\mathrm{dc}}}{2}$

, while the waveform of V_cm is shown in Figure 2. In Figure 2, the U_dc represents the dc bus voltage and the T_s represents the time of a switching cycle. The common-mode voltage V_cm is a four-level waveform under the SVPWM strategy. In this paper, the impact of switching frequency f_s on the common-mode voltage V_cm and bearing voltage V_b is analyzed.

$$V_{\mathrm{cm}}=\frac{1}{3}\left(V_{\mathrm{ag}}+V_{\mathrm{bg}}+V_{\mathrm{cg}}\right)$$

(1)

Under the excitation of high-frequency common-mode voltage, the impedance state of the motor exhibits a capacitive characteristic. As shown in Figure 3, C_ws, C_wr, and C_sr represent the parasitic capacitances of the winding to the stator core and to the rotor, and the stator core to the rotor, respectively. C_b represents the equivalent capacitance of the bearing grease oil film. These parasitic capacitances provide a low impedance coupling path for the high-frequency common-mode voltage.

The generation process of bearing voltage and bearing current can be described by the equivalent circuit shown in Figure 4. The n point represents the neutral point in the star-connected motor. V_cm represents the common-mode voltage output from the inverter, and V_ng represents the common-mode voltage at the motor neutral point. L_c and R_c are the equivalent common-mode inductance and resistance of the cable, respectively, and L_m and R_m are the equivalent common-mode inductance and resistance of the motor winding, respectively. The R_b is the equivalent resistance of the bearing, and S_b is the analog switch in the circuit. After passing through the cable and the motor winding, V_cm generates V_ng at the neutral point of the motor. Under the coupling effect of parasitic capacitances in the motor, a stable bearing voltage V_b is formed at both ends of the bearing lubricating grease film. At this time, the switch S_b in Figure 4 is open, and the change in bearing voltage regularly charges and discharges the oil film capacitance C_b to form the dv/dt capacitive bearing current i_b,cap. The amplitude of i_b,cap is small, and its influence on bearing electric corrosion is generally ignored [20]. When the V_b exceeds the voltage threshold of the lubricating grease oil film, the discharge phenomenon occurs. At the discharge moment, the oil film is no longer stable and the V_b drops to 0 V. At this time, the analog switch S_b in Figure 4 is closed, and C_b is shorted to simulate the breakdown and discharge process of the oil film. The bearing current generated by the discharge is called EDM bearing current i_b,EDM. The amplitude of i_b,EDM is large, and the energy is released instantaneously. The heat released by multiple discharges could melt the rolling elements and raceways, which is the most direct cause of bearing electric corrosion. According to the above analysis, although the coupling paths of i_b,cap and i_b,EDM are the same, they do not occur simultaneously.

2.2. Analytical Calculation Process

According to the common-mode equivalent circuit shown in Figure 4, the V_ng is obtained as shown in Equation (2). Z_c is the equivalent common-mode impedance of the cable, Z_m the equivalent common-mode impedance of the motor winding, and Z_cap is the common-mode impedance of parasitic capacitances inside the motor.

$$V_{\mathrm{ng}}=\frac{Z_{\mathrm{cap}}}{Z_{\mathrm{c}}+Z_{\mathrm{m}}+Z_{\mathrm{cap}}}{V}_{\mathrm{cm}}$$

(2)

Ignoring the bearing resistance R_b, which is generally very small, the relationship between V_b and V_ng is shown in Equation (3). K_BVR is defined as the bearing partial pressure ratio, which is often used to roughly evaluate the electric corrosion degree of the bearing. When the bearing is in a stable rotating state, the bearing oil film thickness is stable. C_b is a constant value and K_BVR can be considered as a constant [21].

$$V_{\mathrm{b}}=\frac{C_{\mathrm{wr}}}{C_{\mathrm{wr}}+C_{\mathrm{rs}}+C_{\mathrm{b}}}{V}_{\mathrm{ng}}=K_{\mathrm{BVR}}\cdot V_{\mathrm{ng}}$$

(3)

According to Equations (2) and (3), the relationship between V_b and V_cm is shown in Equation (4). V_b is the result of the voltage division of V_cm through a common-mode equivalent circuit, and the waveform of V_b is consistent with those of V_cm and V_ng, both of which are four-level waveforms. When the amplitude and frequency of V_cm are determined, V_b is decided by the common-mode impedances of the cable and motor, which in turn determines the magnitude of i_b,EDM.

$$V_{\mathrm{b}}=K_{\mathrm{BVR}}\frac{Z_{\mathrm{cap}}}{Z_{\mathrm{c}}+Z_{\mathrm{m}}+Z_{\mathrm{cap}}}{V}_{\mathrm{cm}}$$

(4)

The accurate calculation of i_b,EDM is very difficult, as it depends on the bearing voltage and the impedance of the bearing lubricating grease oil film. The thickness of bearing oil film highly depends on its speed, load, temperature, and the raceway surface roughness. During the rotation process, the lubricating grease oil film is uneven. When the bearing voltage exceeds the voltage threshold, the oil film would break down and discharge at its weakest position. Therefore, the occurrence of the i_b,EDM can be regarded as irregular, and some studies believe that it is random, following statistical probability. However, it should be noted that the occurrence probability of i_b,EDM depends on the stable amplitude of the V_b and increases with the increase in V_b [22].

3. Analysis Model of a Common-Mode Equivalent Circuit for Bearing Voltage

3.1. Frequency Characteristics Analysis of Bearing Voltage

According to Equation (4), when V_cm is determined, the V_b and i_b,EDM are mainly affected by the common-mode impedance of the cable and motor. Therefore, it is necessary to study the frequency characteristics of the common-mode impedance of the motor. The common-mode equivalent circuit in Figure 4 is simplified as shown in Figure 5, where R_cm, L_cm, and C_cm are the equivalent resistance, the inductance, and capacitance of the simplified common-mode circuit, respectively.

Based on the RLC series equivalent circuit in Figure 5, the variation law of V_ng can be obtained by analyzing the voltage frequency characteristics of C_cm. According to Equation (3), the voltage frequency characteristics of V_b are consistent with V_ng, so the amplitude–frequency characteristics of V_b can be obtained, as shown in Equation (5). After the dc bus voltage of the inverter is determined, the V_cm amplitude is determined and the relationship between the V_b and frequency is obtained, as shown in Equation (6). The corresponding frequency–characteristic curve is shown in Figure 6. The P denotes the peak point, and the O denotes the resonant point of the curve in Figure 6. The ω_P and ω₀ are angular frequencies at points P and O, respectively.

$$H(j\omega )=\frac{\left|{\dot{V}}_{\mathrm{b}}\right|}{\left|{\dot{V}}_{\mathrm{cm}}\right|}=K_{\mathrm{BVR}}\frac{\left|{\dot{V}}_{\mathrm{ng}}\right|}{\left|{\dot{V}}_{\mathrm{cm}}\right|}=K_{\mathrm{BVR}}\frac{1}{\sqrt{{\left(1-{\omega }^2{L}_{\mathrm{cm}}{C}_{\mathrm{cm}}\right)}^2+{\left(\omega C_{\mathrm{cm}}{R}_{\mathrm{cm}}\right)}^2}}$$

(5)

$$V_{\mathrm{b}}=K_{\mathrm{BVR}}{V}_{\mathrm{cm}}\frac{1}{\sqrt{{\left(1-{\omega }^2{L}_{\mathrm{cm}}{C}_{\mathrm{cm}}\right)}^2+{\left(\omega C_{\mathrm{cm}}{R}_{\mathrm{cm}}\right)}^2}}$$

(6)

Angular frequency of the resonant point O:

$${\omega }_0=1/\sqrt{L_{\mathrm{cm}}{C}_{\mathrm{cm}}}$$

(7)

Angular frequency of the peak point P:

$${\omega }_{\mathrm{P}}={\omega }_0\sqrt{1-\frac{{\left({\omega }_0{R}_{\mathrm{cm}}{C}_{\mathrm{cm}}\right)}^2}{2}}$$

(8)

In zone ① in Figure 6, the amplitude of V_b remains basically unchanged, and the V_b in this zone is defined as the reference bearing voltage V_b*. The point N is defined as the bearing voltage attenuation point, and the corresponding amplitude is also V_b*. The angular frequency ω_N of point N is obtained as follows:

$${\omega }_{\mathrm{N}}=\frac{1}{L_{\mathrm{cm}}}\sqrt{\frac{2L_{\mathrm{cm}}}{C_{\mathrm{cm}}}-R_{\mathrm{cm}}^2}$$

(9)

3.2. The Danger Zone and Safe Operating Zone of Bearing Electric Corrosion

As illustrated in Figure 6, the variation trend of V_b is associated with the system common-mode impedance parameters and switching frequency. With the increase in switching frequency, the amplitude of V_b shows a trend of first rising and then decreasing. The frequency–characteristic curve in Figure 6 is divided into four zones. The analysis of each zone is as follows:

(1)

Zone ①: the frequency of common-mode excitation is before the ω_M. With the increase in frequency, the amplitude of V_b increases slowly and the frequency dependence of V_b is low. This zone is defined as the bearing voltage stable zone. There is V_b ≈ V_b* in this region. The V_b is usually in this zone when the motor is driven by an IGBT inverter (typical switching frequency between 2 kHz and 8 kHz).

(2)

Zone ②: the frequency of common-mode excitation is between ω_M and ω_P, and the amplitude of V_b increases significantly with the increase in frequency. This zone is defined as the bearing voltage growth zone. In this zone, there is always V_b > V_b*, and the V_b reaches its peak value at point P.

(3)

Zone ③: the frequency of common-mode excitation is between ω_P and ω_N, and the amplitude of V_b decreases gradually with the increase in frequency. This zone is defined as the bearing voltage drop zone. In this zone, there is always V_b > V_b*, and V_b decreases to V_b* at point N. However, the amplitude of V_b is still large in this zone.

(4)

Zone ④: when the frequency of common-mode excitation exceeds the ω_N, V_b begins to decrease below V_b*, and the rate of decline gradually slows down with the increase in frequency. This zone is defined as the bearing voltage safety attenuation zone. In order to reduce the risk of bearing electric corrosion, it is hoped that the switching frequency of the inverter is located in this zone.

In order to better evaluate the impact of bearing voltage on bearing electric corrosion, the zone in Figure 6 where V_b ≥ 1.1 V_b* is defined as the bearing electric corrosion danger zone. According to Equation (6), the expressions of ω_{d_min} and ω_{d_max} of, respectively, the lower and upper frequency points in this zone are as follows:

$${\omega }_{\mathrm{d}\_\min }=\sqrt{\frac{-0.5\left(C_{\mathrm{cm}}{R}_{\mathrm{cm}}^2-2L_{\mathrm{cm}}+\sqrt{\left.\left(C_{\mathrm{cm}}^2{R}_{\mathrm{cm}}^4-4C_{\mathrm{cm}}{L}_{\mathrm{cm}}{R}_{\mathrm{cm}}^2+3.31L_{\mathrm{cm}}^2\right)\right)}\right.}{C_{\mathrm{cm}}{L}_{\mathrm{cm}}^2}}$$

(10)

$${\omega }_{\mathrm{d}\_\max }=\sqrt{\frac{0.5\left(2L_{\mathrm{cm}}-C_{\mathrm{cm}}{R}_{\mathrm{cm}}^2+\sqrt{\left.\left(C_{\mathrm{cm}}^2{R}_{\mathrm{cm}}^4-4C_{\mathrm{cm}}{L}_{\mathrm{cm}}{R}_{\mathrm{cm}}^2+3.31L_{\mathrm{cm}}^2\right)\right)}\right.}{C_{\mathrm{cm}}{L}_{\mathrm{cm}}^2}}$$

(11)

In order to avoid the risk of bearing corrosion, the selection of switching frequency should try to avoid the danger zone between d_min and d_max in Figure 6. However, the selection of switching frequency is determined by many factors, such as efficiency, volume, power density, electromagnetic interference performance, etc. Therefore, the curve in Figure 6 can provide some references for the selection of the switching frequencies of SiC inverters.

Compared with other zones, zone ④ can obtain a smaller amplitude of V_b. Driven by a traditional IGBT inverter, V_b is often in region ①. However, the SiC device increases the switching frequency of the inverter, causing V_b to be located in zones ② or ③ with a large amplitude. This will increase the frequency and the harm degree of the EDM bearing current, causing serious bearing electric corrosion.

4. Experimental Measurement of Bearing Voltage and Bearing Current

4.1. Experimental Platform and Measurement Methods

The experimental platform is established as shown in Figure 7. An embedded permanent magnet synchronous motor is adopted with 6007 deep groove ball bearings. The bearing manufacturer is SKF, a company headquartered in Gothenburg, Sweden. The rotor materials are permanent magnets and silicon steel sheets. The electrical parameters of the motor are shown in

Table 2. The electrical parameters of the motor.

Parameters	Values
Rated power	8 kW
Rated speed	3000 r/min
Rated torque	26 N·m
Number of pole pairs	4

. The motor is driven by an IGBT inverter or a SiC inverter, with rated powers of 10 kW, respectively. The IGBT inverter is purchased from KEB, a company headquartered in Barntrup, Germany. The SiC inverter is developed in-house in the laboratory. The bearing voltage is measured using a conductive brush. The bearing current is measured through an intrusive measurement method, which requires modification of the motor end cover. An insulating layer is inserted between the bearing outer race and the motor end cover. Additionally, an external connection is established between the bearing outer race and the motor housing by using a short wire beside the motor for measuring bearing current [23]. The SVPWM strategy, 400 V bus voltage, and 0.5 m of unshielded cable are used in the experiment. The SiC transistor and the IGBT transistor used in this paper are the C2M0080120D and IGW40N120H3, respectively. The rise and fall times of output voltages for SiC inverter and IGBT inverter are provided in

Table 3. The rise and fall times of output voltage for inverters.

	SiC Inverter	IGBT Inverter
Rise time of voltage/ns	30	310
Fall time of voltage/ns	42	430

.

For deep groove ball bearings, when the rotational speed is below approximately 300 r/min, the lubricating grease cannot completely envelop the ball, resulting in metal-to-metal contact between the ball and the inner and outer races. The bearing oil film is short-circuited, preventing the establishment of bearing voltage. When the bearing speed is relatively high, the lubricating grease can generally form a stable oil film, allowing for the establishment of bearing voltage [24]. Therefore, in order to ensure the stable establishment of bearing voltage, the motor speed used in the experiment is set at 1200 r/min with a modulation ratio of M = 0.4 in this paper.

4.2. Experimental Results under IGBT and SiC Inverters Drive

The experimental results of the motor neutral point voltage V_ng, bearing voltage V_b, and bearing current were obtained using IGBT and SiC inverters, as shown in Figure 8. i_b,de and i_b,nde are, respectively, driven-end and non-driven-end bearing currents of the motor, and T_b is the temperature of the bearing outer race. In Figure 8, under the IGBT and SiC inverters’ drive, the stable amplitudes of V_b are approximately V_{b_IGBT} ≈ V_{b_SiC} = 6.3 V. It indicates that the stable amplitude of the V_b is significantly influenced by the switching frequency but is only slightly affected by the switching speed. In Figure 8a, the maximum value of i_{b,EDM__IGBT} is 55 mA, while in Figure 8b, the maximum value of i_{b,EDM__SiC} is 57 mA, with the amplitudes being nearly equal. Different high-bandwidth current probes were employed for repeated testing, revealing that the 2 mA current difference is not measurement error but a real difference. An explanation of this phenomenon is as follows: when the bearing rotates steadily, the lubricating grease film is uneven, and the raceway roughness is difficult to predict. Consequently, when breakdown discharge occurs in the oil film, the breakdown impedance is also different, which leads to slightly different amplitudes of i_b,EDM under the same test conditions. In the test conditions shown in Figure 8, both IGBT and SiC inverters were used, and a total of 30 sets of i_b,EDM were captured in each case. The results show that although the bearing voltage amplitudes are equal, all captured amplitudes of i_b,EDM fluctuate around 55 mA, with variations not exceeding 4 mA. This current fluctuation is considered normal and is not a result of measurement error.

Since V_{b_IGBT} and V_{b_SiC} have similar amplitudes, the maximum amplitudes of i_{b,EDM__IGBT} and i_{b,EDM__SiC} are also approximately equal, indicating that the amplitude of V_b determines the energy of the i_b,EDM. Furthermore, from Figure 8, it can be observed that the capacitive bearing current i_b,cap under the IGBT inverter is smaller than that in the SiC inverter, mainly due to the faster switching speed of the SiC inverter compared to the IGBT inverter. According to Table 3, the switching speed of the SiC inverter is approximately one-tenth of that of the IGBT inverter. The amplitude of i_b,cap is small, and the impact on bearing electric corrosion is also small. Under the IGBT inverter drive, i_b,cap is generally neglected. However, under the SiC inverter drive, the impact of i_b,cap on the bearing electric corrosion currently lacks relevant research conclusions.

4.3. Experimental Verification of Frequency Characteristics for Bearing Voltage and Current

The experimental platform in Figure 7 is used for testing, and the measurement results of common-mode parameters of the motor and cable are obtained, as shown in

Table 4. The measured parameters of a common-mode equivalent circuit.

Parameters	Rcm	Lcm	Ccm
Values	12 mΩ	0.97 mH	2.69 nF

. By substituting the parameters into Equations (7)–(11), the theoretical calculation results of points P, O, d_min, d_max, and N in Figure 6 are obtained. as shown in

Table 5. Theoretical calculation results of frequency points for a V_b characteristic curve in the experimental system.

Frequency Points	fd_min	fP	f0	fd_max	fN
Values/kHz	29.6	98.5	98.5	136.1	139.3

.

According to Table 5 and Figure 6, the analyses are as follows. When the switching frequency of the inverter used in the experiment exceeds 29.6 kHz, V_b begins to enter the danger zone in Figure 6. As the switching frequency increases, the amplitude of V_b increases significantly, reaching its maximum value at a frequency of 98.5 kHz. In the range from 98.5 kHz to 136.1 kHz, V_b begins to decrease, but it remains higher than the reference bearing voltage V_b*. Therefore, when the switching frequency falls within the range from 29.6 kHz to 136.1 kHz, there is a significant risk of bearing electric corrosion. According to Figure 6, when the switching frequency exceeds 139.3 kHz, V_b starts to decrease below V_b*. In fact, constrained by electromagnetic interference and the control speed of the main controller, the switching frequency of the SiC inverter for the electric vehicle is generally lower than 100 kHz at present. Therefore, for the motor drive system adopted in the experiment, the V_b is located in zones ① and ② in Figure 6.

The theoretical calculation and experimental results of the V_b under different switching frequencies are obtained in Figure 9. The reference bearing voltage is V_b* = 6.3 V. When the switching frequency is less than 20 kHz, V_b increases slowly. In the range of 20 kHz–80 kHz, V_b increases quickly. Below 40 kHz, the theoretical calculations and experimental results are basically consistent. Above 40 kHz, with the increase in switching frequency, the error between the theoretical calculation and experimental results becomes more significant. The analyses of error sources are as follows. Although the RLC lumped parameter equivalent circuit of the motor is simple, it is not accurate. In addition, there are measurement errors in the extraction of circuit parameters. Although there are errors at high frequencies, the overall variation trend of the bearing voltage is consistent with that of the frequency–characteristic curve depicted in Figure 6.

Figure 10 shows the number of i_b,EDM occurrences (that is, the number of bearing oil film breakdown discharges) with the switching frequency per minute. The number of breakdown discharges was measured by taking the average value of multiple sample datasets. The results show that the increase in V_b could lead to the increased bearing breakdown discharges. The number of i_b,EDM is approximately exponential with the rising switching frequency. Based on Figure 10, the relationship between breakdown discharge times and switching frequency is obtained, as shown in Equation (12). N_d denotes the number of breakdown discharges. For the application in this paper, the values of the variables are A = 16.3, B = 8 × 10⁷, C = 137.9, D = 2, and E = 349.

$$N_{\mathrm{d}}=A+\frac{B}{C\sqrt{\pi /2}}{e}^{-D\frac{{(f\mathrm{s}-E)}^2}{C^2}}$$

(12)

The basic bearing voltage V_b*, especially at low switching frequency, already poses a significant threat to motor bearings. The increased switching frequency of the SiC inverter inevitably results in a further increase in bearing voltage. The dc bus voltage of the motor drive system is upgraded from 400 V to 800 V, which can double the bearing voltage. Therefore, with the increase in dc bus voltage and switching frequency, bearing voltage, and EDM bearing current are fatal to bearing damage, and effective suppression measures must be taken.

5. Design of Common-Mode Filter for Reducing Bearing Voltage and Current

The high switching frequency of the SiC inverter is advantageous for reducing the volume of the filter. Employing a common-mode filter to improve the frequency characteristics of a common-mode equivalent circuit and to suppress bearing voltage is an effective approach to mitigate bearing electric corrosion.

5.1. Theoretical Calculation and Experimental Verification for Common-Mode Filter

The actual operating frequency of the SiC inverter used in the experiment is 50 kHz. According to Table 5, the V_b of the experimental motor is located in zone ② in Figure 6, which is the danger zone. In order to greatly reduce the V_b, it is necessary to design a common-mode filter to ensure that V_b is located in zone ④, so as to reduce the risk of bearing electric corrosion. The common-mode equivalent circuit of the motor drive system with a common-mode filter is shown in Figure 11.

In order to attenuate the V_b by at least half of the reference bearing voltage V_b*, according to Equation (6), the Equation (13) can be obtained:

$$\frac{1}{\sqrt{{\left(1-{\omega }^2\left(L_{\mathrm{choke}}+L_{\mathrm{cm}}\right)C_{\mathrm{cm}}\right)}^2+{\left(\omega C_{\mathrm{cm}}{R}_{\mathrm{cm}}\right)}^2}}\le 0.5$$

(13)

Substituting the parameters in Table 4 into Equation (13), L_choke ≥ 10.33 mH is obtained. The inductance of common-mode filter needs to be greater than 11 mH. In order to achieve V_b ≤ 0.5V_b*, the actual designed common-mode filter has a certain margin, and the final inductance value is 13 mH. There is an error in the actual and theoretical design of the inductance value, which mainly arises from the following three aspects: the presence of other harmonic components in the common-mode excitation V_cm, inherent errors in the lumped parameter equivalent circuit, measurement errors in the extraction of common-mode parameters, and parasitic parameters in the filter. The above factors cause the error between the theoretical and actual inductance values in this paper.

According to the equivalent circuit model shown in Figure 11, when the inductance of the common-mode filter changes, the frequency characteristics of the motor drive system also change accordingly. Correspondingly, the curve of V_b also changes with frequency in Figure 6. According to Equations (7)–(11), the theoretical calculation results of each frequency point at the curve in Figure 6 are shown in

Table 6. Theoretical calculation results of frequency points for the V_b characteristic curve in the experimental system (L_choke = 13 mH).

Frequency Points	fd_min	fP	f0	fd_max	fN
Values/kHz	7.8	26	26	35.9	36.7

by using a 13 mH common-mode filter.

The experimental waveforms are shown in Figure 12. In Figure 12a, the amplitude of V_b is 7.9 V without a common-mode filter, and the maximum amplitude of i_b,EDM is 120 mA. V_b is located in zone ② of Figure 6. In Figure 12b, after using a common-mode filter, the measured amplitude of V_b is 3.1 V, and V_b is located in zone ④ of Figure 6, which is reduced to 0.49 times of the reference value V_b* = 6.3 V. By using a common-mode filter, significant attenuation of V_b is obtained, and no discharge of oil film occurs during the experiment.

5.2. Negative Effects Caused by Improper Design of a Common-Mode Filter

In order to suppress electromagnetic interference in practical applications, a magnetic ring is often used at the output end of inverter, as shown in the red box in Figure 1. The magnetic ring can be equivalent to a common-mode filter with a single turn coil, which has a small inductance. The V_b is usually located in zone ① of Figure 6 when using an IGBT inverter with a low switching frequency. According to Figure 6 and Equation (6), the amplitude of V_b is basically not increased when the common-mode magnetic ring is installed at the output end of inverter. Therefore, the magnetic ring is used to suppress electromagnetic interference while minimizing the negative impact on V_b. However, when using a SiC inverter with a high switching frequency, V_b is located in zone ② in Figure 6. If the magnetic ring is still installed at the output end of the inverter to suppress electromagnetic interference, according to Equation (6), V_b would increase significantly, thereby increasing the risk of bearing electric corrosion.

To illustrate the above issue, a common-mode filter with a small inductance of 3 mH is used for the analysis. The frequency points of the curve in Figure 6 are recalculated and the results are shown in

Table 7. Theoretical calculation results of frequency points for the V_b characteristic curve in the experimental system (L_choke = 3 mH).

Frequency Points	fd_min	fP	f0	fd_max	fN
Values/kHz	14.6	48.7	48.7	67.3	432.8

. According to Figure 6 and Table 7, if the inverter still adopts the switching frequency f_s = 50 kHz, which is close to the resonant frequency of the system in Table 7, the amplitude of V_b is large. As a result, the bearings will face a significant risk of electric corrosion.

Still using the same testing conditions as in Figure 12, the experimental results are shown in Figure 13. The measured amplitude of V_b reaches 13 V, which is 65% higher than that (7.9 V) in Figure 12a. This significantly increases the breakdown times and discharge energy of the bearing oil film. The number of breakdown discharges per minute measured is as high as 238 times, and the maximum EDM bearing current is 250 mA, which is approximately twice that (120 mA) shown in Figure 12a. Based on the theoretical and experimental results above, the switching frequency f_s = 50 kHz in the experiment is close to the peak point frequency in Figure 6, inevitably leading to excessive bearing voltage and serious bearing corrosion.

In summary, for the SiC motor drive system, the design of a common-mode filter or magnetic ring needs to consider the suppression effects on both electromagnetic interference and bearing voltage. It is essential to refer to the design methods proposed in Section 3. Otherwise, improper filter design may exacerbate the bearing electric corrosion.

6. The Suppression Method for Bearing Current in a Motor Drive System with a High-Voltage SiC Inverter

In order to relieve the design pressure of the bearing in the motor drive system with a high voltage and high frequency, the AZSPWM strategy is adopted to weaken the common-mode voltage of the inverter from the source. Then, a common-mode filter is adopted for the output end of the inverter to further reduce the bearing voltage, reducing the discharge times and the discharge energy of the bearing oil film.

6.1. The AZSPWM Strategy

With the SVPWM strategy, the maximum value of the common-mode voltage is U_dc/2 when using the zero vector. A non-zero vector modulation strategy can be used to reduce the common-mode voltage amplitude by canceling the zero vector. Considering the switching loss, modulation ratio, and harmonics, the AZSPWM strategy is adopted in this paper. The comparison of the vector synthesis for SVPWM and AZSPWM-1 in sector I is shown in Figure 14. The idea of AZSPWM-1 is to replace the zero vector by using two non-zero vectors in opposite directions acting at the same time, so that the amplitude of the common-mode voltage is suppressed to U_dc/6 [25].

The AZSPWM strategy is divided into three types: AZSPWM-1, AZSPWM-2, and AZSPWM-3. The suppression effect on the common-mode voltage is the same for all three modulation strategies. For AZSPWM-2 and AZSPWM-3, the two bridge arms of the inverter need to operate simultaneously, leading to increased losses. Therefore, the AZSPWM-1 strategy is adopted. The AZSPWM-1 strategy may increase current harmonics, but the high switching frequency of the SiC inverter can reduce these current harmonics, compensating for this drawback.

With the AZSPWM-1 strategy, the common-mode voltage waveform is shown in Figure 15. The amplitudes are different in the even sector and odd sector, but the maximum value is U_dc/6, which is one-third of the maximum value U_dc/2 under the SVPWM strategy.

6.2. The Suppression Effect of Bearing Voltage and Bearing Current

Still using the same testing conditions as Figure 12, the experimental results are shown in Figure 16. In Figure 16a, the AZSPWM-1 strategy is adopted and the amplitude of V_b is reduced to 2.9 V, which is 63% lower than that of 7.9 V driven by SVPWM in Figure 12a. In Figure 16b, the combination of AZSPWM-1 and the 13 mH common-mode filter is adopted. The amplitude of V_b is reduced to 1.5 V and the V_b is greatly attenuated. During the experiment, no discharge phenomena occurred.

The comparison results of bearing voltage amplitudes and breakdown discharge times are shown in

Table 8. Comparison results of bearing voltage and discharge times under different suppression methods.

Methods	Bearing Voltages/V	Multiples Relative to Vb* = 6.3 V	Breakdown Discharge Times (times/min)
SVPWM	7.9	1.25	65
SVPWM+3 mH common-mode filter	13	2.1	238
SVPWM+13 mH common-mode filter	3.1	0.49	No breakdown discharge
AZSPWM	2.9	0.46	No breakdown discharge
AZSPWM+13 mH common-mode filter	1.5	0.24	No breakdown discharge

under different suppression methods. The combination of AZSPWM-1 and the common-mode filter achieves the best suppression effect, reducing the bearing voltage to 1.5 V. It effectively suppresses the EDM bearing current and is highly suitable for a motor drive system with a high voltage and high frequency.

7. Conclusions

This paper investigates the characteristics and suppression methods of bearing voltage and EDM bearing current under SiC inverter drive. By establishing the common-mode equivalent circuit of the motor drive system, the frequency characteristics of bearing voltage are revealed. The suppression method is proposed, which is suitable for a motor drive system with a high voltage and high frequency. Through theoretical analysis and experimental validation, the following conclusions are drawn.

Compared to a traditional IGBT inverter, the SiC inverter with a high switching frequency increases the amplitude of bearing voltage, exacerbating the risk of bearing electric corrosion. The selection of switching frequency must consider the impact on the bearing voltage and the EDM bearing current.

For motor drive systems with a SiC inverter, the design of the common-mode filter or magnetic ring needs to consider the influence on bearing voltage and current. Otherwise, negative effects may occur, aggravating bearing electric corrosion. The proposed design method of common-mode filter can improve the frequency characteristics of bearing voltage, attenuating the bearing voltage to half of the reference bearing voltage and keeping it in the safe operating zone.

The AZSPWM-1 strategy can attenuate the bearing voltage to around half of the reference bearing voltage. When combining AZSPWM-1 and a common-mode filter, the bearing voltage is reduced to around one-fourth of the reference bearing voltage, achieving the best suppression effect. This method effectively reduces the breakdown times of lubricating grease oil film, which is suitable for motor drives with a high voltage and high frequency in electric vehicles.