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

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Bearing Voltage and Bearing Current in Motor Drive System

#### 2.1. Generation Mechanism and Coupling Path

_{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, 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.

_{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.

_{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

_{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.

_{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].

_{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}.

_{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

_{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.

_{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 ω

_{0}are angular frequencies at points P and O, respectively.

_{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:

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

_{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.

_{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:

_{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.

_{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

#### 4.2. Experimental Results under IGBT and SiC Inverters Drive

_{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.

_{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

_{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.

_{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.

_{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 × 10

^{7}, C = 137.9, D = 2, and E = 349.

_{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

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

_{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.

_{b}by at least half of the reference bearing voltage V

_{b}*, according to Equation (6), the Equation (13) can be obtained:

_{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.

_{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 by using a 13 mH common-mode filter.

_{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

_{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.

_{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.

_{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.

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

#### 6.1. The AZSPWM Strategy

_{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].

_{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

_{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.

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Measured waveforms of V

_{ng}, V

_{b}, i

_{b,de}, and i

_{b,nde}(test conditions: SVPWM, U

_{dc}= 400 V, f

_{s}= 4 kHz, M = 0.4, T

_{b}: 24~26 °C). (

**a**) Under IGBT inverter drive; (

**b**) under SiC inverter drive.

**Figure 12.**Measured waveforms of V

_{ng}, V

_{b}, and i

_{b}(test conditions: SVPWM, U

_{dc}= 400 V, f

_{s}= 50 kHz, M = 0.4, T

_{b}: 24~26 °C). (

**a**) Without common-mode filter; (

**b**) with a 13 mH common-mode filter.

**Figure 13.**Measured waveforms of V

_{ng}, V

_{b}, and i

_{b}(test conditions: SVPWM, U

_{dc}= 400 V, f

_{s}= 50 kHz, M = 0.4, T

_{b}: 24~26 °C, L

_{choke}= 3 mH).

**Figure 14.**Comparison of vector syntheses for different modulation strategies (taking sector I as an example). (

**a**) SVPWM; (

**b**) AZSPWM-1.

**Figure 15.**Diagram of common-mode voltage waveform under AZSPWM-1 strategy. (

**a**) Even sector; (

**b**) odd sector.

**Figure 16.**Measured waveforms of V

_{ng}, V

_{b}, and i

_{b}(test conditions: SiC inverter, AZSPWM-1, U

_{dc}= 400 V, f

_{s}= 50 kHz, M = 0.4, T

_{b}: 24~26 °C). (

**a**) Without common-mode filter; (

**b**) with a 13 mH common-mode filter.

States | S_{0} | S_{1} | S_{2} | S_{3} | S_{4} | S_{5} | S_{6} | S_{7} |

000 | 100 | 110 | 010 | 011 | 001 | 101 | 111 | |

Values | $-\frac{{U}_{\mathrm{dc}}}{2}$ | $-\frac{{U}_{\mathrm{dc}}}{6}$ | $\frac{{U}_{\mathrm{dc}}}{6}$ | $-\frac{{U}_{\mathrm{dc}}}{6}$ | $\frac{{U}_{\mathrm{dc}}}{6}$ | $-\frac{{U}_{\mathrm{dc}}}{6}$ | $\frac{{U}_{\mathrm{dc}}}{6}$ | $\frac{{U}_{\mathrm{dc}}}{2}$ |

Parameters | Values |
---|---|

Rated power | 8 kW |

Rated speed | 3000 r/min |

Rated torque | 26 N·m |

Number of pole pairs | 4 |

SiC Inverter | IGBT Inverter | |
---|---|---|

Rise time of voltage/ns | 30 | 310 |

Fall time of voltage/ns | 42 | 430 |

Parameters | R_{cm} | L_{cm} | C_{cm} |
---|---|---|---|

Values | 12 mΩ | 0.97 mH | 2.69 nF |

**Table 5.**Theoretical calculation results of frequency points for a V

_{b}characteristic curve in the experimental system.

Frequency Points | f_{d_min} | f_{P} | f_{0} | f_{d_max} | f_{N} |
---|---|---|---|---|---|

Values/kHz | 29.6 | 98.5 | 98.5 | 136.1 | 139.3 |

**Table 6.**Theoretical calculation results of frequency points for the V

_{b}characteristic curve in the experimental system (L

_{choke}= 13 mH).

Frequency Points | f_{d_min} | f_{P} | f_{0} | f_{d_max} | f_{N} |
---|---|---|---|---|---|

Values/kHz | 7.8 | 26 | 26 | 35.9 | 36.7 |

**Table 7.**Theoretical calculation results of frequency points for the V

_{b}characteristic curve in the experimental system (L

_{choke}= 3 mH).

Frequency Points | f_{d_min} | f_{P} | f_{0} | f_{d_max} | f_{N} |
---|---|---|---|---|---|

Values/kHz | 14.6 | 48.7 | 48.7 | 67.3 | 432.8 |

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

Methods | Bearing Voltages/V | Multiples Relative to V_{b}* = 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 |

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**MDPI and ACS Style**

Yang, M.; Cheng, Y.; Du, B.; Li, Y.; Wang, S.; Cui, S.
Research on Analysis and Suppression Methods of the Bearing Current for Electric Vehicle Motor Driven by SiC Inverter. *Energies* **2024**, *17*, 1109.
https://doi.org/10.3390/en17051109

**AMA Style**

Yang M, Cheng Y, Du B, Li Y, Wang S, Cui S.
Research on Analysis and Suppression Methods of the Bearing Current for Electric Vehicle Motor Driven by SiC Inverter. *Energies*. 2024; 17(5):1109.
https://doi.org/10.3390/en17051109

**Chicago/Turabian Style**

Yang, Mingliang, Yuan Cheng, Bochao Du, Yukuan Li, Sibo Wang, and Shumei Cui.
2024. "Research on Analysis and Suppression Methods of the Bearing Current for Electric Vehicle Motor Driven by SiC Inverter" *Energies* 17, no. 5: 1109.
https://doi.org/10.3390/en17051109