Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters in a Motor Drive Application

Received March 26, 2021, accepted April 10, 2021, date of publication April 13, 2021, date of current version May 12, 2021. Digital Object Identifier 10.1109/ACCESS.2021.3072967 Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters in a Motor Drive Application ABRAHAM MARQUEZ ALCAIDE 1, (Member, IEEE), XUCHEN WANG 2, (Member, IEEE), HAO YAN 3, (Member, IEEE), JOSE I. LEON 1,4, (Fellow, IEEE), VITO GIUSEPPE MONOPOLI 5, (Senior Member, IEEE), GIAMPAOLO BUTICCHI 2, (Senior Member, IEEE), SERGIO VAZQUEZ 1, (Fellow, IEEE), MARCO LISERRE 6, (Fellow, IEEE), AND LEOPOLDO G. FRANQUELO 1,4, (Life Fellow, IEEE) 1Electronic Engineering department, Universidad de Sevilla, 41004 Sevilla, Spain 2Electrical and Electronic Engineering, The University of Nottingham Ningbo China, Ningbo 315100, China 3School of Civil Aviation, Northwestern Polytechnical University, Xi’an 710072, China 4Department of Astronautic, Harbin Institute of Technology, Harbin 150001, China 5Department of Electrical and Information Engineering, Politecnico di Bari, 70125 Bari, Italy 6Power Electronics, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany Corresponding author: Xuchen Wang ([email protected]) This work was supported in part by the H2020 Spartan project under Grant 821381, in part by the Spanish Science and Innovation Ministry under Project TEC2016-78430-R, in part by the Consejería de Economía, Conocimiento, Empresas y Universidad/Secretaría General de Universidades, Investigación y Tecnología under Project PY18-1340, and in part by the Ningbo Science and Technology Bureau under Grant 2018B10082. ABSTRACT Electric variable speed drives (VSDs) based on two VSDs connected to a multiphase machine are an attractive solution to replace high-power mechanic and hydraulic systems in many sectors of industry and transportation because they present high performance with reduced cost, volume and weight. Among the causes which affect the reliability of dual VSDs, the common-mode current flowing through the machine bearing is an important issue. This paper faces the mitigation of the common-mode current by reducing the common-mode voltage (CMV) generated by the operation of a dual VSD. The CMV reduction is carried out without introducing any extra device and/or passive filtering method. This CMV reduction is performed by applying a specific phase-displacement between the modulation strategies of each single inverter drive. The proposed technique has been evaluated in a down scaled experimental setup in order to test its effectiveness. INDEX TERMS Harmonic analysis, pulse width modulation, common-mode voltage. I. INTRODUCTION The industry is moving from mechanical and hydraulic systems to the electrical drives because they present a better performance with a cost reduction [1]. As an example, permanent magnet synchronous machines (PMSMs) are widely used in electric vehicles owing to their advantages such as high efficiency, reduced cost and high performance [2], [3]. In order to achieve these objectives, the efficient and reliable variable speed drives (VSDs) are critical components of the system. In particular, the use of VSDs in power conversion systems presents many advantages such as high efficiency The associate editor coordinating the review of this manuscript and approving it for publication was Qiuye Sun . and superior dynamic performance because of its better control of machine flux and currents. In recent years, the multi-phase electric machines have attracted a lot of attention and the dual three-phase machine is the most common structure among the multi-phase machine ones [4], [5]. In a dual three-phase machine, two sets of three-phase stator windings increase the fault-tolerant ability and make the integration with conventional three-phase technology relatively simple [6]. Among the applications, it is possible to find multi three-phase systems and more particularly the dual three-phase drive in aerospace and marine applications [7]. Power converters for VSD applications have been intensively developed in the last decades [8], [9]. New multi-level VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 67477 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters FIGURE 1. Dual-drive of a multi-phase PMSM using two three-phase two-level inverters. power converter structures have been proposed and advanced control strategies and modulation techniques have been explored [10], [11]. However, although these converter topologies are available, the penetration in the industry is still limited. The traditional three-phase two-level power converter is nowadays leading the market in most industrial solutions. As an example, in Fig. 1a dual-drive for a multi-phase motor using two three-phase two-level inverters is shown. In the literature, many strategies to control a VSD can be found. Among them, the direct torque control (DTC), field oriented control (FOC) or model predictive-based control are very well-known [12], [13]. In the modulation stage, the methods to operate a three-phase two-level converter can be categorized in two main groups: space vector modulations (SVM) and carrier-based pulse-width modulation (CB-PWM) techniques [10]. Most of available control platforms include a dedicate peripheral to deploy and use the PWM modulation. Therefore, CB-PWM technique is the simplest and most straight-forward way to operate the power converter. Although the use of VSDs presents many advantages, several drawbacks directly affect to the performance, reliability and the remaining lifetime of the system [14]–[16]. As a main concern, the common-mode voltage (CMV) generated by the drive is closely related to the system reliability because of the corresponding bearings degradation. In fact, it has been demonstrated that the CMV is the cause of more than 50% of cases of motor failures [14], [15], [17]. In addition, the shaft voltage and bearing current phenomena also appear in induction machines [18], [19]. As a result of these issues, there is a trend to develop an accurate-enough mathematical approach to estimate and predict an early failure of the machine components [20]–[23]. Bearing degradation through CMV has attracted the attention of researchers in the last years. Multiple approaches have been performed, which can be categorized in two main streams: the CMV filtering via the introduction of external elements and the CMV mitigation considering a proper control strategy and/or modulation technique. Considering the introduction of external elements, passive filtering and the use of active canceler circuits can be found [24]–[27]. Despite of these methods provide good results, the introduction of extra passive filtering elements and/or active devices is undesirable because the increase in cost, volume and weight. On the other hand, if the CMV mitigation is performed by developing new modulation methods, the academia provides several options, most of them based on the proper switching pattern selection using specific SVM techniques [17], [28]–[31]. In [32], [33], the CMV mitigation for the dual drive is achieved applying a SVM method at the expense of developing complex calculations in the modulation stage. This work studies the CMV present in the dual drive application shown in Fig. 1and develops a simple CB-PWM method to mitigate its negative effects on the system. To perform this analysis, the CMV harmonic spectrum based on double Fourier description is carried out. From this analysis, a phase-shift between the PWM operation of both drives is proposed in order to minimize the CMV harmonic distortion. In the proposed method, the CMV mitigation is obtained without external passive filtering elements and/or active CMV canceler circuits. In addition, the proposed technique is easily implementable on the most off-the-shelf mid-range micro-controller control platforms. The rest of the paper is organized as follows: in section II the negative effects of the CMV over the motor bearing and its degradation is presented. Section III analyzes the harmonic spectrum of the CMV as consequence of the dual drive operation. In section IV, the effect of the proposed modulation technique in the machine currents is shown. In section V, the validation of the modulation technique via experimental results is performed and section VII highlights the conclusions of the work. II. BEARING DEGRADATION IN MULTI-PHASE PMSM CAUSED BY THE CMV In general, the motor bearing faults are caused by two reasons, mechanical and electrical. Among the electrical reasons, the shaft current is a key factor. According to bearing manufacturers, 25% of the bearing faults are caused by the shaft current, and this ratio is rising with the development of power electronics devices [34]. When the voltage source inverter (VSI) is operated applying a conventional PWM method, the CMV is not zero, which induces the rotor voltage with the coupling effect of the internal parasitic capacitance of the motor. That rotor voltage provokes a common-mode current flow path with the motor bearing. As shown in Fig. 2, there are three types of parasitic capacitances in the motor: Cwf is the parasitic capacitance between the motor winding and stator core, Cwr is the lumped capacitor that represents the distributed effects from the windings to the rotor, and Crf is the parasitic capacitance between the motor stator core and the rotor. Additionally, Cyis the dc-link to earth capacitance and Rgand Lgare the resistance 67478 VOLUME 9, 2021 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters FIGURE 2. Equivalent circuit model of the motor shaft voltage. and inductance of the ground path, respectively. Cbis the equivalent capacitance of the bearings on the drive side. Then, the bearing voltage ubcan be introduced with the effect of the parasitic capacitance [35]. The bearing faults caused by shaft current can be divided into four types [36]: 1) ∂v ∂tcurrent, which are induced by the ∂v ∂tof the CMV. However, the influence of this fact is small. 2) EDM (Electric Discharge Machining) current. If the shaft voltage exceeds the threshold value of the oil film, the oil film will be broken down, resulting in the discharge phenomenon, which can cause the heat in the bearing and the corresponding lifetime can be reduced. 3) Circuital current, which is induced by the commonmode grounding current at high frequency. It can induce the high-frequency shaft voltage at both ends of the motor rotating shaft and generate the circulating bearing current. 4) Shaft to ground current when the motor frame is badly grounded, there will be voltage difference between the inner and outer rings of the bearing caused by rotor grounding or by driving load grounding. Because of the EDM current, discharge occurs when the current passes through the bearing, which can increase the temperature of the bearing and bearing faults may occur. Therefore, reducing the shaft current is essential to increase lifetime and reliability of the motor system. III. COMMON-MODE VOLTAGE (CMV) HARMONIC DESCRIPTION IN A DUAL DRIVE SYSTEM Considering the model of Fig. 2, there is a common-mode path composed of the converter and the machine. Because both converters are connected to the motor frame through the parasitic capacitance and have the same dc-link, the equivalent common-mode voltage (CMV) of the two-converter system is the summation of the individual CMV of the VSIs as follows: CMV =Vn1O+Vn2O =VaO +VbO +VcO 3+Va0O+Vb0O+Vc0O 3(1) To obtain an analytical expression of the resulting CMV in the six-phase machine, the double Fourier series expression is used. A periodical signal can be mathematically described as x(t)=A00 2+ ∞ X n=−∞ hA0ncos(nω0t)+B0nsin(nω0t)i + ∞ X m=1 ∞ X n=−∞ hAmn cos(mωc+nω0t) +Bmn sin(mωc+nω0t)i(2) where coefficient A00/2 describe the average value of the signal, A0nand B0ncorrespond to the base-bands harmonic components, and Amn and Bmn determine the side-bands harmonic components. Taking into account this fact and considering the traditional PWM approach, the phase voltage of phase xof a single VSI is determined as [8]: VxO(t)=MxVdc 2cos(ω0t+θx) +2Vdc π ∞ X m=1 ∞ X n=−∞1 mJn mπ 2Mxsin (m+n)π 2 ×cos mωct+nω0t+θx (3) where indices mand nrepresents each side-band group (m) and each singular harmonic component inside the group (n). Mxis the modulation index of phase x(x=a,b,c) and θxis the phase displacement of the phase voltage in phase x.Jn(z) is the first kind Bessel function of zand order n. If the modulation indexes of all the phases in the VSI are the same, it is imposed that Mx=M. Also, it can be considered for the sake of simplicity that the phase displacement of phase ais θa=0◦. Following these assumptions, the amplitude of the side-bands harmonics of the phase voltage VxO of the a VSI can be mathematically described as: VxO(n,m)=2Vdc mπJnmπ 2Mxsin (m+n)π 2(4) As the key proposal of this work, in the dual drive system shown in Fig. 1, the phase displacement angle between the triangular carriers of the PWM methods in both VSIs of the dual drive system is considered a degree of freedom in order to improve the CMV of the overall system. In this sense, a phase displacement angle (ϕ) is considered in the triangular carrier of the second VSI. Therefore, the phase VOLUME 9, 2021 67479 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters FIGURE 3. a) Traditional single-carrier PWM modulation for the three-phase two-level motor dual drive system b) Proposed multi-carrier modulation technique for the three-phase two-level motor dual drive system. voltages in second VSI system can be described, analogously to (3), as: Vx0O(t)=Mx0Vdc 2cos(ω0t+θx0) +2Vdc π ∞ X m=1 ∞ X n=11 mJnmπ 2Mx0sin (m+n)π 2 ×cos mωct+ϕ+nω0t+θx0 (5) where ϕis the phase displacement of the carrier signal adopted for the second VSI with respect to the carrier signal adopted for the first one. θx0is the phase displacement of the phase voltage in phase x0(x0=a0,b0,c0). It can be observed that the amplitude of the side-bands harmonics of the phase voltage Vx0Ocan be described similarly as was introduced in (4). Taking into account these expressions, the resulting CMV in the six-phase machine can be determined as the summation of the CMV produced by both VSIs. More specifically, assuming the same value of the modulation index for all the phases (M=Mx=Mx0), each machine CMV side-bands harmonic component can be expressed by: CMV (n,m)=Vn1O(n,m)+Vn2O(n,m) =Vdc 3mπsin (m+n)π 2Jnmπ 2M ·1+ejnθb+ejnθc+ej(mϕ+nθa0) +ej(mϕ+nθb0)+ej(mϕ+nθc0)ej(mωc+nωo)t +1+e−jnθb+e−jnθc+e−j(mϕ+nθa0) +e−j(mϕ+nθb0)+e−j(mϕ+nθc0)e−j(mωc+nωo)t (6) In order to consider a wide frequency range in the resulting CMV, it is possible to consider the CMV Total Harmonic TABLE 1. Multi-phase PMSM parameters. Distortion (THD) with respect to the half of the dc-Link as figure of merit. THDCMV =2 Vdc v u u u t N X m=1 j X n=−j CMV (n,m)2(7) where Nand jare parameters that define respectively the number of harmonic groups and specific frequency components in each group included in the THD calculation. Observing expression (7), it can be seen that the minimum value of the THD is always achieved with a carrier displacement angle ϕequal to 180◦. In order to demonstrate this fact, in Fig 4a the THD has been calculated through simulation with a modulation index Mequal to 0.4, 0.6 and 0.8. In this test, the multi-phase PMSM machine parameters are summarized in Table 1. The THD value has been calculated up to a maximum frequency of 9kHz where the frequency fcin the triangular carriers of the PWM method are equal to 2kHz. Four complete harmonic groups (N=4) have been considered into the THD calculation, while jis fixed to 6. In order to compare the impact of applying ϕ=180◦ in the PWM technique in the dual drive system, the CMV THD has been also computed for the whole modulation index range considering the conventional PWM method where both VSIs apply synchronized PWM methods (ϕ=0◦) (shown in Fig. 3a). Both modulation methods (ϕ=0◦and ϕ=180◦) have been applied considering the scenario reported in Table 1. As can been observed in Fig. 4b, the PWM method with ϕ=180◦is always superior achieving an important reduction of the CMV THD, specially with low values of the modulation index. IV. ANALYSIS OF THE CURRENT RIPPLE CONSIDERING THE PROPOSED CMV MITIGATION TECHNIQUE Considering the dual three-phase PMSM machine shown in Fig. 1, the mathematical description of the stators winding 67480 VOLUME 9, 2021 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters FIGURE 4. a) CMV THD value for a dual-drive system using the parameters reported in Table 1with modulation index equal to 0.4, 0.6 and 0.8 b) CMV THD value for a dual-drive system using the parameters reported in Table 1considering the traditional PWM technique (ϕ=0◦) and the phase-shifted PWM method with ϕ=180◦. FIGURE 5. Experimental laboratory prototype of the dual VSD connected to a multi-phase PMSM. is given by the its corresponding inductance matrix which is written as: ML=         L M0M0M1M2M2 M0L M0M2M1M2 M0M0L M2M2M1 M1M2M2L M0M0 M2M1M2M0L M0 M2M2M1M0M0L         (8) where M0,M1,M2are real numbers. Assuming an internal star connection of each subsystem and according to the current Kirchhoff Law, the currents through the windings fulfill that: ia+ib+ic=0 ia0+ib0+ic0=0 (9) Neglecting the effect of low order back-EMF harmonics on current harmonics at high frequencies (i. e. the switching frequency and its superior multiples) and the voltage drop in the phase resistance, the relationship between high-frequency harmonic voltage (Vh) and high-frequency harmonic current FIGURE 6. FOC control strategy implemented in the experimental setup including the phase displacement between the PWM methods (ϕ=180◦). (ih) is determined by: Vh=ML dih dt (10) where Vhand ihare defined as: Vh=Va,hVb,hVc,hVa0,hVb0,hVc0,hT ih=ia,hib,hic,hia0,hib0,hic0,hT(11) Substituting (8) and (9) into (10), the harmonic voltage of the phase x(x=a,b,c) is determined by: Vx,h=(L+M0)dix,h dt −(M1+M2)dix0,h dt Vx0,h=(L+M0)dix0,h dt −(M1+M2)dix,h dt (12) Considering the CMV calculation and the analysis performed in section III, when the carriers of both VSIs are synchronized (ϕ=0◦) the phase voltages generated in both VSIs are identical and therefore, as ix=i0 x, equation (12) can be rewritten as: Vx,h=Vx0,h=(L+M0−M1−M2)dix,h dt (13) On the contrary, considering the CMV mitigation technique proposed in section III by fixing a carrier phase displacement between both VSIs equal to ϕ=180◦, it is VOLUME 9, 2021 67481 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters FIGURE 7. Results applying the traditional PWM method with synchronized carriers (ϕ=0◦) in both VSIs a) Total CMV b) CMV harmonic spectrum c) Detail of the CMV harmonic spectrum. Results applying the proposed modulation method with carrier phase displacement between the VSIs equal to ϕ=180◦d) Total CMV e) Detail of the total CMV f) CMV harmonic spectrum. FIGURE 8. Results applying the traditional PWM method with synchronized carriers ((ϕ=0◦)) in both VSIs a) Phase currents of drive 1 b) Phase currents of drive 2 c) Harmonic spectrum of current in phase a. Results applying the proposed PWM method with carrier phase displacement between the VSIs equal to ϕ=180◦d) Phase currents of drive 1 e) Phase currents of drive 2 f) Harmonic spectrum of current in phase a. fulfilled that ix= −ix0. In this case, the phase voltages can be described as: Vx,h= −Vx0,h=(L+M0+M1+M2)dix,h dt (14) Then, through direct comparison between (13) and (14), a higher impedance value results in the whole system when a carrier phase displacement between both VSIs equal to 180◦is applied. As a consequence of this 67482 VOLUME 9, 2021 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters higher impedance, the ripple of the current present in the system is reduced. V. EXPERIMENTAL RESULTS In order to validate the harmonic analysis and the effectiveness of the proposed modulation technique, the down-scaled laboratory experimental setup shown in Fig. 5has been considered. The prototype consists of a dual three-phase two-level VSDs connected to a dual-phase PMSM machine. Each single three-phase VSI is built using the IGBT IKW75N60T by Infineon Technologies [37]. Figure 6shows the PMSM control strategy based on the traditional FOC strategy including the proposed CMV reduction method. In this sense, the PMSM is driven by a speed and current double closed control loop. This controller scheme as well as the modulation techniques have been implemented using a rapid control prototype platform PLECS RT box [38]. The details of the multi-phase PMSM machine are listed in Table 1. The operation of the PMSM is analyzed in terms of the total CMV generated applying both modulation method approaches and the results are included in Fig. 7. Because of some limitations present experimental setup to drive the machine, the experiments has been performed considering a reduced dc-link voltage equal to 40V, a switching frequency of 4kHz and a speed reference of 600rpm. The total generated CMV applying the traditional modulation technique with synchronized PWM methods in both VSDs (ϕ=0◦) is represented in Fig. 7a and its harmonic spectrum is shown in Fig. 7b considering also a zoomed detail of the distortion at the carrier frequency and its multiples in Fig. 7c. As it is clearly shown, there is a non-negligible harmonic component located at the switching frequency (with an approximately a magnitude of 50%) and at its multiples as well. On the other hand, the proposed technique applying a 180◦carrier phase displacement between both VSIs is also tested considering the same FOC strategy as well as the same operational conditions in the machine. As it can be observed in Fig. 7d, the peak-to-peak CMV has been considerably reduced compared with that represented in Fig. 7a. In addition, in Fig. 7e is represented a detail of the resulting time-variant CMV. These narrow pulses are provoked, among other reasons, because of the dead time imposed by the IGBT driver circuit in the pulses generated by each VSI. However, as it is illustrated in Fig. 7f, the first (and third) harmonic groups of the resulting CMV harmonic spectrum have been eliminated while the second harmonic group remains unaltered as shown in Fig. 7f. The operation of the PMSM has been also analyzed in terms of the obtained phase currents and the corresponding experimental results are represented in Fig. 8. Following the discussion addressed in section IV, the currents obtained by applying the proposed PWM strategy with ϕ=180◦present a better performance because of the harmonic reduction in high-frequency components. Through a direct comparison between Fig. 8c and Fig. 8f, it is possible to observe this improvement as a harmonic mitigation at switching FIGURE 9. Circuit parameters for the modeling of the parasitic effects of the experimental setup shown in Fig. 5. TABLE 2. THD values considering up to 30kHz. frequency as well as the third carrier-order harmonic content. As it happens with the CMV, the harmonic content located in the second harmonic group remains unaltered. In order to test the proposed PWM strategy with different operational conditions, these experiments have been carried out with different PMSM reference speeds. The resulting harmonic distortion of the total CMV as well as the phase currents THD data, considering up to 9kHz have been summarized in Table 2. As it can be seen from the results, the proposed total CMV mitigation method achieves superior results as expected from the analysis introduced in section III. Additionally, the resulting phase currents THD values are also reduced as expected from the discussion provided in section IV. It is important to notice that each rotational speed corresponds to an specific modulation index value because the FOC method shown in Fig. 6determines the reference voltages to be generated by the VSDs in order to track the speed. It is important to highlight that the obtained results fit well with the expected results determined by simulation and shown in Fig. 4b. The results summarized in Table 2are just three examples to show this fact. VI. IMPACT OF THE RESULTING CMV OVER LEAKAGE CURRENT AND SHAFT VOLTAGE As it was addressed in section II, the introduction of high frequency CMV content accelerates the bearing degradation because of the mentioned leakage currents and shaft voltage. In this sense, due to the impossibility of measuring these magnitudes in the experimental setup, the impact over the leakage current as well as the shaft voltage has been determined using VOLUME 9, 2021 67483 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters FIGURE 10. Resulting shaft voltage from simulation circuit presented in Fig. 9. a) Conventional modulation method b) Proposed modulation method c) Harmonic spectrum for conventional modulation method d) Harmonic spectrum for proposed modulation method. FIGURE 11. Resulting leakage current from simulation circuit presented in Fig. 9applying a) the conventional modulation method b) the proposed modulation method. Leakage current harmonic spectrum applying c) the conventional modulation method d) the proposed modulation method. a specialized simulation environment considering the parasitic model shown in Fig. 9and the measured CMV shown in Fig. 7for both modulation techniques. This electrical model has been conducted following the work presented in [22]. In this sense, the common-mode circuit of the machine winding is composed by an inductive (L) plus resistive (Rs) components. Moreover, the parallel parasitic resistance of the winding (due to insulation) is also considered with a lumped resistor Rp. Additionally, there are two capacitive paths from the windings to the frame which are represented by Cwf and the second path closes through the rotor and represented by Cwr . The first one is the capacitance between the windings and the frame whereas the second is the capacitance between the winding and the rotor. A voltage across the rotor and the frame appears (so-called shaft voltage) and it is an well-known indicator regarding the bearing lifespan. Additionally, some extra capacitive components are required to be introduced. Crf is the capacitance between rotor and the frame and Cbis the capacitance due to the bearings. The current that flows through this capacitance is responsible for the bearing degradation. The other parameters regards the earth connection: Rgand Lgare resistance and inductance of the path connecting the frame of the machine to the earth point of the converter and Cgrepresents the high-voltage capacitors that are usually connected between the dc-link of the converter and earth. The value of the parameters can change depending on the type of the machine (a reduced air-gap, for instance, reduces the Cwf ), however it is always true that a reduced CMV excitation reduces the current through Cb. The corresponding circuit parameters for the experimental setup are properly listed in Fig. 9. 67484 VOLUME 9, 2021 A. M. Alcaide et al.: Common-Mode Voltage Mitigation of Dual Three-Phase Voltage Source Inverters On one hand, it is possible to calculate the induced shaft voltage in the machine by the application of both modulation strategies. The obtained results are shown in Fig. 11. As it can be observed, the application of the conventional modulation technique with ϕ=0◦leads to relatively large shaft voltage as shown in Fig. 11a. If the harmonic spectrum is represented, there is a non-negligible dc component as well as the magnitude of the first and third harmonic groups are high as shown in Fig. 11b. On the contrary, as it is presented in Fig. 11b and Fig. 11d, after the application of the proposed modulation technique with ϕ=180◦, not only the peak-to-peak magnitude of the shaft voltage is reduced but the dc component is eliminated as well as the first and third harmonic groups are greatly mitigated. These results completely fit with the experimental results presented for the CMV reduction. On the other hand, the leakage current has been also calculated using the simulation model and similar conclusions can be drawn as it is shown in Fig. 10. From these results, it can be concluded that the proposed modulation technique presents a positive impact in the operation of the machine since the resulting CMV is mitigated and therefore, the induced shaft voltage and the leakage current are also minimized. VII. CONCLUSION The use of multiphase machines being operated by several converters connected to the same dc-link is nowadays an attractive solution for many motor drive applications. However, VSDs for motor drives present inherent problems related to the reliability of the complete power system. As a main issue, the motor bearing degradation because of the presence of CMV in the VSD is actually a challenge to be overcome. Among the solutions previously provided by literature, many active canceler, passive filtering techniques and some SVM-based modulation methods have been proposed to achieve the mitigation of the CMV. This paper proposes a simple carrier phase displacement between the PWM methods of a dual VSD to mitigate the resulting CMV harmonic content. The simplicity of the proposed method is outstanding compared with previous methods based on SVM strategies. This technique does not require the usage of any external active or passive element and it is easily implementable in most of the digital control platforms. In order to validate theoretically the proposed method, a detailed mathematical model based on double Fourier series of the phase voltages and currents has been provided. From this analysis, it is demonstrated that the best result is achieved when the carrier phase displacement between both VSIs of the dual drive is fixed to ϕ=180◦. The proposed PWM technique has been tested in a down-scaled dual PMSM machine considering different scenarios achieving a superior performance. The impact on the leakage currents and the shaft voltage has been also evaluated. 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