Common-Mode Voltage Mitigation Technique in Motor Drive Applications by Applying a Sampling-Time Adaptive Multi-Carrier PWM Method

Common-mode voltage (CMV) in electric drives causes leakage current causing consequently EMI problems, loss and reduction of their components’ lifetime. Several solutions have been proposed which usually lead to higher cost because additional components are used. This paper is focused on the mitigation of the resulting CMV produced by the operation of the VSD by means of a specifically designed PWM method. The proposal is based on the analysis of the CMV harmonic spectrum using the Fourier analysis. The CMV mitigation is achieved by modifying the time-shift displacement of the carriers each sampling time considering a multi-carrier PWM technique. The resulting method has been evaluated in a down scaled experimental setup and it is easily implementable on mostly off-the-shelf mid-range micro-controller control platforms.


I. INTRODUCTION
Power converters are widely used in multiple scenarios very important for the industry such as the integration of renewable energies, energy storage systems and motor-drive applications including fans, pumps, conveyor belts and electric vehicles, among others [1]. The electric variable speed drives (VSDs) in these systems are a key part in the whole power conversion system. The presence of industrial VSDs has grown in recent years replacing hydraulic and mechanic systems. This fact is mainly propitiated by the VSDs performance increase and the price reduction among others [2].
The associate editor coordinating the review of this manuscript and approving it for publication was Zhong Wu .
New technologies of power devices such as gallium nitride (GaN) or silicon carbide (SiC) are called to substitute the traditional silicon power devices in the VSDs in the near future [3]. Multilevel power converter VSDs have been developed in the last decades and the control and modulation strategies have been substantially improved [4]- [7]. However, despite of these technologies are mature enough and are already available to be used in the current energy scenario, the implementation of these solutions by the industry is still quite limited. Either due to limitations in system implementation, design requirements, power level and/or the slow implementation pace by the industry, the traditional three-phase two-level IGBT silicon-based power converter is the mainstream VSDs solution in the portfolio of the  industrial companies. In Fig. 1 the conventional three-phase two-level IGBT-based power converter for a motor drive application is represented.
Technical literature provides multiple well-suited strategies to control an electric VSD. Among others, it is possible to highlight the direct torque control (DTC), field oriented control (FOC) or model predictive control (MPC) techniques [5], [8]. From the converter operation point of view, the available modulation strategies to be implemented in the three-phase two-level inverter can be categorized in two main streams: space vector modulation (SVM) and carrier-based pulse-width modulation (CB-PWM) techniques [4]. Compared with the SVM method, the CB-PWM technique is the simplest and the most straightforward way to operate a power converter because most of available control platforms include specific hardware to directly implement this modulation technique. In Fig. 2a, the traditional CB-PWM method of a three-phase two-level power converter is shown.
In any case (applying the SVM or CB-PWM methods), the use of a high switching frequency in the VSD leads to many advantages such as the increase of the power density, weight reduction as well as the improvement of the machine controllability because the control of the desired currents and magnetic flux in the machine can be accurately achieved [9]. Despite of these advantages, some drawbacks related with the high-switching frequency affect directly to the performance and reliability of the system [10]- [12]. As an example, a conducted and radiated electromagnetic interference (EMI) appears. In addition, shaft voltage and bearing currents phenomena appear in the induction machines operation [13]- [17].

II. THE IMPORTANCE OF THE COMMON-MODE VOLTAGE IN MOTOR DRIVE APPLICATIONS
One very important issue in motor drive applications is the common-mode voltage (CMV) that is defined as the voltage present between neutral terminal in the load (n) and the middle point of the dc-link (O) represented in Fig. 3. The CMV generated by the VSD directly affects to the reliability of the motor. It has been demonstrated that the CMV is the responsible of the bearing degradation representing more than 50% of the motor failures [10], [11], [18], [19]. Different mathematical models have been developed in order to estimate an early failure of these motor components [20]- [23].
The CMV in the three-phase motor drive system causes leakage current to the ground. As illustrated in Fig. 3, C g is the stray capacitance of the path from the dc-link to ground, which becomes a leakage current path. Besides, since there is parasitic capacitance in the motor neutral point to ground, denoted as C ng , the leakage current flows through the motor frame to ground [24].
In the motor drive application, such a leakage current causes additional harmonics and energy loss in the system. Besides, it introduces electromagnetic interference and even electrical safety issues. For example, the high frequency leakage current may lead to the misoperation of the relay to ground, which is harmful to the motor drive system. The PWM inverters used in motor drive applications also introduce a CMV from the three-phase winding neutral point to ground, and a leakage current flows through parasitic capacitance between stator winding and the motor frame to the ground [25].
It is essential to reduce the CMV in the three-phase motor drive to increase its lifetime and reliability. In this sense, many advances have been performed and multiple solutions can be found in the literature which are summarized in two main categories: the introduction of external elements, and the CMV mitigation via introducing a specific control or modulation strategy. Among the solutions based on the introduction of external elements, the use of filtering techniques and active canceler circuits are very popular [17], [26]- [31]. Although good enough results are obtained, the introduction of extra passive elements and/or new power devices with their ancillary systems and drivers is required. Therefore, the cost of the whole system, its complexity, volume and weight are increased. To the contrary, the CMV reduction via the usage of a proper modulation technique is an attractive solution being studied by the academia and industry. As an example, the switching pattern selection method in SVM has been investigated [18], [28], [30], [32]- [34]. Considering CB-PWM techniques, the available literature also provide some solutions [35], [36]. For instance, in [35], a tri-carrier PWM technique with fixed displacement angles between the carriers equal to [0 • , 120 • , 240 • ] is proposed based on empirical observation.
This paper is focused on the mitigation of the resulting CMV via the modification of the displacement angles of the carriers in a tri-carrier PWM technique during the operation of the VSD. The work develops the analysis of the generated CMV harmonic spectrum. As a consequence of this analysis, the sampling-time adaptive multi-carrier PWM technique shown in Fig. 2b is proposed. In this way, the CMV mitigation is achieved without the use of external active elements and passive filtering techniques.

III. TIME VARIANT COMMON-MODE VOLTAGE HARMONIC DESCRIPTION IN A TWO-LEVEL INVERTER
It is well-known that the CMV is determined by the summation of the phase voltages divided by the number of phases of the VSD. Therefore, considering a three-phase system, the CMV is determined as where V xO is the phase voltage of phase x (x = a, b, c). In order to obtain the analytical expression of the CMV in a three-phase two-level VSD, the Fourier expansion series is considered: where A 0 2 is the dc component, and A n and B n are the n-th harmonic order Fourier coefficients. Figure 4 shows, as an example, a phase voltage generated by the three-phase two-level VSD when the switching signals are generated using the traditional single-carrier PWM method shown in Fig. 2, where a single triangular carrier signal with frequency f c is used. As it is observed in Fig. 4a, the obtained phase voltage can be described as a square pulses trend which depends on the normalized voltage reference (also called duty cycle) shown in Fig. 4b. Additionally, as shown in Fig. 4c, choosing carefully the time origin (t ), each single pulse presents an odd symmetry and the coefficients of the Fourier expansion series are greatly simplified because B n coefficients are zero, leading to where A xn are the Fourier coefficients of the phase voltage V xO and ω c = 2π T c . In addition, as shown in Fig. 4b, D x is the duty cycle defined as the normalized phase voltage of phase x between 0 and 1 as follows: Summarizing, considering the traditional single-carrier PWM approach, the phase voltages in a VSD can be described as: In order to introduce the adaptive multi-carrier PWM approach that considers a different triangular carrier signal per phase, it is necessary to add the displacement angle term VOLUME 9, 2021 between the carriers in (5) as: where φ x is the displacement angle of the carrier associated to phase x. In this way, the time description of harmonic n-th in the phase voltage V xO can be described as: Therefore, substituting (7) into (1), each harmonic component of the CMV is determined. Each individual n-th order harmonic expression of the CMV, CMV n (t) (n ≥ 1), can be evaluated as the addition of the corresponding components in the phase voltages V xO by decoupling the term cos(nω c t − nφ x ) using the well-known trigonometric formula related to cos(a + b) and considering φ a = 0 • as reference:

IV. CMV MITIGATION USING A SAMPLING-TIME ADAPTIVE TRI-CARRIER PWM METHOD
As shown in section III, CMV n (t) is highly dependent on the values of the displacement angles of the carriers φ b and φ c . To illustrate this fact, a test has been done and the simulation results are presented in Fig. 5 and Fig. 6. Initially, from t = 0 to t = 20ms, it is considered the conventional single-carrier PWM strategy shown in Fig. 2 The resulting CMV n (t) waveform signals are represented in Fig. 5 whereas the resulting total CMV and its harmonic spectrum are represented in Fig. 6, colored in blue. It can be observed that the CMV harmonic spectrum presents a high amplitude in the first (n = 1) harmonic component (2kHz).
As it is observed in Fig. 5, each single harmonic component CMV n (t) presents a high similarity with the amplitude modulation technique widely used in the radio transmission field since decades. Analyzing both equations and comparing with the amplitude modulation technique, the magnitudes inside square brackets in (8a) and (8b) act as modulating signals and therefore, modifying their amplitudes it is possible to mitigate the harmonic content of the resulting CMV. In essence, the mitigation of the CMV component of n-th order is based on solving the following system of equations: The analytical solution of (9) has been already provided by the academia [37], [38]. However, due to the nature of the problem and the formulation of the coefficients, it can be proven that the analytical expression does not always provide a valid solution into the set of real numbers and therefore, a single harmonic cancellation can not be assured.
According with the mathematical formulation in (9), a CMV harmonic mitigation can be achieved by the clever determination of the φ b and φ c carrier displacements. The proposed adaptive multi-carrier PWM method considers the carrier phase displacement φ a = 0 • , while the angles φ b and φ c , for the sake of simplicity, only take values equal to 0 • or 180 • . Under this assumption, (8b) remains always zero. In this way, the final values of φ b and φ c (0 • or 180 • ) in order to minimize CMV n (t) are those that will minimize (in absolute value) the mathematical term introduced in (8a). In the proposed method, each sampling time, the term (8a) is eval-  determine the displacement angles of the carriers to mitigate the content of the first harmonic order content of the CMV (CMV 1 (t)) is illustrated in Fig. 7. It is worth to mention that trigonometric functions can be pre-calculated since the cosines of 0 • and 180 • degrees are well-known values. In this sense, the computational burden is not increased significantly.
The simulation results applying the proposed samplingtime adaptive multi-carrier PWM method are represented in Fig. 5 and Fig. 6 from t = 20 ms (drawn in red). It can be observed that CMV 1 (t) (which is the dominant harmonic component) is practically eliminated without a significant increase of the second and the third CMV harmonic groups.
The proposed adaptive multi-carrier PWM approach has been tested considering a modulation index range from 0.2 to 1.1. A comparison in terms of the CMV total harmonic distortion (THD) considering the traditional single-carrier PWM method as well as the tri-carrier PWM method with fixed displacement angles of the carriers equal to [35]) is shown in Fig. 8. As it can be observed, the proposed sampling-time adaptive multi-carrier PWM technique significantly reduces the CMV THD produced by the traditional single-carrier PWM method and also improves the performance given by the tri-carrier PWM with fixed displacement angles.
The harmonic improvement achieved by the proposed adaptive modulation technique can be proven if [35] is analyzed in detail. The fixed angle displacement proposed in [35] effectively eliminates the harmonic component located in [m = 1, n = 0] (following the notation used in the Double Fourier Integral where m defines the harmonic group and n VOLUME 9, 2021 FIGURE 9. Evaluation of the harmonic components of the first group using the tri-carrier modulation.

V. EXPERIMENTAL RESULTS
In order to test the proposed multi-carrier PWM technique and to validate the effectiveness of the analysis, the down-scaled experimental setup shown in Fig. 10 has been used. It is based on a conventional silicon IGBT three-phase two-level inverter tied to a 750 W three-phase permanent magnet synchronous machine (PMSM). The PMSM parameters are listed in Table 1.
The PMSM control and modulation strategies are implemented using the rapid prototyping real-time platform PLECS RT box [39]. Figure 11 illustrates the implemented PMSM control and modulation strategy. From the control strategy point of view, the PMSM is driven considering the traditional FOC [40]. In the modulation stage, the conventional single-carrier PWM method, the tri-carrier PWM technique with fixed carrier displacement angles [35] as well as the proposed sampling-time adaptive multi-carrier PWM  technique have been implemented in order to evaluate the obtained CMV of the power system.
In the experiments, f c = 5kHz, the speed reference is equal to 600rpm and the dc-link voltage is 60V. As the experimental setup has not the capacitor dc-link split-off in two parts, the measurement of CMV has been taken respect to the negative pole. In this sense, the CMV THD values contain a half dc-link voltage mean value. The experimental results are summarized in Fig. 12. The resulting CMV when the conventional single-carrier PWM technique is represented in Fig. 12a and its harmonic spectrum is presented in Fig. 12b. As expected, a non-negligible harmonic distortion is located at the carrier frequency (5kHz) and its multiples.
On the other hand, the tri-carrier PWM method with fixed carrier displacement angles and the proposed sampling-time tri-carrier PWM technique with adaptive carrier displacement angles have been also evaluated. Their corresponding CMV waveforms are represented in Fig. 12c and Fig. 12e, respectively. Applying the proposed PWM method, a clear reduction in the CMV peak-to-peak value can be observed. Taking a look of the resulting CMV harmonic spectrum (drawn in Fig. 12d and Fig. 12f), applying the tri-carrier PWM methods the harmonic component of the CMV located at switching frequency has been considerably reduced without a significant increase of distortion at higher frequencies. As mentioned in section IV, although the conventional tri-carrier PWM method presented in [35] effectively eliminates the dominant harmonic component located at carrier frequency (m = 1, n = 0) a new non-negligible magnitude harmonic component appears in the resulting CMV spectrum (m = 1 n = ±2, depending on the chosen carrier phase-displacement solution set). In addition, the magnitude of the harmonic component in the second group (m = 2) also increases. However, as the proposed adaptive multi-carrier PWM modulation acts over the modulating signal which determines the magnitude of the whole harmonic group, the mitigation of the harmonic distortion is performed in the complete harmonic range as it is clearly shown in Fig. 12f. In addition, as expected observing Fig. 5b and Fig. 6b, the resulting harmonic magnitude of the whole second group remains unaltered while the third harmonic group slightly increases.
The same experiment has been performed in order to evaluate the impact of the modulation techniques in the operation of the PMSM in terms of the phase currents quality. The experimental results are summarized in Fig. 13, where the three-phase currents as well as the harmonic spectrum of the phase a have been plotted applying the three PWM methods for comparison purposes. As it can be observed, considering the proposed adaptive multi-carrier PWM technique, the phase currents experience an increase of the harmonic distortion, similarly to that present in the result obtained applying the tri-carrier PWM method with fixed displacement angles. More particularly, the normalized THD of i a (calculated up to 17kHz) applying all modulation techniques are 3.55% (traditional single-carrier PWM), 6.27% (tri-carrier PWM with fixed displacement angles) and 6.02% with the proposed method. However, it has to be noticed that according with Fig 13b, Fig 13d and Fig. 13f, the magnitude of the distortion in the three-phase currents is quite limited since they are in the range of miliamperes.
The previous experiments have been also performed considering different rotation speed values of the PMSM. A comparison between the resulting CMV as well as i a quality is reported in Table 2, where the THD has been calculated up to 17kHz. It can be observed that the advantages of the proposed method remain.
From these results, it can be concluded that the proposed adaptive multi-carrier modulation technique has a significant positive impact mitigating the CMV harmonic content. In addition, the resulting degradation in the three-phase currents highly depends on the machine's inductance. This inductance is the result of multiple factors such as mechanical requirements as well as the voltage/current ratings, among VOLUME 9, 2021 FIGURE 13. Phase currents (left) and phase a current THD (right) using a) and b) the traditional single-carrier PWM method c) and d) the tri-carrier PWM with fixed displacement angles [35] e) and f) using the adaptive multi-carrier PWM technique.

TABLE 2.
Normalized CMV THD and phase current THD of the phase a considering up to 17kHz using the traditional single-carrier PWM, the fixed carrier phase-displacement angle tri-carrier PWM method [35] and the proposed adaptive multi-carrier PWM technique.
others. In conclusion, in many industrial applications the resulting machine's inductance is high and the increase of the current THD can be negligible making this drawback acceptable. This fact confirms that the proposed multi-carrier modulation method is able to mitigate the impact of the power converter operation over the remaining lifetime of the machine.

VI. IMPACT OF THE CMV OVER THE LEAKAGE CURRENT AND THE SHAFT VOLTAGE
As it has been mentioned previously, the presence of a high CMV value accelerates the bearing degradation because of the provoked leakage currents. In this sense, from captured CMV voltages in Fig. 12, the impact over the leakage current as well as the shaft voltage has been determined using a specialized simulation environment considering the parasitic model shown in Fig. 14. This model has been realized following the work presented in [21]. The common mode circuit of the machine winding consists of inductive (L) and resistive (R s ) components due to the stator's inductance and resistance. Also the parallel parasitic resistance of the winding (due to insulation) is considered with a lumped resistor R p .
From the windings to the frame there are two capacitive paths: the first, represented by C wf , is the capacitance  between the windings and the frame, the second path closes through the rotor. C wr is the capacitance between the winding and the rotor. The voltage across the rotor and the frame is the so-called shaft voltage and it is an important indicator for the bearings reliability. Also, some capacitive components can be found: C rf is the capacitance between rotor and the frame and C b is the capacitance due to the bearings. The current that flows through this capacitance is responsible for the bearing degradation. The other parameters regards to the ground connection: R g and L g are resistance and inductance of the path connecting the frame of the machine to ground of the converter and C g represents the high-voltage capacitors that are usually connected between the DC-link of the converter and ground. The value of the parameters can change depending on the machine type (a reduced air-gap, for example, reduces the C wf ), however it is fulfilled that a reduced CMV excitation reduces the current through C b .
On one hand, it is possible to determine the provoked shaft voltage in the PMSM by the application of different modulation techniques. Firstly, after the application of the fixed-angles tri-carrier modulation method [35], the main harmonic component located at [m = 1, n = 0] is effectively eliminated whereas a new harmonic component located at [m = 1, n = 2] (with an amplitude approximately 3dB lower) appears as it is expected. Additionally, the corresponding dc component remain constant whereas second harmonic group increases (with an amplitude 3dB higher). These results can be consulted in Fig. 15a and 15c. However, considering the proposed modulation technique, as it can be observed in Fig. 15e, the resulting harmonic magnitude in the first group as well as the dc component suffer a great reduction while the second harmonic group remains unaltered. In addition, the leakage current has been also represented and similar positive conclusions can be obtained from Fig. 15. In addition, in order to consider the possible resonances in the bearing voltage and the leakage current, the frequency response of the system depending on the value of C wf has been studied. The obtained results are shown in Fig. 16 where it can be seen that the resonances are always located at high frequencies, not affecting the expected performance.

VII. CONCLUSION
Leakage currents are responsible in electric drives, among others, of the degradation of the motor bearing reducing its lifetime. In this paper a simple modulation technique to reduce the common-mode voltage of the machine (which causes the leakage current) is proposed. This modulation method is based on the use of a triangular carrier per phase of the power converter and the modification, each sampling time, of the displacement angles between the carriers. The displacement angles calculation is very simple computationally and is based on the minimization of the CMV harmonic content at the carrier frequency via the Fourier expansion series. Each sampling-time, a simple iterative process selects the most convenient phase angle displacements of the carriers to achieve the CMV harmonic mitigation without the introduction of extra hardware components in the system. The effectiveness of the proposed method is proven experimentally and it shows a very promising 50% reduction of the leakage current at the expense of an acceptable increase of the phase currents THD.   From 1982 to 1986, he was an Associate Professor with the Department of Electronics Engineering, Sevilla University, where he has been a Professor, since 1986. Since 2016, he has been a 1000 Talent Professor with the Department of Control Science and Engineering, Harbin Institute of Technology. He has participated in more than 100 industrial and research and development projects and has published more than 300 articles, 76 of them in IEEE journals. His current research interests include modulation techniques for multilevel inverters and application to power electronic systems for renewable energy systems. Dr