A Common-Mode Shorting Network to Reduce Common-Mode Excitation of Three-Phase Two-Level Electric Drives

Common-mode voltage and current in an electric machine are undesirable. Although the strategic placement of a common-mode inductor and dc input side capacitors may reduce the common-mode current produced by an electric drive system, the effectiveness of this mitigation is a function of machine parasitic capacitance. This engenders the need to insert another electrical component into the system to effectively mitigate the common-mode current. With this purpose, a common-mode shorting network for an inverter-based drive system is proposed in this work. This network, in conjunction with a common-mode inductor and dc input side capacitors, reduces the machine common-mode voltage and current. The proposed approach is experimentally demonstrated.


I. INTRODUCTION
P ULSE-WIDTH modulated inverters are commonly used in motor-drive systems. This entails rapid switching of power semiconductors which generates ac line-to-ground voltages in the form of rectangular pulses of equal magnitude but variable widths. However, the sum of these line-to-ground voltages is non-zero, resulting in a common-mode (CM) voltage [1]. In a motor drive system, the high frequency components in the CM voltage excite the parasitic capacitances of the machine, which may result in the flow of bearing currents [2]. This contributes to bearing damage by pitting and fluting [1], and may lead to premature failure. Due to the increasing switching frequency of the drives in the recent times, the number of such failures has increased, usually happening relatively sooner after startup [2]. Also, CM voltage results in the flow of CM current in the system, which is not desired as it is associated with electromagnetic interference (EMI).
Several strategies to reduce the CM voltage, and thereby, to reduce the CM current, are set forth in the literature. A fourth inverter leg along with an LC filter is used in a threephase two-level inverter drive [3] to eliminate the electric machine CM voltage. However, this imposes a constraint on the allowable switch states. Modified modulation strategies to reduce the amplitude of the CM voltage by shifting gate signals in carrier-based pulse width modulation (PWM) methods are introduced in [4]. In [5], a modified space vector modulation (SVM) technique is used wherein the reference voltage vector is constructed using only three odd or even states. This results in six variations in the CM voltage in a period of the reference voltage, and thus, only six CM current pulses in a period of the machine phase current. However, the main drawback of this strategy is that the peak value of the reference voltage is limited, thus, limiting the utilization of the dc voltage. This limitation can be overcome by using overmodulation techniques, however, doing so results in undesirable harmonics in the machine currents.
An alternate group of strategies to reduce both the CM current flowing in an electric drive system and the machine CM voltage is through the strategic placement of a commonmode inductor (CMI). One such strategy is set forth in [6]. Therein, a capacitor is connected to the negative dc rail on one end and is grounded close to the motor ground on the other end. Further, a CMI is added on the dc side of the inverter. The disadvantage of this strategy is that the CM current circulates between the inverter and the machine. Thus, this strategy can only be used in systems that are not sensitive to bearing currents. In [7], a filter configuration, which involves the use of an ac side DM LC-filter, capacitors on the dc side and at least one CMI placed within the CM current loop between the dc and ac side capacitors, is proposed to suppress CM current in dc-fed motor drive systems. A drawback of this strategy is that the DM filter inductor has to be able to conduct the rated machine currents.
In this work, a CM mitigation strategy for three-phase twolevel inverter-based electric drives is set forth that is partially based on the strategy presented in [7]. However, the proposed approach does not require the use of a DM LC filter. Instead, it proposes the use of a novel component herein referred to as the common-mode shorting network (CMSN). A CMSN is to be connected in shunt with the electric machine in the drive and does not have to conduct the full machine current. Therefore, it is much smaller in size than a DM filter.
This work is organized as follows. First, the need of this network is justified using an example electric drive system in Section II. Through this example, the strategy to mitigate CM current in such a system is also explained. In Section III, the CMSN is described in more detail. An example prototype is used to demonstrate the mitigation strategy on a laboratory test system and the results are presented in Section IV. Finally, conclusions and suggestions for future work are presented in Section V.

II. COMMON-MODE MITIGATION STRATEGY
A simplified diagram of an electric drive system is shown in Fig. 1. On the left-hand side of the figure, there are a dc source with an output voltage V dc , grounding resistors of resistance R g to bias the dc rail voltages centrally around ground, the dc input side capacitors (also referred to herein as the decoupling capacitors) of capacitance C d that includes the parasitic capacitance from each rail to ground, and a dc side CMI followed by a dc link capacitor of capacitance C dc . The decoupling capacitors are chosen so that they effectively act as a short in the CM, thereby separating the CM equivalent circuit of the dc source from the rest of the system. In the center is a three-phase two-level bridge converter, also called here the power block, with semi-conductor devices S 1 − S 6 mounted on a heat sink. The heat sink is left floating. Parasitic capacitances from the dc rails to heat sink, which is represented by the node S, and ac lines to heat sink are denoted C 1 and C 2 respectively. On the right side of the figure are the CMSN in crimson and a permanent magnet ac machine (PMAC). The machine frame is grounded for safety. It is assumed for now that the stator winding resistance and inductance are negligible and so are the feeder cable resistance and stray inductance. The parasitic capacitances from the feeder cables to ground are designated C fd .
Using the techniques described in [8], the CM equivalent circuit (CMEC) of the system is derived and depicted in Fig. 2. Therein, the CM voltage source is denoted by v pbcm and is given by In (1), v dc is the voltage across the dc-link capacitor C dc (not shown in Fig. 1) and v Sx is the voltage across the switch S x , x = {2,4,6}. The CMI is represented by its CM equivalent circuit [9] between points A and B where In (2) and (3), R so , R po , n s and n p are constants, ω b = 1rad/s and ω = 2πf with f being frequency in Hz. Further, L cm,m and C cm,m denote the measured CM inductance and parasitic capacitance of the CMI respectively. The CMSN is represented as a series L-C circuit (L cm,sn and C cm,sn ) in crimson. The equivalent capacitance from the machine to the machine frame is denoted C mc . The remaining components are the same as those shown in Fig. 1. The CM currents into the decoupling capacitors, the shorting network, the parasitic capacitance of the feeder cables and the machine are denoted i cm,dc , i cm,sn , i cm,fd and i cm,mc respectively. With the system as described, the role of the CMSN is demonstrated in the form of an example. The component parameters used in this example are as follows: C d = 1 µF, R g = 10 k , L cm,m = 41.3 mH, C cm,m = 54.6 pF, R so = 1.9e-7 , n s = 1.76, R po = 7.4e18 , n p = −2.3, ω b = 1 rad/s, C fd = 10 nF, C mc = 1.68 nF, L cm,sn = 6 µH and C cm,sn = 1 µF.
The common-mode equivalent circuit (CMEC) corresponding to Fig. 1 is shown in Fig. 2. Therein, the CM impedance seen by the CM voltage source v pbcm is defined VOLUME 10, 2023 as the equivalent impedance of the circuit between the points B and C. This impedance is given by where Z pp is expressed as Z fd ||Z mc when the CMSN is absent, and as Z sn ||Z fd ||Z mc when the CMSN is present, and where Z dr = Z d ||Z g (8) In (4), the CM impedance offered by the CMI is expressed Also, please note that in (4), the parasitic capacitances from the ac/dc rails to heat sink were neglected since their impedance is typically relatively large. The CM impedance seen by the source for this example is depicted by the upper two subplots in Fig. 3. In each subplot in the figure, the trace in blue corresponds to the circuit in the absence of the CMSN and that in red corresponds to the circuit with the CMSN. It can be seen that in the absence of the CMSN, the impedance seen by the CM voltage source becomes very small at the resonance between 4-5 kHz, which can be problematic in terms of CM current mitigation in the desired frequency range (say 4 kHz to 1 MHz) and especially if the switching frequency is about 4-5 kHz. In the presence of the CMSN, this resonance in the impedance shifts to around 715 Hz, that is, away from the switching frequency component and its harmonics. Thus, the CMSN, when designed accordingly, allows the CMI to effectively mitigate CM current over the desired frequency range.
In practice, the dielectric thickness between the bearings and the races in an electric machine changes with the machine's speed of rotation [10]. Thus, the parasitic capacitance of the machine changes with speed. This capacitance with the CM inductance of the CMI may or may not result in a resonant frequency in a particular range of interest. The CMSN ensures that this resonant frequency lies outside this range regardless of the machine speed. Apart from this, the CMSN diverts the CM current away from the machine as is seen in the third subplot in Fig. 3. Herein, the quantity g m is defined as the transfer ratio between the CM current into the machine i cm,mc to the CM voltage source v pbcm and can be expressed as Observe the CMSN decreases g m by 1-3 orders of magnitude for frequencies between 2 kHz and 100 kHz. The CMSN masks the CM impedance of the machine by acting as a CM short. This allows for the placement of the resonant frequency, arising as a result of the interaction of the CMI and the machine, outside the frequency range of concern.
Thus, it can be concluded that with appropriate capacitors on the dc input side and CMSN on the ac output side (both of which act as shorts in the CM), the CMI is able to reduce the CM current into the machine. The introduction of these components in the electric drive system forms the basis of the CM current mitigation strategy proposed in this paper.
With the CM mitigation strategy in electric drive systems explained, the next step is to physically realize the series L-C combination for a CMSN. Clearly, the goal is for this circuit to be a CM short; however, at the same time it needs to present a very large differential-mode (DM) impedance. This is considered in the next section.

III. COMMON-MODE SHORTING NETWORK
As discussed before, the role of the CMSN will be to offer a very small impedance in the CM so that it effectively acts as a short. At the same time, however, it must offer a very high impedance in the DM in order to allow for the normal functioning of the system. In this work, such a network is constructed by using an appropriate combination of an inductor and capacitors. A schematic of a CMSN is shown in Fig. 4. Therein, the terminals a, b and c are connected to the ac lines feeding the machine, and the terminals a , b and c are connected to ground.
The inductor in the CMSN is constructed so that half the winding from phase a and half the winding from phase b are wound around the first core leg in an interleaved or layered fashion but in opposite directions. Similarly, half the windings from phases b and c, and c and a are wound in a similar fashion around the second and third core legs respectively. Let the flux linkage associated with the half of the a-phase winding that is wound around the first leg be denoted λ a1 and that associated with the second half of the same winding on the third core leg be denoted λ a2 (see Fig. 4). The p in Fig. 4 is Heaviside notation for the time derivative operator. Neglecting the winding resistance, the voltage across the entire a-phase winding v a may be expressed v a = pλ a = pλ a1 + pλ a2 (13) where λ a is the total effective flux linkage associated with the a-phase winding. The voltages across the entire b and c-phase windings can be similarly expressed. It is now assumed for the sake of explanation that the inductor operates in the magnetically linear region. Therefore, the flux linkages λ a1 and λ a2 may be expressed where L n and M n denote the self and mutual inductances associated with the phase windings on each core leg. The a and b-phase currents into the network are denoted by i a,sn and i b,sn respectively. In this way, the relationship between the effective flux linkages and the currents into the network may be written The performance of this inductor can be evaluated either in phase variables as in (14)- (16) or in qd0 variables. Here, the latter is considered as a system-level simulation is easier to carry out in these variables. Also, the inductances become decoupled in the qd0 variables. Thus, transforming (16) to a stationary reference frame [11] yields By virtue of the winding arrangement described earlier, M n ≈ L n . Thus, in the q-and d-axis, that is, in the DM, the inductance of the inductor is large. In other words, In the zero sequence (which is related to CM), the inductance 2 (L n − M n ) is very small and is comprised of leakage inductance. The use of layer-on-layer winding arrangement results in very low leakage inductance and hence, very low CM impedance. It was seen in the last section that the CMSN is to be placed in parallel with the machine. Thus, it sees the same DM and CM voltages as the machine terminals. Despite having a large inductance in the DM, the impedance offered by the inductor at the fundamental frequency component in the DM voltage will be small because of the relatively low fundamental frequency. Capacitors are, therefore, added in series with the inductor to block the fundamental component.
The inductor in a CMSN can be constructed using a C-Y core geometry [12], where the windings are wound around the Cs (see Fig. 5 and 6) as explained in the beginning of this section. The reason such a geometry has been chosen for this inductor as opposed to say a double E-core geometry is because any asymmetry among the three phases results in a CM-DM coupling [13], which is undesirable. The design methodology for a CMSN will be the topic of discussion in an upcoming publication.
In Figs. 5 and 6, the parts in grey represent the magnetic core of the inductor, and the parts in shades of green, orange and crimson represent the phase windings.
An interesting aspect of the CMSN is that at first glance it is reminiscent of a zig-zag grounding transformer [14]. While there are similarities, there are two major differences between these devices. In order to illustrate these differences, the profile view of a normally constructed zig-zag grounding transformer is shown in Fig. 7.
The first difference is that the terminals a , b and c of a CMSN are connected to ground through the capacitors C n , while they are directly connected to ground in the case of a zig-zag grounding transformer. The second difference stems from the strong desire to minimize the CM impedance of the CMSN, and herein, this is achieved via layering half of the a and b-phase windings one top of the other on a core leg, VOLUME 10, 2023 unlike winding them around different positions on the same core leg. This helps in reducing leakage and thereby the CM impedance of the inductor in the network.
The magnetic design of the inductor in the CMSN is about blocking the switching frequency component and its harmonics in the DM current, while the magnetic design of the zig-zag grounding transformer is about blocking the low frequency components in the DM current. This results in the inductor in the CMSN being a very small device, while the zig-zag grounding transformer would be a bigger device in comparison.
This marks an end to the discussion of the CMSN. A prototype will now be used in a test system to demonstrate the strategy proposed herein to mitigate machine CM voltage and current. To this end, the test system and its various components are first discussed in detail in the next section, followed by the presentation of the results from the test studies.

IV. EXPERIMENTAL RESULTS
To demonstrate the CMSN in an electric drive system, three case studies were conducted on the test system shown in Fig. 8. Schematics of the system are shown in Figs. 9-12. This system is a part of the Purdue Reduced Scale Naval DC Microgrid (PRSNDC) system [15]. It consists of the Main Power Generation Module (MPGM) which acts as the primary power source in the system, the Ship Propulsion Module (SPM) which acts as the load, and the dc bus leading from the MPGM to the SPM. In Fig. 9, the dc cable is represented by its π−equivalent circuit whereins R bs and L bs represent the resistance and inductance of the cable, and C bs represents the parasitic capacitance from each cable to ground. The MPGM and SPM power grounds are denoted by 'g mpgm ' and 'g spm ' respectively. The point '0' is the reference node and is at a different potential than the power grounds.
The MPGM (see Fig. 10) consists of a dynamometer which acts as the prime mover and couples through a shaft to a wound-rotor synchronous machine (WRSM). The WRSM is followed by a mechanical and a solid-state circuit breaker, a thyristor-based rectifier and a double-pole LC filter. The filter is followed by a center-tapped grounding system through Z g so that the positive and negative rails to ground voltages are balanced. The MPGM also has a CM inductor CMI 1 and decoupling capacitors of capacitance C c each.  The SPM is depicted in Fig.11. From left to right, it consists of the grounding resistors of resistance R g , decoupling capacitors of capacitance C d , an input filter, a power block wherein the heat sink is left floating, a CMSN and a permanent magnet ac machine (PMAC). The input filter and the power block (combinedly called the power block assembly herein) are also depicted in Fig. 12. Therein, the capacitances C 1 and C 2 are the parasitic capacitances from the dc/ac rails to the heat sink. The PMAC acts as a propulsion motor which is coupled through a shaft to a dynamometer which acts as the mechanical load. Parameters of the MPGM and SPM are listed in Tables 1 and 2.
Observe that the decoupling capacitors of the MPGM (C c from Fig. 10) and the SPM (C d from Fig. 11) form a distributive short in the CM. This short prevents CM interaction between the MPGM and the SPM.
The supervisory control of the MPGM and the SPM are discussed in detail in [15]. For the case studies conducted, focus will be on CM mitigation in the SPM only and the MPGM will act as a dc source with its own CM mitigation components.
A CMSN prototype was designed and constructed in the laboratory to be used in the SPM. The capacitors in the network were selected first so that they may act as an appropriate short in the CM and offer high impedance to the fundamental    Table 3.
A bus-bar-based CMI [16], which is denoted by CMI 2, was used in the SPM.
As mentioned before, three test studies were conducted on the system. The first study pertains to the nominal (base) system, wherein only the components marked in black are present. Therefore, there are no CM mitigation components in this study. In the second study, the components shown in green, that is, the decoupling capacitors of capacitance C d and the CM inductor CMI 2 are added to the system. The capacitors create a CM short on the dc side and the CMI is intended to limit the CM current into the machine. However, it will be seen in the results that the CM current in fact   becomes worse around 10 kHz because CMI 2 and the rest of the system create a resonance around that frequency. Under this condition, the ac output side is not yet appropriately shorted for CMI 2 to become effective. In order to accomplish this, in the third and final study, the CMSN (shown in cyan) is added to the system under consideration in Study 2. The CMSN creates a CM short on the ac side of the inverter, and as would be seen in the test results, reduces the machine CM voltage which is defined by (19). With this, the system VOLUME 10, 2023 follows the recommended strategy where the dc input and ac output sides are shorted in the CM and CMI 2 aids in reducing the CM current into the machine.
A CM equivalent circuit (CMEC) of this test system is shown in Fig. 13. The components in this figure follow the same color scheme as that followed in Fig. 11. Variables of interest in Figs. 11 and 13 are the CM current into the machine i cm,mc and the machine CM voltage v cm,mc . These quantities are defined as where v egs is the voltage difference between the points e and g spm . The voltages v fgs and v ggs are likewise defined. Still referring to Fig. 13, the voltage source v scm and impedance Z s represent the Thevenin equivalent CM voltage source and CM impedance respectively of the MPGM at its dc terminals. The voltage source v pbcm represents the CM voltage associated with the SPM power block. The quantity Z ms represents the parasitic impedance between the MPGM and SPM grounds. The quantities Z d , Z cmi2 and Z fin are the CM impedances of the decoupling capacitors, the CM inductor CMI 2 and the input side filter inductor respectively. Also, the quantities Z 1 , Z 2 , Z sn and Z mc are the CM impedances of the dc rails-to-heat sink, ac feeder lines-to-heat sink, CMSN and the machine feeder cables-to-machine ground respectively.
The CM impedances of the CMSN Z sn and the PMAC Z mc machine are compared in Fig. 14. These impedances and all the following impedances in this section were measured using a Keysight E4990A Impedance Analyzer by appropriately isolating them from the remaining system. It can be seen from the figure that the CM impedance of the CMSN is more than an order of magnitude smaller than the CM impedance of the machine. Thus, the CMSN acts as an effective short on the ac output side. The DM impedance of the CMSN is depicted in Fig. 15. It can be seen that for the region of the low-frequency resonance, the DM impedance of the network is large. Therefore, the network will block the fundamental component, which would be less than equal to 166.67 Hz at 2500 rpm for the SPM. It would also block the switching frequency component and its harmonics (10 kHz and above).
Observe, there is a second resonance present at 50 kHz. This arises as a result of the self-capacitance of the inductor. It can also be seen from Figs. 14 and 15 that in the frequency range of 7 kHz-100 kHz, the CM impedance of the network is more than an order of magnitude smaller than its DM impedance.
The DM and CM impedances of the CMSN inductor are shown in Figs. 16 and 17. It can be seen from Fig. 16 and Table 3 that the measured q-and d-axes inductances are quite close to each other, which is expected as it is a symmetrical inductor. The small difference between the two inductances most likely occurs as a result of the manufacturing imperfections.
In the CM, the inductor has an inductance of approximately 6µH at 1 kHz and this inductance decreases with increasing frequency (see Fig. 17). This decrease in inductance is attributed to the flow of eddy currents in the conductor material at higher frequencies that affects the distribution of the magnetic field [17].
Next, the CM impedance of CMI 2 Z cmi2 is compared with the CM impedance of the rest of the system Z rest in Figs. 18 and 19. Therein, Observe from Fig. 18 that the resonant frequency of CMI 2 is over 1 MHz. Thus, it acts inductive at least until 1 MHz. However, since the magnitude of this impedance follows a curved path as shown, it can be inferred that the apparent inductance of this inductor falls off with frequency [16]. Nevertheless, it offers high inductive impedance through 1 MHz.  It can also be seen that in the absence of the CMSN, the CM impedances of CMI 2 and the rest of the system are equal in magnitude, but are almost out of phase at approximately 14 kHz (see Fig. 18). Thus, there occurs a resonance at this frequency and the net impedance seen by the CM voltage source becomes very small. Conversely, with the CMSN installed, the CM impedance of CMI 2 is at least an order of magnitude larger than that of the rest of the system in the frequency range of 7 kHz-100 kHz, as can be seen in Fig. 19. This facilitates effective mitigation of CM current components in this frequency range.
The CM impedance seen by the source Z sys (neglecting the parasitic capacitances from the dc/ac rails to heat sink) corresponding to the three studies may be expressed and is depicted in Fig. 20  where and is depicted in Fig. 21. Figs. 20 and 21 will become useful in understanding the frequency spectra of the machine CM voltage and current, which are discussed ahead.
In order to demonstrate the proposed strategy, the test system was run with v spm = 400 V, a PMAC machine speed of ω rm = 1500 rpm and the torque command of T * e = 80 Nm. The switching frequency of the SPM inverter was set at 10 kHz. The inverter controls are set forth in [15], a sinetriangle modulation strategy was used (no 3 rd harmonic). Two measurements were recorded for each study-machine CM voltage v cm,mc and machine CM current i cm,mc . The spectral analysis of the measured waveforms for the three studies was carried out as follows. The FFT function in MATLAB R2018b was employed to find the Fourier transforms of the signals. In doing this, a Hann window was used to reduce spectral leakage. The resulting Fourier transforms were then used to find the power spectral density (PSD), from which band power was determined. PSD characterizes a stationary signal in the frequency domain. It describes the power in such a signal per unit of frequency. Band power describes the power contribution of the signal in a given frequency band to the total power of the signal. It is calculated by simply integrating the PSD over the frequency band of interest.
Given a vector x of length L, where L is an even number, the pseudo code used herein for calculating band power is described in Table 4. Therein, x represents the discrete signal in time, F s is the sampling frequency, x dft is the Fourier transform vector of x obtained by using the fft function on the signal x multiplied by the Hann window function w 0 , and f is the corresponding frequency vector, w cf is the Hann window correction factor, x psd is the power spectral density estimate vector, and p band is the average power of the signal x in the frequency band [f 1 f 2 ], such that f 1 < f 2 . The function 'diff' calculates differences between adjacent elements of the argument vector. The resulting power spectra are compared in Figs. 22 and 23.
It can be seen from Fig. 22 that the machine CM voltage v cm,mc decreases in the entire frequency range in going from Study 1 to 2 (that is going from no CM mitigation to including the dc side decoupling capacitors and CMI2), except from 9 kHz to 14 kHz. This is attributed to the occurrence of the resonance in the equivalent impedance seen by the CM voltage source v pbcm around 14 kHz. But with the addition of the CMSN in Study 3, v cm,mc goes down over almost the entire frequency range as the CMSN acts as an effective short in the CM and helps to shift the resonance to a much lower frequency. This is also justified based on the transfer ratio h m (see Fig. 21).
Referring to Fig. 23, comparing Study 1 to Study 2, except for the frequency range of 9 kHz to 14 kHz, the machine CM current i cm,mc decreases with the addition of the decoupling capacitors and CMI 2. This is because CMI 2 results in a decrease in the CM current through the SPM inverter. For the frequency range of around 9 kHz to 14 kHz, however, i cm,mc increases. The increase in the machine CM voltage and current over the frequency range of 9 kHz to 14 kHz in going from Study 1 to Study 2 can be explained in more detail by referring to Figs. 20 and 21. The CM impedance of the system as seen by the source has a resonance around 14 kHz (Study 2). Since the effective CM impedance seen by the source becomes smaller in this frequency range in going from Study 1 to Study 2, the machine CM voltage increases.  This is also justified by the magnitude of the transfer ratio h m shown in Fig. 21. This results in an increase in the machine CM current over this frequency range.
With the addition of the CMSN in Study 3, the machine CM current decreases for all frequencies less than 50 kHz. Beyond 50 kHz, this current increases in going from Study 2 to 3 even though the machine CM voltage decreases. The measurement of CM current is significantly more difficult than CM voltage since it involves the measurements of very small currents in groups of physically large cables and is therefore somewhat less reliable. Another possibility is that imperfections in the CM shorting inductor cause coupling between the CM and DM aspects of the circuit. An extended discussion of this coupling is set forth in [18]. This coupling could drive the increase in the CM current at high frequencies as the CMSN in introduced. In any case, the machine CM current is suppressed over the original system configuration until about 500 kHz. Beyond this, the machine CM impedance is very low. If desired, a low value of external AC side CM inductance could be placed in series with the machine. Alternately, by improving manufacturing and tolerances, the symmetry of the CM inductor could be improved thereby avoiding the coupling between the CM and DM. Reducing the parasitic capacitance in the CM shorting inductor could also be helpful to this end.
To quantify the results in terms of scalar metrics, the rms values of v cm,mc and i cm,mc were computed for the three studies (band-limited to between 1 kHz and 1 MHz using first a first-order high-pass filter followed by a first-order low-pass filter). These are listed in Table 5. It can be seen that in going from Study 1 to Study 3, the rms values of both the voltage and current decrease.
In order to ensure that the insertion of the CMSN in the system does not have a negative impact on its normal functioning, the a-phase current out of the inverter for the three studies is depicted in Fig. 24. It can be observed from the figure that the presence of the CMSN (Study 3) does not bring about a significant (or even a noticeable) difference in the inverter current, which is desirable.

V. CONCLUSION
A CM current mitigation strategy for a three-phase two-level electric drive system is set forth. To this end, a new tool for CM mitigation, herein referred to as a CM shorting network (CMSN), is proposed. This component is installed in parallel to the drive machine. A strong advantage of this approach is that the device does not have to conduct rated machine current. Along with the other components, namely the decoupling capacitors and the CMI, it is seen via experimental results that the CMSN plays an important role in reducing the machine CM voltage and current. The approach was shown to greatly reduce the machine CM voltage over almost the entire frequency range considered, and the machine CM current to a frequency beyond five times the switching frequency. The remaining current increased in going from Study 2 to Study 3. If this current is still objectionable, methods to improve the situation include improving the symmetry of the CMSN inductor, reducing the parasitic capacitance of the CMSN inductor, or adding a small amount of AC side CM inductance in series with the machine, though this last approach would require conducting the full machine current.