Hybrid Foil-Litz Windings for Highly Efficient and Compact Medium-Frequency Transformers

Medium-frequency transformers (MFTs) are key components in solid-state transformers, where they provide galvanic isolation and a certain voltage transfer ratio between a MV grid and a LV bus. Typically, MFTs are operated in the kilohertz range, which results in a significantly reduced volume and material usage compared to 50/60 Hz transformers. Foil conductor is an attractive solution for improving the filling factor and the cost-effectiveness of MFTs, however, the insulation clearances increase the ohmic losses due to the current crowding effect; besides, the electric field hotspots at the winding corners require shielding by equipotential rings. In this work, a new hybrid topology is presented, where the first and last turn of the foil winding package is replaced by turns of litz wire connected in series, one above and one below the foil winding, respectively, such that they act as equipotential shielding rings; besides, the current in the litz turns deflects the magnetic field lines away from the foil edges, decreasing the losses due to current crowding. The effect of the litz rings on the losses is modeled and measured on a hybrid and a standard foil winding prototype; a loss decrease higher than 15% is observed. The verified model is used to compare the conductor and footprint saving between windings designed with litz rings, and with standard equipotential shielding rings; in this respect, a minor amount of litz wire allows reducing losses up to 30%, whereas the conductor utilization and winding height can be decreased more than 20%, improving the power density of the MFT.

for fulfilling the voltage conversion and guaranteeing the required galvanic isolation. The MFT has similar insulation requirements as MV LFTs; in contrast with LFTs, it is operated in the kilohertz range, offering superior compactness and lightweight [9], [10]. The price for these advantages is the use of more complex and therefore more expensive conductors and core materials to keep the frequency-induced losses in an acceptable range. In this respect, the conductor choice is constrained among foil or litz wire, e.g., [11], [12], [13], [14]: litz wire is disfavored by the reduced filling factor, the limited availability and the elevated cost, whereas foil conductor exhibits additional ohmic losses due to the so-called "current crowding" or edge effect, caused by the deformation of the magnetic field due to the insulation clearance to the core [15]. Foil windings exhibit a uniform voltage distribution in the case of steep-fronted PWM voltages [16], which is advantageous for MV SST applications; however, the electric field hotspots at the foil winding corners limit the insulation rating [17]. Equipotential rings are crucial for mitigating the electric field hotspots in MV applications [18], [19], [20], with the disadvantage of increasing the winding footprint and possibly introducing additional losses. Similarly, the state-ofthe-art solutions based on interleaving [21], [22], magnetic field shielding [23] or conductor shaping [24] for reducing ohmic losses in foil conductor are hardly applicable in an MV winding due to the persistence of electric field hotspots and the manufacturing complexity introduced by the insulation requirements.
A new hybrid winding topology based on foil conductor is presented in this paper [6], see Fig. 1, mitigating both the current crowding and the electric field hotspots: the foil winding package is extended and connected in series to two turns of litz wire, forming the first and last turn, one above, and one below the foil winding, such that they act as equipotential shielding rings; besides, their current deflects the magnetic field curvature away from the foil edges, decreasing the ohmic losses due to the current crowding. Since electric field shielding by equipotential rings is a concept already established in the literature on both LFTs and MFTs [18], [19], [20], [25], [26], [27], [28], [29], this work focuses on the advantages offered by the new topology in terms of ohmic loss, conductor usage and winding size.

II. HYBRID FOIL-LITZ WINDINGS A. TOPOLOGY
The new winding topology is based on a standard foil winding, as shown in Fig. 2: two rings made of litz wire are connected in series and positioned around the winding ends [6]. Each litz ring consists of one or multiple turns N L , which add to the N f foil turns and result in a total number of turns N t = N f + 2N L ; in this work N L = 1. As discussed next, this new topology allows reducing the ohmic losses due to current crowding and mitigates the electric field hotspots at the winding corners; besides, the winding leads made of litz wire simplify the connection to the converter, reducing both

TABLE 1. Main Parameters of the Designs F-STD, F-HYB and R-HYB
the proximity losses and the electric field hotspots in standard foil conductor leads [30].

B. CURRENT CROWDING AND LOSS MITIGATION
The effect of the litz ring on the magnetic field H and the current crowding is quantified considering a shell-type MFT with standard foil windings as a reference, denoted F-STD: the coil consists of an inner secondary winding (LV) and an outer primary winding (HV), radially stacked to LV. The magneto quasi-static (MQS) Maxwell equations are solved by the finite element method (FEM), considering a 2D model of the MFT cross-section shown in Fig. 3; the geometrical quantities are summarized in Table 1. Similarly to [31], the    model is analyzed by a second-order discretization, using triangular and rectangular elements in the nonconducting and conducting regions, respectively; the mesh is refined in the conductor regions using at least three layers of elements within the H penetration depth. To reduce the mesh size, the insulation distance between the turns is neglected. In the investigation, the 10 kHz to 30 kHz range is considered, which is often adopted in high-power SST applications [8], [9]; the conductor thickness is selected based on the frequency range of interest [32]. The distance D hv,lv = 25 mm is assumed constant, the reference value D hv,c = 30 mm similar to [19], [33] is compared with the cases D hv,c = 0 and 60 mm; h c is defined based on the winding footprint h m as h c = h m + 2D hv,c .
The analyses on standard foil windings presented in [15], [23], [31] show that D hv,c introduces in H a component perpendicular to the foil, with magnitude H ⊥ , which leads to a strong concentration of current in the edges of the conductor. This is evaluated considering the case D hv,c = 30 mm and f = 20 kHz: the contour plot in Fig. 4 shows that H ⊥ is 1.7 times the maximum magnetic field intensity in the ideal case with D hv,c = 0 mm, i.e., H 0 = N t I/h e , where I is the current in the turn and h e the electrical height of the winding. This leads to a peak in the current density magnitude J that is more than 10 times the case when f = 0 Hz, i.e., J dc = I/h f w f [15], [31].
The distribution of J is analyzed to distinguish the effect of H ⊥ on the current crowding in HV, by considering the cumulative distribution of J along the tangential direction. The cumulative operator F is defined considering the local reference system (x,ỹ) shown in Fig. 3 where γ is the integration variable from 0 toỹ. A linear F (ỹ, J ) indicates a uniform J in the tangential directionỹ, regardless of the distribution of J in the normal directionx. The plot in Fig. 5(a) shows F (ỹ, J ); since the model is linear with the current I, results are normalized by the total current flowing in the cross-section of HV, i.e., N t I. The profile of F (ỹ, J ) with D hv,c = 0 mm and f = 20 kHz overlaps the case with f = 0 Hz since the skin effect occurs only in the normal direction and the current distribution is uniform alongỹ; when D hv,c = 30 mm and f = 20 kHz a stronger edge effect is indicated by F (ỹ, J ): on average, 5% of the total current accumulates in ≈ 1% of the foil at its end. As a consequence, when D hv,c = 30 mm, more than 20% of the total losses are localized in ≈ 1% of the foil at its end. This is shown in Fig. 5(b) by the cumulative function of the ohmic loss density dP in HV, F (ỹ, dP), normalized by the total ohmic losses in the winding P hv . In other words, almost half of the total losses in the foil are concentrated at both foil ends, which can be detrimental to the occurrence of temperature hotspots. In this case, increasing D hv,c to 60 mm does not raise the edge effect any further; similar behavior is observed in [15].
The effect of the litz rings on the current crowding and the ohmic losses is illustrated by considering two alternative implementations of the new topology, as shown in Fig. 6. The variant F-HYB is designed with the same h f as F-STD, resulting in a larger h e and h m ; the strand number n s is defined so that the DC resistance per unit length of the litz wire is equal to the foil in F-STD, and the total conductor utilization in F-HYB is equal to F-STD. The variant R-HYB is designed to match the same footprint h m as F-STD, i.e., with the same h e and reduced h f , which results in a decreased utilization of conductor compared with the previous designs; this design allows evaluating the loss reduction with the litz rings, when the extra space occupied by the litz wire turns in the hybrid topology is filled with foil conductor in the standard one. In both F-HYB and R-HYB, the strand diameter d s is equal to w f and the litz bundle diameter d b is found from [34]; the distance of the litz rings from the foil edges is D r = 2.5 mm, the main design parameters are listed in Table 1. The losses in the litz wire are modeled by homogenization [35], [36].
The design variants with equal h e are considered, i.e., F-STD and R-HYB; these designs have equal maximum magnetic field intensity H 0 ∝ N t /h e , so the results of H ⊥ are normalized consistently. In R-HYB, the curvature of H is partially shifted towards the litz ring, as shown by comparing the corresponding field lines in Figs. 4(a) and 7(a), e.g., s 18 and s 19 near HV; H ⊥ is reduced by more than 1.5 times, as shown in the corresponding insets.
The impact of the reduced H ⊥ on J in the foil conductor is analyzed in HV by F (ỹ, J ), as shown in Fig. 8; the function is normalized by the total current flowing in the cross-section of the foil winding package, i.e., N f I. The plot confirms that in the hybrid topology the current equalization is achieved by a combination of factors: in the cases with equal H 0 , i.e., F-STD and R-HYB, the litz ring shields H ⊥ at the foil ends; in the design variant F-HYB, the litz rings increase also h e , which reduces the overall H 0 and consequently the edge effect. The insets in the same plot show the contour plot of J/J dc , confirming that the current crowding is reduced in both hybrid designs and almost suppressed in F-HYB.
The total ohmic losses P of the three variants are shown in Fig. 9, results are normalized by the losses in F-STD with D hv,c = 30 mm. Both designs with the hybrid topology exhibit lower losses: in F-HYB, the litz ring allows a 33% loss reduction at 20 kHz, where the losses are only 6% higher than the ideal case F-STD with D hv,c = 0 mm. The trend is not monotonic and a minor loss increase is observed at 30 kHz, which is not critical since frequencies above 30 kHz are beyond the typical range of application of 0.2 mm-thick conductors. The design R-HYB offers a 16% loss decrease at 20 kHz, and a reduction of the total conductor utilization by 17% (the conductor length is equal in all designs, so the conductor utilization is proportional to the DC losses). Besides, the reduced h m compared to F-HYB allows fitting the coil in a core window with 15% shorter h c , as indicated in Table 1, increasing the power density and reducing the core volume and losses.

C. ELECTRIC FIELD HOTSPOT MITIGATION
The galvanic barrier of the MFT is provided by the insulation between HV and other metallic parts, including LV and the core; the insulation is designed to limit the electric stress below the strength of its materials and, to improve its compactness, the electric field stress has to be distributed as uniformly as possible [37]. Electric field E concentrations must be avoided, since they can initiate localized partial discharges, impacting the integrity of the whole transformer. However, foil windings are inherently characterized by E hotspots at their corners, due to the sharp edges of foil  conductor [17]. In this scenario, increasing the insulation distance D hv,c and D hv,lv within reasonable thicknesses is rarely sufficient to reduce the electric field intensity E = |E| within the acceptable limit; consequently, the power density of the MFT drops drastically.
The typical E distribution in a foil winding is analyzed, reproducing the applied voltage test scenario [38], [39]: a potential V hv is imposed to both terminals of HV while the core and LV are grounded. The winding is encapsulated in a simplified insulation system consisting of a single, spacecharge-free material, and the region inside the core window is analyzed. The thickness of the foil is w f = 0.2 mm and the edges are assumed perfectly rounded, which is an ideal condition for reducing electric field hotspots at the foil edges; the insulation thickness between the turns is 0.1 mm. The distances D hv,c = D hv,lv and D lv,c = 10 mm are defined, D hv,c is varied up to 60 mm. The electric stress is estimated by solving the electrostatic field equation of E by a FEM model and considering by symmetry only the upper half of the crosssection illustrated in Fig. 3. The results of E are normalized by the characteristic electric field intensity E 0 between the middle surface of HV and the opposite grounded core plane The contour plot of E /E 0 when D hv,c = 30 mm is shown in Fig. 10: E is practically uniform and equal to E 0 in front of the middle surfaces of the coil, where the field lines are parallel; conversely, E concentrates at the external corners of LV and it increases up to E max = 10.8E 0 at the HV winding end, as shown in the insets. In a real design, such nonuniform distribution leads to stressing the dielectric only in a very small region, whereas the rest of the insulation is practically unnecessary. For example, two practical cases are considered assuming V hv = 12 kV and 17.5 kV, and the dielectric strength of epoxy resin 3.5 kV/mm [37]. With V hv = 12 kV, the thickness of resin needed to limit E max < 3.5 kV/mm is D hv,c = 45 mm, as shown in Fig. 11(a); with such distance E 0 ≈ 0.3 kV/mm, so the rest of the insulation is unstressed. With V hv = 17.5 kV, a minimum D hv,c = 60 mm is necessary, as shown in Fig. 11(b); this thickness is normally impractical and introducing additional air clearances reduces further the compactness of the MFT.
The mitigating effect of the litz ring on E max in the design R-HYB is shown by the contour plot of E /E 0 in Fig. 12. The litz ring reduces E max by more than 3.1 times and suppresses the hotspots at the foil corners; as shown in Fig. 11, in the previous examples with V hv = 12 kV and 17.5 kV, it is sufficient D hv,c = 10 mm and D hv,c = 15 mm to ensure E max < 3.5 kV, respectively.
These analyses confirm that the litz rings preserve the E shielding effect of EQP rings [18], [19], [20], [25]; if necessary, the litz bundle can be covered with semiconductive tape or coatings to smooth possible irregularities on its surface, as often done in MV rotating machinery, pulse transformers and MFTs [26], [27], [28], [29]. Since these concepts are already established, the next sections focus on the advantages offered by the new topology in terms of reduced ohmic loss, conductor usage and winding size.

III. EXPERIMENTAL PROOF OF CONCEPTS A. MFT PROTOTYPES
The loss reduction with the litz rings is verified by measurements with two MFT prototypes designed with standard and hybrid foil windings. The variants F-STD and F-HYB are considered: the windings have equal inner dimensions, identical h f , w f and N t , the insulation between the turns is made of 60 μm-polyimide, the main design parameters are listed in Table 2; n s is chosen to match the DC resistance per unit length in the litz and in the foil. The practicality of the new topology is verified under conservative conditions by designing the prototype so that a high H 0 ∝ N t /h e is induced, thus increasing the risk of critical proximity losses in the foillitz connection; h e = 70 mm and N t = 14 is a conservative scenario for MFTs. The prototype F-HYB is shown in Fig. 13, the foil-litz joint is realized by removing the strand insulation for a length d f,l = h f , to provide an adequate surface for the electrical contact with the foil. The end of the foil conductor is folded vertically and shaped circularly, and finally, it is heated and soldered to the litz wire. The electrical connection between the foil and the litz wire is confirmed by comparing the theoretical and the measured DC resistance of LV and HV; measurements are performed by the Agilent 34461 A multimeter, the results are shown in Table 3. The maximum discrepancy between the theoretical and the measured DC resistance in F-HYB is 3% in LV. This discrepancy is attributed to the additional soldered joints at the foil-litz connections and the measurement tolerance; nevertheless, this additional resistance is not considered critical for the operation of the winding and the electrical connection is deemed adequate.

B. MFT PROTOTYPE LOSS MODELING
The assembly of the real MFT prototypes includes additional conductive parts that are excluded for simplification in the  previous analyses, e.g, the foil leads in the foil winding, and the litz soldering and foil-litz connection in the hybrid topology, as shown in Fig. 2. These parts are not included in the previous investigations, which are aimed to illustrate the basic concepts underlying the litz rings, however, they can introduce ohmic losses due to the proximity effect in both prototypes; therefore, such losses are included for comparing the model with measurements. Besides, analyzing this loss contribution in the two prototypes allows evaluating whether, compared with a standard foil winding, the hybrid topology introduces additional risks of a thermal hotspot due to eddy currents in the foil-litz connection and soldering.
These loss contributions are not directly measurable so a detailed model of the ohmic losses in the individual parts of the winding shown in Fig. 2 is required. The total ohmic losses P tot are analyzed by distinguishing the following contributions: r The skin effect and proximity losses in the winding turns P t,t , including litz rings and solderings.
r The proximity losses P c,t in the foil-litz joint; in the standard foil winding, P c,t represents the proximity losses in the foil leads.
r The losses in the external connections P ext of the hybrid and standard foil winding, which are made of litz and foil conductor, respectively. Predicting P tot by a single 3D model requires considerable computational effort; however, ohmic losses in the foil-litz joint cannot be accurately represented by only analytical or 2D numerical models. Therefore, the individual loss contributions are obtained separately by solving the MQS equations as follows: r P t,t is calculated as described in [36], [41], including the losses in the soldered litz by modeling the litz rings as solid conductor for a length d f,l , and as litz wire for the remaining turn length.  r P c,t is calculated by a 3D model including the eddy current only in the foil-litz joint shown in Fig. 2 r P ext is calculated analytically, the equation for the losses due to skin and proximity losses in litz and foil wire are defined in [42]. The losses P tot are proportional with the square of the current intensity and are expressed by the equivalent short-circuit resistance seen from HV, i.e., R ac . The plots in Fig. 14 indicate a 17% decrease of P tot in the hybrid topology; the losses drop mainly in the winding, i.e., P t,t , by up to 27% at 30 kHz. The losses in the foil-litz connection and the foil leads P c,t are not negligible compared with P t,t but similar in both prototypes, whereas P ext is neglectable.
The losses in the foil-litz joint and the soldering P c,t are analyzed to exclude the risk of thermal hotspots. The losses in the foil-litz joint are compared with the losses in the leads of the standard foil winding: as shown in Fig. 14, the difference between P c,t in the standard and the hybrid winding is only 30% at 20 kHz, and less than 45% at 30 kHz, which is a relatively high frequency for 0.2 mm-thick conductors; even in an adverse scenario with high H 0 and proximity effects, the losses in the foil-litz connection are in the same order of magnitude as the standard foil leads, therefore, they do not  introduce additional risks of thermal hotspots. The losses in the litz ring solderings are compared in the extreme case with f = 30 kHz with the total losses in the winding: as shown in Fig. 15, the total losses in the solderings are less than 3% of the total losses in the respective winding, so they are deemed not critical; the losses P tot are verified by measurements next.

C. MEASUREMENTS
The ohmic losses in the MFT prototypes are compared by the resistance R ac , measured at the HV side with short-circuited LV. In the kilohertz range, the MFT is normally supplied a total apparent power with a power factor PF 10%, which can compromise the accuracy in the measurement of the dissipated active power. A method for accurate loss measurement consists in increasing PF by reactive power compensation, connecting a capacitor with known losses P c to the MFT [43]. The measurement is performed at the resonance frequency of the system ω 0 = 2π f 0 , so the total reactive power exchanged with the MFT is provided by the capacitor, and the total power P s is delivered by the supply with PF = 1. This yields where V s , V c and I s are the rms value of the electrical quantities indicated in Fig. 16, and tan δ is the dissipation factor of the capacitor. In the test, the MFT is excited by a Toellner 7621 power supply. The linearity of the losses with I 2 s allows evaluating R ac at a relatively low current; I s ≈ 1 A is chosen to simplify the experimental setup. Measurements are performed by a Lecroy HDO6034 A 12-bit oscilloscope, Lecroy AP015  Fig. 17. The capacitors guarantee tan δ < 5 × 10 −4 up to 50 kHz [44].
Results are shown in Table 4: the hybrid topology exhibits a loss reduction in the 15% to 17% range. The losses predicted by the electromagnetic model approximate the measurements with a deviation lower than 4%. Therefore, the model is deemed reliable and the investigations on the ohmic losses and the hybrid winding are confirmed experimentally for the considered conductor thickness and frequency range.

IV. DESIGN CONSIDERATIONS
Standard foil windings are not always suitable for MV applications due to the electric field hotspots at the winding corners, therefore, the comparison with the hybrid windings shown in Fig. 6 is extended including foil windings with EQP rings [25], as shown in Fig. 18, which are considered as the established state-of-the-art solution to enable foil windings in MV MFTs [18], [19], [20]. The design variant EQP-SS• is considered as a reference and consists of a hollow EQP ring with a thickness 0.1 mm, made of nonmagnetic stainless steel AISI316 (conductivity 1.4 MS/m); in this coil h e = h f , but the footprint h m is larger due to the EQP ring. The variants EQP-Cu• and EQP-Cu• are based on the same configuration as EQP-SS•, with EQP rings made of 0.1 mm-thick copper and solid copper, respectively. The EQP ring has the same d b and D r as the litz ring; the main parameters are listed in Table 5.  Three cases are analyzed: in case 1 the same design reported in Table 1 is considered, in cases 2 and 3, either N t or h f are varied to consider a scenario with larger proximity losses due to more intense H 0 . The losses are analyzed by the verified model; for simplification, the contribution P c,t is neglected since it is similar in both the standard and the hybrid designs, the contribution P c,ext is excluded as negligible; results are normalized with respect to EQP-SS•.
As shown in Fig. 19, the design EQP-SS• has the lowest losses among the designs with EQP rings; the losses due to the EQP ring never exceed 7% of the losses in F-STD. The losses in EQP-Cu• are up to 20% higher, whereas in EQP-Cu• they are more than 50% higher in both cases 1 and 2. The designs with litz rings outperform all other variants between 10 and 30 kHz: in F-HYB, the losses decrease more than 30%; in R-HYB, a loss reduction higher than 15% is observed in case 1. In general, R-HYB offers better performance compared to the EQP designs above 10 kHz, however, it is penalized at low frequencies by the reduced cross-section of the foil conductor.
As shown in Fig. 20, for all study cases, the copper utilized in the variants EQP-SS•, EQP-Cu• and F-HYB is approximately equivalent. The variant EQP-Cu• contains up to 20% more copper than F-STD. The design R-HYB allows reducing the total copper by approximately 15% in cases 1 and 2, and more than 20% in case 3. In all study cases, the variants with EQP ring and F-HYB have a larger footprint h m than F-STD, whereas R-HYB is designed with a reduced h f to conform with the same h m as F-STD, up to more than 20% shorter than the other variants in case 3.
The following design guidelines are valid up to 30 kHz: r The EQP rings for foil winding MFTs should be designed with materials that are either thin, resistive and nonmagnetic, e.g., AISI316, or solid conductor.
r The hybrid winding concept F-HYB is the most effective for reducing ohmic losses; it does not lead to additional conductor weight and can be fitted in the same volume as a winding with EQP rings.
r The hybrid winding concept R-HYB is a compromise solution between ohmic loss reduction, conductor utilization, and winding footprint. These concepts can be extended to higher frequencies after evaluating a suitable foil and litz strand thickness [32], and ensuring that the eddy current losses in the foil-litz soldering are not critical.

V. CONCLUSION
Foil conductor is an attractive solution to improve the filling factor and the cost-effectiveness of MFTs, however, the insulation clearances for medium-voltage applications increase the ohmic losses due to the current crowding effect; besides, the electric field hotspots at the winding corners require shielding by equipotential rings.
A new hybrid topology is presented in this work, developed to mitigate simultaneously both effects: the electric field shielding of equipotential rings is provided by litz rings connected in series to the foil winding; besides, the litz rings shift the magnetic field curvature away from the foil ends, mitigating the current crowding losses. The ohmic loss reduction offered by the new topology is verified experimentally in two prototypes designed with standard and hybrid foil winding, a reduction of more than 15% is observed by a model and confirmed by measurements. Windings designed with the new topology and with standard equipotential rings are compared by the verified model to evaluate the conductor and footprint saving: a winding loss reduction of up to 30% is observed by the new concept, whereas the conductor utilization and the winding height can be decreased by more than 20%. Therefore, this solution pushes forward the constraints in using foil conductor and improves the cost-effectiveness of the design, which eventually supports the advancement of medium-frequency and solid-state transformers.
MITROFAN CURTI (Member, IEEE) received the master's degree from the Warsaw University of Technology, Warsaw, Poland, and the Ph.D. degree from the Eindhoven University of Technology, Eindhoven, The Netherlands. He is currently an Assistant Professor with the Group of Electromechanics and Power Electronics, Department of Electrical Engineering, Eindhoven University of Technology. His research interests include numerical and analytical modeling, analysis, and optimization of electromechanical and electromagnetic systems.
ELENA A. LOMONOVA (Senior Member, IEEE) received the graduation degree (cum laude) in electromechanical and control systems and the Ph.D. degree (cum laude) in 1993 from Moscow Aviation Institute, National Research University, Moscow, Russia, working on powertrain and control systems for autonomous vehicles with multilevel power supply subsystems for on-board loads and laser equipment. She started her industrial career with the research and development company Astrophysics, Moscow, Russiaduring 1982-1987. Afterwards, she moved to MAI, and was active in research, education, and industrial projects during 1987-1997. In 1998, she was with the TUDelft and joined the Eindhoven University of Technology in 2000. In 2009, she was appointed a Full-Time Professor and the Chair of the Electromechanics and Power Electronics Group. Her chair focuses on fundamental and applied research on enabling energy conversion theory, methods and technologies for high-precision, automotive, and medical systems. She is an author and co-author of more than 300 scientific publications and more than 15 patents. Her research interests include various facets of advanced mechatronics, electromechanics, and electromagnetics, including rotary electrical machines, drives, and linear and planar actuation systems. She was the recipient of the prestigious awards -Nagamori (Japan, 2016) and Lifetime Contributions to Magnetics (U.K., Cambridge, 2019).