Dodo6/Topic_Modelling_using_LDA

1Article2 3Power Density Maximization in Medium Frequency4Transformers by Using Their Maximum Flux Density5for DC–DC Converters6Dante Ruiz-Robles 1,*, Edgar L. Moreno-Goytia 1, Vicente Venegas-Rebollar 1 and7Nadia M. Salgado-Herrera 28Graduate Program and Research in Electrical Engineering (PGIIE), Tecnológico Nacional de9México/Instituto Tecnológico de Morelia, Morelia 58120, Mexico; elmoreno@itmorelia.edu.mx (E.L.M.-G.);10vvenegasr@itmorelia.edu.mx (V.V.-R.)112 Instituto de Energías Renovables, Universidad Nacional Autónoma de México: Priv. Xochicalco S/N,12Temixco, Morelos 62580, Mexico; nasahe@ier.unam.mx13* Correspondence: Dante@tecmor.mx; Tel.: +52-443-221-317714115 16Received: 15 February 2020; Accepted: 8 March 2020; Published: 11 March 202017 18Abstract: The medium frequency transformer (MTF) is a key component of various new DC–DC19converters that are designed for applications in modern electrical power grids at medium and high20voltage. To attain the high performance that are necessary for targeting these applications, MFTs21should have high power density and high efficiency as characteristics. For this endeavor, newly22designed MFT procedures, which also take advantages of new core materials, are under23investigation. Differently to other design proposals, most of which use conventional transformer24design procedures based on equating core losses to copper conduction losses, in this paper, an MTF25with a nanocrystalline (VITROPERM 500F) core is designed with a new procedure that is oriented26in aiming the maximum flux density (Bmax). The characteristics of the MFTs that are obtained by27using this procedure are compared with those of the MFTFs that are designed with a conventional28procedure. The results show that by using the proposed technique, we get a 25% reduction in the29winding size, a higher power density, and a lower MTF building cost while maintaining a high30efficiency (>98%). The design methodology is developed through a rigorous mathematical analysis31that is verified with computer simulations in Matlab-Simulink and validated with experimental32results from two MTF laboratory prototypes designed at a flux density of 0.9 T (75% Bmax) and 1.2 T33(Bmax).34Keywords: converter DC–DC; electric vehicles; renewable energies; solid state transformers35 361. Introduction37One of the leading research goals regarding high or medium frequency transformers is the38increase power density while maintaining a high efficiency (98%) [1–6]. These characteristics open39many opportunities to these transformers in a wide range of applications in electrical distribution40grids [1,7–9]. In this paper, we report our research efforts on designing medium frequency41transformers (MTFs) from a different point of view than the conventional ones. The MFT is42fundamental in the development of new DC–DC converters that operate as part of a) photovoltaic43systems [2], b) wind power systems [3], c) solid-state transformers [10], d) electric vehicles [11], e)44diesel generators [12,13], and f) smart grid interfaces. It is worth mentioning that a high-power45density that is maintained at a reasonably high efficiency is desired in DC–DC converters, as well as46in MTFs.47Electronics 2020, 9, 470; doi:10.3390/electronics903047048 49www.mdpi.com/journal/electronics50 51Electronics 2020, 9, 47052 532 of 1654 55In order to design MTFs at a medium-voltage range, several materials have been studied and56analyzed. Among all of them, nanocrystalline-alloys have shown great potential [4]. Nanocrystalline57materials exhibit desirable features at a medium-frequency range that allow MFTs to get higher58power density and efficiency values than with other materials such as silicon steel, ferrites, and59different amorphous materials [10]. The nanocrystalline materials combine the advantageous60properties of soft magnetic materials, such as a high magnetic saturation [14], with their own61properties. These properties are preserved even at higher frequencies and temperatures [15,16].62Therefore, nanocrystalline magnetic cores are greatly suitable for designing medium voltage,63medium frequency transformers. However, the design of transformers with this type of core is not64straightforward, and more research on design procedures is needed [17]. Improved nanocrystalline65magnetic core designs also have opportunities in various other applications [18,19].66The flux density (Bac) that was reported in [5] for MTFs that were designed with nanocrystalline67cores is 75% (0.9 T) of its maximum density flux, Bmax = 1.2 T. For other core materials, e.g., a silicon68steel, the design of transformers at the medium-frequency range is carried out at Bac = 0.5 T and 1 kHz69[6] because if the maximum flux density is reached (Bmax), then the core losses will increase and result70in an efficiency reduction below the minimum required reduction of 98%. However, if the operating71frequency for silicon steel core MTFs is reduced to 600 Hz, as required by the design, then Bac will72increase to 0.6 T [3]. In this case, such a value of Bac is far below the Bmax value that can be obtained73with nanocrystalline materials. It is worth mentioning that in a design, the higher the needed MTF74power density, the higher the required flux density (Bac).75The usual value of Bac for amorphous materials in MTFs operating at 3.6 kHz is 0.5 T [20]. Using76higher flux density in these materials results in higher core losses and lower transformer efficiency.77Moreover, core losses at Bac = 1.2 T and 5 kHz are lower for nanocrystalline (Bmax = 1.2 T) than for78amorphous materials (Bmax = 1.5 T) [20]. Other materials for MTFs cores, such as ferrites, are in use for79frequencies greater than 20 kHz at Bac = 0.35 T [20]. This value of Bac is far lower than the one obtained80with nanocrystalline materials (0.9 T) [2].81It must be stressed that previous research efforts have overlooked the opportunity to design82nanocrystalline cores for MFT-based DC–DC converters with a maximum flux density under certain83conditions. Besides this latter consideration, it is also possible to get a reduction in the number of84winding turns of the MTF and a higher power density while maintaining a high efficiency (98%) by85using a new design procedure. DC–DC converters, with a boosted power density characteristic, can86be applied to a) the interconnection of photovoltaic systems, b) electric vehicles, c) solid-state87transformers, and 4) built-in wind generators. The classical design theory of conventional88transformers [21] states than an optimal design is achieved once the core losses are equal to the copper89conductor losses. By taking into consideration the idea that core losses for nanocrystalline materials90are much lower than copper conduction losses, we can learn that such classical theory cannot be91applied to nanocrystalline materials. Therefore, further research efforts are required to determine the92conditions for which power density can be increased while maintaining a high efficiency in93nanocrystalline cores. This point is addressed in the present paper.941.1. Contributions From This Work.95The main contribution of this paper is the introduction of a novel design procedure that gives96MFT designers a cutting-edge tool for designing efficient MFTs for DC–DC converters at a maximum97flux density. These converters have a niche of opportunity in building smart grid environments.98To assess the effectiveness of this proposal, two MFTs with nanocrystalline cores were designed99at a medium frequency range. The first MFT, MFT1, was designed at 75% of its maximum flux density100(0.9 T). The tests on MFT1 show that the core losses were far lower than the winding losses.101Encouraged by this last result and the favorable thermic properties of nanocrystalline materials, we102designed the second MFT, MFT2, at a maximum flux density, Bmax = 1.2 T. The results were: 1) a 25%103reduction in the transformer winding, 2) a higher power density, and 3) a lower MTF building cost.104These values were achieved while maintaining a high efficiency (> 98%). Thus, an accurate105transformer performance is evidenced in the math analysis, the computer simulations, and the106 107Electronics 2020, 9, 470108 1093 of 16110 111experimental results when using a prototype working at 1 kVA and 250V at 5 kHz. All these results112confirm the effectiveness of the design procedure presented in this work.113This paper is organized as follows. Section 2 introduces the medium-frequency transformer114design procedure and transformer designs at 75% and 100% of Bmax. Section 3 presents the calculation115of the two MFTs, the simulations, and the two MFT prototypes. Section 4 shows the discussion.116Finally, in Section 5, conclusions are presented.1172. Medium-Frequency Transformer Design Procedure1182.1. Transformer Design119The MTF design technique of this work was developed by taking the algorithm proposed in [22]120as a reference. The critical difference of the proposed technique [2], regarding [22] and other design121techniques, including the standard procedure, was the modification about how the losses of the122nanocrystalline cores were computed in the product of areas method [22]. In this way, the resulting123MTF design that was obtained with the proposed technique exhibiting a higher efficiency at a124medium frequency of 5 kHz.125The product of areas method was based on finding a power capacity that could be held by a126core, as stated in Equation (1) [22].127𝐴𝑝 = 𝑊𝑎 𝐴𝑐 =128 129𝑃𝑡 (104 )130𝐵𝑎𝑐 𝑓𝐽𝐾𝑓 𝐾𝑢131 132(1)133 134where 𝐴𝑝 is the product of areas, 𝑊𝑎 and 𝐴𝑐 are the window area and core cross-sectional area,135respectively, 𝑃𝑡 is the apparent power, 𝐵𝑎𝑐 is the magnetic flux density, 𝑓 is the frequency, 𝐽 is the136current density, 𝐾𝑓 is the waveform coefficient, and 𝐾𝑢 is the winding fill factor.137The detailed math calculations on nanocrystalline core selection, winding turns, core losses,138winding losses, and the methodology validation for medium-frequency MTFs were thoroughly139detailed in [2].1402.2. Transformer Design at 75% and 100% of Bmax141A nanocrystalline core transformer was next designed for 75% of Bmax, i.e., Bac = 0.75, Bmax = 0.9 T,1421 kV, 5 kHz, and 10 kVA. The design obtained parameters are shown in Table 1.143The results from calculations were validated with Matlab-Simulink by using an equivalent144circuit of the MTF. Note that for such circuit, the computation of the magnetization and dispersion145branch variables was required. For the dispersion branch, resistances R1 (primary winding resistance)146and R2 (secondary winding resistance) were given by the product of areas method [22]. The147dispersion inductance (Ld) was computed by using Equation (2), which gives accurate results at148medium frequencies (5 kHz) [23].149Table 1. Transformer design at 10 kVA and 0.9 T.150 151Design Data152Uin1531000 V154Uout1551000 V156f1575000 Hz158Iout15910 A160Bac1610.9 T162Np163278164Ns165282166Pcu16787 W168Pfe1691.51 W170Ptot17188.51 W172Efficiency17399.1%174 175Electronics 2020, 9, 470176 1774 of 16178 179Wa180Ac181Ap182 18350.26 cm21842 cm2185100.53 cm2186 187Where the variables in Table 1 are input voltage (Uin), output voltage (Uout), frequency (f), output188current (Iout), flux density (Bac), the number of primary winding turns (Np), the number of secondary189winding turns (Ns), copper conducting losses (Pcu), core losses (Pfe), total losses (Ptot), window area190(Wa), effective cross-section of the core (Ac), and the area product (Ap).191 192𝐿𝑑193 1942195(𝑚1 − 1)(2𝑚1 − 1)196𝑁𝐿1197= 𝜇0198𝑚1 [𝑀𝐿𝑇𝑖𝑠𝑜 𝑚1 𝑑𝑖𝑠𝑜 + 𝑀𝐿𝑇𝑝𝑟𝑖199𝑑𝑖𝑛𝑠1200ℎ𝜔2016202𝑚1 (𝑚2 − 1)(2𝑚2 − 1)203+ 𝑀𝐿𝑇𝑠𝑒𝑐204𝑑𝑖𝑛𝑠22056𝑚22062∆207sin ( 1 ) 4𝛼𝛿 2 (𝑚12 − 1) + 4𝑑𝑝𝑟𝑖 (2𝑚12 + 1)208𝛼𝛿209+ 𝑀𝐿𝑇𝑝𝑟𝑖2102∆ 221124 (sin 1 )212𝛼𝛿2132∆2142 4∆1 (2𝑚2215𝛼𝛿 (216)217+ 1) − 8𝑑𝑝𝑟𝑖 (1 − 𝑚12 ) cos ( 1 )2181219𝛼𝛿220𝛼𝛿221− 𝑀𝐿𝑇𝑝𝑟𝑖2222∆1 222324 (sin224)225𝛼𝛿2262∆2227222822292230𝑚1 sin ( 𝛼𝛿 ) 4𝛼𝛿 (𝑚2 − 1) + 4𝑑𝑠𝑒𝑐 (2𝑚2 + 1)231+ 𝑀𝐿𝑇𝑠𝑒𝑐232𝑚22332∆ 223424 (sin 2 )235𝛼𝛿2364∆223722382239𝑚1 𝛼𝛿 sin ( 𝛼𝛿 ) (2𝑚2 + 1)240− 𝑀𝐿𝑇𝑠𝑒𝑐241𝑚22422∆ 224324 (sin 2 )244𝛼𝛿2452∆22462247𝑚1 8𝑑𝑠𝑒𝑐 (1 − 𝑚2 ) cos ( 𝛼𝛿 )248+ 𝑀𝐿𝑇𝑠𝑒𝑐249]250𝑚22512∆2 225224 (sin253)254𝛼𝛿255 256(2)257 258where:259𝜇0 = vacuum permeability260 261𝑑𝑖𝑠𝑜 = isolation distance262 263𝑑𝑖𝑛𝑠1 = insulation distance between the layers of the primary264 265𝑁𝐿1 = turns per layer266 267𝑑𝑖𝑛𝑠2 = insulation distance between the layers of the secondary268 269ℎ𝜔 = winding height270 271𝑚1 = number of layers in the primary272 273𝑑𝑝𝑟𝑖 = thickness of the primary274 275𝑚2 = number of layers in the secondary276 277𝑑𝑠𝑒𝑐278 279𝑀𝐿𝑇𝑖𝑠𝑜 = mean length of the isolation distance280 281∆1 = penetration ratio of the primary, ∆1 =282 283𝑑𝑝𝑟𝑖284 285𝑀𝐿𝑇𝑝𝑟𝑖 = mean length turns of primary portion286 287∆2 = penetration ratio of the primary, ∆2 =288 289𝑑𝑠𝑒𝑐290 291𝑀𝐿𝑇𝑠𝑒𝑐 = mean length turns of secondary portion292 293𝛼=294 295= thickness of the secondary296 2971+𝑗298𝛿299 300where 𝛿 is the skin depth301 302𝛿303 304𝛿305 306Electronics 2020, 9, 470307 3085 of 16309 310The magnetization inductance (𝐿𝑚 ) is calculated with Equation (3). This equation was proposed311in [21] and validated in [24] for the medium frequency range (5 kHz).312𝐿𝑚 =313 314𝜇𝑟 𝜇0 𝑁 2 𝐴𝑐315𝑙𝑐316 317(3)318 319Where N is the number of turns and 𝑙𝑐 is the mean length of the closed magnetic path around the320core. Equations (2) and (3) are part of the mathematical model of the MTF equivalent circuit321implemented in Matlab-Simulink (see Table 2). The cases of study were simulated by using a voltage322source of 1 kV/5 kHz/10 A.323The resulting waveforms of the input and output voltages and currents are shown in Figure 1.324Though the main application of MTFs is as part of DC–DC converters, in which square waveforms325are used, in this work, for convenience, the sine wave was used instead as the stimulus for purposes326of simulating and experimenting with the MFT prototype. Taking into consideration that core losses327are higher for sine waves than for square waves [25], a reduction in core losses is expected once the328MFT operates with a 5 kHz square wave excitation. Table 3 shows the input voltage, output voltage,329and current (Uin, Uout, Iin, Iout) values that were obtained from simulations. The final efficiency was33098.9%.331Table 2. Required equivalent circuit model data for the simulation of the 10 kVA/0.9 T medium332frequency transformer (MTF).333 334Required Data3351000 V3361000 V337Winding 1 parameters338Iout33910 A340Bac3410.9 T342Np343278344Winding 2 parameters345Pcu34687 W347Pfe3481.51 W349Ptot35088.51 W351Magnetization resistance and inductance352Wa35350.26 cm2354Ac3552 cm2356Uin357Uout358 359Iin360Iout361 362Figure 1. Input and output voltages and currents of the 10 kVA/0.9 T MFT.363Table 3. Voltages and currents of the primary and secondary winding of the 10 kVA/0.9 T MTF.364 365Electronics 2020, 9, 470366 3676 of 16368 369Voltages and currents370Uin (RMS)3711000 V372Uout (RMS)373990.1 V374Iin (RMS)3759.913 A376Iout (RMS)3779.901 A378Efficiency37998.90%380According to the classical transformer design theory, the optimal density flux (Bo) is achieved381when the core losses (Pfe) are equal to the copper conduction losses (Pcu) [21], as shown in Figure 2.382Observe that at Bo, the total MTF losses (Ptot) were at their minimum.383Losses384 385P386Pfe387 388Pcu389Bo390Figure 2. Flux density optimal design point Bo.391 392For the nanocrystalline MTF core, Pfe was lower than Pcu at Bac = 0.9 T, as is shown in Table 1.393Therefore, it was feasible to increase Bac to Bmax, i.e., up to 1.2 T for the nanocrystalline cores394(Vitroperm500F). On these grounds, the resulting design parameters of a 10 kVA/1.2 T MFT are395shown in Table 4.396Table 4. Transformer design data for a 10 kVA/1.2 T MFT.397 398Design Data399Uin4001000 V401Uout4021000 V403f4045000 Hz405Iout40610 A407Bac4081.2 T409Np410209411Ns412212413Pcu41465.4 W415Pfe4162.12 W417Ptot41867.52 W419Efficiency42099.3%421Wa42250.26 cm2423Ac4242 cm2425Ap426100.53 cm2427By comparing the MTF design at 0.9 T with the one at 1.2 T, it can be noticed that Pcu was reduced428from 88.51 to 65.4 W (26.1%) while Pfe and the efficiency increased from 1.51 to 2.12 W (40.3%) and42999.1% to 99.3%, respectively.430By designing at Bmax, a critical reduction in the winding turns was also achieved. For instance,431the 278 turns that were needed for Bac = 0.9 T (see Table 4) were reduced to only 209 turns for Bac = 1.2432T, as presented in Table 2. This represented a turn reduction of 24.8%. The number of winding turns433 434Electronics 2020, 9, 470435 4367 of 16437 438was calculated with Equation (4). It can be noticed that as Bac increased, then the number of turns439decreased.440𝑁𝑝 =441 442𝑉𝑖𝑛 104443𝑘𝑓 𝐵𝑎𝑐 𝑓𝐴𝑐444 445(4)446 447Despite the core losses increment at Bmax, these losses were still lower than the winding losses.448However, these losses were not good enough for new MTFs that were designed by using the449conventional transformer design theory [21], mainly because this theory states that the optimal450design is when core losses are equal to the copper conducting losses.451When increasing Bac to Bmax in nanocrystalline core MTFs, the number of winding turns decreases.452Consequently, the manufacturing cost is lowered while obtaining a higher power density. This can453be achieved without disregarding the main design MTF constrictions discussed in Section 3, such as454the tolerance margin of core saturation that is allowable after exceeding the nominal MTF voltage.455These results showed the favorable magnetic properties of nanocrystalline materials, which456represent a significant improvement over other core materials for MFTs. The improvement in core457materials has significantly reduced power losses. On the other hand, winding technology has458remained relatively much the same.4593. MTF Laboratory Prototypes460As part of the validation of the MFT design procedure focused on Bmax, we built two MFT lab461prototypes: 1) 1 kVA, 5 kHz, 250 V and 0.9 T, which was named MFT1; and 2) 1 kVA, 5 kHz, 250 V462and 1.2 T, which was named MFT2. The parameter values that were obtained from the design463procedure for each MFT are shown in Table 5.4643.1. Transformer Calculation465If Bac increases, then Np decreases, as expressed by Equation (4). Therefore, using Bmax = 1.2 T466(nanocrystalline materials) led to a 25.17% reduction in the number of winding turns from 147 at Bac467= 0.9 T to 110 at Bac = Bmax = 1.2 T (see Table 5).468Table 5. Transformer design data for MFT1 and MFT2.469 470Design Data471Parameter472MFT1473MFT2474Uin475250 V476250 V477Uout478250 V479250 V480F4815000 Hz4825000 Hz483Iout4844A4854A486Bac4870.9 T4881.2 T489Np490147491110492Ns493150494112495Pcu49611.74 W4978.78 W498Pfe4990.62 W5001.12 W501Ptot50212.36 W5039.89 W504Efficiency50598.80%50699.01%507Wa50819.63 cm2 19.63 cm2509Ac5100.95 cm25110.95 cm25124513Ap51418.65 cm 18.65 cm4515A side effect of using Bac = Bmax is the increase of Pfe. However, this increment does not adversely516affect the MTF efficiency that is achieved with nanocrystalline materials. For the designed MFTs, Pfe517increased from 0.62 W (MTF1) to 1.12 W (MFT2).5183.2. Simulation519 520Electronics 2020, 9, 470521 5228 of 16523 524The dispersion and magnetization inductances are parameters that were needed in the525simulations of the MTF behavior under different operation conditions. These parameters were526calculated by using Equations (2) and (3). MFT1 and MFT2 were both simulated in Matlab-Simulink.527Table 6 shows the simulating data of the equivalent circuit of MFT1 and MFT2. A power source528of 250 V at 5 kHz and a 62.5 Ω load were used in this case.529The input/output voltage and current waveforms of MFT1 resulting from simulations are shown530in Figure 3. The RMS values of these waveforms are summarized in Table 7. The efficiency that was531calculated for MTF1 was 98.8%, strictly lower than the 99% that resulted from the simulations. These532results encouraged the building of the lab prototypes.533Figure 4 shows the input/output voltage and current waveforms that resulted from simulating534the MTF2. The RMS values of these waveforms are summarized in Table 7. The difference between535the efficiency that was obtained from simulations and that which was obtained from calculations was536minimal, as they were 99.05% and 99.01%, respectively. These results were also validated with537experimentation.538Table 6. Simulation data for the MFTs.539 540Required Data541MFT1542MFT2543Pout (VA)54410005451000546f (Hz)54750005485000549Winding 1 parameters550Uin (RMS)551250552250553R1 (Ω)5540.27295550.2042556Ld1 (H)5570.000031 0.0000238558Winding 2 parameters559Uout (RMS)560250561250562R2 (Ω)5630.27295640.2042565Ld2 (H)5660.000031 0.0000238567Magnetization resistance and inductance568Rm (Ω)569111270570111270571Lm (H)5720.1945730.1087574 575Uin576Uout577 578(a)579 580Iin581Iout582 583(b)584 585Figure 3. Input and output voltages and currents of MFT1 at 1 kVA.586 587Electronics 2020, 9, 470588 5899 of 16590 591Uin592Uout593 594Iin595Iout596 597(a)598 599(b)600 601Figure 4. Input and output voltages and currents of MFT2 at 1 kVA.602Table 7. RMS values of voltages and currents from simulations of the MFTs.603 604Voltages and currents605Uin (RMS)606Uout (RMS)607Iin (RMS)608Iout (RMS)609Efficiency610 611MFT1612250 V613247.7 V6143.966 A6153.963 A61699%617 618MFT2619250 V620248.25 V6213.98 A6223.97 A62399.05%624 6253.3. MFT Prototypes626The two MTF laboratory prototypes were developed based on the data reported in Table 5. The627prototype, MFT1, was designed with Bac = 0.9 T (Figure 5a), and the second, MFT2, was designed with628Bac = 1.2 T (Figure 5b).629Figure 6 shows MTF1 and the testbed. The prototype was fed with an AC POWER630SOURCE/ANALYZER AGILENT 6834b. At experimentation, the input voltage was set to 250 V, and6315 kHz, to test the MTF1 prototype with a load of 60 Ω.632 633(a)634 635(b)636Figure 5. (a) MFT1 at 0.9 T; (b) MFT2 at 1.2 T.637 638The efficiency of MFT1 that was measured at the laboratory was 98.62%. This value deviated639less than 1% of the theoretical efficiency of 98.8% and the efficiency of 99% from simulations. These640results confirmed the effectiveness of the MTF designs presented in [2].641 642Electronics 2020, 9, 470643 64410 of 16645 646Figure 6. MFT1 lab prototype that was tested by using 1 kVA at 5 kHz.647 648Figure 7 shows the MTF2 prototype in the laboratory. The testbed was the same as the one that649was used to test MFT1. In this case, the efficiency that was measured in the laboratory was 99.01%650while the efficiencies that was obtained from the calculation and simulations were 99.01% and65199.05%, respectively. Table 8 shows the output power, input power, winding losses, core losses, and652total losses of the MFT1 and MFT2 lab prototypes. Due to the increase of the flux density, the core653losses of MFT2 increased, and these were higher compared to those of MFT1. However, the losses in654the winding decreased in MFT2 because the winding was reduced. Additionally, there was a 25%655reduction in winding turns. All together this implies a higher power density and a lower building656cost. These results show the excellence performance of the MTF that was operating at Bmax.657The voltage of the secondary winding of MFT2 also increased and was higher compared to such658a voltage of MFT1. The waveforms are shown in Figure 3; Figure 4 for the simulation cases and Figure6596; Figure 7 for the prototype cases. This effect in the voltage was because of a decrement in the number660of turns in the winding. Such a decrement also led to a reduction of the dispersion inductance, and661from this, a lower dispersed flow was obtained and the voltage of the secondary winding increased.662 663Figure 7. MFT2 lab prototype that was tested by using 1 kVA at 5 kHz.664 665Electronics 2020, 9, 470666 66711 of 16668 669Table 8. Losses and power of input and output of the MFT1 and MFT2 lab prototypes.670 671Measurement672MFT1673MFT2674Input power6751002 W6761015 W677Output power 1005.96 W 1005 W678Core losses6791.15 W6802.02 W681Winding losses68212.84 W6837.97 W684Total losses68514.04 W68610 W687Figure 8 shows the behavior of the efficiency for both transformers at different frequencies. From6883.1 to 4.3 kHz, the efficiency of MFT1 was greater than 98% at nominal power and higher than the689efficiency of MFT2. From 4.4 to 5 kHz, the efficiency of MFT2 was slightly higher. This was due to690the increase in the flux density in the design of MFT2. This condition decreased the frequency range691in which MFT2 began to behave efficiently.692Figure 9 shows the behavior of both MFTs with different load values, from 25% to 150% of the693nominal load (100% = 60 Ω = nominal load). For 125% of the nominal load in MFT2, the output voltage694was 279 V with a current = 4 A. This voltage level was within the tolerance margin that was allowed695above the nominal voltage (12%, 280 V limit). Additionally, the obtained efficiency was higher than69698%. For 150% of the nominal load, the output voltage and current were 288 V and 3.95 A,697respectively. This voltage level exceeded 12% of the nominal voltage level, and the efficiency was698reduced to 86.63%.699 700Figure 8. Efficiency vs. frequency for both MFTs.701 702Figure 9. Efficiency of both MFTs at different loads.703 704Electronics 2020, 9, 470705 70612 of 16707 708Figure 10 shows the thermic images of the MTF prototype that was taken with a Milwaukee709M12TM 7.8 kP thermal camera after 30 minutes of operation at nominal voltages and currents.710Observe that there was a temperature reduction from 75.6 to 75.2 °C between MTF1 and MFT2711operation at the hottest winding point. For dry transformers, the temperature raise was 110/135 °C at712the hottest winding point, and the tolerance of the nanocrystalline cores (VITROPERM 500F) was 105713°C.714 715(a)716 717(b)718 719Figure 10. MFT temperature: (a) MFT1; (b) MFT2.720 721Figure 11 shows the voltage tolerance above the nominal voltage (250 V) that was exhibited by722the MTF2 prototype. In Figure 11a, it is clear that a raise of 12% above the nominal voltage (to 280 V)723did not significantly affect the MTF prototype’s overall behavior. Efficiency remained at 98.8%.724 725Left: CH1 = Uin, CH2 = Uout; right: CH1 = Iin, CH2 = Iout.726(a)727 728Electronics 2020, 9, 470729 73013 of 16731 732Left: CH1 = Uin, CH2 = Uout; right: CH1 = Iin, CH2 = Iout.733(b)734 735Left: CH1 = Uin, CH2 = Uout; right: CH1 = Iin, CH2 = Iout.736(c)737Figure 11. MFT2 maximum voltage tolerance testing: (a) 12%, (b) 13%, and (c) 15%.738 739Similarly, Figure 11b shows the effects of the 13% raising in the voltage above its nominal value,740i.e., from 250 to 283 V. In this case, the MTF2 prototype showed some signs of saturation in the input741voltage, output voltage, current, and efficiency down to 93.88%. The third case, shown in Figure 11c,742explored the effects of raising voltage to 15% above nominal. In this condition, core saturation was743evident, voltage and current waveforms were distorted, and efficiency dropped by up to 86.93%.744Table 9 presents the previous results. Table 10 presents the THD of both MFTs at the voltages shown745in Table 9.746Table 9. Tolerance above the nominal voltage of MFT2.747 748Uin749Uout750Iin751Iout752Efficiency753Nominal voltage (Unom) 250 V 250 V 4.06 A 4.02 A75499.01%75512% above Unom756280 V 279 V 4.55 A 4.48 A75798.11%75813% above Unom759283 V 282 V 4.84 A 4.56 A76093.88%76115% above Unom762287 V 286 V 4.65 A 4.65 A76386.93%764After analyzing the results, it became clear that designing an MFT at maximum flux density is765achievable by using nanocrystalline cores. This type of core has a safe operation zone up to 12% above766the nominal voltage. Additional advantages of the proposed MFT design are a 25% cut in winding767turns, a higher power density, and lower building costs.768Table 10. THD for both MFTs at the voltages shown in Table 9.769 770MFT1771MFT2772THDI THDV THDI THDV773Nominal voltage (Unom) 0.55% 0.52% 0.54% 0.52%77412% above Unom7750.53% 0.54% 2.23% 0.70%77613% above Unom7770.54% 0.53% 4.68% 1.77%77815% above Unom7790.53% 0.53% 8.82% 3.86%780The immediate benefits of designing an MTF at maximum flux density are reflected on781improving DC–DC converters for applications on photovoltaic systems, wind power systems, electric782vehicles, and solid-state transformers.7834. Discussion784 785Electronics 2020, 9, 470786 78714 of 16788 789Table 11 summarizes recent MTF design proposals [1–3,5,6] for comparison purposes. The790comparison is focused on the flux density design method of each proposal. Every proposal in Table79111 includes a laboratory prototype.792Table 11. Design flux density for various MFT proposals.793 794Design flux795density7961.2 T797 798Reference799 800Core801 802Efficiency803 804Power805density80615.62 kW/l807 808This proposal809nanocrystalline810> 99%811Ruiz 2018, [2]8120.9 T813nanocrystalline814> 99%81515.01 kW/l816Bahmani 2016,8170.9 T818nanocrystalline819> 99%82011.5 kW/l821[5]8220.35 T823ferrite824> 99%8259.25 kW/l826Asier 2017, [1]8270.5 T828silicon steel829> 99%8302.96 kW/l831Huang 2017, [6]8320.6 T833Harish 2017, [3]834silicon steel835> 99%8361.29 kW/l837From Table 11, it can be noticed that silicon steel core transformers are commonly designed for838frequencies up to 1 kHz. This can be explained by the fact that higher frequencies cause higher core839losses and lower transformer efficiencies [6]. The selection of the flux density level and operation840frequency for silicon steel cores is done in order to achieve efficiencies higher than 98%. However, if841the flux density increases, the core losses also increases. As a consequence, the efficiency is reduced842below 98%, the minimum acceptable value.843In the case of ferrite cores, the maximum flux density is restricted between 0.4 and 0.5 T. This844restriction also limits the reachable power density. In [1], a ferrite core MTF was designed at Bac = 0.35845T, which is far below the flux density that is achievable with nanocrystalline cores.846On the other hand, nanocrystalline materials have enormous potential to develop reliable and847efficient MTFs that take advantage of maximizing the design flux density to 1.2 T and whose benefits848have been thoroughly exposed in this paper.849Regarding the power density of the works presented in Table 11 and taking into account that a850higher flux density leads to a higher power density, the MFTs with the lowest power density are851those designed with silicon steel at flux densities of 0.5 T [6] and 0.6 T [3], and the lowest frequency,8521 kHz. An MFT with ferrite core [1], mostly for designs at frequencies of 20 kHz, has a higher power853density than those of [3] and [6] despite of having a lower flux density. The MFTs with the highest854power density are those with nanocrystalline cores at a flux density of 0.9 T [2,5]. Therefore, the855innovative proposal of using Bmax at 1.2 T is an attractive option for obtaining a higher power density856than in other proposals, such as in [2] and [5].857The novel design technique focused on Bmax, presented in this paper, is a step forward in reaching858a higher power density for MFTs. This type of MFT is, in turn, an essential element for the upcoming859DC–DC converter.860On the other hand, a comparison is presented in Table 12 between a conventional transformer861at 50 Hz/60 Hz and 1 kVA and an MFT at 5 kHz and 1 kVA.862Table 12. Comparison of a conventional transformer and an MFT.863 864Transformer865 866Power867 868Frequency869 870Volume871 872Weight873 874Power875Density876 877Cost878 87950 Hz/60880783 cm38817 kg8821.28 kW/l883241.18 USD884Hz885MFT8861 kVA8875 kHz88864 cm38890.25 kg89015.62 kW/l89167.87 USD892According to Table 12, the MFT, compared to a conventional transformer, has a 12.23 times lower893volume, a 28 times less weight, a 12.2 times higher power density, and a 3.55 times less cost. These894results corroborate the advantages of MFTs in relation to conventional transformers.895Future research works related to this paper would be: (i) the performance of a finite element896method analysis to find the maximum flux density and design frequency for various MTF core897Conventional898 8991 kVA900 901Electronics 2020, 9, 470902 90315 of 16904 905materials, (ii) the study of different DC–DC converters looking for the widening of the penetration of906MTFs, (iii) the evaluation of core losses by using the finite element method and analytic MTF907computations, (iv) the performance of a temperature analysis for MTFs by using ferrite, silicon steel908and nanocrystalline cores, (v) the evaluation of 60 Hz transformers by using distinct core materials,909and (vi) the elaboration of a design procedure for isolation transformers at a medium frequency.9105. Conclusions911The MFT is a key component in various types of DC–DC converters that are oriented to a912multitude of applications of great interest at present, such as electric vehicles, renewable energy913power sources, and solid-state transformers. To achieve progress in this area, an important point is914to obtain the highest possible power density in the MFT. One of the main challenges to increase power915density, however, is overcoming the winding and core losses in order to avoid getting inefficient916MFTs (< 98%).917This work presents a design procedure for MFTs that are dedicated to increasing the power918density in the MFTs with nanocrystalline cores by using their Bmax (1.2 T) as a design requirement.919The validity of the design procedure was confirmed with simulations and two 1 kVA/5 kHz920laboratory prototypes that were built for this purpose. The first prototype was designed at Bmax = 0.9921T and the second at Bmax = 1.2 T.922The results of this research work illustrate the advantages of designing MFTs at Bmax with923nanocrystalline cores. These advantages are a 25% reduction in the number of winding turns, a higher924power density, a lower construction cost, a slightly higher efficiency (0.4%), and a 12% tolerance over925nominal voltage altogether while maintaining a high efficiency (> 98%).926The design proposal presented in this document is a step forward towards achieving higher927power density in DC–DC converters that further impact applications of the highest importance for928the current and next generation of distribution electrical systems.929Author Contributions: Performed prototype experiments, D.R.-R; conceptualization, D.R.-R., and E.L.M.-G.;930methodology, V.V.-R., and E.L.M.-G.; validation, D.R.-R., and N.M.S.-H.; formal analysis, V.V.-R.; investigation,931D.R-R., and E.L.M.-G.; writing—original draft preparation, D.R-R., and E.L.M.-G.; writing—review and editing,932N.M.S.-H., and V.V.-R.; project administration, V.V.-R., and E.L.M.-G.; all authors contributed to the review of933the paper. 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