MODELING OF A THREE-PHASE APPLICATION OF A MAGNETIC AMPLIFIER

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1 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES MODELING OF A THREE-PHASE APPLICATION OF A MAGNETIC AMPLIFIER L. Austrin*, G. Engdah** * Saab AB, Aerosystems, S Linköping, Sweden, ** Roya Institute of Technoogy, Eectrica Engineering, Teknikringen 33, S-1 Stockhom, Sweden Keywords: magnetic ampifier, modeing, amorphous aoys, three-phase Abstract Appications of new soft magnetic materias, such as amorphous magnetic aoys, have enabed the use of magnetic ampifier (mag amp) technoogy in the design of competitive eectric power reguators. Magnetic ampifiers are used in the power suppy of the Eectronic Fight Contro System in the Swedish "Gripen" fighter-aircraft. This technoogy is attractive in More Eectric Aircraft (MEA) systems due to the possibiity to achieve a compact, robust and a highy reiabe design. This paper describes a suggested approach to mode a three-phase appication of a magnetic ampifier. The mode is based on a magnetic hysteresis MATLAB-mode of the core materia of amorphous magnetic aoys. The basic circuitry is based on a one-phase mag amp circuit extended to a three-phase circuit, anayzed in an engineering too. A key parameter in aircraft and automotive appications is power density [kw/kg]. Impact on weight and performance as a function of the magnetic materia chosen and suppied frequency is presented The demonstrated engineering too offers a very quick method of anayzing if a mag amp design is possibe for the appication by anayzing power osses and efficiency as we as weight and voume. 1 Introduction In the process of designing an eectric power suppy system for an aircraft, parameters ike ow weight and ow osses are important. Reiabiity and robustness are other important factors. In the Saab Gripen aircraft the design of the primary power suppy of the eectric fight contro system was updated by exchanging from a switching transistor reguator to a magnetic ampifier (mag amp). By introducing a mag amp design, weight was saved and we got a more reiabe unit at a ower price. An eectric power suppy system for an aircraft is basicay specified by Mi-Std-7, which specifies a 8 VDC system as we as a three phase 11 VAC, Hz system. By comparing the weight and size of the generators and transformers with units of comparabe rating for the commercia systems /6 Hz, it can be noted that the aircraft units have a significanty ower due to the higher frequency. In the particuar case with the power suppy of the eectric fight contro system in the Saab Gripen fighter we coud take advantage of a specific PM-generator suppying a variabe votage and a variabe frequency varying between and Hz. The higher the frequency the better is the potentia for ower weight. The weight is roughy proportiona to the inverse of the frequency. In the trend of More Eectric Aircraft designs [1], with a power suppy of 7VDC, we note that the generator used, most ikey works with a 1

2 L Austrin, G Engdah higher frequency than Hz. Can we take advantage of a higher operating frequency? A key parameter in designing magnetic ampifiers (mag amps) is ow osses. New amorphous aoys are opening up new possibiities for the technique of designing magnetic ampifiers by offering extremey ow osses. The core osses can be evauated by studying the hysteresis oop, or by studying the equation or diagrams giving the power oss provided by manufacturers. Aternativey the core osses can by verified in tests evauating the osses by eectric or therma methods. The Magnetic Ampifier The operation of a mag amp is based on aternating from unsaturated to saturated state. When the core is saturated the mag amp is conducting, the switch is on. During the foowing haf cyce the mag amp can be reset to an unsaturated state..1 The Ramey Magnetic Ampifier In the Ramey ampifier, Fig. 1, the votage time product for reset is given by U s -U reg and the duration of the negative haf cyce. The mag amp, M is off unti the reset votage time product is baanced and the switch is set on. The rectifying diode handes the positive haf cyce from the power source U s, which is fitered by the LC-fiter and is suppied to the oad R L as DC-power. A typica appication is in switched mode power suppies.. The one-phase Magnetic Ampifier With the sef-saturating circuit in Fig. a sma contro current I C can be used to contro the effective oad votage []. The functiona eements are arranged such that a sef-saturating circuit is achieved. In this design a contro current I c is required for the cores to go from saturated to non-saturated state. Fig.. The one-phase mag amp The one-phase mag amp suffers from sow response time, due to the possibiity of a circuating current in the power windings..3 The Three-phase Magnetic Ampifier The one phase sef-saturating circuit can be extended to a fu 6 puse design. See Fig.3. The output from this mag amp design comprises the combination of the three phases and the six puses to a rectified output. The three-phase magnetic ampifier has a faster response time, compared to the one phase mag amp, since the circuating current wi be imited by the oad R L. Fig. 1. The one-phase Ramey mag amp The advantage of this design is the simpicity and the fast response. Fig. 3. The three-phase mag amp The optimization of the mag amp can be sighty different depending on the oad profie, i.e. whether the mag amp is mosty on or off. For a

3 MODELING OF A THREE-PASE APPLICATION OF A MAGNETIC AMPLIFIER genera design it can be sufficient to ook at the sum of the core and copper osses. 3 The Magnetic Ampifier Loss Mode The core osses can be divided into three different types of osses: - static hysteresis osses - eddy current osses - anomaous osses ( at higher frequencies) The hysteresis osses The hysteresis osses can be expained as the frictiona osses that occurs when the magnetic domains in the materia moves in respect to each other. The hysterisis osses can be evauated by studying the core characteristics. The area of the BH-oop represents the oss energy during one cyce and can be cacuated according to: W = HdB [Ws/m 3 ] (1) The power osses can then be expressed as: f db P = H dt [W/kg] () ρ dt f is frequency [Hz] ρ is weight per unit voume [kg/m 3 H magnetic fied [A/m] B is fux density [T] Eddy current osses An AC magnetic fied wi aways induce eddy current osses in conducting materias. The eddy current osses in the core can be expressed as a function of B, f and the thickness of the magnetic materia. It can be expressed: d π ˆ P e = ( f ) B (3) ρ d is the thickness [m] $B is the ampitude of the mean fux density The anomaous osses are considered to be negect abe in the here studied appications. The tota oss At ower frequencies the tota core osses are the sum of hysteresis and eddy current osses. P h ~ f P e ~ f In an appication the sum of P h and P e is rapidy dominated by P e at increasing frequency. This impies that the osses are dominated by the factor with the highest exponent. The hysteresis mode [3], is extended to incude the frequency dependency []. The extension is performed by introduction of appicabe data for permeabiity and the coercive force for the studied aoy at appicabe frequencies. In Fig. an exampe shows the hysteresis oops for Hz and Hz X-axis B [T], Y-axis H [A/m] Fig.. Hysteresis mode for Metgas 6 TCA The power osses can be cacuated for different frequencies. The core osses is in Fig are verified for Hz and Hz and is in compiance with the core oss curves provided by the vendor, see Fig.. The tota core oss can be expressed as a function of f and B. The hysteresis osses can be expressed: P = k f B () h n max where k h is a constant depending on the materia and n varies between 1, and,, according to Chares Steimetz of Genera Eectric company []. This can be compared with the equations for osses given by the vendor, Metgas for aoy 71A [6]: P = f B [W/kg] () 3

L Austrin, G Engdah The studied amorphous aoys are of interest in design of magnetic ampifiers due to ow osses and the square ness of the characteristics.

4 L Austrin, G Engdah The studied amorphous aoys are of interest in design of magnetic ampifiers due to ow osses and the square ness of the characteristics. Core Area From a chosen materia with maximum fux density, the needed core area A Fe is cacuated. The vot-second product U t is cacuated. U t = B AFe N (6) The fux density span is B, because the fux can be used from over the whoe span from negative to positive B. For a given number of N of turns the corresponding core area is: A U t Fe = (7) N B Length of Copper Wire per Turn The engineering too assumes a squared core cross section, but is not imited to any standard seection. The average turn ength wi be cacuated by as the sum of the ength of the inner turn and the ength of the outer turn divided by. The encapsuation of the core is estimated to add a tota of 1 % of the inner turn ength this gives a factor. for the sides. The inner ength = A Fe ( +.) is the number of sides.. represents the margin of encapsuation. At a winding window utiization factor of 3% the inner diameter of the winding d w can be cacuated according to (π/)d w =(π/)d i (1-.3) d w =.8366 d i Fig.. Core osses for Metgas 6 TCA A Proposed Engineering Design Too The purpose of the proposed design too is to from given input parameters cacuate requested output parameters..1 The Proposed Design Agorithms Agorithms for the magnetic core and copper winding can be expressed as foows, where d i is the core inner diameter without encapsuation, see Fig. 6. ( ) The outer ength A + d ( ) = Fe i Fig.6. The copper winding, cross section. The average turn ength wi be: AFe +. + AFe = ( ( ) ( + d (.163) ) i A. + d.163 [m] (8) = Fe i

5 MODELING OF A THREE-PASE APPLICATION OF A MAGNETIC AMPLIFIER Iron and Core Weight The iron osses per kio can be expressed by a function of frequency and the maximum fux. Such an equation is given by Metgas [] for the amorphous materia 71A, in equation (). For the materia 6TCA data from Fig. data is extracted to give the equation: P = f B (9), which yieds good compiance up to 1 Hz. The osses aso are showed to be approximatey 9 times bigger than in equation (). Data compies with materia from Arnod, Arnogas 1, and fairy we with the Metgas, 6SA1. The weight of the core is: m Fe A ρ (1) = Fe, where Fe is the average iron core ength ρ is density for the different aoys: 71A ρ=79 [kg/m 3 ] 6TCA ρ=718 [kg/m 3 ] 6SA1 ρ=719 [kg/m 3 ] The core osses can be cacuated from the given input parameters and the equations () or (9). As an exampe, the core osses are shown for Metgas 6TCA, defined by equation (9), as a function for different number N of turns. In Fig. 7 cases for N= 1,,, 7, 1 turns are presented with corresponding osses and core weights. Copper The copper osses are basicay depending on the current, the turn ength, number of turns and the copper area A cu. The wire ength is cacuated as an average ength per turn, given in preceding paragraph giving the resistance: N R = ρ k (11) A ρ=*1-8 [ohmm] at 8 [ C] k= skin factor >1 at high frequencies. The skin effect is out of scope of this work, but it can be concuded that there is no impact (ess than 1%) for a wire with a diameter ess than [mm] as ong as the frequency is ess then 1 [Hz]. The copper oss is: P R I = (1) n, where n is the number of phases, except for the one phase appication, where n = due to the % duty cyce. n= for a 1 phase mag amp n=3 for a 3 phase mag amp Weight of Copper Wire The weight of the copper wire is: m = N A ρ (13), where ρ =89 [kg/m 3 ] As an exampe, the copper osses and corresponding copper weights are shown in Fig. 8 for the different cases with N=1,,, 7 and 1. Loss 16 Core , 8,3, 3,9, Weight[gram] / Turns Fig.7. The core osses Loss Copper 16, 1, 1, 1, 8, 6,,,, Weight[gram] / Turns Fig.8.The copper osses

6 L Austrin, G Engdah The Tota Studying the core osses, it can be noted that the oss is decreasing for a higher number of turns, N, whie the copper oss is increasing. One intention of this work is to find a way of minimizing the weight and osses. In the next step, the sum of core and copper osses P tota =P Fe +P are studied. The sum of the osses is shown as a function of the tota weight for the different cases of N in Fig.9. It can be noted that the owest weight coincides with the owest osses in the presented exampe. Core + Copper , 118, 16,1 116,6 171, Weight[gram] / Turns Fig.9. The core and copper osses. A Proposed Engineering Too The proposed engineering too offers a quick method of anayzing whether a mag amp design is possibe for a considered appication. Weight and efficiency are parameters that are anayzed by the proposed too. In aircraft design information such as frequency and weight, must be exchanged between system eve [7] and component eve, and this can be achieved from this engineering too. So far the methodoogy of anayzing the osses is demonstrated by 1) anayzing the hysteresis oop ) comparing the hysteresis oop osses with the power oss diagram, and now finay by using the equations anayzing the osses in the engineering mode. Feature Based on the presented equations and input data, the too cacuates output data ike weight, dimensions and osses. In simiarity with a transistor circuit the mag amp must be designed to meet the requirements of current as we as votage. The difference is that the votage capabiity in the mag amp design is vot during a period of time [Vs]. Usage Numbers of turns are used as input parameters. Seections of different turns are used to evauate weight end osses. The too gives an opportunity to evauate weight end osses for each N. The too wi support the design optimization process, by graphicay showing where we can find the minimum weight and osses, e.g. see Fig 1. For some seected numbers of turns N the studied variabes incuding the osses are graphicay shown and the minima are easiy found, if necessary by seecting additiona N vaues. Note that the design too does not incude any design margins with respect to e.g. toerances in area and materia as we as design margins normay considered due to variations in temperature and aging. The engineering too aso wi not treat the osses in diodes or the contro circuit. Input Parameters Typica input specification-data can be as in tabe 1. Core inner diameter d i [mm] specifies the core without encapsuation. When choosing the wire area the current density [A/mm ] must be considered with respect to cooing capabiity. In our exampes 6. [A/mm ] is chosen, which requires cooing. In the cacuations a winding window utiization factor of 3 % of avaiabe area is used. Tabe 1. Input parameters Input Parameters rrent [A] 37 Votage [V] 7 Frequency [Hz] Phases p 3 Aoy 6 Fux B [T] 1, Area A [mm ] 3,3 Turns N Core d i [mm] Winding window utiization factor % 3 6

7 MODELING OF A THREE-PASE APPLICATION OF A MAGNETIC AMPLIFIER From the given input parameters an Exce program can perform the cacuations and present output parameters and graphs to support a design decision. Cacuation Exampes A feasibe aircraft appication can be a converter for 7 VDC, at a power eve of 1 kw. A few cases (different input data) are studied. The output data can be studied in Tabe. The graphs for minimization of osses and weight can be studied in Fig. 1, 11, 1 and 13. Output Parameters A number of cacuations have been performed with different input parameters, giving the outputs that can be seen in Tabe. The circuits studied in exampe 1 can be seen in Fig.1, and the circuit in exampes - can be seen in Fig. 3. Tabe. Exampes of different cacuations Mag amp Exampe 1 3 rrent [A] Votage [V] Frequency [Hz] 1 6 Phases p Aoy Fux B [T] Area A [mm ] 8 3,3 3,3 3,3 3,3 Turns N 6 Core d i [mm] Outer d [mm] Height [mm] Voume [mm 3 ] Weight [g] Tota weight [g] Tota power [W] Output/core [W] /core [W] Tota osses [W] % Efficiency % It is of specia interest to study the tota weight, the osses and the efficiency. In exampe in Tabe, with Hz it can be noted that the weight and osses are minimized at the same number of turns (N=), as can be seen in Fig. 1. Weight 1 1 Minima for 6TCA 3-phase Hz turns Fig.1. Exampes of coinciding minima 1 1 weight osses When changing the frequency to 1Hz, in exampe 3 in Tabe, it can be noted that that the minima for weight and osses do not fuy coincide, see Fig. 11. Weight Minima for 6TCA 3-phase 1 Hz turns Fig.11. Exampes of spit minima 1 1 weight osses When changing the aoy to 71A, in exampe in Tabe, it aso can be noted that the minima for weight and osses do not coincide, see Fig. 1. 7

8 L Austrin, G Engdah Weight Minima for 71A 3-phase Hz turns Fig.1. Exampes of spit minima weight osses weight of 396 [g], fu advantage of the increased frequency, a weight of 318 [g] is achieved ony when the current density is doubed. In our exampe the current density is kept at 6. [A/mm ]. It can be noted that the higher the fux density, the ower the weight can be. The efficiency for the magnetic ampifiers are as high as 99.3 % and the power density can easiy meet 1 [kw/kg] in the [Hz] appication. The presented data represent the weight minimum. The osses 6.3 [W] can be reduced to.3 [W], in exampe in Tabe, at a weight decreased from 13 [g] to a weight of 3 [g] in an appication working with 6 khz where the minima for weight and osses coincides. See Fig Concusion The concusion is that in an optimized design the osses are minimized by minimizing the weight of the core. The advantage with a design with 6TCA at e.g. Hz, is that the owest osses coincide with the owest weight. Weight Minima for 71A 3-phase 6 Hz turns Fig.13. Exampes of coinciding minima weight osses When the osses coincide with the owest weight the osses in the core are about equa to the osses in the copper wire. In exampe 3 in Tabe, it can be noted that the doubed frequency ( to 1 [khz]) is giving a The concusion is that a core in the 6-famiy is the preferabe aoy in audio frequencies, due to ow osses and ow weight. The 71A aoy might be preferabe in the 6 khz range, with a potentia of efficiency near 99.7 %. At this frequency however the skin effect must be considered. The high reiabiity and robustness aso represents a significant vaue adding to the attraction of magnetic ampifiers in aircraft appications. This work was financed by the Swedish Nationa Aerospace Research Program (NFFP). 7 Reerences [1] Howse, M ''A Eectric Aircraft'' IEE Power Engineer, Voume 17 Issue:, Aug-Sept 3 Page:3-37 [] L. Austrin, J.H. Krah and G. Engdah: A Modeing Approach of a Magnetic Ampifier. Proc. of the Internationa Conference of Magnetism, Rome, Itay, Juy 7-1 August 3. [3] A. Bergqvist: Physica B Condensed Matter, Esevier, 33, p. 3, [] D.C. Jies: Modeing the Effects of Eddy rrent on Frequency Dependent Hysteresis in Eectricay Conducting Media. IEEE transactions on magnetics vo 3, no6, nov 199. [] Eektrische Maschinen, R. Richter, Band 1, Birkhauser Verag, Base 191. [6] Metgas product information, [7] B Johansson, L Austrin, G Engdah, P Krus: Toos and Methodoogy for Coaborative Systems Design Appied on More Eectric Aircraft. Proc. ICAS. 8

RELUCTANCE The resistance of a material to the flow of charge (current) is determined for electric circuits by the equation

RELUCTANCE The resistance of a material to the flow of charge (current) is determined for electric circuits by the equation INTRODUCTION Magnetism pays an integra part in amost every eectrica device used today in industry, research, or the home. Generators, motors, transformers, circuit breakers, teevisions, computers, tape