Electromagnetic Design of Aircraft Synchronous Generator with High Power-Density

Transcription

1 Electromanetic Desin o Aircrat Synchronous Generator with Hih ower-density Thomas Wu and Tony Camarano University o Central Florida, Orlando, FL 3816 Jon Zumbere and Mitch Wol Air Force Research Lab, Wriht atterson, OH Eric S. Lin ANSYS Corp., ittsbur, A 1519 and Hao Huan and Xiaochuan Jia General Electric Aviation Systems LLC, Vandalia, OH This paper discusses the methodoloy or the electromanetic desin o an aircrat synchronous enerator with hih power-density. A new method is proposed to more accurately model the air-ap o a salient pole rotor throuh expandin the inverse o an eective air-ap unction. The correspondin manetic ields rom the rotor and stator windins, as well as the expressions o back EMF, are derived usin the air-ap model. The stator inner diameter and lenth are desined by considerin a proper coolin scheme and maximum peripheral-speed o the rotor. This allows or desin o the stator windin and slot eometry, includin the derivation o a ormula or the stator core thickness. The air-ap and salient pole shoe ace can be desined usin the desired speciications or power actor and torque anle. The rotor windins and eometry are subsequently desined. Followin the above procedure, a 00 KVA hih power-density synchronous enerator with 1 krpm rotational velocity is obtained. Finally, the desin is veriied and inely tuned usin ANSYS RMxprt, Maxwell FEM sotware, and SimuLink. Nomenclature α Cu = coeicient o copper α = air-ap coeicient A = cross-sectional area B,pk B a,pk = ield and phase peak manetic lux density B,pk = air-ap manetic lux density C = number o parallel circuits in a phase windin C 0 = coolin coeicient C = number o turns or a salient pole D r D = rotor and stator bore diameter av = averae air-ap I a,rated = phase windin current I F,rated = ield windin current J J a = ield and phase windin current density K a = coolin technoloy coeicient k B = manetic lux density coeicient k v = ield voltae marin k w = windin actor l = stator lenth 1

2 l L md L mq L m L s l turn m N N a n m θ d p emb ρ Cu R R s r ld S S rated T 0 V Fmax v r W t = total mean lenth o ield windin = direct and quadrature manetizin inductance = ield manetizin inductance = ield-armature mutual inductance = averae lenth o each ield windin turn = number o phases = ield and phase eective number o series turns = revolutions per minute = direct axis anle = number o poles = pole embrace = resistivity o copper = ield and armature resistance = lenth-diameter ratio = number o slots = rated apparent power = reerence temperature = maximum ield voltae = maximum allowable peripheral-speed = pole shoe width I. Introduction N aircrat electrical system is responsible or the eneration, control, and distribution o electrical power Awithin the aircrat. A typical system uses 115 VAC (400 Hz), 70VDC, and 8VDC 1-4. Most contemporary hih power-density aircrat enerators are desined to provide between 30 to 50 kw and operate at anular speeds rom 700 to 7000 rpm. The typical topoloy o an aircrat enerator is shown in Fi. 1. The three-phase synchronous enerator includes an outer stator with the windins distributed accordin to phase and an inner rotor with compact DC windins. The ield windins receive excitation rom a synchronous brushless exciter with threephase windins on the rotor and concentrated windins on the stator. This is used in conjunction with a M brushless exciter. The synchronous enerator, synchronous exciter, and M exciter share the same rotor shat. The number o stator slots can rane rom 4 to 108, dependin on the desired slots per pole per phase. In eneral, a larer number o slots per pole per phase combined with a double layer lap windin structure will reduce the eects o hiher-order harmonics in manetic lux density and air-ap MMF. A typical rane or salient rotor poles is rom to 1. The desin analyzed in this paper is a 30 slot, 10 pole machine with a rated apparent power o 00 kva operatin at 1 krpm. Fiure 1. Aircrat enerator topoloy. The desin methodoloy or the synchronous enerator is discussed in Section. This includes eneral desin considerations, detailed descriptions o the armature and salient rotor windin and eometry desin, and analytical estimation or equivalent model inductances and resistances. Section 3 will explain the process o eneratin a desin solution rom theory as well as implementation usin RMxprt and Maxwell FEM simulation tools.

3 Simulation results and post processin is discussed in Section 4, ollowed by a conclusion o the overall desin process in Section 5. II. Desin Methodoloy A. General Considerations One o the primary desin parameters or machine desin is the maximum allowable peripheral-speed o the rotor. Modern steel-alloys have a rotor peripheral-speed desin limit o about 50,000 t/min (about 50 m/s). The maximum rotor diameter D r can be estimated usin v (in lenth/s) v (in lenth/min) D r r r max n (in rev/min) m m where v r is the maximum allowable peripheral-speed and n m is the rpm o the machine 5. It is important to note that Eq. (1) is an approximation and is used to provide simpliied desin uidance when choosin an appropriate diameter or the rotor. The resistivity o copper windins will vary with temperature. Machine workin temperature varies dependin on application and should be taken into account. The resistivity o copper versus temperature can be calculated usin (1) ( T) ( T ) ( T T ) Cu Cu 0 Cu 0 () where T 0 is a reerence temperature o 0 C, α Cu is equal to.668e-9 Ω in/ C, and ρ Cu is equal to 0.679e-6 Ω in/ C at 0 C. B. Stator Desin The number o armature slots per pole may either be interal or ractional. A m-phase synchronous machine will have S slots that are multiples o m, where is the number o machine poles. However, interal S/ may lead to excessive coin torque because all pole aces will alin with slot mouths simultaneously. A ractional S/ value is enerally used in order to reduce coin torque. Althouh S/ is ractional, the number o slots should still be a multiple o the number o phases. A relationship between machine size and other machine parameters has been derived usin rated phase voltae and current. It can be shown that 60 Srated Dl (3) k w nmkab, pk D and l are the stator bore diameter and stator lenth, respectively. The windin actor k w is or the primary machine harmonic and is derived usin air-ap MMF analysis. The volume o the machine is proportional to Eq. (3) and the ollowin discussions are enerally accurate. A larer K a, which is a parameter or quality o coolin technoloy, will allow or a smaller machine. The aster the machine speed n m, the smaller the volume. A larer ap manetic lux density B,pk can be obtained by usin advanced materials with larer manetic saturation; this will also decrease volume. However, a larer rated apparent power S rated will increase the volume o the machine. A similar approach can be seen in the relationship between machine size, apparent power, and number o poles. The constant relatin these parameters is D l C (4) 0 S 1 1 C0 K e m a C 0 is dependent on the coolin technoloy and should be small in order to reduce machine volume 5. The value o C 0 or the synchronous enerator desin studied in this paper is 9 in 3 /MVA, which is or spray coolin. This number was tuned throuh previous experience and knowlede o the aircrat synchronous enerator coolin technoloy. The lenth-diameter ratio o a machine is deined as the ratio o the lenth and the stator bore diameter, meanin l rld D (6) The machine power ratin depends on D l or a ixed mechanical speed. As r ld increases, the rotor diameter decreases, causin the moment-o-inertia to decrease. In this case, the rotor peripheral-speed will also decrease. As r ld increases, the machine lenth increases and the rotor is prone to exhibit critical requencies at lower speeds. This rated (5) 3

4 can result in shat lexure, causin the rotor to strike the stator. I r ld is too lare, the machine is diicult to cool. However, i r ld is too small, the leakae inductance o end-turns can severely aect machine perormance. Armature conductor cross-sectional area is also dependent on machine coolin. It can be written as I A a arated, / J a C (7) where I a,rated is the rated current or one phase windin and C is the number o parallel circuits in the phase windin. The current density values iven machine coolin in Table 1 can be used or J a 6. Table 1. Current density values dependent on coolin technoloy. Coolin Type J a (A/in ) Enclosed Machine 3000 ~ 3500 Air Surace Coolin 5000 ~ 6000 Air Duct Coolin 9000 ~ Liquid Coolin ~ 0000 Spray Coolin 0000 The armature slot eometry and correspondin dimensions are shown in Fi. In eneral, the ollowin ranes yield a satisactory desin o the armature slot: D s, 0.4s bs 0.6 s, 3bs ds 7 bs, ts s bs S The deined lenth d c can be shown, or a ood desin, to be D d c 1. 6 (8) Fiure. Stator slot eometry. C. Rotor Desin The number o ield conductors is an important desin consideration. Fiure 3 deines the parameters used in the desin o pole eometry and windins. I the averae lenth o each turn o the ield windin is assumed to be l l turn W t (9) then the total mean lenth o the ield windin is approximately l C l turn (10) The number o turns C are assumed to be the same or each salient pole. Assumin that V Fmax is the maximum voltae o the ield windin, is can be shown that Cul kvvf max I F, rated J CuC lturn A 4

5 where A is the cross-sectional area o the ield conductor, k v (0.7-1) provides a certain desin marin, and J is the allowable current density and depends on coolin. Thereore, k (1) VVF max C J l The calculated results will be rounded to an inteer. Reerrin to Fiure 4, the ollowin approximations or the respective eometry will provide a satisactory desin o the salient pole: pemb Wt ( D max )sin( ), Wp ( Dr Ht) 0.45 ~ 0.65, Dra (0.6 ~ 0.7) Dr D (0.3 ~ 0.5) D, H H H ( D D ) /, H (0. ~ 0.3) H The pole embrace p emb or the desin analyzed in this paper is 0.7. sh r tp t p r ra t tp Cu turn (11) Fiure 3. Rotor salient pole eometry and diameters. The phase diaram in Fi. 4 shows relationships between dq currents, ield and phase windin lux linkae, and dq reactance. The resistance o the phase windins in nelected in Fi. 4. The power actor o the load is lain, and the machine is over excited, meanin E A > V Φ. Fiure 4. hasor diaram o the dq currents and voltaes. The relationship between the peak values o the ield and phase manetic lux densities is notated k B B B, pk a, pk (13) and it is assumed that It can be shown usin Fi. 4 that X I X d d qi q E k V A 5 B cos k sin B X tan( ) X s d q tan (14) (15) (16)

6 Typically a power actor is speciied, which then deines Φ. Usin Eq. (15) and Eq. (16) and the assumption X q (0.6 ~ 0.8) X d (17) δ and ζ can be obtained. An estimation o the eective air-ap across the salient pole has been derived as ollows: av ' e ( d ) 1 cos( d ) The ap coeicient is approximately 1 ( Lmq / Lmd ) L / 0.4~0.8 1 ( L / L ) mq Lmd mq md An approximation o the rated ield current usin ield and phase manetic lux densities can be written as (18) (19) I F, rated k 1.5 Nˆ 1 ( / ) cos ( ) I Nˆ (1 ( / )) B a i r a, rated The anle o the phase voltae is assumed to be zero in Eq. (0). The sin o Φ i depends on whether the load is leadin or lain. N a and N are the eective number o series turns in the ield and phase windins, respectively. From Eq. (0), an estimation o the ield conductor cross-sectional area can be determined usin Throuh a similar derivation or (0), an estimation o the averae air-ap is ound: A I J Frated, / (0) (1) (6 / )( Nˆ / )( / B ) 1 ( / ) cos ( ) I k cos sin av a 0, pk i r a, rated B () A unction o the ap versus θ d is obtained by substitutin Eq. (19) and Eq. () into Eq. (18). D. Resistance/Inductance Estimation Analytical estimations or armature and ield resistances, manetizin inductances, and mutual couplins are shown below. These parameters are used or eective modelin o the machine or hih-level system simulation. The armature windin resistance is estimated as R ( N / C)( l )/ A (3) s a Cu turn a where N a is the number o series turns per phase, C is the number o parallel circuits, and l turn is the estimated lenth o a windin turn. The ield windin resistance is estimated as R ( l )/ A (4) Cu The inductances can be estimated usin the ollowin relationships, derived usin the dq rame: 8 ˆ 0 Dl N a LA av LB LA 3 3 Lmd ( LA LB ) LA(1 ) 3 3 Lmq ( LA LB ) LA(1 ) (5) (6) (7) (8) L m 8 ˆ 0 Dl N av (1 ) (9) 6

7 L s 8 NN ˆ ˆ 0 Dl av (1 ) a (30) III. Desin and Simulation Results The analytical desin theory described above can be used to enerate the speciications o eometry, windins, source excitation, and eective resistance and inductance modelin or a hih power-density aircrat synchronous enerator. The desin analyzed here is a 00 kva, 1 krpm, 3-phase machine. The number o poles and slots chosen are 10 and 30, respectively. The operatin temperature is set at 50 C, with a deined maximum ield voltae o 50 V. From these parameters, an analytical desin can be produced. The eometry and machine speciications are put into ANSYS RMxprt modelin sotware to create an initial simulation desin. The enerator speciications are shown in Table. Tables 3 and 4 contain the enerator stator and rotor details, respectively. Fiures 5, 6, and 7 show enerator, stator slot, and rotor pole eometry, respectively. Table 5 shows the exciter speciications, ollowed by exciter rotor and stator details in Tables 6 and 7, respectively. Fiures 8, 9, and 10 show exciter, rotor slot, and stator pole eometry, respectively. Table. Desined enerator parameters. n m = 1000 rpm mechanical speed e = 1000 Hz electrical requency S rated = 00 kva apparent power V Φ = V RMS phase voltae I Φ = A RMS phase current T work = 50 C work temperature V Fmax = 50 V max ield voltae I Fmax = A max ield current S exciter = kva exciter apparent power J a = 0000 A/in armature current density J = 0000 A/in ield current density k B = 1.5 lux density coeicient k v = 0.7 ield desin marin p = 0.95 power actor Φ = power anle δ = torque anle R s = Ω armature windin resistance R = Ω ield windin resistance Fiure 5. Generator eometry. L md = 8.791e-5 H d manetizin inductance L mq = 3.956e-5 H q manetizin inductance L m = H ield manetizin inductance L s = H armature-ield mutual inductance Table 3. Desined enerator stator. S = 30 slots N c = 1 turns per coil D = in stator bore diameter L = in stator lenth D 0 = in stator core diameter k w = windin actor b s0 = 0.05 in stator slot mouth width b s = in stator slot width d s0a = 0.05 in stator slot mouth depth d s0b = 0.05 in stator slot shoulder depth d s1 = in stator slot depth min = in minimum air-ap A slot = in area o stator slot Fiure 6. Generator stator slot eometry. A a = in bare area o each coil A cond = in total area o bare coils per slot 7

8 Table 4. Desined enerator rotor. = 10 poles p emb = 0.7 pole embrace C = 10 turns per rotor pole D r = in rotor core diameter D ra = in rotor diameter at pole bottom D sh =.5383 in shat diameter v r = t/min rotor peripheral speed W t = in pole shoe width H t = in pole shoe depth W p = in pole le width H p = in pole le lenth A slotr = in area o hal rotor slot A = in bare area o ield conductor A condr = in total area o bare conductors Table 5. Desined exciter parameters. n m = 1000 rpm mechanical speed e = 600 Hz electrical requency S rated = 8.5 kva apparent power V Φ = V RMS phase voltae I Φ = A RMS phase current T work = 50 C work temperature V Fmax = 5 V max ield voltae I Fmax = A max ield current S Mexciter = kva M enerator apparent power J a = 0000 A/in armature current density J = 0000 A/in ield current density k B = 1.7 lux density coeicient k v = 0.7 ield desin marin p = 0.95 power actor Φ = power anle δ = torque anle Table 6. Desined exciter rotor (armature). S = 1 slots N c = 3 turns per coil D =.5008 in Rotor diameter L = in rotor lenth v r = 7856 t/min rotor peripheral speed D sh = 1.81 in shat diameter k w = windin actor b a0 = 0.05 in armature slot mouth width b a = in armature slot width d a0a = 0.05 in armature slot mouth depth d a = in armature slot depth min = 0.04 in minimum air-ap A slot = in area o armature slot A a = in bare area o each coil A cond = in total area o bare coils per slot Fiure 7. Generator rotor pole eometry. Fiure 8. Exciter eometry. Fiure 9. Exciter rotor slot eometry. 8

9 Table 7. Desined exciter stator (ield). = 6 poles p emb = 0.75 pole embrace C = 5 turns per rotor pole D s =.549 in Stator bore diameter D sa = in Stator diameter at pole bottom D 0 = 4.53 in Stator core diameter W t = 1.07 in pole shoe width H t = in pole shoe depth W p = in pole le width H p = in pole le lenth A slotf = 0.31 in area o hal ield slot A = in bare area o ield conductor A condf = in total area o bare conductors Fiure 10. Exciter stator pole eometry. RMxprt is used to veriy the dq inductances, armature and ield resistances, and rated apparent power o the enerator. Some ine tunin or conductor cross-sectional area is oten necessary to match the analytical results to the sotware speciications. The desin has some reedom in speciications o the stator slot mouth. Any chane o this eometry will aect the dq inductances. The inductances rom the analytical result are used as a reerence to iterate on the eometry until a satisactory implementation is obtained. Once the desin has been veriied, it is transerred directly into ANSYS Maxwell D and 3D FEM sotware. Fiures 11 and 1 show the D and 3D FEM models, respectively. The D simulation uses only the portion o the model with unique windin structure and assumes the rest o the machine has symmetry. Fiure 11. Maxwell D FEM model. Fiure 1. Maxwell 3D FEM model. In order to veriy the analytical desin, FEM analysis and a lux linkae method or calculatin sel and mutual inductance are used. The lux linkaes can be ound usin a sweep o the ield and phase currents in the Maxwell sotware. Since the machine operates within the manetic saturation reion, the lux linkaes and inductances will vary with current. A numerical unction or the dq inductances versus current is built and compared with the analytical derivations. The analytical values should be approximately equal to the peak inductances versus current. Table 8 shows the numerical results compared with the analytical derivations. Fiure 13 shows the open circuit 3- phase voltae waveorm or the Maxwell models. Table 8. Analytical compared with numerical results. Units are Henry. Inductance Analytical Numerical L md 8.791e e-5 L mq 3.956e e-5 L m L s

10 Fiure 13. Numerical results or phase voltaes. Induced phase voltaes or an open circuit 00kVA, 1 krpm 3-phase synchronous enerator. Field current excitation: 60 VDC. SimuLink is employed to perorm hih-level simulations o the enerator when interaced with control and load 7. Fiure 14 shows the upper-level block diaram o the enerator-exciter synchronous machine attached to a 00 kw load. The detailed SimuLink model or the machine is shown in Fi. 15. This model includes the synchronous enerator, exciter, controller, and rectiiers. The main enerator output voltae and current versus time is shown in Fi. 16, respectively. Fiure 14. Hih-level SimuLink model. Fiure hase synchronous enerator-exciter model. Main blocks rom let to riht: controller, exciter, exciter rectiier, main enerator, main rectiier. 10

11 Fiure 16. Output voltae and current. IV. Conclusion An analytical desin methodoloy has been developed which creates a relatively accurate desin or hih powerdensity aircrat synchronous enerators. Important desin parameters such as rated apparent power, mechanical speed, machine poles, and stator slots can be speciied or a 3-phase enerator. The equations and desin process described in this paper produce a uideline or the machine eometry, windin parameters, and source excitation. FEM simulation and post processin veriy the desin method usin a numerical lux linkae method to conirm machine inductances. The desin methodoloy can be used to develop new and innovative hih power-density synchronous enerators. The perormance o these desins can be simulated, veriied, and optimized to abricate hih-quality, reliable machines. Reerences 1 J. F. Gieras, Advancements in Electric Machines, Spriner, 008, Chap. 4.. C. Krause, O. Wasynczuk, and S. D. Sudho, Analysis o Electric Machinery and Drive Systems, nd Edition, Wiley, C.M. On, Dynamic Simulation o Electric Machinery, rentice Hall, A.E. Fitzerald, C. Kinsley, Jr., and S. D. Umans, Electric Machinery, 6th Edition, pae 70, McGraw-Hill, J. J. Cathey, Electric Machines: Analysis and Desin Applyin MatLab, McGraw Hill, 001, pp T. A. Lipo, Introduction to AC Machine Desin, Wisconsin ower Electronics Research Center, University o Wisconsin, 007, pp Jie Chen, Thomas Wu, Jay Vaidya and Nonlinear Electrical Simulation o Hih-ower Synchronous Generator System, 006 SAE ower Systems Conerence. 11