PULSED POWER ELECTROMECHANICS - PERMANENT MAGNETS VERSUS COPPER COILS

Transcription

1 PULSED POWER ELECTROMECHANICS - PERMANENT MAGNETS VERSUS COPPER COILS By: K.R. Davey R.E. Hebner Proceedings, 6th International Power Modulator Syposiu and 4 High Voltage Workshop, San Francisco, Caliornia, U.S.A., May 3-6, 4, pp PN 86 Center or Electroechanics The University o Texas at Austin PRC, Mail Code R7 Austin, TX 787 (5) /5/4

2 PULSED POWER ELECTROMECHANICS PERMANENT MAGNETS VERSUS COPPER COILS Kent Davey ξ and Robert E. Hebner Center or Electroechanics, Burnet Rd, EME 33 Austin, TX, 78758, USA Abstract A nuber o eerging ilitary systes operate using short, repetitive, high-power pulses. Rotating electroechanical achines incorporating inertial storage are natural candidates or supplying these high power pulses. The short duty cycle characteristic o these devices introduces an interesting physics trade o in the choice o ield excitation. A quantitative coparison o peranent agnet achines to copper coil systes is perored on an equal weigh basis. The results indicate that copper coil based systes using exciters are superior to peranent agnet counterparts in pulsed applications o s and less. The recoended use o copper coils becoes stronger when the issues o agnet lie due to vibration, theral cycling, and slot haronic heating are considered. I. INTRODUCTION Rotary subarine launchers, electroagnetic aircrat launcher, rail guns, active aror, and high power icrowave devices are characterized by high power delivery repeatedly or short duty cycles. The power deand akes it ipractical to have continuous generation capability atching the peak deand. So, soe type o load leveling is required. Typical candidates or load leveling are capacitors or rotating achines. Capacitor banks have the advantage o quick pulse delivery (< s), but the inability o providing ore than a single shot without recharge, and a poor energy / volue ratio (. MW-Hr/ 3 ) []. Rotating achines oer greater lexibility or these applications [][3]. Although ield excitation coils have been the nor in the past, peranent agnet achines are receiving greater attention [4] [5]. Assuing that an electroechanical device is chosen or the task, this paper attepts to address the question, Which ield excitation is better, wound rotor or peranent agnet? This question can be addressed at the level o undaental constitutive properties. The current density allowed in copper coils is dictated by the adiabatic heating it can sustain. The speciic heat, density, and conductivity are the constitutive properties which dictate the teperature rise during the charge cycle, and thus the allowed current density. The axiu change is capped by either the insulation or the aterial elt teperature o the conductor. Magnetic energy can be coputed as the integral o the product o agnetic vector potential with current density over the volue o the conductor. Peranent agnets are liited by the energy product o the agnet, relected through the integrated product o the agnetic ield intensity and agnetic ield density. The coparison is coplicated by secondary issues, aong those being the additional weight required by the exciter o a copper coil syste, and the degradation o the peranent agnet energy product with teperature. Either peranent agnets or copper coils and steel can be considered or use in nearly any design o a pulsed generator. This paper attepts to quantiy the iplications o particular selections in three case studies, a radial lux generator, an axial lux generator, and an inside out design. In each case the air gap ield ro a peranent agnet coniguration, coposed o 45 MGO agnets, is copared to that ro a copper coil coniguration. The current density is chosen coensurate with a C teperature rise. II. CURRENT DENSITY Central to the coparison is the question o how hard the copper coils can be excited. The issue is coplicated by the act that a pulse oring network is the typical load to the generator to provide the ultiate load with the pulse duration and shape needed. Generally, one o two approaches is used to charge the pulse oring network. The irst is that the output current is held constant through the pulse. The second is that the output current ield is raped, consistent with a linearly increasing power, e.g. in the charging o a capacitor. Consider a one turn winding having cross sectional area A, length L, conductivity σ, ass density ρ, carrying current density J. The resistive dissipation in the winding is Work supported in part by the Oice o Naval Research and SAIC Corp. ξ eail: k.davey@ail.utexas.edu

3 ( J A) L P= () σ A Adiabatic heating deands a coensurate teperature change T in δt seconds o Pδt = ρc AL T () p ( ) Substituting () into () yields the current density in this one turn winding independent o area to be ρσ Cp T J = (3) δ t Irrespective o the conductor size, the current density is dictated by the adiabatic teperature jup allowed. The conductivity, density, and speciic heat or copper are respectively S/, kg/ 3 (.33 lbs/in 3 ), and 383 J/kg/K. The conductivity drops to S/ at C. The allowed current density assuing a 58% packing actor, a C rise, with a 9.6 s duty cycle would be Cu = A =.6 (4) Suppose the pulsed power device is charging a capacitor o capacitance C to a inal voltage V in τ seconds with a constant current I a. I the energy source is a lywheel o inertia I with initial speed Ω, the rotational speed will decay as CV Ω= Ω (5) I τ Let β=cv /(I Ω ). Since power is the product o torque and speed, the torque will have the tie dependence IV a τ T = (6) Ω β τ The ield current I will have the sae tie dependence as torque since arature current is controlled as constant. The ield current can be expressed in ters o its end value I e as β τ I = (7) β τ The power dissipation in the rotor conductors with cuulative resistance R over the excitation tie τ is τ τ I e β β β 3 Loss = R I dt = = R ({ tanh ( ) }( )) β Consider a rotor excited with a constant ield current I or τ seconds. The dissipation loss in a rotor excited with this current will be identical to the one in the real rotor i = I =.98 I 3 ({ tanh ( β ) β}( β) ) β Assuing a C change in teperature and a packing raction o 58%, again or a 9.6 second duty cycle, the ending rotor ield current density should be J@58% Cu =.58 I A = 4.99 () Thus, depending on the excitation proile, the current density can be pushed to between.6 and A/ or this choice o a duty cycle. III. (8) (9) Energy Densities o Peranent Magnet versus s A. Case Study # Radial Flux The basic peranent agnet and copper coil test rigs used or coparison are shown in Fig.. The peranent agnet approach is assued to be coposed o 45 MGO agnets at roo teperature in a Halbach array. To ake a air coparison on a weight basis, the equivalent copper rig has to be penalized twice. First, because o the density o the steel and the copper is greater than that the neodyiu iron boron agnet aterial, the steel/copper volue has to be reduced by the increased density. Second, a penalty has to be added or the weight o the exciter that is required i a copper ield coil is eployed but not in a peranent agnet approach. So, or an equivalent weight coparison, the active volue o the copper coil syste ust be saller. In reality, soe coparable penalties should be iposed or the agnet due to the ollowing: o The agnet will not be operated at C, but at a higher teperature. o The ield ro a peranent agnet is always energized. Additional weight penalties should be actored in because resistors are required to liit in-rush current during the charging cycle or a

4 peranent agnet. In addition, thyristors are required to isolate the voltage source ater charging whereas the ield can be isolated and claped with a crow bar circuit ater charging. Fig. Halbach array against a copper coil array with 57% less volue. To quantiy the size reduction appropriate or the copper coils, the weight o the exciter was estiated to be % o the weight o the generator, and the weight o the rotor copper in the generator was estiated to be % o the working weight o the generator. Using these two assuptions, the second penalty against the steel/copper alternative should be about 5%. The weight o the steel and copper used in inset (b) o Fig. is set to be equal to that o three (3 ) Halbach agnets, and then reduced by another 5%. When the density o the copper and steel is considered, the volue o the copper rig (with steel) ust be reduced to 43% o the agnet array. Note the copper has been reduced assuing a % packing actor, so the current density is adjusted accordingly (4.99/.58=8.76) to be consistent with this penalty in allowed volue..7.6 Consider a Coparison (a) Halbach array o 3 blocks 45 MGO agnets Roo teperature ρ=.79 lbs/in 3 Reduce volue o the copper rig to 43% o the agnet rig, ½ the weight Field Coparison (b) Steel array excited with copper coils ρ Stl =.83 lbs/in 3 ρ Cu =.33 lbs/in 3 Assue J= A/ inite eleent solver in saturation. Fig. shows the copper coil produces a signiicantly larger air gap ield, and so a larger current in the stator than the peranent agnet coniguration. B. Case Study # Axial Flux A avored topology or this application using agnets is an axial lux achine in which the stator wraps the rotor and provides the steel or ield closure. A cross-section representative o this arrangeent is shown in Fig. 3. As with case study, the volue o the copper coil available is reduced to.43 o the volue o agnet used, and the copper excited with current density J= A/. The rs air gap ield or the copper and peranent agnet options is.86 T, and.564 T respectively, and the B ield along the segent annotated in Fig. 3 is shown in Fig. 4. Axial Flux Topology Coparison Fig. 3 Transverse topology agnets versus equivalent copper cross-section..5.5 Field Coparison RMS=.86 T Copute ield along this line XX XX XX Copper coil equivalent with 57% less volue.5.4 RMS=.564 T Gap (c) Fig. Magnetic ield density created or a copper coil versus a peranent agnet under pulsed power conditions. For an air gap ranging ro.5 c up to.54 c ( ), the lux through the lower pole ace is coputed using a Distance along Segent (c) Fig. 4 Field coparison or an axial lux topology. Again, the copper coil produces a signiicantly larger air gap ield. C. Case Study #3 Radial Flux using Metal Coated Carbon Fibers

5 While the previous cases ocused on conventional topologies or rotating achines, an unconventional approach was also analyzed. This inside-out achine incorporates the perorance o iron coated carbon ibers bound in a carbon coposite structure. This aterial can be treated as a sot steel backdrop or closure o the agnetic ield. The relative pereability is quite low due to the packing o the ibers, but the saturation o the aterial reains high. An estiate o its BH aterial curve is shown in Fig. 5. The relative pereability at the origin is only 75. The coniguration with this aterial is very avorable to copper, and is shown in Fig. 6. Inertial energy storage is achieved by adding a lywheel, i.e. additional coposite aterial, to the rotor. The agnets and copper are ounted on the inside o the lywheel. The volue o the by 3 agnets is reduced in two and then reduced again to appropriately account or the increased density o copper and steel as shown in inset (b). The rs B ield or 45 MGO agnet and copper becoe respectively.74t and.35 T respectively; the B ield plot coparison is shown in Fig. 7. Fig. 5 Estiated B-H curve or coated carbon iber. Axis o rotation Flywheel (a) by 3 inch agnets within a ½ air gap Field plotted along this line Axis o rotation Flywheel Copper coils (b) Equivalent copper and steel or ½ the volue again reduced by the weight densities or steel and copper Fig. 6 Coniguration using coated carbon coposite ibers or the lywheel Field Coparison Distance along Segent (c) Fig. 7 Coparison o noral B ield in the center o the ½ air gap. IV. Conclusions Peranent Magnets versus s Based on the point designs considered, pulse power generators with duty cycles in the neighborhood o to seconds, or less, can have signiicantly better perorance per unit weight i they are wound rotor achines eploying copper coils rather than peranent agnet achines. The technology developed in this direction will be superior to peranent agnet rotors in ters o power density. Three areas that will urther advance the power density o this technology are as ollows: () Integrating the copper and steel into the lywheel energy containent coponent, () Using high teperature insulators. Although ceraic insulators are diicult to work with, they can easily extend the useul teperature range towards 3 C as opposed to the 8 C used here, (3) Pre-cooling the rotor to allow or a larger adiabatic jup. V. Reerences [] Kent Davey and Robert Hebner, A undaental look at energy storage ocusing priarily on lywheels and superconducting agnetic energy storage, Electric Energy Storage Applications and Technologies EESAT 3 Conerence Abstracts, San Francisco, CA, October 7-9, 3, pp [] W.A. Walls, Rotating Machines or Pulsed Power, Twenty-Fith International Power Modulator Syposiu, High-Voltage Workshop, 3 June-3 July, pp [3] M.D. Driga, S.B. Pratap, S.B., A.W. Walls, and J.R. Kitziller, The sel-excitation process in electrical rotating achines operating in pulsed power regie, IEEE Trans. on Magn., Vol. 37, No., Jan., pp [4] D.R. Kelsall, Pulsed Power Provision by high speed coposite lywheel, IEE Syposiu on Pulsed Power, May 3-4,, pp. 6/-6/5. [5] S.I. Shkuratov, E.F. Talantsev, J.C. Dickens, M. Kristiansen, and J.C. Hernandez, J.C., IEEE Trans. on Plasa Science, Vol. 3, Issue 5, Oct., pp