Version 4
SHEET 1 1856 680
WIRE -192 384 -192 144
WIRE 48 144 -192 144
WIRE 48 176 48 144
WIRE 48 352 48 336
WIRE 48 384 48 352
WIRE 96 352 48 352
WIRE 112 144 48 144
WIRE 352 320 352 304
WIRE 480 320 480 304
WIRE 608 320 608 304
WIRE 816 -16 816 -64
WIRE 816 176 816 144
WIRE 816 336 816 304
WIRE 832 -64 816 -64
WIRE 880 144 816 144
WIRE 1072 -144 1072 -176
WIRE 1072 16 1072 -16
WIRE 1072 176 1072 144
WIRE 1072 336 1072 304
WIRE 1104 -176 1072 -176
WIRE 1104 -16 1072 -16
WIRE 1104 144 1072 144
WIRE 1104 304 1072 304
FLAG 48 464 0
FLAG -192 464 0
FLAG 816 256 0
FLAG 880 144 model_flux
FLAG 608 400 0
FLAG 608 304 L0
FLAG 816 64 0
FLAG 832 -64 model_L
FLAG 480 400 0
FLAG 480 304 theta
FLAG 96 352 1
FLAG 112 144 ph
FLAG 816 416 0
FLAG 352 400 0
FLAG 352 304 th_deg
FLAG 1072 -64 0
FLAG 1104 -176 f0
FLAG 1072 96 0
FLAG 1104 -16 f12
FLAG 1072 256 0
FLAG 1104 144 f24
FLAG 1072 416 0
FLAG 1104 304 f30
FLAG 816 304 0
SYMBOL ind 32 368 R0
WINDOW 3 44 73 Left 0
WINDOW 39 43 100 Left 0
SYMATTR Value Flux={c1}*(V(L0)-{Lsat})*tanh(x/{c1})+{Lsat}*x
SYMATTR SpiceLine Rser=0
SYMATTR InstName L1
SYMBOL current -192 464 R180
WINDOW 0 24 88 Left 0
WINDOW 3 -393 -47 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName I1
SYMATTR Value PULSE(0 {imax} 0 {imax} {imax} 0 {2*imax})
SYMBOL bv 816 160 R0
SYMATTR InstName B1
SYMATTR Value V=sdt(V(1))
SYMBOL bv 608 304 R0
WINDOW 0 34 35 Left 0
SYMATTR InstName B2
SYMATTR Value V=L0(theta)
SYMBOL bv 816 -32 R0
WINDOW 3 -44 132 Left 0
SYMATTR Value V=Lph(I(Vs),theta,Lsat)
SYMATTR InstName B3
SYMBOL voltage 48 240 R0
WINDOW 0 33 42 Left 0
WINDOW 3 35 70 Left 0
SYMATTR InstName Vs
SYMATTR Value 0
SYMBOL voltage 480 304 R0
WINDOW 0 36 32 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V1
SYMATTR Value {theta}
SYMBOL res 32 160 R0
SYMATTR InstName R1
SYMATTR Value {Rw}
SYMBOL bv 816 320 R0
WINDOW 3 -122 132 Left 0
WINDOW 0 -68 7 Left 0
SYMATTR Value I=SDT(dFluxdTheta(I(Vs),theta)*ddt(I(Vs)))
SYMATTR InstName Btorque
SYMBOL voltage 352 304 R0
WINDOW 0 36 32 Left 0
WINDOW 123 0 0 Left 0
WINDOW 39 0 0 Left 0
SYMATTR InstName V2
SYMATTR Value {th_deg}
SYMBOL bv 1072 -160 R0
SYMATTR InstName B8
SYMATTR Value V=table(I(Vs), 0,0, 5,.5329, 10,.7502, 15,.8542, 18,.8861)
SYMBOL bv 1072 0 R0
SYMATTR InstName B6
SYMATTR Value V=table(I(Vs), 0,0, 5,.3512, 10,.5711, 15,.6664, 18,.7080)
SYMBOL bv 1072 160 R0
SYMATTR InstName B7
SYMATTR Value V=table(I(Vs), 0,0, 5,.0796, 10,.1672, 15,.2616, 18,.3070)
SYMBOL bv 1072 320 R0
SYMATTR InstName B9
SYMATTR Value V=table(I(Vs), 0,0, 5,.07054, 10,.1453, 15,.2279, 18,.2727)
TEXT 256 -96 Left 0 !;Params to shape current & theta dependency:\n.param c1=5.25A  ;nonlinearity, curve "bending"\n;phase inductance at full saturation, shapes\n;Lph(i) at low L0 (near unaligned position)\n.param Lsat=Lun ;Lsat will be <= Lun
TEXT -218 -278 Left 0 !.tran {imax}
TEXT 256 -272 Left 0 !;L0(theta)=phase inductance for low currents, see REF2 :\n.func L0(theta) {ml0+ml1*cos(nrp*theta)+ml2*cos(2*nrp*theta)}\n.func dL0dTheta(theta) {-ml1*nrp*sin(nrp*theta)-ml2*2*nrp*sin(2*nrp*theta)}\n.func dFluxdTheta(i,theta) {c1*tanh(i/c1)*dL0dTheta(theta)}\n;nonlinear phase inductance(current,angle,sat.inductance) :\n.func Lph(i,theta,Lsat) {(L0(theta)-Lsat)/cosh(i/c1)**2+Lsat} ;=dFlux/dI
TEXT -224 -232 Left 0 !.param nrp=6  ; #poles, rotor\n.param nrs=8  ;#poles, stator\n.param omega=2*pi ;rot. speed rad/sec\n.param Rw=1m  ;Rwinding\n;aligned, midway, unaligned inductance:\n.param Lal=.134 Lmid=0.075 Lun=0.015\n.param ml0=(Lal+2*Lmid+Lun)/4\n.param ml2=ml0-Lmid\n.param ml1=ml0+ml2-Lun
TEXT 256 56 Left 0 !.param imax=18  ;max. phase current\n;.step param imax list 5 10 15 18\n.param th_deg=0 ;theta/degrees\n.step param th_deg list 0 12 24 30\n.param theta=th_deg*pi/180
TEXT -8 -272 Left 0 !.options plotwinsize=0
TEXT -216 -488 Left 0 ;Attempt for a Simple Approximation of Position dependent Nonlinear Phase Inductance for Reluctance Motor   Vers.14-dec-05/G.Mi\n** schematic supposed to find parameters Lsat , c1 and fine adjust Lal, Lmid, Lun **
TEXT -216 -424 Left 0 ;plot fluxes vs. I(Vs) , see also REF1, Fig.6 .\nREF1) V.K.Sharma, S.S.Murthy: "An Improved Method for the Determination of Saturation Characteristics of Switched Reluctance\nMotors" IEEE Trans. Instr.,Vol.48,No.5, Oct.1999  www.dee.hcmut.edu.vn/vn/bomon/ bmthietbi/dongco_tutro/srm/33.pdf\nREF2) F.R.Salmasi, B.Fahimi: "Modeling Switched Reluctance Machines by Decomposition of Double Magnetic Saliencies"\nIEEE Trans. Mag. Vol 40 No.3, May-2004
TEXT -176 176 Left 0 ;SlewRate=1A/sec
TEXT 632 264 Left 0 ;Inductance\nat I=0
TEXT 496 232 Left 0 ;rotor angle /rad
TEXT 856 344 Left 0 ;I=retarding torque\nwhen rotor is\nmoved
TEXT 1136 -96 Left 0 ;0 degrees
TEXT 272 480 Left 0 ;Alternative Flux-Expression, but this would need adaption of\nderivatives dFlux/dtheta etc. if torque etc. is desired. \nFlux={c1}*(sqrt(V(L0)-{Lsat}))*tanh(sqrt(V(L0)-{Lsat})*x/{c1})+{Lsat}*x
TEXT 1176 -176 Left 0 ;Measured Fluxes\nData from REF1, TABLE1 [b]
TEXT 1144 360 Left 0 ;30 degrees
TEXT 1144 200 Left 0 ;24 degrees
TEXT 1144 40 Left 0 ;12 degrees
TEXT 1072 -456 Left 0 ;Manual Adjustment Procedure:\n1)enter measured Lal,Lmid,Lun.\n  enter imax\n2) enter Tables of measured fluxes\n3) enter stepping of param th_deg\n--run simulations:\n4)adjust c1 for best fit at 0 deg.\n5)adjust Lmid, Lun for\nintermediate/min. position
TEXT 344 208 Left 0 ;rotor angle/deg
TEXT -88 72 Left 0 ;Electrical Model is made up of\nthese components only
RECTANGLE Normal 176 496 0 128 2