braam daniels pulsed linear induction motor

7/31/2019 Braam Daniels Pulsed Linear Induction Motor

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C bank , Lstator

Ls


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1

M dM dz

r ar s

I C V CE

Z th


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Lss n s

Laa n a

M sa M as

M sa Gsa Gsa = ddz M sa .

dV dt

t

t


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F avg = 1T T

0 f (t) dt

T


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M = N 1 12I 2 =N 2 21I 1

F RMS = 1T T

0 (f (t))2 dt

12

T

r ar s


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a x,y,z

B x,y,z

C

c p 1 1]

E

E cap

E magnetic

E ohmic

E work

F x,y,z

f

f 0

f d

Gsa

I a

I s

L

Laa

Lss

lb

M

M as

M sa M sa = M as

m a


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m s

N s a

n

n a

n s

P IGBT Diode RMS Avg

pmag

q

R

Raa

R ss

r ar s

r ai

r ao

r si

r so

s x,y,z

T

V GE

V s

v x,y,z

vs

W aa

W ss


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F z


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V s = I s R s + LssdI sdt

+ M dI adt

+ I adszdt

dM dz

0 = I a Ra + LaadI adt

+ M dI sdt

+ I sds zdt

dM dz


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E cap = 12 CV 2


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r ar s

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f 12 L ss C

r ar s


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f res = 12 LC

1

1

1


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2260


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C bank , LstatorRg

Lstator

V GE


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dI dt


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Lstator

C strayCG

V GE dI dt

Lstraywiring C strayGE

dV dt

C strayCG

V GE

dI dt

dI dt

Lstator C CG

V GE

dI dt


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V GE

Lstraywiring

Lstraywiring

C strayCG

Lstraywiring


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Lstraywiring

Rg


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= LR


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I (t) =V initiald Lss

exp1

2 sin(d t)


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1

M dM dz

r ar s

I C V CE

Z th


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F = q (E + v B )

E

Bz Bx By Bz


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1


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1 6 1 6

1 6 1 6

1 2 1

0

1 1


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1 1 2

1 2

1 2 2 3

vs f

vs = 2 f


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vs

vz


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n


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V s = I s R s + LssdI sdt

+ M sadI adt

+ I adszdt

dM sadz

0 = I a Ra + Laa dI adt+ M as dI sdt

+ I s ds zdt dM asdzds zdt vs

E magnetic =12

Lss I ss +12

Laa I aa + MI ss I aa

M z

F z dz

z

F z (t) =dE magnetic

dz= I a (t) I s (t)

dM dz

F z

m advzdt

= F z = I s (t) I a (t)dM dz

Lss Laa

M dM dz


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sz (t) = sz 0 +t

t 0 vz dt

F zdM dz


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M dM dz

Lss Laa M G

M dM dz z r i

r j

z

m ij = 0r i r j 2k k K (k) 2k

E (k)

k = 4ri r jz2 + ( r i + r j )2


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K (k) E (k)

m mz

m ijz

=0k z

4 (1

k2)

r i r j

2 1 k2 K (k) 2 k2 E (k)

N s

N a N s N a

n s n a

M sa =N s N a

(N s n s )(N a n a )m ij

M sa =N s n s

i =1

N a n a

j =1

M sa =N S N a

(Ns n1)(Ns n2 )N s n s

i =1

N a n a

j =1

m ij

dM sa

dz=

N s n s

i=1

N a n a

j =1

M sa =N S N a

(Ns n s )(Ns n a )N s n s

i =1

N a n a

j =1

m ij

z


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[V ] = [L] [I ][M ] [I ] + [R] [I ]v [G] [I ]

[V ] =V s

0

[L] =Lss 0

0 Laa

[M ] =0 M sa

M as 0

[G] =0 dM sadz

dM asdz 0

[R] =R ss 0

0 Raa

[I ] =I s

I a

[I ] =I s

I a

[[L][M ]]

[[L] + [M ]] [I ] = [V ][R] [I ]vz [G] [I ]

[I ] = [[L] + [M ]]1

[[V ]

[R]

[I ]

vz

[G]

[I ]]


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[I ]t +1 = [[ L]t + [M ]t ]1[[V ]t [R] [I ]t vzt [G]t [I ]t ]

[I ]0 = 0 [V ]0 =

V initial

0 vz 0 = 0

[I ]0 = [[L]0 [M ]0]1[V ]0

[I ]1 = [ I ]0 + t [I ]0 = t [I ]0

[I ]t +1 = [I ]t + t t [I ]

t

F z @ (t +1) = Transpose ([I ]t +1 ) [G]t +1 [I ]t +1

az @ (t +1) =F z @ (t +1)

m a

vz sz

t

[M ] [G]

vz @ (t +1) = vt + t az @ (t +1)

sz @ (t +1) = sz @ (t +1) + t vz @ (t +1)


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[L] [M ] [G]

[M ] [G]

t


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[I ]T

[I ]T [V ] = [I ]T

[[L][M ]] [I ] + [I ]T

[R] [I ][I ]T

vz [G] [I ]

E (t)capcitor = E (t)magnetic + E (t)ohm + E (t)work

E (t)capacitor =12 CV

2initial

t0 [I ]

T [V ]dtE (t)magnetic =

12

t0 [I ]

T

[[L] + [M ]] [I ]dt 12 [I ]T

[[L] + [M ]][I ]E (t)ohm =

t0 [I ]

T

[R] [I ]dtE (t)work =

12

t0 [I ]

T

v [G] [I ]dt = 12 l

0 [I ]T

[G] [I ]dx

E ohm

E ohm = E ohmstator + E ohmarmature

E ohmstator = t f

0R ss I 2s dt

E ohmarmature = t f

0Raa I 2a dt

R ss Raa

R ss R aa


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T stator =E ohmstator

c p;Copper m s

T armature = E ohmarmaturec p;Copper m a

B z

I N l

Bz 0 NI l pmagnetic =

B 2z2 0

haa = 2 b2 pmagneticb2 d2

b d

hss = pmagneticc2 + a2

c2 a2

a c

hss = pmagneticr si

(r so r si )


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h y

Bz


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0 =1

Lss C

d = 20 2 = R2L

1

F z

r ar s lb


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z


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C

E cap = 12 CV 2

U s

U pk

U s

I rms


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I pkr

I pkr = C dV dt

dV dt

I pk

I pk

dV dt

I pkr

E.S.R


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E.S.L

tan

tan i n

P =n

1(V irms )2 2f i C tan


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I rms I pkr

I pkr = C dV dt


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V CE


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V CE S

V GES

I C

I CM

I C

T jmax

o o o


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V CEsat

V CEsat

V I

V GE ( th )

I C V CE


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I C V CE

I c

V CE

V ECsat


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Z th

Z th

Z th

Z th

T j (t) = P (t) Z th + T jinit

P diode (t) = V CEsat (t) I s (t)

P IGBT (t) = V ECsat (t) I s (t)


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T j (t) = T jdiode + T jIGBT + T jinit

= P diode Z th + P IGBT Z th + T jinit

T j < T jmax


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L ss n s

L aa n a

M sa M as

M sa G sa G sa =d

dzM sa .

dV dt

t

t


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r ar s

Lss Laa

M sa Gsa

N s N a

n s n a


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Lss n sn s =


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Laa n an a =

[L]

n s =

n a = 25 N s N a

n N L sim L ref


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n s n a

n s n a

n N M sim M ref Gsim Gref

M G

M sa M as


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M sa Gsa Gsa =d

dz M sa .

Lss Laa M sa

Gsa

M sa Gsa

M sa Gsa

sz (t)

n s

n a


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R =l

k =1

n(2r l )

l n, r l

t


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I (t)ss I (t)aa

F (t)z


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dI dt

dV dt


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I 2

R

o

o

o

o


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hss = pmagnetic r si(r so r si )

=B 2z

2 0 r si

(r so r si )=

0 N s I ssl s2

2 0 r si

(r so r si )

=0 (N s I ss )

2

2l2s r si

(r so r si )= 6 .76

Bz


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B z

haa = 2 b2 pmagneticb2 d2

=0 (N s I ss )

2

2l2s

2 b2b

2

d2 = 2 .65

Bz


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I pkr = C dV dt

C dV dt

V s

dV dt


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dV dt

E capheat =16

t f

0I 2ss ESRdt = 0 .27


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T IGBT = P avgIGBT Z thIGBT


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T Diode = P avgIGBT Z thIGBT

T j = T IGBT + T Diode + T jinitial

Z th


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o

Z th o

Z th o

o

o

o


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E capinitial E capacitor E magnetic E heat E kinetic = 0

t

t

t

t


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t


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t

lb


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G F z

lb


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o o


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r ar s


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E cap =12

CV 2

I 2 ESR3


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I max = V sLss


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3

3


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3

o

oC


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o o


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braam daniels pulsed linear induction motor

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