DFIG Nusmir Mekić

8/17/2019 DFIG Nusmir Mekić

1/29


2/29

C p


3/29


4/29

CO2

CO2

η

(1±30% = ωS


5/29

3 −

4 m/s

15 m/s

25 m/s

P m = 1

2ρv3wπr

2c p(λ)

P m

ρ

kg

/m3

r

vw m/s C p λ

λ = ωtr

vw


6/29

C p

C p

C p

C p

C p λ C p

C p

10 − 15 m/s 15 m/s

20 − 25m/s


7/29

λ

C p

ωs

= 2πf s


8/29

ωs = ωm + ωr

s = ns−n

ns

f r = s ·f s

ωs

ωm ωr

ωm + ωr > ωs


9/29

ωs

ωm ωr

ωm ωr

ωs = ωm + ωr

ωs > ωm ⇒ ωr > 0, s > 0

ωs = ωm ⇒ ωr = 0, s = 0

ωs < ωm ⇒ ωr < 0, s < 0

ωs > ωm

ωr = 0


10/29

ωm > ωs

180◦

sf s


11/29

Rs X s = ωsLs

X m

RFe

Rrs

X rs

= sωsLrs

= ωsLr

V r

V rs

V s

RsI s

jX s R

r/s

I r jX r

V rs

jxµ

I µ


12/29

V s

RsI s jX s R

r/sI r

jX r

Re

s

jX e

s

jxµ

I µ

Z e

P em =

ωsM m p

P em = (U s−RsI s)I s

I s =U s+

U 2s −

4RsωsM m3 p

2Rs

E = U s − I s(Rs + jX s)

U s I s

I m = E

jX µ

I r = I s − I µ

U rs

= E − I r(Rrs

+ jX r)


13/29

U r = sE − I r(Rr + jsX r)

Res

+ jX es

=U r

s

I r

Re + jX e = U r

I r

±30%

−0.3 −0.2 −0.1 0.1 0.2 0.3

0.5

1

s

V r, I r[ p.u.] I r

V r

−200

−100

100

200

s

ϕR

I rV r

ϕr = V r − I r


14/29

V s

I sRsI r

jX s R

r/s jX r

Re

s

jX e

s

jxµ

I µ

Z e

M m =

P emωs/p =

1

ωs/p ·

3I 3r (Rr + Re)

s =

1

ωs/p

3V 2s(Rs + Rr/s + Re/s)2 + (X s + X r + X e/s)2

Rr + Res

s pr = +

(Rr + Re)2 + X 2eR2s + (X s + X r)

2

M mpr = 1

2ωs/p ·

3V 2s

Rs + (X s+X r)X e

Rr+Re−

((X s + X r)2 + R2s) · (1 +

X 2e

(Rr+Re)2)


15/29

π/2

ωt

uA

uB

uC

d

q

ωt

Ψ

ud = kd (ua cos(θ) + ub cos(θ − 2π/3) + uc cos(θ + 2π/3))

uq = kq (ua sin(θ) + ub sin(θ − 2π/3) + uc sin(θ + 2π/3))

u0 = k0 (ua + ub + uc)

θ = ωt−

Ψ

Ψ

kd, kq k0

2/3, 2/3 1/3


16/29

S dq =

32S abc

(kd, kq, k0) = (

2/3 ,

2/3 ,

1/3 )

uduq

u0

=

2

3

cos(θ) cos(θ − 2π/3) cos(θ + 2π/3)sin(θ) sin(θ − 2π/3) sin(θ + 2π/3)

1/√ 2 1/

√ 2 1/

√ 2

uAuB

uC

uAuB

uC

=

2

3

cos(θ) sin(θ) 1/

√ 2

cos(θ − 2π/3) sin(θ − 2π/3) 1/√ 2

cos(θ + 2π/3) sin(θ + 2π/3) 1/√ 2

uduq

u0

uA = U m sin (ωt)

uB = U m sin (ωt − 2π/3)

uC = U m sin (ωt + 2π/3)

ud =

3

2 U m sin (ωt − θ)

uq =

3

2 U m cos (ωt − θ)

u0 = 0

θ = ωt − Ψ

ud =

3

2 U m sin Ψ

uq =

3

2 U m cos Ψ

id =

3

2 I m sin (Ψ− ϕ)

iq =

3

2 I m cos (Ψ− ϕ)

ϕ

P = udid + uqiq

Q = udiq − uqid


17/29

90◦

vds = Rsids + φds

t − ωsφqs

vqs = Rsiqs + φqs

t

+ ωsφds

vdr = Rridr + φds

t − (ωs − ωm)φqs

vqr = Rriqr + φqs

t

+ (ωs − ωm)φds

φds = Lsids + Lµidr

φqs = Lsiqs + Lµiqr

φdr = Lridr + Lµids

φqr = Lriqr + Lµiqs

P s = vdsids + vqsiqs

Qs = vqsids − vdsiqsP r = vdridr + vqriqr

Qr = vqridr − vdriqr

M e = p(φdsiqs − φqsids)

V ds

Rs Ls

+ −

ωsφqsI ds +−

(ωs − ωm)φqrI dr

Rr Lr

V drLµ


18/29

V qs

Rs Ls +−

ωsφdsI qs

+ −

(ωs − ωm)φdrI qr

Rr Lr

V qrLµ

90◦

180◦

vds = 0

vqs = V s = ωsφs

φds = LsI ds + LmI dr = φs

φqs = LsI qs + LmI qr = 0

φdr = LrI dr + LmI ds

φqr = LrI qr + LmI qs

V dr = Rridr +

Lr−

L2m

Ls idr

t −

sωs

Lr−

L2m

Ls

iqr

V qr = Rriqr +

Lr −

L2mLs

iqr

t

+ sωs

Lr −

L2mLs

iqr + sωs

LmV sωsLs

P = −V sLmLs

iqr

Q = V sφs

Ls−

V sLmLs

idr

M e = − pLmLs

iqrφs


19/29

M t = 1

2

ρzR5πC p

λ3 ω2 = K λoptω

2

P = M ω

P = −V sLmLs

iqr

M e = − pLm

Ls

iqrφs

iqr

Q = V sφs

Ls−

V sLmLs

idr


20/29

Qref

idr


21/29

U DC

S 2

S 1

S 3

S 4

Lia

E

+ −U r

+

U r

Lia

E

++

V r = V re jθ

θ


22/29

V r − E = jX rI a

I a = V r − E

jX r

= V re

jθ− E

jX r

E

V

jX I I

ϕ ϑE

V

jX I I ϕ ϑ

E

V jX I

I

ϕ ϑ

E

V jX I

I

ϕ

ϑ

−


23/29

u(t)

ttON

T

γ = tON

T


24/29

+

−

uref (t)

utr(t)


25/29

R1S 1

T 1

+

−

ωt

u(ωt) U aU bU cU srU i

U a, U b, U c

U i U sr U i

U sr

γ

U i = U srγ


26/29

2π/3

R2S 2T 2

+

−


27/29

R1

S 1

T 1

AC/DC DC/AC LC filter

R2

S 2

T 2

ZU S

ωs±30%ωs

70%ωs

130%ωs

P r = (1 − s)P ob

±70%

P el = ±0.3P s


28/29

50Hz


29/29

DFIG Nusmir Mekić

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