influienta energetica a strategiilor de comandausers.utcluj.ro/~birok/sa/curs 6_7_energetica... ·...

Influienta energetica astrategiilor de comanda

Posibilitati de comanda a motorului de inductie

• U/f constant

• U/√f constant

• Fluxul statoric constant

• Fluxul rotoric constant

• Fluxul de magnetizare constant

• Frecventa rotorica constanta

Expresiile fluxurilor in functie de parametrii

( )

RSm

mmRRR

mmsss

III

IjXIjXsR

IjXIjXRU

+=

+

+=

++=

σ

σ

0

Ecuatiile fazoriale in ipoteza neglijarii pierderilor in fier

RS

m

RmR

SmS

XXX

XXXXXX

2

1−=

+=+=

σ

σ

σCu notatiile

Expresiile curentilor

22

22

++

+

+

=

RSR

SRSR

S

RR

S

XXsRRXR

sRX

XsR

UIσ

22

22

++

+

+

=

RSR

SRSR

S

RR

m

XXsRRXR

sRX

XsR

UIσ

σ

22

++

+

=

RSR

SRSR

S

mR

XXsRRXR

sRX

XUI

σ

Relatii dintre curenti

Rm

RR

S IX

sRjX

I+−

=

Rm

RR

m IX

sRjX

I+−

=σ

Rm

RR

S IX

sRX

I

22

+

=

Rm

RR

m IX

sRX

I

22

+

=σ

Expresiile fluxurilor

RmSSS ILIL +=ΨΨΨΨ

( )22

22

++

+

+

=

RSR

SRSR

S

RSRS

SS

XXsRRXR

sRX

sRXXX

U

σ

σ

ωψ

( )22

22

++

+

+

⋅=

RSR

SRSR

S

RR

mm

XXsRRXR

sRX

sRX

LUσ

ψσ

22

++

+

⋅=

RSR

SRSR

S

R

mR

XXsRRXR

sRX

sR

LU

σ

ψ

Expresiile cuplului

22

2

23

++

+

=

RSR

SRSR

S

Rm

S XXsRRXR

sRX

sRX

UpCσ

ω

( ) 222

22

RSRS

SSRk XRXX

XRRs+

+=σ

( )( )( ) 222222

22

23

mSSSRSRS

m

Sk

XRXRXRXXUXpC

+++=

σω

Indicatori de calitate energetica

Puterea aparenta relativa S / SN

Puterea activa relativa P / PN

Curentul relativ absorbit IS / IN

Factorul de putere cosϕ

Randamentul electric ηe

Puterea aparenta relativa

22

22

233

++

+

+

⋅=⋅⋅=

RSR

SRSR

S

RR

S

XXsRRXR

sRX

XsR

UIUSσ

22

22

23

++

+

+

⋅=

RSR

SRSR

S

RR

NNN XXsRRXR

sRX

XsR

IUU

SS

σ

Factorul de putere

22

2

RR

mRSe

XsRX

sRRR

+

+=

22

2

RR

rRR

mSe

XsR

XXsR

XXX+

+

+=σ

σ

Se exprima din schema echivalenta in T a masinii

22cos

ee

e

XRR+

=ϕ

Randamentul electric

ϕcos3 ⋅⋅⋅= SIUPPuterea activa


PIRIRP RRSS

e

22 33 ⋅⋅−⋅⋅−=η

Comanda cu U/f constant

Variatia sk si Ck cu si fara Rs in functie de frecventa

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

f

sk

CkCkN RS=0

Ck

sk

Caracteristici mecanice

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

80

CCN

p.n

Puterea aparenta relativa

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

SSN

CCN

Curentul raportat

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.50.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

ISIN

CCN

Puterea activa relativa

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4

PPN

CCN

Factorul de putere

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

cosϕϕϕϕ

CCN


--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CCN

ηηηηe

Fluxul de magnetizare

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

CCN

ψψψψm

Comanda prin mentinerea constanta a raportului U/√f

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

CCN

p.n

Puterea aparenta raportata

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

CCN

SSN

Puterea activa raportata

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3PPN

CCN

Curentul raportat

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.5 30.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

CCN

ISIN

Factorul de putere

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CCN

cosϕϕϕϕ


--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CCN

ηηηηe

Fluxul de magnetizare

--- 5 Hz

--- 10 Hz

--- 20 Hz

--- 35 Hz

--- 50 Hz

--- 75 Hz

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

CCN

ψψψψm

Comparatia celor doua metode

0 0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

80

CCN

p.n

--- 5 Hz --- 10 Hz --- 20 Hz

--- 35 Hz --- 50 Hz --- 75 Hz

0 1 2 3 4 5 60

10

20

30

40

50

60

70

80

CCN

p.n

Variatia factorului de putere

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CCN

cosϕϕϕϕ

--- 5 Hz --- 10 Hz --- 20 Hz

--- 35 Hz --- 50 Hz --- 75 Hz

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9cosϕϕϕϕ

CCN

Variatia randamentului electric

--- 5 Hz --- 10 Hz --- 20 Hz

--- 35 Hz --- 50 Hz --- 75 Hz

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CCN

ηηηηe

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CCN

ηηηηe

Variatia fluxului de magnetizare

--- 5 Hz --- 10 Hz --- 20 Hz

--- 35 Hz --- 50 Hz --- 75 Hz

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

CCN

ψψψψm

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

CCN

ψψψψm

Variatia curentului

--- 5 Hz --- 10 Hz --- 20 Hz

--- 35 Hz --- 50 Hz --- 75 Hz

0 0.5 1 1.5 2 2.5 30.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

CCN

ISIN

0 0.5 1 1.5 2 2.50.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

ISIN

CCN

Comanda dupa fluxul rotoric

0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

s

UUN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

ωωωω

CCN5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

smax=0.25


5 Hz

10 Hz

0 1 2 3 4 5 6 70

2

4

6

8

10

12

SSN

CCN20 Hz

35 Hz

50 Hz

75 Hz


0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

3

3.5

4

4.5

IIN

CCN

5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


5 Hz

10 Hz

0 1 2 3 4 5 6 70

2

4

6

8

10

12PPN

20 Hz

35 Hz

50 Hz

75 Hz

CCN


0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9cosϕϕϕϕ

5 Hz

10 Hz 20 Hz35 Hz

50 Hz

75 Hz

CCN


0 1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1ηηηη

5 Hz

10 Hz20 Hz 35 Hz 50 Hz

75 Hz

CCN

Comanda dupa fluxul statoric

0 0.05 0.1 0.15 0.2 0.250

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

CCN

UUN


0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

70

80

ωωωω

CCN5 Hz

10 Hz20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

70

80

5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

CCN

ωωωω


0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5SSN

5 Hz

10 Hz20 Hz

35 Hz

50 Hz

75 Hz

CCN


5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

IIN

CCN


0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

PPN

5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

CCN


0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9cosϕϕϕϕ

5 Hz

10 Hz 20 Hz 35 Hz

50 Hz

75 Hz

CCN


0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

5 Hz

10 Hz 20 Hz 35 Hz

50 Hz

75 Hz

CCN

ηηηηe

Comanda dupa fluxul de magnetizare

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2UUN

s5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70

80

ωωωω

CCN

5 Hz 10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

70

80

ωωωω

CCN5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

SSN

CCN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 30.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2IIN

CCN

5 Hz10 Hz

20 Hz35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6PPN

CCN

5 Hz

10 Hz20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9cosϕϕϕϕ

CCN

5 Hz

10 Hz

20 Hz35 Hz 50 Hz

75 Hz


ηηηηe

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CCN

5 Hz

10 Hz20 Hz 35 Hz 50 Hz

75 Hz

Comanda dupa frecventa rotorica constanta

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

CCN

UUN

5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


ωωωω

0 0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

80

CCN5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

SSN

CCN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4IIN

CCN

5 Hz

10 Hz

20 Hz35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4PPN

CCN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.50.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

cosϕϕϕϕ

CCN

5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz


0 0.5 1 1.5 2 2.5

0.4

0.5

0.6

0.7

0.8

0.9

1ηηηηe

CCN

5 Hz

10 Hz

20 Hz35 Hz

50 Hz75 Hz

Comanda dupa frecventa rotorica constantaVariatia randamentului cu frecventa la 4 valori ale cuplului

ηηηηe

-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9

f

C =0.5

ηηηηe

-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9

f

C =1

ηηηηe

f-10 0 10 20 30 40 50 60 70 800

0.10.20.30.40.50.60.70.80.9

C =2.5

ηηηηe

f-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9

C =1.5


cosϕϕϕϕ

f-10 0 10 20 30 40 50 60 70 800.35

0.40.450.5

0.550.6

0.650.7

0.750.8

0.85

C =1

cosϕϕϕϕ

f-10 0 10 20 30 40 50 60 70 800.35

0.40.450.5

0.550.6

0.650.7

0.750.8

0.85

C =2,5

cosϕϕϕϕ

f-10 0 10 20 30 40 50 60 70 800.35

0.40.450.5

0.550.6

0.650.7

0.750.8

0.85

C =2

cosϕϕϕϕ

f-10 0 10 20 30 40 50 60 70 800.35

0.40.450.5

0.550.6

0.650.7

0.750.8

0.85

C =1,5

Caracteristicile mecanice comparate

0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

70

80

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

CCN

ωωωω

ωωωω

0 0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

80

CCN5 Hz

10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

10

20

30

40

50

60

70

80

ωωωω

CCN5 Hz 10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

0 1 2 3 4 5 6 70

10

20

30

40

50

60

70

80

ωωωω

CCN5 Hz

10 Hz20 Hz

35 Hz

50 Hz

75 Hz

ψψψψR

fR

ψψψψm

ψψψψS

Variatia tensiunii la bornenele motorului

0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

s

UUN

5 Hz10 Hz

20 Hz35 Hz

50 Hz

75 Hz

ψψψψR

ψψψψS

ψψψψm

fR

0 0.05 0.1 0.15 0.2 0.2500.20.40.60.81

1.21.41.61.8

5 Hz

10 Hz20 Hz

35 Hz

50 Hz

75 Hz

s

UUN

0 0.5 1 1.5 2 2.500.20.40.60.81

1.21.41.61.82

CCN

UUN

5 Hz

10 Hz20 Hz

35 Hz

50 Hz

75 Hz

0 0.02 0.04 0.06 0.08 0.1 0.12 0.1400.20.40.60.81

1.21.41.61.82

UUN

s5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

Puterea aparenta necesara

ψψψψRψψψψS

ψψψψmfR

0 1 2 3 4 5 6 70

2

4

6

8

10

12SSN

CCN20 Hz

35 Hz

50 Hz

75 Hz

0 0.5 1 1.5 2 2.5 300.51

1.52

2.53

3.54

4.5SSN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz75 Hz

CCN

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5SSN

CCN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4

SSN

CCN

5 Hz10 Hz

20 Hz

35 Hz

50 Hz

75 Hz

Curentul statoric absorbit

ψψψψRψψψψS

ψψψψm fR

0 1 2 3 4 5 6 700.51

1.52

2.53

3.54

4.5IIN

CCN

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3IIN

CCN

0 0.5 1 1.5 2 2.5 30.20.40.60.81

1.21.41.61.82

2.2IIN

CCN

5 Hz10 Hz

20 Hz 35 Hz

50 Hz

75 Hz

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4IIN

CCN

5 Hz

10 Hz

20 Hz35 Hz

50 Hz

75 Hz

Factorul de putere

ψψψψR ψψψψS

ψψψψm fR

0 1 2 3 4 5 6 700.10.20.30.40.50.60.70.80.9

cosϕϕϕϕ5 Hz

10 Hz 20 Hz 35 Hz50 Hz

75 Hz

CCN

cosϕϕϕϕ

f-10 0 10 20 30 40 50 60 70 800.35

0.40.450.5

0.550.6

0.650.7

0.750.8

0.85

C =2,5

0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.9

cosϕϕϕϕ

CCN

5 Hz

10 Hz20 Hz 35 Hz 50 Hz

75 Hz

0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.9

cosϕϕϕϕ5 Hz

10 Hz 20 Hz 35 Hz50 Hz

75 Hz

CCN

Randamentul

ψψψψRψψψψS

ψψψψmfR

ηηηηe

f-10 0 10 20 30 40 50 60 70 8000.10.20.30.40.50.60.70.80.9

C =1.5

0 1 2 3 4 5 6 700.10.20.30.40.50.60.70.80.91ηηηηe

5 Hz

10 Hz 20 Hz 35 Hz 50 Hz

75 Hz

CCN

0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.91

5 Hz10 Hz 20 Hz 35 Hz

50 Hz

75 Hz

CCN

ηηηηe

ηηηηe

0 0.5 1 1.5 2 2.5 300.10.20.30.40.50.60.70.80.91

CCN

5 Hz

10 Hz20 Hz 35 Hz 50 Hz

75 Hz

influienta energetica a strategiilor de comandausers.utcluj.ro/~birok/sa/curs 6_7_energetica... ·...

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