PHASOR DIAGRAM OF SALIENT POLE ALTERNATOR AT LAGGING POWER FACTOR d − axis
See Page 5 for Algorithm Faq
Ff Fad
Fa
Ead
Iq
Faq
Ef
q − axis
δ φ
Eaq
Eaq
l
Ia
I ar a
ER Id
Ia x
Fad
Vt
Ead
Ead = − jI d X d
LEAKAGE REACTANCE COMPONENTS
Eaq = − jI q X q
− j Id xl
∴ ER = E f − jI d X d − jI q X q E f = Vt + I a ra + jI d X d + jI q X q
I ar a
ER = E f + Ead + Eaq s − j Iq xl
Ia xl
Vt = E f − ( I a ra + jI d X d + jI q X q ) = E f − I a ra − jI d X ad − jI q X aq − jI d xl − jI q xl = E f − ER − I a ra − jI d xl − jI q xl X d = X ad + xl X q = X aq + xl X ad − Direct axis armat ure reactance X aq − Quadrature axis armature reactance xl − Leakage reactance
δ − Torque angle or Load angle φ − Power factor angle
Author: MELVIN KOSHY
Email:
[email protected]
PHASOR DIAGRAM OF SALIENT POLE ALTERNATOR AT LEADING POWER FACTOR
d − axis
Fa Fad
Ff
Faq
Ia
Id
Fad
Ead
Ead
φ Faq Iq
q − axis
Ef
δ
ER
Eaq
a
Ia r
Eaq
I ax l
Vt
Author: MELVIN KOSHY
Email:
[email protected]
PHASOR DIAGRAM OF SALIENT POLE MOTOR AT LAGGING POWER FACTOR
d − axis
Faq
Ff
Fad
Fa
ER
Ia ra
Vt Ia xl
−Ead
Eaq
δ φ
Ef
Iq
Ia
− Eaq
q − axis
Id
Ead
Ead = − jI d X ad Eaq = − jI q X aq ER = E f − Ead − Eaq ∴ ER = E f + jI d X ad + jI q X aq Vt = E f + I a ra + jI d X d + jI q X q Vt = E f + I a ra + jI d X ad + jI q X aq + jI d xl + jI q xl = E f + ER + I a ra + jI d xl + jI q xl X d = X ad + xl X q = X aq + xl X ad − Direct axis armature reaction reactan ce X aq − Quadrature axis armature reaction reacta nce xl − Leakage reactance
δ − Torque angle or Load angle φ − Power factor angle
Author: MELVIN KOSHY
Email:
[email protected]
PHASOR DIAGRAM OF SALIENT POLE MOTOR AT LEADING POWER FACTOR
d − axis
Fa Fad
Ff
Faq
Ia ra
Vt
Ia xl
−Ead
ER
Ia
− Eaq
Id
φ
δ Iq
q − axis Ead
Ef
Eaq
Author: MELVIN KOSHY
Email:
[email protected]
PHASOR DIAGRAM OF SALIENT POLE MACHINE Algorithm Draw the field flux Ff (this is the d - axis) EMF lags the flux which produces it by 900 Construct Ef
(this is the q - axis)
Draw Ia at an angle (lagging or leading) to Ef Ia produces Fa Fa can be resolved into Fad (along d-axis) and Faq (along q-axis) Fad produces Ead which lags F ad by 900 Faq produces Eaq which lags F aq by 900 For generator operation E R = E f + Ead + Eaq For motor operation E R = E f − E ad − E aq
Author: MELVIN KOSHY
Email:
[email protected]
