1. SYNCHRONOUS MACHINES - Equivalent circuit - - Phasor diagrams -
SEE 3433
MESIN ELEKTRIK
SYNCHRONOUS MACHINES - Equivalent circuit Phasor diagrams -

2. Per phase equivalent circuit
Steady state conditions:
Rotor rotates at constant speed
Steady state voltage and current in stator and rotor
Transients will not be considered

3. Per phase equivalent circuit
Field current in rotor circuit produces sinusoidal distributed flux
When rotor rotates, the flux will rotate, f
Rotating f induces EMF in stator circuit
Excitation voltage, Ef
Current in stator circuit , Ia, produces flux, a
Flux that does not link rotor circuit
i.e. leakage flux, al
Flux that links rotor circuit
i.e. Armature reaction flux, ar

4. Per phase equivalent circuit
induces voltage, Ear in the stator circuit
ar combines with f producing resultant flux, r
r = ar + f
In terms of voltages induced, this can be written as:
Er = Ear + Ef
ar

5. Per phase equivalent circuitf
r = ar + f r
Er = Ear + Ef Ef
Ear Er
ar Ia

6. Per phase equivalent circuit+ Er 
 Ear + Ef f If f Ef Ia
ar r
Ear Er
r = ar + f
Er = Ear + Ef

7. Per phase equivalent circuitIa
ar
- Ear
Ear
- Ear leads Is by 90o hence can be represented by a voltage across an inductor
Er = Ear + Ef
Ef = Er  Ear
Ef = Er + Ia jXar

8. Per phase equivalent circuitf If Ia
- Ear leads Is by 90o hence can be represented by a voltage across an inductor
Ef = Er + Ia jXar

9. Per phase equivalent circuit
- Ear leads Is by 90o hence can be represented by a voltage across an inductor
Ef = Er + Ia jXar
jXar Ia
 Ear + + Ef  Er f If

10. Per phase equivalent circuit
- Ear leads Is by 90o hence can be represented by a voltage across an inductor
Ef = Er + Ia jXar
jXar + Ea 
jXal + Vt  Ra Ia + Er  f If + Ef 
The leakage in a is represented by a leakage reactance Xal
The stator winding resistance is represented by Ra

11. Per phase equivalent circuit
In per phase equivalent circuit, Xar and Xal is combined as Xs
Xs = Xar + Xal = synchronous reactance
jXs
jXar + Ea 
jXal + Vt  Ra Ia + Ea  + Er  f If + Ef 

12. Phasor diagrams Synchronous generator + Ef  Ia jXs Ra Vt
Ef = Efo = Vt + IaRa + IajXs
Taking Vt as reference, i.e Vt = Vt 0o
Assume Ia lags Vt by angle  Ef
Ia jXa  Ia Vt 
IaRa
 Is known as the power angle

13. Phasor diagrams Synchronous motor + Ef  Ia jXs Ra Vt
Vt = Ef + IaRa + IajXs
Ef = Vt - IaRa - IajXs
Taking Vt as reference, i.e Vt = Vt 0o
Assume Ia lags Vt by angle 
IaRa Ef Ia Vt  
Ia jXa