1. 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 Excitation voltage, E f Rotating  f induces EMF in stator circuit Current in stator circuit, I a, 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  ar  ar combines with  f producing resultant flux,  r  r =  ar +  f induces voltage, E ar in the stator circuit In terms of voltages induced, this can be written as: E r = E ar + E f

5. Per phase equivalent circuit E r = E ar + E f ff EfEf IaIa  ar rr  r =  ar +  f E ar ErEr

6. Per phase equivalent circuit E r = E ar + E f  r =  ar +  f ff EfEf IaIa  ar rr E ar ErEr +Er+Er  E ar + +Ef+Ef ff IfIf

7. Per phase equivalent circuit IaIa  ar E ar - E ar - E ar leads I s by 90 o hence can be represented by a voltage across an inductor E r = E ar + E f E f = E r  E ar E f = E r + I a jX ar

8. Per phase equivalent circuit - E ar leads I s by 90 o hence can be represented by a voltage across an inductor E f = E r + I a jX ar ff IfIf IaIa

9. Per phase equivalent circuit - E ar leads I s by 90 o hence can be represented by a voltage across an inductor E f = E r + I a jX ar ff IfIf IaIa jX ar  E ar + +Ef+Ef +Er+Er

10. Per phase equivalent circuit - E ar leads I s by 90 o hence can be represented by a voltage across an inductor E f = E r + I a jX ar ff IfIf IaIa jX ar +Ef+Ef +Er+Er The leakage in  a is represented by a leakage reactance X al The stator winding resistance is represented by R a +Ea+Ea jX al +Vt+Vt RaRa

11. Per phase equivalent circuit In per phase equivalent circuit, X ar and X al is combined as X s X s = X ar + X al = synchronous reactance ff IfIf IaIa jX ar +Ef+Ef +Er+Er +Ea+Ea jX al +Vt+Vt RaRa jX s +Ea+Ea

12. Phasor diagrams E f = E f  o = V t + I a R a + I a jX s Taking V t as reference, i.e V t = V t  0 o Assume I a lags V t by angle  VtVt IaIa  IaRaIaRa I a jX a EfEf  Synchronous generator +Ef+Ef IaIa jX s RaRa +Vt+Vt  Is known as the power angle

13. Phasor diagrams V t = E f + I a R a + I a jX s Taking V t as reference, i.e V t = V t  0 o Assume I a lags V t by angle  VtVt IaIa  IaRaIaRa I a jX a EfEf  Synchronous motor +Ef+Ef IaIa jX s RaRa +Vt+Vt E f = V t - I a R a - I a jX s