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

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

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

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

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

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

Per phase equivalent circuit Ia 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

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

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

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

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 

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

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