SEE 3433 MESIN ELEKTRIK SYNCHRONOUS MACHINES Equivalent circuit

Per phase equivalent circuit Steady state conditions: Rotor rotates at constant speed Steady state

Per phase equivalent circuit Field current in rotor circuit produces sinusoidal distributed flux When

Per phase equivalent circuit induces voltage, Ear in the stator circuit ar combines with

Per phase equivalent circuit f r = ar + f r Er = Ear

Per phase equivalent circuit Ear + f r = ar + f r f

Per phase equivalent circuit Ia ar - Ear leads Is by 90 o hence

Per phase equivalent circuit Ia f If - Ear leads Is by 90 o

Per phase equivalent circuit - Ear leads Is by 90 o hence can be

Per phase equivalent circuit In per phase equivalent circuit, Xar and Xal is combined

Phasor diagrams j. Xs Ra Synchronous generator Ia + Ef = Ef o =

Phasor diagrams j. Xs Ra Synchronous motor Ia + Ef Vt = Ef +

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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,

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 ar Ia Ear Er

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

Per phase equivalent circuit Ia ar - Ear leads Is by 90 o hence can be represented by a voltage across an inductor Er = Ear + Ef Ef = Er Ear Ef = Er + Ia j. Xar

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

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

Per phase equivalent circuit - Ear leads Is by 90 o hence can be represented by a voltage across an inductor Ef = Er + Ia j. Xar j. Xal j. Xar Ia f If + Ef Ra + + + Er Ea Vt 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 j. Xal j. Xsar j. X Ia f If + Ef Ra + + Ea Er Ea Vt

Phasor diagrams j. Xs Ra Synchronous generator Ia + Ef = Ef o = Vt + Ia. Ra + Iaj. Xs + Vt Taking Vt as reference, i. e Vt = Vt 0 o Assume Ia lags Vt by angle Ef Ia j. Xa Vt Ia I a Ra Is known as the power angle

Phasor diagrams j. Xs Ra Synchronous motor Ia + Ef Vt = Ef + Ia. Ra + Iaj. Xs + Vt Ef = Vt - Ia. Ra - Iaj. Xs Taking Vt as reference, i. e Vt = Vt 0 o Assume Ia lags Vt by angle I a Ra Vt Ia Ef Ia j. Xa