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

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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

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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

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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

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Per phase equivalent circuit E r = E ar + E f ff EfEf IaIa ar rr r = ar + f E ar ErEr

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Per phase equivalent circuit E r = E ar + E f r = ar + f ff EfEf IaIa ar rr E ar ErEr +Er+Er E ar + +Ef+Ef ff IfIf

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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

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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 ff IfIf IaIa

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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 ff IfIf IaIa jX ar E ar + +Ef+Ef +Er+Er

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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 ff 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

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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 ff IfIf IaIa jX ar +Ef+Ef +Er+Er +Ea+Ea jX al +Vt+Vt RaRa jX s +Ea+Ea

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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

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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

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