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lecture15 - EE 740 Professor Ali Keyhani Lecture#15...

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EE 740 Professor Ali Keyhani Lecture #15 Synchronous Machine Sequence Network
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Sequence Networks for Synchronous Machines jXs Ra a If φ Ea jXm Vf Eb jXs Ra jXm b Ec Va jXm jXs Ra c Vb Zn In=Ia+Ib+Ic Vc Where Zn is the Grounding Impedance. Consider the Steady State Operation with: ϖ m Constant Constant Field Current (If) No Saturation Balanced 3 φ windings located 120 ° apart Then we have: Ea = (Ra+jXs+Zn)Ia + (jXm+Zn)Ib + (jXm+Zn)Ic + Va Eb = (Ra+jXs+Zn)Ib + (jXm+Zn)Ia + (jXm+Zn)Ic + Vb 1 Ec = (Ra+jXs+Zn)Ic + (jXm+Zn)Ia + (jXm+Zn)Ib + Vc Which is similar to the transmission line equations in Lecture #14
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Balanced Voltage Set: c Ea = E a Eb = a 2 E 2 a Ec = aE a 2 E b Let Zs = Ra + jXs + Zn Zm = jXm + Zn 3 Then equation ( 1 ) can be written as: Ea Zs Zm Zm Ia Va Eb = Zm Zs Zm Ib + Vb 4 Ec Zm Zm Zs Ic Vc [Eabc] = [Zabc] [Iabc] + [Vabc] 5 Recall that [Eabc] = [Ts] [E 012 ] 6 and [Iabc] = [Ts] [I 012 ] 7 Multiply Eqt. 5 by Ts
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