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I have attached a diagram of a wye connected motor load with open neutral. The circuit shows an inverter state with a DC-bus voltage from terminal A to G (ground). The following equations should hold:

V_AN = Z*Ia + Ea

V_GN = Z*Ib + Eb

V_GN = Z*Ic + Ec

Ia + Ib + Ic = 0

Ea + Eb + Ec = 0 (back EMFs sum to zero)

I want to prove that:

Ea/Ia = Eb/Ib = Ec/Ic

which would mean, according to:

V_AN/Ia = Z + Ea/Ia

V_GN/Ib = Z + Eb/Ib

V_GN/Ic = Z + Ec/Ic

that the impedance + back EMF in each phase can be replaced by the same effective impedance. I have verified this by simulation in LTspice.

This is probably very simple, but it has been bothering me all day. Any help is greatly appreciated.

Thanks!

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# Circuit is driving me nuts

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