Why Are My Phase Voltages the Same in This Motor Circuit?

[milesyoung]

Hi,

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!

 

[milesyoung]

Err, so I made a huge mistake when I did the simulation, Ea/Ia = Eb/Ib = Ec/Ic can't be proven because it doesn't hold :>

I was wondering why the phase voltages for the circuit I posted were the same for a passive circuit with equal phase impedances. This is naturally due to the fact that the phase voltages sum to zero in both cases (when back EMFs sum to zero):

V_AN + 2*V_GN = Z*Ia + Ea + Z*Ib + Eb + Z*Ic + Ec = Z(Ia + Ib + Ic) + Ea + Eb + Ec =>

V_AN + 2*V_GN = 0

which would be the same for the passive circuit.

If you took the time to mull over this, thank you, apologies :)