A 208-V Y-connected synchronous motor is drawing 40 A at unity power factor from a 208-V power system. The field current flowing under these conditions is 2.7 A. Its synchronous reactance is 0.8 Ω. Assume a linear open-circuit characteristic.

The answer is given as:

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However, I do not understand where they got that equation for EA. I was under the impression that the equation for the phase voltage is:

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Wouldn't this mean that the equation for the internal generated voltage is EA = VΦ + jXsIA?

EDIT: My bad. That's the equation for a synchronous generator, not a synchronous motor.

This is the equation for a synchronous motor: enter image description here

  • \$\begingroup\$ TRy again............. \$\endgroup\$ Jul 1, 2019 at 4:57

1 Answer 1


If you supply mechanical power to a synchronous machine, it becomes a synchronous generator generating electrical power.

Electrical power converts the synchronous machine into a motor providing mechanical power.

From Electric Machinery Fundamentals. As a motor:

Synchronous motor

$$V_{\phi} = E_A + j I_A X_S + I_A R_A$$ As a generator: Synchronous Generator

$$V_{\phi} = E_A - j I_A X_S - I_A R_A$$

Note direction of current. The voltage seen at the terminals \$V_{\phi}\$ will depend on whether the synchronous machine takes current or generates current, hence the change of signs. Just Kirchhoff's Voltage Law.


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