How does a synchronous motor know to increase current when the mechanical load is increased?
From the practical viewpoint:


As the load increases, the motor continues to rotate at the same speed, but the phase of the rotating magnetic field lags the applied voltage, so the current increases in an attempt to reduce the phase angle. 
Similarly, if the output shaft is driven from an external mechanical source the phase begins to lead, and the motor starts to generate power back into the supply.


I suspect that your circuit represents the motor under no-load conditions. If the motor was delivering say 100W of mechanical power to its output shaft, then there is no way your circuit can model this (unless R1 is a variable resistor).

I last did maths like this at university 40 years ago, so someone more academic will need to provide a more scholarly answer.