How to Calculate Max Power and Torque Angle of Synchronous Machines (Electrical Power PE Exam)

In this video, I'll teach you how to calculate the maximum power (Pmax) and Torque Angles (Electrical δ and Mechanical α) of synchronous machines for both motors and generators.
Practice Problem:
A 60 Hz 300 rpm synchronous motor has a synchronous reactance of 2.1 ohms, and induced stator voltage of 1.2kV, and a supply voltage of 2.4kV. Determine the electrical phase angle required for maximum active power, the equivalent mechanical torque angle, and the amount of maximum active power. Both voltages are given are line to neutral values.
First, draw your equivalent circuit diagram.
Next, fill in your knowns and look for your unknowns.
Second, write down any formulas that apply such as Synchronous Speed: Ns = (120f)/P
(to relate our synchronous speed to our number of poles).
Power: P = [(Eo*E)/Xs]*Sin(delta)
(to relate active power to our voltages and electrical torque angle).
And Electrical/Mechanical Torque Angle: δ = (αP)/2
(to relate our electrical torque angle to our mechanical torque angle).
Last, solve for the electrical torque angle (δ) that results in the maximum active power and the mechanical torque angle (α) that this occurs at, and the amount of active power (Pmax) under these conditions.
Can you solve it?
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