Question

A 4-pole, 60 Hz,3 phase, wye-connected synchronous motor is connected to an infinite bus of 10kV (line voltage) through a transmission line. The synchronous reactance of the motor is 4Ω, and the inductive reactance of the transmission line is 2Ω. When E is adjusted to 12kV (line voltage), the reactive power at the motor's terminal is zero.

Draw the per-phase equivalent circuit and label the parameters

Answer 1

The per-phase equivalent circuit for a 4-pole, 60 Hz, 3-phase, wye-connected synchronous motor with given reactance values. The circuit includes a voltage source at 12 kV (per-phase), the motor's synchronous reactance, and the transmission line's inductive reactance, and shows the condition where the motor operates at unity power factor with zero reactive power.

Step-by-step explanation:

A scenario involving a synchronous motor connected to an infinite bus through a transmission line. The motor is a 4-pole, 60 Hz, 3-phase, wye-connected motor operating at a line voltage of 10kV. The synchronous reactance of the motor is given as 4Ω (Ohm), and the inductive reactance of the transmission line is 2Ω. We are asked to draw the per-phase equivalent circuit when the internal voltage E is adjusted to 12 kV such that the reactive power at the motor's terminals is zero.

The equivalent per-phase circuit diagram would include the following elements:

• A voltage source representing the internal voltage E of the motor, adjusted to 12 kV/√3 for the per-phase value.
• A series combination of the motor's synchronous reactance (Xs = 4Ω) and the transmission line's inductive reactance (XL = 2Ω).
• The infinite bus represented by the line voltage of 10 kV/√3, since we are dealing with the per-phase equivalent.

In this per-phase equivalent circuit, all parameters are labeled, and it is clear that the motor's terminal voltage equals the infinite bus voltage when the reactive power is zero, indicating the motor is operating at unity power factor.

Answer 2

We assume that the system is a Balanced system and has negligible stator resistance with ideal infinite bus with constant voltage.

E = Line voltage of the motor (12 kV)

R = Stator resistance (assumed negligible)

X = Synchronous reactance of the motor per phase (4 Ω)

Xl = Inductive reactance of the transmission line per phase (2 Ω)

V = Line voltage of the infinite bus (10 kV)

The three phases are represented by a single phase equivalent circuit due to the balanced nature of the system. The stator resistance (R) is negligible compared to the reactances (X and Xl). The line voltage of the motor (E) and the infinite bus (V) are converted to per-phase values by dividing by √3 as it a 3 phase, wye-connected synchronous motor.

In conclusion, the reactances are added in series since they are impedances of the same type (inductive).