A group of identical synchronous motors is connected through a transformer to a 4.16-kV bus at a remote location from the generating plants of a power system. The motors are rated (see table 3) and operate at (see table 3) efficiency when carrying full load at unity power factor and rated voltage. The sum of their output ratings is 4476 kW. The reactance in per unit of each motor based on its own input kVA ratings are X_d" = X₁= 0.20, X₂ =0.20, X₀ =0.04 and each is grounded through a reactance of 0.02 per unit. The motors are connected to a 4.16-kV bus through a transformer bank composed of three single-phase units, each of which is rated 2400/600, 2500 kVA. The 500-V windings are connected in D to the motors and the 2400-V windings are connected in Y. The leakage reactance of each transformer is 10%.

The power system which supplies the 4.16-kV bus is represented by a Thevenin's equivalent generator rated at 7500 kVA, 4.16 kV with reactances of X_d" = X₂ = 0.10 per unit , X₀ = 0.05 per unit, and Xn from neutral to ground equal to 0.05 per unit

Each of the identical motors is supplying an equal share of a total load of 3730 kW and is operating at rated voltage, 85% power factor lag, and 88% efficiency when a single line-to-ground fault occurs on the low-tension side of the transformer bank. Treat the group of motors as a single equivalent motor.

3a. Draw the sequence networks showing values of the impedances

3b. Determine the sub-transient line currents in all parts of the system with pre-fault current neglected

(Note: Each student will be assigned either (1) or (2) parameters in Table 3 for the motor rating.)

(Note: I will be using 550 as the rated voltage and 84.5 as the efficiency in Table 3 for the motor rating.)

 Solution should include:1. Single line diagram of the system described

1. Single line diagram of the system described

2. Sequence network connection diagram with impedances and subtransient currents

3. Detailed calculation of the subtransient current in all parts of the system

a. Calculation of current in the fault

b. Calculation of the prefault current in the lines

c. Current in the fault

d. Current in lines between transformer and fault

e. Current in lines between motor and fault

f. Current in line between bus and transformer

4.. Accuracy of the calculation

5. Analysis of calculation procedure done.