Problems From UNIT I

1) A ∆-connected resistive load of 8000 kW is connected to the low-tension, ∆- connected side of a Y-∆

transformer rated 10,000 kVA, 138/13.8 kV. Find the load resistance in ohms in each phase as measured from line to neutral on the high-tension side of the transformer. Neglect transformer impedance and assume rated voltage is applied to transformer primary.[2.38K]

2) Solve problem 1 if the same resistors are reconnected in Y.[2.38K]

3) Draw the pu impedance diagram for the power system shown in the figure. Neglect resistance, and use a base of 100 MV A, 220 kV in 50 Ω line. The ratings of the generator, motor and transformers are: Generator 40 MV A, 25 kV, X” = 20%, Motor 50 MV A, 11 kV, X” = 30%, Y-Y transformer, 40 MV A, 33 Y-220 Y kV, X = 15%, Y-Δ transformer, 30 MV A, 11 Δ-220 Y kV, X = 15%

[0.29,0.6,0.375,0.5,0.103]4) Taking a base of 100MVA and 11KV in the generator circuit, draw the per unit impedance diagram for the power system shown in the below drawn figure. Neglect resistance. The data of the lines are in ohms. The ratings of the various components are:

Generator: 50 MV A, 12 kV, X = 25% ; Motor: 45 MV A, 13 kV, X = 20%; T1: 50 MV A, 11/220 kV, X = 10%; T2: 30 MV A, 220/22kV, X = 15%; T3: A bank of three 1Φ transformers having rating 15MVA, 230/20KV, X = 10%; Load: 100+j200Ω.

[0.595,0.2,0.165,0.243,0.165,0.2066,0.5,20.66+j41.32]

5) Taking a base of 200MVA and 33KV in the generator circuit, draw the per unit impedance diagram for the power system shown in the below drawn figure. Neglect resistance. The data of the lines are in ohms. The ratings of the various components are:

Generator: 100 MV A, 11 kV, X = 20% ; T1: 50 MV A, 11/220 kV, X = 15%; T2: A bank of three 1Φ transformers having rating 20MVA, 230/33KV, X = 10%; Load: 60+j20Ω.

[0.044,0.033,0.0367,0.0344,4.015+j1.34]

6) The one-line diagram of an unloaded power system is shown below. Reactances of the two sections of transmission line are shown on the diagram. The generators are rated as follows: Generator 1: 20 MVA, 13.8 kV, X”= 0.20 pu Generator 2: 30 MVA, 18.0 kV, X”= 0.20 pu Generator 3: 30 MVA, 20.0 kV, X”=0.20 pu Transformer T1: 25 MVA 220Y/ 13.8∆ kV, X=10% Transformer T2: single phase units each rated 10 MVA, 127/18 kV, X=10% Transformer T3: 35 MVA, 220 Y/22Y kV, X=10% Draw the impedance diagram with all the reactances marked in pu and with letters to indicate points corresponding to one line diagram. Choose a base of 50 MVA, 13.8 kV in the circuit of generator 1.

[0.5,0.2,0.0826,0.275,0.143,0.333,0.1033,0.167]

7) The figure shows the schematic diagram of a radial transmission system. The ratings and reactances of the various components are shown therein. A load of 60 MW at 0.9 power factor lagging is tapped from the 66 KV substation which is to be maintained at 60 kV . Calculate the terminal voltage of the synchronous machine represent the transmission line and the transformers by series reactances only.

[12KV]

8) A 50MVA, 30KV, 3 phase, 60Hz synchronous generator has a synchronous reactance of 9 ohms/phase and a negligible resistance. The generator is delivering rated power at a 0.8 pf lagging at the rated terminal voltage to an infinite bus. (i) Find the Ef and delta (ii) with the excitation held constant at the value found in (i), the driving torque is reduced until the generator is delivering 25MW. Determine the armature current.

[23.557,17.1deg; 0.8073KA, 0.596lagging]

9) Draw the impedance diagram for the power system shown in the figure. Mark impedances in per unit. Neglect resistance, and use a base of 50 kVA, 138 kV in the 40-Ώ line. The rating of the generators, motors, and transformers are: Generator 1: 20 MVA, 18.0 kV, X” = 20% Generator 2: 20 MVA, 18.0 kV, X” = 20% Synchronous motor 3: 30 MVA, 13.8 kV, X”= 20% Three-phase Y-Y transformers: 20 MVA, 138Y/20Y kV, X= 10% Three-phase Y-∆ transformers: 15 MVA, 138Y/13.8∆ kV, X=10%

[0.405, 0.333,0.405,0.105,0.053,0.053,0.25X4Transformers; 0.333X2Transformers]