Question 1.

15 Marks

A three phase transmission line is 480-km long and serves a load of 400 MVA, with 0.8 lagging power factor at 345 kV. The ABCD constants of the line are:-

A=D= 0.8180三1.3o

B= 172.2三84.2o Ω

C= 0.001933三90.4o S

(a)    Determine the sending-end line to neutral voltage, the sending-end current,

and the percentage voltage drop at full load.                                  (4 Marks)

(b)    Determine the receiving-end line to neutral voltage at no load, the sending-

end current at no load and the voltage regulation.                          (6 Marks)

(c)    A series capacitor bank having a reactance of 146.6 Ω is to be installed at the mid-point of the 480 km line above. The ABCD constants for each of 240km

portion of lines are:-

A=D= 0.9534三0.3o

B= 90.33三84.1o Ω

C= 0.001014三90.1o S

Determine the equivalent ABCD constants for the cascaded combination of     the line-capacitor-line using the formula given below, where (A1 B1 C1 D1 ) is in

cascade with (A2 B2 C2 D2)                                                                   (5 Marks)

A= A1A2+ B1C2 ;       B=A1B2+B1 D2     C= A2C1+C2 D1      D=B2C1+D1 D2

Question 2.

15 Marks

Figure  1  shows  the  one-line  diagram  of  a  simple  three-bus  power  system  with generators at buses 1 and 3. The magnitude of voltage at bus 1 is adjusted to 1.05 pu. Voltage magnitude at bus 3 is fixed at 1.04 pu with a real power generation of 200 MW . A load consisting of 400 MW and 250 Mvar is taken from bus 2. Line impedances are marked in per unit on a 100 MVA base and the line charging susceptance’s are neglected.

Figure 1

(a)    Determine the bus admittance matrix-Y of the system shown in Figure 1.

Determine the Bus susceptance matrices B’ and B’’ for this power

system.                                                                                      (4 Marks)

.

(b)    Determine the Values of V2三62   and 三63 using Decouple Load flow

algorithm after the first iteration.                                        (5 Marks)

Where the  elements of the  Jacobian matrix with the initial estimate are given below.

54.28      −33.28      24.86

−27. 14      16.64        49.72

(c)    Determine the Values of V2三62   and 三63 using Fast Decouple load flow  algorithm after the first iteration.                                                 (4 Marks)

(d)    Calculate P1 and Q1 , with the bus voltage  solutions obtained from (b).  (2 Marks)

Question 3.

15 Marks

A single line diagram of a power system is shown in Figure 2, where positive, negative and zero sequence reactances are given. Where positive sequence impedances are not given, they can be taken from their sub-transient reactances.

Figure 2

(a)    For the network shown in Figure 2, construct the bus impedance matrix Z

by adding one element at a time and using the node elimination technique, where necessary. If there is a 3-phase fault through a reactance of 0.1 pu at bus 2, calculate the fault current in pu and in Ampere. Calculate the voltage magnitudes at buses 1 and 2 under the fault condition. Assume that no current was flowing prior to the fault and that the pre-fault voltage at bus

2 was at 1.0 per unit.                                                                    (10 Marks)

(b)     If there is a 3-phase fault through a reactance of 0.1 pu at the middle of

the line, calculate the fault current in Ampere and in per unit.       (5 Marks)

Question 4.

15 Marks

Equipment ratings and per unit reactances for the power system in Figure 3 are given as follows:

Figure 3

Synchronous Generators

G1      100 MVA      25 kV            X1=X2=0.2    X0=0.05

G2      100 MVA       13.8  kV        X1=X2=0.2    X0=0.05

Transformers

T1      100 MVA      25/230 kV                X1=X2= X0=0.05

T2      100 MVA       13.8/230  kV            X1=X2= X0=0.05

Transmission Lines

(a)    Using a 100 MVA, 230 kV base for the transmission lines, draw the per unit

positive, negative and zero sequence networks and reduce them to their Thevenin equivalents, ‘looking in’ at bus 3. Neglect  -Y phase shifts.

(6 Marks) (b)    Compute the  fault current in pu  at the  fault for the following faults at bus

3.                                                                                                    (6 Marks)

(i)       A bolted single line to ground fault  (ii)      A bolted double line to ground fault.

(c)     Also, for the single line to ground fault at bus 3, determine the voltages at the terminals of generators G1 and G2.                                        (3 Marks)

Question 5.                                                                                                   15 Marks

A one generator infinite bus power system is shown in Figure 4. Data for the system is given as follows:  H= 7.5 MJ/MVA; Frequency=50 Hz, MVA Base= 100 MVA, G: X1=X2=j0.26 pu, X0= j0.12 pu; T1 and T2: X1=X2= X0= j0. 12 pu; Line 1 and Line 2: X1=X2=j0.42 pu, X0= j01.26 pu

(a) Initially  EG=E(∞)=1.0  pu  and  P0=0.8  pu.  When  the  mechanical  power  is increased suddenly to 1.25 pu, calculate the maximum value of 6 (6m) for which the  system  will  remain  stable.  Derive  any  necessary  equation.  (7  Marks)