Electrical Power Systems Assignment Sp5 2014

• This is a group assignment and students should work on this assignment in

groups maximum 2 students.

• Only collaboration among students in the same group in allowed.

• Collaboration among students from different groups is not allowed and will be

treated as academic misconduct.

• Each question carries the same mark.

• Document all your workout and answers and make sure you use the correct

units.

• Please submit only one copy of the assignment per group via learnonline.

Q1. For the balanced 3-phase system shown in Figure 1 assume positive phase sequence

(A,B,C).

(a) Determine the voltage V1 phasor, current I2 phasor and the total complex power

supplied by the source.

(b) Calculate the capacitance per phase of the ?capacitor bank (shown in the diagram)

so that the source supplies only the active power.

(c) Use Multisim to verify your results.

(d) What will change if you remove the neutral line? Explain your answer.

Figure 1 Circuit diagram for question Q1.

Q2. The one line diagram of a simple power system is shown in Figure 2. The data of the

system are given in the table below. Choose a base of 100 MVA and 20kV at generator

G1.

(a) Draw the impedance diagram of the system.

(b) Calculate and mark all impedances in puon the diagram.

(c) Calculate the line to line voltage of Bus B in pu and in kV if the motor draws its

rated power at rated voltage and pf = 0.7 lagging.

2

SYSTEM DATA

System

Component

MVA

Rating

Voltage

Rating (kV)

Reactance

G1 150 20.0 10%

G2 100 22.0 15%

T1 100 20/200 5%

T2 100 22/200 10%

T3 300 20/200 5%

T4 50 200/11 10%

M 50 10.0 20% Load S1: 100MW +j20MVAr at 220kV

Load S2: 50MVA pf=0.8 leading at 200kV

Figure 2 One line diagram for question Q2.

3

Q3. A 120 km, 3-phase, 50Hz transmission line has spacing as shown in Figure 3.

Each phase of the line consists of a bundle of four conductors. Each conductor has a

diameter of 2.1793cm and a GMR of 0.8839cm. The bundle spacing is 0.5m.

(a) Calculate the per-phase inductance and the per-phase shunt capacitance of the

line.

(b) Calculate the new bundle spacing if the inductance needs to be reduced by 10%.

(c) Use Matlab to check your results.

Figure 3. Diagram for question Q3.

Q4. A 3-phase, 50Hz transmission line is 350km long. The line has a per phase series

impedance of 0.015+j0.043 ?/km and shunt admittance of j0.56 µS/km. The line

delivers 300MVA, at 0.707 lagging power factor and 200kV to a 3-phase load.

(a) Calculate the ABCD parameters of the line.

(b) Calculate the sending end voltage and the sending end current.

(c) Calculate the voltage regulation and the efficiency of the line.

(d) Calculate the per-phase capacitance of the capacitor bank to be placed at the

receiving end that will improve the voltage regulation by 20%.

Q5. For the 3 bus system shown in Figure 4. values are given in pu on a 200MVA, 200kV

base:

(a) Use Matlab function lfgaussto find power flow solution for the system, accurate

to 0.000001, and draw power flow diagram showing voltages and powers for all

busses and power losses in all lines;

(b) Use Matlab function lfnewtonto check the result obtained in (a);

(c) Use trial method (or repetitive simulations) to estimate the minimum capacitance

that needs to be connected to bus 3 to increase this bus voltage magnitude to

0.99pu. If this capacitance is large enough can it increasebus 3 voltage magnitude

above generator 1 and 2 voltage magnitudes? Document your answers (include

input and output Matlab files).

(d) If G1 can supply maximum 150MVAr what size of capacitor (in terms of reactive

power) should be placed at bus 1 to keep the voltage magnitude of bus 3 at

1.00pu? Explain and document your answer.

12m 12m

4

Figure 4. Diagram for question Q5.

Q6. The one line diagram of a simple four-bus power system is shown in the Figure 5.

Each generator is represented by an emf behind its transient reactance. All impedances

are expressed in per unit on a common 100 MVA base, and for simplicity, resistances

are neglected. The following assumptions are made:

• Shunt capacitances are neglected and the system isconsidered at no-load.

• All generators are running at their rated voltages and rated frequency with their emfs

in phase.

Determine the fault current, the bus voltages, and the line currents during the fault

when:

(a) a balanced three-phase fault with fault impedance Zf= j0.1 pu occurs on bus 3;

(b) a bolted 3-phase fault occurs on bus 1.

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