2004 Exam1 With Solutions

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EE4721 EXAM 1 October 13, 2004 SOLUTIONS Page 1

PROBLEM 1: (25 points)

In the figure below you are given a balanced three phase network with a generator, a transmission

line, a set of transformers and two balanced three phase loads.

The three phase power drawn by the loads:

LOAD 1 is 100 kVA at 0.95 power factor leading.

LOAD 2 is 100 kVA at 0.95 power factor lagging.

The magnitude of the Line to Line voltage at the loads is 4400 volts.

The transmission line series impedance is 5+j0 ohms in each phase.

Find

A) The line current and the P+jQ for LOAD 1

B) The line current and the P+jQ for LOAD 2

C) The Line to Line voltage magnitude at the generator terminals.

D) The P+jQ supplied by the generator

Transmission line LOAD 1 LOAD 2

a

b

c




PROBLEM 2: (25 points)

The system below has one generator connected to a high voltage bus through a stepup transformer T1.

The high voltage generator bus is connected to a transmission line. A load is connected through a step

down transformer T2 at the generator bus.

The equipment or nameplate values for the components are:

G1: 1000 MVA, at 22 KV, Xgen=0.6 pu referred to the generator base, G1 is operating at 21 kv

T1: 1200 MVA, 22Kv to 115Kv, Xt1 = 0.15 per unit referred to the low voltage side

T2: 400 MVA, 12Kv to 115Kv, Xt2 = 0.08 per unit referred to the low voltage side

Line: Zline = 4+j6 ohms (actual impedance)

LOAD: 90 MW and 15MVAR lagging

1) Show all the voltage regions on the original network diagram and label them with their base voltage.

2) Draw the complete per unit network, show all per unit impedances using a network (or system) base of

100 MVA

3) Calculate the per unit voltage at G1

4) Calculate the per unit P and Q at the load

GENERATOR

LOAD

LINE

T1

G1

T2




Problem 3: (20 points)

You are given the per unit parameters for a transmission line shown below:

where Zseries = 0 + j0.8 per unit

and

Ycap = 0 + j0.2 per unit

This problem asssumes that there is no load at bus j, and that is there is no current flow from bus j

(that is, the line is opened at the bus j end).

The voltage at bus j is assumed to be 1.2 per unit volts at zero degrees

Find:

A) The per unit voltage and current at bus i

Ycap/2

i j

Zseries

Ycap/2




Problem 4: ( 30 points)

For the three bus power system below (line impedances are given in per unit):

Bus 1: GENERATOR BUS with P = 2.0 pu MW and Q = 0.5pu MVAR voltage of 0.98 per unit

which is below the scheduled or desired voltage magnitude. Assume that the generator on bus 1 is

operating at its maximum allowed var output.

Bus 2: SWING BUS with voltage 1.0 per unit at zero degrees phase angle

Bus 3: LOAD BUS sith P+jQ load of 4.0+0.9 puj

You may assume that the starting conditions for the powerflow has bus 1 with a voltage of 0.98

pu with zero degrees phase angle, and all other buses at 1.0 pu volts at zero degrees phase angle.

Work the entire problem in per unit.

A) Build the Y matrix for this system.

B) The bus voltage magnitudes and phase angles are the variables in a power flow. Which vari-

ables are known and which are unknown in this problem.

C) Tell which bus P and Q values are known and which are unknown for this problem.

D) Find the expression for the new or corrected voltage at bus 3 using the Gauss Seidel method.

Show all numerical values in this equation. Do not calculate the correction for any other buses.

2

G1

1

SWING

3LOAD

z12 = 0.1j

z23 = 0.3333j

z13 = 0.25j





Problem 2 Part 1









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2004 Exam1 With Solutions