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M A TIKE Ann E

Ouestion 1:

Ouestion 2:

Ouestion 3:

 

Tampere University of Technology
Electrical Engineering

Fundamentals of Electrical and Power Engineering DEE-23106 26.11.2015

Anna Kulmala Programmable calculator allowed 5 guestions/ & 6 pts

A one-phase voltage source is feeding a load through a one-phase feeder. The source voltage

is 155.56cos(377t+109)V. The feeder impedance is 1+j2 O and the load impedance is 10-44

O.

a) Draw the circuit diagram of the network and calculate the current. Draw the phasor
diagram of the current and voltage. (2p)

b) Determine the real power, reactive power, apparent power and the power factor of the
Source. Draw the power triangle, (2p)

€) Determinc the real power, reactive power, apparent power and the power factor of the
load. Draw the power triangle. (2p)

A three-phase power system consisting of one generator, two transformers, a transmission

line and a load is represented in Fig. 1. The parameters of the system are the following:

Generator 1 (G1): 50 MVA, 11 KV, X1 = 0.15, X2=0.1, X0= 0.03 pu

Transformer 1 (T1): 50 MVA, 11/110 KW, X=9%

Transformer 2 (T2): 25 MVA, 110/20 kV, X= 10%

Load 1 (L1): Pyom = 10 MW, 20 kV

Load 2 (L2): Onom = 5 MVAr, 20 kV

a) The loads are modeled using a constant impedance load model such that they consume
their nominal powers at the nominal voltage. The given power is three-phase power and
the voltage 20 kV is the nominal line-to-line voltage. Calculate the impedance values for
the loads. (1p)

b) Draw the positive seguence impedance network of the circuit. Use per unit values. (3p)

€) Calculate the current flowing through the transmission line. The internal emf of the
synchronous generator G1 can be assumed to be 1.05 409 pu. (2p)

 

Fig. 1. The power system of duestion 2.

Fig. 2 presents an electric circuit and all the relevant parameter values are given on the

figure.

< Determine the nodal admittance matrix of the electric circuit. (1p)

e) Calculate the voltages at nodes 3 and 4. (2p)

1) Determine the real and reactive powers injected by the two voltage sources at nodes 1
and 2. (2p)

g) Calculate the powers consumed by the resistive loads Rao and Roo. (1p)

163)
 

 

Tampere University of Technology
Electrical Engineering

Fundamentals of Electrical and Power Engineering DEE-23106 — 26.11.2015
Anna Kulmala Programmable calculator allowed 5 guestions/ & 6 pts

    

1 JX=jO.lpu. 2

  

Fig. 2. The electric circuit of guestion 3.

Ouestion 4:
a) Find symmetrical components of the following three-phase voltage. Draw the phasor
diagrams of the original voltage phasors and the symmetrical components. (2p)

 

 

va 1.05410*
A fe =: 0.9 20]
V. 1.24190*
b) Draw an approximate Bode diagram of the following transfer function. (2p)
a 11159-10%
6) = 501595

c) The Bode diagram of a loop transfer function is given in Fig. 3. Determine the phase and
gain margins of the system. Is the closed-loop system stable? (2p)

203)
Tampere University of Technology
Electrical Engineering

Fundamentals of Electrical and Power Engineering DEE-23106 — 26.11.2015
Anna Kulmala Programmable calculator allowed 5 guestions/ 6 pts

Bode Diagram
100 n

s0|-
60

 

   

Magnitude (dB)
o

 

-100 Ä

 

135

-180|—-——

Phase (deg)

-225 |

 

 

 

-270 ==
10? 10? 1 10? 10
Freguency (Hz)

Fig. 3. Bode diagram of guestion 4c.

 

Ouestion 5: > The freguency response of impedance of a system is shown in Fig. 4. The system is
composed of two passive components with their corresponding eguivalent series resistances

(ESRS).

a) What is the circuit? Draw the circuit and write its s-domain impedance eguation. (2p)
b) Estimate the values of its main passive components. (2p)
c) Estimate the value of the ESRs involved in the system. (2p)

Bode Diagram
T

 

Magnitude (dB)

 

 

Phase (deg)

 

 

 

 

 

10 10? 10 10"
Freguency (Hz)

Fig. 4. Impedance plot of guestion 5.

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m a ss