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Tampere University

Electrical Engineering
EE.EES.300 Fundamentals of Electrical and Power Engineeri

ae er Engineering 16.10.2023
Programmable calculator allowed 5 questions/ 4 6 pls

Ql:
a) Find Thevenin equivalent for the circuit shown in Figure 1. The rms voltage of the sinusoidal voltage
source Vg = 230 20° V and frequency 50 Hz. R1 = 27, R2=8 Q, L1 = 150 mH, L2 = 60 mH and
C=67 uF. [3 pts]
1 Ri C27 RZ:
{_} wn “a

 

 

 

 
 
  
 

—C

 

Figure 1, Electric circuit of Question 1 a).

b) Below are presented unbalanced three-phase voltages for Phases a, b and c. Find the symmetrical
components for the voltage of Phase a. Draw the phasor diagram which includes the original voltage
phasor V, and its symmetrical components. [3 pts]

 

 

Va 1.129° :
Vy] =| 0.821309 | p.u.
YJ L122 —70°

 

Q2:  Three-phase transformer has the following rating plate values: S, = 200 kVA, Up /U,= 20500 /410 V,
2, = 4 % (relative short-circuit impedance), P, = 2295 W (nominal load Josses). (2pts/sub-question)

a) Determine a transformer equivalent circuit (including impedance values) suitable for load flow

studies at the primary potential (20500 V).

b) A constant impedance load having nomi

connected to the transformer secondary. D

transformer.
c) Calculate the load current in amperes at the secondary.

inal power of 50 kVA and power factor 0.9 lagging is
termine the load impedance at the primary side of the

Q3: The electric circuit in Figure 2 comprises three nodes in addition to the reference node 0 (ground), two
voltage sources, reactive branches and one transformer connected as shown in the Figure 2. All the
relevant parameter values are given in Figure 2. (2pts/sub-question)

a) Determine the nodal admittance matrix of the electric circuit.

b) Calculate the voltage at node 2.

¢) Determine the powers injected by two voltage sources at nodes 1 (S:) and 3 (Ss) and the power
flowing, between nodes | and 2 (Siz).

1 jxj0lpu 2 3 $32

jX=j0.1 pau.
<—

         
    
    
 
  
 
 
 

S81?
—

—
Si2?

jX5j0.1 pu.

E=l p.u. E=1.05 p.u.

  
 
 

 
 

jX=j0.15 p.u.

   

Figure 2. The electric circuit of Question 3.

1(2)

 
Tampere University

Electrical Engineering

EE.EES.300 Fundamentals of Electrical and Power Engineering 16.10.2023

Ari Nikander

Q4:

Q5:

Programmable calculator allowed 5 questions/ 4 6 pts

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

is presented in Figure 3. The parameters of the system are the following:

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

Transformer | (T1): 50 MVA, 11/110 kV, X1=X2=X0=9%

Transformer 2 (T2): 25 MVA, 110/20kV, X1 = X2=X0=10%

Transmission line 1: Z1 = Z2 =j30 Q, ZO = 2.3*Z1

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

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

a) The loads are modelled 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 valucs for the loads. {I pts]
b) Draw the positive and zero sequence impedance networks of the circuit. Use per unit values and
50 MVA base power. [3 pts]

c) Calculate the load current (pu) flowing through the transmission line according to the positive
sequence network. The internal emf (field voltage) of the synchronous generator G1 can be assumed
to be 1.05.20° pu. [2 pts]

 

Figure 3. The power system of Question 4.

Figure 4 presents a first order RC circuit. A step change of 10 V is applied to the input voltage tin. Initial
conditions are zero, i.¢. tin and wo are zero,

a) Determine transfer functions for determining vo and im. [3 pts]
b) Apply the inverse Laplace transform and determine the responses for vo and ij; in a time domain.
Utilize the table of Laplace Transforms below, The mathematical expression as a function of time
are acceptable, the graphs are not required, 13 pts]

 

Figure 4. RC circuit of Question 5.

Table a Transforms

L()=E MF} F()=£{F()} SIQ=E*F()} F(s)=2{F(1)}

 

 

1 1 2 ef 1
s sa
n! T(p+1)
tM, n=1,2,3,... QT 4. tf? p>-l a

2(2)