Exam text content

Find the Thevenin equivalent for the circuit shown in Fig. 2. The rms voltage of the
sinusoidal voltage source is 230 V, frequency 50 Hz and phase angle 0°. R1 = 36 Q,
R2 = 10 Q, L1 = 190 mH, L2 = 50 mH and C =79 nF.

 

 

 

ron} Lon. °a

 

 

 

 

 

 

eb
Fig. 2.

Find symmetrical components of the following three-phase voltage phasors. Draw the phasor
diagrams of the original voltage phasors and the symmetrical components.

v,) fizare
i) v, |=|12287°| p.u.
v.| | 12167

Y-Y-connected three-phase transformer has the following rating plate values:100 kVA, 10000/400 V,
Z,= 11.2 % (short circuit impedance), P, = 1620 W (nominal load losses).

i) Determine a transformer equivalent circuit suitable for load flow studies at the primary potential.

ii) Aconstant impedance load having nominal power of 50 kVA and power factor 0.9 lagging is
connected to the transformer secondary. Reflect the load impedance to the primary side of the
transformer.

iii) Calculate the load current when the voltage is nominal.

i) Draw the positive, negative and zero sequence networks for the power system in the figure.

ii) Calculate the Thevenin’s impedances as seen from node 4 for each of the networks.

iii) Calculate the fault current when a single-line-to-ground fault occurs at node 4 with fault impedance Z, = 0 Q.
In this type of fault, the fault current is calculated by connecting the sequence networks in series through an

impedance 3Z,. Note that for this type of fault, the sequence currents are the same i.e. /,, = I, = /ao. Utilize
this when calculating the real fault current from the sequence currents.

 

   

HXyi0.1 pu Kori Xi
4% q)=50.05 pu JXo7=I0.25 pu 5X 0770.25 pu
X%o7i0.1 pu

. 3X(y=J0.1 pu

JXqri0-1 pu

E=Ip.u. ~ jXori0.1 pu

 
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.
c) Determine the powers injected by two voltage sources at nodes 1 (Si) and 3 (Ss) and the power

flowing between nodes | and 2 (Siz).

w

jX=j0.1 p.u. 2
1 jx@et $32

<<

      
 
 

jX=j0.1 pu.

      
   
   

E=1 p.u. E=1.05 p.u.

  

jX=]0.2 p.w. jX=jO.15 p.u.

 

Figure 2. The electric circuit of Question 3.

Fig. 6.1 shows an RC circuit. Compute the time-d i
° . -domain response of th
step change of 10 V is applied to the input voltage u;,. ° © output voltage te when 2

 

Fig. 6.1