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< Tampere University of Technology
Electrical Engineering

Fundamentals of Electrical and Power Engineering DEE-23106 — 17.10.2014

Teuvo Suntio, Enrigue Acha Programmable calculator allowed 5 guestions/ & 6 pts

Ouestion 1:

Ouestion 2:

The impedance of a system composing of two passive components with ohmic loss elements
is shown in Fig. 1. Define the circuit based on the guestions below. Each of the following
subguestions yields 2 pts.

a) What is the circuit? b) Estimate the values of its main passive components, and €)
Estimate the value of the ohmic losses involved in the system.

 

40
30
20
10

-10

Magnitude (dB?)

 

 

 

Phase (deg)
o

 

 

 

 

 

10 10 105 10 10?

Freguency (Hz)
Fig. 1

The two-port network representation of a certain linearized system is presented in Fig 2
inside the dashed line corresponding to
k = Yoda + lo
== =—
Vout = Vin = VA
where the ideal source condition is shown in Fig. 2b and the ideal load condition in Fig. 2a,
respectively. It is well known that the impedances of the source (Fig. 2) and load (Fig. 2b)
will affect the system dynamic behavior. a) Compute the source-affected system description

according to Fig. 2a based on (1) (Hint: %, will change) (3pts), and b) Compute the load-
affected system description according to Fig. 2b based on (1) (Hint: ji will change) (3 pts).

 

 

Fig.2a

 

 

Fig. 2b

 
 

Tampere University of Technology
Electrical Engineering

Teuvo Suntio, Enrigue Acha

Ouestion 3:

Ouestion 4:

Fundamentals of Electrical and Power Engineering DEE-23106 — 17.10.2014

Programmable calculator allowed 5 guestions/ ä 6 pts

The electric circuit in Fig. 3 comprises three nodes in addition to the reference node 0
(ground), two voltage sources, six reactive branches, one of which is capacitive, connected
as shown in the figure. All the relevant parameter values are given on the figure (2p/sub-
guestion).

a) Determine the nodal admittance matrix of the electric circuit.
b) Calculate the voltages at node 2.
c) Determine the powers injected by the two voltage sources at nodes 1 and 3

JA=jO.2 p.u.

 

E=1.10 p.v.

 

 

Fig.3

The one-line diagram shown in Fig. 4 represents a three-phase power network, for which
per-unit values of positive, negative and zero seguence parameters, are available:

a) Built the positive-seguence, negative-seguence and zero-seguence nodal impedance
matrices (3p)

b) Determine the positive-seguence, negative-seguence and zero-seguence Thevenin
impedances, as seen from nodes 1, 2, 3 and 4 (3p)

 

 

23)

CD m-|-00<
2 X 1>j0.1 pu 4
JA 1=j0.1 pu = AA IX 23=j0.1 pu : a A
JX4=10.05 pu JXyj0.1 pu JXoj=j0.25 pu J 97j0.1 pu
JX(93=j0.1 pu IX 237j0.1 pu JX=j0.1 pu
JX(o7]0.1 pu JXo7=j0.1 pu
E,y=1 p.v.
(1)
Ej2370 p.U.
Eg=0 p.U.
Fig.4 =
 

 

Tampere University of Technology
Electrical Engineering

Fundamentals of Electrical and Power Engineering DEE-23106 — 17.10.2014

Teuvo Suntio, Enrigue Acha Programmable calculator allowed 5 guestions/ 6 pts

Ouestion 5:

A single-circuit, three-phase transmission line operating at 60 Hz has the dimensions shown
in Fig. 5. It contains 3 bundled conductors per phase and no earth-wires (also termed ground
wires or shielding wires). The separation between two adjacent conductors in a bundle is 30
cm. The transmission line is 200 km long and is rated at 230 kV. The conductivity of the
ground is 0;=0.01 S/m. The following additional information exists for the phase
conductors:

Rac=0.0798 O:km" (AC resistance of a phase conductor at 60 Hz)
70xt=1.4597 cm (external radius of a phase conductor)

a) Calculate the eguivalent geometric mean radius (GMR) and the eguivalent resistance per
phase of the three-phase transmission line. (1 point)

b) Calculate the total series impedance, in ohms. (4 points)

c) Calculate the positive, negative and zero seguence impedances in ohms.

The permeability of the free space is 1v=47x107 H:m". (1 point)

 

Fig. 5

33)