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Va Tampere University of Technology S h GA Te
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Electrical Engineering
Electric Power Systems DEE-24106 7.3. 2014

Sami Repo, Enrigue Acha Programmable calculator allowed 5 guestions/ä 6 p

Ouestion 1: (a) Starting from the complex nodal current injected into bus &, shown in Fig. 1, derive
expressions for the active and reactive powers injected at node & as a function of nodal
voltages at nodes &, n and m, as well as the two branch admittances that connect to node
k. Express the nodal voltages in either polar or rectangular coordinates (2p).

Vm

 

Figure 1

(b) State all the simplifying assumptions that are applied in the polar-coordinates, Newton-
Raphson power flow method which lead to the Fast Decoupled power flow method
(2p).

(c) Discuss the convergence characteristios of each method and compare these
characteristics with each other (2p).

Ouestion 2: — The power circuit shown in Fig. 2 undergoes a short-circuit fault involving one-phase-to-
ground (conductor in phase A) in bus 4.
A) Calculate the fault current at bus 4 assuming a flat voltage profile of 1.05 p.u. in the four
buses just before the fault occurs and zero fault impedance at bus 4, i.e. Z;= 0+j0 p.u.
(3p).
B) Determine the currents in phase guantities just after the fault occurs, flowing through the
two transmission lines and the transformer (3p).

   
  

  

iX1))0.2 p.u. JAW3j0.1 pu. 4
S - - AA 5 X07ij0.1 Pp-u.
Xmij0.6pu. — jXn=jo.1pu Xorj03pu
jX055j0.1 p.u.
jXmj0.1 p.u.

JXo jo.1 p.u.
xo j0.05 pu.
JK j0.08 p.u.

 

Figure 2

Ouestion 3: — (a) Describe what the skin effect is in connection with the internal impedance of a power
conductor in a transmission line and also describe the so-called long-line effect (2p).

(b) A 350 km, 500 kV three-phase transmission line operating at 50 Hz has the following
positive-seguence parameters: Zy=0.05+j0.25 O/km and Yn=j1.6x10-6 S/km"!. The
transmission line feeds into a bulb supply point of 250 MW at unity power factor at the
rated voltage of 500 kV - Notice that this is a long transmission line. (i) Determine the
voltage regulation (3p) and the three-phase power at the sending end of the line (1p).

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Tampere University of Technology
Electrical Engineering
Electric Power Systems DEE-24106 7.3. 2014

Sami Repo, Enrigue Acha Programmable calculator allowed 5 guestions/ & 6 p

Ouestion 4: — Figure 4 gives the power-angle curves of a power system where synchronous generator

supplies power through two parallel lines into a stiff network. A fault occurs in the middle

point of another line. The fault is successfully disconnected after some time by opening the

circuit breakers at both ends of faulted line, at the same time. P = active power, d= power

angle, sub-indexes 0 and c corresponds to situations before the fault and at the time when the

fault is disconnected, and sub-indexes e and 7 correspond to electrical and mechanical

variables. >

a) Estimate if cases A and B are.stable-based on the egual area criterion and figures. Draw
the accelerating and decelerating areas and the maximum angle into both figures.
Explain your estimations. (2.5 p.)

b) Justify why power curves are different for conditions before fault, during fault and after
fault. (1 p.)

o) Determine a rough estimation of how the generator output power, rotating speed and
power angle functions during different points of case A. Draw the necessary figures to
explain your estimations. (2.5 p.)

Case A Case B
Pc. — before fault Pe - before fault

  

 
 

P

Pe — after fault Pe — after fault

  
 

    

Pe- during ault Pe — during fault

 

 

Figure 4. Power-angle curves.

Ouestion 5: Provide short explanations for the following terms:
a) Steady-state voltage dependency of load demand
b) Over-excitation limiter
c) Freguency droop
d) Price area
€) (n-1) criteria
£) Inertia constant

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