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DEE-24106 ELECTRIC POWER SYSTEMS

Enrigue Acha and Sami Repo
2"4 of March, 2016

Attempt ALL guestions

The numbers in sguare brackets in the right-hand margin indicate the marks allotted to the
part of the guestion against which the mark is shown. These marks are for guidance only.

An electronic calculator may be used provided that it does not have a facility for either
textual storage or display, or for graphical display.
If a calculator is used, intermediate steps in the calculation should be indicated.

O1 (a) Discuss the convergence characteristics of the Newton-Raphson power flow method
emphasizing it guadratic rate of convergence. [2 points]

(b) For the circuit shown in Fig. 1 determine the nodal voltage solution using two
iterations of the power flow Newton-Raphson method. Select bus 1 to be the slack
bus, with a voltage magnitude of 1.05 p.u. and 0 phase angle. The voltage
magnitudes at buses 2 and 3 are kept at 1 p.u. each. To start the iterative solution,
assume 0 phase angles in buses 2 and 3. [4 points]

 

P=0.5p.u.
00 p.v.

   
 
   
   

X,=0.1p.u.

=
P2=0.2p.v.

   
 

Po3=0.5p.v.
=

P1s=0.8p.v.
OLs=0.2p.v.

Fig. 01

02 The power circuit shown in Fig. 2 undergoes a single-phase-to-ground short-circuit
fault in bus 3.

(a) Calculate the short-circuit fault currents (positive, negative and zero seguence)

assuming a flat voltage profile of 1 p.u. in all buses just before the fault occurs and
zero fault impedance, i.e. ZF= 0+j0. [4 points]

(b) Determine the faulted nodal voltages in all buses, in seguence guantities. [2 points]

 
 

X/0.1 p.v.
Xo0.06 p.u.
X(oy>0.04 p.u.

Xy=0.1 p.u. Xo=0.1 p.u. Xu0.1 p.u.
Xo=0.1 p.u. Xoy=0.1 p.v. Xo0.1 pu.
Xo=0.1 p.u. Xoy=0.3 p.u. Xo0.1 p.u.

  
 
  
  

Xay0.1 p.u.
Xoyr0.06 p.v.
Xoy>0.04 p.u.

Fig. 02

03 —Describe with your own words how the freguency control of large interconnected

04

power system like Nordic power system functions. Maximum one page well-structured
answer is allowed.

a) Explain the key mechanisms to keep constant freguency during normal and
disturbance conditions. [3 points]

—b)—Explain the roles and responsibilitios of producers-and -TSO-in liberalized-and

unbundled power system (at least organizational separation of network and
production/retail businesses). [2 points]

c) How freguency control and different electricity markets are related? [1 point]

Figure 3 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, 8 = 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 m correspond to
electrical and mechanical variables.

d) 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. [3 points]

e) Justify why power curves are different for conditions before fault, during fault and
after fault. [1 point]

f) 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 points]
 

Case A Case B
P; — before fault P.— before fault

  
 

 
 

P

P, — after fault P,— after fault

  
 
 

P; — during fault

   

P, — during fault

 

Figure 3. Power-angle curves.

05 Provide short explanations for the following terms [6 points]
a) Surge impedance load
b) Over-excitation limiter
c) PV-curve
d) Speed-droop
e) (n-1) criteria

9) Swing eguation