IEA
Electric Power Systems
Examination in Electric Power Systems
Monday 21 October, 2013, 8.00-13.00
Maximum score for each problem is 10 points. To pass you need 20. Use English or
Swedish for your solutions. Motivate all your answers and draw relevant circuit
diagrams. Allowed: Calculator, formula sheet, TEFYMA or similar.
1
V11
jx13=j0.2
3
V33
PL3+jQL3
PG1+jQG1
jx12=j0.25
jx23=j0.5
jx34=j0.4
4
2
PL4+jQL4
PG2+jQG2
V22
jx24=j0.2
V44
1a.
Set up the p.u. bus admittance matrix for the system above, where p.u.
impedances are given. (3p)
1b.
Prepare for load flow calculation by writing the active and reactive power
balances at bus 2. Use only quantities shown in the figure such as PG, QG, PL,
QL, V,  and x. (4p)
1c.
Suggest a bus type (slack, PV or PQ bus) for each bus. (3p)
2a.
For the system shown in problem 1, determine the (p.u. positive sequence) shortcircuit impedance (Thévenin impedance) at bus 2. Assume that the generators
have xd”=0.1 p.u. and disregard loads. (3p)
2b.
Further assume that the prefault voltage at each generator is 1 p.u. and determine
the p.u. short-circuit capacity at bus 2. (2p)
The network in problem 1 is meshed with several paths from each generator to
each load. If (any) one line is lost and the current limits of the remaining lines
are not exceeded, the loads can still be supplied.
2c.
Does loss of a line increase or decrease three-phase short-circuit current?
Motivate briefly. (1p)
2d.
Voltage sensitivity to load changes is inversely proportional to short-circuit
capacity. Does loss of a line increase or decrease this sensitivity? Motivate! (1p)
2e.
Show that connection of a shunt capacitor increases voltage at a bus where the
Thévenin impedance is entirely inductive. (3p)
OS
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IEA
3.
Electric Power Systems
In order to conveniently analyze the system below all values should be
converted to p.u. on common base: Using 125 MVA and 130 kV as bases for the
transmission lines gives reactance values for each of x=0.72 p.u.
G
T2
T1
V0°
Eq’
Rated values on component bases: G 125 MVA, 11 kV, 50 Hz, x d’=0.25 p.u.
T1 150 MVA, 11/130 kV, xeq=0,07 p.u. T2 125 MVA, 120/72 kV, xeq=0,07 p.u.
3a.
Generator output P = 85 MW, Eq’=11.35 kV and x d’=0.25 p.u. Use MVA base
and voltage base that agree with 125 MVA and 130 kV and determine p.u.
values of P, Eq’ and x d’. (3p)
3b.
Use MVA base and voltage base that agree with 125 MVA and 130 kV and
determine p.u. value of transformer T1 reactance. (3p)
3c.
Transformer T2 has xeq=0,07 and low-side voltage V=70 kV. Use MVA base
and voltage base that agree with 125 MVA and 130 kV and determine p.u.
values of xeq and V. (4p)
4
A zero  three-phase short-circuit occurs on the line side of circuit breaker CB3
in the system below when it operates at steady state. The fault is cleared by
tripping the faulted line as  reaches its post-fault equilibrium value. Use
assumptions common in transient stability analysis and do the following:
xtr
CB1
x1
CB2
H=3 s
Pt=1 p.u.
CB3
x2
CB4
x’d= 0.3 p.u. xtr=0.1 p.u.
Pt
E’ q 
Vbus0
x1= 0.6 p.u.
x2= 0.4 p.u.
E’q=1.3 p.u. Vbus=1 p.u.
4a.
Compute maximum values of active power that can be delivered by the
generator before, during and after the fault. (3p) 
4b.
Draw Pe() and indicate the accelerating area and the maximum decelerating
area. (2p)
4c.
Compute relevant equilibrium values of . (3p)
4d.
Compare the two areas in b. numerically. Is the system transiently stable? (2p)
OS
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IEA
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Electric Power Systems
Somewhere in Småland, a zero  earth fault occurs in the a-phase on the 20 kV
side of a 20 MVA, 130/20kV /Y transformer fed from a 130kV, 50 Hz system.
The network feeding the transformer can be described as Thévenin equivalents
for positive sequence (VTH1=130 kV, ZTH1), negative sequence (VTH2=0,
ZTH2=ZTH1) and zero sequence (VTH0=0, ZTH0).
The transformer has series reactance Xeq and the neutral point of the Y winding
is either left unconnected or grounded through a reactance Xn=Ln – a Petersen
coil. The transformer phase shift can be ignored.
The transformer feeds a new 40 km long 20 kV cable. It can be represented by a
-link with R=X=0 leaving only shunt capacitance represented by susceptances
(jC/2) jB/2. jB1=jB2=jB0=j0,016 p.u. using base values 100 MVA and 20 kV.
5a.
Draw the three sequence diagrams of the system (including network, transformer
and cable) as seen from the 20 kV bus. Let the reactance Xn be connected
through a switch. (3p)
5b.
With the switch open and transformer ungrounded, consider the fault situation:
 Set all series impedances Xeq, ZTH1, ZTH2 and ZTH0 to zero as they are small
compared to 1/B.
 Redraw the diagrams that are now connected by the fault.
 Determine the capacitive earth fault current in the a-phase in Amps.
(Hint: B1 should not influence the fault current.) (4p)
5c.
With the switch closed (and series impedances still zero), show that the fault
current (for this fault) can be brought to zero by selecting a certain value of Xn.
(2p)
5d.
Determine the p.u. value of the reactance Xn that cancels the capacitive earth
fault current. (1p)
GOOD LUCK!
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