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20-02-16v

No IAN

DEE-24106 Electric power systems Angle stability

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1. A) A 60 Hz four pole turbogenerator rated 500 MVA, 22 kV has an inertia constant
of H=7.5 MJ/MVA. Find J:5x500 = 1350 3750 Ma
(a) the kinetic energy stored in the rotor at synchronous speed and
(b) the angular acceleration if the electrical power produced by the generator is
400MW and the mechanical input power to the generator is 552 MW (the rotational
losses are neglected). D 0 K — 264 E 5
B) If the acceleration calculated in A) remains tonstant for a period of 15 cycles, find
the change in the angle 5 in electrical degrees in that period and the speed in
revolutions per minute at the end of 15 cycles. Assume that the generator is
synchronized with a large system and has no accelerating torgue before the 15-cycle
period begins.

C) The generator is delivering rated megavolt-amperes at 0.8 power factor (lagging)
when a fault reduces the electrical power output by 40%. Determine the accelerating
torgue in newton-meters at the time the fault occurs. Neglect losses and assume
constant power input to the shaft.

2. A) The power delivered by a generator (on the left end of figure 1) through the
depicted system is 0.8 per unit when both the terminal voltage of the machine (V;)
and the voltage of the infinite bus are 1.0 pu. Determine the power-angle eguation
for the system during the specified operating conditions.

j0.5

E' V:

Xe'=j0.2 jO.1
O <

 

 

 

 

 

 

10.5
Figure 1.

B) If a three-phase fault occurs on the power system at a point on one of the
transmission lines at a distance of 30% of the line length away from the sending-end
terminal of the line, determine

(a) the power-angle eguation during the fault and

(b) the swing eguation. Assume the system is operating under the conditions
specified in problem 2A when the fault occurs. Let H=5.0 MJ/MVA.

3. Find the steady state power transfer limit of a system consisting of a generator
(eguivalent reactance 0.50 pu) connected to an infinite bus through a series
reactance of 1.0 pu. The terminal = of the generator is held at 1.20 pu and the
voltage of the infinite bus is 1.0 pu.

€ 405 (0 PANT Nu = Hippi
& 2 , ; | 3 ale i
* 1204 il = pev TAA
Els — > Jlailx kut - 63 Ind

 
 

4. A generator is supplying power (P=176 MW, power factor cos) = 0,8ina) through a
transformer and two transmission lines to a stiff system as depicted in Figure 2. At
certain moment, a three phase fault occurs at location A (at the beginning of the
line). The protection of this line is such that the circuit breakers at both ends of the
line open at a time corresponding to power angle 8, = 50?. Fast auto-reclosing of the
faulted line is started at a time corresponding to power angle ö> = 857. However, the
auto-reclosing is unsuccessful due to a permanent fault and the circuit breakers thus
open again at a time corresponding to power angle 83 = 120". Is this system stable?
Use the egual area criterion for the stability analysis. Losses are not taken into
account.

 

 

 

 

 

 

 

 

 

 

 

 

1 2
= F270km
( x=0,350/km
1 P
= - EN stif
10,5 kV 10,5/220 kV network
200MVA 200MVA 220 kV
xa=160% x =10%
xg=20%
Figure 2.

5. A generator is connected to a stiff system (voltage 1.0 pu) via a double line. Figure 3
represents the reactances and voltages of the system in per unit values. At certain
moment, a three phase fault occurs at location P. Conseguently, the circuit breakers
A and B trip simultaneously and remain in the open position. The generator supplies
1.0 pu power before the fault. Determine the critical clearing angle &r ie. the
maximum value which the power angle may reach so that the system still maintains
its stability. Use the egual area criterion for the stability analysis.

j0,15 — j0,30 j0.15

= jo,10]
(=
AP B

E,=1,30 U=1,0
x'=j0,30

 

 

 

ON