UNIT-V POWER SYSTEM STABILITY

UNIT-V
POWER SYSTEM STABILITY
1. Derive swing equation for a single machine connected to infinite bus system.




2. A 400 MVA synchronous machine has H1=4.6 MJ/MVA and a 1200 MVA machines H2=3.0 MJ/MVA. Two machines operate in parallel in a power plant. Find out Heq relative to a 100MVA base.





3. A 100 MVA, two pole, 50Hz generator has moment of inertia 40 x 103 kg-m2.what is the energy stored in the rotor at the rated speed? What is the corresponding angular momentum? Determine the inertia constant h.

4. The sending end and receiving end voltages of a three phase transmission line at a 200MW load are equal at 230KV.The per phase line impedance is j14 ohm. Calculate the maximum steady state power that can be transmitted over the line.

5. Explain Equal area criterion in transient stability.





6. A single line diagram of a system is shown in fig. All the values are in per unit on a common base. The power delivered into bus 2 is 1.0 p.u at 0.80 power factor lagging. Obtain the power angle equation and the swing equation for the system. Neglect all losses.



7. Explain critical clearing angle and critical clearing time in transient stability.






8. A 50Hz synchronous generator capable of supplying 400MW of power is connected to a larger power system and is delivering 80MW when a three phase fault occurs at its terminals, determine (a) the time in which the fault must be cleared if the maximum power angle is to be -85˚ assume H=7MJ/MVA on a 100MVA base (b) the critical clearing angle.



9. A 2220 MVA, 24KV and 60 Hz synchronous machine is connected to an infinite bus through transformer and double circuit transmission line, as shown in fig. The infinite bus voltage V=1.0 p.u .The direct axis transient reactance of the machine is 0.30 p.u, the transformer reactance is 0.20 p.u, and the reactance of each the transmission line is 0.3 p.u,all to a base of the rating of the synchronous machine. Initially, the machine is delivering 0.8 p.u real power and reactive power is 0.074 p.u with a terminal voltage of 1.0 p.u. The inertia constant H=5MJ/MVA. All resistances are neglected. A three phase fault occurs at the sending end of one of the lines, the fault is cleared, and the faulted line is isolated. Determine the critical clearing angle and the critical fault clearing time.


The current flowing into the infinite bus is

The transfer reactance between internal voltage and the infinite bus before fault is
X = Xg +XT +Xtr.line
X = 0.3 + 0.2 +0.3/2 = 0.65
The transient internal voltage is
E = V +j X I = 1.0+ (j0.65) (0.8- j0.074)
= 1.17
Since both lines are intact when the fault is cleared, the power angle equation before and after the fault is


The initial operating angle is given by = 0.8
δ0 = 26.388 = 0.46055 rad
δmax =180º - δ0 = 153.612 =2.681rad

Critical clearing angle


δc =
Critical clearing time tc = = = 0.26 second
10. A synchronous generator is connected to a large power system and supplying 0.45 pu MW of its maximum power capacity. A three phase fault occurs and the effective terminal voltage of the generator becomes 25% of its value before the fault. When the fault is cleared, generator is delivering 70% of the original maximum value. Determine the critical clearing angle.



11. Find the critical clearing angle of the power system shown in fig. for a three phase fault at the point F. Generator is supplying 1.0 p.u MW power under pre-fault condition.





12. What are the factors influencing transient stability?

13. What are the numerical integration methods of power system stability? Explain any one methods.
i. Point by point method or step by step method
ii. Euler method
iii. Modified Euler method
iv. Runge-Kutta method(R-K method)

Step by step method