Question

Consider the classical power system where one generator is connected to the infinite bus through two transmission lines. We want to study the transient stability for a fault on one of the two lines. The generator parameters are as follows: Pm = 1, H = 4, KD = 5, x'd = 0.25, E' =1.4. The transmission line where the fault occurs has a line reactance of 0.6 pu. The other transmission line that remains in service has a line reactance of 0.75 pu.a) Suppose the fault occurs at the middle of the line. Write out the swing equations for the pre-fault,fault-on and post-fault systems.

Answer 1

Solution:

Power system stability is a very important issue for guaranteeing continuous sustainable power transmission to load centers. Power system stability guarantees acceptable operating points under normal operating conditions and to adjust to new acceptable operating points as the power system suffers abnormalities like faults of different types or even under load variations. One of the stability issues is maintaining synchronism among synchronous machines forming up the power system. The power system is continuously subjected to various disturbances. Still, the system and the perturbation size caused by a specific disturbance in comparison to the size and capability of the whole interconnected systems so that the effects on the system could not be predicted. Large disturbance occurs on the power system like severe lightning strikes, and loss of transmission line. The ability of a power system to maintain the power flow following a large disturbance and sustain an acceptable operating condition is called transient stability.

Given Data:

Pm = 1, H = 4, KD = 5, x'd = 0.25, E' =1.4.

Let us consider a power system with a generator connected to the infinite bus with two transmission lines as follows:

The pre-fault swing equation for generator which occurs on one transmission line with line reactance 0.6 pu

therefore, P_m - P_e = 1 - 1.64 sin

The during Fault Swing equations for generating the electrical power of generator 1 is zero because the fault is close to the line  

therefore the swing equation is ?/180f . dho² /dho t² = P_m

= 1

The post Fault Swing equations for generator

From the system numerical analysis and results it can be clearly concluded that the system shows ruggedness and reliability in its operational behavior as it can adjust rapidly to its new operating points and stay running satisfactorily but the system enters the runaway condition as the fault clearing time is dramatically increased.