Power system stability-FAULT Analysis.pptx

Power system stability

1. POWER SYSTEM STABILITY Lesson Summary 1. Small Signal Stability 2. Examples

2. Instructional Objective On completion of this lesson a student should be able to : Explain the concept of small Signal stability. Develop the mathematical model for small signal stability. Analyze small signal stability for single machine infinite bus system

3. Cont … In this lesson, we will continue the discussion with the small signal stability. W hen the disturbance to the system is much smaller we can think of linearizing the swing equation of the machine and use linear system analysis. Consider the problem of small signal stability for a single machine infinite bus system.

4. Cont … A disturbance of a of very small magnitude, occurs and perturb the system variables for very small values. The equation is non-linear, but at the operating point, normal operation before the disturbance and if the disturbance is small, we can linearize this dynamic equation, about that point and study the perturbation, as a linear system analysis.

5. Cont … The roots of this polynomial tell us about the dynamics of this system. This is how we analyze the dynamics of a linear system.

6. Cont … What we are looking at is, whether due to the small perturbations about the operating point . The system is going to come back to the same operating point or it is going to runaway. That is, whether the oscillations get damped out or these oscillations will buildup and the system will get desynchronized from the rest of the system.

7. Power angle characteristic for a synchronous machine (Gen and Motor)

8. Cont … The big dashed waveform is a cylindrical rotor machine power angle characteristic for the cylindrical rotor machine in the generating mode a nd motoring mode. The solid line is for a salient pole machine; It is a combination of the two dashed curves. The small curve representing a second harmonic term or reluctance term due to/saliency of the machine poles.

9. Cont … Initially the slope which is the synchronizing coefficient is positive. When we slowly increase the mechanical input to the machine. What is going to happen?

10. Cont … The power output and delta angle will keep on increasing gradually . So , machine operating point will keep on moving. That is delta angle will keep on increasing . Since , we are increasing the mechanical input and electrical power output is also increasing and there is an increase in delta angle , therefore the machine is running in synchronous condition .

11. Cont … That is the machine speed remains synchronized. We keep on doing this , till we reach this maximum point . Now , suppose , if we increase the mechanical input by a very small amount at this point delta angle will again increase and cross the 90 degrees with the electrical output of the machine reducing therefore, there is going to be a difference between the two powers.

12. Cont … The machine will accelerate and delta angle will keep on increasing. So , delta angle increases, then further the power output of the machine will further decrease . And this will continue and the system will lose synchronism, because the speed will keep on increasing. Even, if we have not increased the mechanical power, beyond this value . So , this point is, where we can get the maximum power output from the machine.

13. Cont … We cannot get any more power output from the machine even if we work the machine very gradually . So , we call this point as the maximum power output or Pmax and we also call this point as the steady state stability limit . That is the machine will lose its stability if we try to operate beyond this point even if there is no dynamics or transient taking place and the system is all the time working in steady state.

14. Cont … At the steady state stability limit, the value of the synchronizing coefficient is 0. Beyond this point the slope becomes negative. A lpha is positive, which means the system is going to become unstable. The roots come in the right half of the S plane, which shows instability, because the dynamics or the oscillations are going to build up.

15. Cont … T he slope for the salient pole machine is larger than the slope for the cylindrical rotor machine in the normal operating region. That is in the stable operating region. That is the salient pole machines are more, stiff and the change in their delta angle for a given increasing power output is much less compared to that of the cylindrical rotor machine.

16. Cont … T he maximum power point for a salient pole machine is reached, below 90 degrees whereas for a cylindrical rotor machine is the maximum power is reached at 90 degrees with no dynamics building up. Going back to small disturbances the swing equation is written as follows:

17. Cont … Starting at delta 0 at t equal to 0 . A perturbation of delta, delta 0 and then the system will go through a dynamics. If we have the damping coefficient d is positive the system goes through some oscillations and slowly dying out and finally, the system will reach the angle delta 0 again .

18. Cont … But, if the value of d the damping coefficient is negative then we go through this second curve, where we find that these oscillations are gradually building up and the system will finally, lose synchronism , because delta angle will keep on going higher and higher and after sometime, it will be a runaway situation.