# Quantiative criteria for instability system

Hi, all. I'm trying to analyse angle stability of machines in the system, which costs me a lot of time because I have to run dynamic simulation over and over again to find CCT (critical clearing time).

That's so I came up with an idea to run it automatically. The script isn't so hard, I guess I can deal with it, but the problem is how to identify if a system stability or not.

Manually, I could say if a system is instability by some signs, such as that machines' speeds and angles are seperated largely, or voltages drop below 0.5 (voltage stability), etc. However, defining a quantitative criteria which works for every machines in the system is not as easy.

I came some ideas for the criteria, but not so sure about them:

- the difference between any 2 machine's angles isn't bigger than 100 degree.
- The difference between any machine's speed and the average speed of the system must be smaller than 0.1. Average speed is calculated like this: Sum((Machine speed)*(machine inertia constant))/ (Sum Inertia constants)
- d Delta/dt turn sign (from negative to positive or vice visa) more than once, in which Delta is the difference between angle of interested machine and reference machine.

I want to know is there any available function in pss/e that can distinguish instability system? If not, is there any other idea to make it?