Dear Umair Shahzad ,

I suggest to use Droop control as suitable index for power system frequency stability. you can see full details of Droop control in paper below.

1- A novel control strategy for grid connected hybrid renewable energy systems using improved particle swarm optimization

droop control

Droop control is not an index - it is the typical frequency control strategy for medium term frequency stability.

For an index of the transient stability during a fault, a simple (but good) indicator is the maximum rotor angle swing.

After the fault, indices of the frequency stability should be some function of both the maximum magnitude of the frequency deviation and how long it takes to get back to normal levels.

e.g. search "power system stability classification"

"Power system stability can be broadly classified into rotor angle, voltage and frequency stability. Each of these three stabilities can be further classified into large disturbance or small disturbance, short term or long term."

I guess the definitive article will be the IEEE report by Kundur et al

Rotor angle is the answer as mentioned by Tom Berry

But rotor angle is only for transient stability, For frequency stability, is post-fault frequency a good measure?

If you are doing post-fault simulations, then you could use RMS or mean square of the frequency deviation from the final steady state value as an index. Basing the index on a square of the deviation gives more weighting to larger deviations, taking the mean square over a period will take into account how quickly the system reaches steady state.

This article may be helpful

Article Power System Frequency Stability and Control: Survey

Tom Berry Thanks!

Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact.

index for describing power system frequency stability

Rotor Angle Stability:

Large-disturbance rotor angle stability or transient stability

Use FACTS device especially SSSC

I think the indices such as nadir frequency and rate of change of frequency (ROCOF) are important for frequency stability

It seems that the signals such as Delta Phi or Delta omega are useful for this purpose. Also, you can use the ITAE and ....

In many papers, these indices have been used for identifying the frequency deviation such as below:

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Already mentioned rotor angle theta or rotor accelerations as well as rotor speed that all found by roto angle also shock with PSS devices used