The main advantage of using a higher model of the generator (typically 6th order model ) is the ability to capture accurate dynamics similar to the real-world.

As you might already know from the control theory, the first-order model only provides a simple increase or decrease response but a second-order model provide a bit sophisticated response: overshoot, under-shoot response and so on....

I would say the major disadvantage of using a higher model will be the increase in computational time as well the necessity to validate with experimental results.

Using a higher model requires many parameter values unlike a simple model, thus, the choice will simply depend on the available parameter values.

The following book provides generator parameters for some of the synchronous generators:

https://www.academia.edu/34885349/Power_Systems_Control_and_Stability_2nd_Ed_by_P_M_Anderson_a_a_Fouad_pdf

Please note the duality between this problem and the pendulum .

Higher order models are

used to take care

of nonlinearity in the

system.

I hope this help

The selection of an appropriate modeling details is based on the target. If you would like to capture more details electromechanical/electromagnatic dynamics, then more details are preferable. It is a matter of compromise between simplicity and accuracy. In many transient stability studies, only the 2nd order dynamic model of the machine is used for simulating the electromechanical dynamics. If the field circuit dynamics are of interest, then the 3rd order dynamics is used.

Prof. Omar hits critical issues, which are the uncertainty and the unavailability of many parameters.

I fully agree with prof. Mohamed EL-Shiny and Prof. Omar H. Abdalla.

Choice of complex model is based on the problem before hand and accuracy depends on the ability to get correct values for the parameters.

Dear Subin Koshy, as Mohamed EL-Shimy wisely clarified, the selection of the model will depend of the level of detail you want to capture. Regarding that, a key factor is defining the time scale of your problem.

For instance, if you are simulating slow controls, such as tertiary frequency control, it would be overkill to use a 6th-order model of the synchronous machine and 2nd-order model is more than adequate. This is because the reaction time of your controller is in the order of minutes, so basically all electric quantities will be in steady-state (or your system will be already unstable) by the time your controller react.

On the other end of the spectrum, if you are analyzing electric insulation or the effect of lightning in a power system, controllers play no role but a 6th-order model is not enough. So you will have high-order models (typically a polynomial one obtained by system identification) with capacitances and other nonlinear effects usually ignored in stability studies.

In between these two extremes, you have several types of stability (PLL, rotor angle, voltage, frequency), protection and power quality (harmonics, flickers, sags, swells etc) studies. For each one of them, you may or may not simplify your generator model, ignore certain controllers and so on. In summary, proper modelling of a synchronous machine and a power system is not only hard science, but also a bit of art.

Some interesting references:

Article Microgrid Stability Definitions, Analysis, and Examples

IEEE Guide for Synchronous Generator Modeling Practices and Parameter Verification with Applications in Power System Stability Analyses

https://ieeexplore.ieee.org/document/9020274/

A Tutorial on Dynamics and Control of Power Systems with Distributed and Renewable Energy Sources Based on the DQ0 Transformation

http://www.mdpi.com/2076-3417/8/9/1661

Tutorial on the Impact of the Synchronous Generator Model on Protection Studies

https://cms-cdn.selinc.com/assets/Literature/Publications/Technical%20Papers/6328_Tutorial_NF-GB-SS_20111220_Web2.pdf?v=20191007-202645

Feel free to contact me if you want more specific references to your problem.

I think that impact on the response time of the genertor