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Your alternative 1:
Model GENCLS is not intended to be used for physical generators. It can be used to model the short Circuit Power and inertia of an equivalent generator, representing the rest of the system (Outer system).
Here the rest of the system has more than 19900 generators and the Study System only have 100 gens. The damper Windings are not represented in GENCLS so it is better to use a real generator model, like GENROU, with standard values, for all generators in the Outer System. You can also add a simple exciter if you want, e.g. SEXS.
Alternative 2:
GNETting all unknown generators is possible. The problem is that 99.5% of the system will be a passive network without any voltage source. It is only the voltage dependency of the loads that stabilises the voltage! There will thereby be no in-feed of short Circuit Power from the Outer System.
Hence, I would recommend to go for alternative 1 and use GENROU instead of GENCLS, especially if bad damping is detected when GENCLS is used.