How we can enhance the power of large gas generator, what parameters have to change or improve. Can it take place without any improvement or changing in Turbine design?
If you mean an electrical generator that runs off gas, then there are way to extract more power with the same fuel flow, or decrease fuel flow at the same power output (i.e. to increase efficiency).
There are many companies using Organic Rankin Cycle (ORC) to recover waste heat from the exhaust.
Besides adding an OR the intake air to the compressor can be pre cooled thus increasing its density and augmenting power. A second method used more recently in a number of engines is by injecting water (fog or spray) in between stages of the compressor for the same objective. In this second case the air is denser but it also involves dealing with higher humidity.
To obtain more power than the designed calculation you may have effects on other components of the turbine. For example if your generator is running on gas turbine you will be ptobably able yo mske more power ftom the generator by increasing the fuel burning teperature within the combution chamber. However, in this way the life of internal parts of the turbine and generator us shortened.
From a performance perspective even a small reduction of the clearance between the turbine blades and the casing will increase the engine's power. However, this option should be implemented in a careful manner for avoiding any risks.