what are the advantages / disadvantages in terms of protection, stability and economic consideratin if a 4 pole generator is coupled with a Gas turbine (5100 rpm) through a load gera box?
This may be too simplistic, the gas turbine speed of 5100 RPM will not work as a direct drive. The four pole generator on a 60 hertz system rotates at 1800 RPM, if it were 6 pole it would operate at 1200 RPM, 2 poles 3600 RPM ad nauseam.
The economics involved would involve the total design from mechanism diameters, forces, initial cost, maintenance expectations, materials etc.
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You can't connect directly and get a useful frequency, so you must use a gearbox (or chain drive, belt drive, etc.). It is unclear what you are trying to compare. Gas turbine vs diesel? Direct drive vs reduction drive?
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