In ships, the distribution net work is limited to ship, the few KVA/MW demand could be supplied by single alternator, and power factor control could be done by exciter current to field, and as there is no system stability problem, used power factor could be .9 to .95 lag for better efficiency(lowering the current for equal load demand), fuel saving would be, but not considerable like alternator supplied power system, as (IsqarR) line loss is very less compare to power system, as line length is limited and the power factor of domestic equipment and lightening used are quit high . Saving could be calculated, easily as supply is limited to ship, and supplied by single alternator.

Sorry, what is a coefficient, which you named as "power correction"? The line of corrections is long enough...:)

Could be supplied by a single generator but never is.  Prime mover is a separate generator from other systems.

For the majority of ship types, the fuel used for electrical loads is a very small fraction of that used for main propulsion (the main exceptions to this are cruise ships and other types that have extremely high hotel loads relative to main propulsion). Having said that, there are a number of companies providing systems that aim to improve the efficiency of the on board electrical consumers which includes power factor correction, soft starting, and Variable Frequency Drives (VFD) for pumps to improve operational efficiencies etc. When it comes to calculating these potential savings, it is highly dependent on the scale of the hotel load on board the vessel, and is calculated on a ship by ship basis from recorded usage data to determine if there is a business case. Estimates of these savings can be obtained from case studies by such companies (e.g. DESMI Optisave).