Abstract-The maximum allowed per unit value of the synchronous reactance of a synchronous generator is normally decided by the grid codes in order to maintain the stability of the system. For the converter-fed synchronous hydrogenerator, the steady state stability can be maintained by the frequency converter. In this paper the constraint on the synchronous reactance is relaxed from 1.2 per unit to 2.0 per unit and then removed altogether. The cost of the active materials and the net present value of the cost of losses are calculated for each case and compared. Three different nominal frequencies are also used to find which one gives the lowest total cost. The total generator cost is reduced when the synchronous reactance is increased. The lowest cost of the 50 Hz designs are lower than the cost of the 25 and 75 Hz designs.