Hello Mr Reactive.
It sounds to me like you are describing one of our machines.

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I think from your description that these resistors are definitely what I call "field Discharge Resistors" Other Posts here have given other names but that is the nature of an international forum such as this.
If they were resistors in series with the stator, They would have to be located in a high voltage enclosure and not simply placed on top of the control panels.
During DOL Starting of a synchronous machine, such as used on these MG Sets, Most of the starting Torque Comes form the Amortisseur windings, which is a relatively simple looking winding consisting of two rings, one on each end of the rotor, with a few bars ( perhaps 19mm diameter )going axially through the extremity of each of the salient poles.
THe ones I deal with look very much like the so called "Squirell Cage"
When Power is first applied and the rotor is stationery, The rotating magnetic field produced by the stator induces some pretty large currents in the salient pole windings at line frequency. The behaviour is much the same as a Current Transformer, so we MUST provide a path for it otherwise we can get some dangereously high voltages.
DC Field excitation is not on at this time, so we need to provide an alternative path for these currents. Field discharge resistors are used to short out the two ends of the Field supply wires until such times as the DC field excitation is applied to the field.
As the motor accelerates, the frequency falls (with the relative frequency between the rotor and the stator) until it reaches 0 Frequency at synchronous speed. The amplitude of the current drops off during the last 10 or 15 % of the speed range.
Usually the DC field is applied at about 95 to 98% synchronous speed.
These resistors are sized to handle the large induced currents, and the resistance value is selected which will keep the voltage safely below the insulation rating of the windings. Obviously, higher values of resistance will give higher voltages.
During a normal MG Set Start These resistors get very hot, Thus the large physical size.
To answer your question, the magnitude of the Starting Line current is not affected by changes to the value of these resistors, Just the resistor terminal voltage generated by the induced currents and the Total power dissipated by the resistors ( Power = I^2 R ) Where "I" is fixed. There is probably some minimum value, but I do not know the criteria for this.
The Starting current is governed by the design of the Motor Stator windings. The duration of the high starting currents is dependent on the inertia of the rotating part of the MG Set assembly, The mine winders I have dealt with, usually only have two generators, Compared to up to 6 in other applications, So, if my memory serves me right, The starting time should be less 5 or 6 seconds.
on Other Jobs, the starting current has been reduced by inserting Reactors in series with the motor stator windings, and shorted out once the speed gets up above some set speed. As mentioned above, All Of this sort of equipment would have to be located in a High VOltage enclosure and switched by High voltage circuit breakers.
Hope this long winded description helps you understand the starting process.
Best Regards
Tom