Systems and methods for determination of gas turbine fuel split for head end temperature control

A rotary machine comprising:

• a compressor configured to compress a flow of inlet air;
• a combustor comprising a first combustion zone, a second combustion zone, at least one first fuel nozzle, and at least one second fuel nozzle, wherein said at least one first fuel nozzle is configured to channel a first flow of fuel to said first combustion zone, and said at least one second fuel nozzle is configured to channel a second flow of fuel to said second combustion zone, and wherein said combustor is configured to receive the flow of inlet air, and wherein a fuel split is a fraction of a total flow of fuel that is channeled to said second combustion zone;
• and a computing device comprising a digital simulation of said rotary machine, wherein said computing device is configured to:
• (i) determining a current operating temperature of said first combustion zone using said digital simulation;
• (ii) determining a target operating temperature of said first combustion zone;
• (iii) simultaneously determining a derivative of the current operating temperature of said first combustion zone with respect to a current fuel split using said digital simulation;
• (iv) calculating a calculated fuel split that results in a calculated operating temperature of said first combustion zone using numerical methods;
• and
• (v) channeling the first flow of fuel to said first combustion zone and the second flow of fuel to said second combustion zone, wherein the first flow of fuel and the second flow of fuel are determined by the calculated fuel split;
• and
• (vi) iterating steps i-v until the calculated fuel split equals a target fuel split, wherein the target fuel split is the fuel split that results in the target operating temperature.