Method of determining a combustor exit temperature and method of controlling a gas turbine

A method of determining an exit temperature of a gas exiting a combustor of a gas turbine for use in controlling the gas turbine, the method comprising:

• determining a mass flow and a temperature of fuel being delivered to the combustor through calculation, the determining the mass flow of fuel being delivered to the combustor being at least partially based on measurements from gas turbine instrumentation;
• determining a mass flow and a temperature of air being delivered to the combustor, the determining of the mass flow of air being based on calculations comprising:
• determining a mass flow of the gas exiting the combustor through a calculated estimation using measurements from the gas turbine instrumentation,
• the determined mass flow of fuel being delivered to the combustor;
• determining a temperature dependence of an approximation of a specific heat capacity of the gas exiting the combustor;
• and
• determining a separate predetermined start exit temperature of the gas exiting the combustor based on:
• the determined mass flow and temperature of fuel being delivered to the combustor,
• the determined mass flow and temperature of air being delivered to the combustor,
• the determined temperature dependence of the approximation of the specific heat capacity of the gas exiting the combustor;
• wherein the determining of the exit temperature of the gas exiting the combustor comprises establishing an iteration equation and applying the iteration equation to at least the separate predetermined start exit temperature to obtain an initial calculated exit temperature,
• wherein the determining the exit temperature of the gas exiting the combustor further comprises defining an interation threshold and iteratively applying the iteration equation to repeatedly obtain a subsequent calculated exit temperature from a previous initial calculated exit temperature,
• wherein the iteratively applying the iteration equation is stopped if a difference between the subsequent calculated exit temperature and the previous initial calculated exit temperature is smaller than the iteration threshold,
• wherein a final subsequent calculated exit temperature is obtained from a final iteration of the iteratively applying the iteration equation after stopping the iteratively applying the iteration equation, and
• wherein the exit temperature of the gas exiting the combustor is the final subsequent calculated exit temperature;
• and
• performing a first mathematical integration of a first difference between the exit temperature of the gas exiting the combustor and a predetermined threshold temperature over a time interval, if the first difference is greater than zero, thereby obtaining a first integral value;
• and
• cooling the turbine section with a cooling fluid having a cooling fluid temperature;
• and
• performing a second mathematical integration of a second difference between the determined combustor exit temperature and a sum of the cooling fluid temperature and a difference threshold over a time interval, if the second difference is greater than zero, thereby obtaining a second integral value;
• and
• controlling the gas turbine based on the first and second integral values by at least one of:
• modifying delivery of fuel and/or air to the combustor and maintaining delivery of fuel and/or air to the combustor.