A new methodology to solve non-linear equation systems using genetic algorithms. Application to combined cyclegas turbine simulation

This paper shows a methodology to sort out the equations of a non-linear system in order to solve it by the fixed-point method. The arrangement of the equations is established by a genetic algorithm that deals with a population of possible resolution processes of the system. The method is specially useful in the following situations: first, when the system is very non-linear and has many variables (where the Newton–Raphson method does not work properly); second, when the number of equations and variables may be altered because the equation system may change in each simulation and, therefore, more than one only solution process is needed if the fixed-point process is employed. As an example, the methodology has been applied to solve the equation system that models the behaviour of a heat recovery steam generator of a combined cycle power plant at full load and part load conditions.