Vector statement of simultaneous equations method of material and energy balances when calculating actual indicators of thermal efficiency of gas turbine plants

A scalar formulation of the problem of regularization of material flows in respect to gas turbine units is known. It allows you to consider the maximum permissible overall imbalance of mass and energy, as well as the maximum deviation of parameter values adjusted according to the results of balancing of their initial values. At the same time, there is no possibility to consider the individual standardized metrological characteristics of the measuring instruments used to obtain the initial values of the controlled parameters. The problem of simultaneous equations of the material and energy balances of a gas turbine unit is formulated in a vector value within the framework of Tikhonov’s regularization concept when solving ill-posed problems. To solve the problem, the authors have used the analytical method, the method of iteration of analytical solutions, as well as the method of statistical programming. Analytical and numerical solutions of the stated problem are obtained. They, among other things, consider restrictions on the range of permissible parameter values which are determined by the standardized metrological characteristics of measuring instruments. The impact of the applied method of balancing procedure on the results of calculation of the thermal efficiency indicators of gas turbine plants is shown. To apply thermal efficiency indicators of gas turbine units in the systems of automated monitoring, it is recommended to use a vector formulation of the problem of simultaneous equations when solving it by the method of iterations of analytical solutions or by the method of statistical programming. The developed methodology makes it possible to determine reasonable actual values of the indicators of equipment thermal efficiency under condition of the coincidence of the permissible error of the gross efficiency values of a gas turbine plant, calculated according to direct heat and indirect heat balances.