The paper presents a description of used methods and exemplary mathematical models which are classified into theoretical-empirical models of thermal processes. Such models encompass equations resulting from the laws of physics and additional empirical functions describing processes for which analytical models are complex and difficult to develop. The principle of developing, advantages and disadvantages of presented models as well as quality prediction assessment were presented. Mathematical models of a steam boiler, a steam turbine as well as a heat recovery steam generator were described. Exemplary calculation results were presented and compared with measurements.
Research oriented on identification of operating states variations with the application of mathematical models of thermal processes has been developed in the field of energy processes diagnostics. Simple models, characterised by short calculation time, are necessary for thermal diagnostics needs. Such models can be obtained using empirical modelling methods. Good results brings the construction of analytical model with auxiliary empirical built-in functions. The paper presents a mathematical model of a steam-water cycle containing mass and energy balances and semiempirical models of steam expansion line in turbine as well as heat transfer in exchangers. A model of steam expansion line in a turbine is worked out with the application of a steam flow capacity equation and an internal efficiency of process equation for each group of stages for the analysed turbine. A model of a heat exchanger contains energy balance and the relation describing heat transfer in an exchanger, proposed by Beckman. Estimation of empirical equations coefficients was realised with the application of special and reliable measurements. Estimation criterion was a weighted relative sum of the remainder squares. There are exemplary calculations results presented in the final part of paper.
In recent years, we can observe the development of the thermal diagnosis and operating control systems based on measuring techniques and mathematical modelling of processes improvement. Evaluation of the actual operating state is insufficient to make an optimal operating decisions. Thus, information about the influence of the operating parameters' deviations from the reference state on indicators describing energy consumption of the process (for example specific heat consumption or specific energy consumption) is also necessary. The paper presents methods for generation the information about the influence of the steam-water cycle operating parameters on specific heat consumption in a turbine's cycle. A mathematical model of steam-water cycle for a CHP (Cogeneration - also Combined Heat and Power) unit is being worked out. Methods for calculation of operating deviations with the application of correction curves and a mathematical model are described. Exemplary calculation results are presented.