The article discusses the importance of small hydro power plants in the Polish power system and defines the legal conditions for the operation of small hydro power plants. The phenomena occurring in the hydrological system of small hydro power plants and their impact on the natural environment were analyzed. An analysis of phenomena occurring in the hydrological system and the activity of small hydro power plants that are operating on the Radunia River helped us identify relations between different types of power plants working in cascades and possibilities of power generation control in period of several days. The above-mentioned analysis has been used in the development of a mathematical model of a hydroelectric plant and cascades of hydroelectric plants. The numerical simulations carried out concerned both the self-operating power plant and a cascade of two identical objects of this type. There is a possibility for small hydro power plant to run as a base load power plant and during periods of high demand as well (peak demand or unexpected loss of generation in the power system). A single hydroelectric power plant can deal with varying peak load demands while adding a second stage increase those abilities. A cascade of reservoir hydropower plants has a much greater ability to store energy and give it back in time. In addition, the existence of a second power plant equipped with a surge reservoir allows for a significant reduction in the amplitude of flows in the river below the cascade, which will reduce the negative impact of the cascade on the environment.
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.