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The Francis hydro-turbine is a typical nonlinear system with coupled hydraulic, mechanical, and electrical subsystems. It is difficult to understand the reasons for its operational failures, since the main cause of failures is due to the complex interaction of the three subsystems. This paper presents an improved dynamic model of the Francis hydro-turbine. This study involves the development of a nonlinear dynamic model of a hydraulic unit, given start-up and emergency processes, and the consideration of the effect of water hammer during transients. To accomplish the objectives set, existing models used to model hydroelectric units are analyzed and a mathematical model is proposed, which takes into account the dynamics during abrupt changes in the conditions. Based on these mathematical models, a computer model was developed, and numerical simulation was carried out with an assessment of the results obtained. The mathematical model built was verified on an experimental model. As a result, a model of a hydraulic unit was produced, which factors in the main hydraulic processes in the hydro-turbine.

The relevance of the study is due to the development herein of a model for reliability optimization of stand-alone power systems with wind turbines and electrochemical power storage devices, with special emphasis within this model put on the specifics of power equipment operation. The key feature of the model developed is that it enables us to factor in the requirements to be met by the equipment as arising from the considerations of dynamic stability of the stand-alone system. When simulating battery storage operating modes, the charge-discharge limits as well as the remaining charge in the storage are taken into account. Thus, the reduction of the total number of considered mixes of the equipment being commissioned is achieved, the computational efficiency of the reliability optimization method is increased, while the validity of modeling results is improved. Development of methods for optimization of reliability of stand-alone electric power systems with wind turbine installations and electrochemical power storage devices while meeting requirements for electrodynamic stability. A stand-alone power system that is assumed to be located in the coastal area of Lake Baikal in the Kabansky State Nature Reserve, Republic of Buryatia, Russia, serves as the object of the study. Calculations are based on multiple simulation of modes of operation of the electric power system by means of the Monte Carlo method. The values of random variables are modeled as per specified laws of distribution and fault rate indicators of power equipment. Modeling of power generation at wind turbines is based on a detailed analysis of real-life weather data (average hourly wind speed, air density and humidity). The method of reliability optimization of stand-alone power systems with wind turbines and electrochemical energy storage devices was developed so as to take into account the requirements to be met by electric power equipment in terms of dynamic stability. The optimization criterion is the minimum expected value of the cost of produced electricity. Power redundanct and energy storage devices are used as means of reliability assurance. The results of calculations attest to the fact that for the natural and climatic zone under consideration, the use of vertical axis wind turbines in a stand-alone power system proves more efficient than the use of horizontal axis wind turbines