Mathematical Modeling and Investigation of Optimal Operating Modes of a Micro Hydropower Plant Hydraulic Turbine

Abstract

This paper investigates the determination of optimal operating parameters of a micro-hydropower plant hydraulic turbine equipped with bucket-type blades, designed to operate under variable water discharge and head conditions. The process of converting the hydraulic and kinetic energy of the water flow into mechanical energy is mathematically modeled, and the interrelationships among the main geometric and energy parameters of the hydraulic turbine are analyzed. The relationships between water discharge, hydraulic head, turbine rotational speed, torque, mechanical power, and efficiency are determined based on analytical expressions. In addition, a computational algorithm is developed to determine the optimal installation angle of the bucket-type blades and to select the optimal operating conditions of the hydraulic turbine. Based on the computational results, the optimal turbine parameters are evaluated for operating conditions with a water discharge varying within the range of 0.003–0.009 m³/s. It is determined that, at a hydraulic head of 30 m and a total water discharge of 0.018 m³/s, the optimal rotational speed of each hydraulic turbine is 540 rpm, while the mechanical power is 2150 W. The total mechanical power transmitted from the two hydraulic turbines to the generator is 4300 W. These results demonstrate the feasibility and effectiveness of the proposed turbine configuration for operation under variable water-flow conditions