Energy Engineering - Wind, Hydro and Geothermal Power Generation

Exam test 1

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Wind, Hydro and Geothermal Power Generation AY 2021-22 Example of Test - 1 Prof. Paolo Silva Time: 90 minutes Instructions for the exam: 1) Clearly indicate your name on all the sheets you will deliver. 2) Give a synthetic and clear answer to as many questions as possible. The final score will be normalized according to the average results. 3) Talk with colleagues and / or cheating will cause the cancellation of the exam. 1. Consider a three-bladed, horizontal-axis wind turbine with a rotor diameter of 110 m coupled to a full scale converter. Analyze the behavior of the turbine in the following conditions: cut-in, a wind speed between the cut-in and nominal condition, nominal condition, cut-off. For each point indicate the wind speed and the expected/calculated values of C p, λ tip, rotational speed and electrical power output (assume reasonable values for the main parameters). Qualitatively plot the points on a graph with respect to the wind speed. (5 points) 2. Plot the lay-out of a geothermal direct steam cycle with 2 pressure laminations and draw the corresponding T-s diagram. Please highlight the main technical issues related to the plant op- eration. (5 points) 3. Considering a run-of-river plant based on a diversion channel, define the flow duration curve and show how it can be used to obtain an optimal preliminary design of the turbine. Please show how it is possible to graphically evaluate the annual flow rate elaborated by the turbine (it is not necessary to give a numerical example, just provide a qualitative evaluation). (5 points) 4. Explain the concept and the calculating method of the Levelized Cost of Electricity (LCOE) for renewable energy sources (RES). Comparing different power plants/RES with the same invest- ment cost (€/kW), what are the most important factors affecting the LCOE? (5 points) Exercise (10 points) A three-bladed horizontal axis wind turbine is equipped with a variable speed and variable pitch regulation system. The turbine has a rotor diameter of 130 m, a rated wind speed of 11 m/s and is designed for an optimal λ tip equal to 7,5. Knowing that the machine fluid-dynamic performance is equal to 81% (ratio between the real Cp and the Cp of Betz), the efficiency of the gearbox is equal to 97% and the mechanical-electric generator efficiency is equal to 97,8 %, compute (i) the rated electric power developed in the design condition at sea level, 1 atmosphere and 25°C (the air density in these conditions is equal to 1,225 kg/m 3) (2 points). Calculate (ii) the rotational speed at design conditions (1 point). Assuming the validity of the Betz theorem, calculate (iii) the pitch angle at the blade tip knowing that the optimal incidence angle is equal to 8° (4 points). The electrical power developed by the turbine at the cut-in speed is equal to 235 kW. Assuming that the turbine has no lower limitations for rotational speed and considering the same mechanical and electrical efficiency of the design condition, determine (iv) the wind speed at cut-in conditions (2 points) and (v) the machine rotational speed (1 point). Exercise (10 points) AD 13273 m2 WID nom 10820,8 kW W Betz 6412,3 kW Wpale 5194 kW W el 4927 kW Cp 0,480 om ega 1,269 rad/s 12,12 rpm u [m/s] vD [m/s] w [m/s] Teta [rad] Teta [°] Gamma [°] tip 82,50 7,33 82,83 0,0886559 5,1 -2,92 W rotor 247,7 kW W Betz 305,8 kW WID 516,1 kW v cut-in 3,99 m/s omega cut -in 4,40 rpm 0,460 rad/s om ega cut -in 0,460 rad/s