Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation (AY 2022-23) 6 th February 2023 Prof. Paolo Silva Time: 90 minutes Instructions f or the examin ation: 1) Clearly indic at e your nam e on all the s heets you will deli ver. 2) G ive a s ynthetic and c lear ans wer to as man y ques tions as poss ible. The f inal sc ore will be n ormaliz ed acc ording to the averag e res ults . 3) T alk with c oll eagu es and / or c heating will c aus e the c anc ellati on of the exam. 1. Consider a three-bladed, large-scale horizontal axis wind turbine whose control strategy is designed to operate at sea lev el based on undisturbed wind speed measurement. How would the power curv e change if the same turbine were installed in the mountains, respectiv ely (i) with no adjustment of the regulation strategy and (ii) with adjustments? (5 points) 2. With reference to geothermal power plants, what are hybrid cycles and in which cases are they applied? What are the potential adv antages ov er both direct and indirect cycles? (5 points) 3. W hat are the effects of a gust on a modern large-scale wind turbine? What are the methods and technol- ogies to mitigate its negative effects? (5 points) 4. How does the ecological flow affect the annual energy production of a hydroelectric plant? What kind of plants are affected by this limitation? Explain how to calculate the reduction in energy production and plot the effect on the flow duration diagram. (5 points) Exercise (11 points) A three-bladed horizontal axis wind turbine is equipped with a variable speed and v ariable pitch regulation system. The turbine has a rotor diameter of 123 m, a rated wind speed of 11.5 m/s, a nominal electrical power output of 5 MW and is designed for an optimal λ tip equal to 7.8 (air density 1.225 kg/m 3). Knowing that the efficiency of the gearbox is equal to 97% and the mechanical-electric generator efficiency is equal to 97.6 %, compute (i) the machine fluid-dynamic performance (ratio between the real Cp and the Betz Cp) (2 points) and (ii) the rotational speed at design conditions (1 point). Assuming the v alidity of the Betz theorem, calculate (iii) the pitch angle at the blade tip knowing that the optimal incidence angle is equal to 8° (3 points). The electrical power dev eloped by the turbine at the cut-in speed is equal to 141 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 in cut-in conditions (1 point) and (v) the variation of the pitch angle with respect to the design conditions (1 point). Finally, considering a wind speed of 7 m/s, calculate (v) the resultant of the axial forces on the nacelle (2 points) and (vi) the torque produced ov er the low speed shaft (1 point). What are the assumptions you need to consider in this case? Results (exercise) AD 11882 m2 WID nom 11068,8 kW W Betz 6559,3 kW Wrot or 5281 kW Cp 0,477 Eta 80,5% omega 1,459 rad/s 13,93 rpm u [m/s] vD [m/s] w [m/s] Teta [rad] Teta [°] Gamma [°] tip 89,70 7,67 90,03 0,0852629 4,9 -3,11 W rot or 148,9 kW W Betz 185,0 kW WID 312,2 kW v cut-in 3,50 m/s No pitch variation! vD 4,7 m/s mass flow rate 67927 kg/s F ax 317,0 kN Mechanical power 1191,10 kW omega 0,89 rad/s 8,48 rpm torque 1341,6 kNm