Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation AY 2021-22 21 st June 2022 Prof. Paolo Silva Time: 90 minutes Instructions for the examination: 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 large scale three-bladed horizontal axis wind turbine, designed to operate at stand- ard conditions (0 m a.s.l. and 15°C, corresponding to an air density of 1.225 kg/m 3). Provide a numerical example for a real machine, by assuming characteristic wind speeds and calculating the respective rotational speed and power output. Discuss the modifications you will make to the control system in order to operate the turbine at an altitude of 3000 m a.s.l. with an average ambient temperature of 5°C. How will the characteristic wind velocities and rotational speed change? (5 points) 2. Draw the temperature-heat diagram and the plant layout for a binary geothermal plant coupled to an Organic Rankine Cycle with 2 pressure levels. Number the points on both schemes and discuss the importance of evaporation pressure on net electric efficiency and second law effi- ciency. (5 points) 3. Discuss the strategic importance of hydroelectric power plants with respect to the increasing dispatching requirements of the electricity grid. What is the role of different kinds of hydro plants in the electric system? (5 points) 4. Discuss the potential advantages of vertical axis wind turbine technology (VAWT) over the state of the art of three-bladed HAWT for off-shore applications. (5 points) Exercise (11 points) A run-of-river hydroelectric plant with a Kaplan turbine, in a diversion-channel configuration, is placed in corre- spondence of a hydraulic head of 15 m and located on a river with flow rates described by the following duration curve: Days Q [m3/s] 0 60 10 12 120 12 365 2 Assuming a linear trend of the duration curve between the points described in the table and considering an eco- logical flow requested for the site equal to 0.5 m 3/s, (i) identify the nominal flow rate of the plant which at a first analysis appears to be suitable for maximizing the plant's profitability, knowing that the plant cost is proportional to its power (2 points). Knowing that the minimum operating flow of the turbine is equal to 25% of the nominal value, calculate (ii) the number of days of operation (2 points) and (iii) the annual volume of water derived by the plant (2 points). Moreover, knowing that the penstock has a diameter of 2 m, a length of 44 m, and a dimensionless friction coeffi- cient of 0.03, determine (iv) the net hydraulic head in nominal conditions (1 point) (density of water 1000 kg/m 3). Please note that the distributed friction losses are calculated as: ∆������������= ������������ ∙ ������������ ������������ ∙ ������������ ������������ 2 2 Considering for simplicity that friction losses in all hydraulic conditions are equal to the nominal value, calculate (v) the average annual productivity of the plant (2 points), knowing that the hydraulic efficiency of the turbine is equal to 90% in conditions of nominal flow rate, equal to 80% (simplified hypothesis) in all other conditions and that the organic-electric efficiency is equal to 88%. Finally calculate (vi) the nominal plant power (1 point) and (vii) the equivalent operating hours expected (1 point). Results – exercise (i) Q nom [m3/s] 11,5 Qmin m3/s 2,875 AQ/gg 0,0408 (ii) working days 331 m3/year part I 1,19E+08 m3/year part II 1,31E+08 (iii) m3/year tot x 1000 250263 A penstock [m2] 3,14 v penstock [m/s] 3,66 DH 0,451 (iv) net head [m] 14,549 prod I [MWh] 3744 prod II [MWh] 3657 (v) prod tot [MWh] 7401 prod tot [MJ] 2,66E+13 (vi) Pnom [kW] 1300 (vii) heq 5693