Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation AY 2021-22 25 st July 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 three-bladed, horizontal-axis wind turbine whose regulation strategy is designed to operate at sea level according to the only measured value of undisturbed wind speed. How would the power curve change if the same turbine is installed at 4000 m asl respectively (i) with no adjustment of the regulation strategy and (ii) with adjustments? (5 points) 2. Provide a definition of the Levelized Cost of Electricity (LCOE) for renewable power plants. How is it affected by the availability of the renewable source? What are the other parameters affect- ing the LCOE? (5 points) 3. Consider a medium-head hydro power plant whose flowrate allows the adoption of either a Kaplan or a Francis turbine. Explain the aspects that must be considered to choose the optimal kind of turbine. (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 wind farms and especially for floating applications. (5 points) Exercise (11 points) A geothermal source has the following characteristics at the outlet of the well: temperature 180°C, enthalpy 1050 kJ/kg. Consider a single flash direct steam cycle cogenerative plant, based on a cooling tower condenser with a condensation pressure of 0.075 bar. The flash pressure is 3.3 bar. Design the lay-out of the plant (i) with all the components (1 point), considering that the cogenerative heat exchanger is fed by the separated liquid from the flash chamber. Neglecting the presence of non-condensable gases and considering a temperature of 50°C at the outlet of the cogenerative heat exchanger, calculate (ii) the mass flow rate of the geothermal fluid that should be extracted from the well to obtain a net electric power output of 8 MW, knowing that the electric power consumption of all the auxiliary components of the steam cycle is 440 kW, and that the isentropic efficiency and the organic-electric efficiency of the turbogenerator are respectively equal to 80% and 93% (4 points). Then determine (iii) the vapor fraction at the outlet of the steam turbine (1 point) and (iv) the net electrical efficiency of the plant (2 points), assuming a minimum temperature of reinjection equal to 45°C (c p of the geothermal fluid in the liquid phase equal to 4.4 kJ/kgK). Calculate also (v) the cogenerative thermal power output (2 points), and (vi) the first-law efficiency at nominal conditions (1 point). Thermodynamic properties of water at saturation Liquid Vapor P sat [bar] T sat [°C] h liq.sat. [kJ/kg] s liq.sat. [kJ/kgK] v liq.sat. [m3/kg] h vap.sat [kJ/kg] s vap.sat. [kJ/kgK] v vap.sat. [m3/kg] 3.3 136 .8 575 .5 1.7059 0.00100 2729. 0 6.9589 0.553 8 0.075 40.3 168 .8 0.5763 0.00101 2574 .9 8.2523 19.2391 Results (exercise) Xv is 0,832 h is 2169,5 kJ/kg Dh is 559,5 kJ/kg Dh 447,6 kJ/kg h 2281,4 kJ/kg P el 8440 kW m vap. 20,28 kg/s Xv 0,2204 m geothermal 92,02 kg/s m liq 71,7 kg/s Xv 0,878 Q th cog 27405 kW hmin 189,4 kJ/kg Q th max 79191 kW Eta el net 10,10% Eta th 34,6% Eta I 44,7%