Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation AY 2021-22 11 th April 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. Considering a large scale three-bladed horizontal axis wind turbine, discuss the regulation strat- egies adopted by the control system in the range between the nominal and cut-off wind speed, explaining the main pros and cons of each of them. In particular highlight the velocity triangle modification introduced by a gust. (5 points) 2. Considering a geothermal power plant, highlight pros and cons of a binary cycle configuration versus a direct-steam cycle one. Which kind of geothermal source has the greatest advantages in adopting a binary cycle? (5 points) 3. Consider a pumped-storage hydro power plant operating with a nominal head of 250 m and a given average head loss within the penstock of 15 m. Explain how to compute the minimum energy price differential required to make the operation of the plant cost-effective. Illustrate the assumptions made for the unknown parameters. (5 points) 4. Discuss the characteristics of floating technology with respect to offshore wind installations based on foundations. What are the main advantages and disadvantages? (5 points) Exercise (10 points) A geothermal source has the following characteristics at the outlet of the well: temperature 180°C, enthalpy 1800 kJ/kg. Consider a single flash direct steam cycle plant, based on a cooling tower condenser with a condensation pressure of 0.07 bar. The flash pressure is 7.7 bar (see table below). Design the lay-out of the plant (i) with all the components (1 point) in the hypothesis of mixing the two liquid flows coming respectively from the condenser and the demister. Neglecting the presence of non-condensable gases, 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 15 MW, knowing that the electric power consumption of all the auxiliary components of the steam cycle is 950 kW, and that the isen- tropic efficiency and the organic-electric efficiency of the turbogenerator are respectively equal to 80% and 93% (4 points). Determine (iii) the net electrical efficiency of the plant (1 point), assuming a minimum temperature of reinjection equal to 44°C (Cp of the geothermal fluid in the liquid phase equal to 4.4 kJ/kgK). Consider a plant modification based on a hybrid scheme in which the liquid output from the flash chamber feeds an ORC binary cycle by means of a heat exchanger which cools it down to 51°C (for the rest of the system take the same assumptions). Compute (iv) the total net electric power output of the plant (2 points), knowing that second law efficiency of the ORC cycle is 52% and the condens- ing temperature is the same as the direct steam cycle. Finally (v) check that the reinjection temper- ature is higher than the minimum reinjection temperature (2 points). 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] 7.7 168 .8 714 .0 2.0302 0.00100 2765 .9 6.6727 0.2491 0.07 39.0 163.4 0.5591 0.00101 2572.6 8.2767 20.5310 Results Xv is 0,792 h is 2071,9 kJ/kg Dh is 694,0 kJ/kg Dh 555,2 kJ/kg h 2210,7 kJ/kg P el 15950 kW m vap. 30,89 kg/s Xv 0,5293 m geothermal 58,36 kg/s m liq 27,5 kg/s Xv 0,850 hmin 185,3 kJ/kg Q th max 94242 kW Eta el net 15,92% T m, ln 106,9 °C Eta Lorentz 17,9% Eta binary cycle 9,28% Q in ORC 14245 kW P el net ORC 1322,6 kW P el net tot 16323 kW Eta el net, tot 17,32% T reinjection 44,7 °C