Energy Engineering - Wind, Hydro and Geothermal Power Generation

Exam test 2

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Wind, Hydro and Geothermal Power Generation AY 2021-22 Example of Test - 2 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. Draw the power-to-wind speed characteristic curve of a modern large scale wind turbine. Con- sidering the adoption of a frequency converter that doesn't cover the full range of velocity varia- tion requested between the cut-in and the nominal wind speed, qualitatively plot on the same graph the following curves: coefficient of performance, pitch angle, tip-speed-ratio and rotational speed, justifying your answer. (5 points) 2. Consider an Organic Rankine Cycle coupled to a binary geothermal plant. Discuss the oppor- tunity of adopting a regenerative scheme. Under what conditions can it be convenient? (5 points) 3. Please describe the different classifications available for hydroelectric power plants, discussing their different role in the electric system. With reference to a high head, is it possible to have a weir-integrated or a run-of-river hydro plant? (5 points) 4. Explain the concepts of “Energy pay-back time” and “Energy Return On Investment” for a re- newable power plant and identify the main items that have to be considered for their definition. If possible, give some examples of renewable technologies. (5 points) Exercise (10 points) A geothermal source has the following characteristics at the outlet of the well: temperature 185°C, enthalpy 1100 kJ/kg. Consider a single flash direct steam cycle cogenerative plant, based on a cooling tower condenser with a condensation pressure of 0,07 bar. The flash pressure is 4,4 bar (see table below). 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, with an outlet temperature of the geothermal fluid equal to 48°C. 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 11 MW, knowing that the electric power consumption of all the auxiliary components of the steam cycle is 700 kW, and that the isentropic efficiency and the organic-electric efficiency of the turbogenerator are respectively equal to 81% and 93% (4 points). Then determine (iii) the vapor fraction at the outlet of the steam turbine (2 points) and (iv) the net electrical efficiency of the plant (1 point), assuming a minimum temperature of reinjection equal to 44°C (C p of the geothermal fluid in the liquid phase equal to 4.4 kJ/kgK). Finally calculate (v) the cogenerative thermal power output (1 point), 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] 4.4 147 .1 619. 6 1.8120 0.00100 2741. 9 6.8623 0.4226 0.07 39.0 163.4 0.5591 0.00101 2572.6 8.2767 20.5310 Exercise (10 points) Xv is 0,817 h is 2131,1 kJ/kg Dh is 610,8 kJ/kg Dh 494,8 kJ/kg h 2247,1 kJ/kg P el 11700 kW m vap. 25,43 kg/s Xv 0,2264 m geothermal 112,33 kg/s m liq 86,9 kg/s Xv 0,865 Q th 37890 kW hmin 185,3 kJ/kg Q th max 102755 kW Eta el net 10,7% Eta th 36,9% Eta I 47,6%