Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation (AY 2022-23) 16 th January 2023 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 three-bladed horizontal axis wind turbine, explain why the pitch angle of the blade has to vary along the radius (the blade is said to be "twisted"). Draw the velocity triangles respectively at the hub, the average radius and the tip of the blade, graphically showing a situation where the pitch angle is zero. (5 points) 2. Plot the lay-out of a geothermal direct steam cycle with 2 lamination pressures and draw the correspond- ing T-s diagram. Compared to a cycle with 1 lamination pressure (with same thermodynamic conditions of the geothermal source), what are the differences in terms of scaling effects for the demisters and the turbine respectively, of turbine O&M costs, and plant auxiliary consumptions? (5 points) 3. What are the most promising technologies for floating off-shore wind turbines? Discuss advantages and disadvantages of the different technical solutions, also considering the construction phases and O&M issues. (5 points) 4. Consider a pumped-storage hydro power plant operating with a nominal head of 1100 m and a given average head loss within the penstock of 44 m. Compute the “round trip efficiency” and the minimum energy price differential required to make the operation of the plant cost-effective. Illustrate the assump- tions made for the unknown parameters. (5 points) Exercise (11 points) A geothermal source has the following characteristics at the outlet of the well: pressure 11 bar, vapor fraction 80%, mass flowrate 18 kg/s. Draw the power plant lay-out based on a direct stem cycle in a configuration without the atmospheric vessel (1 point) and determine the net power output (3 points), considering a con- densing pressure of 0.08 bar and assuming a steam turbine isoentropic efficiency of 87% and a generator organic-electric efficiency of 97%. Calculate the net electric efficiency considering a minimum reinjection tem- perature equal to the condensing temperature and an overall auxiliary consumption of 650 kW (1 point). Determine the annual generated electricity (1 point), the levelized cost of electricity (LCOE) (2 point) and the cost of avoided CO 2 (3 points) of the plant, given a CO 2 content in the geothermal fluid equal to 0.1% by weight and considering that the system is operated for 7300 equivalent hours a year, total plant cost is 36 million € and annual variable costs are 4% of the investment cost. The cost of avoided CO 2 is the additional cost of electricity production to avoid the emission of one ton of CO 2 into the atmosphere, considering for a conven- tional reference plant a LCOE of 85 €/MWh and a specific emission of 380 g CO2 /kWh. In all cases the Capital Carrying Charge is equal to 12% (CCC is the share of investment costs related to an average year). THERMODYNAMIC PROPER TIES OF WATER AT SAT URATION liquid vapor PRESSURE [BAR] Temperature [°C] h liq.sat. [kJ/kg] s liq.sat. [kJ/kgK] h vap.sat [kJ/kg] s vap.sat. [kJ/kgK] 11 184 .1 781 .1 2.18 2779 .67 6.55 0.08 41.5 173 .86 0.59 2577 .11 8.23 Exercise (results) enthalpy 2380,0 kJ/kg entropy 5,7 kJ/kgK Vapour fraction 0,78 h isentropic 2048,5 kJ/kg enthalpy out 2143,5 kJ/kg Mechanical power 9160 kW gross electric power 8885 net electric power 8235 kW Q in max 39712 kW eta net, el 20,7 % Energy 60118 MWh annual O&M costs 1,44 M€ annual total cost 5,76 M€ LCOE 95,8 €/MWh CO2 51,8 kg/h CO2 6,3 kg/MWh cost of avoided CO2 28,9 €/tCO2