Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

Wind, Hydro and Geothermal Power Generation AY 2021-22 17 th January 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 th e av erag e r esults. 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 re- spectively at the hub, the average radius and the tip of the blade, graphically showing a situation where the pitch angle is negative. (5 points) 2. Consider a direct geothermal plant exploiting a liquid-dominant source. Explain the reason why a lamination valve before the demister can be convenient by an energy point of view, despite the irreversibility introduced. What are the consequences of lamination in terms of O&M issues? (5 points) 3. Draw the plant scheme of a hydro-pumped storage plant based on binary groups. Describe its start-up procedure in the pumping mode, discussing the hydraulic and electrical connections of the groups. (5 points) 4. Explain the definition of “grid parity” for a renewable power plant, distinguishing between the concept of grid parity in terms of price and cost. How can the growing share of electricity from renewables affect respectively the average cost of kWh and the balancing costs of the electric grid in a long-term perspective? (5 points) Exercise (10 points) A three-bladed horizontal axis wind turbine is equipped with a variable speed system. The turbine has a rotor diameter of 132 m and a rated wind speed of 11 m/s. Knowing that the machine fluid- dynamic performance is equal to 81% (ratio between the real Cp and the Betz Cp), the efficiency of the gearbox is equal to 97% and the mechanical-electric generator efficiency is equal to 96.3 %, compute (i) the nominal electric power in the design condition at sea level, 1 atmosphere and 25°C (the air density in this condition is equal to 1.225 kg/m3) (3 points). Evaluate the performance of the same machine when installed at 4500 m altitude a.s.l. (above sea level) with a reference ambient temperature of 4°C (pressure gradient with altitude equal to 10 Pa/m): calculate (ii) the value of the rated wind speed which would allow to produce the same nominal power, assuming to be able to modify the control system in order to keep the same fluid dynamic performance (3 points). With respect to the previous installation at sea level, what are the ratios respectively between (iii) the axial forces on the rotor (2 points) and (iv) the centrifugal forces on the blades (2 points)? Exercise (results) AD 13685 m2 WID nom 11156 kW W Betz 6611 kW Wrot or 5355 kW W el 5002 kW Cp 0,480 F ax 901523 N P 56325 Pa ro' 0,742 kg/m3 v1' nom 13,00 m/s F ax ' 762870 N Fcentr'/Fcentr 1,40 Fax'/Fax 0,85