Energy Engineering - Power Production from Renewable Energy

Full exam

POWER PRODUCTION FROM RENEWABLE ENERGY AY 202 2-23 10th July 2023 Prof. Andrea Giostri Time: 1.5 hours NAM E and SURNAME :.......................................................................... ........................................................................ COURSE and CFU :................... .......................................................................... ...................................... ...................... Instructions for the examination: 1) Clearly indicate your name on all the sheets you will deliver. 2) The score refers to exercises done in a comprehensive manner with exact numerical results. Numerical results correct but not accompanied by explanations will not be taken into account. The final score can be normalized according to the average results. 3) Answer briefly and clearly only to the asked questions. Calculations and explanations which do not respond to the questions will not be considered for evaluation even if correct. 4) Talking with colleagues and / or cheating will cause the cancellation of the exam. 5) All the needed data for the resolution of exercises lies on this paper. It is NOT ALLOWED to use material other than this (e.g. books, clipboard etc.). Exercise 1 (15 points ) It should be evaluated the installation of a PV plant for residential applications. The PV plant is installed on the roof of a house (3. 8 x 8. 2 m), the azimuth of the house is -10° (the azimuth is determined starting from south direction, positive counterclock -wise) and the tilt of the roof is 30°. Assuming the PV module and inverter characteristics reported in the following table, determine the nominal power installed (AC) and the number of inverters (Discuss the obtained results and choices , check ing the constraints on the power and voltage - do not check the conditions at minimum and maximum temperature ) (5 points) . Single Cell electric characteristics Inverter Power @STC 5.17 W Power input in CC 2650 W open circuit voltage @STC 0.66 V Maximum voltage 600V Voltage at MPPT@STC 0.628 V Power point operating voltage 260 -500 V Power coefficient -0.38%/ °C Power output in AC 2500 W Number of cells per module 60 STC (1000 W/m 2 and 25°C) Module size ( l x w) in mm 1660 x 990 NOCT (@800 W/m 2 and T amb 20°C) 45°C Calculate the electric power produced assuming only losses due to (i) incidence angle, (ii) operating temperature in condition s with zenith and azimuth angle of the sun equal to 60° and -10° respectively, an ambient temperature equal to 2 3°C, a 460 W/m 2 Global Horizontal Irradiation and 130 W/m 2 Diffuse Horizontal Irradiance . Neglect the ground albedo ( 6 points). ������������� ������������= ������������� ������������������������������� ������ + ������������� ������������������������������� ������ ������������� (������������− ������) Where θ S is the incidence angle of solar radiation , θ ZS is the zenith angle, β is the roof tilt, ψ s and ψ are the solar and roof azimuth angles respectively. What would be the electric power produced by the same number of panels installed on a two -axis tracking system? ( 4 points) Exercise 2 (15 points) It is required to calculate the diameter of a wind turbine which produces 485 0 MWh in a year assuming an availability of 9 1%, a mechanical -electric efficiency equal to 95.5% and wind speed frequencies reported below (use the average value of wind speed for each range; remember that Cp is defined as the ratio between mechanical power at the rotor shaft and ideal power content of the wind). The wind turbine is located at 800 m asl (pressure gradient with altitude equal to -10 Pa/m) and the average air tempera ture is 17 °C (Molar mass of air equal to 28.9 kg/kmol) (5 points). Wind speed range (m/s) Frequency (%) Cp (%) 0-3 35 0 6 (range 4 -8) 22 38 11 (range 9 -13) 16 45 16 (range 14 -18) 11 14. 5 22 (range 19 -25) 9 5. 5 >25 7 0 Determine the rated power of the wind turbine and the equivalent hours (3 points). Identify the rotational speeds assuming a tip -speed ratio equal to 6. 7 (2 points). Management students: Calculate the cost of electricity assuming a wind turbine rotor cost of 20000 €/m, and the generator plus structure accounts for 500 €/kW. Installation costs are equal to 25% of bare equipment and a capital recovery factor (CRF) equal to 12%. Maintenance cost accounts for 15 €/MWh (5 points) Energy students and Mechanical students : Assuming the validity of the Betz theorem , d etermine the axial force on the structure and the torque on the rotor shaft at the rated wind speed (3 points). Finally draw the velocity triangles at tip (report the values of the drawn velocities and angle between relative velocity and peripheral velocity) (2 points) . POWER PRODUCTION FROM RENEWABLE ENERGY AY 202 2-23 10 th July 2023 Prof. Andrea Giostri Time: 1 hour NAM E and SURNAME :.......................................................................... ........................................................................ COURSE and CF U: ................... ................................................................................................................ ...................... 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. OPEN QUESTIONS (points 18 ) 1. Consider a modern wind turbine (large in size) and draw an ideal Power -speed curve highlighting and defining cut -in speed, rated speed and cut -off speed. Explain the control strategy that allow the best performance operating between the cut -in wind speed and the rated wind speed. 2a. For Mechanical Engineering students and Management Engineering students : Describe and discuss the ideal characteristics of a solar collector for CSP and explain the functi on of a selective coating. 2b . For Energy Engineering students (8 CFU) : Consider a single -flash configuration to produce electricity from a liquid dominant geothermal source. Draw the layout (consider the presence of non -conde nsable gases in the geothermal fluid). Explain how to choose the flashing chamber pressure to maximise the net power output. MULTIPLE -CHOICE QUESTIONS (points 12) Answer to the following 15 questions. Select the box with correct answer (0.8 points if correct , -0.3 points if wrong ). For a Horizontal Axis Wind Turbin es: Active stall is obtained by the variation of pitch angle and the rotational speed The pitch angle along the blade height increases with the radius If the number of blades increases → optimum tip speed ratio decreases ❑ true ❑ true ❑ true ❑ false ❑ false ❑ false Consider the electricity generation from two different renewable energy sources (namely A and B): heq → Equivalent hours LCOE_A =2* LCOE_B if Inv.Cost_A=2*Inv.Cost_B The impact on “duck curve” issue depends on the dispatchability of A and B If A → PV plant and B → Geoth. it is probable that heq_A>heq_B ❑ true ❑ true ❑ true ❑ false ❑ false ❑ false Consider a vertical surface : GD,sky → diffuse radiation from sky vault (Hp: isotrope) GB→ Beam radiation GD,ground → diff . rad from ground (Hp: isotrope) Z → Zenith angle The fraction s of G D,sky and GD,ground that imp inge onto the surface are the same The fraction of incident Gb is equal to cos( z) The optical efficiency varies along the day ❑ true ❑ true ❑ true ❑ false ❑ false ❑ false Consider a photovoltaic (PV) module : The adoption of a tw o-axis tracker allows the maximum electricity production Th e inverter is characterized by efficiency in the range 70% -85% Single crystal Si guarantees a higher conversion efficiency than multi -crystalline Si ❑ true ❑ true ❑ true ❑ false ❑ false ❑ false Consider the V -I curve of a PV cell , if the irradiation decreases : ISC decreases and V OC slightly increases The MPPT conditioner decreases both current and voltage The bypass diode is fundamental to solve issues related t o overheating due to this off -design operation ❑ true ❑ true ❑ true ❑ false ❑ false ❑ false