Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POW ER PRODUCTION FROM RENEW ABLE ENERGY AY 2021-22 8 th September 2022 Prof. Silva Time: 1.5 hours Ins truc tions for the examinati on: 1) Clearly indicate your name on all the s heets you will deli ver . 2) The scor e r efers to exercises done in a c ompr ehensi ve manner with exac t numerical res ults . Numeric al res ults corr ect but not accom panied by expl anati ons will not be taken into account. The final score c an be normali zed accor ding to the average r esults . 3) Talking with c olleagues and / or c heati ng will c aus e the cancellation of the exam. 4) All the needed data for the res olution of exercis es lies on this paper . It is NOT ALLOW ED to use materi al other than this ( e.g. books , cli pboar d etc.). Exercise 1 (16 points) Consider a geothermal plant based on v apour-dominated reserv oir, direct-steam , single-flash. The geothermal fluid composition on mass base is 95% H 20 and the remaining is N 2 (MM N2=28 kg/kmol). Temperature of the geother- mal fluid 190°C Turbine isentropic efficiency 87% Pressure of the geothermal fluid 12,6 bar Steam turbine generator effi- ciency 97% Mass flowrate of the geother- mal fluid 44 kg/s Condensing pressure 0,1 bar Enthalpy of the water (mix- ture of liquid and v apour) 2500 kJ/kg Auxiliaries for heat rejection 15 kW el/MW th Non -condensable gas com- pressor i sentropic efficiency 81% Non -condensable gas compres- sor motor efficiency 94% Design the lay-out of the plant with all the components (1 points). Calculate the net power output of the geo- thermal plant considering a pressure after lamination valve of 9 bar) (6 points). Determine the net electric efficiency (2 points). Energy Engineering students: Considering a solar multiple equal to 1,2 calculate the solar field area of parabolic trough collectors necessary to increase the geothermal fluid temperature up to 370°C (enthalpy 3196,4 kJ/kg, entropy 7,26 kJ/kgK) (3 points) and determine the resulting net power output and ov erall efficiency of the hybrid plant, neglecting the pressure losses in the solar field and the piping thermal losses (4 points) Solar fi eld optical efficiency 77% Design DNI 800 W/m 2 Collector thermal losses 75 W/m 2 Incidence Angle 15° Mechanical and Management Engineering students: Calculate the heat input necessary to increase the geothermal fluid temperature up to 370°C with a biomass boiler (enthalpy 3196,4 kJ/kg, entropy 7,26 kJ/kgK) (2 points) and determine the resulting net power output, ov erall efficiency of the hybrid plant (3 points), and annual consumption of biomass (boiler efficiency is 87%, operating hours are 8000 and LHV biomass =13 MJ/kg) (2 points). liquid vapour p, bar T, °C h, kJ/kg s, kJ/kg -K h, kJ/kg s, kJ/kg -K 0,1 45,8 191,8 0,65 2584,8 8,15 9 175,4 742,6 2,09 2772,1 6,62 12,6 190,0 807,5 2,24 2784,3 6,50 Exercise 2 (14 points) Mechanical and Energy Engineering students The installation of a PV plant for residential applications should be ev aluated. The PV plant is installed on the roof of a house (5.5 x 8 m), the azimuth and the tilt angles of the roof are respectively -20° and 25° (the azimuth is determined starting from south direction, positive counterclock-wise). Assuming the PV module and inverter characteristics reported in the following table, determine (i) the number of inv erters (2 points) and (ii) the max- imum nominal power installed (AC) (3 points), discussing the results. Single Cell electric characteristics Inverter Power at MMPT @STC 5.17 W Max 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 Max p ower output in AC 2500 W Module characteristic s N° of cells (series connected) 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 (iii) the yearly electricity produced (4 points) and (iv) the equivalent hours (1 point), assuming only losses due to incidence angle, operating temperature and inverter. Assume an average zenith and azimuth angle of the sun equal to 45° and 0° respectively, an average ambient temperature equal to 15°C, an av erage 700 W/m 2 Direct Normal Irradiance and 80 W/m 2 diffuse horizontal irradiance. Neglect the ground albedo. Equivalent hours of solar radiation are 1800. cos cos cos sin sin cos( ) SZSZSSθ θ β θ β ψψ =+− = where θ S is the incidence angle, 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 (v ) the electricity produced (3 points) and (vi) the equivalent hours (1 point) by the same number of panels installed on a two axis tracking system? Exercise 2 (14 points) Management Engineering students A three-bladed horizontal axis wind turbine is equipped with a variable speed and v ariable pitch regulation system. The turbine has a rotor diameter of 110 m, a rated wind speed of 11 m/s and is designed for an optimal λ tip equal to 7,85. 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 96,7% and the mechanical-electric generator efficiency is equal to 97,3%, compute (i) the nominal electric power output at the design condition at sea level: 1013 mbar and 25°C, with a correspondent air density equal to 1,225 kg/m 3 (2 points). Calculate (ii) the rota- tional speed of the turbine at the same condition (1 point). Giv en the electrical power output at the cut-in speed, equal to 168 kW, assuming that the turbine has no limitations to the rotational speed and considering constant mechanical and electrical efficiencies, determine (iii) the wind speed at cut-in conditions (2 points), and (iv) the machine rotational speed (1 point). After that, evaluate the performance of the machine when installed at 4000 m altitude a.s.l. (abov e sea level) with a reference ambient temperature of 8°C (pressure gradient with altitude equal to 10 Pa/m), in particular calculate (v) the corrected values respectively of the rated wind speed (2 points), (vi) the cut-in wind speed (2 points), and (vii) the angular v elocities (2 points). Finally determine (viii) the rated wind speed in case of power limitation of the machine to 1900 kW electric power output (2 points). Results Exercise 1 vapor fraction of geothermal fluid 85,6 % pressure after lamination valve 9 bar liquid at lamination pressure 742,64 kJ/kg vapour at lamination pressure 27 72,14 kJ/kg vapor fraction 86,6% turbine steam flow rate 36,20 kg/s turbine N2 flow rate 2,20 kg/s 58,80 cp N2 1,0393 kJ/kgK enthalpy (iso) at turbine outlet 2096,13 kJ/kg enthalpy (real) at turbine outlet 2184,01 kJ/kg turbine gross power ou tput 20936 kW beta compressor 10,10 isentropic efficiency 81% T iso 617,61 K T real 414,5 °C 687,66 Electricity consumption compressor 896,7 kW Q condenser 72106,8 kW heat rejection Auxiliary consumption 1081,6 kW net power output 189 58 kW Q in 96811,0 kW net electric efficiency 19,58 % Solar hybrid plant Pressure at solar field outlet 12,6 bar enthalpy 3196,4 kJ/kg Q tot fluid 29519 kW Area 68120 m^2 entropy 7,260 kJ/kg K enthalpy iso 2300,5 kJ/kg enthalpy reale 2417,0 kJ/kg turbine gross power output 32319,0 kW heat rejection Auxiliary consumption 1208,1 kW net power output 30214 kW Q in 151307,0 kW net electric efficiency 20,0 % Biomass hybrid plant Q in 29519 kW Net power output 30214 kW (see above calculation) Q biomass 33930 kW overall net electric efficiency 23,1% annual heat input 271441 MWh annual biomass consumption 75168 t Exercise 2 (Mechanical and Energy Engineering) Power (single module) 310,2 W cos incidence angle 0,92 Voltage 39,7 V Incidence radiation 721 W/m^2 MPPT voltage 37,7 V temperature 37,5 °C Number of modules 24 mod. power avg 213,1 W Total power DC 7444,8 W average power AC 4825 W Number of inverters 2,81 electricity 8686 kWh h eq 1237 h Number of inverters 3 Modules for each inver- ter 8 two axis tracking (cos) 1 Power DC (inverter) 2481,6 W radiation 776 W/m2 Voltage 317,6 V temperature 39,3 °C Voltage MPPT 301,6 V power 227,7 W Power AC (inverter) 2341,1 W average AC 5156,5 W Power AC 7023 W electricity 9282 kWh h eq 1322 h Exercise 2 (Management Engineering) AD 9503 m2 WID nom 7747,5 kW W Betz 4591,1 kW Wrot or 3719 kW W el 3499 kW Cp 0,480 omega 1,570 rad/s 14,99 rpm Wrot or 178,6 kW W Betz 220,4 kW WID 372,0 kW v cut-in 4,00 m/s omega cut -in 0,571 rad/s 5,45 rpm P 61300 Pa ro' 0,786 kg/m3 v1' cut -in 4,64 m/s v1' nom 12,75 m/s omega' nom 1,8202 rad/s 17,4 rpm omega' cut -in 0,6616 rad/s 6,3 rpm v rated 10,40 m/s WID nom 4201,7 kW W Betz 2489,9 kW Wrot or 2017 kW W el 1898 kW