Estimation Of Solar Radiation PDF

31/10/2023 Introduction Our planet faces significant challenges in the twenty- first century beca...

31/10/2023 Introduction Our planet faces significant challenges in the twenty- first century because energy consumption is expected to double globally during the first half of this century. Faced with increasingly constrained oil supplies, humanity must look to other sources of energy, such ESTIMATION OF SOLAR as solar, to help us meet the growing energy demand. Solar radiation is the most important natural energy RADIATION resource because it drives all environmental processes acting at the surface of the Earth. The Sun provides the Earth with an enormous amount of energy. The energy stored by the oceans helps maintain the temperature of the Earth at an equilibrium level that allows for stability for a broad diversity of life. Although the solar energy source is inexhaustible Sun–Earth Geometric Relationship and free, it is not the most convenient energy The amount and intensity of solar radiation reaching source due to its intermittent nature. the Earth’s surface depends on the geometric In contrast, modern lifestyles demand a continuous relationship of the Earth with respect to the Sun. and reliable supply of energy. However, there are The position of the Sun, at ways to overcome these shortfalls. any moment at any place In order to understand solar energy, this chapter on Earth, can be estimated by two types of discusses the resources, including energy irradiated calculations: from the Sun, the geometrical relationship between 1. simple equations where the inputs are the Sun and the Earth, and orientation of energy the day of the year, receivers, as well as the importance of acquiring time, latitude, and longitude, reliable solar information for engineering design, 2. calculations through operation, and management of solar technologies. complex algorithms valid for a limited period varying from 15 to 100 years; Figure Earth–Sun geometric relationships 1  31/10/2023 Declination Angle () of the sun varies daily and is calculated from the Table : Declination and Earth–Sun Distance of the Representative Averaged Days for Months following relation: where n is the day of the year. Position of the Sun with Respect to a Horizontal Surface In addition to the fixed celestial coordinate systems on the sky, to describe the Sun’s position with respect to a horizontal surface on Earth at any time, the following angles are important i. Solar altitude anlge (αs), Apparent Path of the Sun ii. Zenith angle (θz), The Earth rotates at an approximately constant rate on its iii. Solar azimuth angle (γs), and axis once in about 24 hours. Such rotation in the eastward iv. Hour angle (ω) direction gives the sense that the Sun moves in the opposite direction. The so-called ecliptic is the apparent path that the Sun traces out in the sky while it goes from east to west during the day. Solar altitude angle (αs): it is measured in degrees from the horizon of the projection of the SOLAR ALTITUDE ANGLE radiation beam to the position of the Sun. When the Sun is over the horizon, αs = 0° and when it is is the angular distance between the imaginary directly overhead, αs = 90°. horizontal plane on which you are standing and the sun in the sky it tells at what height the sun is in the sky. In the morning and evening, the sun is low in the sky, near the horizon (the solar elevation is close to 0°) at solar noon, the solar elevation angle is highest since the sun is overhead Fig. Position of the Sun in the sky relative to the solar angles. 2  31/10/2023 SOLAR ALTITUDE ANGLE PV MODULE AND ALTITUDE ANGLE Zenith angle (θz) : it is the angle of the Sun relative to a line Hour angle (ω) it is the angular distance between the perpendicular to the Earth’s surface. Sun’s position at a particular time and its highest position for that day when crossing the local meridian at the solar noon. Because the Earth rotates approximately once every 24 hours, the hour angle changes by 15° per hour and moves and the zenith angle is given by through 360° over the course of the day. The hour angle is defined to be zero at solar noon, a negative value before crossing the meridian (morning), and a positive after crossing (afternoon). Solar azimuth angle (γs), it is the angle on the horizontal plane Hour angle  and solar time ST in hours are related as: between the projection of the beam radiation and the north– south direction line. Positive values of γs indicate the Sun is west of south and negative values indicate when the Sun is east of south for northern hemisphere and vice-versa for the southern hemisphere. 3  31/10/2023 SUN RISE AND SUN SET ANGLE SAMPLE Let’s take the example of an area with 32.22° latitude. Calculate the sun’s elevation angle on March 3rd at 10:00 AM, 12:00 noon, and 2:00 PM. THEORETICAL POWER INTERCEPTED ESTIMATION OF SOLAR POWER BY THE EARTH E = Ks * πR2 = 1361 * 3.1416 * (6,371)2 So = L / (4  rs-e2) = 3.9 x 1026 W = 1370 W/m2 4 x  x (1.5 x 1011m)2 = 173.5 x 1015 W Eout = ( T4) x (4  re2) 4  31/10/2023 Solar energy & Solar cells How do solar cells work? Solar cells Sunlight Electricity transform (solar energy) Photovoltaic sunlight into effect electricity this electron reflection now has more e- energy When this usually glass excited state happens inside a light material, it is protective layer transmission absorption called the n-layer photovoltaic semiconductors junction absorption effect p-layer e- e- e- e- ground state How do solar cells work? What are solar cells made from? Most common material = silicon e- protection layer First developed for the space program n-layer n-layer P-doped Si Highest efficiencies of any type of solar cell junction junction junction Long lifetimes – very stable p-layer p-layer B- or Ga-doped Si Requires thick layers of Si  relatively expensive Rigid & brittle  limits potential applications Single crystal - 26% Polycrystalline - 20% Amorphous - 13.4% e- e- e- e- e- e- e- + + + 1  31/10/2023 What do you think some challenges with solar energy might be? Key challenge: Improving efficiency They don’t work amount of electricity produced at night or in Efficiency = They don’t use all the Sun’s amount of sunlight received cloudy weather energy incoming solar radiation incoming solar radiation New solar materials ideally need 1000 watts/sq meter 1000 watts/sq meter to be: — Efficient — Inexpensive — Abundant materials — Non-polluting / non-toxic Storage 800 W heat 200 W electricity 800 W heat 200 W electricity New materials to replace Si Perovskites Perovskites are materials with a specific structure called ABX3 Advantages Organic cells Perovskites — Maximum efficiency = 23.7% Methyl ammonium lead triiodide perovskite. Image from NREL. — Variable band gaps  can be designed for specific applications — Very efficient absorber of high-energy light Dye-sensitized cells Quantum dots Single crystal Si  can be combined with other low-energy absorbers 11.9% 15.6% 16.6% 23.7% 26.1% Disadvantages — Most use lead = extremely toxic Maximum efficiency — Poor stability Image from Solliance. 2  31/10/2023 Quantum Dots Organic PV Cells OPVs can be made of any organic (carbon-containing) 4 nm 5 nm 6 nm QDs are tiny particles only a few molecule that absorbs light and can donate/accept nanometers wide electrons 2 nm 3 nm Image via TCI America. Image via University of Rochester. Image via Wikimedia Commons. Image via BBC. Advantages Disadvantages Advantages Disadvantages —Most use cadmium or lead — Low efficiency (at least so far) — Flexible! — Band gaps change with QD size = extremely toxic  can be deposited on different materials — Not very stable  can be designed for specific applications — Degrades when exposed to water — Many possible combinations  no effective protective coatings yet — small size means good power to weight ratio and UV light — Inexpensive to produce Dye-sensitized solar cells EXISTING SOLAR TECHNOLOGIES examples of dyes DSSCs are made of three parts: dye, TiO2, and liquid electrolyte Solar Photovoltaic (PV) Solar Hot Concentrated Solar Power Water Advantages — Easy to make e- — Semi-flexible and semi-transparent — Work in low-light  potentially could be used indoors e- e- e- e- Disadvantages e- e- e- electrolyte — Low efficiencies (so far) e- e- — Requires expensive materials like Pt light — Uses liquids  makes it difficult to use in all weather TiO2 dye Pt 3  31/10/2023 SOLAR TECHNOLOGY: SOLAR TECHNOLOGY: PV COMPONENTS PV SYSTEMS Battery-less, grid-tied – grid connection, can be with or Cell without net metering more than 90% of all installed PV in the US Battery-based, grid-tied – batteries plus ability to put power onto the grid Off-grid – only tied to a battery bank PV-direct – e.g. solar signs, street lights, solar calculator Panel / Module PV Array SOLAR TECHNOLOGY: MOUNTING SOLAR TERMS: SYSTEM COSTS Solar PV systems can be ground mounted or roof mounted Hardware Costs Solar Panels Balance of System Total System Soft Costs Cost Financing Permitting Customer Acquisition Installation Maintenance 4  31/10/2023 SOLAR TERMS: SOFT SOLAR TERMS: SOLAR CELL, COSTS MODULE, PANEL, ARRAY & SYSTEM SOLAR PV TERMS: INVERTER, SOLAR TERMS: METER, DISCONNECT BALANCE OF SYSTEM Inverter The balance of system Disconnect or BOS encompasses all components of Switch a photovoltaic system other than the photovoltaic panels. Utility Grade Solar Meter Wiring Disconnect Switches Mounting System Inverter Solar Generation Meter These requirements may vary by utility. The outlay of these items can vary visually. 5  31/10/2023 SOLAR TERMS: SOLAR TERMS: SYSTEM COSTS INTERCONNECTION The technical and Up until the 1970s Hardware Costs procedural requirements utilities owned all Solar Panels necessary to connect PV Balance of System system to the electricity generation and thus grid. had total control over Total the process of how systems connected to System the grid. Soft Costs Cost Financing Permitting Customer Acquisition Installation Maintenance ENERGY TERMS: BASE SOLAR TERMS: NET LOAD AND PEAKING POWER METERING Electrical power demand Net metering allows for the rises and falls during the delivery of excess course of a typical day. electricity generated back to Base load power - the the utility grid for minimum amount of use elsewhere. electricity used on the grid. This offsets electricity provided Peaking power - the by the utility to the maximum amount of customer during electricity used both the billing period. anticipated and unanticipated. 6  31/10/2023 THE COST OF SOLAR THE COST OF SOLAR PV PV 25% drop in price 2010 - 2012 Tracking the Sun VI: The Installed Cost of Photovoltaics in the US from 1998-2012 (LBNL) 7  31/10/2023 ENERGY SOURCES AND CONVERSION PROCESSES THERMODYNAMIC PATHWAY INTRODUCTION PHOTOTHERMAL CONVERSION Solar radiation can be considered as electromagnetic In the case of photothermal conversion, the absorption of solar radiation increases the kinetic energy of atoms, which leads to waves having different wavelength ranges as well as heat generation, while it increases potential energy of the atoms photon gas having photons of different values of during photovoltaic energy conversion leading to current flow to energy content the load The interaction of solar radiation with material and PHOTOVOLTAIC CONVERSION exchange of energy converts solar radiation into The solar photovoltaic energy conversion is a process of useful form of energy, such as thermal energy and converting solar radiation directly into electricity, in which electrical energy through photothermal and the potential energy of absorber material increases due to photovoltaic conversion processes respectively absorption of solar radiation and causes flow of charges 1  31/10/2023 Energy balance diagram of solar PV module Thermodynamic pathway (Vos, 1987) The thermodynamic analysis of energy conversion system provides insight understanding that can be used to improve efficiency and performance of the system. The solar photovoltaic energy conversion is a process of converting solar radiation directly into electricity, in which the potential energy of absorber material increases due to absorption of solar radiation and causes flow of charges. A solar photovoltaic cell absorbs solar radiation having energy, equal to or higher than, the energy bandgap of PV material to generate electron-hole pairs, i.e., charge carriers ENERGY MODEL THE EQUATION The energy model of solar PV cell is based on the first law of thermodynamics, which shows that the solar radiation (QS) received over the PV surface is partly reflected back from the top glass (QR) and partly absorbed by the PV module. A = Area of the PV module The absorbed solar radiation energy is distributed in the following G = Incident solar irradiance components: - energy loss to the environment from the top glass through radiative (QRD) and convective heat transfer (QC) - useful heat energy from the back surface (Bottom Glass) of PV module which can be utilized for heating purpose (QU) - electrical energy (PM) h = convective heat transfer coefficient  = reflection coefficient ε = emissivity 2  31/10/2023 Reflection Coefficient of PV panel INCIDENT SOLAR IRRADIANCE Monocrystalline Solar Panels – Reflects between 0.2% and 0.35% Incident solar radiation to normal refers to solar radiation falling perpendicular on a surface, ie, having an angle of 90° to the surface Polycrystalline Solar Panels – Reflects between 0.25% and 0.40% Incident radiation is the measure of the solar energy that is incident Thin-Film Solar Panels – Reflects between 0.50% and 15.0% on a specific area over a period of time The amount of solar radiant energy falling on a surface per unit area and per unit time is called irradiance STEFAN BOLTZMAN LAW CONVECTIVE HEAT TRANSFER The rate of heat transfer by emitted radiation is determined by the Stefan-Boltzmann law of radiation (5.67 × 10−8 J/s · m2 · K4) 3  31/10/2023 PROBLEM 1. A body of emissivity, e = 0.75, the surface area = 300 cm2 and temperature = 227 oC is kept in a room at a temperature of 27 oC. Using the Stefans-Boltzmann law, calculate the initial value of net power emitted by the body. 2. Hot air at 80°C is blown over a 2 m by 4 m flat surface at 30°C. If the average convection heat transfer coefficient is 55 W/m2°C, determine the rate of heat transfer from the air to the plate, in kW. 4  02/12/2023 HYDR0-ELECTRIC DAM HYDROPOWER Impoundment facility Technology Hydropower Technology Pumped Impoundment Diversion Storage 1  02/12/2023 Dam Types Arch Dams Arch Arch shape gives strength Gravity Less material (cheaper) Buttress Narrow sites Embankment or Earth Need strong abutments Concrete Gravity Dams Buttress Dams Face is held up by a Weight holds dam in series of supports place Lots of concrete Flat or curved face (expensive) 2  02/12/2023 Embankment Dams Pumped Storage Earth or rock During Storage, Weight resists water pumped from flow of water lower reservoir to higher one. Water released back to lower reservoir to generate electricity. Pumped Storage POWER COMPUTATION Operation : Two pools of Water Upper pool – impoundment Lower pool – natural lake, river or storage reservoir Advantages : Production of peak power Can be built anywhere with reliable supply of water Caliraya Dam 3  02/12/2023 PROBLEM PROBLEM A dam 357 feet high has an effective head of A hydroelectric plant that will be constructed has an average annual rainfall of 139 cm. Only 82% of the rainfall can be collected and 75% of 235 ft. The typicsl flow of water is 2200 cfs. If the impounded water is available for power. The catchment area is 206 km2 with an available head of 23 m. Hydraulic friction loss is 6%, the turbine and generator has an efficiency turbine efficiency is 78% and generator efficiency is 93%. If the water of 80% determine the power that it can will flow to a rectangular outlet with base of 4 m and that the depth of flowing water is 3 m, determine the average power that could be generate in kW generated if the velocity of water is 2 m/s 4  25/02/2024 What Makes Wind Global Wind Patterns Why Wind Energy? How does a wind turbine work Clean, zero emissions NOx, SO2, CO, CO2 Wind (moving air that contains kinetic energy) Air quality, water quality blows toward the turbine's rotor blades. Climate change Inside the nacelle (the main body of the Reduce fossil fuel dependence turbine sitting on top of the tower and behind Energy independence the blades), the generator in the nacelle Domestic energy—national security converts this kinetic energy into electrical Renewable energy No fuel-price volatility 1  25/02/2024 Wind Turbine Components How a Wind Turbine Operates Wind Turbine Perspective Workers Blade 112’ long Nacelle 56 tons Tower 3 sections 2 25/02/2024 3 25/02/2024 4 25/02/2024 5  25/02/2024 Residential Wind Systems and Net Wind Farms Metering AC to Grid Wind Turbine AC Utility Meter AC Electrical AC Voltage Circuits DC Voltage Input Input Main Utility Inverter & Breaker Panel Interconnects Potential Impacts and Issues Impacts of Wind Power: Noise Property Values Noise Visual Impact Land Use Wildlife Impact Properly siting a wind turbine can mitigate many of these issues. 6  25/02/2024 Wildlife Impacts Philippine renewable energy resources Top Common Human-caused Threats to Birds A US-NREL study shows the following: 3,000,000,000 2,500,000,000 2,400,000,000 - Wind resources – over 10,000 km2 with 76,000 MW of potential installed capacity. Median/Avg. Estimated 2,000,000,000 - Micro-hydro applications – potential capacity of at least 500 KW in Luzon and Mindanao islands - Solar radiation nationwide – an annual potential average of 1,500,000,000 1,000,000,000 5.0 – 5.1 KWh/m2/day 599,000,000 - Mini-hydro potential capacity of 1,784 MW capacity for 888 500,000,000 sites 214,500,000 6,600,000 25,500,000 234,012 - Ocean energy resources – potential CAPACITY OF ABOUT 0 Cats Building Glass Collision - Collision - Collision - Vehicles Collision - Land- 170,000 MW Communication Towers Electrical Lines based Wind Turbines - Biomass ( Bagasse ) total potential of 235 MMBFOE Hazard Type Source: New and Renewable Energy Laboratory (USA) – E. Karunungan ( Department of Energy, Philippines Renewable energy development projects status Luzon Grid Green Power Nueva Ecija Biomass (18 MW)=2011 Pangasinan Biomass 1 (18 MW)=2011 Resource Existing Number of plants On-going Pagudpud Wind (40 MW) Burgos Wind (86 MW) – 6 MW=2009 Pangasinan Biomass 2 (18 MW)=2013 capacity (MW) in operation projects 40 MW=2010 40 MW=2011 Balintingon River (44 MW)- Northwind pamplona (30 MW)=2015 2015 Geothermal 2,027.07 14 geothermal plants 10 projects offered to private investor ( 300 – 500 CFB Phase II (50 MW)-2010 Pagbilao Exp. (400 MW) MW )thru Contracting Redondo Coal Fired (2x150 MW)-2012 Quezon Power Exp.(500 MW) Round Pantabangan Expansion (78 Energy World CCGT MW) (2x150 MW) = 2011 Hydro 3,367.07 21 large hydro, 52 mini- 4 mini-hydros, 14 large Kalayaan CBK Expansion hydro, 61 micro hydro hydro under evaluation (360 MW)-2013 2x300 MW Coal-Fired Wind 33.2 33 MW In Ilocos Norte, 5 KW NPDC wind farm, 7 sites GN Power (600 MW) Camarines in 180 KW in on resource assessment Legend: 2012 Batanes, 6 KW in Boracay Natural Gas First Gen San Gabriel (550 MW)-2011 Solar 5.161 960 KW – CEPALCO, Sunpower Phil Solar Ilijan Expansion (300 MW) Cagayan e Oro Plant/rural electrification HEP 729 KW Camarines Sur projects Geothermal Tanawon Geo (40 MW)-2011 Rangas Geo (40 MW)-2015 1 MW Isabela Manito-Kayabon Geo (40MW)-2016 Biomass 20.93 Coal-Fired Ocean R & D activities – Demo CCGT projects in Leyte/Mindanao Private Sector Initiated Power Projects Source: E. Karunungan ( Department of Energy )/Philippine Daily Inquirer Source: Department of Energy 7  25/02/2024 Visayas Grid Mindanao Grid CEPALCO Cabulig HEP (8 MW) DMCI Concepcion Minergy Bunker Fired 2011 Tagoloan HEP(68 MW) Power Corporation (20 MW)-2010 2012 (100 MW) Aklan HEP (41 MW)-2012 2012 Villasiga HEP (8MW)-2013 Toledo Expansion Green Power (246 MW) Southern Leyte Geo Biomass(18 MW)-2010 Global Business Phase I-2010 (80 MW) Power Corp (164 MW) Green Power Panay Phase II-2011 2016 Phase I-2010 (36 MW)-2010 HEDCOR Sibulan Inc. Phase II-2011 AGUS 3 HEP(225 MW) (42.5 MW) 2011 Oct 2009 Dauin Geo (40 MW) P A N A Y 2010 Legend: Conal Holding CFTPP KEPCO SPC Power (200 MW)-2011 (200 MW) Biomass Sultan Kudarat Coal EDC Nasulo 2011 (200 MW)-2012 Geothermal Hydroelectri (20 MW) EDC Mindanao Geothermal 3 HEDCOR Tamugan. 2011 (50 MW) (34.5 MW)-2010 Geothermal 2014 Coal-Fired Private Sector Initiated Power Projects Private sector initiated power projects Source: Department of Energy Source: Department of Energy Energy supply mix of the Philippines, MTOE 1993 % Share 1995 % Share 2000 % Share 2005 % Share 2007 % Share INDIGENOUS ENERGY 15.49 53.07 15.43 46.51 19.48 49.07 21.20 54.57 21.97 55.69 OIL 0.45 1.53 0.13 0.39 0.06 0.14 0.61 1.57 0.63 1.59 NATURAL GAS - 0.00 0.00 0.01 0.01 0.02 2.70 6.95 3.03 7.69 COAL 0.80 2.73 0.68 2.05 0.71 1.80 1.52 3.91 1.80 4.55 Subtotal 16.73 57.33 16.24 48.96 20.26 51.03 26.03 67.01 27.42 69.52 HYDRO 1.25 4.29 1.55 4.68 1.94 4.89 2.09 5.37 2.13 5.41 GEOTHERMAL 4.87 16.70 5.28 15.90 10.00 25.19 8.52 21.92 8.78 22.27 BIOMASS (Bagasse and Other RE) 8.12 27.82 7.79 23.48 6.76 17.02 5.77 14.84 5.56 14.10 SOLAR AND WIND 0.00 0.00 0.00 0.01 0.01 CME 0.00 0.00 0.00 0.03 0.08 Subtotal 14.25 48.81 14.62 44.06 18.70 47.10 16.37 42.14 16.51 41.87 NET IMPORTED ENERGY 13.70 46.93 17.75 53.49 20.22 50.93 17.65 45.43 17.48 44.31 OIL 13.02 44.62 16.84 50.77 16.39 41.30 13.94 35.87 13.40 33.96 COAL 0.67 2.30 0.90 2.72 3.82 9.63 3.71 9.55 4.08 10.34 ETHANOL 0.00 - - 0.00 0.00 0.00 0.01 0.00 TOTAL ENER GY 29.19 100.00 33.18 100.00 39.69 100.00 38.85 100.00 39.44 100.00 GROWTH RATE (Total Energy), % 5.49 2.93 0.10 1.81 Self Sufficiency % 53.07 46.51 49.07 54.57 55.69 Source: Department of Energy From unproductive agricultural farm to a wind farm 8  25/02/2024 Specifications of NorthWind Power System Renewable Electric Capacity Worldwide Turbine’s hub height - 70 meters Blade length - 41 meters Rotor diameter - 82 meters Windswept area - 5,281 sq. m. *** Ground level to center of nacelle The turbine are oriented facing the sea, effectively eliminating windbreaks and achieving terrain roughness of class 0. Annual generation capacity - 74,482 MWh Wind turbine arrangement - Single row Spacing - 326 meters Orientation - North Prevailing wind direction - Northeast China Leads the World in Wind Why Such Growth? …costs are low! Capacity Total Installed Generating Capacity (MW) Increased Turbine Size R&D Advances Manufacturing Improvements 1979 2000 2004 2017 40 cents/kWh 4-6 cents/kWh 3-4.5 cents/kWh Less than 5 cents/kWh Source: Global Wind Energy Council 9  16/04/2023 WIND KINETIC ENERGY Wind power calculation WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION Wind mass ENERGY AND MASS EQUATION It is mass contained in the volume of air that will flow through the rotor. For the HAWT, the volume of air is cylindrical 1  16/04/2023 WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION DENSITY OF AIR AT VARIOUS TEMPERATURE WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION RELATIONSHIP BETWEEN POWER AND ROTOR DIAMETER PRINCIPLES INVOLVED IN THE ANALYSIS - Conservation of mass - Conservation of energy - Conservation of momentum 2  16/04/2023 WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION Conservation of mass - mass of the air never changes, no matter how the constituent parts rearrange themselves. CONSERVATION OF MOMENTUM - Wind speed is reduced ( energy is extracted from the wind) - there is a change in momentum (M – mass * speed) ACCORDING TO NEWTON’S LAW F = movo – m2v2 WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION BETZ LIMIT OF WIND TURBNES - In 1919, Albert Betz had postulation on the efficiency of wind BETZ LIMIT FORMULA turbines POWER FORMULA 3  16/04/2023 WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION POWER COEFFICIENT (Cp) BETZ LIMIT MEANING Wind rotors in an idealized conditions can extract, at Maximum power extracted most, 59.3% of energy contained in the wind. This is Cp = ---------------------------------------------- an important limit because it defines the upper limit of the efficiency of any rotor disk type energy Power available extracting device that is placed in the flow of a fluid WIND KINETIC ENERGY CALCULATION WIND KINETIC ENERGY CALCULATION Consider a 1-MW rated wind turbine with rotor diameter of 70 m and data provided by the turbine manufacturer in the table WIND SPEED (M/S) Actual POWER (kW) below. 2 5 a. Calculate the turbine swept area 4 50 b. Plot the turbine power curve 6 150 c. Generate the Betz limit power expected at the wind velocity 8 400 range 10 660 d. Plot the Betz limit curve 12 900 e. Check if the turbine is within the Betz limit at all wind speeds 14 1000 4  16/04/2023 SOLUTION GRAPH Wind Energy and Power PROBLEM Atmospheric pressure differences accelerate and impart kinetic energy into the air A turbine has a rotor diameter of 2 m at Wind energy conversion machines (WEC) convert wind energy into electrical or mechanical forms power rating of 2 kW at 12 m/s. Check if How much power can we extract? the turbine will pass the Betz limit test at 12 m/s wind speed Power  K.E. 12 (mass )  (velocity)2 time  time mass  density  area  velocity time AV 3 Power  1 2 (density)  area  (velocity)3  2 5  16/04/2023 Wind Power - Example Wind Power – Example, cont. Example: P 1.2 kg m 4m 10 m s  3 2 3 V = 10 m/s 2 A = (2 m)2 = 4 m 2 kg  m 2 kg  m m m = 1.2 kg/m 3  2400  2400 2   2400 N  s3 s s s http://enneagon.org/footprint/jpg/dvc01w.jpg N m P  2400  2400 W Theoretical Maximum http://z.about.com/d/gonewengland/1/0/5/C/leaf5.gif s AV 3 Power  1 2 (density)  area  (velocity)3  Betz Limit: 59.3% of the theoretical is the maximum amount 2 extractable by a wind energy conversion device (WEC) PBetz  0.593 (2400 W )  1423.2 W Practical Maximum 6