Lecture #3 Solar Tracking and Solar Concentrating 1. angle of incidence on moving surfaces (solar tracking). examples of tracking options: 1- and -axis systems 3. concentrating solar radiation 4. concentrators, concentration ratio, CPC 5. concentrating solar power plant (CSP)
Solar radiation components Direct (beam), diffuse and re3lected (from ground) components; their sum is the total solar radiation G b G d G r h,h = horiontal, T = /lted tot = total n = normal d = diffuse b =direct
Total solar radiation on the surface G b Direct (beam), diffuse and re3lected (from ground) components; their sum is the total solar radiation Horiontal surface G d h,h = horiontal, T = /lted tot = total n = normal d = diffuse b =direct G r G b,n G b,n θ θ G tot, H = Gb, n cos + Gd, H = $!#!" θ = G b, H Tilted surface Total radia/on = beam+diffuse+reflected G tot, T = Gb, T + Gd, T + Gr, T G b, H + ρ cosθi cosθ + G d, H g( Gb, H + Gd, H 1+ 1 ) cos cos s s +
How to increase the amount of available solar radiation? Optimie the orientation (γ ) and inclination of the surface: minimie the angle of incidence (θ i ) = cos(θ i ) à1 Fixed position: 3ixed inclination/tilt (s or β), 3ixed aimuth angle: surface orientation to the south (γ=0), tilt= latitude +/- 0 o Solar tracking : to increase amount of beam radiation by moving the surface with the sun; - axis tracking (surface always towards the sunà θ i =0); 1-axis tracking (1 axis 3ixed, 1 axis moves)
Options for orientation of a solar collector Fixed position: 3ixed inclination/tilt (s or β), 3ixed aimuth angle. If collector orientation is to south (γ=0) Angle of incidence of beam/direct solar radiation is cosθ i = sinθ sin s cosγs + cos s cosθ cosθ = sinφ sinδ + cosδ cosω cosφ Tilt angle typically +/- 0 deg + latitude of the site Solar tracking options: to increase amount of beam radiation; - axis tracking (collector always towards the sun θ i =0); 1-axis tracking ( 1 axis 3ixed, tracking along one axis)
Tracking: surface vector not fixed,, but angles s and γ change G aur pinta G θ s s α y y x γ s sout x γ Directional vectors of the Sun and the surface Solar vector: Surface vector: G aur = sin θ cosγsi sinθ sin γsj + cosθ k G = 1 G pin = sin scosγ i sin ssinγ j + cossk The angle of incidence is the angle between these two vectors Gaur Gpin cos θi = = sin s sinθ cos( γ γ s) + cos s cosθ G G aur pin
Solar -axis tracking
1-axis tracking 1-axis tracking: the surface follows the position of the in respect to one axis only and tries to minimie the θ i Nomenclature: o NS-axis, EW-tracking = North-South axis 3ixed, tracking in East-West direction o Aimuth tracking = the surface follows the sun in the aimuth-plane o EW-axis, NS-tracking= East-West axis 3ixed, tracking in North-South direction
Position vector s Sun G N Tracking option: find the nearest point of G N on the rectangle perimeter to the corner where the Sun is cos θ G s θ i θ G s = sun s normal vector North G = normal vector of surface N G s = 1 West sin θ γ sin θ cos γ y East sin θ sin γ South x
Method to calculate the indicence angle for a, 1-axis tracking (case NS-tracking, EW-axis) Solar normal vector: G s Surface normal vector: G N G = solar normal vector s cos θ Angle of incidence θ i θ G = surface normal vector N choose G s = 1 North West sin θ γ s sin θ cos γ s y East sin θ sin γ s South x
Method to calculate the indicence angle for a, 1-axis tracking (case NS-tracking, EW-axis) Solar normal vector: G Surface normal vector: G s N = sin θ cosγsi sinθ sin γsj + cosθ k = sin θ cosγsi + cosθ k cos θ G s G N θ i θ G = solar normal vector s G = surface normal vector N choose G s = 1 North Angle of incidence cosθ = i G G s s G G N N γs sin θ cos + cos θ = 1 cos θ + sin θ cos γs West sin θ sin θ sin γ s γ s sin θ cos γ s y East = cos θ + sin θ cos γs South x G = 1 noon: γ s =0 à cosθ i =1 morning/evening γ s =90 à cosθ i = cosθ
$ Incidence angle for tracking options Derived using the same principle as in previous slide; aimuth and enith angles have been opended Option axis NS EW tracking direction stable s=0 s=90 stable s=90 cos θ i + sin s sinθ cosγ + cos s cosθ cosδ sin sin γ s = cos θ sinθ sinθ cosγ cos θ = sinφ sinδ + cos sin ssinθ cosγ + cos s cosθ sinθ cosγ 1/ (sin δ + cos δ cos ω) EW NS NS NS EW s=0 s=90 sinθ cosθ tan s cosγ + cos (cos (cos θ + cos sin θ cos( θ s cos( θ s γ = γ ) s δ sin ω + cos δ cos ω) 1/ δ sin θ / cos EW γ = γ s ) Two-axis 1 Fixed flat plate cos s cosθ + sinθ sin scos( γ s γ ) ω + cos s) 1/ θ ω δ cosφ cosω cos s = cosθ cosθ i Braun, J.E. ja J.C. Mitchell, Solar Energy, Vol. 31, No. 5, 439 (1983); P. Lund, PhD dissertation, 1984
Application to Finnish conditions q How much more solar radiation could tracking provide on a surface? q In this example +50..60% Total solar radiation in Finland Kokonaissäteily Suomessa (vaaka+axis) kokonaissäteily, kwh/m,kk 300 50 00 150 100 50 Helsinki (vaaka) Helsinki (axis) Jyväskylä (vaaka) Jyväskylä (axis) Sodankylä (vaaka) Sodankylä (axis) Vaaka=horiontal 0 1 3 4 5 6 7 8 9 10 11 1 kuukausi
Ex 1: total radiation versus orientation Helsinki with different orietation and tracking options (vaaka=horiontal, pysty=vertical)
Concentrated solar radiation Principles of concentrating solar radiation Different concentrators Concentrated Solar Power (CSP) plants
Introduction to concentrating solar collectors Only direct radiation can be concentrated to a focal point D or 3D solar tracking Parabolic surfaces, heliostat (3lat mirror) concentrators Concentration ratio C= collecting surface area/absorbing surface area; heat losses drops as 1/C C= 60-100 à 400 o C C >00 à 600-1000 o C
Principle of a Concentrating Solar Power Plant (CSP) Concentrator + steam turbine (Rankine) Yearly ef3iency 15-5% Heat storage à 5-7 hours more operational time per day Large CSP: 350 MW (USA); Spain 50-100 MW Under construction 1000 MW à potential in EU 05 around 37,000 MW Costs 100-150 /MWh Peter Lund 01
Maximum concentration ratio (1) Principle: increasing power density (W/m ) on the surface through concentrating solar radiation De3ining the concentration ratio (C) in an optical system (e.g. lens, mirror) Optical system A' C = A A' A Thermodynamicaö limit for concentration (C max ): Simpli3ied energy balance of a concentrator S = 1kW/m ; σ = Stefan-Bolmann constant C=1 à T=364 K T=Sun s temperature à C~ 40000 4 σt = CS
Maximum concentration ratio Concentration ratio (through optics) a C = = a' n' sinθ ' nsinθ C max (θ ' = 90 ) = 1 sinθ Assume that the media are the same (n=n ) as in a collector; D = -dimensional collector geometry (e.g. parabolic through), 3D= 3-dimensional collector geometry (e.g. parabolic dish) C D max = 1 sinθ C 3D max = ( D C ) max = 1 sin θ
D- Parabolic concentrator A parabolic concentrator (the parabola rotates around its axis) forms an image and is non-ideal, but can reach high concentration ratios The sun and the optical axis (y-axis) of the parabolic surface need to be aligned to re3lect the radiation to the focal point (at distance f from 0) C = A a A p = X A L πal = sinϕ π sinθ c θ i
Optical ray tracing Example of how sun rays re3lect with 0 (position vector looks to sun) and 6 degree misalignment of the axis from the sun; re3lecting parabolic D surface
Effect of misalignment angle on the fraction of reflected radiation reaching the focal point High concentration ratio requires good mirror quality and accurate tracking; σ= optical error (quality of the re3lecting surface); Observe that the misalignment allowed with a concentrator is low!
How to make an ideal concentrator? Non-imaging optics - Compound Parabolic Concentrator (CPC) If a parabola surface (y=x ) rotates around its y-axis à parabolic concentrator (image forming optics) If a parabola surface (y=x ) rotates around its tangentà compound parabolic concentrator (non-image forming optics) = IDEAL CONCENTRATOR Focal point Aperture Concentrator axis Parabola axis The CPC re3lects all rays within an incoming angle of ±θ to the outlet (where an absorber or solar cell) θ θ +θ i -θ i
Different CPCs CPC applications mainly for low concentration ratios C= 5 (à large θ, tracking not critical and short length Cheep and easy to manufacture E.g. CPC + solar cell ; a booster back-mirror for a vacuum tube solar collector
Different CPC applications Water disinfection Solar heating
Group Work # 3 In a -3 person team, discuss 5 min the following question (+5min joint discussion): How would you realie a -axis tracking system? How to get the surface to point directly to the Sun?