heliostat field design for solar thermochemical processes*sfera.sollab.eu › ... ›...
TRANSCRIPT
Heliostat field design for solar
thermochemical processes*Robert Pitz-Paal
DLR - Solar Research
based on: Robert Pitz-Paal, Nicolas Bayer Botero, Aldo Steinfeld Heliostat field layout optimization for high-temperature solar thermochemical processing Solar Energy, Volume 85,
Issue 2, February 2011, Pages 334-343
2
Classification of CRS-Tools
calculation speed
degr
eeof
det
ail
layout optimisation
performance calc.
system layout
system analysis
component analysis
simulation of operations
optimisation of operations
SFERA Winter School Solar Fuels & Materials Page 15
3
N
SE W
Heliostat Field Optimization
Maximizing annual energy output
or
Minimizing production cost
by variation of
Design parameters
heliostat position
tower height
receiver aperture
…
Operation parameters
operation temperature
…
4
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• coordinate systems:
• tower coordinate system
• sun angles• azimuth 0° = south• elevation 90° = zenith
• receiver coordinate systems
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
x
y
SFERA Winter School Solar Fuels & Materials Page 16
5
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• time system:
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
Jun11 h
10 h
9 h
8 h
7 h
6 h
5 h
13 h
14 h
15 h
16 h
17 h
18 h
Mai/JulMai/Jul
Apr/AugApr/Aug
Mär/SepMär/Sep
Feb/OktFeb/Okt
Jan/NovJan/Nov
Dez
11 h
10 h
9 h
8 h
13 h
14 h
15 h
16 h
0
10
20
30
40
50
60
70
80
90
60 90 120 150 180 210 240 270
Vormittag NachmittagMittag12 h
6
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• time system:
• 7 months: Dec, Jan/Nov, Feb/Oct, Mar/Sep, Apr/Aug, Mai/Jul, Jun• days/month: 31 61 59 61 61 62 60• one representative day per month (21st)• local solar time, hourly intervals
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
SFERA Winter School Solar Fuels & Materials Page 17
7
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• radiation model:• tabulated data• clear sky model from Hottel (1976):
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
ETatmo IRRtimedayhLATtDNI ),,,()(
600
650
700
750
800
850
1 2 3 4 5 6 7 8 9 10 11 12
DN
I [W
/m²]
LAT 35°N, 0m, solar noon
8
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• atmospheric attenuation:
• agrees well with Pittman/Vant-Hull at
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
0 0.5 1 1.5 2 2.5 3
Slant Range [km]
Tra
nsm
issi
vity
[-]
Pitman/Vant-Hull
HFLCAL
)(),( range slantfyxatmo
Rho_H2O 7 g/m³Vis 40 kmH 0 kmh_tower 0.1 km
SFERA Winter School Solar Fuels & Materials Page 18
9
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• cosine factor
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
10
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• shading
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
SFERA Winter School Solar Fuels & Materials Page 19
11
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• blocking
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
12
Background
Design and optimization of solar tower systems require the
calculation of the reflected beam in the target plane
SFERA Winter School Solar Fuels & Materials Page 20
13
Background
Design and optimization of solar tower systems require the
calculation of the reflected beam in the target plane
Deviations from ideal
concentration:
• non-parallel rays
• alignment error
• shape error
• slope error
• diffuse reflection
• (off-axis-reflection)
14
Background
statistical approach (ray-tracing) analytical approach (convolution)
SEMI
221122121211 ),(),(),(),( dydxdydxyyxxSyyxxEyxMyxI
0 0
2/)(
)()(!!2
),(22
i jji
ijyx
yHxHji
CeyxI
SFERA Winter School Solar Fuels & Materials Page 21
15
HFLCAL Approach
²2
²
²2
1)(
r
erF
HFLCAL uses a simplified convolution approach:
The reflected image of each heliostat is approximated by a circular normal
distribution (“Gaussian”) 222qualitybeamsunerrorbeam
0
0.05
0.1
0.15
0.2
0.25
0.3
-5 -4 -3 -2 -1 0 1 2 3 4 5
2
sun mirror
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
r [mrad]
pro
bab
ilit
y [-
]
"Kuiper"
"Gaussian"
16
Accuracy of Mathematical Model
²2
²
²2
1)(
r
erF
0
20
40
60
80
100
120
140
160
180
200
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
ray-tracing
HFLCAL
• Pettit, Vittitoe and Biggs (1983) found good agreement when beam error 2 sun
• Central Limit Theorem: „superposition of a great number of any distributionsconverges towards a normal distribution“
0
20
40
60
80
100
120
140
160
180
200
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
ray-tracing
HFLCAL
perfect mirror realistic mirror
222qualitybeamsunerrorbeam
SFERA Winter School Solar Fuels & Materials Page 22
17
Accuracy of Mathematical Model
²2
²
²2
1)(
r
erF
How to chose the correct value for beam error ?
total sigma error
0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
slope error (normal) [mrad]
tota
l sig
ma
[mra
d]
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
4.0%
4.5%
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
slope error (normal) [mrad]
RM
S (
HF
LC
AL
-Ray
Tra
cin
g)
222qualitybeamsunerrorbeam
18
Accuracy of Mathematical Model
tracking errors influence the amount of intercepted energy
2222 )2( trackqualitybeamsunerrorbeam
21 axisaxistrack
SFERA Winter School Solar Fuels & Materials Page 23
19
Accuracy of Mathematical Model
astigmatism influences the size and shape of the reflected beam
222astigmerrorbeamtotal
;1cos
;cos
fSLRdW
fSLRdH
s
t
SLRWH facethelsfacethelt
astigm 4
2,
2,2
1
20
Accuracy of Mathematical Model
single mirror, incident angle 37.6° (left: HFLCAL, right: ray tracing)
astimgatism influences the size and shape of the reflected beam
222astigmerrorbeamtotal
-2.4 -1.9 -1.4 -1.0 -0.5 0.0 0.5 1.0 1.4 1.9 2.4
kW/m²
21-24
18-21
15-18
12-15
9-12
6-9
3-6
0-3
-2.4 -1.9 -1.4 -1.0 -0.5 0.0 0.5 1.0 1.4 1.9 2.4
[kW/m²]
21-24
18-21
15-18
12-15
9-12
6-9
3-6
0-3
SFERA Winter School Solar Fuels & Materials Page 24
21
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• intercept
• aimpoint = center: analytical solution
• aimpoint center: numerical solution
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
apertureinc dde
2
22
2
22
1
22
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• intercept
• aimpoint = center: analytical solution
• aimpoint center: semi-analytical solution
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
apertureinc dde
2
22
2
22
1
SFERA Winter School Solar Fuels & Materials Page 25
23
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• intercept
• free form: numerical solution
),,(),,(),,(),()(),,( &cos tyxtyxtyxyxFtDNItyxP incsbatmoreflMirinc
apertureinc dde
2
22
2
22
1
24
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• secondary transmission
),,(),(),,( sec tyxPyxtyxP increc
SFERA Winter School Solar Fuels & Materials Page 26
25
Performance Calculation
Given: Heliostat, Heliostat Positions, Aim Points, Tower, Receiver, (Secondary)Task: calculate annual performance
• solar field power
• thermal power
• annual performance
)()()( tPtPtQ fieldconversionfieldthermal
iifield tyxPtP ),,()(
tthermalthermal
tfieldfield
tQtwE
tPtwE
)()(
)()(
26
Layout Calculation
Given: Heliostat, Tower, Receiver, (Secondary)Task: calculate heliostat positions
1. calculation of hypothetical heliostat positions
• bilinear expansion• bilinear with central “gap”• slip planes• (heliostats in rows)• user defined algorithm
SFERA Winter School Solar Fuels & Materials Page 27
27
Layout Calculation
Given: Heliostat, Tower, Receiver, (Secondary)Task: calculate heliostat positions
1. calculation of hypothetical heliostat positions
• bilinear expansion• bilinear with central “gap”• slip planes• (heliostats in rows)• user defined algorithm
maximum density zone
expand with u = au + r x bu
slip plane: add heliostat to each gap
28
Layout Calculation
Given: Heliostat, Tower, Receiver, (Secondary)Task: calculate heliostat positions
2. calculation of field performance
3. selection of best performing heliostats
SFERA Winter School Solar Fuels & Materials Page 28
29
Field Performance Matrix
Given: Heliostat, Heliostat Positions, Tower, Receiver, (Secondary)Task: calculate field efficiency for any sun angle
30
Optimization
Given: Heliostat, Positioning Alg., Tower, Receiver-Type, (Secondary)Task: optimize layout parameters
distribute heliostats
calculate all time points
chose best heliostats
optimizationalgorithmmanipulatessystemparameters
optimize for-power per m² reflective area-least cost of thermal receiver power
SFERA Winter School Solar Fuels & Materials Page 29
31
Optimization for Power Generation vs. Chemical Processes
Power Generation
Typical temperatures below 1300 K
Typical solar concentration <1000 suns
Process temperature defined bypower cycle
Controlled independently of solar input by adjustment of mass flow rate
Chemical processes
Typical temperature above 1300K
Typical solar concentration >1000 suns
Use of secondary concentrators
Process temperature defined bychemical process
Process temperature depends on solar power to receiver (changes over time!)
Reactor model and chemical reaction characteristicsimpact field design
32
Assumptions to estimate theoretical upper limit
the reactor temperature is uniform
convection and conduction heat losses are neglected
transient heat losses during start-up and shut-down are neglected
reaction achieves completion, e.g. there are no chemical side products considered
no purge gases are used
SFERA Winter School Solar Fuels & Materials Page 30
33
Target function for optimizationSimplified Model Approach
Two Example Reactions..ZnO dissociation ( 2000K)
ZnO Zn + 0.5O2
Coal gasification ( 1400K)
C + H2O CO + H2
4aperturelossesthermal
a0reaction
prreaction
lossesthermalreactioninsolar,0
exp
)()(in
TATPRTEkAT
dTcTHTP
TPTPPT
T
steps timeallin solar,
steps timeallr
chemicaltosolar
)(
P
T(T) H
34
Parameters
Heliostat size 10 / 120 m²
Beam Quality3.3; 3.0; 2.7 mradincl. sunshape
Design powerto reactor
1; 10; 100 MW
Tower Height
1 MW 40m
10 MW 120m
100 MW 250m
Heliostat spacing
SFERA Winter School Solar Fuels & Materials Page 31
35
Multimodal objective function:Different configurations lead to very similar optima
Case 1 Case 2
tyreflectivi0.87 0.87
inecos0.8873 0.8863
shadingblockin&0.9075 0.8888
nattenuatio0.9654 0.9688
erceptint0.8339 0.8625
ondarysec0.9146 0.9228
receiver0.5868 0.5686
total0.3026836 0.3026597
36
ResultsComparison of fields (10MW – 10m²)
reference field optimized for design point concentration of 500 suns
field = 69,27 %
optimization target: chemical yield Coal gasification.
field = 61,8 %solar-chemical=39,1%
peak concentration = 2555 sunsmean concentration = 2107 suns
optimization target: chemical yield zinc oxide dissociation
field = 55 %solar-chemical=30,6%
peak concentration = 4798 sunsmean concentration = 3679 suns
SFERA Winter School Solar Fuels & Materials Page 32
37
Efficiencies [%] Reactor operating conditions
ZnO dissociation Field Intercept Secondary Optical Reactor Total
Average
Operating
Temperature
[K]
Peak
Operating
Temperature
[K]
Flux
Density
[MW/m²]
1 MW
10m2 Heliostat 66.7 86.4 92.1 53,1 55.5 29.5 1910 2014 4.5
10 MW
120m2 Heliostat 67.3 86.0 92.2 53.4 55.9 29.8 1912 2013 4.6
100 MW; 3 cavities
120m² Heliostat 63.7 88.7 91.7 51.8 57.0 29.2 1920 2017 4.8
Efficiencies [%] Reactor operating conditions
Coal gasification Field Intercept Secondary Optical Reactor Total
Average
Operating
Temperature
[K]
Peak
Operating
Temperature
[K]
Flux
Density
[MW/m²]
1 MW
10m2 Heliostat 69.9 95.4 92.9 61.9 66.0 40.9 1308 1469 2.2
10 MW
120m2 Heliostat 69.4 95.2 93.1 61.5 66.3 40.8 1307 1470 2.9
100 MW; 3 cavities
120m² Heliostat 65.4 96.2 93.1 58.6 66.8 39.9 1308 1483 2.5
38
Comparison to solar electric systems
Chemical conversion through electrolysis:
Assume rec=0.92 , cycle=0.45 , electrolys=0.8
tot=0.699 *0.92* 0.45 * 0.8 = 0.23
Efficiencies [%] Reactor operating conditions
Thermal Receiver 500 kW/m²
Field Intercept Secondary Optical Reactor Total
1MW
10m² Heliostat 72.4 96.5 - 69.9 - -
10MW
120m² Heliostat 70.0 97.5 - 68.2 -
100MW; Northfield
120m² Heliostat 64.5 99.5 - 64.2 - -
n/a
SFERA Winter School Solar Fuels & Materials Page 33
39
Sensitivity Analysis: Impact of beam quality
a) d)
ZnO C-Gasif.
The perfect mirror
The perfect mirror
40
Sensitivity Analysis: Impact of tower height
ZnO C-Gasif.
b) e)
SFERA Winter School Solar Fuels & Materials Page 34
41
Sensitivity Analysis: Impact heat recovery / inlet temp.
ZnO C-Gasif.
a) b)
42
Summary
Optimization methodology of heliostat fields for solar tower applied to high-temperature chemical reactions
Application to dissociation of Zinc oxide and coal gasification with optimum estimation:
Zinc oxide dissociation: 2000 K and 5000 suns
Coal gasification: 1400 K and 2000 suns
Excellent secondary optics are required to achieve these conditions
Penalties up to 25 % in field efficiencies due to need of high temperature heat of chemical reactions
Systems still show efficiency benefits over solar electrochemical concepts
High temperature reaction concepts very sensitive to beam quality and tower height
SFERA Winter School Solar Fuels & Materials Page 35