heliostat field design for solar thermochemical processes*sfera.sollab.eu › ... ›...

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 5

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



• time system:


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



• 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



7



• radiation model:• tabulated data• clear sky model from Hottel (1976):


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



• atmospheric attenuation:

• agrees well with Pittman/Vant-Hull at


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


9



• cosine factor


10



• shading



11



• blocking


12

Background

Design and optimization of solar tower systems require the

calculation of the reflected beam in the target plane


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


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


17


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


tracking errors influence the amount of intercepted energy

2222 )2( trackqualitybeamsunerrorbeam

21 axisaxistrack


19


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


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


21



• intercept

• aimpoint = center: analytical solution

• aimpoint center: numerical solution


apertureinc dde

2

22

2

22

1

22



• intercept

• aimpoint = center: analytical solution

• aimpoint center: semi-analytical solution


apertureinc dde

2

22

2

22

1


23



• intercept

• free form: numerical solution


apertureinc dde

2

22

2

22

1

24



• secondary transmission

),,(),(),,( sec tyxPyxtyxP increc


25



• 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


27

Layout Calculation


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


2. calculation of field performance

3. selection of best performing heliostats


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


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


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


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


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


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


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


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)


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


heliostat field design for solar thermochemical processes*sfera.sollab.eu › ... ›...

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