Campo code: a practical framework to design Solar

Campo code: a practical framework to design Solar Tower Systems Francisco J. Collado, Jesús Guallar

CSP Sevilla 2017, 21-22 Noviembre

1

Generation of radially staggered heliostat fields n 

“Radial staggered” should be the preferred option as compared with “cartesian” and “Fibonacci” (bio-mimetical) ones (Luis Crespo, SolarPACES 2017)

n 

DELSOL3 (1986): Radial and azimuthal spacing for 11x11 zones § 

(ηopt calculated only for the heliostat in the centre of the zone) LH

n 

CAMPO (2012): Nhel1 & two non-dim. radial spacing § 

ΔRmin

ΔRmin=DM*⎷3/2

(ηopt calculated for each and every mirror in the field)

CSP Sevilla 2017, 21-22 Noviembre

LW Δaz1

2

Campo: radially staggered (Nrowsi max. density)

ZONE 1

Δaz1=2π/Nhel1; R1=DM*Nhel1/2π

400

0.7

ZONE 2

350

ΔR1=Δr1(-)DM=ΔRmin=DM⎷3/2

0.65

ZONE 1

300

∆R2(m)=∆r2(−)*DM(m)

Δr1=0.866

DM

200

0.55

ZONE 2

∆R1(m)=∆r1(−)*DM(m)

150

Δaz2= Δaz1 /2 (Nhel2=2*Nhel1) ΔR2=Δr2*DM Nrows2=round(2*R1/ΔRmin) ZONE 3

[m]

Nrows1=round(R1/ΔRmin)

0.6

250

50

0 0

ΔR3=Δr3*DM

CSP Sevilla 2017, 21-22 Noviembre

0.5

∆az1 (rad)

100

R1(m) 0.45

50

100

150

200

250

300

350

400

[m]

3

Instantantaneous heliostat optical efficiency ηi Z

HR

intercept, fint (Spot shape, D, cosω, σs )

RR γ

attenuation, fatt(D, dust in the air) D

THT

ρ, reflectivity (mirror availability) n

Y, North blocked area

t

shadowed area

ped. height

X, East

CSP Sevilla 2017, 21-22 Noviembre

cosω, incidence cosine ω s ID

fsb (free s&b area)

Sun

4

Shadowing and blocking in campo (TMY) 150

shadowing heliostat

North problem heliostat

1

100

"shoulder" blocking heliostats

50

αt=315º sector 1

[m]

sector 7

0.9 sector 2

αt=275º

0

sector 3

sector 6

sector 4 sector 5

−50

600

αt=40º

αt=90º

400 0.8

αt=110º

αt=180º

200

"nose" blocking heliostat

α =225º t

0.7

[m]

−100

−150 −150

−100

−50

0

50

100

0 0.6

150

[m]

−200 5

0.5

4s 0

2s

2b 5s

1b

1s

−400

−5

0.4

3s −10

[m]

3b

−15

1

3t

2

−20

Day=345; Solar hour=9 ; R [m]=313.5443; α =−90º; 90º−ε =16.5312º; THT=120 t s fsb=0.501; zona=3; fila=2; num=91

4 5 −25

−30 −30

−600

s

−20

−10

0

10

20

30

−600

−400

−200

0

200

400

600

0.3

[m]

40

[m]

CSP Sevilla 2017, 21-22 Noviembre

5

TMY-Almería, ηfield month (7) solar time ID (W/m2) 9 10 21(January) 11 12 . . 7 8 9 172 (June) 10 11 12 9 10 355 (December) 11 12

month(12)

562 708 775 775

January

693 835 905 939 955 960 489 653 730 753

. .

. .

June July December

sunshine hours (nhj) 152.8

. .

314.3 395.7

. .

160.6

ηannual,i {annual wheighted ave.} =f(ηi,ndj,nhj,ID,i)

CSP Sevilla 2017, 21-22 Noviembre

ηfield=(Σfieldηannual,i)/Nhel (Almería-PSA)

6

Design of the collector field for Noor-III-like (150 MWe) Dimension

Almería

Noor III

DNI [kwh/m /year] Annual sunshine hours Solar field area Number of heliostats Heliostat mirror area Heliost. Diagonal DH Tower optical height THT Receiver power Rec. Diameter RD Receiver height RH Nominal electric power Thermal storage hours

2268 2879,8 185 Ha 2650 2 115.72 m (HE35) 15.7 m 140 m 120 MWth 8.1 m 10.6 m 19.9 MWe 15 h

2500 3100 550 Ha 7400 2 178.5 m (HE54) 19.67 m 200, 225, 250, 275 m 6 660 MWth 14, 16, 18, 20, 22 m 1.2*DR m 150 MWe 7.5

2

Comments

GAST, Marrakesch

Assumed

Assumed

Sener (SolarPACES 2016)

Define:

60

0.866

•  The layout (Nhel1, Δr1, Δr2, Δr3) of the collector field (1st optimization) •  [THT, RR] (HR=1.2*DR) •  Minimum LCOE=(FCR*Invest. Costs+Annual O&M costs)/(Annual Electr.*Ava) CSP Sevilla 2017, 21-22 Noviembre

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Optimum layouts for Nhel=7400, Sener HE54, Almería (1) 2000

0.75

ηfield=57.58

η

=69.69 η

zone1

=62.41 η

zone2

0.75

ηfield=57.96

zone3

Nhel1=660 Nhel2=2640 Nhel3=4100

1500

2000

=52.52

η

=69.68 η

zone1

=61.10 η

zone2

=54.05

zone3

Nhel1=660 1500 Nhel2=2640 Nhel3=4101

0.7

0.7

ηmin=42.6100

ηmin=46.4140

1000

1000

0.65

0.65 500

[m]

0.6

0

[m]

500

0.6 0

0.55 −500

0.55

−500 0.5

−1000

−1000

−1500 −2000

σ =1.53 ρ=0.9*0.99 s ∆r2=1.0 ∆r3=2.0 Nh1=60 THT=250 m; RR=9.0 m; HR=22.0 m −1500

−1000

−500

0 [m]

500

1000

1500

CSP Sevilla 2017, 21-22 Noviembre

0.45 2000

0.5

σ =1.53 ρ=0.9*0.99 s ∆r2=0.866 ∆r3=1.6 Nh1=60 −1500 THT=250 m; RR=9.0 m; HR=22.0 m −1500

−1000

−500

0 [m]

500

1000

1500

8

Optimum layouts for Nhel=7400, Sener HE54, Almería (2) 2000

2000

0.75

ηfield=58.05

η

=69.68 η

zone1

=61.10 η

zone2

=56.39

field

zone3

Nhel1=660 1500 Nhel2=2640 Nhel3=4100

0.75

η

=54.21

ηzone1=69.64 ηzone2=60.85 ηzone3=51.39

1500 Nhel1=660 Nhel2=2640 Nhel3=4099

0.7 ηmin=45.6050

0.7 ηmin=42.9380

1000

1000

0.65

0.65

500 0.6

0.6

[m]

[m]

500

0

0

0.55 0.55

−500

−500

0.5 0.5

−1000

σ =1.53 ρ=0.9*0.99 s ∆r2=0.866 ∆r3=1.8 Nh1=60 −1500 THT=250 m; RR=9.0 m; HR=22.0 m −1500

−1000

−500

0 [m]

500

1000

1500

CSP Sevilla 2017, 21-22 Noviembre

−1000

σ =1.53 ρ=0.9*0.99 s ∆r2=0.866 ∆r3=1.6 Nh1=60 −1500 THT=250 m; RR=8.0 m; HR=19.0 m −1500

−1000

−500

0 [m]

500

1000

0.45

1500

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Annual (average) energy balance of the receiver

Annual energy on the receiver ER

(Noor-III)

Annual energy absorbed Eabs

DNI= 2500 (kWh/m2/yr) ER (kWht)=DNI (kWh/m2/yr) x Am (m2) x Nhel x ηfield

Sunshine hours= 3100

Eabs=αsER-Lossesthermal; ηrec=Eabs/ER= αs-Lossesthermal /ER ​𝐿𝑜𝑠𝑠𝑒𝑠↓𝑡ℎ𝑒𝑟𝑚𝑎𝑙 =(​𝑄↓𝑟𝑎𝑑 +​𝑄↓𝑐𝑜𝑛𝑣 ) ​𝑁↓ℎ𝑜𝑢𝑟𝑠 =[𝜀 𝜎 (​𝑇↓𝑤𝑎𝑙𝑙↑4 −​𝑇↓𝑎𝑚𝑏↑4 )+​ℎ↓𝑚𝑖𝑥 (​ 𝑇↓𝑤𝑎𝑙𝑙 −​𝑇↓𝑎𝑚𝑏 ) ] ​𝑁↓ℎ𝑜𝑢𝑟𝑠 ​𝐴↓𝑅  Twall,o=900 K=627 ºC < 650º C, “(αs) Absortance do not decrease with time” (Ho, 2014) Tsalt,o=838 K

ΔTo=900-838=62 ºC; Tsalt,i=563 K

Twall,i=Tsalt,i+ΔTo =625 K

(q’’ constant)

Twall,mean=(Twall,o+Twall,i)/2=(900 K+625 K)/2=763 K CSP Sevilla 2017, 21-22 Noviembre

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Field and net efficiency 7400 heliostats 62 Nhel=7400, Twall,max =900 K, σs=1.53 mrad,ρ=0.9 x 0.99

60

ηfield

Annual efficiency (%)

58

56

ηabs=ηrec x ηfield

54

52 (89,15%)

(88,21%)

(ηrec=87,17%)

ηabs

(90,17%)

50 (90.89%)

THT 200 m THT 225 m THT 250 m THT 275 m

48

46 7,0

CSP Sevilla 2017, 21-22 Noviembre

8,0

9,0 10,0 11,0 Receiver radius [m]

12,0

11

Net annual electric energy ENET 650

Net annual electric production (GWh-e)

ENET=ηabs*DNI*Am*Nhel*εpower 630

εpower=εpiping*εstorage*εcycle*εauxiliary 610

εcycle=0.412 (SAM, 2017) 590

εauxiliary=0.9 (SAM, 2017) THT 200 m 570

THT 225 m THT 250 m THT 275 m

550 7,0

8,0

9,0 10,0 Receiver radius [m]

CSP Sevilla 2017, 21-22 Noviembre

11,0

12,0

12

LCOE (SAM-NREL costs models, 2017) 13,0

CDirect =[CHEL+ CREC (AR)+ CTOW(TH)+CPOW+CTES]*1.07

12,9

THT=200 m THT 275 m

12,8

THT 250 m

LCOE [c/kWhe]

THT=225 m

12,7 12,6

𝐿𝐶𝑂𝐸=​𝐹𝐶𝑅 𝑥 𝐶𝑎𝑝. 𝐶𝑜𝑠𝑡𝑠+ 𝑂&𝑀 𝑐𝑜𝑠𝑡𝑠/​𝐸↓𝑁𝐸𝑇 𝑥𝑃𝑙𝑎𝑛𝑡 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦  𝐹𝐶𝑅(𝐹𝑖𝑥𝑒𝑑 𝐶ℎ𝑎𝑟𝑔𝑒 𝑅𝑎𝑡𝑒)=0.075 (𝑆𝑎𝑛𝑑𝑖𝑎, 2011) 𝐶𝑎𝑝. 𝐶𝑜𝑠𝑡𝑠=𝐶𝐷𝑖𝑟𝑒𝑐𝑡+𝐶𝐼𝑛𝑑𝑖𝑟𝑒𝑐𝑡 𝐶𝐼𝑛𝑑𝑖𝑟𝑒𝑐𝑡=𝐶𝐿𝑎𝑛𝑑+ 𝐶𝐸𝑃𝐶 𝑜𝑤𝑛𝑒𝑟+𝐶𝑆𝑎𝑙𝑒𝑠 𝑇𝑎𝑥 𝐶𝐻𝐸𝐿=$130/ (SolarPACES 2017) 𝑚2 𝑃𝑙𝑎𝑛𝑡 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦=0.9 (𝑆𝑎𝑛𝑑𝑖𝑎, 2011) 𝑂&𝑀 𝐶𝑜𝑠𝑡𝑠=$66/(𝑘𝑊−𝑦𝑟)+($3/MWhe)* 𝐸𝑛𝑒𝑡

12,5 12,4 12,3 12,2 6,0

7,0

8,0 9,0 Receiver radius [m]

10,0

CSP Sevilla 2017, 21-22 Noviembre

11,0

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Conclusions • 

Campo is a Matlab© code suited for the optimized design of heliostat fields

• 

Whole layout defined with only three parameters: Nhel1, Δr2(-), Δr3(-)

• 

Optical efficiency of each and every mirror in the field

• 

Annual incident energy (TMY-Almería) for 7400 heliostats in about 180 s

• 

Combined with annual thermal losses and εpower, gives net electricity (LCOE)

CSP Sevilla 2017, 21-22 Noviembre

14

Acknowledgments The authors want to thank the Spanish Minister of Economy and Competitiveness, and the European Fund for Regional Development for the funding of this research through the research project ENE2015-67518-R (MINECO/FEDER)

CSP Sevilla 2017, 21-22 Noviembre

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