pv systems and farm design

PV Systems and Farm Design

M. A. Alam

alam@purdue.edu

Electrical and Computer Engineering

Purdue University

West Lafayette, IN USA

1

Theory and Practice of Solar Cells: A Cell to System Perspective

33

Outline

1) Configurations of PV systems

2) Principles of fixed tilt farm design

3) Calculation of yearly energy yield

4) Conclusions

M. A. Alam, PV Lecture Notes

Collection of

independent

2-level PV

nm

p-n junction solar cellCell

ModulePanel

Rooftop

PVSolar farm

nm-𝜇m cm-m km

Fabrication,

Device physics,

Manufacturing

Reliability, LCOE

Course outline: A multiscale problem

M. A. Alam, PV Lecture Notes

4

Cells, modules, panel

CC

Charge

controller

Battery/

storage

Inverter

AC

source/

grid

Distribution

panel

System Integration: Sysmbols

M. A. Alam, PV Lecture Notes

6

Stand-alone PV systems

Simple

Low cost

Calculators

Irrigation

More expensive

Off-grid

Many home PV

Variety of electronicsM. A. Alam, PV Lecture Notes

7

Solar homes: Grid-connected PV

Hybrid:

Multiple sources

Both AC/DC loads

PV connected to

Power-grid

M. A. Alam, PV Lecture Notes

8

Community PV: Microgrid and Solar Farms

M. A. Alam, PV Lecture Notes

9

Power

optimizer

Aside: Inverter configurations

Central Micro String Micro with

Power-optimizerM. A. Alam, PV Lecture Notes

10

1212

Outline

1) Configurations of PV systems

2) Principles of fixed tilt farm design

3) Calculation of yearly energy yield

4) Conclusions

M. A. Alam, PV Lecture Notes

0

100

200

300

4001300

1350

1400

1450

J F M A M J J A S O N DMonth

ly

(kW

-hr/m

2)

𝐼 0(W

/m2)

Extra-

terrestrial

Monthly GHI

𝐼0(𝑑𝑛) = 𝐼0(1 + Δ cos 2𝜋 𝑑𝑛 /𝐷)

Δ = 2(𝑅max– 𝑅min)/𝑑

Sunlight varies with seasons

13

How to tilt a solar module (i.e. determine 𝛽)

𝛼𝛽𝜃𝑧

𝐼𝑑𝑖𝑟 = 𝐼𝑏 sin 𝛼 + 𝛽 = 𝐼𝑏 cos(𝜃𝑧 − 𝛽)

𝐼𝑏

M. A. Alam, PV Lecture Notes 14

𝜃𝑧 varies throughout the year

𝛿 = 23.450 sin2𝜋 𝑑 − 80

365

𝛼

𝜃𝑧𝛿

𝛼(𝑑) = 90 − 𝐿 ± 𝛿(𝑑)

𝜃𝑧(𝑑) = 𝐿 ∓ 𝛿(𝑑)

North

South

𝜃𝑧,𝑤 = 𝐿 + 23.45

𝜃𝑧,𝑠 = 𝐿 − 23.45

δ ≡ Sun declination angle

March 21st (Vernal

Equinox)≡ 80 days

An empirical rule for tilt

𝜃𝑧(𝑑) = 𝐿 ∓ 𝛿(𝑑)

𝜃𝑧,𝑤 = 𝐿 + 23.45

𝜃𝑧,𝑠 = 𝐿 − 23.45

𝛽 = 𝐿 − 10

𝛽 = 0.69𝐿 + 3.7

𝛽𝑠 = 𝜃𝑧,𝑠 𝛽𝑤 = 𝜃𝑧,𝑤

Optimize integral over daily

intensity and solar angle for given 𝛽

Summer intensity is higher:

Two tilt, summer/winter:

𝛽

16

Example: How to tilt a module

𝛽 = 𝐿 − 10 30.27 3.50 21.23

𝛽 = 0.69𝐿 + 3.6 31.79 12.92 24. 83

𝛽𝑠 = 𝜃𝑧,𝑠

Lafayette Madras Shanghai

40.27𝑁 13.5 𝑁 31.23 𝑁

𝛽𝑤 = 𝜃𝑧,𝑤 63.72

16.82

36.95

−9.95

54.68

7.78

17

18

Tilt angle, Electrical vs. mechanical, Air vs. water cleaning

Aside: Cleaning considerations

M. A. Alam, PV Lecture Notes

Three components of irradiance

19

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏𝑘𝑇 = 𝐼𝐺𝐻𝐼/𝐼0cos(𝜃𝑍)

Standalone yield: Direct light

𝛼𝛽𝜃𝑧

𝐼𝑑𝑖𝑟 = 𝐼𝑏 sin 𝛼 + 𝛽 = 𝐼𝑏 cos 𝜃𝑧 − 𝛽

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏

𝐼𝑏

M. A. Alam, PV Lecture Notes 20

Stand-alone yield: diffuse component

𝛽

𝐼𝑑𝑖𝑓𝑓 =𝐼𝑑2න𝛽

𝜋

sin 𝜃 𝑑𝜃 =𝐼𝑑 1 + cos 𝛽

2

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏

𝐼𝑑

𝛽

𝐼𝑑

21M. A. Alam, PV Lecture Notes

Stand-alone yield: albedo

𝛽

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏ℎ

𝑉𝐹 =𝑆1 + 𝑆2 – 𝑆3 + 𝑆4

2ℎ

𝑆1

𝑆2

𝑆3

𝑆4

𝑉𝐹 =ℎ + 𝑠 – (0 + 𝑠2 + ℎ2 + 2𝑠ℎ cos 𝛽)

2ℎ

𝑉𝐹 =1

21 + 𝑟 − 1 + 𝑟2 + 2𝑟 cos 𝛽 → (1 − cos 𝛽)/2

𝑟 = Τ𝑠 ℎ → ∞

𝑠

ℎ

𝐼𝑎𝑙𝑏 = 𝐼𝐺𝐻𝐼 𝑅𝐴 𝑉𝐹

M. A. Alam, PV Lecture Notes 22

Stand-alone module: Energy yield

𝛼𝛽𝜃𝑧

𝐼𝑑𝑖𝑟 = 𝐼𝑏 cos(𝜃𝑧 − 𝛽)

𝐼𝑏

𝐼𝑑𝑖𝑓𝑓 =𝐼𝑑 1 + cos 𝛽

2

𝐼𝑎𝑙𝑏 = 𝐼𝐺𝐻𝐼 𝑅𝐴(1 − cos 𝛽)/2

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏

23M. A. Alam, PV Lecture Notes

Summer zenith: 𝜃𝑍𝑠Winter zenith: 𝜃𝑍𝑤

𝜃𝑍𝑠𝜃𝑍𝑤

ℎℎ𝑦

ℎ𝑥𝜃𝑍𝑤

𝑟𝑠

𝑝

𝛽

Row spacing in Lafayette, IN

SBR ≡ 𝑟𝑠/ℎ𝑦 = tan 90 − 𝛼 = tan 𝜃𝑧𝑤,𝑝

𝑝/ℎ = cos(𝛽) + sin(𝛽) tan 𝜃𝑧𝑤,𝑝

SBR ≡ 𝑟𝑠/ℎ𝑦 = tan 90 − 18.14 =3.05

M. A. Alam, PV Lecture Notes 27

Farm yield per unit area: direct beam

𝛼𝛽𝜃𝑧

𝐼𝑑𝑖𝑟 = 𝐼𝑏 sin 𝛼 + 𝛽 ℎ/𝑝 = 𝐼𝑏 cos 𝜃𝑧 − 𝛽 × ℎ/𝑝

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏

𝐼𝑏

𝑝

ℎ

M. A. Alam, PV Lecture Notes 30

Farm yield: diffused energy collection

𝛽

𝐼𝑇 = 𝐼𝑑𝑖𝑟 + 𝐼𝑑𝑖𝑓𝑓 + 𝐼𝑎𝑙𝑏

𝐼𝑑

𝛼 + 𝛽

𝐼𝑑

𝛼

𝐼𝑑𝑖𝑓𝑓(𝜉) =𝑝

ℎ×𝐼𝑑2න𝛽+𝛼(𝜉)

𝜋

sin 𝜃 𝑑𝜃 =𝑝

ℎ×𝐼𝑑 1 + cos(𝛼 +𝛽 )

2

M. A. Alam, PV Lecture Notes 31

3333

Outline

1) Configurations of PV systems

2) Principles of fixed tilt farm design

3) Calculation of yearly energy yield

4) Conclusions

M. A. Alam, PV Lecture Notes

Variety of Solar Farms

M. A. Alam, PV Lecture Notes 34

-80 -60 -40 -20 0 20 40 60 800

20

40

60

80

-80 -60 -40 -20 0 20 40 60 800

1

2

3

4

-80 -60 -40 -20 0 20 40 60 800

12345

period

Row spacing

Northern hemisphere,

South facing panels

Southern hemisphere,

North facing panels

Latitude (deg.)

SBR

(m)

Pan

el tilt (

deg.

)

Yearly Yield (kW-hr/m2)

Monofacial solar farms

M. A. Alam, PV Lecture Notes

35

W

Albedo contribution to Monofacial Farms

• 𝑅𝐴 = 0.2• 1-2 % gain in YY

• 1-2o increase in optimum tilt angle

• < 1% reduction in LCOE*

M. A. Alam, PV Lecture Notes

36

(c) (d)

1 2

(e) (f)

𝑝

ℎ𝑟

0 1 2 30.1

0.2

0.3

0.4

0.5

p/h

Daily

Energ

y/farm

are

a

(kW

-hr/

m2)

(g) (h)

𝑟 = 0

𝑟 = 0.5ℎ

(a)(i)

(a)(ii)

0

20

40

Impro

vem

ent,

%0.4 0.45 0.5 0.55 0.6 0.65

80

100

120

140

160

Annual mean-clearness indexA

nnual Y

ield

(kW

-hr/

m2)

Monofacial

(10% soiling loss)

Latitude 40 N

GvBF vs. mono

GvBF vs. vBF-1

-180-120-60

060

120180

Longitude

(b)

W

Ground-sculpted bifacial farms

M. A. Alam, PV Lecture Notes

39

Land-cost inclusive optimization

40

(a) = 0 = 15(b) (c) = 100

M. A. Alam, PV Lecture Notes

4141

Conclusions

PV design must be understood in a system context.

Given the weather information, it is relatively easy to

calculate the energy yield for stand-alone modules as

well as solar farms.

The increasing cost of land and wide-spread PV

deployment are encouraging the PV industry to

explore novel technologies (e.g. bifacial PV) and farm

topologies (e.g. floating solar).

An end-to-end cost-benefit analysis is essential to

create a farm that is ideally suited to a location. M. A. Alam, PV Lecture Notes

Self-study Quiz

Which direction does 90 degrees Azimuth indicate?

Names the light-components one must sum to calculate the

energy yield.

What is the cross-string method? Why do we need this

technique?

How does the albedo light collection by a module in a farm

compare to that of an stand-alone module?

What type of solar benefit the most from ground-sculpting?

When should one use floating solar farms compared to

normally tilted solar farms?

42

M. A. Alam, PV Lecture Notes