optimal cable sizing in pv systems: case study

APPLICATION NOTE OPTIMAL CABLE SIZING IN PV SYSTEMS: CASE STUDY

Lisardo Recio Maillo

June 2013

ECI Publication No Cu0167

Available from www.leonardo-energy.org

Publication No Cu0167

Issue Date: June 2013

Page i

Document Issue Control Sheet

Document Title: Application Note – Optimal Cable Sizing in PV Systems: case study

Publication No: Cu0167

Issue: 02

Release: Public

Author(s): Lisardo Recio Maillo

Reviewer(s): Hans De Keulenaer, Fernando Nuno

Document History

Issue Date Purpose

1 Oct 2009 Initial Public Release

2 June 2013 Revision in the framework of the Good Practice Guide

3

Disclaimer

While this publication has been prepared with care, European Copper Institute and other contributors provide

no warranty with regards to the content and shall not be liable for any direct, incidental, or consequential

damages that may result from the use of the information or the data contained.

Copyright© European Copper Institute.

Reproduction is authorized providing the material is unabridged and the source is acknowledged.



Page ii

CONTENTS

Summary ........................................................................................................................................................ 1

Introduction .................................................................................................................................................... 2

Design phase .................................................................................................................................................. 5

Design to maximum allowed current ..................................................................................................................... 5

Design to maximum allowed voltage drop ............................................................................................................. 8

Resulting section ..................................................................................................................................................... 8

Calculation of the economic section ............................................................................................................... 9

Conclusions ................................................................................................................................................... 16



Page 1

SUMMARY It is often beneficial to over-size the cross-section of electricity cables compared to the standard values that

follow out of voltage and current calculations. In the large majority of cases, oversizing has a positive influence

on the Life Cycle Cost of the installation. The investment in larger cable is easily paid back by the reduction of

Joule losses inside the cable and the subsequent savings on electricity bills.

When the cable is part of a photovoltaic (PV) installation, the investment in a larger-than-standard cable is

paid back even faster than in other installations. This is because the allocated electricity price for a PV

installation is higher than the market price thanks to the feed-in tariff of green certificates. In other words: the

energy losses that are avoided in a PV installation lead to an even bigger financial reward than in other

installations.

Increasing the cable cross section in PV installations also creates additional technical and environmental

benefits.



Page 2

INTRODUCTION

This analysis was carried out for a 100 kW PV plant located in Spain.

PV PLANT FEATURES

Location: Valencia, Spain

Panel installation mode: fixed, tilted at 30 degrees facing south

Number of panels in series in each array : 16

Number of arrays: 33

Maximum ambient temperature: 50 °C

Cable type: Tecsun (PV) (AS) (special cable for photovoltaic systems—lifespan 30 years, maintenance free)

System installation: open mesh tray (without thermal influence of other circuits)

PV MODULES

Nominal power: 222 W

Current at maximum power: IPMP = 7.44 A

Voltage at maximum power: Upmp = 29.84 V

Short Circuit Current: Icc = 7.96

MISCELLANEOUS

Inverter power = plant nominal power: 100 kW

Modules peak power: 16 x 33 x 222 W = 117,216 W = 117.216 kW

The entire installation comprises three blocks of eleven arrays each, connected respectively into three junction

boxes (CCG1, CCG2, and CCG3) (see picture of CCG1 below).



Page 3

Figure 1 – Electric lines distribution.

We will focus on the line between the CCG1 junction box and the inverters. Two cables are used.



Page 4

Figure 2 – Junction box.

We calculate the voltage and current for each junction box at the point of maximum power. We then derive

the cable section for the main DC line from this.

VOLTAGE

For a given array, the panels are connected in series, so the total voltage of one array is the sum of the

voltages of the individual modules. This is the applicable voltage at the junction box level.

U = Upmp x 16 = 29.84 V x 16 = 477.44 V

CURRENT

The total current per junction box is the sum of the currents of the individual arrays. There are 11 arrays per

junction box.

I = Ipmp x 11 = 7.44 x 11 = 81.84 A



Page 5

Figure 3 –View of an array

DESIGN PHASE

DESIGN TO MAXIMUM ALLOWED CURRENT

The applicable code in Spain is Low Voltage Regulation.

This code states that the calculated maximum current has to be increased by a margin of 25% when designing

an installation (ITC-BT 40 article).

A temperature correction must be added to this, since the operational temperature of the cable will reach 50

°C. Standard UNE 20460-5-523 for outside installations (Table A.52-1 bis) states that a temperature correction

must be applied when the operational temperature reaches 40 °C or more.

Table 52-D1 for an ambient temperature of 50 °C and cable type Tecsun (thermostable) gives a coefficient of

0.9. Taking into account that the cable will be exposed to the sun, the correction factor 0.9 will be applied

twice.

I ' = 1.25 x 81.84 / (0.9 x 0.9) = 126.3 A

126.3 A is the corrected design value of the current. We will now use this value in Table A.52-1a to determine

the cable section.

Cable is lying on a grill type rack (Category F in the table). The insulation type used on Tecsun (PV) (AS) cable is

XLPE2. This leads to a minimum cable section of 25 mm2 for a copper conductor (see table below).



Page 6

Table 1 – Design to maximum allowed current – Applicable table for sizing the conductor.

A1 PVC3 PVC2 XLPE3 XLPE2

A2 PVC3 PVC2 XLPE3 XLPE2

B1 PVC3 PVC2 XLPE3 XLPE2

B2 PVC3 PVC2 XLPE3 XLPE2

C PVC3 PVC2 XLPE3 XLPE2

E PVC3 PVC2 XLPE3 XLPE2

F PVC3 PVC2 XLPE3 XLPE2

mm²

1,5 11 11,5 13 13,5 15 16 16,5 19 20 21 24 25

2,5 15 16 17,5 18,5 21 22 23 26 26,5 29 33 34

4 20 21 23 24 27 30 31 34 36 38 45 46

6 25 27 30 32 36 37 40 44 46 48 57 59

10 34 37 40 44 50 52 54 60 65 68 76 82

16 45 49 54 59 66 70 73 81 87 91 105 110

25 59 64 70 77 84 88 95 103 110 116 123 140

35 72 77 86 96 104 110 119 127 137 144 154 174

50 86 94 103 117 125 133 145 155 167 175 188 210

70 109 118 130 149 160 171 185 199 214 224 244 269

95 130 143 156 180 194 207 224 241 259 271 296 327

120 150 164 188 208 225 240 260 280 301 314 348 380

150 171 188 205 236 260 278 299 322 343 363 404 438

185 194 213 233 268 297 317 341 368 391 415 464 500

240 227 249 272 315 350 374 401 435 468 490 552 590

300 259 285 311 360 396 423 481 525 565 630 674 713

2.5 11.5 12 13.5 14 16 17 18 20 20 22 25 -

4 15 16 18.5 19 22 24 24 26.5 27.5 29 35 -

6 20 21 24 25 28 30 31 33 36 38 45 -

10 27 28 32 34 38 42 42 46 50 53 61 -

16 36 38 42 46 51 56 57 63 66 70 83 82

25 46 5,050 54 61 64 71 72 78 84 88 94 105

35 - 6,161 67 75 78 88 89 97 104 109 117 130

50 - 73 80 90 96 106 108 118 127 133 145 160

70 - - - 116 122 136 139 151 162 170 187 206

95 - - - 140 148 167 169 183 197 207 230 251

120 - - - 162 171 193 196.5 213 228 239 269 293

150 - - - 187 197 223 227 246 264 277 312 338

185 - - - 212 225 236 259 281 301 316 359 388

240 - - - 248 265 300 306 332 355 372 429 461

300 - - - 285 313 343 383 400 429 462 494 558

Conductor numbers with types of insulation

Required cross section

Cu

Al

Maximum current after temperature correction (A)



Page 7

Table 2 – Design to maximum allowed current – Example.



Page 8

DESIGN TO MAXIMUM ALLOWED VOLTAGE DROP

We again use Article ITC-BT 40 of the Low Voltage Regulation: ‘The voltage drop between the generator and

the point of connection to the Public Distribution Network or indoor installations shall not exceed 1.5% at

nominal current.’

We assume that the main DC line is responsible for 1% of the voltage drop and the remaining 0.5%

corresponds to the rest of the cabling.

The maximum allowed voltage drop is:

e = 0.01 x 477.44 V = 4.77 V

In this case, the cable section is defined as follows (this is also applicable for AC single phase):

Where

L: length of the line (positive + negative) 2 x 45 = 90 m

I: nominal current 81.84 A

γ: conductivity of copper (at 70 °C1) 46.82 m/Ω.mm

2

e: Maximum voltage drop 4.77 V

This leads to:

35 mm2

RESULTING SECTION

The resulting minimum cross section is 35 mm².

This cross section fulfils both criteria of the Low Voltage Regulation code (maximum current and maximum

voltage drop).

1 We take 70 °C as the approximate value resulting from an environment temperature of 50 °C increased by 20

°C due to conductor heating through the Joule effect.



Page 9

CALCULATION OF THE ECONOMIC SECTION Increasing the conductor section leads to higher investment cost but also to lower losses. In this chapter we

analyse the pay-back time for conductor sections larger than those defined by standards.

The power losses in an electrical line are defined by:

P = R • I ²

Where R is the resistance and I the current.

Thus, the energy lost in a time t is:

Ep = R • I ² • t

The time distribution of the current follows the solar radiation (maximum during the day and zero during the

night). Therefore:

Ep = ∫ R(t) • I²(t) • dt

R(t) can be considered approximately constant, without significant error. In our example, we take the values of

R at 70 °C.

Ep ≈ R² • ∫ I(t) • dt

To simplify the calculation, we will use the sum of discrete values (see the Figure 4 below). We start from the

hourly incident radiation values for each month of the year (Satel-light source: http://www.satel-light.com).

Ep ≈ R · Σ (Ii2 · ti)

For time intervals of one hour, the final expression is:

Ep ≈ R · Σ Ii2

http://www.satel-light.com/



Page 10

Figure 4 –Discretization of solar radiation and current.

We make the following assumptions:

The current is proportional to the solar radiation

The nominal current is, for a crystalline silicon module, 90% of the short-circuit current (Icc)

The standard conditions of a module are given for a solar radiation of 1,000 W/m2

The current for one array is:

Ii = 0.9 x Icc · Gi/1,000 = 0.9 x 7.96 x Gi/1,000 = 7.164 x 10-3

· Gi (A)

Where Gi is the solar irradiation in W/m2

There are 11 arrays per junction box:

I(ti) = 11 x Ii = 0.078804 x Gi (A)

Where I(ti) is the annual average current2 at the hour i on the main DC line.

The energy loss in the main DC line will be:

Ep ≈ R · Σ I(ti)2 = 0.0788042 x R · Σ Gi

2 (kWh)

And the cost of losses (energy lost and not sold at the applicable feed-in tariff (FIT)) is:

Cp ≈ FIT (€/kWh) x Ep (kWh) (€)

2 For this example we use the average annual current. In a more developed analysis we should proceed to the

sum of the current during each single hour of the year.



Page 11

The corresponding resistance for a section of 35 mm2 (copper) is 0.0006102 Ω / m (at 70 °C). These values are

fed into the spreadsheet as follows (see Table).

Gi (W/m2)

Ii = 0.0788 * Gi (A)

I2^2 (A^2)

Pu = R35*L*Ii^2 = 0.0006102 * Ii^2 (W/m)

P = Pu*L = Pu* 90 (W)

Ep = P * 365/1,000

(kWh)

Cp = 0.3 * Ep (0.3 €/kWh)

(€)

Cp=0.44*Ep (0.44

€/kWh) (€)

hr J F M A M J J A S O N D

Annual hours

Average current

Square of average current

Power loss per meter of

line

Total power loss

Total energy losses

Cost of losses

Cost of losses

6-7 0 0 0 0 2 4 2 0 0 0 0 0 1 0.079 0.006 0.000 0.000 0.000 0.00 0.00

7-8 0 2 30 11 36 45 35 16 3 2 5 0 16 1.261 1.590 0.001 0.090 0.033 0.01 0.01

8-9 32 93 166 98 139 150 136 109 79 55 113 42 101 7.959 63.349 0.039 3.510 1.281 0.38 0.56

9-10 178 286 352 263 298 308 304 278 237 222 299 201 268 21.119 446.032 0.272 24.480 8.935 2.68 3.93

10-11 330 474 530 453 468 479 482 459 419 415 459 349 443 34.910 1,218.720 0.744 66.960 24.440 7.33 10.75

11-12 450 617 668 626 611 641 649 633 571 581 579 468 591 46.573 2,169.060 1.324 119.160 43.493 13.05 19.14

12-13 522 704 741 748 737 750 785 774 704 696 629 530 693 54.611 2,982.380 1.820 163.800 59.787 17.94 26.31

13-14 545 729 749 821 812 815 857 849 785 729 611 529 736 58.000 3,363.970 2.053 184.770 67.441 20.23 29.67

14-15 503 684 719 807 797 822 877 874 790 714 534 460 715 56.345 3174.743 1.937 174.330 63.630 19.09 28.00

15-16 400 571 618 744 730 763 822 815 719 628 396 344 629 49.568 2456.958 1.499 134.910 49.242 14.77 21.67

16-17 253 408 456 611 608 655 695 682 581 479 222 185 487 38.378 1472.836 0.899 80.910 29.532 8.86 12.99

17-18 81 196 271 447 462 497 537 505 402 296 49 35 315 24.823 616.194 0.376 33.840 12.352 3.71 5.43

18-19 1 29 91 269 284 322 347 314 216 116 0 0 166 13.081 171.125 0.104 9.360 3.416 1.02 1.50

19-20 0 0 10 104 127 157 168 133 64 10 0 0 65 5.122 26.238 0.016 1.440 0.526 0.16 0.23

20-21 0 0 1 13 32 49 48 26 3 0 0 0 14 1.103 1.217 0.001 0.090 0.033 0.01 0.01

21-22 0 0 0 0 0 7 6 0 0 0 0 0 1 0.079 0.006 0.000 0.000 0.000 0.00 0.00

/mo 205.

9 300 338 376 384 404 422 404 348 309 244 196 328 Total annual 364.142 109.24 160.22

Table 3

The length of the cable being analysed is considered to be 45 meters.

Two scenarios are analysed, (1) using the former FIT of 44 c€/kWh and (2) using the current FIT set at 30

c€/kWh. Those lead to annual savings of €160 and €109 respectively.

So now that we have determined the variable cost of energy losses, this must be compared to the investment

cost of cable.

For the case study section of 35 mm²:

C35 = 90 x Ps + 109.23 x t (€)

Where:

Ps: cable price (€ / m)

t: time (years)



Page 12

Generalizing for a cable of a section S:

Cs = 90 x Ps + 109.23 x 35 / S x t (€)

We can now easily calculate the payback period for each section of conductor beyond 35 mm², as well as the

savings over 30 years.

FIT 0.30 €/kWh

Ps (€/m) Cs = 90 x Ps + 109.23 x 35/S x t (€) Payback

(years)

Savings over 30

years = 30 x (Cs-

C35) (€)

4.43 C35 = 398.7 + 109.23 x t -- 0

6.02 C50 = 541.88 + 76.461 x t 4.36 840

8.11 C70 = 730 + 54.61 x t 6.06 1,307

11.66 C95 = 1,049.4 + 40.243 x t 9.43 1,419

14.45 C120 = 1,300.5 + 31.86 x t 11.65 1,419

18.45 C150 = 1,660.5 + 25.487 x t 15.07 1,250

23.43 C185 = 2,108.7 + 20.665 x t 19.3 947

29.90 C240 = 2,691 + 15.93 x t 24.57 507

FIT 0.44 €/kWh

Ps (€/m) Cs = 90 x Ps + 160.21 x 35/S x t (€) Payback (years)

Savings over 30

years = 30 x (Cs-C35)

(€)

4.43 C35 = 398.7 + 160.21 x t -- 0

6.02 C50 = 541.88 + 112.147 x t 2.98 1,298

8.11 C70 = 730 + 80.105 x t 4.13 2,072

11.66 C95 = 1,049.4 + 59.02 x t 6.43 2,385

14.45 C120 = 1,300.5 + 46.728 x t 7.94 2,503

18.45 C150 = 1,660.5 + 37.382 x t 10.27 2,408

23.43 C185 = 2,108.7 + 30.31 x t 13.16 2,187

29.90 C240 = 2,691 + 23.364 x t 16.75 1,813



Page 13

The savings calculated here should be multiplied by 3, since the installation consists of three identical parts

with a nominal power of 100 kW each. This still assumes that the three main DC lines have the same length (45

metres).

Figure 5 – Life Cycle Cost of various cable sections with applicable FIT = 30 c€/kWh.

When the applicable feed-in tariff (FIT) is 30 c€/kWh, the most economical sections are 70mm² and 95mm².



Page 14

Figure 6 – Life Cycle Cost of various cable sections with applicable FIT = 44 c€/kWh.

When the applicable feed-in tariff (FIT) is 44 c€/kWh, the most economical sections are 95mm² and 120mm².

If the PV installation uses solar trackers, the pay-back time becomes even shorter. Indeed, solar trackers

improve the utilization of the solar radiation (see graph below) and therefore result in a higher average current

through the cables.



Page 15

Figure 7 – Recovered radiation according to the installation type: fix tilt 0º / fix tilt 30º / trackers (location:

Valencia, Spain).

The cumulated savings achieved by applying the most economic cross section instead of the standard cross

section for this installation of 100 kW and a Feed-In Tariff of 30 c€/kWh, is around €4,000 (Net Present Value

= €2,000 using an annual rate of 3.5%). The payback period is about six years.

If the applicable Feed-In Tariff is 44 c€/kWh, then the cumulated savings reach €7,000 (Net Present Value of

€3,600 using an annual rate of 3.5%).

The table below shows the impact of different interest rates when considering an initial overinvestment and

the resulted cumulated savings over a period of 30 years.

Interest rate (%) 0 0.5 1 1.5 2 2.5 3 3.5 4 5 6 7

Net Present Value (FIT 30

c€/kWh) 3,921 3,561 3,234 2,940 2,676 2,436 2,217 2,019 1,839 1,524 1,263 1,038

Net Present Value (FIT 44

c€/kWh) 7,137 6,468 5,868 5,325 4,833 4,389 3,987 3,621 3,285 2,706 2,217 1,806



Page 16

CONCLUSIONS In general terms, it is always worth performing an economic cable sizing analysis. This is especially the case in

renewable energy installations, since the applicable Feed-In Tariff will be higher than the wholesale market

price of electricity and often higher than the consumer retail price.

In addition to the improved profitability of the project, an increased cable cross section has additional

advantages:

Electric lines with lower load, improving the lifespan of the cables

If the plant is expanded, the cables can remain in service

A better response to potential short-circuits

Improved Performance Ratio (PR) of the plant

Associated environmental benefits (including among others, a reduction of CO2 emissions)

optimal cable sizing in pv systems: case study

Business

cu0167 issue date

cable section

pv installations

photovoltaic pv installation

pv systems

pv installation lead

standard cable

larger cable