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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 or 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.

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- 1. 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
- 2. 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.
- 3. Publication No Cu0167 Issue Date: June 2013 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
- 4. Publication No Cu0167 Issue Date: June 2013 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.
- 5. Publication No Cu0167 Issue Date: June 2013 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).
- 6. Publication No Cu0167 Issue Date: June 2013 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.
- 7. Publication No Cu0167 Issue Date: June 2013 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
- 8. Publication No Cu0167 Issue Date: June 2013 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 mm 2 for a copper conductor (see table below).
- 9. Publication No Cu0167 Issue Date: June 2013 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)
- 10. Publication No Cu0167 Issue Date: June 2013 Page 7 Table 2 – Design to maximum allowed current – Example.
- 11. Publication No Cu0167 Issue Date: June 2013 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 °C 1 ) 46.82 m/Ω.mm 2 e: Maximum voltage drop 4.77 V This leads to: 35 mm 2 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.
- 12. Publication No Cu0167 Issue Date: June 2013 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 (Ii 2 · ti) For time intervals of one hour, the final expression is: Ep ≈ R · Σ Ii 2
- 13. Publication No Cu0167 Issue Date: June 2013 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/m 2 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/m 2 There are 11 arrays per junction box: I(ti) = 11 x Ii = 0.078804 x Gi (A) Where I(ti) is the annual average current 2 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.
- 14. Publication No Cu0167 Issue Date: June 2013 Page 11 The corresponding resistance for a section of 35 mm 2 (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)
- 15. Publication No Cu0167 Issue Date: June 2013 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
- 16. Publication No Cu0167 Issue Date: June 2013 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.
- 17. Publication No Cu0167 Issue Date: June 2013 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.
- 18. Publication No Cu0167 Issue Date: June 2013 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
- 19. Publication No Cu0167 Issue Date: June 2013 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)

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