a n economic cable sizing in pv systems case...

APPLICATION NOTE ECONOMIC CABLE SIZING IN PV SYSTEMS: CASE

STUDY

Lisardo Recio Maillo

July 2017

ECI Publication No Cu0167

Available from www.leonardo-energy.org

Publication No Cu0167

Issue Date: July 2017

Page i

Document Issue Control Sheet

Document Title: Application Note – Economic cable sizing in PV systems: case study

Publication No: Cu0167

Issue: 03

Release: Public

Content provider(s) /

Author(s): Lisardo Recio Maillo, Eduard Bullich Massagué, Mònica Aragüés

Peñalba, Andreas Sumper

Editorial and language review Bruno De Wachter (editorial), Noel Montrucchio (English language)

Content review: Hans De Keulenaer, Creara

Document History

Issue Date Purpose

1 October

2009

Initial publication

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

3 July 2017 Reworked after review

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

General remarks ..................................................................................................................................................... 2

System description ......................................................................................................................................... 3

PV plant features .................................................................................................................................................... 3

Characteristic curves of the PV array ..................................................................................................................... 5

Calculating the cable cross-section according to the standards ....................................................................... 8

Design to maximum allowed current ..................................................................................................................... 8

Design to maximum allowed voltage drop ........................................................................................................... 10

Calculation of the most economic cable cross-section .................................................................................. 15

Layout 1 ................................................................................................................................................................ 16

Layout 2 ................................................................................................................................................................ 20

Optimal Layout ..................................................................................................................................................... 24

Conclusions ................................................................................................................................................... 25

References .................................................................................................................................................... 26



Page 1

SUMMARY When sizing electric cables for PV installations it is a common practice to select cabling that meets the

minimum regulatory requirements. This is done to minimize upfront costs. However, choosing a larger cable

cross section than legally required reduces energy losses. The purpose of this paper is to establish the optimal

cable cross-section for a PV installation that will minimize its life cycle cost.

In some countries, the allocated price for electricity generated by PV systems is higher than the market price

thanks to the feed-in tariff or green certificates. When this is the case, energy losses become even more costly.

In other words, reducing the energy losses of a PV plant by increasing the cable cross-section leads to an even

bigger financial return than in other electrical installations.

The PV installation layout is one of the determining factors for establishing the length and minimum cross-

section of each cable. A careful study of all the lay-out options can significantly lower the life-cycle cost of the

installation.



Page 2

INTRODUCTION The annual installed PV capacity is steadily growing around the world. Environmental concerns, fossil fuel price

variability, PV technology advances and cost reductions are making this type of renewable electricity

generation increasingly competitive.

This paper presents an analysis on how to select of the optimum cable size for a PV system. The analysis is

illustrated with an actual business case study.

The first chapter provides a detailed description of all the relevant characteristics of the PV system under

study.

The second chapter is devoted to the calculation of the minimum cable size to comply with current regulations

and technical requirements. It serves to illustrate the common practice for selecting the cable cross-section,

which results in minimum upfront costs.

The third chapter evaluates the economic benefit of selecting a larger cable cross-section than the minimum

that is legally required. It demonstrates that in a large majority of cases the financial optimum lies at a larger

cross-section than what the standard prescribes. If Feed-in-Tariffs (FITs) or other financial incentives for PV

generated electricity apply, energy losses become even more costly and the economically optimal cable cross-

section will even be larger. It is demonstrated that the PV installation layout is an important factor in reducing

its life-cycle cost.

GENERAL REMARKS

The methodology that has been used when sizing the PV plant cables is generic, but the results are specific to

the particular case study analyzed in this document and cannot be generalized to cases with other conditions.

It is especially important to mention that these results can be affected by the location of the PV plant. The

benefits of oversizing the cables come from the power loss reduction that compensates for the initial

investment. If the PV plant is placed in an area with a lower irradiation profile than the one considered in this

study, the loss reduction will be lower and as a result, the optimal cable cross-section will be smaller. For the

same reason, the optimal cable cross-section will increase with increasing irradiation levels, e.g. through PV

panels that can change their orientation based on the data provided by solar trackers.

In the present analysis, it is assumed that the PV plant is installed in a country that benefits from feed-in

tariffs. Feed-in tariffs are policy mechanisms designed to promote investment in renewable energy

technologies. However, they are country dependent and evolve over time. Furthermore, they are different for

each technology and installation size. Feed-in tariffs are currently being phased-out and replaced by more

market-oriented mechanisms (e.g. tenders) in many countries.

In this application note, the over-sizing of cables refers to the practice of choosing a larger cable cross-section

than what is strictly required by the technical standards.



Page 3

SYSTEM DESCRIPTION An actual case study is used to explain the principles of optimal cable sizing however the same method can be

applied to other PV system types and/or sizes.

PV PLANT FEATURES

The system under study is a 100 kW PV plant located in Valencia, Spain. It consists of 3 PV arrays of 39 kW at

standard conditions (25 0C and 1,000 W/m

2). Each array is composed of 11 strings of 16 PV modules connected

in series. The PV array configuration is shown in Figure 1. Based on this configuration, the maximum output of

each PV array at the above mentioned standard conditions and operation at the maximum power point is as

follows:

Udc-array = 477.44 V

Idc-array = 81.84 A

Parray= 39.07 kW

The PV inverter has a rated power of 100 kW. We shall analyze two configurations:

In the first configuration (Figure 2), the output cables of the three junction boxes are joined at the

inverter input. Consequently, these cables must be sized following the PV array rating.

In the second configuration (Figure 3), the output cables are connected at the output of the junction

boxes. This results in a shorter cable length, but requires a higher current rating for the PV inverter

cable.

Note that the PV inverter is rated at 100 kW, while the total PV power at standard conditions is 39.07 x 3 =

117.21 kW.

Figure 1 – PV Array Configuration.



Page 4

Figure 2 – PV Plant Layout. Configuration 1.

Figure 3 – PV Plant Layout. Configuration 2.

Finally, Table 1 summarizes the PV plant data.



Page 5

PV plant general characteristics

Location

Panel

installation

mode

Maximum

ambient

temperature

Minimum

ambient

temperature

Rated power

Valencia, Spain

Fixed, tilted

300,

facing south

50 0C 0

0C 100 kW

PV array characteristics (at 25 0C and 1,000 W/m

2)

Active power

At MPP Current at MPP

Voltage at the

maximum

power point

(MPP)

Short circuit

current

Number of

parallel strings

Number of

series modules

per string

39.07 kW 81.84 A 477.44 V 87.56 A 11 16

PV module characteristics (at 25 ºC and 1,000 W/m2)

Nominal

power Current at MPP Voltage at MPP

Short circuit

current

222 W 7.44 A 29.84 V 7.96 A

Table 1 – General PV Plant Characteristics.

CHARACTERISTIC CURVES OF THE PV ARRAY

The purpose of the following study is to enable the optimal design of the conductor cross section for those

cables interconnecting the junction boxes with the PV inverter. To do so, the current and voltages of the PV

arrays must be studied beforehand. The characteristics of the PV modules and the array layout are

summarized in Table 2. The characteristic voltage-current and voltage-power curves are shown in Figure 4 and

Figure 5. If these curves are not available, they can be obtained from Table 2, which applies the equations

explained in [1] Development of generalized photovoltaic model using MATLAB Simulink.

PV module

Number of series connected cells 60

Nominal Power (W) 222

MPP voltage (V) 29.84

MPP current (A) 7.44

Open circuit voltage (V) 36.22

Short circuit current (A) 7.96

Short circuit current temperature coefficient (%/0C) 0.03

Open circuit voltage temperature coefficient (%/0C) -0.34

PV array

Number of series modules per string 16

Number of parallel strings per array 11

* PV MODULE CHARACTERISTICS ARE AT 1,000 W/M2 AND 25 0C

Table 2 – PV array characteristics used for modeling the characteristic curves.



Page 6

As shown in Figure 4, the short circuit and the maximum power point (MPP) currents vary proportionally with

the irradiance while the MPP and open circuit voltages remain nearly constant. In contrast, Figure 5 reveals

that the MPP and short circuit currents do not depend on the temperature while the voltages increase linearly

with the temperature decrease.

Figure 4 – I-V and PV characteristic of the PV array as a function of the irradiation (T=25 0C).

Figure 5 – I-V and PV characteristic of the PV array in function of the temperature (G=1,000 W/m2).

It can be concluded from Figure 4 and Figure 5 that the maximum MPP voltage, which is at the minimum

considered temperature of the area, is 533 V and the maximum MPP current (corresponding to the higher

irradiation) is 81.84 A.

In accordance with these values, the maximum currents and voltages for the two layouts are summarized in

Table 3, where CCGx-CCGy refers to the cables that interconnect the junction box x to the junction box y (see

Figures 2 and 3) and CCGx-Inverter refers to the cable connecting the junction box x to the inverter.



Page 7

Layout configuration 1

Cable Maximum MPP

current (A)

Maximum Short

Circuit current (A)

Maximum MPP

voltage (V) Length (m)

CCG1-Inverter 81.84 88.5 533 90

CCG2-Inverter 81.84 88.5 533 45

CCG3-Inverter 81.84 88.5 533 90


Cable Maximum MPP

current (A)

Maximum Short

Circuit current (A)

Maximum MPP

voltage (V) Length (m)

CCG1-CCG2 81.84 88.5 533 45

CCG3-CCG2 81.84 88.5 533 45

CCG2-Inverter 245.52 265.5 533 45

Table 3 – Maximum currents and voltages in the cables.



Page 8

CALCULATING THE CABLE CROSS-SECTION ACCORDING TO THE STANDARDS Due to its location, the installation must comply with the REBT 2002 (Spanish Low Voltage Electrotechnical

Regulation) and particularly with the ITC-BT 40 (Complementary Technical Instruction ‘Low voltage generation

systems’). When designing installations for other countries, their specific regulations must be considered. In

this case, the afore-mentioned legislation establishes two design criteria for the minimum cable section:

maximum current allowed and maximum voltage drop.

DESIGN TO MAXIMUM ALLOWED CURRENT

According the ITC-BT 40, the cable current must be sized for a current no lower than 125% of the maximum

generator current. This current corresponds to the short circuit current at the maximum irradiation and

maximum temperature.

The cable temperature will reach 50 0C As specified in the UNE 20460-5-523 Standard for outdoor installations,

a correction coefficient of 0.9 must be applied at 50 0C. Taking into account that the cable will be exposed to

the sun, an additional correction factor of 0.9 is applied.

Table 4 shows the result of applying the above mentioned correction factors to obtain the minimum

admissible current of the different cables.


Cable

Maximum Short

Circuit current, Isc-max

(A)

Minimum admissible current:

Isc-max·1.25/(0.9·0.9) (A)

CCG1-Inverter 88.5 136.57




Cable

Maximum Short

Circuit current, Isc-max

(A)

Minimum admissible current:

Isc-max·1.25/(0.9·0.9) (A)

CCG1-CCG2 88.5 136.57

CCG3-CCG2 88.5 136.57


Table 4 – Minimum admissible current for selection of the cable cross section.

The cable lies on a grill-type rack (Category F in Table 5). The insulation type used on the Tecsun (PV) (AS) cable

is XLPE2. Based on Table 4 and Table 5, the minimum cross section for a copper conductor is shown in Table 6.



Page 9

Table 5 – Maximum allowed current in function of the cross section, insulation and installation configuration.

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 10


Cable Minimum admissible

current (A)

Minimum cross

section (mm2)

CCG1-Inverter 136.57 25




Cable Minimum admissible

current (A)

Minimum cross

section (mm2)

CCG1-CCG2 136.57 25

CCG3-CCG2 136.57 25


Table 6 – Minimum cross section for the different cables studied.

DESIGN TO MAXIMUM ALLOWED VOLTAGE DROP

In compliance with the Tecsun (PV) (AS) cable specifications, the maximum permissible operating voltage in

direct current (DC) systems is 900/1800 V. In this case study, the maximum voltage of the installation (533 V)

does not exceed this value. Therefore, the cable insulation is appropriate.

The maximum allowed voltage drop is checked for all cables. The ITC-BT 40 is used for the maximum allowable

voltage drop calculation: 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 the nominal current. It is important to

note that in the system analyzed, there is a power converter connected between the generator and the point

of connection to the public network. This requirement does not include any specification regarding what

happens if there is a voltage transformation between the generator and the connection point. Nevertheless, as

specified above, when applying the technical requirements established in [2] (Technical specifications for grid-

connected systems) the maximum voltage drop in DC cables turns out to be 1.5 and (referred to the MPP

voltage and current at 25 0C and 1,000 W/m

2 [3] (Technical handbook. The installation of ground photovoltaic

plants over marginal areas).

Assuming that the main DC lines are responsible for 1% of the total DC voltage drop and the remaining 0.5%

corresponds to the rest of the cabling, the voltage drop can be obtained (STC sub index refers to standard

ambient conditions):

MPP voltage: 477.44@ STCmppV V

Maximum allowed voltage drop: 77.401.0 @max STCmppVV V

Maximum current for voltage drop calculation (single array): 84.81@ STCmppI A

Maximum current for voltage drop calculation (three arrays): AI STCmpp 245.52@

Cable resistance:

1

S

LR



Page 11

Where:

L is the total cable length (positive + negative)

S is the cross section

2/82.46 mmm is the cooper conductivity at 70

0C

Note that the maximum current corresponds to the maximum short circuit current which is at 50 0C

The voltage drop at each cable is shown in Table 7:


Cable STCmppI @ (A)

Cross

section

(mm2)

L positive

+ negative

(m)

R (Ω) Voltage drop

STCmppIRV @ (V)

CCG1-Inverter 81.84 25 180 0.1538 12.5854

CCG2-Inverter 81.84 25 90 0.0769 6.2927

CCG3-Inverter 81.84 25 180 0.1538 12.5854


Cable STCmppI @ (A)

Cross

section

(mm2)

L positive

+ negative

(m)

R (Ω) Voltage drop

STCmppIRV @ (V)

CCG1-CCG2 81.84 25 90 0.0769 6.2927

CCG3-CCG2 81.84 25 90 0.0769 6.2927

CCG2-Inverter 245.52 150 90 0.0128 3.1463

Table 7 – Voltage drop calculation at each cable.

As shown in Table 7 all cables exceed the maximum voltage drop (note that for configuration 2, the total

voltage drop is 6.29+3.15 V). Hence, the cross section must be increased. For configuration 1, the cables are in

parallel. This means that the minimum cross section can be calculated as follows (note that L is the total cable

length, positive + negative):

max

@

minV

ILS

STCmpp

Table 8 shows the minimum cross section and the cable selection for configuration 1:



Page 12


Cable

STCmppI @

(A)

L

positive +

negative

(m)

Minimum cross section

(mm2)

Cable selection

according to Table 5

(mm2)

CCG1-Inverter 81.84 180 65.96 70

CCG2-Inverter 81.84 90 32.98 35

CCG3-Inverter 81.84 180 65.96 70

Table 8 – Minimum cross section for cables of configuration 1 and the corresponding cable selection.

In contrast, configuration 2 has cables in series. In this case the CCG1-CCG2-Inverter or CCG3-CCG2-inverter

paths have to be studied. The voltage drop will be:

inverterCCGCCGCCGinverterCCGCCGCCG VVVVV 223221

Path CCG1-CCG2-inverter is considered. So, the voltage drop can be written as:

inverterCCG

inverterCCG

CCGCCG

CCGCCG

CCGCCG

S

IL

S

ILV

inverterCCG

STCmppSTCmpp

2

2

21

21

212

@@

The length L is equal for both cables, and the current of CCG2-inverter is three times that of the current of the

CCG1-CCG2. So, the voltage drop can be re-written as:

26.431

221

21

@

inverterCCGCCGCCG

CCGCCG

SSI

LV

STCmppV

The condition has been found to comply with the voltage drop:

2

221

0.02731

mm

SS inverterCCGCCGCCG

As can be observed, there are many options to choose among the cross sections. Finding the minimum amount

of cable is imperative, in order to minimize the total volume of cable. As the cable CCG3-CCG2 is equal to the

cable CCG1-CCG2:

inverterCCGinverterCCGCCGCCGCCGCCG SLSLVol 2221212

As the cable length is equal for all cables, in our case:

inverterCCGCCGCCG SSLVol 2212

A simple optimization problem can be formulated:

- Objective function: Volf min



Page 13

- Voltage drop constraint: 2

221

027.031

mm

SS inverterCCGCCGCCG

- Thermal constraints (maximum current limitation): 2

21 25mmS CCGCCG

2

2 150mmS inverterCCG

Solving the optimization problem: 2

21 4.82 mmS CCGCCG

2

2 8.201 mmS inverterCCG

Now, appropriate cable sections can be selected using Table 5.

CASE A

The CCG2-inverter cable section is fixed at2

2 240mmS inverterCCG , as it is the next possible eligible value in

Table 5 for this section. As this value is greater than the minimum required value for the section, the cable size

associated with the other section can be reduced while still maintaining the voltage drop under its threshold

value. The optimization problem is now solved again but with the added constraint:

2

2 240mmS inverterCCG

So, the minimum section for cable CCG1-CCG2 that satisfies the thermal and voltage drop constraints is found:

2

21 69mmS CCGCCG

So, according to Table 5, the section that will be chosen is:

2

21 70mmS CCGCCG

CASE B

The CCG1-CCG2 cable section is fixed at2

21 95mmS CCGCCG , as it is the next possible eligible value in Table

5 for this section. As this value is greater than the minimum required value for the section, the cable size

associated with the other section can be reduced while still maintaining the voltage drop under its threshold

value. The optimization problem in now solved again but with the added constraint:

2

21 95mmS CCGCCG

So, the minimum section for cable CCG2-inverter that satisfies both the thermal and voltage drop constraints is

found:

2

2 182.1mmS inverterCCG

So, according to Table 5, the section that will be chosen is:

2

2 851 mmS inverterCCG



Page 14

RESULT FOR CONFIGURATION 2

In this case, option B produces the solution with the minimum amount of cable volume, involving a total

volume of 0.0338 m3 (in comparison with option A that involves 0.0342 m

3 1) as summarized in Table 9. Note

that as cables are placed in series, when considering the total voltage drop constraint, the minimum cross

section of cables CCG1-CCG2 and CCG3-CCG2 depends on the cross section of the cable CCG2-Inverter and vice

versa (see 4th

column in Table 9).

Layout configuration 2—Option b.

Cable STCmppI @

(A)

L

positive +

negative

(m)

Minimum cross section

(mm2)

Cable selection

according to Table 5

(mm2)

CCG1-CCG2 81.84 90 Depends upon the other

cables 95

CCG3-CCG2 81.84 90 Depends upon the other

cables 95

CCG2-Inverter 245.52 90 Depends upon the other

cables 185

Table 9 – Cable selection for configuration 2.

The next chapter will demonstrate that minimizing the total cable conductor material will not minimize the

life-cycle cost of the installation. When it comes to the life-cycle cost, the added energy losses have a far

bigger weight than the cost of the conductor material.

1 Option A: (70+70+240)·10

-6·90=0.0342 m

3

Option B: (185+95+95)·10-6

·90=0.0338 m3



Page 15

CALCULATION OF THE MOST ECONOMIC CABLE CROSS-SECTION In the previous chapter, the minimum required cable sections were calculated. In this chapter we will carry out

an economic study to obtain the optimal cable cross-section and cable lay-out from the point of view of the

life-cycle cost.

The instantaneous power losses of a cable can be calculated as:

)()()( 2 tItRtPloss (W)

Where:

R(t) (positive + negative cable) is expressed in Ω

I(t) is expressed in A

R(t) can be considered constant without significant error. We take values of R at 70 0C, so the energy lost is

obtained as:

dttIREloss )(2 (J)

When simplifying the equation, we may consider the current as constant during time period Δt (expressed in

hours), the energy loss can be approximated as:

iiloss tIRE 2 (Wh)

If all time intervals are of one hour, the total energy loss is:

2

iloss IRE (Wh)

From Figure 4 and Figure 5, it can be observed that the MPP current is approximately directly proportional to

the irradiation. Using the reference MPP current at 25 0C and 1,000 W/m

2 (Impp = 81.84 A per PV array), so the

current can be written as:

GG

G

GII

ref

mpp 08184.01000

84.81 (A)

Where:

G is the irradiation in W/m2.

The energy loss in kWh can be expressed as:

22

1000

08184.0iloss GRE (kWh)

Then, the cost of losses (energy lost and not sold at the applicable feed-in tariff (FIT)) can be expressed as:

FITEC lossloss (€)



Page 16

where FIT is the feed-in tariff expressed in €/kWh. In case no feed-in tariffs apply, this term should be replaced

by an estimation of the average price at which the PV electricity is sold to the grid, or the average cost of

avoided grid electricity consumption through PV energy self-consumption (€/kWh).

Once the cost of losses for a specific cable section and length Cs1-L1 is found, the cost for any cable cross section

can be easily obtained as:

1

1

11 L

L

S

SCC k

k

LsLs kk (€)

LAYOUT 1

Firstly we calculate the cost of the losses in all cables and their minimum cross section. For this purpose, the

annual irradiation profile is obtained. Table 10 shows the irradiation profile, the calculation of energy losses

and the associated cost for the CCG2-inverter cable.

Table 10 – Cost of energy loss calculation for CCG2-inverter cable; layout 1.

The annual cost of energy losses for any cable section and length can be obtained:

- For FIT=0.3 €/kWh: S

LL

SC

lossE 38.4890

35·4.1241 (€)


LL

SC

lossE 93.7090

35·4.1822 (€)

Considering an annual interest rate of i, the net present value (NPV) for 30 years of cable lifetime is obtained

as:

30

1 1

1min

kkSS

iCFInvInvNPV

1h·∑di·Gi2

di=Num. days of

month i

Eloss

(0,081842/1000)·R·∑Gi2

Cost 1

FIT=0,3 €/kWh

Cost 2

FIT=0,44 €/kWh

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

It corresponds to

∑Gi2 for 1 year at

each daytime kWh € €

6-7 0 0 0 0 2 4 2 0 0 0 0 0 728 0,0 0,0 0,0

7-8 0 2 30 11 36 45 35 16 3 2 5 0 179623 0,1 0,0 0,0

8-9 32 93 166 98 139 150 136 109 79 55 113 42 4350669 1,6 0,5 0,7

9-10 178 286 352 263 298 308 304 278 237 222 299 201 27195465 10,0 3,0 4,4

10-11 330 474 530 453 468 479 482 459 419 415 459 349 72639193 26,7 8,0 11,8

11-12 450 617 668 626 611 641 649 633 571 581 579 468 128996582 47,5 14,2 20,9

12-13 522 704 741 748 737 750 785 774 704 696 629 530 177980959 65,5 19,6 28,8

13-14 545 729 749 821 812 815 857 849 785 729 611 529 202015670 74,3 22,3 32,7

14-15 503 684 719 807 797 822 877 874 790 714 534 460 193632618 71,2 21,4 31,3

15-16 400 571 618 744 730 763 822 815 719 628 396 344 154164651 56,7 17,0 25,0

16-17 253 408 456 611 608 655 695 682 581 479 222 185 97792866 36,0 10,8 15,8

17-18 81 196 271 447 462 497 537 505 402 296 49 35 48096449 17,7 5,3 7,8

18-19 1 29 91 269 284 322 347 314 216 116 0 0 16667947 6,1 1,8 2,7

19-20 0 0 10 104 127 157 168 133 64 10 0 0 3116332 1,1 0,3 0,5

20-21 0 0 1 13 32 49 48 26 3 0 0 0 201525 0,1 0,0 0,0

21-22 0 0 0 0 0 7 6 0 0 0 0 0 2586 0,0 0,0 0,0

1127033863 414,6 124,4 182,4

G (W/m2)

TOTALS (annual values)

Cable CCG2-inverter (positive + negative): L=2·45 m, S=50 mm2, total R=0.0549 Ω



Page 17

In which LPInv sS minmin

and LPInv sS represents the initial investment (PS is the cost of a cable of

section S in €/m shown in Table 11). CF is the cash flow calculated as Closs for the minimum section minus Closs

for the section under study.

Cable cross section

(mm2)

Ps

(€/m)

35 4.43

50 6.02

70 8.11

95 11.66

120 14.45

150 18.45

185 23.43

240 29.90

Table 11 – Price of cables.

For the CCG2-inverter cable, the results are shown in Figure 6 and Figure 7 and summarized in Table 12. The

performance for the CCG1-inverter and CCG3-inverter cables is shown in Figure 8, Figure 9 and Table 13.

Figure 6 – NPV for different cable sections and different interest rate. FIT=0.3 €/kWh. CCG2-inverter Cable;

layout 1.



Page 18

Figure 7 – NPV for different cable sections and different interest rate. FIT=0.44 €/kWh. CCG2-inverter Cable;

layout 1

FIT=0.3 €/kWh FIT=0.44 €/kWh

Interest rate

(p.u)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

0.00 120 1742 11 120 2974 7

0.01 95 1377 11 120 2432 8

0.02 95 1109 12 120 1992 8

0.03 95 889 13 120 1630 8

0.04 70 744 11 95 1341 7

0.05 70 625 11 95 1120 7

0.06 70 525 12 95 935 8

0.07 70 441 13 70 801 5

0.08 70 369 15 70 696 5

0.09 70 308 16 70 606 5

0.10 70 255 19 70 529 5

Table 12 – Economic performance for the CCG2-inverter cable election; layout 1.



Page 19

Figure 8 – NPV for different cable sections and different interest rate. FIT=0.3 €/kWh. CCG1-inverter and cable

CCG3-inverter Cables; layout 1.

Figure 9 – NPV for different cable sections and different interest rate. FIT=0.44 €/kWh. CCG1-inverter and

CCG3-inverter cables; layout 1.



Page 20


Interest rate

(p.u)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

0.00 120 414 23 120 1139 16

0.01 95 205 22 120 820 17

0.02 95 94 25 120 561 19

0.03 95 3 30 120 348 21

0.04 70 0 - 95 191 20

0.05 70 0 - 95 99 23

0.06 70 0 - 95 22 28

0.07 70 0 - 70 0 -

0.08 70 0 - 70 0 -

0.09 70 0 - 70 0 -

0.10 70 0 - 70 0 -

Table 13 – Economic performance for the CCG1-inverter cable and for the CCG3-inverter cable election; layout

1.

These results show that sizing the cables as required by the minimum standards does not minimize the cost. In

other words, oversizing power cables can be advantageous from an economic point of view.

The lower the interest rate, the larger the optimal cross section because lower interest rates lead to higher

benefits for energy loss reduction. As a result, the investment cost for oversizing the cables is compensated

further by the loss reduction.

Moreover, the benefits produced by the loss reduction increase with an increasing FIT, resulting in a greater

optimal cross section.

In the case study, over-sizing is beneficial for the CCG2-inverter cable. For the longer CCG1-inverter and CCG3-

inverter cables, oversizing is only profitable in the event of low interest rates.

In the present study, the total savings from applying the most economic sections for the whole PV plant is

between 529 € and 5,252 € depending on the FIT and the interest rate.

LAYOUT 2

For this layout, the annual cost of energy loss for CCG1-CCG2 and for CCG3-CCG1 cables can be evaluated with

the same formulas shown in section 6.1 because the currents are the same. These formulas are as follows:


LL

SC

lossE 38.4890

35·4.1241 (€)


LL

SC

lossE 93.7090

35·4.1822 (€)



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In contrast to this, the CCG2-Inverter cable carries three times the current of the previous cables. As the

energy losses are proportional to the square of the current, the annual energy loss cost for this cable is

expressed as:


L

S

LC

lossE 42.43538.4831 2 (€)


L

S

LC

lossE 37.63893.7032 2 (€)

The benefits for all cables and all sections can now be computed. Figure 10, Figure 11 and Table 14 show the

results for cables CCG1-CCG2 and CCG3-CCG2. Cable oversizing is only profitable for a high FIT value. However,

oversizing the main CCG2-inverter cable leads to a considerable savings (Figure 12, Figure 13 and Table 15),

even for lower FIT values. In this layout, the benefits of applying the economically optimal cross-section

instead of the minimum cross-sections are between 0 and 1891 € depending on the interest rate and the FIT.

Figure 10 – NPV for different cable sections and different interest rate. FIT=0.3 €/kWh. CCG1-CCG2 and CCG3-

CCG2 cables; layout 2.



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Figure 11 – NPV for different cable sections and different interest rate. FIT=0.44 €/kWh. Cable CCG1-CCG2 and

cable CCG3-CCG2; layout 2.


Interest rate

(p.u)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

0.00 120 120 27 120 169 18

0.01 95 0 - 120 110 20

0.02 95 0 - 120 62 23

0.03 95 0 - 120 23 27

0.04 95 0 - 95 0 -

0.05 95 0 - 95 0 -

0.06 95 0 - 95 0 -

0.07 95 0 - 95 0 -

0.08 95 0 - 95 0 -

0.09 95 0 - 95 0 -

0.10 95 0 - 95 0 -

Table 14 – Economic performance for the cable CCG1-CCG2 and for the cable CCG3-CCG2 election; layout 2.



Page 23

Figure 12 – NPV for different cable sections and different interest rate. FIT=0.3 €/kWh. Cable CCG2-inverter;

layout 2.

Figure 13 – NPV for different cable sections and different interest rates. FIT=0.44 €/kWh. Cable CCG2-inverter;

layout 2.



Page 24


Interest rate

(p.u)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

Optimal

section

(mm2)

NPV

(€)

Payback

(years)

0.00 240 827 12 240 1553 9

0.01 240 671 13 240 1254 9

0.02 240 505 14 240 1012 10

0.03 240 369 16 240 813 10

0.04 240 257 17 240 648 11

0.05 240 164 19 240 512 11

0.06 240 86 22 240 397 12

0.07 240 20 28 240 301 13

0.08 185 0 - 240 219 14

0.09 185 0 - 240 149 16

0.10 185 0 - 240 89 18

Table 15 – Economic performance for the cable CCG2-inverter; layout 2.

OPTIMAL LAYOUT

The previous results show that oversizing is more profitable for layout configuration 1. However, this does not

imply that configuration 1 is the most profitable. To decide the optimal layout, the total life cycle costs of the

optimal cables must be analyzed for both configurations.

The total life cycle cost is the sum of the cable prices plus the cost of the yearly losses, taking into account the

interest rate. Figure 14 shows a cost comparison between layout 1 and layout 2 for a FIT=0.3 €/kWh and

proves that layout 1 is a better option than layout 2 in this case.



Page 25

Figure 14 – Cost of the installation vs. interest rate and layout configuration. FIT=0.3 €/kWh. Optimal cable size

for each layout is considered.

CONCLUSIONS

The following conclusions can be drawn from the results obtained in this report:

From an economic point of view, sizing power cables according to the minimum standard

requirements is rarely the best option. Performing an economic optimization analysis of the power

cables is recommended to maximize the profit from PV installations. Most probably, this will lead to a

larger cable cross-section than what is prescribed by the standards.

The lay-out of power cables can also affect the economic performance of the PV system. Analyzing

different possible lay-outs can result in a greater benefit.

The optimal cable section can depend on factors such as the solar irradiance profile, the feed-in tariff

(or other financial incentives for PV electricity), the PV plant lay-out and the length of the power

cables.

The larger the cable cross-section is chosen for a particular PV installation, the slower the ageing of

the cable—an additional benefit.



Page 26

REFERENCES

[1] Huan-Liang Tsai, Ci-Siang Tu, and Yi-Jie Su. “Development of generalized photovoltaic model using matlab Simulink”, In Proceedings of the World Congress on Engineering and Computer Science, Oct 2008

[2] IDAE, “Pliego de condiciones técnicas de instalaciones conectadas a red”, 2011. Available online, http://www.idae.es/ [accessed on 23-01-2017]

[3] G Nofuentes, J Muñoz, D Talavera, J Aguilera, J Terrados, “Technical handbook. The installation of ground photovoltaic plants over marginal areas”, PVs in BLOOM Project—a new challenge for land valorisation within a strategic eco-sustainable approach to local development, 2011

http://www.idae.es/

a n economic cable sizing in pv systems case...

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