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 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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Optimal Cable Sizing in PV Systems: Case Study
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
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
ï· Location: Valencia, Spain
ï· Panel installation mode: fixed, tilted at 30 degrees facing south
ï· Number of panels in series in each array : 16
ï· Number of arrays: 33
ï· Maximum ambient temperature: 50 °C
ï· Cable type: Tecsun (PV) (AS) (special cable for photovoltaic systemsâlifespan 30 years, maintenance
free)
ï· System installation: open mesh tray (without thermal influence of other circuits)
PV MODULES
ï· Nominal power: 222 W
ï· Current at maximum power: IPMP = 7.44 A
ï· Voltage at maximum power: Upmp = 29.84 V
ï· Short Circuit Current: Icc = 7.96
MISCELLANEOUS
ï· Inverter power = plant nominal power: 100 kW
ï· 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 â 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 â 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 âView 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).
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 âą I ÂČ
Where R is the resistance and I the current.
Thus, the energy lost in a time t is:
Ep = R âą I ÂČ âą t
The time distribution of the current follows the solar radiation (maximum during the day and zero during the
night). Therefore:
Ep = â« R(t) âą IÂČ(t) âą dt
R(t) can be considered approximately constant, without significant error. In our example, we take the values of
R at 70 °C.
Ep â RÂČ âą â« I(t) âą 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 â R · ÎŁ (Ii
2
· ti)
For time intervals of one hour, the final expression is:
Ep â R · ÎŁ Ii
2
13. Publication No Cu0167
Issue Date: June 2013
Page 10
Figure 4 âDiscretization of solar radiation and current.
We make the following assumptions:
ï· The current is proportional to the solar radiation
ï· The nominal current is, for a crystalline silicon module, 90% of the short-circuit current (Icc)
ï· 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 â R · ÎŁ 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 â FIT (âŹ/kWh) x Ep (kWh) (âŹ)
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.
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 (âŹ)
We can now easily calculate the payback period for each section of conductor beyond 35 mmÂČ, as well as the
savings over 30 years.
FIT 0.30 âŹ/kWh
Ps (âŹ/m) Cs = 90 x Ps + 109.23 x 35/S x t (âŹ)
Payback
(years)
Savings over 30
years = 30 x (Cs-
C35) (âŹ)
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 âŹ/kWh
Ps (âŹ/m) Cs = 90 x Ps + 160.21 x 35/S x t (âŹ) Payback (years)
Savings over 30
years = 30 x (Cs-C35)
(âŹ)
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 â Life Cycle Cost of various cable sections with applicable FIT = 30 câŹ/kWh.
When the applicable feed-in tariff (FIT) is 30 câŹ/kWh, the most economical sections are 70mmÂČ and 95mmÂČ.
17. Publication No Cu0167
Issue Date: June 2013
Page 14
Figure 6 â Life Cycle Cost of various cable sections with applicable FIT = 44 câŹ/kWh.
When the applicable feed-in tariff (FIT) is 44 câŹ/kWh, the most economical sections are 95mmÂČ and 120mmÂČ.
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 â Recovered radiation according to the installation type: fix tilt 0Âș / fix tilt 30Âș / 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 câŹ/kWh, is around âŹ4,000 (Net Present Value
= âŹ2,000 using an annual rate of 3.5%). The payback period is about six years.
If the applicable Feed-In Tariff is 44 câŹ/kWh, then the cumulated savings reach âŹ7,000 (Net Present Value of
âŹ3,600 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
câŹ/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
câŹ/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:
ï· Electric lines with lower load, improving the lifespan of the cables
ï· If the plant is expanded, the cables can remain in service
ï· A better response to potential short-circuits
ï· Improved Performance Ratio (PR) of the plant
ï· Associated environmental benefits (including among others, a reduction of CO2 emissions)