optimal cable sizing in photovoltaic systems

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Renewable Energy

Lisardo Recio Maíllo Product Manager

Prysmian Cables and Systems

October, 2009

Optimal cable sizing in PV systems

Even higher than in other installations

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The optimal cross section sizing for an electrical cable in photovoltaic systems: even bigger than in other installations Over-sizing the cross section of a cable beyond the result of voltage and current theoretical calculations is, in most of cases, a worth investment that is easily amortised by the electricity bill savings (reduction of Joule losses). In the case of a photovoltaic (PV) installation, the allocated price for energy (feed-in tariff) is much higher than the market price, getting amortised much faster. Additionally, it creates additional environmental benefits.

1 Introduction The analysis is carried out for a PV plant of 100 kW located in Spain.

PV plant features:

• Location: Valencia, Spain

• Panels installation mode: fixed tilt of 30 ° South oriented

• Number of panels in series in each array : 16

• Number of arrays : 33

• Maximum ambient temperature: 50 º C

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

• System installation: the 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


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

Picture 1 : Tecsun Cable (PV) (AS) - Special cable for photovoltaic systems - lifespan 30 years, maintenance free

The whole is grouped into 3 blocks of 11 arrays each, connected respectively into three junction boxes (CCG1, CCG2 and CCG3) (see picture here below for CCG1).


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Picture 2 : Electric lines distribution We will focus on the line between the junction box CCG1 and the inverters. Two cables are used.


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Picture 3 : Junction Box We calculate, per junction box, the voltage and current at the point of maximum power. Derived from this we will determine the section of cable to be used for the main DC line.

VOLTAGE For a given array, the panels are connected in series, so the voltage of the array is the sum of the voltage of the 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 is the addition of the current of each single array. There are 11 arrays per junction box.

I = IPMP x 11 = 7.44 x 11 = 81.84 A


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Picture 4 : View of an array


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2 Design phase

2.1 Design to maximum allowed current The applicable code in Spain is the Low Voltage Regulation.

This code states that the maximum current value has to be increased by 25% for design purposes (ITC-BT 40 article).

It has also to be applied a Temperature correction, as the applicable temperature on the cable reaches 50ºC (beyond 40ºC as stated by standard UNE 20460-5-523 for outside installations – Table A.52-1 bis).

The table 52-D1 for ambient temperature of 50ºC and cable type Tecsun (thermostable) gives a coefficient of 0.9. Taking into account the fact that the cable is exposed to sun, the 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 value of current. We will 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 of Tecsun (PV) (AS) cable is XLPE2. This leads to a section of 25 mm2 for copper conductor (see table below).


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Picture 5 : Current design – applicable table for sizing the conductor

2.2 Design to maximum allowed voltage drop We use again the same 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 of 1% 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


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

eILS

.

.γ

=

Where

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

• I: nominal current 81,84 A

• γ: conductivity of copper (at 70ºC1) 46.82 m/Ω.mm2

• e: Maximum voltage drop 4,77 V

This leads to :

298,3277,482,46

84,8190 mmx

xS == 35 mm2

2.3 Resulting section The resulting section is 35 mm², as this is the one filling the 2 criteria (allowed intensity and maximum voltage drop).

1 We take 70ºC as the approximate value resulting from an environment temperature of 50 º C increased by 20ºC due to conductor heating by Joule effect.


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3 Calculation of the economic section

Increasing the conductor section leads to higher investment cost but also to lower generation losses. In this chapter we analyze the pay-back time of conductor sections beyond the size defined by standards.

The power losses in an electrical line is 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). In other words:

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 get the calculation simpler, we will use the sum of discrete values (see the picture below), as we have the values of incident radiation, per hour, for each month of the year (Satel-light source: http://www.satel-light.com).

Ep ≈ R · Σ (Ii2 · ti)

For time intervals of 1 hour, the final expression is:

Ep ≈ R · Σ Ii2

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


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Picture 6 : Discretization of solar radiation and current

We make the following assumptions:

• The current is proportional to solar radiation

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

• The standard conditions of a module are given for a solar radiation of 1000 W/m2

The current for one array is: Ii = 0,9 x Icc · Gi/1000 = 0,9 x 7,96 x Gi/1000 = 7,164 x 10-3 · Gi (A)

Where Gi is the solar irradiation in W/m2

There are 11 arrays per junction box:

Iti = 11 x Ii = 0,078804 x Gi (A)

Where Iti is the annual average current2 at the hour “i” on the main DC line.

The energy loss in the main DC line will be:

2 For this example we use the annual average current. In a more developed analysis we should proceed to the sum of each single hour of the year.


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Ep ≈ R · Σ Iti2 = 0,0788042 x R · Σ Gi

2 (kW·h)

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

Cp ≈ FIT (€/kW·h) x Ep (kW·h) (€)

The corresponding resistance for a section of 35 mm2 (copper) is 0.0006102 Ω / m (at 70 º C). These values are fed into the spreadsheet as follows (see the picture).

It is considered a length of the analyzed cable of 45 meters.

Two scenarios are analyzed, using the former FIT of 44 c€/kWh and using the current FIT set at 30 c€/kWh. Those lead to annual savings of 160€ and 109€ respectively.

We have determined the variable cost of energy losses. This has to be confronted to the investment cost of cable.

For the case study section of 35 mm ²:

C35 = 90 x Ps + 109.23 x t (€)


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Where:

Ps: cable price (€ / m)

t: time (years)

Generalizing for a cable of a section “S” whatever:

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

Therefore we can now easily calculate the payback period for each section of conductor beyond 35 mm ², as well as the savings over 30 years.

FIT 0,30 €/kW.h

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 1307

11,66 C95 = 1049,4 + 40,243 x t 9,43 1419

14,45 C120 = 1300,5 + 31,86 x t 11,65 1419

18,45 C150 = 1660,5 + 25,487 x t 15,07 1250

23,43 C185 = 2108,7 + 20,665 x t 19,3 947

29,90 C240 = 2691 + 15,93 x t 24,57 507

FIT 0,44 €/kW.h

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 1298

8,11 C70 = 730 + 80,105 x t 4,13 2072


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11,66 C95 = 1049,4 + 59,02 x t 6,43 2385

14,45 C120 = 1300,5 + 46,728 x t 7,94 2503

18,45 C150 = 1660,5 + 37,382 x t 10,27 2408

23,43 C185 = 2108,7 + 30,31 x t 13,16 2187

29,90 C240 = 2691 + 23,364 x t 16,75 1813

The savings calculated here should be multiplied by 3, as the installation is made of 3 identical parts to 100 kW nominal power. Always under the assumption that the 3 main DC lines of have the same length (45 m).

Picture 7 : 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 70 mm ² and 95 mm ².


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Picture 8 : 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 95 mm ² and 120 mm ².

In the case of use of solar trackers, the payback time is shortened due to increased current generated by a better utilization of solar radiation (see graph below).


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Picture 9 : Recovered radiation according to the installation type : fix tilt 0º / fix tilt 30º / trackers. Location Valencia (Spain) It has been analyzed the use of bigger cable sections in order to reduce enery losses. The cumulated savings for this installation of 100 kW and Feed-In Tariff of 30 c€/kWh is around 4000 € (Net Present Value = 2000 € using an annual rate of 3.5%). The payback period is about 6 years. If the applicable Feed-In Tariff is 44 c€/kWh, then the cumulated savings reach 7000 € (Net Present Value of 3600 using an annual rate of 3,5%).

The table below shows the impact of different interest rates when considering the initial overinvestment and the cumulated savings along 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) 3921 3561 3234 2940 2676 2436 2217 2019 1839 1524 1263 1038

Net Present Value (FIT 44 c€/kWh) 7137 6468 5868 5325 4833 4389 3987 3621 3285 2706 2217 1806


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4 Conclusions In general terms the economic sizing analysis is always worth to be carried out, but especially in renewable energy installations, as the applicable Feed-In Tariff is higher than the wholesale market price and often higher than consumer retail price.

Together with an improved profitability of the project, there are additional advantages when using bigger cable sections:

• Electric lines with lower load, which improves the lifespan of the cables;

• If the plant is to be enlarged, the cables can be maintained;

• A better response to potential short-circuits;

• Improved Performance Ratio (PR) of the plant;

• Associated environmental benefits (CO2 emissions and other)

Tecsun (PV) (AS) cables are designed for a lifespan of 30 years without any maintenance.

Recio Lisardo Maíllo

Product Manager

Prysmian Cables & Systems

optimal cable sizing in photovoltaic systems

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