INGECON SUN POWER STATION

LOW VOLTAGE CONNECTION SIZING

BETWEEN INVERTERS &
TRANSFORMER

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Ingeteam Power Technology S. A. ABN0000IMC18_.docx

Tabla de contenido / Table of contents

1 AIM AND SCOPE ......................................................................................................................................... 3

2 SYSTEM DESCRIPTION ............................................................................................................................. 4
3 BUSBAR SIZING VALIDATION ................................................................................................................... 6
3.1 MAXIMUM ADMISSIBLE CURRENT .................................................................................................. 6
3.1.1 DUAL INVERTER ............................................................................................................................ 8
3.1.2 SINGLE INVERTER ........................................................................................................................ 9
3.2 MAXIMUM TEMPERATURE ............................................................................................................. 10
3.2.1 DUAL INVERTER .......................................................................................................................... 10
3.2.2 SINGLE INVERTER ...................................................................................................................... 11
3.3 SHORT CIRCUIT ............................................................................................................................... 13
3.3.1 DUAL INVERTER .......................................................................................................................... 14
3.3.2 SINGLE INVERTER ...................................................................................................................... 14
3.4 CONCLUSIONS ................................................................................................................................ 15
4 LV CABLE SIZING VALIDATION ............................................................................................................... 16
4.1 MAXIMUM ADMISSIBLE CURRENT ................................................................................................ 16
4.2 SHORT CIRCUIT ............................................................................................................................... 17
4.3 CONCLUSIONS ................................................................................................................................ 19
5 MV CABLE SIZING VALIDATION .............................................................................................................. 20
5.1 MAXIMUM ADMISSIBLE CURRENT ................................................................................................ 20
5.2 SHORT CIRCUIT ............................................................................................................................... 21
5.3 CONCLUSIONS ................................................................................................................................ 22
6 GROUNDING CABLE SIZING VALIDATION ........................................................................................... 23
6.1 SHORT CIRCUIT ............................................................................................................................... 23
7 THERMAL LOSSES ................................................................................................................................... 25
7.1 LV BUSBARS .................................................................................................................................... 25
7.2 LV CABLES ....................................................................................................................................... 26
7.3 LV TOTAL LOSSES .......................................................................................................................... 27
8 ANNEX I: EXAMPLE OF SELECTED FLEXIBLE COOPER BAR ............................................................. 28
9 ANNEX II: EXAMPLE OF SELECTED MV CABLE .................................................................................... 29

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1 AIM AND SCOPE
The aim of this document is to justify the election of the Low voltage connections used in the Power Stations
between de Dual Power Max B series and the LV/HV transformer.

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2 SYSTEM DESCRIPTION
Electrical connection between Dual Power Max B Series and MV transformer is carried out by two flexible
2
insulated copper bars of 100 x 10 mm for each phase, in order to handle a current of 3200A. The maximum
2
current density will be 1,6 A / mm

Isometric view of two Dual inverter connected to a transformer.

This copper bars are located inside an IP54 metallic enclosure in order to protect them from weather
harshness, complying with the requirements for outdoor installation.

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 Plant view with and without cover

Electrical connection between Dual Power Max B Series and busbar is carried out by Omerin Silicoul flexible
2
insulated copper of 4x120 mm for each phase, in order to handle a current up to 1600A.

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3 BUSBAR SIZING VALIDATION
2
The sizing of the busbar has been made with 1,6 A / mm . Next paragraphs show the validation of the model,
based on the standard DIN 43671.
2
Each phase has two flexible insulated copper bars of 100 x 10 mm , similar than the one showed on Annex I.

The input data to be considered in the calculation is:

Rated current per phase and per bar:

Irms=1500x2=3000A @ 30ºC of ambient temperature (AC current ≤ 1,000m)

Irms=1388x2=2776A @45ºC of ambient temperature (AC current ≤ 1,000m)

Irms=1350x2=2700A @50ºC of ambient temperature (AC current ≤ 1,000m)

Maximum absolute temperature that can be achieved in the busbar: 105ºC (limitation due to the
insulation layer of the busbar)

Calculation busbar based on a 2100m height.

Number of bars per phase: 2 (Dual) / 1 (Single inverter)

3.1 MAXIMUM ADMISSIBLE CURRENT

According to DIN 43671, the maximum current capability of a busbar is given by the next table and a
correction factor related to the altitude, indoor / outdoor application, maximum admissible temperature on the
bar, bar arrangement.

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛

𝐼𝑚𝑎𝑥 =
𝑘

Where:

 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5
The values of k1 to k4 are provided by DIN 43671 as follows:

 k1 electrical conductivity factor. It is determined by:

Cooper conductivity is 56 m/(Ω∙mm²) and therefore k1 = 1.

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  k2 temperature factor depends on the ambient temperature (θu) and maximum admissible
temperature on the busbar (θs).

Considering ambient temperature (θu) of 30 ºC and a maximum admissible temperature on

the busbar (θs) of 100ºC, then k2 = 1,58.
Considering ambient temperature (θu) of 45 ºC and a maximum admissible temperature on
the busbar (θs) of 100ºC, then k2 = 1,37.
Considering ambient temperature (θu) of 50 ºC and a maximum admissible temperature on
the busbar (θs) of 100ºC, then k2 = 1,30.

 k3 arrangement factor:

With 1 insulated bars, k3 = 1.

With 2 insulated bars, k3 = 0,85.

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  K5 altitude factor

For indoor application, at 2,100m altitude, k5 =0,987.

Maximum current capability before correction according to DIN 43671

3.1.1 DUAL INVERTER

For 2 insulated bars of 100 x 10 mm at 60Hz, maximum current capability before correction will be 2850 A.

Correction factor will be:

 @ 30ºC 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5 = 1 · 1,58 · 0,85 · 0,987 = 1,3255

 @ 45ºC 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5 = 1 · 1,37 · 0,85 · 0,987 = 1,1493
 @ 50ºC 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5 = 1 · 1,30 · 0,85 · 0,987 = 1,0906

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And therefore, maximum current capability according to DIN 43671

 3.777 A @ 30ºC
 3.275 A @ 45ºC
 3.108 A @ 50ºC

As a conclusion, the sizing proposed for dual inverter solution, comprising two flexible cooper bars of 100 x 10
mm per phase is correct.

3.1.2 SINGLE INVERTER

For 1 insulated bars of 100 x 10 mm at 60Hz, maximum current capability before correction will be 1810 A.

Correction factor will be:

 @ 30ºC 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5 = 1 · 1,58 · 1 · 0,987 = 1,5594

 @ 45ºC 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5 = 1 · 1,37 · 1 · 0,987 = 1,3521
 @ 50ºC 𝑘 = 𝑘1 · 𝑘2 · 𝑘3 · 𝑘5 = 1 · 1,30 · 1 · 0,987 = 1,2831

And therefore, maximum current capability according to DIN 43671

 2.822 A @ 30ºC
 2.447 A @ 45ºC
 2.322 A @ 50ºC

As a conclusion, the sizing proposed for single inverter solution, comprising a flexible cooper bar of 100 x 10
mm per phase is correct.

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3.2 MAXIMUM TEMPERATURE

3.2.1 DUAL INVERTER

According to the standard DIN43671, the final temperature in the cooper bar could be calculated as follows:

The maximum current capability is 3.777 A @ 30ºC, 3.275 A @ 45ºC, 3.275 A @ 45ºC & 3.108 A @ 50ºC

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 2850 𝐴

𝐼𝑚𝑎𝑥@30°𝐶 = →𝑘= → 𝑘 = 0,7546
𝑘 3777 𝐴

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 2850 𝐴

𝐼𝑚𝑎𝑥@45°𝐶 = →𝑘= → 𝑘 = 0,8702
𝑘 3275 𝐴

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 2850 𝐴

𝐼𝑚𝑎𝑥@50°𝐶 = →𝑘= → 𝑘 = 0,9170
𝑘 3108 𝐴

K1 = 1; k3 = 0,85; k5 =0,987

K2 factor could be calculated as:

𝑘2 = (𝑘1 ∙ 𝑘3 ∙ 𝑘4 )/𝑘

1 ∙ 0,85 ∙ 0,987
𝑘2@30°𝐶 = → 𝑘2@30°𝐶 = 1,1118
0,7546

1 ∙ 0,85 ∙ 0,987
𝑘2@45°𝐶 = → 𝑘2@45°𝐶 = 0,964
0,8702

1 ∙ 0,85 ∙ 0,987
𝑘2@50°𝐶 = → 𝑘2@45°𝐶 = 0,9149
0,9170

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By this way, the final cooper bar temperature (T f) is:

 𝑇𝑓@30°𝐶 ≅ 66°𝐶
 𝑇𝑓@45°𝐶 ≅ 73°𝐶
 𝑇𝑓@50°𝐶 ≅ 82°𝐶

3.2.2 SINGLE INVERTER

According to the standard DIN43671, the final temperature in the cooper bar could be calculated as follows:

The maximum current capability is 2.822 A @ 30ºC, 2.447 A @ 45ºC, 2.322 A @ 50ºC,

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 1810 𝐴

𝐼𝑚𝑎𝑥@30°𝐶 = →𝑘= → 𝑘 = 0,6413
𝑘 2822 𝐴

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 1810 𝐴

𝐼𝑚𝑎𝑥@45°𝐶 = →𝑘= → 𝑘 = 0,7396
𝑘 2447 𝐴

𝐼max 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡𝑖𝑜𝑛 1810 𝐴

𝐼𝑚𝑎𝑥@45°𝐶 = →𝑘= → 𝑘 = 0,7795
𝑘 2322 𝐴

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K1 = 1; k3 = 1; k5 =0,987

K2 factor could be calculated as:

𝑘2 = (𝑘1 ∙ 𝑘3 ∙ 𝑘4 )/𝑘

1 ∙ 1 ∙ 0,987
𝑘2@30°𝐶 = → 𝑘2@30°𝐶 = 1,539
0,6413

1 ∙ 1 ∙ 0,987
𝑘2@45°𝐶 = → 𝑘2@45°𝐶 = 1,3345
0,7396

1 ∙ 1 ∙ 0,987
𝑘2@50°𝐶 = → 𝑘2@45°𝐶 = 1,2662
0,7795

By this way, the final cooper bar temperature (T f) is:

 𝑇𝑓@30°𝐶 ≅ 96°𝐶
 𝑇𝑓@45°𝐶 ≅ 97°𝐶
 𝑇𝑓@50°𝐶 ≅ 94°𝐶

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3.3 SHORT CIRCUIT

The busbar will be justified for a maximum short circuit current of 65kA, and operating time range 200ms. The
minimum section (mm²) based on the calculation method in the standard UNE-HD 60364-5-54:2015, will be:

Cu Cu
B (ºC) 234,5 B (ºC) 234,5
Qc (J/ºC mm3) 0,00345 Qc (J/ºC mm3) 0,00345
p20 (ohm·mm) 0,000017241 p20 (ohm·mm) 0,000017241
(sqrt(Qc(B+20)p20) 226 (sqrt(Qc(B+20)p20) 226
ti 77 ti 97
tf 140 tf 140
ln(1+tf-ti/B+ti) 0,184192465 ln(1+tf-ti/B+ti) 0,121963993
k 96,99 k 78,93

Dual inverter Single inverter

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Considering a short circuit current of 65kA rms, and a fault time of 200ms, the minimum section values are as
follows:

3.3.1 DUAL INVERTER

“k” factor for Copper and PVC insulation is k=96.99.

- 299,71 mm² for withstanding the short circuit on copper busbar. The copper busbar section per phase
is 2000 mm² for dual inverter.

The minimum general operating time range for a relay (protection N.51) is 43ms. This value must be added to
the switch trip time (switchgear MT), estimated in 80ms. The result is 123 ms, faster than estimated time.

The minimum general operating time range for a LV relay (protection N.51) is below 50ms.

As a result, we can conclude that the busbar size selected is enough to withstand short circuit current up to a
65kA prospective value.

The fault current withstands capability math with flexible insulated copper busbar for 1 second give us a value
of 193,98kA.

3.3.2 SINGLE INVERTER

“k” factor for Copper and PVC insulation is k=78.93.

- 368,29 mm² for withstanding the short circuit on copper busbar. The copper busbar section per phase
is 1000 mm² for dual inverter.

The minimum general operating time range for a relay (protection N.51) is 43ms. This value must be added to
the switch trip time (switchgear MT), estimated in 80ms. The result is 123 ms, faster than estimated time.

The minimum general operating time range for a LV relay (protection N.51) is below 50ms.

As a result, we can conclude that the busbar size selected is enough to withstand short circuit current up to a
65kA prospective value.

The fault current withstands capability math with flexible insulated copper busbar for 1 second give us a value
of 78,93kA.

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3.4 CONCLUSIONS

Flexible insulted cooper busbar 100x10x1 mm² are appropriate to connect the inverters to the power
transformer in Skid Power Stations, by maximum current admissible calculation, by maximum temperature
calculation and by short circuit current. Flexible option will be used as it is easier to connect between different
elements.

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4 LV CABLE SIZING VALIDATION
The input data to be considered in the calculation is:

Rated current per phase and per bar:

Irms=1500x2=3000A @ 30ºC of ambient temperature

Irms=1388x2=2776A @45ºC of ambient temperature

Irms=1350x2=2700A @50ºC of ambient temperature

4.1 MAXIMUM ADMISSIBLE CURRENT

According to the technical features defined by the manufacturer, the results are shown in figure below for
current/temperature conditions (Ta=60ºC):

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The maximum current will be 640A per wire, 2560A for the total section.

Applying correction factors due to standard IEC60364-5-52 the maximum permissible current will be as
follows:

2560A x0.79 (number of circuits in contact) x1 (number of layers) = 2022,4A.

4.2 SHORT CIRCUIT

The cable connection will be justified for a maximum short circuit current of 65kA, and operating time range
200ms. The minimum section (mm²) based on the calculation method in the standard UNE 20460-5-54, will
be:

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 Cu
B (ºC) 234,5
Qc (J/ºC mm3) 0,00345
p20 (ohm·mm) 0,000017241
(sqrt(Qc(B+20)p20) 226
ti 110
tf 180
ln(1+tf-ti/B+ti) 0,184978884
k 97,20

Considering a short circuit current of 65kA rms, and a fault time of 200ms, the minimum section values are as
follows:

“k” factor for Copper and silicone insulation (worst case scenario ti=110ºC, tf=180ºC) is k=97,2

- 299,06 mm² for withstanding the short circuit on silicone insulated copper cable. The silicone
insulated copper cable section per phase is 480 mm²

The minimum general operating time range for a MV relay (protection N.51) is 43ms. This value must be
added to the switch trip time (switchgear MT), estimated in 80ms. The result is 123 ms, faster than estimated
time.

The minimum general operating time range for a LV relay (protection N.51) is below 50ms.

As a result, we can conclude that the silicone insulated copper cable size selected is enough to withstand
short circuit current up to a 65kA prospective value.

The fault current withstands capability math with silicone insulated copper cable for 1 second give us a value
of 46,656kA.

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4.3 CONCLUSIONS

Silicone insulated cooper cable 4x120 mm² is appropriate to connect the inverters to the power transformer in
Skid Power Stations, by maximum current admissible calculation, by maximum temperature calculation and
by short circuit current.

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5 MV CABLE SIZING VALIDATION
The input data to be considered in the calculation is:

Power transformer size (13.2kV / 0,69kV):

RP=5379kVA @30ºC

RP=4976kVA @45ºC

RP=4840kVA @50ºC

Rated current per phase:

Irms=235.3A @ 30ºC of ambient temperature

Irms=217.7A @45ºC of ambient temperature

Irms=211.7A @50ºC of ambient temperature

5.1 MAXIMUM ADMISSIBLE CURRENT

According to the technical features defined by the MV XLPE aluminum cable manufacturer, the results are
shown in figure below for current/temperature conditions:

The maximum current will be 335A per wire, at 40ºC ambient temperature in the shade.

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Applying correction factors due to standard IEC60364-5-52 the maximum permissible current will be as
follows:

@30ºC 335A x1 (number of circuits in contact) x1 (number of layers) x1.10 (temperature factor) x0,9
(exposed to the sun) = 331.65A

45ºC  335A x1 (number of circuits in contact) x1 (number of layers) x0.95 (temperature factor) x0,9
(exposed to the sun) = 286.43A

50ºC 335A x1 (number of circuits in contact) x1 (number of layers) x0.89 (temperature factor) x0,9 (exposed
to the sun) = 268.34A

5.2 SHORT CIRCUIT

The cable connection will be justified for a maximum short circuit current of 20kA, and operating time range
200ms. The minimum section (mm²) based on the calculation method in the standard UNE 20460-5-54, will
be:

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 Al
B (ºC) 228
Qc (J/ºC mm3) 0,0025
p20 (ohm·mm) 0,000028264
(sqrt(Qc(B+20)p20) 148
ti 90
tf 250
ln(1+tf-ti/B+ti) 0,40755935
k 94,48

Considering a short circuit current of 20kA rms, and a fault time of 200ms, the minimum section values are as
follows:

“k” factor for XLPE insulated aluminum cable (worst case scenario ti=90ºC, tf=250ºC) is k=94,48.

- 94,66 mm² for withstanding the short circuit on XLPE insulated aluminum cable. The XLPE insulated
aluminum cable section per phase is 150 mm²

The minimum general operating time range for a MV relay (protection N.51) is 43ms. This value must be
added to the switch trip time (switchgear MT), estimated in 80ms. The result is 123 ms, faster than estimated
time.

The minimum general operating time range for a LV relay (protection N.51) is below 50ms.

As a result, we can conclude that the XLPE insulated aluminum cable size selected is enough to withstand
short circuit current up to a 20kA prospective value.

The fault current withstands capability math with XLPE insulated aluminum cable for 1 second give us a value
of 16,398kA.

5.3 CONCLUSIONS
XLPE isolated aluminum cable 1x150 mm² is appropriate to connect the MV transformer to the MV
switchgears in Skid Power Stations, by maximum current admissible calculation, by maximum temperature
calculation and by short circuit current. Note that it´s possible to install 1x95 mm², but this size has been
selected due to a greater availability.

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6 GROUNDING CABLE SIZING VALIDATION
The input data to be considered in the calculation is:

- XLPE copper insulation cable

- Ti=Tamb

6.1 SHORT CIRCUIT

The cable connection will be justified for a maximum short circuit current for each type of neutral system (as
shown below). The minimum section (mm²) based on the calculation method in the standard UNE 20460-5-
54, will be:

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 Cu
B (ºC) 234,5
Qc (J/ºC mm3) 0,00345
p20 (ohm·mm) 0,000017241
(sqrt(Qc(B+20)p20) 226
ti 50
tf 250
ln(1+tf-ti/B+ti) 0,532384178
k 164,90

Considering the worst case scenario of short circuit current, and a fault time according to each circuit (1s
RMU, 200ms rest), the minimum section values are as follows:

Time K Minimum Proposed

Element Icc3 (kA) Icc2 (kA) Ti (˚C) Tf (˚C)
(s) factor S.(mm²) S.(mm²)
Ring Main Unit 20 17.32 1.0 40.0 250.0 170,35 105.03 150
Inverter
65 56.29 0.2 40.0 250.0 170,35 152.66 175
transformer
Inverter 65 56.29 0.2 40.0 250.0 170,35 152.66 175
Auxiliary
65 56.29 0.2 40.0 250.0 170,35 152.66 175
transformer
LV Panel 1.45 - 0.2 40.0 250.0 170,35 3,93 6

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7 THERMAL LOSSES

7.1 LV BUSBARS

The thermal losses are calculated for a copper busbar length of 1 meter per phase 100x10x1mm, between
inverters and transformer

Material Copper
ρ20= 0,01724 Ωmm2/m
α20= 0,00393
Working Temperature 100
ρ (WT)= 0,02401532
Number of conductors by phase 10
Section (mm2) by conductors 100 mm2
Length by phase(m) 1 m
Resistance (WT) by phase conductor 0,00024015 Ω
i= 1503 A
Thermal losses (WT) by phase 54,25 W
Total thermal losses (3 phases) by single inverter 162,75 W
Total thermal losses (3 phases) by dual inverter 325,50 W
Total thermal losses SKID 3 inverters 488,26 W
Total thermal losses SKID 4 inverters 651,01 W

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7.2 LV CABLES

The following thermal losses are calculated for a silicone insulated copper wiring between inverters of the
same dual inverter

These losses are divided in two.

OMERIN SILICOUL from inverter 2 to busbar

Section 120 mm2
Resistence, 20ºC 0,164 ohms/km
Num cables /phase 4 un
Length 4,5 m
alpha 0,00392
Working temperature 110 ºC
Resistance, 100ºC 0,2218592 ohms/km
Resistance per single wire 0,00099837 ohms
Total Phase Current 1503 A rms
Current per single wire 375,75 A rms
Power losses per single wire 140,957 W
Total power losses 1691,489 W

OMERIN SILICOUL from inverter 1 to busbar

Section 120 mm2
Resistence, 20ºC 0,164 ohms/km
Num cables /phase 4 ud
Length 1,5 m
alpha 0,00392
Working temperature 110 ºC
Resistance, 100ºC 0,2218592 ohms/km
Resistance per single wire 0,00033279 ohms
Total Phase Current 1503 A rms
Current per single wire 375,75 A rms
Power losses per single wire 46,986 W
Total power losses 563,830 W

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7.3 LV TOTAL LOSSES

As a result the total power losses per skid inverter are:

Total thermal losses (3 phases) by single inverter 162,75 W

Total thermal losses (3 phases) by dual inverter 325,50 W
Total thermal losses from inverter 1 to busbar 563,830 W
Total thermal losses from inverter 2 to busbar 1691,489 W
Total thermal losses from inverter 3 to busbar 563,830 W
TOTAL LOSSES SKID 3 INVERTERS 3307,99 W
TOTAL AC POWER INVERTER 1793 kW
TOTAL LOSSES (%) AC BUSBAR (SINGLE / DUAL) 0,0907 %
TOTAL LOSSES (%) INTERNAL AC CABLE (SINGLE) 0,3145 %
TOTAL LOSSES (%) INTERNAL AC CABLE (DUAL) 0,6289 %

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8 ANNEX I: EXAMPLE OF SELECTED FLEXIBLE COOPER BAR

Ingeteam Power Technology S. A. ABN0000IMC18_.docx

9 ANNEX II: EXAMPLE OF SELECTED MV CABLE

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