2016 COSTOminimov03

Costo mínimo en Líneas de Transmisión

Teoría Teo ría,, aná anális lisis is y eje ejempl mplo o

Juan Baut Bautist ista a – Pro Profes fesor or Princ Principal ipal

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Ejem Ej empl plo o de cál cálcu culo lo Se tiene el Proyecto que se diseñará con los datos siguientes:

TENSION Kv

220

DEMANDA MAXIMA MAXIMA M VA

110

HORAS / AÑO

8760

COSTO COST O ENE ENERGIA (ctvs US$/Kw $/Kw h)

5,00

VIDA ECONOMICA (años)

IMPUESTOS + SEGUROS (% de la Inversion inicial

20

2,40

TASA RENDIMIENTO %

12

CORRIENTE (AMP)

289,02

frcc fr

0,13387878

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Ejem Ej empl plo o de cálc cálcul ulo… o… Los conductores que serán utilizados como alternativas son los siguientes: ITEM

SECCION (mm2)

DIAMETRO (mm)

PESO UNITARIO (kg/m)

PESO POR RESISTENC KILOMETR IA O (kg / km ) (Ohm/km)

COSTO UNITARIO (US$/kg)

DIAMETRO (mm)

PESO UNITARIO (kg/m)

30 0

21,7 9

0,781

781

0,1 200

6,1

2

32 6

23,5 5

0,912

912

0,1 030

6,6

ITEM

SECCION (mm2)

Item

 AA AC 62 01

1

PESO POR RESISTENC KILOMETR IA O (kg / km ) (Ohm/km)

COSTO UNITARIO (US$/kg)

R  ACA R 18/19

1

29 8

2 2,3 5

0,8 36

83 6

0 ,1 05 6

5 ,9 6

2

33 0

2 3,6 0

0,9 09

90 9

0 ,0 95 0

6 ,4 8

3

40 4

2 6,1 1

1,1 15

1 11 5

0 ,0 77 0

7 ,7 0

4

43 3

2 7,0 2

1,1 95

1 19 5

0 ,0 72 6

8 ,1 7

3

37 0

25,1 5

1,034

10 34

0,0 908

7,2

5

45 5

2 7,7 0

1,2 56

1 25 6

0 ,0 69 0

8 ,5 3

4

47 6

28,1 4

1,295

12 95

0,0 725

8,7

6

46 9

2 8,1 4

1,2 85

1 28 5

0 ,0 67 0

8 ,7 6

5

50 6

29,2 3

1,391

13 91

0,0 660

9,5

7

50 7

2 9,6 0

1,4 00

1 40 0

0 ,0 61 4

9 ,3 8

8

52 0

2 9,6 1

1,4 34

1 43 4

0 ,0 60 5

9 ,5 9

6

52 1

29,7 0

1,441

14 41

0,0 630

9,8

9

54 7

3 0,3 8

1,5 50

1 55 0

0 ,0 57 0

1 0,0 0

Item

 AC SR

5,5

Item

 ACA R 30/31

1

29 8

2 2,3 5

0,83 6

836

0 ,1 05 60

6,9 7

2

33 0

2 3,6 0

0,90 9

909

0 ,0 88 50

7,5 8

3 4

40 4 43 3

2 6,1 1 2 7,0 2

1,11 5 1,19 5

1 1 15 1 1 95

0 ,0 72 20 0 ,0 67 45

9,0 1 9,5 6

5

45 5

2 7,7 0

1,25 6

1 2 56

0 ,0 64 10

9,9 8

6

46 9

2 8,1 4

1,28 5

1 2 85

0 ,0 62 20

1 0,2 5

7

50 7

2 9,6 0

1,40 0

1 4 00

0 ,0 57 65

1 0,9 7

8

52 0

2 9,6 1

1,43 4

1 4 34

0 ,0 54 30

1 1,2 2

9

54 7

3 0,3 8

1,55 0

1 5 50

0 ,0 53 43

1 1,7 0

1

30 0

24,5 5

1,240

12 40

0,0 913

2

31 8

25,1 5

1,302

13 02

0,0 87

5,8

3

356,5

26,6 8

1,456

14 56

0,0 777

6,4

4

397,5

28,1 4

1,628

16 28

0,0 696

7,0

5

45 0

29,5 1

1,725

17 25

0,0 622

7,8

6

47 7

30,3 8

1,829

18 29

0,0 587

8,1

7

516,7

31,6 5

1,982

19 82

0,0 541

8,7

8

556,5

32,8 4

2,130

21 30

0,0 503

9,3

9

59 6

33,9 9

2,282

22 82

0,0 441

9,7

10

63 6

35,3 6

2,429

24 29

0,0 392

10,3

11

71 5

37,2 1

2,738

27 38

0,0 342

11,0

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Ejem Ej empl plo o de cálc cálcul ulo… o…

Se requiere: 1.seleccionar el conductor (material y 1.seleccionar sección) mas conveniente para la construcción de la línea de transmisión en 220 kV kV del Pr Proyecto to.. 2.¿Cuál es el costo mínimo anual de la 2.¿Cuál línea?

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Solución 1. Cálculo de la corriente de transmisión. 2. Cálculo del Factor de recuperación (FRC) del capital

TENSION Kv

220

DEMANDA MAXIMA MAXIMA M VA

110

HORAS / AÑO

8760

COSTO ENERGIA (ctvs US$/K S$/Kw w h)

5,00

VIDA ECONOMICA (años)

IMPUESTOS + SEGUROS (% de la Inversion inicial

20

2,40

TASA RENDIMIENTO %

12

CORRIENTE (AMP)

289,02

frc fr c

0,13387878

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Conductor ACAR 18/19

ITEM

SECCION (mm2)

DIAMETRO (mm)

PESO UNITARIO (kg/m)

PESO POR KILOMETR O (kg / km)

RESISTENCIA (Ohm/km)

COSTO UNITARIO (US$/kg)

R

 COSTO TOTAL DEL CONDUCTO R US$/km

RECUPERACION  ANUAL DE LA INVERSION EN CONDUCTOR (US$)

IMPUESTOS + SEGUROS (2.5% del Costo)

SUBTOTAL  A N UA L CONDUCTOR+IM PUESTOS+SEGU R OS

COSTO PERDIDAS ENERGIA

TOTAL COSTOS US$

P M E N OR OR COSTO

 ACAR  AC AR 18/19 18 /19

3993,23

1

2 98

22,35

0 ,836

83 6

0,1 05 6

5,96

498 2,56

667 ,06

16,01

683,0 7

3 863,54

45 46,61

2

3 30

23,60

0 ,909

90 9

0,0 95 0

6,48

589 0,32

788 ,59

18,93

807,5 1

3 475,73

42 83,24

3

4 04

26,11

1 ,115

1115

0,0 77 0

7,70

858 5,50

1 14 9,42

27,59

1177 ,00

2 817,17

399 4,1 7

4

4 33

27,02

1 ,195

1195

0,0 72 6

8,17

976 3,15

1 30 7,08

31,37

1338 ,45

2 656,19

399 4,6 3

5

4 55

27,70

1 ,256

1256

0,0 69 0

8,53

10713 ,68

1 43 4,33

34,42

1468 ,76

2 524,47

399 3,2 3

6

4 69

28,14

1 ,285

1285

0,0 67 0

8,76

11256 ,60

1 50 7,02

36,17

1543 ,19

2 451,30

399 4,4 9

7

5 07

29,60

1 ,400

1400

0,0 61 4

9,38

13132 ,00

1 75 8,10

42,19

1800 ,29

2 246,42

404 6,7 1

8

5 20

29,61

1 ,434

1434

0,0 60 5

9,59

13752 ,06

1 84 1,11

44,19

1885 ,30

2 213,49

409 8,7 8

9

5 47

30,38

1 ,550

1550

0,0 57 0

10,0 0

15500 ,00

2 07 5,12

49,80

2124 ,92

2 085,44

421 0,3 6

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Conductor ACAR 18/19 Costos por km en función a la sección del conductor (ACAR 18/19) SUBTOTAL ANUAL CONDUCTOR+IMPUESTOS+SEGUROS 5000,00

4500,00

4000,00

3500,00

3000,00

2500,00

2000,00

1500,00

1000,00

500,00

COSTO PERDIDAS ENERGIA

TOTAL COSTOS US$

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Conductor ACAR 30/31

DIAMETRO (mm)

PESO UNITARIO (kg/m)

PESO POR KILOMETR O (kg / km)

RESISTENC IA (Ohm/km)

COSTO UNITARIO (US$/kg)

 COSTO TOTAL DEL CONDUCTO R US$/km

RECUPERACION  ANUAL  ANUA L DE LA INVERSION EN CONDUCTOR (US$)

IMPUESTOS + SEGUROS (2.5% del Costo)

SUBTOTAL  A N UA L CONDUCTOR+IM PUESTOS+SEGU R OS

COSTO PERDIDAS ENERGIA

TOTAL COSTOS US$

ITEM

SECCION (mm2)

Item

 ACA  A CA R 30/31

1

298

22 ,35

0 ,8 36

836

0 ,1 0 560

6 ,97

5 8 2 6,92

7 8 0 ,10

18 ,72

7 9 8 ,82

3 8 63 ,54

46 6 2 ,3 7

2

330

23 ,60

0 ,9 09

909

0 ,0 8 850

7 ,58

6 8 9 0,22

9 2 2,45

22 ,14

9 4 4 ,59

3 2 37 ,91

41 8 2 ,5 1

3

404

26 ,11

1 ,1 15

1 11 5

0 ,0 7 220

9 ,01

1 0 04 6 ,15

1 3 4 4 ,97

3 2 ,28

1 3 7 7 ,25

2 6 4 1 ,55

4 0 1 8 ,8 0

4

433

27 ,02

1 ,1 95

1 19 5

0 ,0 6 745

9 ,56

1 1 42 4 ,20

15 2 9 ,46

36 ,71

1 5 6 6,16

2 4 6 7 ,77

4 0 3 3 ,9 3

5

455

27 ,70

1 ,2 56

1 25 6

0 ,0 6 410

9 ,98

1 2 53 4 ,88

16 7 8 ,15

40 ,28

1 7 1 8,43

2 3 4 5 ,20

4 0 6 3 ,6 3

6

469

28 ,14

1 ,2 85

1 28 5

0 ,0 6 220

1 0 ,25

1 3 17 1 ,25

17 6 3 ,35

42 ,32

1 8 0 5,67

2 2 7 5 ,69

4 0 8 1 ,3 6

7

507

29 ,60

1 ,4 00

1 40 0

0 ,0 5 765

1 0 ,97

1 5 35 8 ,00

20 5 6 ,11

49 ,35

2 1 0 5,46

2 1 0 9 ,22

4 2 1 4 ,6 7

8

520

29 ,61

1 ,4 34

1 43 4

0 ,0 5 430

1 1 ,22

1 6 08 9 ,48

21 5 4 ,04

51 ,70

2 2 0 5,74

1 9 8 6 ,65

4 1 9 2 ,3 9

MENOR COSTO

4018,80

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Conductor ACAR 30/31

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Conductor AAAC 6201

DIAMETRO (mm)

PESO UNITARIO (kg/m)

PESO POR KILOMETR O (kg / km)

RESISTENC IA (Ohm/km)

COSTO UNITARIO (US$/kg)

 COSTO TOTAL DEL CONDUCTO R US$/km

RECUPERACION  ANUAL  ANUA L DE LA INVERSION EN CONDUCTOR (US$)

IMPUESTOS + SEGUROS (2.5% del Costo)

SUBTOTAL  A N UA L CONDUCTOR+IM PUESTOS+SEGU R OS

COSTO PERDIDAS ENERGIA

TOTAL COSTOS US$

ITEM

SECCION (mm2)

Item

 AA A C 6201 620 1

1

300

21 ,79

0 ,7 81

781

0 ,1 2 00

6 ,1

4 7 6 4,10

6 3 7 ,81

15 ,31

6 5 3 ,12

4 3 90 ,39

50 4 3 ,5 1

2

326

23 ,55

0 ,9 12

912

0 ,1 0 30

6 ,6

6 0 1 9,20

8 0 5 ,84

19 ,34

8 2 5 ,18

3 7 68 ,42

45 9 3 ,6 0

3

370

25 ,15

1 ,0 34

1034

0 ,0 9 08

7 ,2

7 4 4 4,80

9 9 6 ,70

2 3 ,92

1 0 2 0 ,62

3 3 22 ,06

43 4 2 ,6 8

4

476

28 ,14

1 ,2 95

1295

0 ,0 7 25

8 ,7

1 1 2 6 6 ,50

1 5 0 8 ,35

36 ,20

1 5 4 4,55

2 6 52 ,53

41 9 7 ,0 7

5

506

29 ,23

1 ,3 91

1391

0 ,0 6 60

9 ,5

1 3 2 1 4 ,50

1 7 6 9 ,14

42 ,46

1 8 1 1,60

2 4 14 ,71

42 2 6 ,3 2

6

521

29 ,70

1 ,4 41

1441

0 ,0 6 30

9 ,8

1 4 1 2 1 ,80

1 8 9 0 ,61

45 ,37

1 9 3 5,98

2 3 04 ,96

42 4 0 ,9 4

MENOR COSTO

4197,07

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Conductor AAAC 6201

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Conductor ACSR 

DIAMETRO (mm)

PESO UNITARIO (kg/m)

PESO POR RESISTENC KILOMETR IA O (kg (kg / km ) (Ohm/km)

COSTO UNITARIO (US$/kg)

 COSTO TOTAL DEL TOTAL CONDUCTO R US$/km

RECUPERACION  ANUAL DE LA INVERSION EN CONDUCTOR (US$)

IMPUESTOS + SEGUROS (2.5% del Costo)

SUBTOTAL  A N UA L CONDUCTOR+IM PUESTOS+SEGU R OS

COSTO PERDIDAS ENERGIA

TOTAL COSTOS US$

ITEM

SECCION (mm2)

Item

 AC SR

1

3 00

2 4 ,55

1 ,2 40

1 240

0 ,0 9 13

5 ,5

6 8 2 0 ,00

9 1 3 ,0 5

2 1 ,9 1

9 3 4 ,9 7

3 3 4 0 ,36

4 2 7 5 ,3 2

2

3 18

2 5 ,15

1 ,3 02

1 302

0 ,0 87

5 ,8

7 5 5 1 ,60

1 0 1 1 ,00

2 4 ,2 6

1 0 3 5 ,26

3 1 8 3 ,03

4 2 1 8 ,3 0

3

3 5 6 ,5

2 6 ,68

1 ,4 56

1 456

0 ,0 7 77

6 ,4

9 3 1 8 ,40

1 2 4 7 ,54

2 9 ,94

1 2 7 7 ,4 8

2 8 4 2 ,78

4 1 2 0 ,2 5

M E N OR OR COSTO

4108,73

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Mínimo cos ostto anual del Pro roye yec cto y conductor sele se lecc ccio iona nado do en 220 kV

Mínim Mínimo o Costo para para cada cada tipo de d e conduct con ductor  or   ACA  ACAR R 18/19

3993,23 399 3,23

 ACA  ACAR R 30/31

4018,80 401 8,80

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Mínimo cos ostto anual del Pro roye yec cto y conductor sele se lecc ccio iona nado do en 138 kV

Mínim Mínimo o Costo para para cada cada tipo de d e conduct con ductor  or   ACA  ACAR R 18/19 18 /19

7425 74 25,02 ,02

 ACA  ACAR R 30/31 30 /31

7254 72 54,78 ,78

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Mínimo cos ostto anual del Pro roye yec cto y conductor sele se lecc ccio iona nado do en 500 kV

Mínim Mínimo o Costo Cost o pa p ar a cada cada tipo de condu co nductor  ctor   ACA  ACAR R 18/19 18 /19

1431 14 31,05 ,05

 ACA  ACAR R 30/31 30 /31

1546 15 46,81 ,81

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Anális Anál isis is co comp mpar arat ativ ivo o co con n di dife fere ren nte tes s te tens nsio ion nes de tra tr ansmisión ¿Qué se puede concluir?

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¿Qué defectos tiene el pro roc cedimiento empl ple eado do? ?

1. ¿Tiene efecto en el costo mínimo la inclusión de los

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Potenci Pote ncia a med media ia de tran transmi smisió sión n

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Considerando un conductor de cobre de sección Ѕ y un conductor de aluminio de sección 1,4 Ѕ, ambos de la misma longitud y recorridos por la misma corriente durante el mismo tiempo, se tiene: Εcu=ρcu

ℓ l2max ·Δt = 18,35·10-9 ℓ l2max · Δt Ѕ

Εal=ρal

[4]

Ѕ

ℓ l2max ·Δt = 30,3 ·10-9 ℓ l2max · Δt =

1,4Ѕ

Εal=21,64 · 10-9

1,4Ѕ

ℓ l2max · Δt Ѕ

[5]

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Comparando los valores de [4] y [5], se concluye que, aumentando la sección del conductor eléctrico de aluminio en 40%, las pérdidas de energía en este conductor aún son 18% superiores a las del conductor de cobre. Ese sería el caso, por ejemplo, de un conductor de cobre de sección nominal 50mm 2  y de aluminio 70 mm2 .

3.2. Pérdida joule en presencia de corriente armónica Las corrientes armónicas pueden ser importantes fuentes de pérdidas joule en las instalaciones eléctricas, impactando así los costos operativos de las instalaciones. Se debe calcular el valor de la resistencia eléctrica en cada frecuencia (R h) presente en el espectro armónico. En seguida, se calcula la pérdida joule para cada resistencia a partir de la ecuación Ε(h)=Rh·lh2·Δt, donde lh es la corriente armónica de orden  h.  En los circuitos donde existe la presencia del conductor neutro se debe calcular también la pérdida en ese conductor, una vez que el valor de la corriente armónica no neutra puede ser significativo. Rh, que es el valor de la resistencia del cable en una frecuencia dada, difiere del valor de la resistencia en corriente continua normalmente presentada en los catálogos proporcionados por los fabricantes. Eso se debe principalmente al fenómeno conocido como efecto superfi la corriente alterna de mayor frecuencia tiende a circular predominantemente por la superficie exterior del conductor, causando así cial:  la una disminución en la sección efectiva del conductor y, consecuentemente, un aumento en la resistencia eléctrica aparente del cable. La Gráfica 1 muestra una forma de obtener el valor de la resistencia en corriente alterna en función de la fr ecuencia a partir del valor de la resistencia en corriente continua y la Tabla 1 muestra los valores de la resistencia en corriente continua.

Rca/Rcc

50 45 40 35 30 25 20

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Tabla 1: Resistencia en corriente continua (resistividad de acuerdo con NCh 2625.Of2001)  Sección nominal (mm2)

Resistencia máxima del conductor a 20ºC (Ω/km)

1.5 2.5 4 6 10 16 25 35 50 70 95 120 150 185 240 300 400

12.2 7.3 4.59 3.06 1.84 1,15 0.734 0.524 0.367 0.262 0.193 0.153 0.122 0.0992 0.0765 0.0612 0.0459

4: DIMENSIONAMIENTO ECONÓMICO DE CONDUCTORES ELÉCTRICOS CONFORME A LA NORMA NCh 2625.Of2001 4.1 - Introducción Para la determinación de la sección económica de un conductor para un cierto circuito, sea en baja o media tensión, se debe utilizar la norma NCh 2625.Of2001.

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 en las prescripciones de la referida Norma, la inflación fue omitida considerando que afectará tanto al costo del dinero como al costo de la energía. Si estos puntos fueran considerados para el mismo período de tiempo y el efecto de la inflación fuera aproximadamente la misma para ambos, la elección de una sección económica puede ser llevada a cabo satisfactoriamente sin introducir la complicación adicional de la inflación.

•

 para calcular el valor presente del costo de las pérdidas es necesario elegir valores apropiados al futuro desarrollo de la carga, aumentos anuales del precio de kWh y una tasa de descuento anual por la vida económica del cable que podría ser de 25 años o más.

•

 las fórmulas propuestas en la Norma son directas, pero en su aplicación debe ser dada la debida consideración a la hipótesis de que los parámetros financieros asumidos permanecerán inalterados durante la vida económica del cable.

•

 en la Norma, hay dos abordajes para el cálculo de la sección económica, basados en los mismos conceptos financieros. La primera, donde una serie de secciones de conductores está siendo considerada, es calcular una gama de corrientes económicas para cada una de las secciones del conductor previsto para las condiciones de instalación específica y entonces seleccionar aquella sección cuyo rango contiene el valor requerido para la carga. Este abordaje es apropiado donde varias instalaciones semejantes están siendo consideradas. El segundo abordaje, que puede ser más satisfactorio cuando una única instalación está involucrada, es calcular el área de la sección transversal óptima para la carga exigida y entonces seleccionar la sección nominal del conductor más próxima.

•

Siguiendo este Manual, nos enfocaremos solo en el segundo abordaje, por ser de aplicación más directa en la mayoría de las situaciones prácticas.

4.2. Ecuaciones para dimensionamiento económico de conductores de acuerdo con el segundo abordaje de NCh 2625.Of2001 La Sección Económica (Ѕec) de un conductor eléctrico puede ser determinada por la expresión [6] que utiliza parámetros calculados por las expresiones [7] a [10]. Ѕec=1000 · l2max · F · ρ20 · B · [1 + α20 (θm-20)]

0,5

[6]

A

Q (1 + i/100)

[7]

B= (1 + yP + yЅ) · (1 + λ1 + λ2)

[8]

F=NP ·NC · (T · P + D) ·

N

Q=Σ(r n-1)= 1-r N   n=1 1-r

[9]

r= (1 + a/100)2 · (1 + b/100) (1 + i/100)

[10]

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donde: Ѕec: sección económica (tamaño económico) del

conductor (mm 2). lmax: carga máxima prevista para el circuito en el primer año, el valor medio máximo en 1h(A). F: magnitud auxiliar. ρ20: resistividad eléctrica del material conductor a 20ºC (Ωm) B: magnitud auxiliar. α20: coeficiente de temperatura de la resistencia del conductor a 20ºC (K-1). θm: temperatura media de operación del conductor (ºC). A: componente variable del costo por unidad de longitud en relación a la sección (tamaño) del conductor ($/m · mm 2). NP: número de conductores en fase por circuito. NC: número de circuitos que s oportan el mismo tipo y valor de carga. T: tiempo de operación con máxima pérdida joule (h/año). P: costo de un watt-hora al nivel de la tensión pertinente [%/W.h]. D: cargo debido a la demanda cada año [$/W.año]. Q: magnitud auxiliar. i: tasa de descuento usada para calcular valores presentes (%). yP: factor de efecto de proximidad, conforme IEC 60287-1-1. yЅ: factor de efecto superficial, conforme IEC 60287-1-1. λ1: factor de pérdida de cubierta, conforme IEC 60287-1-1. λ2: factor de pérdida de armadura, conforme IEC 60287-1-1. r: magnitud auxiliar. N: período cubierto por los cálculos financieros, conocido también como "vida económica" (año). a: aumento anual en l max (%). b: aumento anual en P, no cubierto por la inflación (%).

Observaciones: 1: Como 1:  Como la sección económica es el resultado que se espera obtener de la ecuación [6] y las unidades yp, yЅ, λ1 y λ2 (que hacen parte del cálculo) dependen de la sección (tamaño) del conductor, es necesario entonces hacer una primera suposición sobre la sección económica probable del cable para que los valores razonables de las unidades mencionadas puedan ser calculados. Puede ser necesario recalcular si la sección económica fuera muy diferente. Sin embargo, para efecto de la determinación de la sección económica, de un modo general, esas unidades pueden ser despreciadas para cables de baja tensión (≤1kV) y cables de media tensión (≤36.2kV). 2: Es 2:  Es poco probable que Ѕec calculada por la expresión [6] sea exactamente igual a una sección nominal normalizada (…16; 25; 35; 50…mm2). Donde así, el costo deberá ser calculado para las secciones nominales normalizadas mayores y menores adyacentes y elegida la más económica.

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3:   Las pérdidas dieléctricas que ocurren en ciertos tipos de cables, particularmente de alta tensión (> 36.2 kV) pueden ser 3: significativas y debe ser consideradas cuando se hace la selección de la sección económica del conductor. conductor. Las pérdidas en el dieléctrico son calculadas usándose fórmulas de IEC 6287-1-1. Sin embargo, para efecto de la determinación de la sección económica, de un modo general, esas unidades pueden ser despreciadas para cables de baja tensión (≤ 1 kV) y cables de media tensión (≤ 36.2 kV). 4: Aplicando 4:  Aplicando la ecuación [6] es necesar io conocer el valor de θm. La Norma NCh2625.Of 20 01 ofrece una fórmula simple para hacer una estimación de la temperatura de operación basada en observaciones de cálculos típicos donde la elevación de la temperatura operativa promedio de un conductor de sección económica, durante su vida económica, queda en la zona de 1/3 de la elevación que ocurriera para su máxima capacidad térmica nominal permisible. Esta aproximación puede resultar en errores en la sección del conductor y en los costos totales que no son mayores de aproximadamente 2%. Sin embargo, pueden suceder errores más grandes donde la combinación del costo de instalación, del costo de pérdidas y del crecimiento de la carga lleva a la temperatura del conductor al máximo valor permisible, durante los años finales del periodo económico. En general, un valor más exacto de la resistencia del conductor sólo afectará la selección de la sección económica en casos marginales. Si, para casos particulares, fuera deseada mayor precisión, se puede utilizar el método de cálculo indicado en el Anexo B de la Norma NCh2625.Of 2001. Así, de de forma general, se tiene: tiene:

[11]

θm=(θ-θa) / 3 + θa

  donde: θ:temperatura temperatura máxima nominal del conductor para el tipo θa: temperatura ambiente promedio [ºC].

de cable considerado [ºC].

5. En 5.  En la aplicación de la ecuación [6] es necesario conocer el valor de A. Por lo tanto, se debe considerar el costo total de instalación de un conductor que incluye el costo del cable, de sus terminaciones, de los elementos de canalización eléctrica (tuberías, molduras, bandejas y escalerillas portaconductores, portaconductores, canaletas, etc.) y de la mano de obra del ensamblaje. Considerando que los costos de los cables varían según su tipo (tipo de material conductor, tipo de aislamiento, tensión nominal, etc.), que los costos de las canalizaciones eléctricas eléctricas dependen de la forma elegida para su instalación y la mano de obra varía según el tipo de cable y canalización eléctrica eléctrica que serán instalados, es necesario que sean preparadas tablas de costo totales de instalación que consideren esas alternativas.

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Tabla 2: Determinación de A Sección nominal del cable (mm2)

Costo inicial (CI) [$/m]

A [$/m·mm2]

Cable

Instalación (línea eléctrica + mano de obra)

Total

25 35

2.463,51 2.702,72

3.998,74 4.020,16

6.462,25 6.722,88

(6.722,88 - 6.462,25) / (35 - 25)= 26,06

50

3.059,75

4.059,43

7.119,18

(7.119,18 - 6.722,88) / (50 - 35)= 26,42

70

3.538,17

4.109,42

7.647,59

(7.647,59 - 7.119,18) / (70 - 50)= 26,42

95

4.134,41

4.170,11

8.304,52

(8.304,52 - 7.647,59) / (95 - 70)= 26,28

120 150

4.727,08 5.441,14

4.234,38 4.305,78

8.961,46 9.746,92

(8.961,46 - 8.304,52) / (120 - 95)= 26,28 (9.746,92 - 8.961,46) / (150 - 120)= 26,18

185

6.276,59

4.391,47

10,668,06

(10.668,06 - 9.746,92) / (185 - 150)=26,32

240

7.586,89

4.527,14

12.114,03

(12.114,03 - 10.668,06) / (240 - 185)= 26,29

300

9.015,01

4.673,52

13.688,53

(13.688,53 - 12.114,03) / (300 - 240)= 26,24

400

11.396,40

4.919,87

16.316,27 (16.316,27 - 13.688,53) / (400 - 300)= 26,28 Prome romeddio 26,2 6,28

Para la utilización de la ecuación [6] es más práctica la utilización del valor promedio de A para todas las combinaciones de secciones según la tabla 2. En est e ejemplo, A es igual a 26,28$/m·mm2 .

5: ASPECTOS ECONÓMICOS Para combinar los costos iniciales de compra e instalación con los costos de pérdida de energía que surgen durante la vida económica de un conductor eléctrico, es necesario expresarlos en valores económicos comparables, que son los valores que se refieren al mismo punto en el tiempo. Es sabido que, cuanto menor la sección nominal de un conductor eléctrico, menor es su costo inicial de adquisición e instalación y mayor su costo operativo durante su vida útil. Multiplicándose el valor obtenido en [1] por el precio del Wh cobrado por la distribuidora de energía (o calculado para la fuente de generación propia) se obtiene el costo de la pérdida de energía (operativa) del conductor eléctrico. De este modo, el costo total para instalar y operar un cable durante su vida económica, expresado en valores presentes, es calculado según la siguiente ecuación:

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Donde: CI: es el costo inicial de instalación del cable en su longitud total, [$]. CJ: es el costo operativo equivalente en la fecha en que la instalación fue comprada, osea, el valor presente de las pérdidas  joule  jou le durant dur antee la l a vida v ida económic econ ómicaa de d e N años año s [$]. [ $]. La Gráfica 1 presenta las curvas típicas del costo operativo (CJ) y costo inicial de una instalación (CI) en función de la sección (tamaño) (tamañ o) nominal de los conductores. Costo ($) COSTO TOTAL

COSTO INICIAL

 VALOR MÍNIMO Costo Operativo (pérdidas joule)

Sección (mm 2) Ѕtec Ѕec > Ѕtec

Ѕec

corresponde a costo total mínimo

Gráfica 1: Costo inicial y costo operativo de los cables en función de la sección nominal.

En la Gráfica 1, sumándose punto a punto las dos curvas (costo inicial y costo operativo), se tiene, para cada sección nominal,

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Denomínase como sección económica de un circuito ( Ѕec), aquella sección que resulta con el menor costo total de instanlación y operación de un conductor eléctrico durante su vida económica c onsider onsiderada. ada. De acuerdo a la NCh2625.Of2001, el costo total (CT) puede ser calculado por: CT=CI + l2max · R · ℓ · F

[$]

[13]

donde: lmax: corriente del proyecto (carga) máxima prevista para el circuito en el primer año, el valor medio máximo en 1h [A]. ℓ: longitud del cable [m]. F: calculado por la ecuación [7]. R: resistencia c.a. aparente del conductor por unidad de longitud, considerando tanto el efecto superficial como el efecto de proximidad, (y p, y Ѕ), y las pérdidas en las mallas metálicas y en la armadura, ( λ1, λ2), [Ω/m]. El valor de R en función de la sección normalizada Ѕ del conductor debe ser considerado en la temperatura promedio de operación del conductor(θm) y calculado por la siguiente expresión: R(Ѕ)= ρ20 · β[1 + α20 · (θm - 20)] · 106

[14]

Ѕ

6: DIMENSIONAMIENTO AMBIENTAL DE CONDUCTORES CON DUCTORES ELÉCTRICOS 6.1. Introducción A lo largo del ciclo de vida de los alambres y cables eléctricos, eléctricos , las más significativas significativa s emisiones de CO 2 (gas de efecto invernadero) son producidas cuando los conductores están siendo utilizados en el transporte de energía eléctrica, siendo relativamente pequeñas en la fase de fabricación y desecho de esos productos. Esas emisiones de CO 2 son resultantes de la generación extra de energía necesaria para compensar las pérdidas joule en la conducción de corriente eléctrica por el circuito. Como lo vimos en las secciones anteriore s, es posible reducir la pérdida de energía (joule) y la consecuente emisión de CO 2 a través del aumento de la sección del conductor por la aplicación del criterio de Dimensionamiento Económico. 6.2. Reducción de las emisiones de CO  en la generación de energía por el aumento de la sección.

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Z1= N[Np · Nc · l2 · (R1 - R2) · 10-3 · T · ℓ · K1]

[15]

donde: Z1: cantidad anual de reducción de emisiones de CO 2, [kg-CO2]. Np: número de conductores en fase por circuito. Nc: número de circuitos que llevan el mismo tipo y valor de carga. l: carga, [A]. ℓ: longitud del cable, [km]. R1: resistencia del conductor por unidad de longitud dimensionado por el criterio técnico (menor sección), [Ω/km], calculada conforme la ecuación [14]. R2: resistencia del conductor por unidad de longitud dimensionado por el criterio económico (mayor sección), [Ω/km], calculada conforme la ecuación [14]. T: tiempo de operación por año [h/año]. K1: emisiones de CO2 en el momento de la generación por ubnidad de energía eléctrica, [kg-CO 2/kWh]. Este valor varía conforme la característica de la matriz energética de cada país, siendo mayor en los casos donde fuentes primarias de energía son más contaminanates (combustibles fósiles) y menor donde las fuentes primarias son más limpias y renovables (hidráulica, solar, eólica, etc.). En el caso de Chile, datos de 2006 indican un valor de K 1=0.294 kg-CO2/kWh.

6.3. Aumento de las emisiones de CO, en la fabricación de conductores por el aumento de la sección El aumento de la sección de los conductores cuando son dimensionados por el criterio económico tiene como consecuencia directa el aumento en las emisiones de CO2 en el proceso completo de fabricación de los cables elécricos, desde la fase de extracción del metal conductor en la mina hasta el desecho del producto después de su utilización (ciclo de vida del producto). Eso se debe al hecho de que

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terística de la matriz energética de cada país y del proceso de extracción y fabricación del metal, siendo mayor en los casos donde fuentes primarias de energía son más contaminantes (combustibles fósiles) y menor donde las fuentes primarias son más limpias y renovables (hidráulica, solar, eólica, etc.). En el caso de Chile, K 2= 4.09 kg-CO2/kg-Cu que es aquel que corresponde a la producción del cátodo de cobre electrolítico. Tabla 3 – Peso de cobre en cables Sección nominal (mm2)

Peso total aproximado (kg/km)

1.5 2.5 4 6 10 16

13.4 22.3 35.6 53.4 89.0 142

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El circuito tiene 100 metros de longitud, la temperatura ambiente promedio es de 40*C y la carga máxima en el primer año es de 150 A (incluyendo las componentes armónicas-THD 3=38%). Con tasa de crecimiento del 1% al año. Se estima que el circuito permanezca en plena operación durante 4,000 horas por año. El costo considerado de un watt/hora en el nivel de la tensión pertinente es de 35.707 $/kWh en el primer año, con aumento anual del 3% (sin considerar el efecto de la inflación). No será considerado el costo de la demanda. Será adoptado el valor promedio de A=26.28 $/m · mm 2, según la Tabla 2. El análisis será efectuado para un periodo de 20 años (vida económica), considerándose una tasa de capitalización para el cálculo del valor presente de 6% al año.

a) Determinación de la magnitud auxiliar r De acuerdo con d enurrdado, se tiene: a = 1% (aumento anual de carga); b = 3% (aumento anual del costo de energía); i = 6% (tasa de descuento). Aplicándose la ecuación [10], resulta r=0.991.

b) Determinación de la magnitud auxiliar Q De acuerdo con el enunciado, se tiene N = 20 años (vida económica). El valor de r fue obtenido en a) y vale 0.991. Aplicándose la ecuación [9], resulta Q = 18.418.

c) Determinación de la magnitud auxiliar B

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e) Primer cálculo de ia sección económica S ec De acuerdo con el enunciado: lmax=150A (carga máxima prevista para el circuito en el primer año); A=26,28$/m·mm2. De acuerdo con d), F=7.445,14. De acuerdo con NCh 2625 Of2001: ρ20=18.35·1O-9 Ωm (resistividad eléctrica del cobre a 20ºC) α20=0.0068 K-1 (coeficiente de temperatura para la resistencia del cobre a 20ºC). De acuerdo con c), B = 1.0. De acuerdo con el enunciado: θ =70°C (temperatura máxima nominal del conductor para el cable considerado); θa=40°C (temperatura ambiente promedio). Aplicándose la ecuación [11]: θm=(θ-θa)/3+θa=(70-40)/3+40=50ºC Finalmente, ubicándose ubicándose la ecuación [6] resulta S ec=350 mm2, que no es una sección de conductor normalizada. Así, como lo indicado anteriormente, anteriormente, en esta situación el costo total deberá ser calculado para las secciones nominales normalizadas normalizadas mayores y menores ad2 2 yacentes (300 mm  y 400 mm ) y escogida la sección más económica entre las dos.

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- Para el cable 300 mm2: CT(300)= CI + CJ= 1.368.853,00 + 1.233.663,62=$2.602.516,62. - Para el cable 400 mm2: CT(400)= CI+CJ= 1.631.627,00 + 925.247,72=$2.556.874,72.

Por lo tanto, el conductor de 400 mm 2 es la sección económica (Ѕec) elegida. g) Dimensionamiento técnico del drcuito según la Norma NCh Elec.4/2003 El dimensionamiento técnico a seguir considera solamente el criterio de capacidad de transporte de conducción de corriente con la aplicación de los factores de corrección previstos en la norma NCh Elec.4/2003 (temperatura, cantidad de conductores en la tubería). Para simplificar este ejemplo, no son considerados los cálculos relativos a la caída de tensión, la protección contra sobrecargas y cortocircuitos que normalmente deben ser realizados en un proyecto. Conductores de fase: - Factor de Corrección de la Capacidad de Transporte de Corriente por Variación de Temperatura Ambiente (f t)-Tabla Nº 8.9- 40ºC ambiente ➝f = 0.87 (página 39 NCh Elec.4/2003). t - Factor de Corrección de Capacidad de Transporte de Corriente por Cantidad de Conductores en Tubería (f n)-Tabla 8.8➝ f n=1.0 (página 39 NCh Elec.4/2003). - Tabla 8.7 - (página 37 NCh Elec.4/2003) - Grupo 2 ➝#70 mm2 ➝ ltabla=207A ➝lЅ=207.0.87.1=180A.

Por lo tanto, el conductor de 70 mm2 es la sección técnica (Ѕec) elegida.

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Aplicándose la ecuación [13] con los parámetros CI (multiplicar valores de la Tabla 2 por la longitud ℓ), lmax (150A) y F (calculado) y con ℓ= 100 m (enunciado), se obtiene:  CT(70)= CI+CJ= 764.759,00 + 5.287.129,81=$6.051.888,81. 5.287.129,81=$6.051.888,81.

i) Comparación económica entre las secciones obtenidas por los criterios de dimensionamiento económico y dimensionamiento técnico. La tabla 4 resume los cálculos realizados. Tabla 4: Resumen de los cálculos CI Criterio

Sección nominal

Económico Técnico

CJ [en 20 años]

CT [en 20 años]

($)

% (ec/tec)

($)

% (ec/tec)

($)

% (ec/tec)

400

1.631.627,00

213

925.247,72

18

2.556.874,72

42

70

764.759,00

100

5.287.129,81

100

6.051.888,81

100

De la Tabla 4, se concluye que, a pesar del cable dimensionado por el criterio económico (400 mm 2  ) tener un costo inicial (CI) más del doble (2.13 x) del cable calculado por el criterio técnico (70 mm 2 ), el cable 400 mm 2  presenta un costo debido a las pérdidas joule (CJ) a lo largo de la vida económica considerada en el ejemplo (20 años) de apenas 18% de aquella presentada por el cable 70 mm 2  . En relación al costo total (CT), el cable dimensionado por el criterio económico tiene un costo de 42% del cable dimensionado por el criterio técnico. En relación al período de retorno de las Inversiones, de la Tabla 4, se tiene: - diferencia entre los costos iniciales por los criterios técnico y económico = $ 1.631.627,00 1.631.627,00 - $ 764.759,00 = $ 866.868,00; - diferencia entre los costos de pérdida joule de los dos criterios (en valor presente) = $ 5.287.129,81- $ 925.247,72= $ 4.361.882,09 4.361.882,09

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•

•

en circuitos que funcionan muchas horas por año, con corrientes que no presentan grandes variaciones; en circuitos donde el criterio de dimensionamiento técnico técnico que prevaleció fue el de capacidad de transporte de conducción de corriente. En este caso, se obtuvo la menor sección nominal posible y, en consecuencia, la mayor resistencia eléctrica y pérdida de energía.

Una ventaja adicional del dimensionamiento de un conductor por el criterio económico es que habrá un aumento de su vida útil debido al hecho de que el cable trabaja a menores temperaturas. Además, el conductor presentará un mejor comportamiento en relación a las corrientes de sobrecarga y cortocircuito.

 j) Dimensionamiento ambiental Considerando el cable dimensionado por el criterio económico (400 mm 2) y el cable dimensionado por el criterio técnico (70 mm 2), se tiene el siguiente dimensionamiento ambiental: Conforme al enunciado, N p=3; Nc=1; l=150A; T=4,000 h/año; ℓ=100 m=0.1 km. =623 kg/km y W =3,560 kg/km.

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De esa forma, el dimensionamiento económico económico y ambiental del conductor del ejemplo en cuestión resulta en la sección nominal de 400 2 mm . Ese dimensionamiento también atiende a todos los criterios de dimensionamiento técnico conforme NCh Elec.4/2003, particularmente en los requisitos de capacidad de transporte de conducción de corriente, caída de tensión y presencia de armónicas. La especificación final del circuito en cuestión considerando el dimensionamiento económico y ambiental es la siguiente:

3 x 400 mm2 + 1 x 50 mm 2 (PE) ¿POR QUÉ EL COBRE ES AMPLIAMENTE UTILIZADO   EN SISTEMAS ELÉCTRICOS?  La principal razón para usar el cobre en los sistemas eléctricos es su excelente conductividad eléctrica. El cobre tiene la resistencia eléctrica más baja entre todos los metales no preciosos. Como se sabe, hay otros materiales que pueden ser utilizados como con ductores eléctricos, ya que casi

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Otra razón para la preferencia de cobre en las plantas en general y en los edificios, en particular, es la facilidad y la fiabilidad de la aplicación de empalmes y terminaciones con conductores de cobre, porque no requieren materiales, herramientas y técnicas especiales para obtener resultados satisfactorios. Otras características importantes que hacen el cobre un metal ampliamente usado en la electricidad es su resistencia mecánica y durabilidad, propiedades ideales en aplicaciones complejas tales como grúas, cables para la minería y transporte, entre otros.

8: REFERENCIAS - NCh Elec.4/2003: Instalaciones de consumo en baja tensión; S.E.C, 2003. - NCh 2625.Of2001: Optimización Optimización económica en el dimensionamiento de cables de potencia; potencia; INN Chile, 2001.

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9: TABLAS Tabla N° 8.7 Intensidad de Corriente admisible para Conductores Aislados Fabricados según Normas Europeas Secciones Milimétricas.Temperatura de Servido: 70°C; Temperatura Ambiente: 30°C Corriente Admisible Amperes (A) Sección nominal (mm2) Grupo 1 Grupo 2 Grupo 3 0,75 12 15 1 11 15 19 1,5 15 19 23 2,5 20 25 32 4 25 34 42 6 33 44 54 10 45 61 73 16 61 82 98

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