Mathcad - Ampacity Calculation

POWER CABLE AMPACITY (132 kV)

132 kV, 1200 mm2 In trench section In !! crossin" section In !#ct $%nk &or crossin" section

Final Ampacity calculation N7144.xmcd

1

22.03.2013

CO'TE'T( Variable ata (!eneral)

4

Po)er C%$*e Am+%cit C%*c#*%tions 1.

A" #e$i$tance o% "onductor

13

2.

ielectric &o$$ per 'nit &ent %or te *n$ulation

1+

3.

&o$$ Factor %or ,etallic -creen and -eat

1+

4.

"alculation o% ermal #e$i$tance

21

+.

"ond "onduc ucto torr emp emper erat atur ure e #i$e #i$e abo/ abo/e e te te Ambi Ambien entt

2

.

"ontinuou$ "urrent "arryin "apacity o% one 132 kV circuit

2

7.

#eduction %actor o% one 132 kV "ircuit

2

.

-upe -uperr po$ po$it itio ion n met meto od d to calc calcul ulat ate e int inter erac actio tion n o% o% ru ru  132 132 kV cabl cable e circuit and to exi$tin 400 kV cable circuit$

3

#edu #educt ctio ion n %ac %acto torr o% o% inte intera ract ctio ion n o% o% ru ru  132 132 kV kV cab cable le circ circui uit$ t$ it it te te to exi$tin 400 kV cable circuit$

+1

.

Po)er C%$*e Im+e-%nce C%*c#*%tions 1.

5o$iti/e6Neati/e -euence *mpedance

7

2.

8ero *mpedance

7


2

22.03.2013

CO'TE'T( Variable ata (!eneral)

4

Po)er C%$*e Am+%cit C%*c#*%tions 1.

A" #e$i$tance o% "onductor

13

2.

ielectric &o$$ per 'nit &ent %or te *n$ulation

1+

3.

&o$$ Factor %or ,etallic -creen and -eat

1+

4.

"alculation o% ermal #e$i$tance

21

+.

"ond "onduc ucto torr emp emper erat atur ure e #i$e #i$e abo/ abo/e e te te Ambi Ambien entt

2

.

"ontinuou$ "urrent "arryin "apacity o% one 132 kV circuit

2

7.

#eduction %actor o% one 132 kV "ircuit

2

.

-upe -uperr po$ po$it itio ion n met meto od d to calc calcul ulat ate e int inter erac actio tion n o% o% ru ru  132 132 kV cabl cable e circuit and to exi$tin 400 kV cable circuit$

3

#edu #educt ctio ion n %ac %acto torr o% o% inte intera ract ctio ion n o% o% ru ru  132 132 kV kV cab cable le circ circui uit$ t$ it it te te to exi$tin 400 kV cable circuit$

+1

.

Po)er C%$*e Im+e-%nce C%*c#*%tions 1.

5o$iti/e6Neati/e -euence *mpedance

7

2.

8ero *mpedance

7


2

22.03.2013

POWER CABLE AMPACITY CALC.LATIO'( *9" 027 : "*!#9 ;! 1<03


3

22.03.2013

"A&9 =59> 132 kV ?&59 cable@ 12$mm@ copper conductor@ lead : 59 $eated /BR. *N-A&&A*BN 5&A"9> A' A* < '.A.9. 5#BC9"> A' A* 2 6 9A@ #AN-"B N7144

VARIABLE !ATA A E*ectric%* (stem !%t%

400000 U p_400 :=

(5a$e to pa$e /oltae@ V)

132000 U p_132 :=

(5a$e to pa$e /oltae@ V)

fc := 50

(Freuency@ D)

ω := 2.π fc

(Anular %reuency@ D)

63000 Iccs_400 :=

(,ax. eart<%ault current in cable $eat@ A)

31500 Iccs_132 :=

(,ax. eart<%ault current in cable $eat@ A)

tcc := 0.5

(-ort
1102.3 P400tr :=

(ran$mi$$ion capacity %or induced /oltae calculation@ ,VA)

P400hdd := 568


P400rc := 800


Inom_400tr :=

P400tr

(

U p_400⋅ 10

Inom_400hdd :=

Inom_400rc :=

(Nominal tran$mi$$ion current in trenc@ A)

)⋅

−6

(

(Nominal tran$mi$$ion current in  cro$$in@ A)

)⋅

−6

(

U p_400⋅ 10

(Nominal tran$mi$$ion current in road cro$$in@ A)

)⋅

Inom_400hdd = 820

3

P400rc −6

Inom_400tr = 1591

3

P400hdd U p_400⋅ 10

ω = 314.2

Inom_400rc = 1155

3


4

22.03.2013

B C%$*e Constr#ction !%t% n := 1

(Number o% load
n p := 1

(Number oc conductor$ in parallel)

dc := 45

(iamenter o% conductor@ mm)

1200 Acc :=

("ro$$<$ection o% copper condutor@ mm2 )

tc1 := 0.9

(ickne$$ o% conductor binder6$ellin tape@ mm)

dc0 := dc + 2 ⋅ tc1

(iamenter o% conductor@ includin binder tape@ mm)

tc2 := 1.5

(A/arae tickne$$ o% conductor $creen@ mm)

tcs := tc1 + tc2

(otal tickne$$ o% conductor $creen@ mm)

tcs = 2.4

dc1 := dc + 2 tcs

( iameter o% conductor@ includin $creen@ mm)

dc1 = 49.8

ti := 16

(,in. a/arae tickne$$ o% in$ulation@ mm)

din := dc + 2 tcs + 2 ti

(9xternal diamenter o% in$ulation@ excludin $creen@ mm)

tinss := 1.8

(,in. a/. tickne$$ o% in$ulation $creen@ mm)

(

d bst := din + 2 tinss

)

(iameter o/er in$ulation $creen@ mm)

tst1 := 0.9

(ickne$$ o% $ellin tape6beddin@ mm)

d bcs := d bst + 2 tst1

(iameter o/er $ellin tape6beddin@ mm)

tcms :=

d bcs − dc

(ickne$$ beteen condcutor and metal $eat@ mm)

2

tls := 3.6

(A/. tickne$$ o% lead $eat@ mm)

dals := d bcs + 2 tls

(iameter o/er lead $eat@ mm)

dlad := dals − tls

(,ean diameter o% lead $eat@ mm)

dmm := dals − tls

(,ean eometric diameter o% lead $eat@ mm)

−6 Alad := π tls d bcs + tls 10

(

)

("ro$$<$ection o% lead $eat@

m2 )

tos := 4.7

(A/. tickne$$ o% outer co/erin@ includin -" $kin@ mm)

do := dals + 2 tos

(9xternal diameter o% te cable@ mm)


+

dc0 = 46.8

din = 81.8

d bst = 85.4

d bcs = 87.2

tcms = 21.1

dals = 94.4 dlad = 90.8 dmm = 90.8 −3 Alad = 1.027 × 10

do = 103.8

22.03.2013

C E*ectric%* Ch%r%cteristics −6 15.1 × 10 ! o :=

(.". re$i$tance o% te conductor at 20E"@ Bm6m)

−8 ρcoppr := 1.7241 × 10

(9lectrical re$i$ti/ity o% "opper@ Bm6m) < *9" 027<1<1@ able 1

−8 21.4 × 10 ρlad :=

(9lectrical re$i$ti/ity o% &ead@ Bm6mm) < *9" 027<1<1@ able 1

! E*ectric%* Coe&&icients

0.37 " p :=

(5roximity e%%ect coe%%icient acc. to "ire tecnical paper nE272@ ;orkin !roup 1.03)

0.44 " s :=

(5roximity e%%ect coe%%icient acc. to "ire tecnical paper nE272@ ;orkin !roup 1.03)

E Ins#*%tion Ch%r%cteristics ε p := 2.4

(#elati/e permitti/ity o% in$ulation)

0.001 tan# δ$ :=

(&o$$ %actor o% te in$ulation)

4 Therm%* Resisti5ities ρ%lp := 3.5

(emal re$i$ti/ity o% ?&59@ .m6; acc to *9" 027<2<1)

ρ p := 3.5

(emal re$i$ti/ity o% 59@ .m6; acc to *9" 027<2<1)

ρ b := 6

(emal re$i$ti/ity o% $ellin tape$@ .m6;)

ρsc := 2.5

(emal re$i$ti/ity o% -6"@ .m6;)

ρ p&c := 6

(emal re$i$ti/ity o% 5V"@ .m6; acc to *9" 027<2<1)

ρsr := 1.2

(emal $oil re$i$ti/ity at road cro$$in @ .m6;)

ρst := 1.2

(emal $oil re$i$ti/ity in trec (-tabili$ed $ourroundin @ .m6;)

ρ bntonit := 1.0

(emal re$i$ti/ity o% bentonite @ .m6;)

ρconcrt := 1.0

(emal $oil re$i$ti/ity o% concrete o% te duct bank @ .m6;)

ρhdd := 1.0

(emal $oil re$i$ti/ity o%  $ection @ .m6;)




22.03.2013

 Tem+er%t#res %n- Tem+er%t#re Coe&&icients

Θma% := 90

(,ax. operatin temperature o% conductor. E")

Θc1 := 250

(,ax. $ort
Θms := 80

(,ax. orkin temperature o% te lead $eat@ E")

Θcs1 := 250

(Final eart<%ault temperature o% copper ire $creen@ E")

Θcs2 := Θms

(*nitial eart<%ault temperature o% copper ire $creen@ E")

Θl1 := 180

(Final eart<%ault temepratre o% lead $eat@ E")

Θc'ro(nd := 40

(,ax. round temperature@ E")

Θ bntonit := 70

(,ean temperature o% te medium %illin beteen cable and duct@ E")

77.3 Θap :=

(,ean temperature o% air in$ide te road cro$$in pipe@ E")

−3 αc20 := 3.93 × 10

("on$tant copper temperature coe%%icient@ 16E")

−3 αlad := 4 × 10

(emperature coe%%icient o% lead $eat re$i$tance. 16E")

βc := 234.5

(#eciprocal o% temperature coe%%icient o% re$i$tance copper)

)c := 226

("on$tant o% copper)

βs := 230

(#eciprocal o% temperature coe%%icient o% re$i$tance lead)

)s := 41

("on$tant o% lead)


7

22.03.2013

 T+ic%* Tro#"h cross6sction 132 kV Circ#it

1150 h'cb_tr := h'1ca_tr := h'cb_tr −

(i$tance %rom round $ur%ace to cable bottom@ mm) do

2

(i$tance %rom round $ur%ace to cable axi$@ mm)

s tr := 200

(Axial $pacin o% conductor #@=@ in trenc@ mm)

s ctr := 2100

("enter to "enter di$tance o% cable circuit$ in trenc@ mm)

Θm_tr := 81.5

(;orkin temperature o% te lead $eat in trou@ E")




h'1ca_tr = 1098

22.03.2013

I !! Crossin" 132 kV Circ#it

t pip_hdd := 15

(ickne$$ o% 59 duct all@ mm)

di pip_hdd := 195

(*n$ide diameter o% 59 duct@ mm)

(

)

do pip_hdd := di pip_hdd + 2 pip_hdd t

(Butdi$e diamenter o% 59@ mm)

tbt := 50

(ickne$$ o% bentonite layer around te cable@ mm)

s hdd := do pip_hdd

(Axial $pacin o% te conductor$ in  $ection@ mm)

7000 + *hdd :=

 1  2

+

do pip_hdd = 225

3 

do 3  pip_hdd (i$tance %rom road le/el to te tre%oil center@ mm)

Θm_hdd := 80


*hdd = 7242




22.03.2013

7 T+ic%* Ro%- Crossin" 132 kV Circ#it

t pip_rc := 10

(ickne$$ o% 59 duct all@ mm)

di pip_rc := 180

(*n$ide diameter o% 59 duct@ mm)

(

)

do pip_rc := di pip_rc + 2 t pip_rc

(Butdi$e diamenter o% 59@ mm)

tbt := 50

(ickne$$ o% bentonite layer around te cable@ mm)

1800 +,- :=

(;idt o% te uct bank@ mm)

 ,- := 550

(eit o% te uct bank@ mm)

1225 h',- :=

(ept o% te uct bank centre@ mm)

/ := 3

(Number o% cable$ o% al% duct bank$)

s rc := 300

(Axial $pacin o% te conductor$ in road cro$$in@ mm)


10

do pip_rc = 200

22.03.2013

s crc := 2100

("enter to "enter di$tance o% cable circuit$ in trenc@ mm)

1325 h'cb_rc :=

(i$tance %rom round $ur%ace to cable bottom@ mm)

h'db_rc := h'cb_rc +

t pip_rc

do

h'1ca_rc := h'cb_rc −

h'da_rc := h'db_rc −

(i$tance %rom round $ur%ace to duct bottom@ mm)

2

(i$tance %rom round $ur%ace to cable axi$@ mm)

2 di pip_rc

(i$tance %rom round $ur%ace to duct axi$@ mm)

2

80.5 Θm_rc :=

h'db_rc = 1330

h'1ca_rc = 1273

h'da_rc = 1240


8 !et%i*s o& +%r%**e* r#nnin" 900 kV C%$*es in Tro#"h (ection 1100 h'400_tr :=

(urial dept %rom round $ur%ace to cable bottom@ mm)

2800 , 400a_400b_tr :=

(Axial di$tance beteen 400 kV and 400 kV "ircuit$@ mm)

2100 , 400a_132_tr :=

(Axial di$tance beteen 400 kV clo$e$t and 132 kV "ircuit$@ mm)

4900 , 400b_132_tr :=

(Axial di$tance beteen 400 kV %urte$t and 132 kV "ircuit$@ mm)

400_tr := 600

(Axial di$tance beteen o% te 400 kV circuit$@ mm)

2500 A400 :=

("ro$$ $ection o% copper conductor@ mm 2)

−6 9.7232 × 10 ! A_400_tr :=

(A" re$i$tance o% te conductor@ Bm6m)

0.0901 λ 1a_tr_400 :=

(&o$$ %actor %or $creen and $eat o% pa$e 1)

λ 1b_tr_400 := 0.0605


λ 1c_tr_400 := 0.0601


1.08 +d400 :=

(ielectric &o$$e$@ ;6m)


11

22.03.2013

I !et%i*s o& +%r%**e* r#nnin" 900 kV C%$*es in !! (ection 7500 h'400_hdd :=


do400pip := 280

(ickne$$ o% 59 pipe@mm)

400_hdd := do400pip = 280


7000 + *400hdd :=

 1  2

+

3  3 

do400pip (i$tance %rom road le/el to tre%oil center@mm)

hl400 := *400hdd − 400_hdd ⋅

bl400 := *400hdd + 400_hdd ⋅

3 3 3

(urial dept o% te upmo$t cable$@mm)

hl400 = 7140

(urial dept o% te deepe$ cable$@mm)

bl400 = 7463

3

3000 , 400a_400b_hdd :=


3000 , 400a_132_hdd :=


6000 , 400b_132_hdd :=


−6 9.754 × 10 ! A_400_hdd :=


λ 1_hdd_400 := 0.1

(&o$$ %actor %or $creen and $eat )

7 !et%i*s o& +%r%**e* r#nnin" 900 kV C%$*es in Ro%- Crossin" (ection 1350 h'400_rc :=


2800 , 400a_400b_rc :=


2100 , 400a_132_rc :=


4900 , 400b_132_rc :=


400_rc := 300


−6 9.723 × 10 ! A_400_rc :=


λ 1a_rc_400 := 0.0899



12

22.03.2013

0.0604 λ 1b_rc_400 :=


λ 1c_rc_400 := 0.0600


1 AC Resist%nce o& Con-#ctor !C Resist%nce o& Con-#ctor " coppr # Θ$ := 1 + αc20# Θ − 20$

(

)

! := ! o⋅ " coppr Θma%

(Factor)

(

)

" coppr Θma% = 1.3

(.". re$i$tance o% conductor at max. operatin temperature@ Bm6m) −5 ! = 1.925 × 10

! 20 := ! o

(.". #e$i$tance o% condcutor at 20E"@ Bm6m)

−5 ! 20 = 1.51 × 10

11 C%$*es in tro#"h 111 (kin E&&ect 4%ctor %s :=

s :=

8 π fc ! %s

( 10− 7) ⋅ " s

(Factor)

%s = 1.695

4

(-kin e%%ect %actor)

192 + 0.8%s

s = 0.0415

4

112 Pro:imit e&&ect &%ctor % p :=

8π fc !

−7

10

(Factor %or conduit$)

" p

% p = 1.554

2  % 4   d  2  192 + 0.8 % 4   dc   ( p) p c + 1.18  p# s $ :=    0.312  4  s    s   4 4   ( % p) + 0.27 192 + 0.8 ( % p)   192 + 0.8% p  

( )

 p str = 0.006

113 AC Resist%nce o& the Con-#ctor

(

( ))

!cac_tr := ! ⋅ 1 + s +  p s tr

(A.". re$i$tance o% conductor at max. operatin temperature @ Bm6m) −5 !cac_tr = 2.017 × 10


13

22.03.2013

(

( ))

!cac_tr20 := ! 20⋅ 1 + s +  p s tr

(A.". re$itance o% condcutor at 20E" temperature@ Bm6m) −5 !cac_tr20 = 1.6 × 10

12 C%$*es in !! 121 (kin e&&ect &%ctor s = 0.0415

122 Pro:imit e&&ect &%ctor

(

)

 p s hdd = 0.00469

123 AC Resist%nce o& the Con-#ctor

(

(

))

!cac_hdd := ! ⋅ 1 + s +  p shdd

(A.". re$i$tance o% conductor at max. operatin temperature@ Bm6m) −5 !cac_hdd = 2.014 × 10

(

(

))

!cac_hdd20 := ! 20⋅ 1 + s +  p shdd

(A.". re$i$tance o% conductor at 20E" temperature@ Bm6m) −5 !cac_hdd20 = 1.6 × 10

13 C%$*es in !#ct B%nk %t Ro%- crossin" 131 (kin e&&ect &%ctor s = 0.0415

132 Pro:imit e&&ect &%ctor

( )

 p s rc = 0.00263

133 AC Resist%nce o& the con-#ctor

(

( ))

!cac_rc := ! ⋅ 1 + s +  p src

(A.". re$i$tance o% conductor at max. operatin temperature@ Bm6mm) −5 !cac_rc = 2.01 × 10


14

22.03.2013

(

( ))

!cac_rc20 := ! 20⋅ 1 + s +  p src

(A.". re$i$tance o% conductor at 20E" temperature@ Bm6m) −5 !cac_rc20 = 1.6 × 10

2 !ie*ectric Loss +er .nit Len"th &or the Ins#*%tion ε p

 :=

−9

  din  

⋅ 10

("apacitance o% eac pa$e aain$t te $creen $urroundin@ F6m6pa$e) − 12  = 268.7 × 10

18. ln

  dc1  

U o :=

U p_132

(5a$e to neutral /oltae@ V)

3

3 Ic := Uo⋅ ω⋅ ⋅ 10

("arin current per conductor@ A6km)

2 +d := ω⋅ ⋅ Uo ⋅ tan# δ$

(ielectric lo$$e$ per unit lent per pa$e@ ;6m)

3 U o = 76.2 × 10

Ic = 6.43

+d = 0.49

3 Loss 4%ctor &or the Met%**ic (creen %n- (he%th (1) Equivalent Resistance of Lead Sheath

(

)

( Θm − 20) ⋅ αlad

" lad Θm := 1 +

(Factor)

1.05 " lad20 :=

(

)

!s lad Θm :=

 ρlad   Alad 

 ρlad   Alad 

⋅ " lad( Θm)

(.". re$i$tance o% te lead $eat at teta E"@ Bm6m)

−6

⋅ " lad# 20 $ = 208.39 × 10

(,ax. .". metallic $eat re$i$tance at 20E"@ Bm6m)

(2) General

( )

m Θm :=



 ⋅ 10− 7

ω

 !slad( Θm) 

(

)

(

(

)

4π ω

)

ρs Θm := ρlad⋅ " lad Θm

β 1 Θm :=

(9lectrical re$i$ti/ity o% te lead $eat at $creen temperature)

( 107) ⋅ ρs( Θm)


1+

22.03.2013

( )

's Θm := 1

(Note < For lead $eat cable$ $ can be take a$ unity and

( β1⋅ ts)

4

12 12 × 10

can be nelected < *9" 027<1<1)

31 Circ#*%tion Loss 4%ctor /C*23;2 o& IEC ;02<=6161 /1 Circ#*%tin" *oss c%*c#*%tion &or three sin"*e6core c%$*es in &*%t &orm%tion, )itho#t tr%ns+osition, she%thes $on-e- %t $oth en-s /C*%#se 232 − 7.  2s  ⋅ ln  flat# s$ := 2.ω⋅ 10  dlad 

 m_flat := 2 ω⋅ 10

(#eactance o% -eat per unit lent@ Bm6m)

−7

⋅ ln# 2 $

(,utual reactance per unit lent o% cable beteen te $eat o% an outer cable and conductor@ Bm6m) −6  m_flat = 43.552 × 10

P# s$ := flat# s$ + m_flat

 m_flat

# s$ := flat# s$ −

3

/% Centre C%$*e

(

)

λ 1flat_a Θm , s , ! ac :=

(

(

)

!slad Θm

 !s

! ac

)

# s$

(

(

)

lad Θm

2

2

+ # s $

)

λ 1flat_cba Θm , s , ! ac := λ 1flat_a Θm , s , ! ac 0.004 ⋅

2

(;ere lent$ o% minor $ection$ are unkno@ multiply by %actor o% 0.004)

/$O#ter c%$*e Le%-in" +h%se

(

)

λ 1flat_b Θm , s , ! ac :=

(

( )

2

!slad Θm

0.75⋅ P # s$

! ac

2 2  !s Θm) + P# s$ ( lad 

)

(

)

λ 1flat_cbb Θm , s , ! ac := λ 1flat_b Θm , s , ! ac 0.004 ⋅

+

0.25 # s$

(

)

!s lad Θm

2

2

+

+ # s$

2



( )

2 !slad Θm ⋅ P# s$ ⋅ # s$ ⋅ m_flat 3 +  !slad Θm

( )

2

+ P# s$

2

 !s

(

)

lad Θm

2

+ # s $

2

 

(;ere lent$ o% minor $ection$ are unkno@ multiply by %actor o % 0.004)

/$O#ter c%$*e L%""in" +h%se

(

)

λ 1flat_c Θm , s , ! ac :=

(

)

2

!slad Θm

0.75⋅ P # s$

! ac

2 2  !s  lad( Θm) + P# s$


+

0.25 # s$

( )

!slad Θm

1

2

2

+  # s$

+ 2

(



)

2 !slad Θm ⋅ P# s$ ⋅ # s$ ⋅ m_flat 3 +  !slad Θm

(

)

2

+ P# s$

2

 !s

( )

lad Θm

2

+ # s$

2

 

22.03.2013

(

)

(

)

λ 1flat_cbc Θm , s , ! ac := λ 1flat_c Θm , s , ! ac 0.004 ⋅

(;ere lent$ o% minor $ection$ are unkno@ multiply by %actor o % 0.004)

/2 Circ#*%tin" *oss c%*c#*%tion &or three sin"*e6core c%$*es in tre&oi* &orm%tion $on-e- %t $oth en-s /C*%#se 231 − 7.  2. s  ⋅ ln  trf # s$ := 2.ω⋅ 10 dlad



(#eactance o% -eat per unit lent@ Bm6m)



−4  trf shdd = 1.006 × 10

(

(

)

λ 1_trf Θm , s , ! ac :=

( )

!slad Θm

1

! ac

1+

 !slad( Θm)  

(

)

)

(

trf # s $

)

λ 1_trf_cb Θm , s , ! ac := λ 1_trf Θm , s , ! ac 0.004 ⋅

2

 (;ere lent$ o% minor $ection$ are unkno@ multiply by %actor o % 0.004)

32 E-- C#rrent Loss 4%ctor /C*23;1 o& IEC ;02<=6161 (1) Eddy Current loss calculation formula for the three single-core cales in trefoil formation

 m Θ 2   d  2 ( m) lad λ 0_t ( Θm , s) := 3 ⋅  ⋅ 2  2 s   1 + m( Θm) 

(

) 

(

)

( )

∆1_t Θm , s := 1.14 m Θm

2.45

+ 0.33 ⋅

 dlad  

2s

0.92 m( Θm) + 1.66



∆2_t Θm , s := 0

(

)

λ 1_t Θm , s , ! ac :=

 !slad( Θm)  

! ac



⋅ 's( Θm) ⋅ λ 0_t ( Θm , s) ⋅ ( 1 + ∆1_t ( Θm, s) + ∆2_t ( Θm, s) )

(2) Eddy Current loss calculation formula for three single-core cales in flat formation % Centre c%$*e

 m Θ 2   d  2 ( m) lad λ 0a( Θm , s) := 6  ⋅ 2  2s  1 + m( Θm)   Final Ampacity calculation N7144.xmcd

( 9ddy current lo$$ %actor %or cable$ in trou)

17

22.03.2013

(

)

(

)

( )

∆1a Θm , s := 0.86 m Θm

d 3.08  lad 

⋅



1.4 m( Θm) + 0.7



2s

∆2a Θm , s := 0

(

 !slad( Θm) 

)

λ 1a Θm , s , ! ac :=

! ac





⋅ 's( Θm) ⋅ λ 0a( Θm, s) ⋅ ( 1 + ∆1a( Θm , s) + ∆2a( Θm , s) )

$ O#ter c%$*e *e%-in" +h%se

 m Θ 2   d  2 ( m) lad λ 0b( Θm , s) := 1.5 ⋅ 2  2 s  1 + m( Θm)  

(

)

(

)

0.16 m( Θm) + 2

)  2s 

∆1b Θm , s := 4.7 m Θm

(

d 0.7  lad 

(9ddy current lo$$ %actor %or cable$ in trou)

d 3.3  lad 

1.47 m( Θm) + 5.06

( )  2s 

∆2b Θm , s := 21 m Θm

(

)

λ 1b Θm , s , ! ac :=

 !slad( Θm)  ! ac





⋅ 's( Θm) ⋅ λ 0b( Θm , s) ⋅ ( 1 + ∆1b( Θm , s) + ∆2b( Θm, s) )

C O#ter c%$*e *%""in" +h%se

 m Θ 2   d  2 ( m) lad λ 0c( Θm , s) := 1.5 ⋅ 2  2 s  1 + m( Θm)  

(

)

∆1c Θm , s :=

(

( ( )

)

( ( )

)

2 + m Θm − 0.3

) 

(

)

∆2c Θm , s := 0.92 m Θm

(

) (

0.74 m Θm + 2 m Θm

)

λ 1c Θm , s , ! ac :=



 !slad( Θm)  

0.5

2

d 3.7  lad 

⋅

! ac



2s

(9ddy current lo$$ %actor %or cable$ in trou)

⋅

 dlad  

2s

( ) +1

m Θm



( ) +2

m Θm



⋅ 's( Θm) ⋅ λ 0c( Θm, s) ⋅ ( 1 + ∆1c( Θm , s) + ∆2c( Θm , s) )


1

22.03.2013

33 Loss 4%ctor &or (he%th %n- screen 331 Loss 4%ctor &or (he%th in tro#"h −6 !s lad Θms = 258.403 × 10

(

)

(

)

(

)

(

)


λ 1flat_cba Θms , str , !cac_tr = 0.0043 ("irculatin current lo$$ %actor on lead $eat o% centre cable)

λ 1flat_cbb Θms , str , !cac_tr = 0.0095 ("irculatin current lo$$ %actor on lead $eat o% outer leadin cable)

λ 1flat_cbc Θms , str , !cac_tr = 0.0095 ("irculatin current lo$$ %actor on lead $eat o% outer lain cable)

(

)

(

)

(

)

λ 1a Θms , str , !cac_tr = 0.0577

(9ddy current lo$$ %actor on lead $eat o% centre cable)

λ 1b Θms , str , !cac_tr = 0.0152

λ 1c Θms , str , !cac_tr = 0.0152

(

)

(9ddy current lo$$ %actor on lead $eat o% outer cable leadin pa$e)

(9ddy current lo$$ %actor on lead $eat o% outer cable lain pa$e)

(

)

(

λ 1a_tr Θm , s , ! ac := λ 1flat_cba Θm , s , ! ac + λ 1a Θm , s , ! ac

)

(&o$$ %actor %or metallic $creen$6$eat %or cable$ in trou@ pa$e 1)

(

)

λ 1a_tr Θms , str , !cac_tr = 0.0621

(

)

(

)

(

λ 1b_tr Θm , s , ! ac := λ 1flat_cbb Θm , s , ! ac + λ 1b Θm , s , ! ac

)


(

)

λ 1b_tr Θms , str , !cac_tr = 0.0247

(

)

(

)

(

λ 1c_tr Θm , s , ! ac := λ 1flat_cbc Θm , s , ! ac + λ 1c Θm , s , ! ac

)


(

)

λ 1c_tr Θms , str , !cac_tr = 0.0247

(

)

λ 1_tr := λ 1a_tr Θms , str , !cac_tr = 0.0621


(&o$$ %actor u$ed %or current ratin calculation)

1

22.03.2013

332 Loss 4%ctor &or (he%th %n- (creen in !! −6 !s lad Θms = 258.4 × 10

(

)

(


)

λ 1_trf_cb Θms , shdd , !cac_hdd = 0.0067

(

("irculatin current lo$$ %actor)

)

λ 1_t Θms , shdd , !cac_hdd = 0.0233 (9ddy current lo$$ %actor on lead $eat o% centre cable)

(

)

(

)

(

λ 1_hddf Θm , s , ! ac := λ 1_trf_cb Θm , s , ! ac + λ 1_t Θm , s , ! ac

)

(&o$$ %actor %or metallic $creen6$eat %or tre%oil %ormation)

(

)

λ 1_hddf Θms , shdd , !cac_hdd = 0.03

(

)

λ 1_hdd := λ 1_hddf Θms , shdd , !cac_hdd = 0.03

(&o$$ %actor u$ed %or current ratin calculation)

333 Loss 4%ctor &or (he%th %n- (creen in Ro%- crossin" −6 !s lad Θms = 258.403 × 10

(

)

(

)

(

)

(

)


λ 1flat_cba Θms , src , !cac_rc = 0.0072 ("irculatin current lo$$ %actor on lead $eat o% centre cable)

λ 1flat_cbb Θms , src , !cac_rc = 0.0127 ("irculatin current lo$$ %actor on lead $eat o% outer leadin cable)

λ 1flat_cbc Θms , src , !cac_rc = 0.0127 ("irculatin current lo$$ %actor on lead $eat o% outer lain cable)

(

)

λ 1a Θms , src , !cac_rc = 0.0257

(9ddy current lo$$ %actor on lead $eat o% centre cable)

−3 (9ddy current lo$$ %actor on lead $eat o% outer cable leadin pa$e) λ 1b Θms , src , !cac_rc = 6.584 × 10

(

)

(

)

λ 1c Θms , src , !cac_rc = 0.0066

(

)

(

(9ddy current lo$$ %actor on lead $eat o% outer cable lain pa$e)

)

(

λ 1a_rc Θm , s , ! ac := λ 1flat_cba Θm , s , ! ac + λ 1a Θm , s , ! ac

)


(

)

λ 1a_rc Θms , src , !cac_rc = 0.0329


20

22.03.2013

(

)

(

)

(

λ 1b_rc Θm , s , ! ac := λ 1flat_cbb Θm , s , ! ac + λ 1b Θm , s , ! ac

)


(

)

λ 1b_rc Θms , src , !cac_rc = 0.0193

(

)

(

)

(

λ 1c_rc Θm , s , ! ac := λ 1flat_cbc Θm , s , ! ac + λ 1c Θm , s , ! ac

)


(

)

λ 1c_rc Θms , src , !cac_rc = 0.0193

(

)

λ 1_rc := λ 1a_rc Θms , src , !cac_rc = 0.0329 (&o$$ %actor u$ed %or current ratin calculation)

9 C%*c#*%tion o& Therm%* Resist%nce 91 Therm%* Resist%nce $et)een on con-#ctor %n- she%th, T1 /C*2111 o& IEC ;02=16261 911 Therm%* Resist%nce o& $in-er t%+e o5er con-#ctor 10 :=

ρ b

2π

 dc0 

⋅ ln

(ermal re$i$tance beteen one conductor and -6"@ .m6;)

dc

 

10 = 0.0375

912 Therm%* Resist%nce o& (>C screen o5er $in-er t%+e 11 :=

ρsc

2π

 dc1 

⋅ ln

 dc0 

(ermal re$i$tance beteen one conductor and in$ulation $eat@ .m6;) 11 = 0.0247

913 Therm%* Resist%nce o& ?LPE ins#*%tion 12 :=

ρ%lp

2π

 din 

⋅ ln

(ermal re$i$tance beteen one conductor and -6"@ .m6;)

 dc1  12 = 0.2764

919 Therm%* Resist%nce o& (>C screen o5er ins#*%tion 13 :=

ρsc

2π

 d bst 

⋅ ln

 din 


(ermal re$i$tance beteen one conductor and metallic $eat@ .m6;) 13 = 0.0171 21

22.03.2013

91@ Therm%* Resist%nce o& (>C Be--in" $e*o) Le%- (he%th ρ b

14 :=

2π

 d bcs 

⋅ ln

(ermal re$i$tance beteen -ellin tape@ .m6;)

 d bst  14 = 0.0199

91; Therm%* Resist%nce one con-#ctor %n- she%th, T1 1 := 10 + 11 + 12 + 13 + 14

1 = 0.3757

92 Therm%* Resist%nce $et)een (he%th %n- Armo#r, T2 /C* 212 o& IEC ;02<=6261 2 := 0

(No armourin)

2 = 0

93 Therm%* Resist%nceo& o#ter co5erin", T3 /C* 213 o& IEC ;02<=6261

ρ p

3 :=

2π



2.tos 



dals

⋅ ln 1 +

(ermal re$i$tance o% outer co/er@ .m6;)



3 = 0.0529

99 Therm%* Resist%nceo& c%$*e s#rro#n-in", T9 /C* 22 o& IEC ;02<=6261 991 C%$*es in tro#"h For 3 cable$ a/in uneual $eat lo$$e$@ laid in %lat %ormation and eually $paced apart

( :=

( 2.h'1ca_tr )

( = 21.158

do

(1 := ln ( +

(

2 ( −1

 ρsoil  

(1 = 3.745



2  2⋅ h'1 ca_tr  

)  2π  ⋅ (1 + ln 1 +   

4trn ρsoil :=

str

9xternal ermal #e$i$tance %or current ratin calculation in trou (to u$ed at numerator o% te %inal %ormula)@ .m6;

 

( )

4trn ρst = 1.632


22

22.03.2013

Mathcad - Ampacity Calculation

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