Mathcad - Ampacity Calculation

POWER CABLE AMPACITY (132 kV)

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

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

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

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

"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

3

Inom_400rc = 1155

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

(

tos := 4.7

)

("ro$$<$ection o% lead $eat@

m2 )

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

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;)

 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)

 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

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 := Θm_hdd := 80

 1  2

+

do pip_hdd = 225

3 

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


*hdd = 7242

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$)

do pip_rc = 200

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)

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 :=


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

4

s = 0.0415

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)

(

( ))

!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)

(

( ))

!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) 

(

)

(

) :=

(

)

ρs Θm := ρlad⋅ " lad Θm

β Θ

4π ω

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

( )

'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  lad( Θm) + P# s$

)

(

)

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

+

0.25 # s$

(

)

!s lad Θm

2

+ # s$

+ 2



( )

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 :=

(

)

!slad Θm



0.75⋅ P # s$

2

+

0.25 # s$

(

2

+

)

2 !slad Θm ⋅ P# s$ ⋅ # s$ ⋅ m_flat





 

(

)

(

)

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

 λ 0a( Θm , s) := 6 

(

2 2 )   dlad 

m Θm

⋅



)



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

(

)

(

)

( )

∆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 :=

0.5

2

d 3.7  lad 

⋅



 !slad( Θm) 

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) )

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)

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 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

 d bst 

⋅ ln

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

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;

  4

( ρ ) = 1.632

(

 ρsoil  

 1 + 0.5⋅ ( λ 1a_tr ( Θms , str , !cac_tr ) + λ 1c_tr ( Θms , str , !cac_tr ) )  

)  2π  ⋅ ( (1) +  

4trd ρsoil :=

⋅ ln 1 +

( 1 + λ 1b_tr ( Θms , str , !cac_tr ) )

 

2  2⋅ h'1 ca_tr  



str

 

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

( )

4trd ρst = 1.649

992 C%$*es in !! For 3 cable$ a/in eual $eat lo$$e$@ laid in tre%oil %ormation and eually $paced ap art

9921 Therm%* resist%nce o& $entonite $et)een c%$*e %n- +i+e

41hdd :=

 ρ bntonit   di pip_hdd  

2π

ln

 

do

(ermal re$i$tance o% bentonite beteen cable and pipe@ .m6;)



41hdd = 0.1004

9922 Therm%* resist%nce o& +i+e m%teri%*

42hdd :=

 ρ p   do pip_hdd  ln

(ermal re$i$tance o% pipe material@ .m6;)

 2π   di pip_hdd 

42hdd = 0.0797

9923 Therm%* resist%nce o& soi* hl := *hdd − shdd⋅

bl := *hdd + shdd⋅

(land :=

3 6

)

4land ρsoil :=

hl = 7113

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

bl = 7307

(u i$ calculated it re%erence to te centre line o% te deepe$t duct$(non
do pip_hdd



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

3

2.bl

(1land := ln (land + 

(

3

(

land

2

 

−1

   ρsoil (1 + ln  2 π  land  

(1land = 4.867

  2 2 # 2 bl$ + ( s hdd)  + ln   s hdd  

 2  # 2 hl$ + 2    2 shdd    2  shdd 

2

(

)

4land ρhdd = 2.099

9929 Tot%* Therm%* resist%nce o& c%$*e s#rro#n-in" T9

(

)

(

)

4hdd ρsoil := 41hdd + 42hdd + 4land ρsoil

9xternal ermal #e$i$tance %or current ratin calculation in @ .m6;>

(

)

4hdd ρhdd = 2.3

993 C%$*e in -#ct %t ro%- crossin" /re&erence to hottest c%$*e n3 For 3 cable$ a/in uneual $eat lo$$e$@ laid in %lat %ormation and eually $paced apart

9931 Therm%* resist%nce o& $entonite $et)een c%$*e %n- +i+e

41rc :=

 ρ bntonit   di pip_rc  

⋅ ln

 

2π

do




41rc = 0.0876

9932 Therm%* resist%nce o& +i+e m%teri%*

42rc :=

 ρ p&c   do pip_rc   2π 

⋅ ln


 di pip_rc 

42rc = 0.1006

9933 E:tern%* therm%* resist%nce o& +i+e m%teri%*



% :=

 1  ⋅  ,-  ⋅  4  −  2   +,-   π   2  

  +  2 ,  2    ,-  ,-   ⋅ ln 1 +   + ln +,-  2  2  ,  2  

%

r b := 

(,- :=

(9ui/alent radiu$ o% te duct bank@ mm)

r b = 357.897

h',(,- = 3.423

r b

(

 / 2 )  2π  ⋅ ( ρsoil − ρconcrt ) ⋅ ln(,- +  (,-

43_corr ρsoil :=

 

 

−1

4

(ρ )

0.182

9939 Therm%* resist%nce o& c%$*e sorro#n-in" T9

(r :=

2⋅ h'1 ca_rc

(r = 12.731

do pip_rc



(1r := ln (r + 

(

)

43m ρsoil :=

 2 (r − 1 

(1r = 3.236

 ρconcrt   

2π



2  2h'1ca_rc  

⋅ (1r + ln 1 +

 





src

 

+ 43_corr ( ρsoil) 9xternal ermal #e$i$tance %or current ratin calculation in duct bank (to u$ed at numerator o% te %inal %ormula)@ .m6;

( )

43m ρsr = 1.379

(

)

43rd ρsoil :=


2π

⋅ (1r +

 

 1 + 0.5⋅ ( λ 1a_rc ( Θms , src , !cac_rc) + λ 1c_rc( Θms , src, !cac_rc) )  

( 1 + λ 1b_rc ( Θms , src , !cac_rc) )



⋅ ln 1 +

 

 2⋅ h'1ca_rc   2



src

 

+ 43_corr ( ρsoil)

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

( )

43rd ρsr = 1.384

993@ Tot%* Therm%* resist%nce o& c%$*e s#rro#n-in" T9

(

)

(

)

4m ρsoil := 41rc + 42rc + 43m ρsoil

9xternal termal re$i$tance %or current ratin calculation in duct bank to be u$ed at numerator o% te %inal %ormula@ .m6;)

( )

4m ρsr = 1.5677

(

)

(

)

4rc ρsoil := 41rc + 42rc + 43rd ρsoil

9xternal termal re$i$tance %or current ratin calculation in duct bank to be u$ed at te denominator o% te %inal %ormula@ .m6;)

( )

4rc ρsr = 1.5723

@ Con-#ctor Tem+er%t#re Rise %$o5e the Am$ient Tem+er%t#re Θtr := Θma% − Θc'ro(nd

(emperature ri$e o% te conductor it re$pect to te $urroundin$ o% trou@ E") Θtr = 50

Θhdd := Θma% − Θc'ro(nd

(emperature ri$e o% te conductor it re$pect to te $urroundin$ o% @ E") Θhdd = 50

Θrc := Θma% − Θc'ro(nd

(emperature ri$e o% te conductor it re$pect to te $urroundin$ o% road cro$$in@ E") Θrc = 50

; Contin#o#s C#rrent C%rrin" C%+%cit /A ;1 C%$*es in tro#"h /C#rrent %s % &#nction o& soi* therm%* resisti5it ρsoil := 0.8, 0.9 .. 2.3

(Variable termal re$i$ti/ity o% $oil@ .m6;)



 )) I1tr ( ρsoil) :=  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd( ρsoil) ) 

(

)

(

(

)

P1 tr ρsoil := I1tr ρsoil U p_132⋅ 10

(

)

I1tr ρsoil =

(

Θtr − +d⋅ 0.51 + n⋅ 2 + 3 + 4trn ρsoil

ρsoil =

−6

⋅ 3

(ran$mi$$ion 5oer in ,VA)

(

)

P1tr ρsoil =

1237

0.8

282.8

1183.3

0.9

270.5

1136

1

259.7

1093.8

1.1

250.1

1055.9

1.2

241.4

1021.6

1.3

233.6

990.3

1.4

226.4

961.7

1.5

219.9

935.4

1.6

213.9

911

1.7

208.3

888.4

1.8

203.1

867.3

1.9

198.3

847.7

2

193.8

829.2

2.1

189.6

811.9

2.2

185.6

795.5

2.3

181.9

( )

(A)

( )

(,VA)

I1tr ρst = 1055.9 P1 tr ρst = 241.4

2 = 22.485 +c_tr := I1tr ρst ⋅ !cac_tr

( )

(k;6km)

= 1.396 +s_tr := λ 1_tr ⋅ +c_tr

(k;6km)

+d_tr := +d = 0.49

(k;6km)

= 24.37 +total_tr := +c_tr + +s_tr + +d_tr

(k;6km)

Final /eri%ication o% te $creen6$eat temperature

(



)



(

)

Θfin_tr ρsoil := Θma% − 1⋅ !cac_tr ⋅ I1tr ρsoil



2

+

+d

2



( )

Θfin_tr ρst = 81.5 Θm_tr = 81.5

;2 C%$*es in !! /C#rrent %s % &#nction o& soi* therm%* resisti5it

ρsoil := 0.8, 0.9 .. 2.3

(

)

(

)

I1hdd ρsoil :=




Θhdd − +d⋅ 0.51 + n⋅ 2 + 3 + 4hdd ρsoil



!cac_hdd ⋅ 1 + n⋅!c ac_hdd ⋅ 1 + λ 1_hdd 2 + n⋅!cac_hdd ⋅ 1 + λ 1_hdd 3 + 4hdd ρsoil

(

(

(

)

P1 hdd ρsoil := I1hdd ρsoil U p_132⋅ 10

(

)

I1hdd ρsoil =

ρsoil =

)

(



))

(

)(

(

)) 

−6

⋅ 3


(

)

P1hdd ρsoil =

1018

0.8

232.8

973

0.9

222.5

934

1

213.4

898

1.1

205.4

867

1.2

198.1

838

1.3

191.6

812

1.4

185.6

788

1.5

180.1

766

1.6

175.1

746

1.7

170.5

727

1.8

166.1

709

1.9

162.1

693

2

158.4

677

2.1

154.8

663

2.2

151.5

649

2.3

148.4

(

)

(A)

(

)

(,VA)

I1hdd ρhdd = 933.6 P1 hdd ρhdd = 213.4

2 = 17.558 +c_hdd := I1hdd ρhdd ⋅ !cac_hdd

(k;6km)

= 0.527 +s_hdd := λ 1_hdd ⋅ +c_hdd

(k;6km)

+d_hdd := +d = 0.49

(k;6km)

(

)

= 18.57 (k;6km) +total_hdd := +c_hdd + +s_hdd + +d_hdd


(



)



(

)

Θfin_hdd ρsoil := Θma% − 1⋅ !cac_hdd ⋅ I1hdd ρsoil

(



2

+

+d

2



)

Θfin_tr ρhdd = 80.1 Θm_hdd = 80

;3 C%$*es in -#cts %t ro%- crossin" /C#rrent %s % &#nction o& soi* therm%* resisti5it

ρsoil := 0.8, 0.9 .. 2.3




 )) I1rc( ρsoil) :=  !cac_rc⋅ 1 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) 2 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) ( 3 + 4rc( ρsoil) ) 

(

)

(

(

)

P1 rc ρsoil := I1rc ρsoil U p_132⋅ 10

(

)

I1rc ρ soil =

(

Θrc − +d⋅ 0.51 + n⋅ 2 + 3 + 4m ρsoil

ρsoil =

−6

⋅ 3


(

)

P1rc ρsoil =

1208

0.8

276.3

1175

0.9

268.7

1145

1

261.8

1117

1.1

255.3

1090

1.2

249.3

1066

1.3

243.7

1043

1.4

238.4

1021

1.5

233.5

1001

1.6

228.8

982

1.7

224.5

964

1.8

220.3

946

1.9

216.4

930

2

212.6

914

2.1

209

899

2.2

205.6

885

2.3

202.4

( )

(A)

( )

(,VA)

I1rc ρsr = 1090 P1 rc ρsr = 249.3

2 = 15.099 +c_rc := I1hdd ρsr ⋅ !cac_rc

( )

= 0.497 +s_rc := λ 1_rc⋅ +c_rc +d_rc := +d = 0.49

= 16.09 +total_rc := +c_rc + +s_rc + +d_rc


(



)



(

)

Θfin_rc ρsoil := Θma% − 1⋅ !cac_rc ⋅ I1rc ρsoil



2

+d

+

2



( )

Θfin_rc ρsr = 80.9 Θm_rc = 80.5

= Re-#ction 4%ctors =1 R41 C%$*es in tro#"h &or 5%rio#s !e+ths %n- L%in" 6 di$tance %rom round $ur%ace to cable axi$ h'ca := 600 , 700 .. 2000

(Variable i$tance$ o% "able$ %rom round $ur%ace@ mm)

# 2.hr $

(t_!1# hr $ :=

do



2  (t_!1# hr $ − 1 

(1t_!1# hr $ := ln (t_!1# hr $ + 

(

)

4trn_!1 ρsoil , hr :=

(

)

4trd_!1 ρsoil , hr :=

 ρsoil  



2 2 ⋅ hr    # hr $ + ln 1 +

⋅ (1t_!1

 2 π  



 str  


 ρsoil  


 2 π  



⋅ (1t_!1# hr $ +


 2⋅ hr   ⋅ ln 1 +

 

2

 str  




 ( )) I1tr_!1( ρsoil , hr ) :=  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd_!1( ρsoil, hr ) ) 

(

)

(

Θtr − +d⋅ 0.51 + n⋅ 2 + 3 + 4trn_!1 ρsoil , hr

(

)

P1 tr_!1 ρsoil , hr := I1tr_!1 ρsoil , hr U p_132⋅ 10

(

)

!1 ρsoil hr :=

 I1tr_!1( ρsoil , hr ) 

−6

⋅ 3


h'ca =

(

)

!1t ρst , h'ca =

(

)

I1tr_!1 ρst , h'ca =

(

)

1600

1800

P1tr_!1 ρst , h'ca =

600

1.099

1160

265

700

1.071

1131

259

800

1.048

1107

253

900

1.03

1087

249

1000

1.014

1070

245

1100

1

1056

241

1200

0.988

1043

238

1300

0.977

1031

236

1400

0.967

1021

233

1500

0.958

1012

231

1600

0.95

1003

229

1700

0.943

995

228

1800

0.936

988

226

1900

0.929

981

224

2000

0.923

975

223

270

A = 257.5 < : r  ; o P P1 n tr_!1 ( ρ st , h'ca) 245 o i s s i m s n 232.5 a r 7 220 600

800

1000

1200

1400 h'ca

abl *ain' dpth: mm

2000

=2 R42 C%$*es in !! crossin" &or 5%rio#s !e+ths %n- L%in" 6 di$tance %rom round $ur%ace to cable axi$ h'ca := 3500 , 4000.. 15000

hl_!2# hr $ := hr − s hdd⋅

bl_!2# hr $ := hr + s hdd⋅

(!2# hr $ :=


3


3 3


6

2. bl_!2# hr $

(u#F2 i$ calculated it re%erence to te centre line o% te deepe$t

do pip_hdd

duct$(non


(1c_!2# hr $ := ln (!2# hr $ + 

(

)

43c_!2 ρsoil , hr :=

(

(

!2# hr $

2

   ρsoil ( # hr $ + ln 2 π  1c_!2   

)

 

−1

  2 2 # 2 bl_!2# hr $ $ + ( s hdd)  + ln   s hdd   

(

 2  # 2 hl_!2# hr $ $ + 2    2 shdd    2 # bl_!2# hr $ − hl_!2# hr $ $ +  2    shdd 

2

)

4c_!2 ρsoil , hr := 41hdd + 42hdd + 43c_!2 ρsoil , hr

9xternal ermal #e$i$tance %or current ratin calculation in @ .m6;>

(

)

4hdd ρhdd = 2.3

(

)

(

)

I1hdd_!2 ρsoil , hr :=



Θhdd − +d⋅ 0.51 + n⋅ 2 + 3 + 4c_!2 ρsoil , hr



!cac_hdd ⋅ 1 + n⋅!cac_hdd ⋅ 1 + λ 1_hdd 2 + n⋅!c ac_hdd ⋅ 1 + λ 1_hdd 3 + 4c_!2 ρsoil , hr

(

(

(

)

P1 hdd_!2 ρsoil , hr := I1hdd_!2 ρsoil , hr U p_132⋅ 10

(

)

!2t ρsoil , hr :=

 I1hdd_!2 ( ρsoil, hr )  

(

) 

I1hdd ρhdd

)

(

(

)(

−6

⋅ 3



))


(

)) 

h'ca =

(

)

!2t ρhdd , h'ca =

(

)

(

)

I1hdd_!2 ρhdd , h'ca = P1hdd_!2 ρhdd , h'ca =

3500

1.073

1002

229

4000

1.059

988

226

4500

1.046

977

223

5000

1.035

967

221

5500

1.026

958

219

6000

1.018

950

217

6500

1.01

943

216

7000

1.003

937

214

7500

0.997

931

213

8000

0.991

925

212

8500

0.986

920

210

9000

0.981

916

209

9500

0.976

911

208

10000

0.972

907

207

10500

0.968

904

207

11000

0.964

900

206

11500

0.96

897

205

12000

0.957

893

204

12500

0.954

890

204

13000

0.951

887

203

13500

0.948

885

202

14000

0.945

882

202

14500

0.942

880

201

15000

0.94

877

201

230

A = 222.5 < : r  ; o P P1 n hdd_!2 ( ρ hdd , h'ca) 215 o i s s i m s n 207.5 a r 7 200 3500

5142.9

6785.7

8428.6

10071.4 h'ca

11714.3

13357.1

15000

=3 R43 C%$*es in -#ct$%nk &or ro%- crossin" &or 5%rio#s !e+ths %n- L%in" 6 di$tance %rom round $ur%ace to cable axi$ h'ca := 600 , 700 .. 2000



do



2

∆h',-# hr $ := hr +

(,-_!3 # hr $ :=




 ,-



2

+ t pip_rc − do pip_rc − 200 +

∆h',-# hr $ r b

  2  /  )  2π  ⋅ ( ρsoil − ρconcrt ) ⋅ ln(,-_!3 # hr $ + (,-_!3 # hr $  − 1

(

4r_corr_!3 ρsoil , hr :=

(rc_!3# hr $ :=

2 hr do pip_rc



(1rc_!3 # hr $ := ln (rc_!3# hr $ + 

(

 ρconcrt  

) 

43rn_!3 ρsoil , hr :=

2  (rc_!3# hr $ − 1 

2π



⋅ (1rc_!3

 

2 2 ⋅ hr    # hr $ + ln 1 + + 4





str

 

(

)

r_corr_!3 ρsoil , hr

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

(


) 

43rd_!3 ρsoil , hr :=

2π

⋅ (1rc_!3 # hr $ +

 

+ 4r_corr_!3 ( ρsoil, hr )

 1 + 0.5⋅ ( λ 1a_rc ( Θms , src , !cac_rc) + λ 1c_rc ( Θms , src, !cac_rc) )  

2 2 ⋅ hr    ⋅ ln 1 + ...

( 1 + λ 1b_rc ( Θms, src, !cac_rc) )



 

 str  


(

)

(

)


(

)

(

)


4rn_!3 ρsoil , hr := 41rc + 42rc + 43rn_!3 ρsoil , hr

4rd_!3 ρsoil , hr := 41rc + 42rc + 43rd_!3 ρsoil , hr

(

)

I1rc_!3 ρsoil , hr :=

 

(

(



))

Θrc − +d⋅ 0.51 + n⋅ 2 + 3 + 4rn_!3 ρsoil , hr !c

1

n !c

(1

λ

) 2

!c

(1

λ

) ( 3

4

(

)) 

hr

(

)

(

)

P1 rc_!3 ρsoil , hr := I1rc_!3 ρsoil , hr U p_132⋅ 10

(

)

!3t ρsoil , hr :=

h'ca =

−6

⋅ 3


 I1rc_!3( ρsoil, hr )  

( )

I1rc ρsr

(



)

!3t ρsr , h'ca =

(

)

I1rc_!3 ρsr , h'ca =

(

)

1600

1800

P1rc_!3 ρsr , h'ca =

600

1.093

1192

273

700

1.063

1159

265

800

1.04

1134

259

900

1.02

1112

254

1000

1.004

1094

250

1100

0.989

1079

247

1200

0.977

1065

244

1300

0.966

1053

241

1400

0.956

1043

238

1500

0.947

1033

236

1600

0.939

1024

234

1700

0.932

1016

232

1800

0.925

1009

231

1900

0.918

1002

229

2000

0.913

995

228

275

A = 263 < : r  ; o P P1 ρ , h' n rc_!3( sr ca) 251 o i s s i m s n 239 a r 7 227 600

800

1000

1200

1400 h'ca

2000

=9 R49 C%$*es in tro#"h &or &or 5%rio#s "ro#n- tem+er%t#res Θ'ro(nd := 30 , 31 .. 50

(

)

Θ!4 Θ'ro(nd := Θma% − Θ'ro(nd



 ( )) ⋅ n p I1c_!4( ρsoil , Θ'ro(nd ) := !cac_tr ⋅ 1 + n⋅!c ac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd( ρsoil) )  

(

)

(

)

(

)

P1 c_!4 ρsoil , Θ'ro(nd := I1c_!4 ρsoil , Θ'ro(nd U p_132⋅ 10

(

)

!4c ρsoil , Θ'ro(nd :=

Θ'ro(nd =

(

Θ!4 Θ'ro(nd − +d⋅ 0.51 + n⋅ 2 + 3 + 4trn ρsoil

−6

⋅ 3


 I1c_!4( ρsoil, Θ'ro(nd) 

( )

I1rc ρst



(

)



(

)

(

)

!4c ρst , Θ'ro(nd = I1c_!4 ρst , Θ'ro(nd = P1c_!4 ρst , Θ'ro(nd =

30

1.062

1158

265

31

1.053

1149

263

32

1.044

1139

260

33

1.035

1129

258

34

1.026

1119

256

35

1.016

1108

253

36

1.007

1098

251

37

0.997

1088

249

38

0.988

1077

246

39

0.978

1067

244

40

0.968

1056

241

41

0.958

1045

239

42

0.948

1034

236

43

0.938

1023

234

44

0.928

1012

231

45

0.918

1001

229

46

0.907

989

226

47

0.897

978

224

48

0.886

966

221

49

0.875

954

218

=@ R4@ C%$*es in !! crossin" &or &or 5%rio#s "ro#n- tem+er%t#res Θsoil := 20 , 21 .. 40

(

)

Θ!5 Θsoil := Θma% − Θsoil



 )) I1c_!5( ρsoil , Θsoil) := n p !cac_hdd ⋅ 1 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd ) 2 + n⋅!c ac_hdd ⋅ ( 1 + λ 1_hdd ) ( 3 + 4hdd( ρsoil) )  

(

(

)

)

(

)

P1 c_!5 ρsoil , Θsoil := I1c_!5 ρsoil , Θsoil U p_132⋅ 10

(

)

!5c ρsoil , Θsoil :=

Θsoil =

(

(

Θ!5 Θsoil − +d⋅ 0.51 + n⋅ 2 + 3 + 4hdd ρsoil

−6

⋅ 3


 I1c_!5( ρsoil , Θsoil)  

(

)

I1hdd ρhdd

(



)

!5c ρhdd , Θsoil =

(

)

I1c_!5 ρhdd , Θsoil =

(

)

P1c_!5 ρhdd , Θsoil =

20

1.187

1109

253

21

1.179

1101

252

22

1.17

1092

250

23

1.161

1084

248

24

1.152

1076

246

25

1.144

1068

244

26

1.135

1059

242

27

1.125

1051

240

28

1.116

1042

238

29

1.107

1034

236

30

1.098

1025

234

31

1.088

1016

232

32

1.079

1007

230

33

1.069

998

228

34

1.06

989

226

35

1.05

980

224

36

1.04

971

222

37

1.03

962

220

38

1.02

953

218

39

1.01

943

216

=; R4; C%$*es in !#ct $%nk %t ro%- crossin" &or &or 5%rio#s "ro#n- tem+er%t#res Θ'ro(nd := 30 , 31 .. 50

(

)

Θ!6 Θ'ro(nd := Θma% − Θ'ro(nd



 ( )) ⋅ n p I1c_!6( ρsoil , Θ'ro(nd ) := !cac_rc⋅ 1 + n⋅!cac_rc ⋅ ( 1 + λ 1_rc) 2 + n⋅!c ac_rc⋅ ( 1 + λ 1_rc) ( 3 + 4rc( ρsoil) )  

(

(

)

)

(

)

P1c_!6 ρsoil , Θ'ro(nd := I1c_!6 ρsoil , Θ'ro(nd U p_132⋅ 10

(

)

!6c ρsoil , Θ'ro(nd :=

Θ'ro(nd =

(

Θ!6 Θ'ro(nd − +d⋅ 0.51 + n⋅ 2 2 + 3 + 4m ρsoil

−6

⋅ 3


 I1c_!6( ρsoil, Θ'ro(nd) 

( )

I1rc ρsr



(

)



(

)

(

)

!6c ρsr , Θ'ro(nd = I1c_!6 ρsr , Θ'ro(nd = P1c_!6 ρsr , Θ'ro(nd =

30

1.097

1196

274

31

1.088

1186

271

32

1.078

1176

269

33

1.069

1166

266

34

1.059

1155

264

35

1.05

1145

262

36

1.04

1134

259

37

1.03

1123

257

38

1.02

1112

254

39

1.01

1102

252

40

1

1090

249

41

0.99

1079

247

42

0.979

1068

244

43

0.969

1057

242

44

0.958

1045

239

45

0.948

1033

236

46

0.937

1022

234

47

0.926

1010

231

48

0.915

998

228

49

0.904

986

225

50

0.892

973

222

== R4= C%$*es in tro#"h t ro#"h &or &or 5%rio#s c%$*e se+%r%tion s ca := 200 , 250 .. 600

(t_!7 :=

( 2.h'1ca_tr ) do



(1t_!7 := ln (t_!7 + 

(

)

4trn_!7 ρsoil , s :=

(

)

4trd_!7 ρsoil , s :=

2  (t_!7 − 1 

 ρsoil  



 2π  



 ρsoil  


⋅ (1t_!7 + ln 1 +

 2π 

⋅ ( (1t_!7) +



2  2⋅ h'1 ca_tr  



s

 

(




(

))

1 + λ 1b_tr Θms , str , !cac_tr

⋅ ln 1 +

 

2  2⋅ h'1ca_tr  



s




 ( )) I1c_!7( ρsoil , s) :=  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd_!7( ρsoil , s) ) 

(

)

(

Θtr − +d⋅ 0.51 + n⋅ 2 2 + 3 + 4trn_!7 ρsoil , s

(

)

P1c_!7 ρsoil , s := I1c_!7 ρsoil , s U p_132⋅ 10

(

)

!7c ρsoil , s :=

s ca =

−6

⋅ 3


 I1c_!7( ρsoil, s)  

( )



(

)

I1tr ρst

!7c ρst , sca =

(

)

I1c_!7 ρst , sca =

(

)

P1c_!7 ρst , sca =

200

1

1056

241

250

1.022

1079

247

300

1.041

1099

251

350

1.058

1117

255

400

1.073

1133

259

450

1.087

1147

262

500

1.099

1161

265

550

1.111

1173

268

600

1.122

1184

271

 

< Mirror +rinci+*e %++*ie- &or +%r%**e* #ne#%** *o%-e- c%$*e circ#its /(#+er +osition <1 C%$*es in tro#"h $et)een 132 132 kV Br#"" Circ#it %n- 2 Circ#its Circ#its 900 kV Visc%s

Pa_400 := 100 , 200 .. 1200

,%02_%1 :=

(Variable loadin o% parallel runnin 400 kV cable@ ,VA)

( ,400b_132_tr + 400_tr )

2

+ ( h'1ca_tr − h'400_tr )

2

(di$tance beteen ?02 and ?1@ mm) 3 5.500 × 10 ,%02_%1 = 5.500

,%02_%1m :=

( ,400b_132_tr + 400_tr )

2

+ ( h'1ca_tr + h'400_tr )

2

(di$tance beteen ?02 and mirror imae ?1@ mm) 3 5.923 × 10 ,%02_%1m = 5.923

,%02_%2 :=

( ,400b_132_tr )

2

+ ( h'1ca_tr − h'400_tr )

2

(di$tance beteen ?02 and ?2@ mm) 3 4.900 × 10 ,%02_%2 = 4.900

,%02_%2m :=

( ,400b_132_tr )

2

+ ( h'1ca_tr + h'400_tr )

2

(di$tance beteen ?02 and mirror imae ?2@ mm) ,

3

5.370 5.370 10

( ,400b_132_tr − 400_tr )

, %02_%3 :=

2

+ ( h'1ca_tr − h'400_tr )

2

(di$tance beteen ?02 and ?3@ mm) 3 , %02_%3 = 4.300 × 10

( ,400b_132_tr − 400_tr )

, %02_%3m :=

2

+ ( h'1ca_tr + h'400_tr )

2

(di$tance beteen ?02 and mirror imae ?3@ mm) 3 , %02_%3m = 4.829 × 10

( ,400a_132_tr + 400_tr )

, %02_%4 :=

2

+ ( h'1ca_tr − h'400_tr )

2

(di$tance beteen ?02 and ?4@ mm) 3 , %02_%4 = 2.700 × 10

( ,400a_132_tr + 400_tr )

, %02_%4m :=

2

+ ( h'1ca_tr + h'400_tr )

2

(di$tance beteen ?02 and mirror imae ?4@ mm) 3 , %02_%4m = 3.482 × 10

( ,400a_132_tr )

, %02_%5 :=

2

+ ( h'1ca_tr − h'400_tr )

2

(di$tance beteen ?02 and ?+@ mm) 3 , %02_%5 = 2.100 × 10

( ,400a_132_tr )

, %02_%5m :=

2

+ ( h'1ca_tr + h'400_tr )

2

(di$tance beteen ?02 and mirror imae ?+@ mm) 3 , %02_%5m = 3.040 × 10

( ,400a_132_tr − 400_tr )

, %02_%6 :=

2

( ,400a_132_tr − 400_tr )

, %02_%6m :=

+ ( h'1ca_tr − h'400_tr ) 2

2

+ ( h'1ca_tr + h'400_tr )

(di$tance beteen ?02 and ?@ mm) 2

3 , %02_%6 = 1.500 × 10

(di$tance beteen ?02 and ?@ mm) 3 , %02_%6m = 2.661 × 10

I400tr # P$ :=

# P⋅ 1000$

(

("urrent in te 400 kV circuit a$ a %unction o% te tran$mitted poer@ A)

3⋅ 400)

(

)

1591 I400tr P400tr =

(

)

+400_atr # P$ := ! A_400_tr ⋅ 1 + λ 1a_tr_400 ⋅ I400tr # P$

2

+ +d400 (9$timated lo$$e$ in te 400 kV pa$e a circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m)

(

)

+400_atr P400tr = 27.911

(

)

+400_btr # P$ := ! A_400_tr ⋅ 1 + λ 1b_tr_400 ⋅ I400tr # P$

2

+ +d400 (9$timated lo$$e$ in te 400 kV pa$e b circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m)

(

)

+400_btr P400tr = 27.182

(

)

+400_ctr # P$ := ! A_400_tr ⋅ 1 + λ 1c_tr_400 ⋅ I400tr # P$

2

+ +d400 (9$timated lo$$e$ in te 400 kV pa$e c circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m)

(

)

∆Θ%02_%1 ρsoil , P :=

(

)

∆Θ%02_%2 ρsoil , P :=

(

)

∆Θ%02_%3 ρsoil , P :=

(

)

∆Θ%02_%4 ρsoil , P :=

(

)

∆Θ%02_%5 ρsoil , P :=

(

)

∆Θ%02_%6 ρsoil , P :=

1 2π

1 2π

1 2π

1 2π

1 2π

1 2π

(

 ,%02_%1m 

⋅ ρsoil⋅ +400_atr # P$ ⋅ ln

 ,%02_%1   ,%02_%2m 

⋅ ρsoil⋅ +400_btr # P$ ⋅ ln

 ,%02_%2 

 ,%02_%3m 

⋅ ρsoil⋅ +400_ctr # P$ ⋅ ln

 ,%02_%3   ,%02_%4m 

⋅ ρsoil⋅ +400_atr # P$ ⋅ ln

 ,%02_%4   ,%02_%5m 

⋅ ρsoil⋅ +400_btr # P$ ⋅ ln

 ,%02_%5 

 ,%02_%6m 

⋅ ρsoil⋅ +400_ctr # P$ ⋅ ln

 ,%02_%6 

)

(

)

(emperature ri$e at te $ur%ace o% cable produced by te poer o% %urte$t 400 kV circuit and di$$pated in cable ?02)



(emperature ri$e at te $ur%ace o% cable produced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable ?02)



(

)

(

)

(

)

∆ΘPtr ρsoil , P :=  ∆Θ%02_%1 ρsoil , P + ∆Θ%02_%2 ρsoil , P + ∆Θ%02_%3 ρsoil , P + ∆Θ%02_%4 ρsoil , P ...  + ∆Θ%02_%5 ρ soil , P + ∆Θ%02_%6 ρsoil, P



(

)

(

)



(otal ri$e abo/e ambient temperature at te $ur%ace o% te ?02 cable@ o$e ratin i$ bein determined@ cau$ed by te poer di$$pated by te oter cable$ in roup)



 ( Θtr − ∆ΘPtr ( ρsoil , P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4trn( ρsoil) ) )  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd( ρsoil) ) 

(

I1132_400tr ρsoil , P :=

(

)

P1132_400tr ρsoil , P :=

(

)

(

)(

(

3 ⋅ 132)

I1132_400tr ρsoil , P ⋅

1000

(

!4tr ρsoil , P := !4c ρsoil , Θc'ro(nd + ∆ΘPtr ρsoil , P

))

(#eduction Factor due to 400 kV circuit)

(

Pa_400 =

)

(

I400tr Pa_400 =

)

∆ΘPtr ρst , Pa_400 =

(

!4tr ρst , Pa_400

)

(

=

I1132_400tr ρst , Pa_400

100

144

0.37

0.965

1052

200

289

0.55

0.963

1050

300

433

0.85

0.96

1047

400

577

1.28

0.956

1042

500

722

1.83

0.95

1036

600

866

2.5

0.943

1029

700

1010

3.3

0.935

1020

800

1155

4.21

0.926

1010

900

1299

5.25

0.915

998

1000

1443

6.41

0.903

985

1100

1588

7.69

0.889

970

1200

1732

9.1

0.874

953

)

=

0.97

r t 4 8 ! : r o t c a 8 n o i t c ( d  !

0.95

(

)

I1132_400tr ρst , P400tr = 969 0.93

(

!4tr ρst , P a_400

(

) 0.92

0.9

0.88 100

283.3

466.7

650

833.3

P a_400

ransmission Po;r: <=A 2 = 18.947 +c_tr_final := I1132_400tr ρst , P400tr ⋅ !cac_tr

(

)

+s_tr_final := λ 1_tr ⋅ +c_tr_final = 1.176 +d_tr_final := +d = 0.49

)

P1 132_400tr ρsr , P400tr = 222

1016.7

1200

(A)

(,VA)

<2 C%$*es in !! $et)een 132 kV Br#"" Circ#it %n- 900 kV Visc%s Circ#it

hl = 7113

(urial dept o% te upmo$t 132 kV cable@ mm)

bl = 7307

(urial dept o% te deep$t 132 kV cable@ mm)

P b_400 := 50 , 100 .. 600


,02_1 :=



,400b_132_hdd −

shdd 



2

2



+ ( bl − hl400)

2

(di$tance beteen =02 and =1@ mm) 3 , 02_1 = 5.890 × 10

,02_1m :=



,400b_132_hdd −



s hdd 

2



2

+ ( bl + bl400)

2

(di$tance beteen =02 and mirror imae =1@ mm)

,02_2 :=

,02_2m :=

,02_3 :=

,02_3m :=

,02_4 :=

,02_4m :=

,02_5 :=



shdd



2

,400b_132_hdd −

+



s hdd



2

,400b_132_hdd −



shdd



2

,400b_132_hdd −

s hdd



2



,400a_132_hdd −

shdd 



2



,400a_132_hdd −

shdd

2

2

+ ( bl + bl400)

2

(di$tance beteen =02 and mirror imae =2@ mm) 3 , 02_2m = 15.953 × 10

+ ( bl400 − bl)

2

(di$tance beteen =02 and =3@ mm) 3 , 02_3 = 5.750 × 10

400_hdd 

2



+ ( bl + bl400)

2


2

+ ( bl − hl400)



2

(di$tance beteen =02 and =2@ mm)

2



2

2 3 , 02_2 = 6.030 × 10



2

2

−

+ ( bl400 − bl)

400_hdd 

400_hdd 


2

+ ( bl + bl400)



+

2 3 , 02_4 = 2.892 × 10

shdd 



 , −  400a_132_hdd

+

2



2

−



,400b_132_hdd −

400_hdd 

2


400_hdd 

2

+ ( hl400 − bl)



2

2

(di$tance beteen =02 and =+@ mm) 3 , 02_5 = 3.032 × 10

,02_5m :=



shdd



2

,400a_132_hdd −

+

400_hdd 

2

2

+ ( bl + hl400)



2

(di$tance beteen =02 and mirror imae =+@ mm) 3 , 02_5m = 14.761 × 10

,02_6 :=

,02_6m :=



shdd



2

,400a_132_hdd −

−



shdd



2

,400a_132_hdd −

400_hdd 



2

−

2

400_hdd 

2



+ ( bl400 − bl)

2

(di$tance beteen =02 and =@ mm) 3 , 02_6 = 2.752 × 10

2

+ ( bl + bl400)

2


I400hdd# P$ :=

# P⋅ 1000$

(


3 ⋅ 400)

(

)

I400tr P400hdd = 820

)

(

+400_hdd # P$ := ! A_400_hdd ⋅ 1 + λ 1_hdd_400 ⋅ I400hdd # P$

2


(

)

+400_hdd P400hdd = 8.292

(

1

)

∆Θ02_1 ρsoil , P :=

(

2π

1

)

∆Θ02_2 ρsoil , P :=

(

2π

1

)

∆Θ02_3 ρsoil , P :=

(

2π

1

)

∆Θ02_4 ρsoil , P :=

(

2π

1

)

∆Θ02_5 ρsoil , P :=

(

2π

1

)

∆Θ02_6 ρsoil , P :=

2π

 ,02_1m 

⋅ ρsoil⋅ +400_hdd # P$ ⋅ ln

 ,02_1   ,02_2m 


 ,02_2   ,02_3m 


 ,02_3   ,02_4m 


 ,02_4   ,02_5m 


 ,02_5   ,02_6m 


 ,02_6 

(

)

(

)

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% %urte$t 400 kV circuit and di$$pated in cable =02)



(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable =02)

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable y02)

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable =02)

(

)

(

)

(

)

∆ΘPhdd ρsoil , P :=  ∆Θ02_1 ρsoil , P + ∆Θ02_2 ρsoil , P + ∆Θ02_3 ρsoil , P + ∆Θ02_4 ρsoil , P ...  + ∆Θ02_5 ρsoil, P + ∆Θ02_6 ρsoil , P



(

)

(

)



(otal ri$e abo/e ambient temperature at te $ur%ace o% te =02 cable@ o$e ratin i$ bein determined@ cau$ed by te poer di$$pated by te oter cable$ in roup)

 ( Θhdd − ∆ΘPhdd( ρsoil , P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4hdd( ρsoil) ) )  !cac_hdd ⋅ 1 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) 2 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) ( 3 + 4hdd( ρsoil) ) 

Θ'ro(nd := 30 , 31 .. 50 I1132_400hdd ρsoil , P :=

(

(

)

P1132_400hdd ρsoil , P :=



(

)(

I1132_400hdd ρsoil , P ⋅

1000

3 ⋅ 132)

(

P b_400 =

)

I400hdd P b_400 =

(

)

∆ΘPhdd ρhdd , P b_400 =

(

)

!5hdd ρhdd , P b_400 =

(

)

I1132_400hdd ρhdd , P b_400 =

50

72

1.43

0.985

920

100

144

1.64

0.983

918

150

217

1.99

0.979

914

200

289

2.49

0.974

910

250

361

3.12

0.967

903

300

433

3.89

0.959

896

350

505

4.81

0.949

886

400

577

5.86

0.938

876

450

650

7.06

0.925

863

500

722

8.39

0.91

849

550

794

9.87

0.893

834

600

866

11.49

0.874

816

0.99

d d h 5 8 ! : r o t c a 8 n o i t c ( d  !

0.97

(

)

(

)

I1132_400hdd ρhdd , P400hdd = 828 (A) P1 132_400hdd ρhdd , P400hdd = 189 (,VA)

0.94

(

!5hdd ρ hdd , P b_400

) 0.92

0.89

0.87 50

141.7

233.3

325

416.7

P b_400

ransmission Po;r: <=A

(

+c_hdd_final := I1132_400hdd ρ hdd , P400hdd

)

= 0.414 +s_hdd_final := λ 1_hdd ⋅ +c_hdd_final +d_hdd_final := +d = 0.49

2

⋅ !cac_hdd = 13.799

508.3

600

<3 Ro%- crossin" -#ct$%nks $et)een 132 kV Br#"" Circ#it %n- 2 Circ#its 900 kV Visc%s

Pc_400 := 100 , 150 .. 800

, "02_"1 :=


( ,400b_132_rc + 400_rc )

2

+ ( h'1ca_rc − h'400_rc )

2

(di$tance beteen 02 and 1@ mm) 3 , "02_"1 = 5.201 × 10

, "02_"1m :=

( ,400b_132_rc + 400_rc )

2

+ ( h'1ca_rc + h'400_rc )

2

(di$tance beteen 02 and mirror imae 1@ mm) 3 , "02_"1m = 5.824 × 10

, "02_"2 :=

( ,400b_132_rc )

2

+ ( h'1ca_rc − h'400_rc )

2


, "02_"2m :=

( ,400b_132_rc )

2

+ ( h'1ca_rc + h'400_rc )

2


, "02_"3 :=

( ,400b_132_rc − 400_rc )

2

+ ( h'1ca_rc − h'400_rc )

2

(di$tance beteen 02 and 3@ mm)

( ,400b_132_rc − 400_rc )

, "02_"3m :=

2

+ ( h'1ca_rc + h'400_rc )

2


( ,400a_132_rc + 400_rc )

, "02_"4 :=

2

+ ( h'1ca_rc − h'400_rc )

2


( ,400a_132_rc + 400_rc )

, "02_"4m :=

2

+ ( h'1ca_rc + h'400_rc )

2


( ,400a_132_rc )

, "02_"5 :=

2

+ ( h'1ca_rc − h'400_rc )

2

(di$tance beteen 02 and +@ mm) 3 , "02_"5 = 2.101 × 10

( ,400a_132_rc )

, "02_"5m :=

2

+ ( h'1ca_rc + h'400_rc )

2

(di$tance beteen 02 and mirror imae +@ mm) 3 , "02_"5m = 3.360 × 10

( ,400a_132_rc − 400_rc )

, "02_"6 :=

2

+ ( h'1ca_rc − h'400_rc )

2

(di$tance beteen 02 and @ mm) 3 , "02_"6 = 1.802 × 10

( ,400a_132_rc − 400_rc )

, "02_"6m :=

2

+ ( h'1ca_rc + h'400_rc )

2

(di$tance beteen 02 and @ mm) 3 , "02_"6m = 3.181 × 10

I400rc # P$ :=

# P⋅ 1000$

(


3 ⋅ 400)

(

)

I400rc P400rc = 1155

(

)

+400_arc # P$ := ! A_400_rc ⋅ 1 + λ 1a_rc_400 ⋅ I400rc # P$

2


(

)

+400_arc P400rc = 15.209

(

)

+400_brc # P$ := ! A_400_rc ⋅ 1 + λ 1b_rc_400 ⋅ I400rc # P$

2

+ +d400 (9$timated lo$$e$ in te 400 kV pa$e b circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m)

(

)

+400_brc P400rc = 14.827

(

)

+400_crc # P$ := ! A_400_rc ⋅ 1 + λ 1c_rc_400 ⋅ I400rc # P$

2

+ +d400 (9$timated lo$$e$ in te 400 kV pa$e c circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m)

(

)

+400_crc P400rc = 14.822

(

)

∆Θ"02_"1 ρsoil , P :=

(

)

∆Θ"02_"2 ρsoil , P :=

(

)

∆Θ"02_"3 ρsoil , P :=

(

)

∆Θ"02_"4 ρsoil , P :=

(

)

∆Θ"02_"5 ρsoil , P :=

(

)

∆Θ"02_"6 ρsoil , P :=

 ,"02_"1m 

1 2π

⋅ ρsoil⋅ +400_arc # P$ ⋅ ln

 ,"02_"1 

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% %urte$t 400 kV circuit and di$$pated in cable 02)

 ,"02_"2m  (emperature ri$e at te $ur%ace o% cable p roduced by te poer

1 2π

⋅ ρsoil⋅ +400_brc # P$ ⋅ ln

 ,"02_"2 

 ,"02_"3m 

1 2π

⋅ ρsoil⋅ +400_crc # P$ ⋅ ln

 ,"02_"3   ,"02_"4m 

1 2π

⋅ ρsoil⋅ +400_arc # P$ ⋅ ln

 ,"02_"4 

o% %urte$t 400 kV circuit and di$$pated in cable 02)

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% %urte$t 400 kV circuit and di$$pated in cable 02)

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable 02)

 ,"02_"5m  (emperature ri$e at te $ur%ace o% cable p roduced by te poer

1 2π

⋅ ρsoil⋅ +400_brc # P$ ⋅ ln

 ,"02_"5 

 ,"02_"6m 

1 2π

⋅ ρsoil⋅ +400_crc # P$ ⋅ ln

(

 ,"02_"6 

)

(

)

o% clo$e$t 400 kV circuit and di$$pated in cable 02)

(emperature ri$e at te $ur%ace o% cable p roduced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable 02)

(

)

(

)

(

)

∆ΘPrc ρsoil , P :=  ∆Θ"02_"1 ρsoil , P + ∆Θ"02_"2 ρsoil , P + ∆Θ"02_"3 ρsoil , P + ∆Θ"02_"4 ρsoil , P ...  + ∆Θ"02_"5 ρsoil , P + ∆Θ"02_"6 ρsoil , P



(

)

(

)



(otal ri$e abo/e ambient temperature at te $ur%ace o% te 02 cable@ o$e ratin i$ bein determined@ cau$ed by te poer di$$pated by te oter cable$ in roup)



 ( Θrc − ∆ΘPrc( ρsoil, P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4m( ρsoil) ) )  !cac_rc⋅ 1 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) 2 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) ( 3 + 4rc( ρsoil) ) 

(

I1132_400rc ρsoil , P :=

(

)

P1132_400rc ρsoil , P :=

(

)

(

)(

(

3 ⋅ 132)

I1132_400rc ρsoil , P ⋅

1000

(

!6rc ρsoil , P := !6c ρsoil , Θc'ro(nd + ∆ΘPrc ρsoil , P

))


(

Pc_400 =

)

I400rc Pc_400 =

(

)

∆ΘPrc ρsr , Pc_400 =

(

)

!6rc ρsr , Pc_400 =

(

)

I1132_400rc ρsr , Pc_400 =

100

144

0.45

0.995

1086

150

217

0.54

0.994

1084

200

289

0.67

0.993

1083

250

361

0.84

0.991

1081

300

433

1.05

0.989

1079

350

505

1.29

0.987

1076

400

577

1.57

0.984

1073

450

650

1.89

0.981

1069

500

722

2.24

0.977

1065

550

794

2.64

0.973

1061

600

866

3.07

0.968

1056

650

938

3.53

0.963

1051

700

1010

4.04

0.958

1045

750

1083

4.58

0.952

1038

800

1155

5.16

0.946

1032

1

c r 6 8 ! : r o t c a 8 n o i t c ( d  !

0.99

(

)

(

)

1032 (A) I1132_400rc ρsr , P400rc = P1132_400rc ρsr , P400rc = 236 (,VA)

0.98

(

!6rc ρ sr , P c_400

) 0.96

0.95

0.94 100

216.7

333.3

450

566.7

683.3

P c_400

ransmission Po;r: <=A

(

+c_rc_final := I1132_400rc ρsr , P400rc

)

2

= 21.394 ⋅ !cac_rc

+s_rc_final := λ 1_rc⋅ +c_rc_final = 0.704 +d_rc_final := +d = 0.49

800

D Re-#ction 4%ctors D1 R4?1 C%$*es in tro#"h &or 5%rio#s !e+ths %n- L%in" )ith inter%cion o& 900 kV circ#its h'ca := 600 , 700 .. 2000

, %02_%1a# hr $ :=

, %02_%1ma # hr $ :=

, %02_%2a# hr $ :=

, %02_%2ma # hr $ :=

, %02_%3a# hr $ :=

, %02_%3ma # hr $ :=

, %02_%4a# hr $ :=

, %02_%4ma # hr $ :=

, %02_%5a# hr $ :=

, %02_%5ma # hr $ :=

, %02_%6a# hr $ :=

, %02_%6ma # hr $ :=

(Variable i$tance$ o% "able$ axi$ %rom round $ur%ace o% 132 kV circuit@ mm)

( ,400b_132_tr + 400_tr )

2

+ ( hr − h'400_tr )

( ,400b_132_tr + 400_tr ) ( ,400b_132_tr )

2

2

2

( ,400a_132_tr + 400_tr )

2

( ,400a_132_tr + 400_tr ) 2

( ,400a_132_tr )

2

2

( ,400a_132_tr − 400_tr )

(di$tance beteen ?02 and ?3@ mm)

2

(di$tance beteen ?02 and mirror imae ?3@ mm)

2


2


2

(di$tance beteen ?02 and ?+@ mm)

2

+ ( hr − h'400_tr )

2

2

+ ( hr + h'400_tr )

+ ( hr + h'400_tr )

( ,400a_132_tr − 400_tr )


+ ( hr + h'400_tr )

+ ( hr − h'400_tr )

2

2

+ ( hr − h'400_tr )

2



+ ( hr − h'400_tr )

( ,400b_132_tr − 400_tr )

2

2

+ ( hr + h'400_tr )

( ,400b_132_tr − 400_tr )


+ ( hr + h'400_tr )

+ ( hr − h'400_tr )

( ,400b_132_tr )

( ,400a_132_tr )

2

2

(di$tance beteen ?02 and mirror imae ?+@ mm)

2

+ ( hr + h'400_tr )

(di$tance beteen ?02 and ?@ mm)

2


I400tra :=

( P400tr ⋅ 1000) (


3 ⋅ 400)

I400tra = 1591

(

)

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e a circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_atra = 27.911

(

) 

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e b circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_btra = 27.182

(

) 

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e c circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_ctra = 27.172

+400_atra := ! A_400_tr ⋅ 1 + λ 1a_tr_400 ⋅ I400tra

+400_btra := ! A_400_tr ⋅ 1 + λ 1b_tr_400 ⋅ I400tra

+400_ctra := ! A_400_tr ⋅ 1 + λ 1c_tr_400 ⋅ I400tra

(

)

∆Θ%02_%1a ρsoil , hr :=

(

)

∆Θ%02_%2a ρsoil , hr :=

(

)

∆Θ%02_%3a ρsoil , hr :=

(

)

∆Θ%02_%4a ρsoil , hr :=

(

)

∆Θ%02_%5a ρsoil , hr :=

(

)

∆Θ%02_%6a ρsoil , hr :=

(

1 2π

1 2π

1 2π

1 2π

1 2π

1 2π

 ,%02_%1ma # hr $ 

⋅ ρsoil⋅ +400_atra ⋅ ln

 ,%02_%1a# hr $   ,%02_%2ma # hr $ 

⋅ ρsoil⋅ +400_btra ⋅ ln

 ,%02_%2a# hr $ 

 ,%02_%3ma # hr $ 

⋅ ρsoil⋅ +400_ctra ⋅ ln

 ,%02_%3a# hr $   ,%02_%4ma # hr $ 

⋅ ρsoil⋅ +400_atra ⋅ ln

 ,%02_%4a# hr $   ,%02_%5ma # hr $ 

⋅ ρsoil⋅ +400_btra ⋅ ln

 ,%02_%5a# hr $ 

 ,%02_%6ma # hr $ 

⋅ ρsoil⋅ +400_ctra ⋅ ln

 ,%02_%6a# hr $ 

)

(

)







(

)

(

)

(

)

∆ΘPtra ρsoil , hr :=  ∆Θ%02_%1a ρsoil , hr + ∆Θ%02_%2a ρsoil , hr + ∆Θ%02_%3a ρsoil , hr + ∆Θ%02_%4a ρsoil , hr ...  + ∆Θ%02_%5a ρsoil , hr + ∆Θ%02_%6a ρsoil , hr



(

)

(

)



(otal ri$e abo/e ambient temperature at te $ur%ace o% te ?02 cable@ o$e ratin i$ bein determined@ cau$ed by te poer di$$pated by te oter cable$ in roup)

(

# hr $ :=

# 2.hr $



(1t_!1 # hr $ := ln (t_!1# hr $ + 

(

)

4trn_!1 ρsoil , hr :=

(

2  (t_!1 # hr $ − 1 

 ρsoil  



2 2 ⋅ hr   # hr $ + ln 1 +

⋅ (1t_!1

 2π  

 str  



 ρsoil  


)  2π  ⋅ (1t_!1# hr $ +  

4trd_!1 ρsoil , hr :=


2 2 ⋅ hr    ⋅ ln 1 +


 

 str  




(

 ( Θtr − ∆ΘPtra( ρsoil, hr ) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4trn_!1( ρsoil, hr ) ) )  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd_!1( ρsoil , hr ) ) 

(

)

I1tr_!1 ρsoil , hr :=

(

)

P1 tr_!1 ρsoil , hr := I1tr_!1 ρsoil , hr U p_132⋅ 10

(

⋅ 3


)  ) I1  132_400tr ( ρsoil , P400tr ) 

!1 t ρsoil , hr :=

h'ca =

−6



(

I1tr_!1 ρsoil , hr

(

)

∆ΘPtra ρst , h'ca =

(

)

!1 t ρst , h'ca =

(

)

I1tr_!1 ρst , h'ca =

(

)

P1tr_!1 ρst , h'ca =

600

4.7

1.139

1104

252

700

5.4

1.101

1067

244

800

6

1.07

1037

237

900

6.6

1.043

1011

231

1000

7.2

1.02

989

226

1100

7.7

1

969

222

1200

8.2

0.982

951

218

1300

8.6

0.966

936

214

1400

9

0.951

922

211

1500

9.4

0.939

910

208

1600

9.7

0.927

899

205

1700

9.9

0.917

889

203

1800

10.1

0.908

880

201

1900

10.3

0.899

872

199

2000

10.5

0.892

864

198

1.14

r t 1.09 1  8 ! : r 1.04 o t c !1 ( ρ , h' ) a t st ca 8 n 0.99 o i t c ( d  0.94 ! 0.89 600

833.3

1066.7

1300

1533.3

h'ca

,pth of cabl circ(it: mm

1766.7

2000

D2 R4Y1 C%$*es in !! crossin" &or 5%rio#s !e+ths  L%in" )ith inter%ction o& 900 kV circ#its h'ca := 3500 , 4000.. 15000

, 02_1a# hr $ :=

, 02_1ma# hr $ :=

, 02_2a# hr $ :=

, 02_2ma# hr $ :=

, 02_3a# hr $ :=

, 02_3ma# hr $ :=

, 02_4a# hr $ :=

, 02_4ma# hr $ :=

, 02_5a# hr $ :=



,400b_132_hdd −

(Variable i$tance$ o% "able$ %rom round $ur%ace@ mm) s hdd 



2



,400b_132_hdd −



s hdd



2



shdd



2



s hdd



2

,400b_132_hdd −



shdd



2

,400b_132_hdd −



,400a_132_hdd −

shdd 





2

,400a_132_hdd −

2

shdd



2

+ ( hr + bl400)

+ ( bl400 − hr )

400_hdd 


2


2



2

2

+ ( hr + bl400)

2


2







−


2



2

2

2



2


+ ( bl400 − hr )

400_hdd 

400_hdd 

s hdd 



,400a_132_hdd −

+

2

2



2

−


+ ( hr + bl400)

400_hdd 

+

2

2



2



,400b_132_hdd −

+ ( hr − hl400)

shdd 



,400b_132_hdd −

2



+

s hdd

+ ( hr − hl400)

2


2

+ ( hr + bl400)

400_hdd 

2

2


2



400_hdd 

+ ( hl400 − hr )

2

(di$tance beteen =02 and =+@ mm)

2 2

, 02_6a# hr $ :=



shdd



2

,400a_132_hdd −

, 02_6ma# hr $ :=

I400hdda :=



s hdd



2

,400a_132_hdd −

( P400hdd⋅ 1000) (

−

400_hdd 

2

+ ( bl400 − hr )



2

400_hdd 

−

2

2

(di$tance beteen =02 and =@ mm)

2



+ ( hr + bl400)

2



3 ⋅ 400)

I400hdda = 820

)

(

+400_hdda := ! A_400_hdd ⋅ 1 + λ 1_hdd_400 ⋅ I400hdda

2

+ +d400 (9$timated lo$$e$ in te 400 kV pa$e a circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_hdda = 8.292

(

)

∆Θ02_1a ρsoil , hr :=

(

)

∆Θ02_2a ρsoil , hr :=

(

)

∆Θ02_3a ρsoil , hr :=

(

)

∆Θ02_4a ρsoil , hr :=

(

)

∆Θ02_5a ρsoil , hr :=

(

)

∆Θ02_6a ρsoil , hr :=

(

1 2π

1 2π

1 2π

1 2π

1 2π

1 2π

 ,02_1ma# hr $ 

⋅ ρsoil⋅ +400_hdda ⋅ ln

 ,02_1a# hr $   ,02_2ma# hr $ 


 ,02_2a# hr $   ,02_3ma# hr $ 


 ,02_3a# hr $   ,02_4ma# hr $ 


 ,02_4a# hr $   ,02_5ma# hr $ 


 ,02_5a# hr $   ,02_6ma# hr $ 


 ,02_6a# hr $ 

)

(

)

(emperature ri$e at te $ur%ace o% cable produced by te poer o% %urte$t 400 kV circuit and di$$pated in cable =02)



(emperature ri$e at te $ur%ace o% cable produced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable =02)

(emperature ri$e at te $ur%ace o% cable produced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable y02)

(emperature ri$e at te $ur%ace o% cable produced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable =02)

(

)

(

)

(

)

∆ΘPhdda ρsoil , hr :=  ∆Θ02_1a ρsoil , hr + ∆Θ02_2a ρsoil , hr + ∆Θ02_3a ρsoil , hr + ∆Θ02_4a ρsoil , hr ...  + ∆Θ02_5a ρsoil, hr + ∆Θ02_6a ρsoil, hr



(

)

(

)



(otal ri$e abo/e ambient temperature at te $ur%ace o% te =02 cable@ o$e ratin i$ bein determined@ cau$ed by te

hl_!>1# hr $ := hr − s hdd⋅

bl_!>1# hr $ := hr + s hdd⋅

(!>1# hr $ :=

3


3 3


6

2. bl_!>1# hr $

(u#F2 i$ calculated it re%erence to te centre line o% te deepe$t

do pip_hdd



(1c_!>1 # hr $ := ln (!>1# hr $ + 

(

(

!>1# hr $

2

   ρsoil ( 1c_!2 # hr $ + ln 2π    

)

43c_!>1 ρsoil , hr :=

(

duct$(non
 

−1

 2 2  # 2 bl_!>1# hr $ $ + ( s hdd)  + ln   shdd   

)

(

 2  # 2 hl_!>1# hr $ $ + 2    2 s 2  hdd   # bl_!>1# hr $ − hl_!>1 # hr $ $ +  2    shdd 

2

)

4c_!>1 ρsoil , hr := 41hdd + 42hdd + 43c_!>1 ρsoil , hr

9xternal ermal #e$i$tance %or current ratin calculation in @ .m6;



(

 ( Θhdd − ∆ΘPhdda( ρsoil , hr ) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4c_!>1 ( ρsoil, hr ) ) )  !cac_hdd ⋅ 1 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) 2 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) ( 3 + 4c_!>1 ( ρsoil , hr ) ) 

(

)

I1hdd_!>1 ρsoil , hr :=

(

)

P1 hdd_!>1 ρsoil , hr := I1hdd_!>1 ρsoil , hr U p_132⋅ 10

(

)

!>1t ρsoil , hr :=

)   I1132_400hdd ( ρsoil , P400hdd)  

(

I1hdd_!>1 ρsoil , hr

−6

⋅ 3


h'ca =

(

)

∆ΘPhdda ρhdd , h'ca =

(

)

I1hdd_!>1 ρhdd , h'ca =

3500

5.7

942

4000

6.5

921

4500

7.2

901

5000

8

884

5500

8.7

868

6000

9.3

854

6500

9.9

842

7000

10.3

832

7500

10.5

824

8000

10.6

818

8500

10.6

814

9000

10.5

811

9500

10.3

810

10000

10

808

10500

9.8

808

11000

9.5

807

11500

9.2

807

12000

8.9

807

12500

8.7

807

13000

8.4

807

13500

8.1

807

14000

7.9

807

14500

7.7

807

15000

7.4

807

(

)

!>1t ρhdd , h'ca = 1.138 1.112 1.089 1.068 1.049 1.032 1.018 1.005 0.996 0.989 0.984 0.98 0.978 0.977 0.976 0.976 0.975 0.975 0.975 0.975 0.975 0.975 0.975 0.975

1.14

d d h 1.11 1 > 8 ! : 1.07 r o t !>1 ( ρ , h' ) c t hdd ca a 8 1.04 n o i t c ( d 1  ! 0.97 3500

5416.7

7333.3

9250 h'ca

11166.7

13083.3

15000

(

)

P1hdd_!>1 ρhdd , h'ca = 215 210 206 202 199 195 193 190 188 187 186 185 185 185 185 185 185 185 185 185 185 185 185 185

D3 R481 C%$*es in -#ct$%nk &or ro%- crossin" &or 5%rio#s !e+ths %n- L%in" )ith inter%ction o& 900 kV circ#its h'ca := 750 , 1000 .. 3000

, "02_"1a# hr $ :=

, "02_"1ma # hr $ :=

, "02_"2a# hr $ :=

, "02_"2ma # hr $ :=

, "02_"3a# hr $ :=

, "02_"3ma # hr $ :=

, "02_"4a# hr $ :=

, "02_"4ma # hr $ :=

, "02_"5a# hr $ :=

, "02_"5ma # hr $ :=

, "02_"6a# hr $ :=

(Variable i$tance$ o% "able$ axi$ %rom round $ur%ace@ mm)

( ,400b_132_rc + 400_rc )

2

+ ( hr − h'400_rc )

( ,400b_132_rc + 400_rc ) ( ,400b_132_rc )

2

2

2

( ,400a_132_rc + 400_rc )

2

( ,400a_132_rc + 400_rc ) 2

( ,400a_132_rc )

2

)

(di$tance beteen 02 and mirror imae 2@ mm)

+ ( hr − h'400_rc )

2


(

2


2


2


2

(di$tance beteen 02 and +@ mm)

2

+ ( hr − h'400_rc )

2

2

+ ( hr + h'400_rc )

+ ( hr + h'400_rc )

2

2

+ ( hr + h'400_rc )

+ ( hr − h'400_rc )

( ,400a_132_rc − 400_rc ) (

2



+ ( hr − h'400_rc )

( ,400b_132_rc − 400_rc )

2

2

+ ( hr + h'400_rc )

( ,400b_132_rc − 400_rc )


+ ( hr + h'400_rc )

+ ( hr − h'400_rc )

( ,400b_132_rc )

( ,400a_132_rc )

2

2

(di$tance beteen 02 and mirror imae +@ mm)

2

(di$tance beteen 02 and @ mm)

)

2

I400rca :=

⋅ ( P400rc 1000 )

(


3 ⋅ 400)

I400rca = 1155

(

)

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e a circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_arca = 15.209

(

) 

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e b circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_brca = 14.827

(

) 

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e c circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_crca = 14.822

+400_arca := ! A_400_rc ⋅ 1 + λ 1a_rc_400 ⋅ I400rca

+400_brca := ! A_400_rc ⋅ 1 + λ 1b_rc_400 ⋅ I400rca

+400_crca := ! A_400_rc ⋅ 1 + λ 1c_rc_400 ⋅ I400rca

(

)

∆Θ"02_"1a ρsoil , hr :=

(

)

∆Θ"02_"2a ρsoil , hr :=

(

)

∆Θ"02_"3a ρsoil , hr :=

(

)

∆Θ"02_"4a ρsoil , hr :=

(

)

∆Θ"02_"5a ρsoil , hr :=

(

)

∆Θ"02_"6a ρsoil , hr :=

 ,"02_"1ma # hr $ 

1 2π

⋅ ρsoil⋅ +400_arca ⋅ ln

 ,"02_"1a# hr $   ,"02_"2ma # hr $ 

1 2π

⋅ ρsoil⋅ +400_brca ⋅ ln

 ,"02_"2a# hr $ 

 ,"02_"3ma # hr $ 

1 2π

⋅ ρsoil⋅ +400_crca ⋅ ln

 ,"02_"3a# hr $   ,"02_"4ma # hr $ 

1 2π

⋅ ρsoil⋅ +400_arca ⋅ ln

 ,"02_"4a# hr $   ,"02_"5ma # hr $ 

1 2π

⋅ ρsoil⋅ +400_brca ⋅ ln

 ,"02_"5a# hr $ 

 ,"02_"6ma # hr $ 

1 2π

⋅ ρsoil⋅ +400_crca ⋅ ln

(

 ,"02_"6a# hr $ 

)

(

)

(emperature ri$e at te $ur%ace o% cable produced by te poer o% %urte$t 400 kV circuit and di$$pated in cable 02)



(emperature ri$e at te $ur%ace o% cable produced by te poer o% clo$e$t 400 kV circuit and di$$pated in cable 02)



(

)

(

)

(

)

∆ΘPrca ρsoil , hr :=  ∆Θ"02_"1a ρsoil , hr + ∆Θ"02_"2a ρsoil , hr + ∆Θ"02_"3a ρsoil , hr + ∆Θ"02_"4a ρsoil , hr ...  + ∆Θ"02_"5a ρsoil, hr + ∆Θ"02_"6a ρsoil , hr



(

)

(

)



(otal ri$e abo/e ambient temperature at te $ur%ace o% te 02 cable@ o$e ratin i$ bein determined@ cau$ed by te poer di$$pated by te oter cable$ in roup)



∆h',-_!)1# hr $ := hr +



do



+ pip_rc − do pip_rc − 200 + ,t 2 

∆h',-_!)1# hr $

(,-_!)1# hr $ :=

r b

 2  /  )  2π  ⋅ ( ρsoil − ρconcrt ) ⋅ ln(,-_!)1# hr $ +  (,-_!)1# hr $

(

4r_corr_!)1 ρsoil , hr :=

(rc_!)1 # hr $ :=

 

−1

2hr do pip_rc



(1rc_!)1 # hr $ := ln (rc_!)1# hr $ + 

(

)

43rn_!)1 ρ soil , hr :=

2  (rc_!)1# hr $ − 1 




⋅ (1rc_!)1

 

2π

2 2⋅ hr   # hr $ + ln 1 + + 4





s tr

 

(

)

r_corr_!)1 ρsoil , hr


(


) 

43rd_!)1 ρsoil , hr :=

2π

⋅ (1rc_!)1 # hr $ +

 

+ 4r_corr_!)1 ( ρsoil , hr )

 1 + 0.5⋅ ( λ 1a_rc ( Θms , src , !cac_rc) + λ 1c_rc ( Θms , src , !cac_rc) )  

( 1 + λ 1b_rc ( Θms , src, !cac_rc) )



2 2 ⋅ hr    ⋅ ln 1 +

 



s tr

 


(

)

(

)


(

)

(

)


4rn_!)1 ρsoil , hr := 41rc + 42rc + 43rn_!)1 ρsoil , hr

4rd_!)1 ρsoil , hr := 41rc + 42rc + 43rd_!)1 ρsoil , hr



 ( Θrc − ∆ΘPrca( ρsoil, hr ) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4rn_!)1 ( ρsoil, hr ) ) I1rc_!)1( ρsoil , hr ) :=  !cac_rc⋅ 1 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) 2 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) ( 3 + 4rd_!)1 ( ρsoil , hr ) ) 

(

)

(

)

(

)  )

P1 rc_!)1 ρsoil , hr := I1rc_!)1 ρsoil , hr U p_132⋅ 10

(

)

!)1t ρsoil , hr :=

 I1

I1rc_!)1 ρsoil , hr

(

P

−6

⋅ 3


...

h'ca =

(

)

∆ΘPrca ρsr , h'ca =

(

)

(

!)1t ρsr , h'ca =

)

(

I1rc_!)1 ρsr , h'ca =

750

3.337

1.062

1095

250

1000

4.282

1.007

1039

237

1250

5.094

0.967

998

228

1500

5.76

0.937

966

221

1750

6.274

0.913

942

215

2000

6.648

0.894

923

211

2250

6.898

0.879

907

207

2500

7.047

0.867

894

204

2750

7.115

0.857

884

202

3000

7.122

0.848

875

200

1.1

c r 1.05 1 ) 8 ! : r 1 o t c !)1 ( ρ , h' ) a t sr ca 8 n 0.94 o i t c ( d  0.89 ! 0.84 750

1125

1500

1875

2250

h'ca

,pth of cabl circ(it: mm

2625

)

P1rc_!)1 ρsr , h'ca =

3000

D9 R4?2 C%$*es in tro#"h &or 5%rio#s soi* resisti5iti )ith inter%cion o& 900 kV circ#its

ρsoil := 0.8, 0.9 .. 2.3




 ( Θtr − ∆ΘPtr ( ρsoil, P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4trn( ρsoil) ) )  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd( ρsoil) ) 

(

I1tr_!2 ρsoil , P :=

(

)

P1 tr_!2 ρsoil , P :=

(

)

!2 t ρsoil , P :=

ρsoil =

)(

(

3 ⋅ 132)

I1tr_!2 ρsoil , P ⋅

1000

(

) I1132_400tr ( ρst , P)

I1tr_!2 ρsoil , P

(


)

!2 t ρsoil , P400tr =

(

)

I1tr_!2 ρsoil , P400tr =

(

)

P1tr_!2 ρsoil , P400tr =

0.8

1.208

1171

268

0.9

1.147

1112

254

1

1.093

1059

242

1.1

1.044

1012

231

1.2

1

969

222

1.3

0.96

930

213

1.4

0.923

895

205

1.5

0.889

862

197

1.6

0.857

831

190

1.7

0.828

802

183

1.8

0.8

776

177

1.9

0.774

750

172

2

0.75

727

166

2.1

0.727

704

161

2.2

0.705

683

156

2.3

0.684

663

151

1.2

1.1

r t 2  8 ! : 1 r o t c !2 ( ρ , P a t soil 400tr ) 8 n o 0.8 i t c ( d  ! 0.7

0.6 0.8

1.1

1.3

1.6

1.8

2.1

2.3

ρ soil

oil thrmal rsisti&it: ?.m@+

D@ R4Y2 C%$*es in !! crossin" &or 5%rio#s soi* resisti5it )ith inter%cion o& 900 kV circ#its

ρsoil := 0.8, 0.9 .. 2.3




 ( Θhdd − ∆ΘPhdd ( ρsoil , P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4hdd( ρsoil) ) )  !cac_hdd ⋅ 1 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) 2 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) ( 3 + 4hdd( ρsoil) ) 

(

I1hdd_!>2 ρsoil , P :=

(

)

P1 hdd_!>2 ρsoil , P :=

(

)

!>2t ρsoil , P :=

(

)(

I1132_400hdd ρsoil , P ⋅

3 ⋅ 132)

1000

( (

I1hdd_!>2 ρsoil , P

) )


ρsoil =

(

)

(

!>2t ρsoil , P400hdd =

)

I1hdd_!>2 ρsoil , P400hdd =

(

0.8

1.12

927

212

0.9

1.057

875

200

1

1

828

189

1.1

0.949

785

180

1.2

0.902

747

171

1.3

0.859

711

163

1.4

0.819

678

155

1.5

0.782

648

148

1.6

0.748

619

142

1.7

0.715

592

135

1.8

0.685

567

130

1.9

0.656

543

124

2

0.628

520

119

2.1

0.601

498

114

2.2

0.576

476

109

2.3

0.551

456

104

1.1

1

d d h 2 > 8 ! 0.9 : r o t c !>2t( ρsoil , P400hdd ) a 8 n 0.8 o i t c ( d  ! 0.7

0.6 0.8

1.1

1.3

1.6

1.8

ρ soil


2.1

2.3

)

P1hdd_!>2 ρsoil , P400hdd =

D; R482 C%$*es in !#ct $%nk &or crossin" &or 5%rio#s soi* resisti5it )ith inter%cion o& 900 kV circ#its ρsoil := 0.8, 0.9 .. 2.3




 ( Θrc − ∆ΘPrc( ρsoil , P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4m( ρsoil) ) )  !cac_rc⋅ 1 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) 2 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) ( 3 + 4rc( ρsoil) ) 

(

I1rc_!)2 ρsoil , P :=

(

)

P1 rc_!)2 ρsoil , P :=

(

)

!)2t ρsoil , P :=

ρsoil =

)(

(

I1132_400rc ρsoil , P ⋅

3⋅ 132)

1000

(

) I1132_400rc ( ρsr , P) I1rc_!)2 ρsoil , P

(


)

!)2t ρsoil , P400rc =

(

)

I1rc_!)2 ρsoil , P400rc =

(

P1rc_!)2 ρsoil , P400rc

0.8

1.13

1165

266

0.9

1.094

1128

258

1

1.06

1094

250

1.1

1.029

1062

243

1.2

1

1032

236

1.3

0.973

1003

229

1.4

0.947

977

223

1.5

0.923

952

218

1.6

0.899

928

212

1.7

0.878

905

207

1.8

0.857

884

202

1.9

0.837

863

197

2

0.818

844

193

2.1

0.8

825

189

2.2

0.783

807

185

2.3

0.766

790

181

)

=

1.13

1.06

c r 2 ) 8 ! 0.98 : r o t c !)2 ( ρ , P a t soil 400rc) 8 n o 0.91 i t c ( d  ! 0.83

0.76 0.8

1.1

1.3

1.6

1.8

2.1

2.3

ρ soil


D> R4?3 C%$*es in tro#"h &or 5%rio#s soi* tem+er%t#res )ith inter%cion o& 900 kV circ#its Θ'ro(nd := 30 , 31 .. 50

(

)

Θ!3 Θ'ro(nd := Θma% − Θ'ro(nd



( Θ!3 ( Θ'ro(nd) − ∆ΘPtr ( ρsoil , P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4trn( ρsoil) )  )  !cac_tr ⋅ 1 + n⋅ !cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd( ρsoil) ) 

(

I1tr_!3 ρsoil , P , Θ'ro(nd :=

(

)

P1 tr_!3 ρsoil , P , Θ'ro(nd :=

(

)

!3 t ρsoil , P , Θ'ro(nd :=

)(

(

I1tr_!3 ρsoil , P , Θ'ro(nd ⋅

3 ⋅ 132)

1000

(

I1tr_!3 ρsoil , P , Θ'ro(nd

(

I1132_400tr ρsoil , P

)

)


Θ'ro(nd =

(

)

!3 t ρst , P400tr , Θ'ro(nd =

(

)

(

30

1.114

1080

247

31

1.103

1070

245

32

1.092

1059

242

33

1.081

1048

240

34

1.07

1037

237

35

1.059

1026

235

36

1.047

1015

232

37

1.036

1004

229

38

1.024

992

227

39

1.012

981

224

40

1

969

222

41

0.988

957

219

42

0.976

946

216

43

0.963

933

213

44

0.95

921

211

45

0.938

909

208

46

0.925

896

205

47

0.911

883

202

48

0.898

870

199

49

0.885

857

196

50

0.871

844

193

1.12

r 1.07 t 3  8 ! : r 1.02 o t c !3 ( ρ , P a t st 400tr , Θ'ro(nd ) 8 n 0.97 o i t c ( d  ! 0.92

0.87 30

33.3

)

I1tr_!3 ρst , P400tr , Θ'ro(nd = P1tr_!3 ρst , P400tr , Θ'ro(nd =

36.7

40

43.3

Θ'ro(nd

oil mprat(r: ?

46.7

50

D< R4Y3 C%$*es in !! crossin" &or 5%rio#s soi* tem+er%t#res )ith inter%cion o& 900 kV circ#its Θ'ro(nd := 30 , 31 .. 50

(

)

Θ!>3 Θ'ro(nd := Θma% − Θ'ro(nd

( Θ!>3( Θ'ro(nd) − ∆ΘPhdd( ρsoil, P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4hdd( ρsoil) )  )  !cac_hdd ⋅ 1 + n⋅!cac_hdd ⋅ ( 1 + λ 1_hdd) 2 + n⋅ !cac_hdd ⋅ ( 1 + λ 1_hdd) ( 3 + 4hdd( ρsoil) ) 

Θ'ro(nd := 30 , 31 .. 50 I1hdd_!>3 ρsoil , P , Θ'ro(nd :=

(

(

)

P1 hdd_!>3 ρsoil , P , Θ'ro(nd :=

(

)

!>3t ρsoil , P , Θ'ro(nd :=

Θ'ro(nd =



)(

(

I1hdd_!>3 ρsoil , P , Θ'ro(nd ⋅

1000

(

I1hdd_!>3 ρsoil , P , Θ'ro(nd

(

I1132_400hdd ρsoil , P

(

3 ⋅ 132)

)


) )

!>3t ρhdd , P400hdd , Θ'ro(nd =

(

)

(

I1hdd_!>3 ρhdd , P400hdd , Θ'ro(nd =P1hdd_!>3 ρhdd , P400hdd , Θ'ro(nd

30

1.123

929

212

31

1.111

920

210

32

1.099

910

208

33

1.087

900

206

34

1.075

890

204

35

1.063

880

201

36

1.051

870

199

37

1.038

859

196

38

1.026

849

194

39

1.013

838

192

40

1

828

189

41

0.987

817

187

42

0.974

806

184

43

0.96

795

182

44

0.946

783

179

45

0.932

772

176

46

0.918

760

174

47

0.904

748

171

48

0.89

736

168

49

0.875

724

166

50

0.86

712

163

)

1.12

d d 1.07 h 3 > 8 ! 1.02 : r o t !>3 ( ρ , P c t hdd 400hdd , Θ'ro(nd ) a 8 0.96 n o i t c ( d  0.91 ! 0.86 30

33.3

36.7

40

43.3

46.7

50

Θ'ro(nd


DD R483 C%$*es in !#ct $%nk &or crossin" &or 5%rio#s soi* tem+er%t#res )ith inter%cion o& 900 kV circ#its Θ'ro(nd := 30 , 31 .. 50

(

)

Θ!)3 Θ'ro(nd := Θma% − Θ'ro(nd



( Θ!)3( Θ'ro(nd) − ∆ΘPrc( ρsoil, P) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4m( ρsoil) )  I1rc_!)3( ρsoil , P , Θ'ro(nd ) :=  !cac_rc⋅ 1 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) 2 + n⋅!cac_rc⋅ ( 1 + λ 1_rc) ( 3 + 4rc( ρsoil) )  (

)

P1 rc_!)3 ρsoil , P , Θ'ro(nd :=

(

)

!)3t ρsoil , P , Θ'ro(nd :=

)(

(

I1rc_!)3 ρsoil , P , Θ'ro(nd ⋅

3 ⋅ 132)

1000

(

I1rc_!)3 ρsoil , P , Θ'ro(nd

(

I1132_400rc ρsoil , P

)

)


Θ'ro(nd =

(

)

!)3t ρsr , P400rc , Θ'ro(nd =

(

)

I1rc_!)3 ρsr , P400rc , Θ'ro(nd =

(

30

1.108

1143

261

31

1.098

1132

259

32

1.087

1122

256

33

1.077

1111

254

34

1.066

1100

251

35

1.055

1089

249

36

1.045

1078

246

37

1.034

1066

244

38

1.022

1055

241

39

1.011

1043

239

40

1

1032

236

41

0.989

1020

233

42

0.977

1008

230

43

0.965

996

228

44

0.953

984

225

45

0.941

971

222

46

0.929

959

219

47

0.917

946

216

48

0.904

933

213

49

0.892

920

210

50

0.879

907

207

1.12

d 1.07 d h 3 > 8 ! 1.02 : r o t c !>3t( ρ hdd , P400hdd , Θ'ro(nd ) a 8 n 0.97 o i t c ( d  ! 0.92

0.87 30

33.3

36.7

40

43.3

Θ'ro(nd


46.7

50

)

P1rc_!)3 ρsr , P400rc , Θ'ro(nd =

D10 R4?9 C%$*es in tro#"h &or 5%rio#s c%$*e se+%r%tion )ith inter%cion o& 900 kV circ#its s ca := 200 , 250 .. 600

( )

, %02_%1b s ca :=

( )

, %02_%1mb s ca :=

( )

, %02_%2b s ca :=

( )

, %02_%2mb s ca :=

( )

, %02_%3b s ca :=

( )

, %02_%3mb s ca :=

( )

, %02_%4b s ca :=

( )

, %02_%4mb s ca :=

( )

, %02_%5b s ca :=

( )

, %02_%5mb s ca :=

( )

, %02_%6b s ca :=

( )

, %02_%6mb s ca :=

( ,400b_132_tr + sca)

2

( ,400b_132_tr + sca) ( ,400b_132_tr )

2

( ,400b_132_tr )

2

2

( ,400a_132_tr + sca)

2

( ,400a_132_tr + sca)

( ,400a_132_tr )

2

2

( ,400a_132_tr − sca)



2


2


2


2

(di$tance beteen ?02 and ?+@ mm)

2

+ ( h'1ca_tr − h'400_tr ) 2

2

+ ( h'1ca_tr + h'400_tr )

+ ( h'1ca_tr + h'400_tr )

( ,400a_132_tr − sca)


2

+ ( h'1ca_tr + h'400_tr )

+ ( h'1ca_tr − h'400_tr )

2


+ ( h'1ca_tr − h'400_tr )

2


2

+ ( h'1ca_tr − h'400_tr )

2

2

+ ( h'1ca_tr + h'400_tr )

+ ( h'1ca_tr + h'400_tr )

( ,400b_132_tr − sca)

2

2

+ ( h'1ca_tr − h'400_tr )

( ,400b_132_tr − sca)

( ,400a_132_tr )

+ ( h'1ca_tr − h'400_tr )

(di$tance beteen ?02 and mirror imae ?+@ mm)

2

+ ( h'1ca_tr + h'400_tr )



I400trb :=

⋅ ( P400tr 1000 )

(

("urrent in te 400 circuit a$ a %unction o% te tran$mitted poer@ A)

3⋅ 400)

I400trb = 1591

) 

(

+400_atrb := ! A_400_tr ⋅ 1 + λ 1a_tr_400 ⋅ I400trb

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e a circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_atrb = 27.911

)

(

+400_btrb := ! A_400_tr ⋅ 1 + λ 1b_tr_400 ⋅ I400trb

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e b circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_btrb = 27.182

) 

(

+400_ctrb := ! A_400_tr ⋅ 1 + λ 1c_tr_400 ⋅ I400trb

2

+ +d400

(9$timated lo$$e$ in te 400 kV pa$e c circuit a$ a %unction o% te tran$mitted poer 5 at 400 kV@ ;6m) +400_ctrb = 27.172

(

)

∆Θ%02_%1b ρsoil , sca :=

(

)


(

)


(

)


(

)


(

)


(

1 2π

1 2π

1 2π

1 2π

1 2π

1 2π

 ,%02_%1mb( s ca)  (emperature ri$e at te $ur%ace o% cable produced by te poer

⋅ ρsoil⋅ +400_atrb ⋅ ln

 ,%02_%1b ( sca) 

o% %urte$t 400 kV circuit and di$$pated in cable ?02)


⋅ ρsoil⋅ +400_btrb ⋅ ln

 ,%02_%2b ( sca) 



⋅ ρsoil⋅ +400_ctrb ⋅ ln

 ,%02_%3b ( sca) 



⋅ ρsoil⋅ +400_atrb ⋅ ln

 ,%02_%4b ( sca) 

o% clo$e$t 400 kV circuit and di$$pated in cable ?02)


⋅ ρsoil⋅ +400_btrb ⋅ ln

 ,%02_%5b ( sca) 



⋅ ρsoil⋅ +400_ctrb ⋅ ln

 ,%02_%6b ( sca) 

)

(

)


(

)

(

)

(

)

∆ΘPtrb ρsoil , sca :=  ∆Θ%02_%1b ρsoil , sca + ∆Θ%02_%2b ρsoil , sca + ∆Θ%02_%3b ρsoil , sca + ∆Θ%02_%4b ρsoil , sca ...  + ∆Θ%02_%5b ρsoil , sca + ∆Θ%02_%6b ρsoil , sca



(

)

(

)

(otal ri$e abo/e ambient temperature at te $ur%ace o% te ?02 cable@ o$e ratin i$ bein determined@ cau$ed by te



( 2.h'1ca_tr )

(t_!7b :=

do



(1t_!7b := ln (t_!7b + 

(

)

4trn_!7b ρsoil , sca :=

(

)

4trd_!7b ρsoil , sca :=

2  (t_!7b − 1 

 ρsoil  



 2π  



 ρsoil  


⋅ (1t_!7b + ln 1 +

⋅ ( (1t_!7b ) +

 2π  

2  2⋅ h'1 ca_tr  



s ca


 




⋅ ln 1 +

 

2  2⋅ h'1 ca_tr  



s ca




(

 ( Θtr − ∆ΘPtrb( ρsoil, sca) ) − +d⋅ 0.51 + n⋅ ( 2 + 3 + 4trn_!7b( ρsoil , sca) ) )  !cac_tr ⋅ 1 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) 2 + n⋅!cac_tr ⋅ ( 1 + λ 1_tr ) ( 3 + 4trd_!7b ( ρsoil , sca) ) 

(

)

I1tr_!4 ρsoil , sca :=

(

)

P1 tr_!4 ρsoil , sca := I1tr_!4 ρsoil , sca U p_132⋅ 10

⋅ 3


( )  ) I1  132_400tr ( ρsoil , P400tr ) 

(

!4 c ρ soil , sca :=

s ca =

−6



I1c_!7 ρsoil , sca

(

)

!4 c ρst , sca =

(

)

I1tr_!4 ρst , sca =

(

)

P1tr_!4 ρst , sca =

200

1.089

974

223

250

1.113

995

228

300

1.134

1014

232

350

1.152

1029

235

400

1.169

1043

239

450

1.184

1056

241

500

1.197

1068

244

550

1.21

1078

246

600

1.222

1088

249

 

POWER CABLE IMPE!A'CE CALC.LATIO'(

Mathcad - Ampacity Calculation

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