This document discusses voltage drop calculation in cable lines. It provides information on the data required to start calculations, including cable parameters, load characteristics, installation scheme, and maximum allowed voltage drop. It then covers calculations for simple radial lines under conditions of constant current and constant power. For constant current, the voltage drop is calculated based on cable resistance and reactance, line length, and load current. For constant power, an iterative method is used to calculate the voltage at the end of the line based on load power and reactive power. Sample calculations are shown for both cases.

1. Angelo Baggini, angelo.baggini@unibg.it, Bergamo University - Engineering Department
Via Marconi 5, 24044 Dalmine (BG) – Italy
Voltage drop calculation in cable lines

2. Voltage drop calculation in cable lines
1. Data required to start
A. Cable parameters
B. Load characteristics
C. Distribution Scheme
D. Maximum voltage drop
2. Voltage drop calculation
in case of:
A. Radial line
1. constant current
2. constant power
B. Shunted line
C. Long line

3. Voltage drop calculation in cable lines
Data required to start

4. Data required to start
1. Cable parameters (affecting voltage drop)
• R Resistance
• X Reactance
• C Capacitance
• G Conducance
2. Load characteristics
• Impedance
• Power
• Current
3. Installation characteristics
• System type, rated frequency and voltage
• Line length (L)
• Type of distribution
4. Maximum allowed voltage drop
• technical standards
• proper working conditions of loads
• steady state conditions - transient conditions

5. Voltage drop calculation in cable lines
Data required to start
Cable parameters
A

6. Data required to start
Cable parameters
R L

7. Data required to start
Cable parameters
R L
C

8. Data required to start
Cable parameters
R L
C G

9. Data required to start
Cable parameters – Long lines
R L
C
R L
C G
R L
R L
C
R L
C G
R L
R L
R L
C G
R L
…
…
…

10. Data required to start
Cable parameters
R L
C
R L
C G
R L

11. Data required to start
Cable parameters
R
𝑅𝑅 = ρ(θ)
1
𝑆𝑆
(Ω/m)
𝐿𝐿 =
µ
2π
𝑙𝑙𝑙𝑙
2𝐷𝐷
𝑑𝑑
(H/m)
L
D
d

12. Data required to start
Cable parameters
G
C 𝐶𝐶 =
2πε
𝑙𝑙 𝑙𝑙
2𝐷𝐷
𝑑𝑑
(F/m)
D
d

13. T(r)=90°C
Data required to start
LV Cable parameters
Rated
section
(mm2)
d.c.
(Ohm/km)
a.c.
(Ohm/km)
d.c.
(Ohm/km)
a.c.
(Ohm/km)
Flexible
conductor
Flexible
conductor
Rigid
conductor
Rigid
conductor
1.5 16.95 16.95 15.4 15.4
2.5 10.17 10.17 9.45 9.45
4 6.31 6.31 5.88 5.88
6 4.20 4.20 3.93 3.93
10 2.43 2.43 2.33 2.33
16 1.54 1.54 1.47 1.47
25 0.99 0.99 0.93 0.93

14. F=50 Hz
Data required to start
LV Cable parameters
Rated
section
(mm2)
Unipolar
(Ohm/km)
Multipolar
(Ohm/km)
Unipolar
(Ohm/km)
Multipolar
(Ohm/km)
G-SETTE G-SETTE G-SETTE + G-SETTE +
1.5 0.146 0.103 0.144 0.100
2.5 0.135 0.095 0.132 0.094
4 0.126 0.090 0.122 0.087
6 0.118 0.085 0.144 0.083
10 0.106 0.079 0.105 0.078
16 0.099 0.076 0.098 0.075
25 0.095 0.075 0.093 0.074
Elastomeric insulation

15. (Data required to start)
Service reactance
Theoretically only for …
Practically …
R L M
33323213133
323222121222
31321211111
ILjIMjIMjIRE
IMjILjIMjIRE
IMjIMjILjIRE
⋅+⋅+⋅+⋅=
⋅+⋅+⋅+⋅=
⋅+⋅+⋅+⋅=
ωωω
ωωω
ωωω ( )( )
( )( )
( )( ) 3333
2
33
22
2
2222
111
2
111
IMLjRILjIMjIMjIRE
IMLjRIMjILjIMjIRE
IMLjRIMjIMjILjIRE
SSSSS
SSSSS
SSSSS
⋅−+=⋅+⋅⋅+⋅⋅+⋅=
⋅−+=⋅⋅+⋅+⋅⋅+⋅=
⋅−+=⋅⋅+⋅⋅+⋅+⋅=
ωωαωαω
ωαωωαω
ωαωαωω
SMLL S −=

16. MV cable resitance
(50 Hz – 90 °C)
Source Prismyan catalogue 2014

17. MV cable reactance
(50 Hz – 90 °C)
Source Prismyan catalogue 2014

18. MV cable reactance
(50 Hz – 90 °C)
Source Prismyan catalogue 2014

19. MV cable reactance
(50 Hz – 90 °C)
Source Prismyan catalogue 2014

20. MV HEPR cable capacitance
Source Prismyan catalogue 2014

21. Voltage drop calculation in cable lines
Data required to start
Load type
B

22. Load type
Costant impendance
Constant power
… statistically also the ones at costant impedance became at constant power
… sometime loads are considered having a constant current
Z

23. Voltage drop calculation in cable lines
Data required to start
Installation characteristics
C

24. Distribution scheme
Simple radial
Shunted
Rated frequency and voltage
LOAD
LOAD 3LOAD 2LOAD 1
L
L3L2L1

25. Voltage drop calculation in cable lines
Data required to start
Maximum allowed voltage drop
D

26. Data required to start
Maximum allowed voltage drop
Technical standards
• LV Utilization: IEC 60364
• 4% general loads
• 5% lighting
Proper working conditions of loads
• Steady state conditions
• 2% ?
• Transient conditions
• 10% ?
(indirect reference to EN 50160)

27. Voltage drop calculation in cable lines
Simple radial scheme
Constant current

28. Voltage drop calculation
Simple radial scheme - Constant current
AC
DC
RAC L
RAC L
RDC

29. Voltage drop calculation
Simple radial scheme - Constant current
AC
∆V = K L I (RAC cosϕ + X sinϕ) < ∆VM
K = 2 for single-phase lines
K = √(3) for tree-phase lines
DC
∆V = 2 L I RDC
• Cable R and X
• Line length (L)
• Load Current I (standard)
• Phase displacement (ϕ) (standard)

30. Load
I=50 A, 400 V 3 phase
Installation
T=40 °C
L=100 m
Maximum Voltage drop
steady-state 2%
inrush 10%
Cable Type
3 conductors – EPR
Voltage drop calculation
Simple radial scheme - Constant current

31. T(r)=90°C
Voltage drop calculation
Simple radial scheme - Constant current
Rated
section
(mm2)
d.c.
(Ohm/km)
a.c.
(Ohm/km)
d.c.
(Ohm/km)
a.c.
(Ohm/km)
Flexible
conductor
Flexible
conductor
Rigid
conductor
Rigid
conductor
1.5 16.95 16.95 15.4 15.4
2.5 10.17 10.17 9.45 9.45
4 6.31 6.31 5.88 5.88
6 4.20 4.20 3.93 3.93
10 2.43 2.43 2.33 2.33
16 1.54 1.54 1.47 1.47
25 0.99 0.99 0.93 0.93

32. F=50 Hz
Voltage drop calculation
Simple radial scheme - Constant current
Rated
section
(mm2)
Unipolar
(Ohm/km)
Multipolar
(Ohm/km)
Unipolar
(Ohm/km)
Multipolar
(Ohm/km)
G-SETTE G-SETTE G-SETTE + G-SETTE +
1.5 0.146 0.103 0.144 0.100
2.5 0.135 0.095 0.132 0.094
4 0.126 0.090 0.122 0.087
6 0.118 0.085 0.144 0.083
10 0.106 0.079 0.105 0.078
16 0.099 0.076 0.098 0.075
25 0.095 0.075 0.093 0.074
Elastomeric insulation

33. Voltage drop calculation
Simple radial scheme - Constant current
∆V(S) = K L I (R cosϕ + X sinϕ) < ∆VM
∆V(6) = 29,52 V
∆V% = ∆V/V = 13,54% > 2%
K = √(3)
R(6)= 4,20 (ohm/km)
X(6)=0.083 (ohm/km)
L=100 m
cosϕ =0.8

34. Voltage drop calculation
Simple radial scheme - Constant current
∆V(S) = K L I (R cosϕ + X sinϕ) < ∆VM
S= 6 mm2  ∆V% = 13,4% > 2%
S=10 mm2  ∆V% = 4.3 % >2%
S=16 mm2  ∆V% = 2.7% > 2%
S=25 mm2  ∆V% = 1.8%< 2% ∆V(25)= 7.25 V
K = √(3)
R(10)= 2.430 (ohm/km)
X(10)=0.078 (ohm/km)
L=100 m
cosϕ =0.8

35. Voltage drop calculation
Simple radial scheme - Constant current
RAC L RLOAD LLOADI
E = ((RAC+RLOAD)+j (LAC+LLOAD)) I
LOAD

36. Voltage drop calculation in cable lines
Simple radial scheme
Constant power

37. Voltage drop calculation
Simple radial scheme - Constant power
111 jQPA +=LOAD
*
3 1
1
1 





=
E
A
I
V0
0 1
R jX
LOADV0
E0
LOAD
R jX
V1
E1

38. Voltage drop calculation
Simple radial scheme - Constant power
L
3
)()(
3
jQ-P
)(
1
1111
1
11
⋅
+−++
=⋅⋅+=∆
E
xPrQjxQrP
E
LjxrE
111 jQPA +=
3E
jQ-P
*
3 1
11
1
1
1 =





=
E
A
I
E0
LOAD
R jX
E1

39. Voltage drop calculation
Simple radial scheme - Constant power
( ) ( )
33
1
2
2
1
11
2
2
1
11
10 




 +−
+




 +
+= L
E
xPrQ
L
E
xQrP
EE
L
3
)(
L
3
)(
1
11
1
11
10 ⋅
+−
+⋅
+
=−=∆
E
xPrQ
j
E
xQrP
EEE
L
3
)(
L
3
)(
1
11
1
11
10 ⋅
+−
+⋅
+
+=
E
xPrQ
j
E
xQrP
EE
0E
1E L
3
)(
1
11
⋅
+
E
xQrP
L
3
)(
1
11
⋅
+−
E
xPrQ
j

40. Voltage drop calculation
Simple radial scheme - Constant power
( ) ( ) ( )
( )L
E
xQrP
E
E
xQrP
EL
E
xQrP
EL
E
xQrP
EE
3
L
33
1
3
1
11
1
11
12
1
11
1
2
1
11
10
+
≅∆
+
+=




 +
+=




 +
+≅�
111 jQPA +=
3E
jQ-P
*
3 1
11
1
1
1 =





=
E
A
I
E0
LOAD
R jX
E1

41. Voltage drop calculation
Simple radial scheme - Constant power
( )L
E
xQrP
E
3 1
11 +
≅∆
111 jQPA +=
3E
jQ-P
*
3 1
11
1
1
1 =





=
E
A
I
E0
LOAD
R jX
E1
( ) ( )
3 2
1
11
2
1
11
L
V
xQrP
L
E
xQrP
E
E
V
V +
=
+
≅
∆
=
∆

42. Voltage drop calculation
Simple radial scheme - Constant power
BUT
E1 is the voltage at the end of the line while usually we
know the voltage at the begin of the line!
( )L
E
xQrP
E
3 1
11 +
≅∆
111 jQPA +=
3E
jQ-P
*
3 1
11
1
1
1 =





=
E
A
I
E0
LOAD
R jX
E1

43. Load
P=6 MW
Q=4,5 Mvar,
20 kV 3 phase
Installation
T=20 °C
L= 5 km
Cable Type
1X – XLPE
Voltage drop calculation
Simple radial scheme - Constant power

44. Voltage drop calculation
Simple radial scheme - Constant power
Parameter Value
I (A) – approximated - 216,5
Section (mm2) 70
Capacity (A) 255
r (Ω/km) 0,346
x (Ω/km) 0,131

45. Voltage drop calculation
Simple radial scheme - Constant power
Iteration (k) ∆V (V) V1 (V)
0 666,375 19333,63
1 689,343 19310,66
2 690,162 19309,84
3 690,192 19309,81
( )L
V
xQrP
V
1
11 +
≅∆
( )L
E
xQrP
E
3 1
11 +
≅∆
)(
0
)1(
1
kk
VVV ∆−=+

46. Voltage drop calculation in cable lines
Shunted scheme
Constant power

47. Voltage drop calculation
Simple radial scheme - Constant power
• Neglecting P and Q of fed lines (i+…)
• Same section for the entire line
( )
i
i
TiTi
i L
E
xQrP
E
3
1
+
≅∆ −
TiTiTi jQPA +=
*
3 





=
i
Ti
i
E
A
I
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3

48. Voltage drop calculation
Simple radial scheme - Constant power
TiTiTi jQPA +=
*
3 





=
i
Ti
i
E
A
I
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3
( )
( ) ( )( )
( ) ( )( )L
L
L
12
1
321321
1
1
22
2
3232
2
2
32
3
33
3
3
V
QQQxPPPr
V
V
V
QQxPPr
V
V
V
xQrP
V
V
+++++
≅
∆
+++
≅
∆
+
≅
∆

49. Voltage drop calculation
Simple radial scheme - Constant power
TiTiTi jQPA +=
*
3 





=
i
Ti
i
E
A
I
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3
V V Vi
k
i i
k( ) ( )+
−= −1
1 ∆ V V Vi
k
i
k
i
k( ) ( ) ( )+
= −1
∆
( ) ( )( )
( ) ( )( )
)1(
10
)1(
1
1
1
321321)1(
1
)0(
10
)0(
1
1
0
321321)0(
1
VVV
L
V
QQQxPPPr
V
VVV
L
V
QQQxPPPr
V
∆−=
+++++
≅∆
∆−=
+++++
≅∆

50. Voltage drop calculation
Simple radial scheme - Constant power
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3
1. Selection of the section according with
• current rating (L1)
• Total approx voltage drop
2. Voltage drop calculation on each line
segment (iterated)
3. Current calculation (iterated)
*
3 





=
i
Ti
i
E
A
I
( )∆V
rP xQ
V
i
Ti Ii
i≅
+
0

( )
x+
1 N
1=i10
0
01
0
1
0






−=
+
−≅∆−=
∑∑
∑∑
=
==
iTiiTi
N
i
i
TiTi
N
i
i
N
i
N
LQLPr
V
V
L
V
xQrP
VVVV
�

51. Voltage drop calculation
Simple radial scheme - Constant power
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3
Parameter
Node
0 1 2 3 4
V (kV) 20 ? ? ? >19
L (km) -- 6 0,4 1 0,2
P (MW) -- 2,3 3 1 1
Q (Mvar) -- 1 2 0,5 0,5
L4
LOAD 4
4
Ref. Conductor temperature 90 °C
AIR

52. Voltage drop calculation
Simple radial scheme - Constant power
Selection of the section - current rating
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
A
E
A
I
T
29,240
3
*
0
0
0 =





=
Parameter
Node
0 1 2 3 4
V (kV) 20 ? ? ? ?
L (km) -- 6 0,4 1 0,2
P (MW) -- 2,3 3 1 1
Q (Mvar) -- 1 2 0,5 0,5
PT (MW) 7,3 7,3 5 2 1
QT (Mvar) 4 4 3 1 0,5

53. MV cable current capacity
(RG7H1M1 Cu 1X)
Source Prismyan catalogue 2014
AIR

54. Voltage drop calculation
Simple radial scheme - Constant power
Selection of the section - current capacity
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
A
E
A
I
T
29,240
3
*
0
0
0 =





=
Parameter
Node
0 1 2 3 4
V (kV) 20 ? ? ? ?
Li (km) -- 6 0,4 1 0,2
P (MW) -- 2,3 3 1 1
Q (Mvar) -- 1 2 0,5 0,5
PTi (MW) 7,3 7,3 5 2 1
QTi (Mvar) 4 4 3 1 0,5
50 mm2

55. MV cable resitance
(50 Hz – 90 °C)
Source Prismyan catalogue 2014

56. MV cable reactance
(50 Hz – 90 °C)
Source Prismyan catalogue 2014

57. Voltage drop calculation
Simple radial scheme - Constant power
Selection of the section – Voltage drop
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
18,607kVx+
1 4
1=i
4
10
04 =





−= ∑∑=
iTi
i
iTi LQLPr
V
VV
Parameter
Node
0 1 2 3 4
V (kV) 20 ? ? ? ?
Li (km) -- 6 0,4 1 0,2
P (MW) -- 2,3 3 1 1
Q (Mvar) -- 1 2 0,5 0,5
PTi (MW) 7,3 7,3 5 2 1
QTi (Mvar) 4 4 3 1 0,5
PTi Li -- 43,800 2,000 2,000 0,200
QTi Li -- 24,000 1,200 1,000 0,100
50mm2
r=0,495
x=0,150

58. Voltage drop calculation
Simple radial scheme - Constant power
Selection of the section – Voltage drop
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
18,990kVx+
1 4
1=i
4
10
04 =





−= ∑∑=
iTi
i
iTi LQLPr
V
VV
Parameter
Node
0 1 2 3 4
V (kV) 20 ? ? ? ?
L (km) -- 6 0,4 1 0,2
P (MW) -- 2,3 3 1 1
Q (Mvar) -- 1 2 0,5 0,5
PTi (MW) 7,3 7,3 5 2 1
QTi (Mvar) 4 4 3 1 0,5
PTi Li -- 43,800 2,000 2,000 0,200
QTi Li -- 24,000 1,200 1,000 0,100
70mm2
r=0,344
x=0,140

59. Voltage drop calculation
Simple radial scheme - Constant power
Selection of the section – Voltage drop
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
19,233kVx+
1 4
1=i
4
10
04 =





−= ∑∑=
iTi
i
iTi LQLPr
V
VV
Parameter
Node
0 1 2 3 4
V (kV) 20 ? ? ? ?
L (km) -- 6 0,4 1 0,2
P (MW) -- 2,3 3 1 1
Q (Mvar) -- 1 2 0,5 0,5
PTi (MW) 7,3 7,3 5 2 1
QTi (Mvar) 4 4 3 1 0,5
PTi Li -- 43,800 2,000 2,000 0,200
QTi Li -- 24,000 1,200 1,000 0,100
95mm2
r=0,248
x=0,130

60. Voltage drop calculation
Simple radial scheme - Constant power
Accurated Voltage drop calculation
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
Parameter
Node
0 1 2 3 4
PTi Li -- 43,800 2,000 2,000 0,200
QTi Li -- 24,000 1,200 1,000 0,100
r PTi Li + x QTi Li -- 13,9824 0,652 0,626 0,0626
95 mm2
r = 0,248
x = 0,130
( )
i
i
TiTi
i L
V
xQrP
V �
+
≅∆

61. Voltage drop calculation
Simple radial scheme - Constant power
Accurated Voltage drop calculation
L3L2L1
LOAD 3LOAD 2LOAD 1
0 1 2 3 L4
LOAD 4
4
95 mm2
r = 0,248
x = 0,130
( )
i
i
TiTi
i L
V
xQrP
V �
+
≅∆
)(
0
)1(
1
kk
VVV ∆−=+
Node (i) 0 1 2 3 4
rPTiLi + xQTiLi -- 13,9824 0,652 0,626 0,0626
Iteraction (k) V (kV) DV (kV) V (kV) DV (kV) V (kV) DV (kV) V (kV) DV (kV) V (kV)
0 20 0,699 19,301 0,0338 19,242 0,0325 19,209 0,0033 19,206
1 -- 0,724 19,276 0,0339 19,242 0,0326 19,209 0,0033 19,206
2 -- 0,724 19,276 0,0339 19,242 0,0326 19,209 0,0033 19,206

62. Voltage drop calculation in cable lines
Long lines

63. Long lines
< 300 km < 220 kV
R/2 XL/2
XC
R/2 XL/2

64. Long lines
< 300 km < 220 kV
R/2 XL/2
XC
R/2 XL/2
L/2L/2
LOAD 2«LOAD 1»
0 1 2
Higher is the number of T more accurated is the result
LOAD 2

65. Long lines
R XL
XC
R XL
Q = k XL I2
Q = XL I2 - k w C V2
SHORT
LONG

66. Voltage drop calculation in cable lines
1. Data required to start
A. Cable parameters
B. Load characteristics
C. Distribution scheme
D. Maximum voltage drop
2. Voltage drop calculation in case of:
A. Radial line
1. constant current
2. constant power
B. Shunted line
C. Long line

67. Thank you
| Presentation title and date
For more information please contact
Angelo Baggini
Università di Bergamo
Dipartimento di Ingegneria
Viale Marconi 5,
24044 Dalmine (BG) Italy
email: angelo.baggini@unibg.it
ECD Engineering Consulting and Design
Via Maffi 21 27100 PAVIA Italy