C.
To estimate the voltage drop insulated wires and cables for
heavy (big) cross-sections single- and three-phase-overhead
line, the active resistance well the inductive resistance
must considered.)
P 1,732 cos for three-phase current
P for direct current
Reactive power (var)
Q sin for single phase current (A.- and
Nominal current
Active current
I (A)
Reactive current
Iw cos
Blindstrom
I0 sin
Apparent power (VA)
S for single phase current (A. C.):
U (Rw cos sin 10–3
(V)
Three-phase:
U 1,732 (Rw cos sin 10–3
(V)
Da
di
Da
d
FORMULAS POWER ENGINEERING
. C.)
S 1,732 for three-phase current
Active power (W)
P cos for single phase current (A. C.
U0 phase-to-earth voltage
U0 Voltage between conductor and earth metallic
covering (shields, armouring, concentric conductor)
U Voltage between two outer conductors
U0 U/
3 for three-phase current systems
U0 U/2 for single-phase and direct current systems
U0/U0 outer conductor earth-connected for C.
• for direct current
of known current =
2 l
(v)
q
for single phase
alternative current
u =
2 cos l
(v)
q
for three-phase current =
1,732 cos l
(v)
q
• for direct current
of known power =
2 P
(v)
q U
for single phase
alternative current
u =
2 P
(v)
q U
for three-phase current =
l P
(v)
q U
u voltage drop(V) cross-section (mm2
)
U operating voltage (V) working current Ampere)
P power (W) length the line
Rw effective resistance ()/km) m
L Inductance (mH/km) (Kappa) electrical conductivity
L induktiver Widerstand conductors (m/ mm2
)
( )/km) -copper 58
at 314) -Alu 33
Nominal voltage
The nominal voltage expressed with two values alternative
current U0/U (Volt).1145
Y
Cross section
• for direct current and single
phase alternative current =
2 l
(mm2
)
one-phase current
u
of known current =
1,732 cos l
(mm2
)
for three-phase current u
• for direct current and single
phase alternative current =
2 P
(mm2
)
of known power
u U
for three-phase current
q =
l P
(mm2
)
u U
Voltage drop
For low voltage cable network normal operation, is
advisable voltage drop 3-5%.
The formula for single-phase (A.)
Q 1,732 sin for three-phase current
(Voltampere reactiv) tan
Phase angle
is phase angle between voltage and current
cos 1,0 0,9 0,8 0,7 0,6 0,5
sin 0,44 0,6 0,71 0,8 0,87
Insulation resistance
Riso =
Siso
In
Da
10 –8
(M km)
l d
6SHFLęF,QVXODWLRQUHVLVWDQFH
Rs 108
In
Da outer diameter over insulation (mm)
d conductor diameter (mm)
di inner diameter insulation (mm)
l length the line (m)
Siso Spec.
On exceptional case, higher values (up 7%) can permitted
in case network-extension short-circuit. resistance insulation materials cm)
Mutual capacity (CB) for single-core,
three-core and H-cable)
CB =
r 103
(nF/km)
18 In
Inductance
Single-phase 0,4 (In 0,25) mH/km
r
three-phase 0,2 (In 0,25) mH/km
r
Da distance mid mid
of both conductors
r radius conductor (mm)
r dielectric constant
0,25 factor for low frequency
Earth capacitance
EC 0,6 CB
Charging current (only for three-phase current)
ILad 10–6
A/km Ader bei Hz
Charging power
PLad ILad U
Leakage and loss factor
G tan (S) f
C Capacity
tan tan loss factor
C
S Siemens 1
1
Dielectric loss
Dv U2
2 tan 10–6
(W/km)
f Hz
tan PE/VPE cables 0,0005
EPR 0,005
Paper-single core, three-core, H-cable 0,003
Oil- lled and pressure cable 0,003
PVC-cable 0,05
It should noted that for the current load the insulated
cables and wires selected cross-section, the power ratings
table also considered
