Formulas of Power Engineering

Crosssection
for direct  and single phase alternating current
(current given)
q = 
1 x I x l 
(mm²) 
κ x u 



for threephase current 
q = 
1.732 x I x cosφ x l 
(mm²) 
κ x u 
for direct  and single phase alternating current
(capacity given)
q = 
2 x I x P 
(mm²) 
κ x u x U 



for threephase current 
q = 
l x P 
(mm²) 
κ x u x U 
Voltage drop
For low voltage cable network of normal operation, a voltage drop of 35% is adviseable.
Exeption: higher values (7%) can be permitted in case of network extension or in short circuit.
for direct current (current given)
single phase alternating current (current given)
u = 
2 x I x cosφ x l 
(V) 
κ x q 
for threephase current
(current given)
u = 
1.732 x I x cosφ x l 
(V) 
κ x q 
for direct current (capacity given)
u = 
2 x l x P 
(V) 
κ x q x U 
single phase alternating current (capacity given)
u = 
2 x l x P 
(V) 
κ x q x U 
for threephase current (capacity given)

u 
= 
Voltage drop (V) 
U 
= 
Operating voltage (V) 
P 
= 
Power (W) 
R_{W} 
= 
Effective resistance (Ω/km) 
L 
= 
Inductance (mH/km) 
ωL 
= 
Inductive resistance (Ω/km) 


ω = 2 π f at 50 Hz = 314 
q 
= 
Crosssection (mm²) 
I 
= 
Working current (A) 
l 
= 
Length of line (m) 
κ 
= 
Electrical conductivity of conductors 


(m/Ω x mm²) 


κ Copper: 58 


κ Aluminum: 33 

Nominal voltage
The nominal voltage is to be expressed with two values of alternating current U_{0}/U (in V).
U_{0} 
= 
voltage between conducter and ground or metallic covering (shield, armoring, concentric conductor) 
U 
= 
voltage between two outer conductors 
U_{0} 
= 
U/√3 for threephase current systems 
U_{0} 
= 
U/2 for single phase and direct current systems 
U_{0}/U_{0} 
= 
1 outer conductor is grounded for single phase and direct current systems 

Nominal current
I in A
Active current
I_{W} = I x cosφ
Reactive current
I_{0} = I x sin φ
Active power
S = U x I for single phase current
S = 1.732 x U x I for threephase current
Apparent power
P = U x I x cosφ for single phase current
P = 1.732 x U x I x cos φ for threephase current
P = U x I for direct current
Reactive power
Q = U x I x sin φ for single phase current
Q = 1.732 x U x I x sin φ for threephase current
(Voltampere reactive) Q = P x tan φ
Phase angle
φ is a phase angle between voltage and current
cos φ 
= 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 

sin φ 
= 
0 
0.44 
0.6 
0.71 
0.8 
0.87 


Insulation resistance
R_{Insu} = 
S_{Insu} 
x In 
Da 
x 10^{8} (MΩ x km) 
l 
d 
Specific insulation resistance
R_{S } = 
R x 2π x l x 10^{8} 
In 
Da 
di 

Da 
= 
Outer diameter over insulation 
d 
= 
Conductor diameter 
di 
= 
Inner diameter of insulation 
l 
= 
Length of the line 
S_{Insu} 
= 
Spec. resistance of insulation materials (Ω x cm) 

Mutual capacity
for single conductor, threecond. and Hcable
C_{B} = 
ξr x 10³ 
(nF/km) 
18 In 
Da 
d 
Inductance
singlephase
0.4 x ( In 
Da 
+ 0.25) mH/km 
r 
threephase
0.2 x ( In 
Da 
+ 0.25) mH/km 
r 

Da 
= 
Distance mid to mid of both conductors 
r 
= 
Conductor radius 
ξr 
= 
Dielectric constant 
0.25 
= 
Factor for low frequency 

Ground capacitance
E_{C} = 0.6 x C_{B}
Charging current
(only for threephase)
I_{Lad} = U x 2 π f x C_{B} x 10^{6} (A/km per conductor at 50Hz)
Charging power
P_{Lad} = I_{Lad} x U
Leakage and loss factor
G = tanδ x ωC(S)
tanδ = G/ωC 
ω 
= 
2 π f 
C 
= 
Capacity 
tanδ 
= 
Loss factor 
S 
= 
Siemens = 1/1Ω 

Dielectric loss
DV = U² U x 2 π f x C_{B} x tan x 10^{6} (W/km)
It should be noted that for the current load of the insulated cables and wires of selected crosssection, the power ratings are to be considered.
To estimate the voltage drop of insulated cables and wires with large crosssections of single and threephase overhead line, the active resistance as well as indictive resistance must be considered.
Formula for single phase:
U = 2 x l x I x (R_{W} x cosφ + ωLx sinφ) x 10^{3} (V)
Formula for threephase
U = 1.732 x l x I x (R_{W} x cosφ + ωLx sinφ) x 10^{3} (V) 
f at 50Hz
tanδ PE/VPE cables 
~ 0.0005 
EPR 
~ 0.005 
Paper single conductor, threeconductor, Hcable 
~ 0.003 
Oilfilled and pressure cable 
~ 0.003 
PVCcable 
~ 0.05 
