In a cable a short circuit causes very extreme stresses which are proportional to the square of the current: • A temperature rise in the conducting components subjected to current flow such as conductor, screen, metal sheath, armour. Indirectly the temperature of adjoining insulation and protective covers also increases, • electro-magnetic forces between the current-carrying components. The temperature rise is important for its effect on ageing, heat pressure characteristics etc., and should be limited to a permissible short-circuit temperature. The thermo-mechanical effects of the current shall also be considered. For a given short-circuit duty therefore the short-circuit capacity of a cable installation is to be investigated with respect to all these parameters. For multi-core cables in most instances the thermal effect - related to the magnitude of fault current and clearance time - is the critical parameter, since the cable will normally have enough mechanical strength. With single-core cables however, in addition, the mechanical effect - related to the magnitude of the peak short-circuit current - is of such significance that, next to the thermal, the mechanical with- stand of both cable and its supports is to be investigated. Also accessories must be rated with respect to thermal and mechanical short-circuit stresses. The short-circuit withstand of a cable system is not quantitatively defined with regard to permissible number of repeated short circuits, degree of deformation or destruction or impairment quality. It is expected, however, that a cable installation will remain safe in operation and that any deformation remains within tolerable limits even after several short circuits.

1. Angelo Baggini, angelo.baggini@unibg.it, Bergamo University - Engineering Department
Via Marconi 5, 24044 Dalmine (BG) – Italy
Short circuit withstand of power cables

2. Introduction
Cable sizing is the
process of selecting
appropriate sizes for
electrical power cable
conductors.
A Short-circuit is an accidental or a deliberate
connection across a comparatively low resistance or
impedance between two or more points of a circuit
which usually have differing voltage
A short circuit current
is a current flowing through the short circuit
(IEV 603-02-28)

3. Introduction
Rated current Short circuit current
From“GEINDUSTRIALPOWERSYSTEMSDATABOOK”

4. The main types
of short-circuits

5. The main types of short-circuits
A. Three-phase
B. Phase-to-phase
C.Phase-to-phase-to-earth
D.Phase-to-earth
BALANCED UNBALANCED

6. The characteristics
of short-circuit

7. The characteristics of short-circuit
Bolted fault
very high magnitude characrerized by phases
“bolted” together to create a zero impedance
connection
Arcing fault
An arc-fault occurs when loose or corroded
connections make intermittent contact and causes
sparking or arcing between the connections.

8. | Presentation title and date

9. The characteristics of short-circuit
Duration
self-extinguishing, transient and steady-state
Origin
Mechanical
Internal or atmospheric overvoltages
Insulation breakdown due to heat, humidity or a corrosive environment
Location
inside or outside a machine or an electrical switchboard

10. Consequences
of short-circuits

11. Consequences of short-circuits
.
At the fault location
• Damage to insulation
• Welding of conductors
• Fire
• Electrical arcs
On the faulty circuit
• Electrodynamic forces
• Excessive temperature rise
On other circuits nearby
• Voltage dips
• Shut down of a part of network
• Dynamic instability
• Disturbances in control/monitoring circuits

12. | Presentation title and date

13. Determinants
of short-circuit currents

14. Determinants of short-circuit currents
Short circuit currents depend on the following factors:
• voltage level and actual operating voltage
• neutral conditions (TT, TN, IT)
• impedance of the system between any generation unit
• short-circuit location
• impedance of the short-circuit
• number of generation units in the system
(short circuit power)

15. Distance from generators
Near-to-generator
The influence of the changing reactance
of generators cannot be neglected
Far-from-generator
The AC component remains constant
throughout the total time duration of the
short-circuit
The influence of the changing reactance of generators
can be neglected

16. Parameters
of the short-circuit current

17. Parameters of the short-circuit current
Initial symmetrical short-circuit current Ik’’
The current Ik’’ is the r.m.s value of the short-circuit current
at the initial symmetrical short circuit. In case of short circuit
far-from-generator sinusoidal current Ik'' is almost constant
during the fault
Peak short-circuit current Ip
Depending on the feeding source of the short-circuit, different
considerations have to be taken to calculate the peak short-
circuit current. Short-circuits in low-voltage systems normally
are single-fed short-circuits
Decaying (aperiodic) component Idc
value between the top and bottom envelope of a shortcircuit
current decaying from an initial value to zero
Steady-state short-circuit current Ik
Short-circuits in low-voltage systems normally are far-from-
generator short-circuits. The steady-state short-circuit current
is identical to the initial symmetrical short-circuit current

18. Parameters of the short-circuit current
(taking into account the protection)
• The total time duration of the
short-circuit current consists of
the operating time of the
protection devices and the
total breaking time of the
switchgear
• The short-circuit breaking
current is the RMS value of
the short-circuit current at
switching instant, i.e., at time
of operating the circuit-breaker
The r.m.s. value of the short-
circuit current, combined with
the total time duration, is a
measure for the thermal effects
of the short-circuit Ref. FUSE

19. Symmetrical and Asymmetrical currents
The words “symmetrical” and “asymmetrical” describe the shape of the AC waves
about the zero axis.
Symmetrical: the envelopes of the peaks are symmetrical around the zero axis
Asymmetrical: the envelopes of the peaks are not symmetrical around the zero axis

20. Maximum and minimum
short circuit currents

21. Maximum and minimum short circuit currents
In the case of cables, two values of short-circuit current shall
be evaluated:
• Maximum (begin of the line)
• Minimum (end of the line)
IT1N160 In160Ik=30 kA
U=400 V
Iz=134 A

22. Minimum short-circuit currents
The minimum short-circuit current is needed for the
design of protection systems and the minimal setting of
protection relays
Important when
• Cables are long and the source impedance is
relatively high

23. Maximum short-circuit currents
The maximum short-circuit current is the main design
criteria for the rating to withstand the effects of short-
circuit currents
It is used to determine
• The thermal stress on the cable
• The mechanical withstand capacity of the cable
and
• The breaking capacity of the circuit breakers
• The making capacity of the circuit breakers

24. | Presentation title and date
Thermal stresses

25. Short-Circuit Thermal Rating
It is required to determine the cross-sectional areas of
conductor and screen in respect to short-circuit thermal
stress.

26. Short-Circuit Thermal Rating
STRESS RATING

27. Stress
Thermally equivalent short-circuit current Ith
The actual short-circuit current contains:
• a decreasing direct current component (m)
• a superimposed alternating current component (n)
nmII kth += ′′

28. Stress
Thermally equivalent short-circuit current Ith
nmII kth += ′′

29. Stress
Thermally equivalent short-circuit current Ith
nmII kth += ′′

30. Rating
Short-circuit Capacity of a Conductor Ithz
The heat generated is mainly
stored into the conductor
 A = nominal cross-sectional area of the conductor
 tk = Short-circuit duration
 θa = conductor temperature at the beginning of a short-circuit*
 θe = permissible short-circuit temperature taking into account the insulation
and conducting layers which are in contact with the conductor
 Jthr = rated short-time current density defined for a rated short-circuit duration
tkr = 1 s
* Usually assumed equal to the maximum permissible temperature
k
kr
thrthz
t
t
JAI =

31. Short-Circuit Capacity of Screens,
Metal Sheaths and Armour
Line-to-earth short circuit in a three-
core cable with common screen in a
low resistance aerthed network
Double earth fault in three screened
single-core cables in insulated network

32. Short-Circuit Capacity of Screens,
Metal Sheaths and Armour
•The screens, the metal sheaths or the armour
carry short-circuit currents and become heated
•The fault current carried
divided in the inverse proportion to the impedance of the individual current path
Depending on the type of the short-circuit and the method of cable-laying:
Determination of short-circuit capacity
the same rules apply as for conductors
Duration of the short circuit
heat is transferred to the adjacent layers

33. Thermo-Mechanical
stresses

34. Thermo-Mechanical Forces and Expansion
Due to the high temperature rise during a short circuit a
significant expansion of the conductor occurs
Δl
l
Δh
l
θα ∆=∆ thll
θα
π
∆=∆ th)
2l
(h
αThCu=16,210-61/K-αThAl=22,810-61/K

35. Effect of Thermal Expansion in Cables
The conductor produces a linear dependant force
under conditions of temperature rise
The progression depends on
• material
• shape
• construction
The temperature rise of a conductor produces a longitudinal movement
and a compressive force dependant on:
• Type of conductor
• Adhesion of the insulation
• Type of cable
• Method of fixing
θα ∆⋅⋅= ⋅thA EFth
ECu=1151091/K-EAl=651091/K
A=CrosssectionalArea
∆l=∆h=0

36. Effect of Thermal Expansion in Cables
Installation
Longitudinal expansion is equally divided over the full lenght
Multi-core cables:
over long, straight runs
arranged in a wavy line
fixed to leave a free loop
Single-core cables:
long straight runs in a wavy line
fixed to supports
large distances to permit deflection

37. Electromagnetic stresses

38. Electro-dinamyc stresses
Currents in conductors laying side by side produce
electromagnetic forces between the conductors
• Opposite direction currents produce a repulsion force
• Same direction currents produce an attractive force
+ . + +

39. Electromagnetic forces
Current force Fs per unit lenght
2
s
2
F
a
Iso
π
µ
=′
+ +a

40. Electromagnetic forces
for other arrangement
in a common cover over all conductors within items such as clamps, binder
tapes
FF sl ′′ = α
FF sb ′′ = β

41. | Presentation title and date
Electromagnetic forces

42. 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