Dependance On Installation Site
The selection of number of
cable cores basically depends on the type of system where it is going to be installed.
Generally we have two types of systems:
- A perfectly balanced system and
- A system with some degree of unbalance (or Unbalanced System).
Generally cable sizing includes below parameters:
- Cable installation conditions and the load it will carry
- Continuous current rating of the cable
- Voltage drop and short circuit considerations
- Earth fault loop impedance
Here, I am going to describe that how the number of cores can be selected.
3-Core Cables
These cables are used generally for a
perfect balanced 3-phase system.
When the currents on the 3-live wires of a 3-phase system are equal and
at an exact 120° phase angle, then the system is said to be balanced.
The 3-phase loads are identical in all respects with no need of a
neutral conductor.
An important example of 3-phase load is electric motor and that is why, they are fed through 3-Core cables in most cases.
3.5-Core Cables
A 3-phase system may have a neutral wire. This wire allows the 3-phase system to be used at
higher voltages while it will still support lower voltage single phase loads.
It is not likely in such cases that the loads will be identical, so the neutral will carry the
out-of-balance current of the system.
The greater the degree of imbalance, the larger the neutral current.

3-5-core cable construction (figure by mitesh-raval.blogspot.com)
When there is
some degree of unbalance
and the amount of fault current is very small, then 3.5 core cables are
used. In these types of cables, a neutral of reduced cross section as
compared to the 3-main conductors is used, which is used to carry the
small amount of unbalanced currents.
4-Core Cables
When there is
severe out-of-balance conditions, the amount of fault current will raise to a very high level. Generally in the case of
linear loads, the neutral only carries the current due to imbalance between the phases.

4-core PVC insulated and sheathed copper conductor power cable
The
non-linear loads
such as switch-mode power supplies, computers, office equipment, lamp
ballasts and transformers on low loads produce third order harmonic
currents (
Definition of Harmonics and Their Origin) which are in the phase of all the supply phases.
These
currents do not cancel at the star point of a three-phase system as do
normal frequency currents, but add up, so that the neutral carries
very heavy third harmonic currents.
That is why the neutral of the cable feeding the equipment are not reduced and made with cross sectional area same as that of the main conductor to carry this high amount of current.
5 and 6-Core Cables
Some conditions may arrive when the amount of
fault (neutral) current
becomes very large than the phase currents. When the load concerned to
this type of situation is fed through a multi-core cable, it is
necessary to use a 5-Core or 6-Core Cable.

5-core PVC insulated and sheathed copper conductor power cable
In this condition,
two (or three) conductors can be used in parallel formation to carry the high amount of generated unbalanced currents.