Page 67 - Energize October 2022

TECHNICAL

shown in Figure 1. C s is the capacitance between any core
and the sheath and C c is the core-to-core capacitance (i.e.
capacitance between any two conductors). In Figure 1, the
three C c are delta connected and the C s are star connected due
to the sheath forming a single point N. The circuit in (a) can be
simplified as shown in (b). Outer points A, B and C represent
cable cores and the point N represents the sheath. The
whole three-core cable is equivalent to three star-connected
capacitors each of capacitance C s + C 1, (where C 1 = 3 C c) as
shown in (c).
Cable capacitance depends on the diameter of the cores,
the distance between cores and between cores and sheath.
For a given cable construction and core diameter this will
be determined by the thickness of the insulation, which is
determined by the operating voltage of the cable. For the same
core size, higher voltage cables have lower capacitance. For the Figure 2: Variation of load current with length of cable
same operating voltage, cables with higher ampacity, i.e., larger
core diameters, have higher capacitance. transferred to the load. The cut-off distance corresponds to the
power transfer limit of the cable.
Charging current The current flowing in the cable under load conditions
The capacitance of a distribution cable will cause continuous will depend on the nature and power factor of the load. For a
current, referred to as the charging current, to flow even when purely resistive load with a power factor (PF) of 1, and ignoring
no load is connected. The limit to cable length (cutoff) is reached the cable inductance, the load current will decrease with the
when the charging current equals the current rating of the cable. length of the cable as shown in Figure 2, where I c is the charging
Ignoring the resistance of the line and the distributed nature current, I l the load current, I m the ampacity of the cable, L m the
of the capacitance, the charging current will be given by: cutoff length, and L the length of the cable.
A similar graph would apply with a PF close to 1.
From the graph it can be seen that allowable load drops
sharply after a length of approximately 0,75 of the cutoff length,
Where f = frequency, C = capacitance, and V = the applied voltage and there is very little drop in allowable load for cable lengths
less than 0,4 of the cutoff length. Increasing the allowable load
Operating voltage and charging current current from 92% of I m to 98% of I m would require halving the
The charging current of a cable increases as the operating cable length.
voltage increases, assuming cable capacitance remains the same. Any practical cable would be required to deliver a
Higher voltage cables have thicker insulation and hence greater substantial portion of I m to the load. Cable length is often set
spacing between conductors, and so also lower capacitance, but by system requirements, and the choice of cable and operating
the relationship between cable voltage and capacitance is not voltage will determine the portion of I m which can be delivered
direct. to the load.
For cables of the same ampacity, a higher voltage rated cable Although the cutoff length is of theoretical interest, it has
will have higher charging current and hence a shorter cutoff no practical value, as no power cable would be operated to this
length. Capacitive reactance is independent of voltage. Higher limit. The aim of designing a distribution system is to maximise
voltage cables will usually run at lower currents, but the charging the power transfer and minimise losses, so no cable would be
current will increase with voltage, thus limiting the length of allowed to operate with a high percentage level of charging
higher voltage cables. Lower voltage will result in lower charging current.
current and longer distances. However, if an upper limit is set for charging current,
then the charge current limited (CCL) cut-off length can be
Limiting effects of charging current calculated.
Under loaded conditions, the cable carries reactive current to Table 1 Gives examples of cut-off lengths of three-core XLPE
charge the line, the active current for line losses, and the useful MV cable rated at different voltages, of approximately the same
active and reactive currents for the load. This imposes limits on ampacity, and CCL cutoff lengths when the charge current is
the current-carrying capability of the cable. The charging current limited to 10% of the cable rating.
reduces the amount of current, and hence power that can be At low values of charge current the CCL becomes very
delivered to the load, or inversely, the load that can be served by sensitive to small changes. For example, to increase the power
the cable. There is a cut-off distance where line charging current transfer from 90% delivered power to 95% requires halving the
is equal to the current rating of the cable, and no power can be length of the cable.

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