**The question of why all electric transmission and distribution circuits cannot be run underground to avoid the visual and other effects is often posed. The main argument against constructing underground systems is usually financial. But costs are not the only limitation. The basic laws of electricity limit how physically long an underground cable can be.**

These limits are relatively unimportant on overhead lines but will severely limit the length of underground cable systems, especially high voltage systems. The limiting factor here is the capacitance of the cable, which is much higher than overhead lines and has a much greater effect on performance.

There are two main limiting effects of cable capacitance: The Ferranti effect, and charging current. The Ferranti effect results in the voltage at the far end of a cable exceeding the voltage at the input end under unloaded or lightly loaded conditions. The cable charging effect results in the capacitive current flowing in the cable under loaded and unloaded conditions. With high enough value of capacitance, the charging current can exceed the rated current. Underground lines have many times the line charging current that an overhead line, depending on line voltage. If a line is long enough the charging current could be equal to the total amount of current the line can carry. This will severely limit its ability to deliver power. The charging current can also have an impact on the operation of protective devices and must be taken into account when calculating the settings of such devices.

**Charging current**

The capacitance of a transmission system will cause continuous current to flow even when no load is connected. This is referred to as the charging current. Underground cables have 20 to 75 times the line charging current of overhead lines [1]. Cable capacitance increases with length of the cable, and with increased capacitance, the charging current drawn is also increased. The limit to cable length (cut-off) is reached when the charging current equals the current rating of the cable.

Ignoring the resistance of the line and the distributed nature of the capacitance, the charging current will be given by:

*I _{c} = V/X_{c} = V×2πfC*

where:

*f* = frequency

*C* = capacitance

The current flowing in the cable cannot exceed the ampacity of the cable, and thus the charging current reduces the amount of current, and hence power that can be delivered to the load, or inversely, the load that can be served by the cable. The current flowing in the cable under load conditions will depend on the nature and power factor of the load. For a pure resistive load with a power factor (PF) of unity (i.e. 1), and ignoring the cable inductance, the load carried will decrease with distance as shown in Fig 1. The graph represents Ic as the charging current, Il the load current, Im the ampacity of the cable, Lm the cut-off length and L the length of the cable.

Similar graph would apply with a PF close to 1.

The graph in Fig. 1 shows that allowable load drops sharply after a length of approximately 0,75 of the cut-off length, and there is very little decrease in allowable load for cable lengths less than 0,4 of the cut-off length. Increasing the allowable load current from 92% to 98% of Im would require halving the cable length.

Any practical cable would be required to deliver a substantial portion of Im to the load. Cable length is often set by system requirements, and the choice of cable and operating voltage will determine the portion of Im which can be delivered to the load.

**Operating voltage and charging current**

The charging current of a cable increases as the operating voltage increases, assuming cable capacitance remains the same. Higher voltage cables have thicker insulation and hence greater spacing between conductors, and so also lower capacitance, but the relationship between cable voltage and capacitance is not direct. For cables of the same ampacity, a higher voltage rated cable will have higher charging current and hence a shorter cut-off length.

Capacitive reactance is independent of voltage. High voltage transmission will usually run at lower currents, but the charging current will increase with voltage, thus limiting the length of high voltage cables. A lower voltage will result in lower charging current, and thus longer distances.

Table 1 provides examples of cut-off lengths cable for single-core cross-linked polyethylene (XLPE) high voltage (HV) cable rated at different voltages, for approximately the same ampacity.

Table 2 provides examples of cut-off lengths cable for single-core XLPE HV cable rated at different voltages, for approximately the same power transmission capacity.

**Limiting effects of charging current**

Under loaded conditions, the cable carries the reactive current to charge the line, the active current for line losses, and the useful active and reactive currents for the load. This imposes

limits on the current carrying capability of the cable. For a selected transmission distance, the current margin remaining after the line is charged corresponds to the useful current for the load. There is a cut-off distance at which the cable is fully loaded with line charging current. In that case, no power can be transferred to the load. That cut-off distance corresponds to the transmission limit of the cable, based on the current limitation.

Rated voltage (kV) |
Current rating (A) |
Capacitance (µF/km) |
Cut-off length (km) |

500 | 1076 | 0,12 | 48,9 |

400 | 1098 | 0,15 | 58,2 |

345 | 980 | 0,13 | 69,5 |

220 | 1001 | 0,15 | 96,5 |

132 | 1020 | 0,18 | 136,6 |

**Cable capacitance calculations**

Capacitance exists between the conductors of a cable and between the conductors and sheath. The capacitance existing in a three-core cable is illustrated in Fig. 2.

Consider a three-cored symmetric underground cable as shown in Fig. 2.

Let *C _{S}* be the capacitance between any core and the sheath and

The 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 same operating voltage, cables with higher ampacity, i.e. larger core diameters, have higher capacitance. The charging current can be calculated as:

*I = 2πf(C _{S} + 3C_{C})V Amperes*

**Ferranti effect and voltage rise effects**

The Ferranti effect results in the rise in voltage at the receiving end above the voltage at the sending end, on lightly loaded or unloaded power transmission circuits. In extreme cases the voltage can exceed the rated value of the line. The effect is due to the capacitance and inductance of the line acting together. It occurs on very long transmission lines but because the capacitance of cables is much higher it occurs at much shorter lengths and is more prevalent.

In electrical engineering, the Ferranti effect is an increase in voltage occurring at the receiving end of a long transmission line, which is much more than the voltage at the sending end. This occurs when the line is energised, but this occurs in case of very light load or when the load is disconnected. The capacitive line charging current is responsible for voltage imbalance which produces a voltage drop across the line inductance that is phase with the sending end voltages while considering the line resistance as negligible at the same time.

Rated voltage (kV) |
Current rating (A) |
Capacitance (µF/km) |
Cut-off length (km) |

400 | 853 | 0,12 | 56,6 |

345 | 980 | 0,13 | 69,5 |

220 | 1561 | 0,18 | 125,5 |

Therefore, both the line inductance and capacitance are mainly responsible for this phenomenon. The relative voltage rise is proportional to the square of the transmission line length. The Ferranti effect has much more pronounced effect in underground cables, may be even in short lengths, because of their high capacitance. The extent of the voltage rise may be estimated using a simplified model of the cable. Underground cable is usually modelled as lumped T or π sections (Fig. 3).

A simplified explanation of the Ferranti effect on an approximate basis can be obtained by lumping the inductance and capacitance parameters of the line into a single π section as shown in Fig. 4.

where:

*C* = The capacitance per unit length (µF/km).

*L* = The inductance per unit length (Mh/km).

From the π model of the cable [3]

where:

*Z* = The series impedance (R+ jwLl)

*Y* = The shunt admittance (jwCl)

*l* = Is the length of the cable (km)

Under no load conditions I_{r} = 0, but under low load conditions it can be ignored.

Neglecting resistance:

This equation shows that (V_{s} – V_{r}) is negative. That is, V_{r} > V_{s}. This equation also shows that the Ferranti effect depends on frequency and electrical length of the line. The Ferranti effect voltage rise factor is the ratio of the receiving end voltage to the sending end voltage.

It is clear from the equation that the voltage rise factor is proportional to the square of the line length. Doubling the line length will increase the voltage rise factor by four times.

**Mitigation**

There are a few ways in which the effect of charging current can be mitigated, some practical and others a little more creative.

*Shunt reactive compensation*

Inductance may be added at the ends of the cable or at intermediate points, to counteract the effects of capacitance. Where transformers are involved at the ends, additional windings may be provided to insert the necessary reactance. The effect of shunt reactance is to decrease the reactive current flowing in the circuit and thus allow a higher load current to flow. Ideally, full compensation would be beneficial, but this is avoided because of possible resonance.

*DC transmission systems*

A move to install underground transmission cables may require a conversion from AC to DC transmission. Long underground DC transmission systems are possible. DC transmission does not suffer from the same problems as AC. DC transmission has its own additional costs, primarily converter stations. The insulation requirements for DC cables are lower than for AC and hence costs are lower.

HVDC transmission systems are normally associated with overhead lines but cable-based systems have been developed. DC cable systems do not have problems with cable capacitance charging. Overhead MV and LV DC systems are in use in distribution networks and could be extended to underground cable networks in cases where AC cable systems are being considered.

DC cable systems have been installed in a number of countries, and low capacity DC, such as DC light, have been developed to serve the distribution sector. Studies are still needed to determine the effects on the NE power grid of a widespread conversion to DC transmission.

*Optimising cable voltage*

An innovative solution is proposed by Deb [3]. Because the charging current is dependent upon the voltage, operating the cable at a voltage below the rated voltage will reduce the charging current. Using the method proposed in [3], an optimum operating voltage can be determined. Transmission voltage is considered optimal when it enables maximal power transfer capability. This approach takes the point of view that the rated voltage is not the operating voltage but is the upper boundary for the operating voltage. A study using this approach found that between 130 and 184 km voltage reduction increases power transfer capability and above 184 km voltage reduction was inevitable [4].

**References**

[1] NEI: “*Underground vs. Overhead Transmission and Distribution”*, *www.puc.nh.gov/2008IceStorm/ST&E%20Presentations/NEI%20Underground%20Presentation%2006-09-09.pdf*

[2] K Daware: *“**Capacitance of underground cables”*, Electricaleasy.com, 2017/04.

[3] G Deb: “*Ferranti effect in transmission lines*”, IJECE Vol. 2, No. 4, August 2012.

[4] T Vrana: “*Optimal Transmission Voltage for Very Long HVAC Cables”*, Energy procedia Vol. 94, September 2016.

Send your comments to energize@ee.co.za

The post Effects of MV and HV cable capacitance on operational limits appeared first on EE Publishers.

Source: EE plublishers