# Ground Return Current Behaviour in High Voltage Alternating Current Insulated Cables

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## Abstract

**:**

## 1. Introduction

- ➢
- EHV overhead lines with any number of earth wires [1];
- ➢
- Milliken conductors [2];
- ➢
- Harmonic behaviour of high voltage direct current (HVDC) cables [3];
- ➢
- Distribution line carrier (DLC) in medium voltage (MV) network [4];
- ➢
- Alternating current (AC) gas Insulated transmission Lines (GILs) [5];
- ➢
- AC high-speed railway supply [6].

## 2. Fault Occurrence in a Cross-Bonded Single Circuit Cable Line by Means of Multiconductor Cell Analysis

_{s}and y

_{p}must be computed at 20 °C). The use of PTs has been chosen in tune with the Great Britain installation but MCA can consider also un-transposed cable lines.

**Table 1.**Geometric and electric data of XLPE-insulated single-core cable. XLPE: cross-linked polyethylene; PE: polyethylene; CB: cross-bonding.

Cable type insulation | Unit | XLPE |
---|---|---|

Voltage levels after IEC 62067 | kV | 220/380 (420) |

Cross sectional area/material | mm^{2} | 2500/Cu M-type |

Conductor diameter | mm | 64.3 |

Conductor screen diameter d_{0} | mm | 68.7 |

Insulation diameter d_{1} | mm | 122.8 |

Insulation screen diameter | mm | 126.1 |

Metallic shield diameter/material | mm | 131.3/Al welded |

Jacket of PE diameter | mm | 142.4 |

Overall diameter | mm | 142.4 |

Per unit length 50 Hz resistance of phase conductor at 20 °C | mΩ/km | 8.4827 |

Per unit length series Inductance | mH/km | 0.5431 |

Per unit length shunt Leakance (50 Hz) with loss factor tanδ = 0.0007 | nS/km | 48.4 |

Per unit length shunt Capacitance with ε_{r} = 2.3 | μF/km | 0.22 |

Per unit length zero sequence impedance z_{0} | Ω/km | 0.0547 + j·0.0612 |

Line length | km | 10.8 |

Cell length | m | 10 |

Earth resistivity | Ω·m | 100 |

Substation earthing resistances R_{A} and R_{B} | Ω | 0.1 |

Major section CB box resistance R | Ω | 5 |

Link resistance R_{cont} between screens at earthing sites | mΩ | 1 |

**Figure 2.**Subdivision of the single-circuit cable line in cross-bonding with indication of cells and minor and major sections (not to scale).

_{GR}| upon this parameter is also shown.

**Figure 3.**Faulted UGC: screen current magnitudes along the line CB with phase transpositions (PTs); FAULT at midline.

**Figure 4.**Faulted UGC: ground return current magnitude and angle along the line (CB with PTs); FAULT at midline.

_{GR}| on the circuit parameters and the fault locations the following Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9 are very helpful.

**Figure 5.**Faulted UGC: ground return current magnitudes along the line (CB with PTs) for different CB box resistances; FAULT at midline.

**Figure 6.**Faulted UGC: ground return current magnitudes along the line (CB with PTs) for different earth resistivities; FAULT at midline.

**Figure 7.**Faulted UGC: ground return current magnitudes along the line (CB with PTs) for different substation grid resistances; FAULT at midline.

**Figure 8.**Faulted UGC: ground return current magnitudes along the line (CB with PTs) for different fault locations.

^{9}Ω). If the CB box resistance is high (e.g., R = 20 Ω) the ground return current decreases meaningfully (it reduces from 1.65 kA to 0.5 kA of Figure 5). The sharing of fault current in the screens is rather unaffected by the CB box resistances but, of course, with lower ground return current there are higher current in the screens. Therefore, it is demonstrated that an important role is played by the CB box resistances (at major section location) which are responsible for the injection of current into the earth and hence for the creation of |I

_{GR}|.

_{cont}= 1 GΩ). It is not a theoretical case since it has been employed in the St. Johns Wood-Elstree UGC [23,24]: a 20 km long 400 kV cross-linked polyethylene (XLPE)-insulated cable system. In this UGC, the continuous cross-bonding method has been employed since it is a tunnel installation [25] and could not use a distributed earthing system inside the tunnel. This practice is very convenient for ground return current (since CB becomes a kind of SB with the differences that the screens are transposed) but not for screen induced voltages since there are not locations along the line where the screens are linked to the earth anymore (but at the substation locations). The sensitivity of ground return current on the soil resistivity is less important than that on CB box resistances.

_{earth}= 20 Ω·m, 100 Ω·m, 1000 Ω·m and 10000 Ω·m unchanged with the CB box resistances = 5 Ω. It is worth noting that ρ

_{earth}= 20 Ω·m is representative of British soil conditions for the vast majority of locations. All the above mentioned results are based on the assumption that the two earthing grid substation resistances are equal to 0.1 Ω. This is rather reasonable for an EHV substation. A range where this resistance can change is about 0.02 ÷ 0.3 Ω depending upon the substation extension and the earth resistivity. The ground return current is extremely sensitive to the substation grid resistances which are mostly responsible for the screen voltage behaviour. The higher is the substation grid resistances the more the screens are “floating”. Since the line length is not great, the substation grid resistances (together with the lumped resistances of CB boxes) play a key role in the I

_{GR}. In order to understand this influence, in Figure 7, by fixing the values of CB box resistances (i.e., 5 Ω), different ground return current magnitude behaviours are shown (for a midline short circuit between phase 2 and screen 5) with different substation grid resistances from R

_{sub}= 0.02 Ω to R

_{sub}= 1.00 Ω.

_{GR}| behaviour changes very slightly. In order to confirm it, Figure 8 shows |I

_{GR}| behaviour for three short-circuit locations:

- at S substation;
- at R substation;
- at 3.9 km from S substation.

#### Ground Return Current in Double Circuit Underground Cable

_{GR}| behaviour, during a short circuit on a faulted circuit, lessens due to the presence of the unfaulted circuit screens. Figure 10 shows the sharing of short circuit current magnitude on the different screens: the unfaulted circuit screens subtract current to the ground. This is confirmed by the comparison of |I

_{GR}| in Figure 4 with that of Figure 11. Ground return current for two different fault locations is shown in Figure 12.

**Figure 10.**Faulted double-circuit UGC: screen current magnitudes along the line (CB with PTs); FAULT at midline.

**Figure 11.**Faulted double-circuit UGC: ground return current magnitudes along the line (CB with PTs); FAULT at midline.

**Figure 12.**Faulted double-circuit UGC: ground return current magnitudes along the line (CB with PTs) for two different locations.

## 3. Comparison with k-Factors

_{ss}= self-impedance of screen, Z

_{c1s1}= mutual impedance between phase conductor and screen, Z

_{s1s2}= mutual impedance between two adjacent cables, Z

_{s1s3}= mutual impedance between outer cables. These impedances can be easily computed by means of Carson-Clem formulae [7]. Substation resistances are not considered in Equation (3) whereas in Equation (2) they can be accounted for. Equation (4) is given by IEC 60909-2 [20] (and IEC 60909-3 [21]) for cables in trefoil arrangement, where R

_{S}= resistance of metallic screen (Ω/km), μ

_{0}= 4π·10

^{−4}(H/km), r

_{Sm}= 0.5(r

_{S_in}+ r

_{S_out}) (m), d

_{12}= distance between adjacent cables (m), d

_{13}= distance between outer cables (m).

**Table 2.**Comparison between multiconductor cell analysis (MCA) and k-factor for short circuit along the line A.

Short circuit location | |k| L.M. Popović | |k| MCA |
---|---|---|

$\ell =\frac{1}{4}L$ | 0.0083 | 0.0082 |

$\ell =\frac{1}{2}L$ | 0.0166 | 0.0165 |

$\ell =\frac{3}{4}L$ | 0.0249 | 0.0248 |

#### 3.1. Cross-Bonded Cable

_{GR}| along the line and the short circuit current |I

_{1P}| at fault location.

## 4. Comparison with ElectroMagnetic Transient Program-Restructured Version

**Figure 15.**Screen voltage magnitudes comparison between MCA and ElectroMagnetic Transient Program-Restructured Version (EMTP-RV) under phase-to-screen short circuit in a single circuit UGC.

## 5. Comparison with Sequence Theory

**Figure 17.**Faulted UGC: positive and zero sequence circuit for single-phase short circuit at midline.

_{1P}| = 58.588 kA) is at 3.9 km from substation S, whereas the maximum fault current is for a fault at substation R (|I

_{1P}| = 59.278 kA).

CB fault location Faulted screen 8 with corresponding phase 2 | MCA (kA) | SI (kA) | $100\cdot \frac{\text{MCA}-\text{SI}}{\text{MCA}}(\%)$ |
---|---|---|---|

Substation S | 61.186 | 61.171 | 0.0245 |

Substation R | 61.438 | 61.436 | 0.0033 |

5.4 km from Sub. S | 58.619 | 58.622 | −0.0051 |

**Figure 19.**Faulted double circuit UGC: positive and zero sequence circuit for single-phase short circuit at sending-end.

## 6. Conclusions

_{GR}behaviour. The paper deals with the I

_{GR}computation in faulty occurrence but some authors have also shown it in steady-state regimes [7]. The following conclusions can be drawn:

- ➢
- ➢
- The short circuit |I
_{GR}| is significantly influenced by the different values of both the major section CB box resistances and the substation grid ones since the metallic screens are earthed at each major section and at the substation sites: the lower the value of substation grid resistances the lower the magnitude of ground return current; - ➢
- The use of sequence impedance approach only for short circuit computations gives slight errors since the transposed UGCs are a rather symmetric system. Of course, the sequence theory approach cannot give |I
_{GR}|; - ➢
- The double-circuit UGC gives (in the same conditions of single-circuit UGC) lower ground return current magnitudes;
- ➢
- k-factors are valid for solid bonded cables. They are not applicable to cross-bonded UGCs whether single-circuit or a double- circuit;
- ➢
- IEC 60909-2 and 60909-3 give k-factors only for solid bonded three single-core cables laid in trefoil and flat configurations so that no evaluation is possible for cross-bonded cables which are the usual screen arrangement of HV-EHV cables. IEC k-factor applied to SB cables in flat laying gives an underestimate of about 10%.

## Conflicts of Interest

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**MDPI and ACS Style**

Benato, R.; Sessa, S.D.; Guglielmi, F.; Partal, E.; Tleis, N.
Ground Return Current Behaviour in High Voltage Alternating Current Insulated Cables. *Energies* **2014**, *7*, 8116-8131.
https://doi.org/10.3390/en7128116

**AMA Style**

Benato R, Sessa SD, Guglielmi F, Partal E, Tleis N.
Ground Return Current Behaviour in High Voltage Alternating Current Insulated Cables. *Energies*. 2014; 7(12):8116-8131.
https://doi.org/10.3390/en7128116

**Chicago/Turabian Style**

Benato, Roberto, Sebastian Dambone Sessa, Fabio Guglielmi, Ertugrul Partal, and Nasser Tleis.
2014. "Ground Return Current Behaviour in High Voltage Alternating Current Insulated Cables" *Energies* 7, no. 12: 8116-8131.
https://doi.org/10.3390/en7128116