# Steady State Assessment of Shunt Compensated EHV Insulated Cables by Means of Multiconductor Cell Analysis (MCA)

## Abstract

**:**

## 1. Introduction

## 2. Brief Recalls to Shunt Compensation Features

_{ξ}depends upon the shunt compensation degree, whose value can be computed by means of the criteria developed in the next subsection, which refer to the single-phase circuit. The value of Y

_{ξ}is obviously different depending upon these two different situations. In case of Figure 1, Y

_{ξ}can be computed as in Equation (1):

- ξ
_{sh}= shunt compensation degree; - c = UGC kilometric capacitance (F/km);
- d = cable line length (km).

_{ξ}and Y

_{ξ}' in case of lumped compensation also at intermediate locations (see Figure 2) becomes:

#### The Determination of Shunt Compensation Degree by Means of Single-Phase Circuit

_{o}(assumed U

_{o}= 230 kV) and the short-circuit subtransient impedance Z'' (for simplicity purely inductive Z'' = jX'').

_{o}/I''

_{sc}(from network studies): since the values of subtransient short circuit current I''

_{sc}(three-phase at S) in EHV networks can be foreseen in the range 10 $\xf7$ 50 kA, X'' corresponds to 23 $\xf7$ 4.6 Ω. In order to respect the standard switching levels (e.g., 1050 kV) with a conservative margin, it seems advisable that the phasor U''

_{oR}does not exceed the magnitude U

_{m}/ $\sqrt{3}$ = 242.5 kV: such target can be reached by introducing in (5) a suitable compensation degree which suitably modifies the parameters A and C. In the hypothesis that, once the transient phenomena have extinguished, the voltage regulation restores again at port S the rated value U

_{o}= 230 kV, it is possible to compute:

_{NL}(which the circuit breaker b must interrupt in case of de-energization of the no-load cable): for this current the Standards on the Circuit Breaker (§ 4.107 of [4]) suggest the limit value of 400 A. After all, both the following additional constraints must be fulfilled (by assigning a suitable compensation degree ξ

_{sh}):

_{oR}≤ 242.5 kV

_{NL}| ≤ 400 A

_{sh}, unless there is an agreement with the manufacturer for a circuit breaker with higher I

_{NL}.

_{sh}which fulfills the relations (7) or (8): it shows which is the more limiting criterion as a function of the line length. It appears almost trivial to note that the considerations regarding the additional constraint of (7) must be performed also for the energization by the port R, by introducing for the parameters U

_{o}and X

^{"}suitable values in consideration of the supply grid linked to R: the detection and the choice of the “best end switching” [5] are mentioned by CEGB as effective experienced practices in network operations. Moreover, the cases where the steady state capacitive power absorbed by the cables (Q

_{NL}= 3U

_{o}I

_{NL}) exceeds the ability of synchronous generators (dangerous self-excitation conditions), located in close proximity of the cable installation, must be avoided. In any case, it is advisable that the TSO, when planning a new link, performs both detailed power flows and network simulations.

**Figure 4.**Limit lengths due to the constraints (7) and (8) for cable of Table 1.

**Figure 5.**Reactive compensation degree as a function of cable length due to the constraints (7) and (8) for cable of Table 1 and X'' = 20 Ω.

Cable cross-sectional area | mm^{2} | 2500 Cu |

Conductor diameter (Milliken type with six sectors) | mm | 63.4 |

XLPE insulation diameter | mm | 119.9 |

Metallic screen diameter | mm | 130.1 Al |

Screen cross-sectional area | mm^{2} | $\cong $ 500 |

PE jacket diameter | mm | 141.7 |

Total mass | kg/m | 37 |

## 3. Insertion of Shunt Reactors in the MCA

**Y**to be overlapped in the right locations. There are two methods to compute the admittance matrix

_{Eξ}**Y**; the former is a direct calculation by the inspection method as in Figure 6. The latter is computing firstly the matrix

_{Eξ}**Z**(6 × 6), as shown in (9), where Z

_{Eξ}_{ξ}= 1/Y

_{ξ}. Successively by matrix inversion, it is possible to obtain the admittance matrix

**Y**= (

_{Eξ}**Z**)

_{Eξ}^{−1}. The computation of the shunt susceptance Y

_{ξ}has been already presented in Section 2.

## 4. Case Study

_{sh}= 0.608). The UGC is cross-bonded (CB) with phase transpositions (PTs).

Multiconductor cell length | km | 0.125 | |

Cable drum (Minor section) | km | 0.625 | |

Cross-bonding section Length (Major section) | km | 1.875 | |

Substation earthing | R_{E} | Ω | 0.1 |

Earth resistivity | ρ_{soil} | Ω m | 100 |

Cross-bonded box resistance | R | Ω | 10 |

Screen resistance at 78.2 °C (50 Hz) | r_{sh} | mΩ/km | 70.0 |

Link resistance | r_{E} | mΩ | 1 |

Shunt compensation degree | ξ_{sh} | 0.608 | |

Number of shunt compensation stations | 4 (or 2) | ||

Ampacity | A | 1788 | |

Load at receiving-end | MW + jMvar | 1214 + j0 |

**Figure 8.**Subdivision of the CB single-circuit cable line with indication of lumped shunt compensation locations.

**Figure 11.**Screen voltage and current magnitudes along the compensated single-circuit cable in CB with PTs.

**Figure 13.**Screen voltage magnitudes along the compensated single-circuit cable in CB with PTs at no-load.

**Figure 17.**Phase current magnitudes along the compensated single-circuit cable in CB without PTs and compensated only at the two ends (as in Figure 1).

## 5. Conclusions

## Acknowledgement

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**MDPI and ACS Style**

Benato, R.
Steady State Assessment of Shunt Compensated EHV Insulated Cables by Means of Multiconductor Cell Analysis (MCA). *Energies* **2012**, *5*, 168-180.
https://doi.org/10.3390/en5010168

**AMA Style**

Benato R.
Steady State Assessment of Shunt Compensated EHV Insulated Cables by Means of Multiconductor Cell Analysis (MCA). *Energies*. 2012; 5(1):168-180.
https://doi.org/10.3390/en5010168

**Chicago/Turabian Style**

Benato, Roberto.
2012. "Steady State Assessment of Shunt Compensated EHV Insulated Cables by Means of Multiconductor Cell Analysis (MCA)" *Energies* 5, no. 1: 168-180.
https://doi.org/10.3390/en5010168