Elsevier

Electric Power Systems Research

Volume 150, September 2017, Pages 137-143
Electric Power Systems Research

Core laying pitch-long 3D finite element model of an AC three-core armoured submarine cable with a length of 3 metres

https://doi.org/10.1016/j.epsr.2017.05.008Get rights and content

Highlights

  • This paper deals with three-core armoured submarine cables.

  • The power losses in core, screens and armour are computed by a finite element model.

  • The model is 3-meter-long and takes the core and armour wire strandings into account.

  • A 3D FEM model of 3-meter-long three-core cable is presented for the first time.

Abstract

This paper presents a complete three metre long 3D finite element method (FEM) model of a three-core submarine armoured cable. In this model, the different laying pitches of cores and armour steel wires are correctly taken into account. For the first time in technical literature, a 3 m long model has been successfully solved. The CPU times are very high i.e. about 70 h (mesh plus solver). IEC 60287-1-1 gives a strong overestimation of armour and screen power losses and consequently an important underestimation of cable current rating. It is worth noting that IEC gives an overestimation even if a 2D model is considered, i.e. the stranding is not taken into account.

Introduction

The growing interest in the renewable energy sources, and the possibility of using large scale storage installations [1], [2] in order to overcome the problems related to the non-programmable sources, requires versatile and compact interconnection systems. Submarine three-core cables represent a great opportunity to link off-shore wind farms [3] with the electrical grid and energy storage installations. Moreover, it is worth noting that three-core cables could be a very interesting solution in case of multi-purpose structures which host in the same facility power transmission systems and other types of installations, such as gas or water pipes [4].

Therefore, the total amount of power losses in a.c. three-core armoured submarine cables is a paramount issue in order to correctly compute the current rating [5]. As it is well known, the cores and the armour wires are stranded with different laying pitches for mechanical reasons.

IEC does not consider these layings and gives a strong overestimation of screen and armour power losses, mostly because it disregards that the helically lay of the armour wires and core conductors performs a cancelling effect of the induced current in the armour. It is worth noting that IEC gives an overestimation even if a 2D model is considered, i.e. the stranding is not taken into account; however, 2D model presents the same limitations of IEC if compared to real measurements.

In order to have an overview of the international experience on power loss computation for armoured three-core power cables, an analysis of the most significant contributions in the scientific literature [6], [7], [8], [9], [10], [11] is summarised in this section, and the most relevant conclusions are here reported. The main aspects, on which the three-core power cable researches focused, are:

  • Representing three core power cables by means of finite element method (FEM), by taking into account armour and conductive layers;

  • Highlighting the effects of different laying designs in terms of power loss reduction;

  • Comparing the IEC 60287 power loss computation approach with real measures or simulations.

For example, in Ref. [6], 2D and 3D FEM analysis of three core armoured cables are described and the simulation results are discussed in comparison with the losses calculated according to IEC 60287. The FEM model represents a three-core armoured cable, in which armour and cores are stranded in opposite directions. The model length is 1/3 of the core laying pitch.

In Ref. [8] a FEM model is developed with 10 straight armour wires around three twisted phase conductors. The wires are assumed to be nonconductive in order to simplify the model, and to reduce the mesh inside the wires. In these conditions, a substantial decrease of armour losses can be obtained by increasing the effective pitch length between the armour and the phases. The losses at rated current are much lower than the IEC 60287 predicted ones, and the potential to optimise a design is significant if a more accurate model is used to calculate the cable losses.

In Ref. [9], measurements of a 245 kV 3 × 1 × 630 mm2 armoured and unarmoured cable are presented along with a description of the data processing of the measured quantities. The armoured cable has a higher loss than the unarmoured one.

In Ref. [10] armour losses are measured and calculated during the design process of submarine cables using IEC 60287-1-1 formulae. In this paper, armour losses are investigated on two different high voltage (HV) three-core submarine power cables. One cable is with full steel armour wires, the other one with armour composed of steel and polyethylene (PE). It has been observed that the substitution of steel wires with PE wires reduces armour losses and that the IEC approach for power loss computation involves overestimations.

In Ref. [11] the measured armour losses of an armoured three-core cable are compared with 2.5 FEM model results and with IEC 60287 procedures and, once again, it has been demonstrated that IEC 60287 approach could imply considerable overestimations of cable power losses. Moreover, in the paper, the basic principle of cancellation by stranding/twisting is presented. What clearly yields within this context is that there are not technical contributions which analyse the total armour and core laying pitches by means of FEM approach [6], [7], [8], [9], [10], [11]. This is due to the fact that the typical laying pitch length for such cables is some meters (from 1 to 3 m), and it involves a considerable computational complexity of FEM models which require very powerful computer and very long CPU times.

It is worth highlighting that the idea of using in FEM analysis core laying pitches which are shorter than the real ones, in order to reduce CPU time and model complexity, does not allow representing the real electromagnetic interaction between the conductive elements of the cable. Therefore, from one hand, it is not possible to calculate the cable power losses correctly and consequently it is difficult to identify an optimal three-core cable layout in terms of laying pitch length and stranding direction. On the other hand, it is evident that the longitudinal cable construction influences the cable total power losses [6], [7], [10].

All the technical community agrees that the IEC 60287 approach is very conservative [6], [8], [9], [10], [11], [12], [13].

With regard to the armour magnetic permeability, Ref. [6] compares the results of a three-core cable model considering an armour permeability function inferred by measurements with the model results obtained by a constant permeability value: the results are very similar. Therefore, the hypothesis of considering an armour constant permeability value is acceptable.

Besides FEM analysis [14] of three-core armoured cables, scientific literature offers analytical approaches as well [15], [16], [17], [18], [19], [20], [21]. A very interesting approach is proposed in Ref. [19] in order to include the stranding of wires into impedance calculations.

Section snippets

Two-dimensional analysis of three-core armoured cables

The considered three-core armoured submarine cable is shown in Fig. 1: its geometric parameters are reported in Table 1 whereas the electrical ones in Table 2.

In order to have a deep understanding of the phenomena occurring without stranding, it seems necessary to analyse the electric behaviour of voltage and current phasors by assuming a two-dimensional symmetry which corresponds to the absence of the strandings.

In order to have a wide overview of the available commercial and free FEM

Three-dimensional analysis of three-core armoured cables

In this section the power loss computation of an armoured three-core cable by means of a 3D FEM model is presented. Different FEM software were used in order to implement such a model but, even by decreasing the mesh density (within certain limits in order to have a realistic solution), only Flux 3D successfully managed a length of 3 m, without aborting the simulation.

A first very important 3D simulation is a 3 m three-core cable, which has all the electrical and geometrical characteristics

Cable of real length: further researches

In order to have a confirmation of the last sentences of the previous section, by means of FEM, it would be necessary to simulate the length of a real cable or at least a periodicity. In order to simplify the problem with shorter laying periodicities, it would be possible to reduce both the core and armour laying pitches. However, the model assumption of 3 m for core laying pitch and 2 m for armour one reflects the real laying pitches used, for mechanical reasons, in real three-core submarine

Conclusions

The paper demonstrates that a ratio of 2/3 between armour and core laying pitches is very effective in order to strongly lessen the armour induced current losses. In this regard, both unilay and contralay strandings offer good possibilities to reduce the circulating currents in the armour.

The choice of considering (and the success of having simulated it for the first time in technical literature) a 3 m long cable is useful to understand the interaction between screen induced currents and armour

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