Heating of Cables Due to Fault Currents

Balázs Novák, Zoltán Ádám Tamus Department of Electric Power Engineering

Budapest University of Technology and Economics Budapest, Hungary

nbalazs@eik.bme.hu

László Koller Department of Electronics and Cybernetics

Kalmár Sándor Institute of Information Technology Kecskemét, Hungary

koller.laszlo@vet.bme.hu

Abstract— The metal screen of new type of medium and high voltage single-core underground cables is comprised of helically applied copper wires embedded in a semiconductive layer. The distribution of current and power among the thin wires is non-uniform in a three-phase system, what can lead to their non-uniform heating, especially during fault conditions. The paper investigates this problem with 2D finite element models. The simulations are based on the coupling of the electromagnetic and thermal fields.

Keywords-underground cables; transient heating; fault current; finite element method

I. INTRODUCTION The prevailing single-core underground cable types used

today in new power distribution installations comprise a screen composed of several metal – usually copper – wires. These wires are applied helically with a very long length of lay over a semiconductive layer covering the conductor insulation, and they are embedded into a semiconductive material. A narrow and very thin metal tape is wound over them in the opposite direction (see Fig. 1a), and connects the wires electrically along one turn of its helix.

If an AC current flows in the cable conductor, it induces eddy currents and emf (electromotive force) in the metallic screen. If it is a single-core cable in a three-phase system, the emf can lead to potential difference between the separate cable screens and the ground. In order to eliminate this electric potential, the screens can be bonded and grounded at one or both ends of the cables [1 - 3]. Bonding at both ends generates further, circulating eddy currents and additional losses. The magnitude of the current and the losses in the screen – or generally in any metal sheath or armour – highly depends on its cross section [4]. The same phenomenon occurs in metal enclosed switchgears, where the losses in the enclosures can amount to the conductor losses [5]. Besides the degree of the losses, it is also important that the distribution of the power within the cross section and along the perimeter of a conductor is not uniform, if its size is comparable to the skin depth of the electromagnetic field in the conductor material [6]. In our case, this means that the separate screen-wires – although they are connected at certain points – might carry different amount of currents even within one cable.

Since the electric and thermal conductivities of the

semiconductive layers are low [7, 8], the induced power loss and therefore the heat are created largely in the wires, and during short, transient operation the temperature cannot be balanced between them. The degree of thermal non-uniformity is of primary importance, since the insulation of the cable might be exposed to high temperatures locally, at its contact with the metal components. The highest anomalies are expected in case of earth-faults, during which high zero sequence currents can flow in the grounded metal screen. In power distribution systems, where the neutral is not directly grounded (on medium voltage in Hungary - MV), double earth-faults, namely two earth-faults of two different phases at two points, can cause high zero-sequence fault current. In systems, where the transformers’ neutral is grounded (on high voltage in Hungary - HV), an earth-fault of one or two phases can cause significant currents in the screen. We try to demonstrate the importance of this question with 2D finite element (FE) simulations of a MV and a HV cable.

II. THE MODEL Although the exact simulation of the investigated cable

structure requires 3D modeling, with some considerations, a 2D model can also give meaningful results. First, the wires are almost parallel with the axis of the cable. Second, the tape, having a smaller pitch, enables a current to flow between neighboring wires at their contacts with the tape, thus it reduces the influence of the wires’ twists on the electromagnetic field’s distribution. And third, since the tape is very thin and narrow, its influence on the thermal field’s distribution can be neglected, that is it does not significantly improve the temperature balance. Accordingly, a 2D model can be created (Fig. 1b), in which the tape is considered in the 2D nature of the model.

Figure 1. Single-core cable structure (a) and its 2D model (b). 1. conductor;

2. inner semicon. layer; 3. conductor insulation; 4. outer semicon. layer; 5. screen-wires; 6. copper tape; 7. semicon. bedding; 8. sheath insulation.

This work was supported by the H-TEC Kft. (Hungarian Subsidiary of HYUNDAI Heavy Industries Co. Ltd.) by providing the FE tool for the calculations.

978-1-4244-6301-5/10/$26.00 @2010 IEEE

Two cable types were simulated, one MV (6/10 kV) and one HV (76/132 kV) one with an aluminum connductor having a cross section of 240 and 630 mm2, the screen is composed of 0.8 and 1 mm thick copper wires. According to the manufacturer’s catalogue [9], the total screen cross section is 25 and 105 mm2 that means 50 and 134 pieces of wires equally distributed along the outer semiconductor’s circumference. The rated currents of the cables were IR = 421 A and IR = 671 A. The conductor insulation was XLPE (5.5 mm and 18 mm thick), whereas the outer insulation was PVC (1.9 mm and 3.9 mm). The cables were tested in flat and trefoil formation, having 70 mm distance between them in the first arrangement and touching each other in the second one (Fig. 2). They were buried into the soil at a depth of 1 m. The total size of the FE model was adjusted to three times the skin depth of the encompassing soil.

A coupled field FE model took into account both the electric and thermal material properties of the cable components and the soil as well [10 - 13]. We used the ANSYS™ software for the simulations. Since the duration of the faults was well above one period of the frequency f = 50 Hz of the excitation, the electromagnetic model was set to harmonic mode and the thermal model to transient. We selected a time step of 50 ms, namely two and a half periods that meant 20 steps in one second. This time step selection gives useful results even for the first steps, since, after two periods, the exact time function of the current can be neglected [14]. Consequently, the use of a transient electromagnetic model is not necessary. The temperature change within one step is small enough not to influence the temperature dependent electromagnetic properties significantly. At the end of each step, the temperature values from a thermal simulation were read into the electromagnetic model, which provided the Joule-heat to the next thermal step. An initial steady-state calculation, assuming an excitation with the cables’ rated current (high-load), supplied the initial temperatures in some cases, whereas in other simulations, the fault started from a no-load condition, meaning an initial temperature of 20 °C all over the model.

Elements representing infinity terminated the boundaries of the electromagnetic model, whereas in the thermal model, a constant temperature of Touter = 20 °C was prescribed at the soil’s outer edges. In the electromagnetic model, three-phase symmetric voltages excited the cables (Fig. 3). We achieved this by defining an electrical circuit with voltage sources, resistors implementing the loads, and with lumped impedances representing and assigned to the FE cable conductors and screens. The soil was also modeled in the circuit with a lumped impedance, plus with two resistors of Rg1 = Rg2 = 10 Ω, taking into account the grounding resistance at the end of the cables. By adjusting the different resistance values, different loading conditions, like asymmetric or symmetric faults or loads, can be set in the model.

III. POWER DISTRIBUTION Fig. 4 illustrates the steady-state power density distribution

along the surface of the cable conductors and the total power of the individual screen-wires for a symmetric, three-phase load imposing a rated current on the cables. In these, and in all the

Figure 2. Flat (a) and trefoil (b) layout of the cables in a three-phase system.

Figure 3. Voltage excitation.

subsequent polar diagrams, the distance from the center of one circle represents the calculated value – in this case power or power density – and the angle from the horizontal axis corresponds with the real geometric location of a screen-wire (dots) or a point on the perimeter of the conductor (continuous line). The arrangement of the polar diagrams indicates the relative position of the cables to each other, but – as radius has other meaning – not their distances. Note that the center does not necessarily mean zero.

Practically no current flows in the low conductivity semiconductive material, therefore the power density is negligible there, and not shown in the diagram. In the conductors, the symmetrical current is constrained to regions near the neighboring phases, whereas in the screen, the outer wires farther from the other cables carry a higher portion of the induced currents.

In case of faults causing high zero-sequence current, the total cross section of the cable-screens highly influences the total loss and the power distribution. Smaller the cross section, more uniform the power distribution is, although the total loss is increased [4]. We can compare this effect caused by the earth-fault of phase A and a two-phase earth-fault of phases A

Figure 4. Steady-state power density distribution along the circumference of the cable conductors and the total power of the screen-wires in case of three-phase

symmetrical load; (a) flat, (b) trefoil arrangement.

Figure 5. Power in the individual screen-wires of the MV and the HV cable in case of single phase and two-phase earth-faults in flat (a) and trefoil (b)

arrangement. The faulty phases were A, or A and B together.

and B in Fig 5a and 5b. The MV cables contain a smaller amount of screen-wires, and the current and thus the power is more evenly divided among the screens of the individual phases. Whereas it is clear that in the HV cables, a much higher portion of the fault current is carried by the screen of the faulty phase, and a more remarkable power-difference can be seen between the wires of its screen. It is interesting that in case of a two-phase fault the screen of only one of the faulty phases is highly loaded, whereas the other one carries even less current than the screen of the healthy phase. In the cases above, a current of Ifault = 20 kA and Ifault = 7 kA was flowing in the faulty phases of the HV and MV cables respectively. It is worth noting that, due to the temperature dependent electromagnetic material properties, the power distribution also varies in time; the diagrams of Fig 5. show

the losses at the beginning of the fault, assuming a uniform initial temperature of 20 °C.

Comparing the flat and trefoil configurations, the smaller losses at similar fault currents imply that the current is more uniformly divided in the screens of the trefoil one (Note the different scale of the two diagrams!). This indicates a more favorable behavior during earth-faults.

IV. TEMPERATURE DISTRIBUTION Although the low thermal conductivity semiconductive

bedding inhibits the temperature flow between the individual screen-wires, the cable insulation and the bedding do not mean perfect thermal insulation. As we can see in Fig 6, the

heating of the conductors dominate the steady-state temperature distribution of the screen. It is because the induced power in the screen-wires during symmetrical loading is comparatively less than the power in the conductors (Note: In Fig. 4, the continuous and dotted lines have different dimensions, thus they cannot be directly compared.). Consequently, the character of Fig. 4 is not reflected here: the temperature is higher near the adjacent cables, since the cables heat up each other. It seems to be interesting at first, that the HV cables in trefoil formation are less heated, although they touch each other, letting less heat to be transferred to the soil. This can be the cause of the much less Joule-heat induced in the screen, which power highly depends on the distance of the phases and the cross section of the screen [4]. Higher is the distance, higher this loss is [2].

If an earth-fault current flows through the screen having a smaller cross section than the conductor, the power created in the small wires highly contribute to the temperature increase. It is a favorable coincidence that the wires farthest from the neighboring cables are heated the most, namely opposite from the steady-state maximums. For short faults, the steady-state character can still dominate the temperature distribution as in the MV cable, in Fig. 7, after 1 s of the earth-fault of phase A. Nonetheless, the power of the screen-wires (Fig. 5) is reflected more in the temperature distribution of the flat HV cable. Longer the fault, more pronounced the character of the power distribution is in the temperature, as it has been plotted in Fig 8, showing the case of a 3 s long two-phase earth-fault. The latter fault started from a no-load condition, that is the initial temperature was uniform, 20 °C. This enables us to estimate the real temperature rise along the perimeter of the conductors and in the separate screen-wires.

Figure 6. Steady-state temperature distribution along the conductor surface and in the screen-wires; (a) flat, (b) trefoil.

Figure 7. Temperature distribution after a single-phase earth-fault of phase A, lasted for 1 s; (a) flat, (b) trefoil. The initial temperature was obtained from a

steady-state simulation.

Figure 8. Temperature distribution after a two-phase earth-fault of phase A and B, lasted for 3 s; (a) flat, (b) trefoil. The initial temperature was uniform, 20 °C.

V. CONCLUSIONS This paper investigated the heating of single-core power

cables during single-phase and two-phase earth-faults. These can cause high zero-sequence currents flowing in the sheath or the screen. If the metallic screen is composed of thin wires – like in most of the cables used nowadays in power distribution systems – not just the power, but also the temperature of the individual wires can differ, as they are almost insulated thermally. In case of symmetrical, three-phase loading, the heating of the cable conductors largely determine the steady-state temperature distribution, whereas during earth-faults, the non-uniform power between the wires essentially shapes the distribution of the temperature.

During permanent, symmetrical load, the losses in the screens are constrained farther from the adjacent phases. However, the heat from the other cables offsets this effect making the temperature higher at the inner sides. During earth-faults, in the cable of the faulty phase, most of the power is concentrated also to the outer parts of the screen. In this case, the Joule-heat of the screen exceeds that of the conductor, and it will dominate the temperature distribution. If the fault is very short, and superimposed on a high operational load, it can appear as a balancing effect on the steady-state temperature.

It is important, that large screen cross-section can be disadvantageous both during symmetrical loading [4], and in case of earth-faults. A smaller cross section can lead to a more balanced current distribution and less Joule-heat, not just within the screen of one cable, but also between the screens of the individual phases. The layout of the cables is of a considerable importance, too. The touching trefoil configuration has a more favorable earth-fault behavior, as the zero-sequence current is divided more evenly among the screens of the cables. This results in less local power and temperature rise than in a flat arrangement, exposing the insulation to less thermal stress.

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