# Using EMTP-ATP and ANSYS programs for determination of dielectric stress of medium voltage cables.

1. INTRODUCTION

The main part of medium voltage electrical industry systems is operated with cables lines. All plastic cables on the voltage level 1, 6, 10 and 22 kV are used for the transmission of the electric energy mainly.

The damage of cables can be caused by the mechanical stress and then by the humidity penetration. The insulating system can be damaged by the electrical and the temperature stress at normal and fault states. Last mentioned fault states are with the short-period, but the activity of these states can accelerates degrading process of insulating system and cause of disruptive discharge in the durability life. This fact is caused by the inception of partial discharges (Slaninka, 1989). Cables lines with plastic materials are sensitive on the inception of partial discharges. It is desirable in order that electro-insulating material must have high specific dielectric strength and the maximum of dielectric stress has to be at the allowed limit.

The maximum dielectric stress is influenced by form of the electric field at specific voltage. Where, the electric field is defined by the cable construction and by parameters of individual parts of dielectrics. The intensity of electric field is not constant in the heterogeneous filed of cable line, but the intensity of electric field is dependent on the position data at the cable dielectric.

[FIGURE 1 OMITTED]

The main target of the electric field solving is location of the position with the maximum value of the electric field intensity for variety of running and fault states of the cable line.

Results from this analysis are applicable for the optimizing of the cable line design and the medium voltage system too.

2. MATHEMATICAL MODEL OF MEDIUM VOLTAGE CABLE IN EMTP-ATP AND ANSYS

Results from mathematical modelling of the electric field of the medium voltage 3phases enclosing pipe 6AYKCY 3x70/16 are introduced within this chapter. The electric field of the mentioned cable line is simulated with using program ANSYS for the running state. The place with maximum dielectric stress is located with the program ANSYS too. The section of the cable 6AYKCY 3 x 70/16 is shown in the Fig. 1, where "1" is aluminum core, "2" PVC isolation, "3" cushioning cover, "4" inner sheath, "5" tape1, "6" cooper concentric conductor, "7" tape2 and "8" is PVC outer sheath.

The mathematical model of the cable line 6AYKCY 3 x 70/16 was created in the program ANSYS as a next. The core of ANSYS program uses principle of Finite Element Method. The cable is modelled as a geometrical dissociation of individual layers with the specification of basic parameters. Individual layers are defined by material density (kgx[m.sup.-3]), specific thermal conductivity (Wx[m.sup.-1]x[K.sup.-1]), specific resistance (Wxm), specific heat capacity (Jx[kg.sup.-1]x[K.sup.-1]) and relative permeability (-). The solution of the electric field distribution was realized for the no-load state of the cable at supply by source 6kV, 50 Hz. The result of the simulation is shown in the Fig. 2. From Fig. 2 is evident, that the maximum dielectric stress is on the core surface in the cores intersection. It is state, when the applied voltage is line-to-line voltage. The maximum dielectric stress value was defined by the simulation about electric field intensity 1,93 kVx[mm.sup.-1]. The maximum value of dielectric stress, which is guaranteed by producer for the PVC insulation, is in the interval (2,8-3,3) kVx[mm.sup.-1]. It is evident, that the maximum value of dielectric stress was not exceeded. On the other side, it is necessary to respect, that this analysis was realized for the running state.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

In the case inception of the 1polar earth-fault in the medium voltage system is insulation of the cable line extremely stressed by increasing of the amplitude voltages at phases without fault. The voltage in the phase with the fault is limited by resistance of the electric arc (See Fig. 3). The mathematical model of the tested medium voltage system with the cable lines was created in the program EMTP-ATP. The mathematical pre-processor ATPDraw was used in the concrete. This model was used for the definition of earth-fault influence on the cable line insulationThe cable line has size 2000 meters with the total capacitive current c. 2A. 1polar earth-fault was simulated as a 1phase arc earth-fault; the mathematical model of electric arc respects Mayr theory in the EMTP-ATP (Misak, 2007). Final courses of instantaneous values of voltages at arc earth-fault are shown in the Fig. 3. The course of current by fault is shown in the Fig. 3 too. All courses were obtained with the using mathematical modeling in the EMTP-ATP and verified by real experiments in the medium voltage system Power Station Detmarovice. The increasing of voltage without fault to line-to-line voltage 6kV and drop of voltage with fault to value limited by the resistance of the electric arc is evident from the Fig. 3.

The new analysis distribution of the electric field intensity was realized repeatedly for the case inception of the arc earth-fault in the medium voltage analyzed system. Analysis was executed by the program ANSYS too.

The solution of the electric field distribution at cable 6AYKCY 3x70/16 for the fault state is introduced in the Fig. 4. There is representation of the extreme stress with the amplitude 3,34 kVx[mm.sup.-1]. This value is over the limited allowed dielectric stress.

Furthermore, the dielectric stress of the electric insulation is increased in the case, when initial conditions are changed by time--dependence resistance of the electric arc (Van der Sluis, 2001).

3. MATHEMATICAL MODEL OF CABLE IN ANSYS

For the examination of electric stress of an insulation system, there is necessary to find time and space distribution of the electric field intensity. It is familiar that electric field with intensity vector has irrotational character, also term conservative is used. We can obtain two forms of Maxwell equation--differential or integral--related to an intensity of electric field vector, electric induction and charge, with the mutual conversion by the help of Stokes' integral theorem. Direct mathematic solution with vector of the intensity is complicated, so it can be done with the help of scalar electric potential (Hanka, 1975; Vanderline, 2005). It is a single-valued function of location, continuous at a boundary, what is favourable to numerical modelling.

[FIGURE 4 OMITTED]

Physical model was simplified by omitting the tape areas 5 and 7 in Fig. 1. The cable is assumed to be infinity long and solved problem is two-dimensional. There were used two-dimensional, eight-node elements PLANE121 with one degree of freedom (voltage) at each node. This element is based on the electric scalar potential formulation, and it is applicable to a 2D electrostatic and time-harmonic quasi-static electric field analyses. Model was realized with a number of 56 637 nodes and 20 278 elements. Next simplification is a constant permittivity.

Defined materials are considered as a linear--independent to the field quantities and isotropic--the same in all of directions.

Problem is solved as a range of static analyses for defined instants of time and particular voltage amplitudes. It is assumed three-phase cable and it means three time-dependent instantaneous voltages or potentials at each phase conductor.

Self and mutual capacitances of a general multi-electrode system with a certain configuration can be solved by the Simpson's mirroring method and by calculation of capacitance coefficients, also with the aid of FEM or directly with Ansys internal macro CMATRIX.

4. CONCLUSION

The possibility of using mathematical programs for the technical diagnostic of insulation system was verified within this paper. Methods of mathematical modelling were used for the optimizing of cable line design and medium voltage system for running and fault states too. Results of simulation were verified within real experiments at medium voltage system in the Czech Republic.

5. REFERENCES

Misak, S. (2007). Mathematical Model of Electric Arc at High Voltage Systems. Proceedings of the 18th International DAAAM Symposium, Katalinic, B. (Ed.), vol. 18, October 2007 page numbers (14-17), ISSN 1726-9679.

Hanka, L. (1975). Theory of Electromagnetic Field, SNTL, Praha.

Vanderline, J. (2005). Classical Electromagnetic Theory. Kluwer Academic Publishers, 1-4020-2699-4, USA.

Slaninka, P. (1989). Cable Technic 1, SVST, ISBN 80-227-0026-6, Bratislava.

Van der Sluis, L. (2001). Transients in power systems, John Wiley & Sons Ltd., ISBN 0-471-48639-6, England.