Electro-gas model breaking of capacitive currents within high voltage SF6 circuit breaker

Hamid Zildžo, Rasim Ga�anovi�, Halid Matoruga University of Sarajevo

Department of Electrical Engineering Zmaja od Bosne bb, Sarajevo, B&H

hamid.zildzo@etf.unsa.ba, rasim.gacanovic@etf.unsa.ba, halid.matoruga@etf.unsa.ba

Abstract— This paper presents the modeling of coupled turbulent flow of SF6 gas and the electric field in high voltage switch gear during the interruption of capacitive currents, by using the so-called electric-gas flow model fields. Specifically, for a number of positions moving and stationary contacts during turn-off, the flow parameters of SF6 gas and the electric field between the contacts has been simultaneous calculated with finite element method. Using the calculated density of SF6 gas distribution and electric field strength at the reference conditions in the gas, one can calculate the real dielectric stress of the contacts position during switching-off of capacitive currents. During the modeling fluid flow SF6 gas applied the k-� turbulence model and the Simplex method corrected by Chorin and Gresho.

Keywords - turbulent flow of SF6 gas; electric field in high voltage switching; electric-gas flow model fields; Finite Element Method; Navier Stokes equations

I. INTRODUCTION The most important SF6 gas parameter, which is calculated

at any given point in time is the fluid density. Changing the density is proportional to defining the change in dielectric strength between contacts - space in relation to calculated dielectric strength under reference conditions in SF6 gas. For example, Nagata [1] demonstrated this principle for temperatures less than 1100 (K). Eliason and Schade [2] showed good agreement with Pashen`s law for the change of the gas temperature below 2300 (K). The aim was to determine the minimum contacts speed for switching - of where there will be no re-dielectric breakdown caused by interruption of capacitive currents.

II. MATHEMATICAL MODEL Numerical forecasting breakdown strength consists of

three step for a number of positions of contacts during the disconnection of capacitive current:

� In the first step, calculate the parameters of 2D unsteady turbulent flow of compressible viscous fluid - SF6 gas, using the Simplex procedure from Patankar and Spalding corrected by Chorin and Gresho, [3].

� In the second step calculating the dielectric stresses, ie. the calculation distribution of electric field between contacts space under reference of SF6 gas conditions.

� In the third step, using the results from previous two stages, carry out forecasting breakdown voltage between contacts distance using a procedure proposed by Okamoto and Kuwahara [4]-[6].

A. 2D Compressible viscous fluid flow equations In the parameters calculation of 2D unsteady turbulent

flow of compressible viscous fluid SF6 gas the following settings are used:

� Setting general parabolic differential equations of conservation of mass, conservation of momentum (Navier Stokes equations), turbulence kinetic energy conservation, conservation of dissipation of turbulence kinetic energy and energy conservation using the Patankar and Spalding Simplex procedure for the general 2D fluid flow corrected by Chorin and Gresho [3], adapted to the general concept of the finite element method;

� Discretization of the conservation equations using a generalized procedure Galerkin weight remains in Finite Element Method. Discretization is performed by 2D finite element-triangle;

� The introduction of turbulence in the conservation equations using two equation k-� turbulence model;

� In the procedure of solving those equations conservation is necessary to take into account the initial and boundary conditions. For all the above mentioned conservation equations used all three types of conditions (Dirichlet, Neumann and combined conditions). In conservation equations of turbulence, kinetic energy and its dissipation along the solid boundary dissipation functions, are used to Launder and Spalding with coefficients which are given empirically as a function of types of solid surface boundaries (Stubley, Klebanoff, Panofsky and Dutton), [3] and [7]. This way satisfies the boundary conditions dissipation, while avoiding unnecessary fragmentation of the finite element mesh along the border;

� To accelerate the convergence of k-� turbulence model it’s needed to linearize the original article of the

978-1-4577-0746-9/11/$26.00 ©2011 IEEE

Raithby [3] in the equations conservation kinetic energy of turbulence and its dissipation;

� Evaluating the efficiency, stability and accuracy of selected numerical procedures.

The following variables are used or solving the parameters of 2D fluid flow SF6 gas: density, velocity components, pressure, temperature, turbulence kinetic energy and its dissipation rate, then laminar, turbulent and effective coefficient of dynamic viscosity and thermal conductivity, and coefficient of specific heat capacity.

Using the following equation, [3] and [5]: � The equation of mass conservation

���� � �

�������

�� � ����� ��� � � (1)

where: � - Density fluid ����- r velocity component ��� - z velocity component

� The equations of momentum conservation - the Navier-Stokes equations

� ����� � ������ � ������ � !� � "#

$ ����%�&�����' (2) where: ���� - Velocity of fluid �� – Pressure of fluid �� - Effective coefficient of viscosity for the next time step integration, and is calculated as the sum of the known coefficient of viscosity �( laminar and turbulent viscosity coefficient ��:

��)*� � �( �� ��)*� (3) �� - Turbulent viscosity coefficient is calculated using the k-� turbulence model, based on the known values of empirical constants c� and values of turbulent kinetic energy k and its dissipation � calculated in the previous step "n" to integrate in time using the following formula:

��)*� � +" �,)�-.)

%+" � +/0123 ' (4)

F�

-vector of volume forces acting on the observed fraction of fluid (the most famous are the gravity force, buoyancy force, electromagnetic force, etc.).

� The equation of energy conservation

� 4 +5 4 �6�� � ��� 78� �6

��9 � ��� 78� �6

��9 � ���6�� �

��� 4 +5 4 7��� �6�� � ��� �6

��9 � :; (5) where: <�- Temperature of fluid; +5- Specific heat of fluid at constant pressure; 8��- Effective coefficient of thermal conductivity for the next step of integration in time, and is calculated as the sum of the known coefficient of laminar and turbulent thermal conductivity coefficient of thermal conductivity:

8�)*� � 8( �� 8�)*� (6)

using k-� turbulence model. 8�)*� - Coefficient of turbulent thermal conductivity is calculated using the calculated turbulent viscosity coefficient ��)*� for at the moment of time "n +1" and turbulent Prandtl`s =� number of heat (which usually amounts to =� � �3>), using the following terms.

8�)*� � "?@AB�

C? (7)

:; - Thermal source.

� The equation turbulent kinetic energy conservation

The equation of conservation of kinetic energy of turbulence, is given by:

� �D�� � "#

CE F�� ��� 7� �D

��9 � �GD��GH � � 7��� �D

�� � ��� �D��9 ���� IJ K7���� 9

- � 7�� 9 � 7� �� 9-L � 7� �� � ��

�� 9-M � �.

(8) where: k - Kinetic energy of turbulence. =D- Prandtl`s number for turbulent kinetic energy of turbulence (taken �=D=1.0).

� The equation turbulent kinetic energy dissipation conservation

The equation of conservation of turbulent kinetic energy dissipation, is:

� �N

�� � "#CO F�� �

�� 7� �N��9 � �GN

��GH � � 7��� �N�� � ��� �N��9 �

� PBN"?D � IJ K7���� 9

- � 7�� 9 � 7� �� 9-L � 7� �� � ��

�� 9-M � PG�NG

D

(9) where: . - Degree of turbulence kinetic energy dissipation; +�Q +- - Constants which have value: +� � R3SS� and +- � R3>J; =N-Turbulent Prandtl number for dissipation of kinetic energy of turbulence (taken =N � R3T).

� The state of fluid equation

The fluid equation of state implies the dependence of fluid density on pressure and temperature, given by:

� � ����Q <��������� (10)

Many fluid are assumed to have � � +/0123. However, the gas must take into account the density dependence of pressure and temperature. This dependence is taken into account by means of known relations and coefficients for ideal gases, or by using experimental data for real gases.

� Experimental equations of fluid

Experimental equation coefficients laminar viscosity and laminar thermal conductivity are set as a function of pressure and temperature as it follows:

�( � �(���Q <� 8( � 8(���Q <� +5 � +5���Q <� (11)

For solving equation’s (1)-(11) used Simplex method

corrected by Chorin and Gresho [3], adapting of the concept of finite element. Simplex method, consists of the following eight steps, which are addressed in each discretized point of integration in time step:

� Solving the Navier Stokes equations in r direction for the estimated value of speed

� Solving the Navier Stokes equations in z direction for

the estimated value of speed

� Solving Poisson's equation to correct pressure

� Solving the equation for the correction of the r components of velocity

� Solving the equation for the correction of the z

components of velocity

� Solving the equation of kinetic energy of turbulence conservation

� Solving the equation of kinetic energy dissipation of

turbulence conservation

� Solve the equation of energy conservation

The partial differential equations described in eight steps

Simplex method can be summarized with the general parabolic partial differential equations given by the expression:

UV WXW2 � W

W� YZVWXW� [ �

WW\ YZV

WXW\ [ �

�]V 7��� �V�� � ��� �V��9 � ^V (12)

Domain of calculation is discretized by finite element

method, using a procedure Galerkin`s weight residue of the general parabolic Equation (12), will produce a solution in a system of coupled differential equations, given by:

_`a bcVc� d) � _eafXg) � fhg) (13)

The solution of the system coupled differential Equation

(13), after application of the famous Wilson � method, can be displayed in the form of systems of linear algebraic equations given by:

i �j�kAB _`a � l_eam fXg)*� � �R � l�fhg) � lfhg)*� �

�� i �j�kAB _`a � �R � l�_eam fXg) (14)

During the solving a system of linear algebraic Equation (14) it will receive the value of the unknown function �X general parabolic partial differential Equation (12) at the integration point in time will be given. So, the described general procedure of solving parabolic partial differential equations should be applied to all of eight step Simplex procedure corrected by Chorin and Gresho at every moment in time integration.�

B. Calculation distribution of electric field under reference SF6 gas conditions

Distribution of electric fields in-between contacts under reference SF6 gas conditions described the Laplace equation n 4 op � � (15)

where: n – Dielectrical permitivity; p – Electrical potential.

C. Calculation of dielectric strength in-between contacts

Estimation of critical values of electric fields in SF6 gas, according to Kuwahara [5], [8], [9] and [10] can be performed using linear proportions change with the change of dielectric strength of SF6 gas density, as it follows:

qP� � qrs� t�u (16)

where: qP��- Critical value of the electric fields in SF6 gas in real conditions;

qrs� - The critical value of electric fields in SF6 gas in nominal conditions; v - Calculated value of the density of SF6 gas in real conditions; �r - Calculated value of the density of SF6 gas in nominal conditions. Estimation of critical values of breakdown voltage in SF6 gas, it can be done using the estimated values of critical electric field, using the following expression:

� wP� � qrs� xs�xyzs wr� ��� �

where:

wr - Reference voltage; q{zs- Electric field on the stationary arc contact at the reference voltage wr.

Fig. 1. Finite element mesh switching to the position of contacts during the switching-off

After substution the Equation (16) in Equation (17), one can write:

wP� � xus��uxyzs � � +/012 4 � � |��������������������

Equation (18) shows that the estimate of the breakdown voltage in SF6 gas can be made directly the calculating the distribution density of SF6 gas.

III. CALCULATION EXAMPLE

Numerical modeling of dielectric strength in-between contacts distances - SF6 gas was performed by the example of the switching element [11] that is embedded in a series of switches manufactured by Energoinvest Co., for indoor and outdoor installation, which works on the principle of increased use of thermal energy ports. To this purpose the computer program COMSOL Multiphysics was used. The focus was the observation of many number contacts position after a successful switching-off of capacitive current. The aim was to determine the minimum contacts speed, and to prevent re-breakdown of SF6 gas during the next interruption of capacitive current.

Fig. 2. Breakdown voltage in-between contacts space of switching element at reference conditions of SF6 gas

Fig. 3. The pressure in the compression cylinder when switching off the switch without load

Fig. 4. Speed of contacts when switching off the switch without load

Observation begins at the moment when nozzle Laval type leaves extra clip, and ends at the moment of full contact spacing. Simulate real gas is designed as in databases, the gas equation of state coefficients of laminar dynamic viscosity is defined, laminar thermal conductivity and specific heat capacity as a function of various values of pressure and temperature [12], [13] are set. For the calculation of the flow of gas used for the initial boundary conditions that define the internal flow, external flow, the flow at the boundary (wall) and the flow of the symmetrical boundary.

Fig. 5. The distribution velocity of SF6 gas for the monitored position of the contacts at the switching-off of the case-break speed v=6,5 m/s

Fig. 6. A change in time of pressure SF6 gas in the vicinity of arcing contacts in case of switch-off speed v = 6.5 m / s

Experimental studies are important for two reasons:

� Application of test results with previous surveys as input data for numerical modeling of a new prototype switching element.

� Checking the results of numerical modeling of a new prototype switching element for switching tests in High power laboratory.

The paper used the following measurement results were obtained in studies related family of switches:

� Functions of the breakdown voltage in-between contacts distance, the pressure of the compression cylinder, moving walks contacts and speed of contacts during the turn-off switch without load, [14], are shown in Fig. 2, Fig. 3 and Fig. 4.

The performed numerical prediction of dielectric strength between contact distance in the switching element [11] in terms of gas density changes as a result of expiration of the nozzle. The observed switching element has successfully met all the tilt tests. When generating the mesh in the integration step observing the position of contacts in the direction of energization, the benefits generated by the initial finite element mesh. Only a small portion of the input region with the fixed arcing contact, his screen and the compression cylinder piston, generates for each new position of contacts. In this way, it provides the necessary continuity of originality temporal boundary condition parameters for all subsequent steps integration in time, the number of required computer operations network in the generator is reduced to a minimum.

Fig. 7. A change in time of pressure SF6 gas in the vicinity of arcing contacts in case of switch-off speed v = 6.5 m / s

Fig 1 shows the finite element mesh generated for a single observed position of the contacts during switching-off. For the same position of the contacts, the calculated distribution of velocity, pressure and the electric field are given in Fig. 5, Fig. 6, Fig. 7 and Fig. 8, respectively.

Fig. 8. Distribution of electrical potential for an observed position of the contacts at the switching-off – case: break speed v=6,5 m/s

Fig. 9, shows the calculated change of density as a function

of SF6 gas in-between contacts space in the vicinity of the movable and stationary contacts. Using the Equation (18), and the function of density in Fig. 9, the breakdown strength in between contacts space is calculated, and the results are shown in Fig. 10.

Fig. 9. Changes in time of density of SF6 gas in the vicinity of arcing contacts in case of switch-off speed v=6,5 m/s

Fig. 10. The estimated value of breakdown voltage in the vicinity of a stationary arc contact in between contacts distance

IV. CONCLUSION From this example calculation, the following can be

concluded: � The numerical procedures for predicting the

breakdown voltage are shown as a function in-between contacts space where it takes into account changes in density of SF6 gas during the expiration of the nozzle.

� A series of calculation with different speeds of interruption contacts was conducted.

� The analysis of the diagram in Fig. 10, can be concluded that the minimum speed-break contacts is � � S3}~�� 1� �, that there will be no re-break down of SF6 gas.

� The conducted review can only be applied for interrupting small currents, ie. without taking into account the arc model.

� Furthermore, the observed switching element was tested to breaking investigations in the High Power Laboratory KEMA in Netherlands, where has successful the small capacitive current interruption test.

REFERENCES

[1] M. Nagata, Y. Yokoi, I.Miyachi, ''Electrical Breakdown Characteristics in High Temperature Gases'', Electrical Engineering in Japan, Volume 97, Issuse 3, pages 1-6, 1977.

[2] B. Eliasson and E. Schade, “Electrical breakdown of SF6 at high temperature (<2300K)”, Int. Conf. Phenomena in Ionized Gases, Vol. 1, pp. 409-411, 1977.

[3] Minkowycz, W.J., Sparrow, E.M., Shneider, G.E., Pletcher, R.H., Handbook of Numerical Heat Transfer, (A Wiley –Interscience Publication, New York, 1986.).

[4] Okamoto, M., Ishikawa, M., Suzuki, K., Ikeda, H., Computer Simulation of Phenomena Associated with Hot Gas in Puffer-Type Gas Circuit Breaker, (IEEE Transaction on Power Delivery Vol. 6., No 2., April 1991.)

[5] Kuwahara, H., Tanabe, T.,Yoshinaga, K.,Sakuma, S., Ibuki, K., Yamada, K.,Investigation of Dielectric Recovery Characteristics of Hot SF6 Gas after Current Intterruption for Developing New 300 kV and 550 kV Gas Circuit Breakers, (IEEE Tranactions on Power and Systems, Vol. PAS 103, No 6, June 1984.)

[6] Hong-Kyu Kim, Jin-Kyo Chong, Ki-Dong Song, Analysis of Dielectric Breakdown of Hot SF6 Gas in a Gas Circuit Breaker, Journal of Electrical Engineering & Technology Vol.5, No. 2, pp. 264-269,2010.

[7] Jaluira, Y., Torrance, K.E. Computanional Heat Transfer, (Hemisphere Publishing Corporation, Washington, 1986.)

[8] [8] Xiaoming Liu; Tao Tang; Yundong Cao; Yunxue Zhao; Danyu Huang; , Performance analysis of high voltage SF6 circuit breaker based on coupling computation of electric-gas flow field Automation Congress, WAC 2008. Hawaii,2008.

[9] Ph. Robin-Jouan and M. Yousfi, “New Breakdown Electric Field Calculations for SF6 High Voltage Circuit Breaker Applications,” Proceedings of Gas Discharge and Their Applications – Xi’an, China, pp. 317-320, 2006.

[10] M. Yousfi, Ph. Robin-Jouan, Z. Kanzari, “Breakdown Electric Field Calculations of Hot SF6 for High Voltage Circuit Breaker Applications,” IEEE Trans. On Dielect.Elect. Insulation, Vol. 12, No. 6, pp. 1192-1200, 2005.

[11] Gaji�, Z., Odre�ivanje uticaja geometrije sklopnih elemenata potisnih i srodnih SF6 prekida�a i struje prekidanja na isklopnu pogonsku energiju u procesu gašenja elektri�nog luka, (disertacija, Elektrotehni�ki fakultet, Sarajevo, 1988.).

[12] Krenek, P., Neni�ka, V.,Electrical Conductivity, Thermal Conductivity and Viscosity of SF6 at the Temperatures 1000 – 50000 oK in the Pressure Range 0.1 – 1.4 Mpa, (Acta technica �SAV, No 5, pp. 549-579, 1983.)

[13] L. S. Frost and R. W. Liebermann, “Composition and transport properties of SF6 and their use in a simplified enthalpy flow arc model,” Proc. IEEE, Vol. 59, pp. 474-485, Apr. 1971.

[14] Kapetanovi�, M., Gavrilovi�, M., Dielektri�na �vrsato�a me�ukontaktnog razmaka SF6 prekida�a nakon gašenja luka, (XX Savjetovanje elektroenergeti�ara Jugoslavije, Bled, 1989.).