CHAPTER 2 ESTIMATION OF BREAKDOWN VOLTAGES IN SMALL INSULATION GAPS AN EMPIRICAL APPROACH

Transcription

1 17 CHAPTER 2 ESTIMATION OF BREAKDOWN VOLTAGES IN SMALL INSULATION GAPS AN EMPIRICAL APPROACH 2.1 INTRODUCTION Insulation materials of different types viz. gaseous, liquid and solid are used to make the design of transformers reliable. Air at atmospheric pressure is the most common gaseous insulation. The breakdown in air is of considerable importance to design engineers of transmission lines and power apparatus. In case of resin cast transformers, unavoidable small voids of the order of a few millimetres lead to partial discharges. Transformer oil is the most common liquid insulating medium used in most of the power apparatus as insulation as well as heat transfer fluid. The quality of the transformer oil plays an important role in the reliable and efficient functioning of the power apparatus. The physical and molecular characteristics of the oil determine its dielectric strength and heat transfer characteristics. The inter-turn and inter-disc insulation in oil filled transformer windings are generally of oil-impregnated paper (OIP). The thickness of OIP between turns is around 0.2 to 1.5mm and between the discs it is around 4 to 12 mm (Karsai et. al., 1987). The breakdown characteristic of a composite dielectric such as OIP is a mixed phenomenon which depends on many physical and electrical factors. The charges accumulated in OIP insulation interface play an important role in determining its insulation strength. There are only a few published data available on the intrinsic strength of OIP

2 18 insulation (Naidu et. al., 1989). Hence, it becomes inevitable for design engineers to study the breakdown characteristics of air, transformer oil and OIP in small gaps. The present status of the insulation coordination in power apparatus shows the need for more data on breakdown characteristics of small gaps in gaseous, liquid and solid insulation. Apart from the physical, chemical and electrical characteristics of the insulating medium, breakdown depends on many other factors like electrode material, electrode geometry, atmospheric conditions and type of the applied voltage (AC, DC or Impulse) etc. Hence, attempts have been made to study the behavior of insulations under small gaps with different electrode geometries to incorporate the extreme electrical field configurations in a practical transformer. Transformer oil with relative permittivity 2.2 and kraft paper of 0.12mm thickness with relative permittivity 3.5 from a single manufacturer have been used in the entire study. A systematic approach using Finite Element Method (FEM) is used to choose the appropriate electrode configurations. Breakdown under different types of voltages, AC, DC and Impulse is measured for all insulation under chosen electrode conditions for different gap distances. An effort is made to express the breakdown voltages in terms of the maximum electric field (E max ) calculated using FEM, which will be helpful in predicting the breakdown voltage for intermediate gap distances. 2.2 EFFECT OF ELECTRODE MATERIAL ON BREAKDOWN VOLTAGE The electrode material plays an important role in the breakdown of dielectric materials. As stated by Ushakov (2003), processes on an electrode surface and its immediate neighbourhood plays a part in dielectric breakdown

3 19 of various media and influence their short and long-term electric strength. Their contributions include emission of electrons and holes from electrodes desorption of occulated gases transformation of the field distribution in the inter electrode gap due to charging of oxide films formed on the electrode surface and dielectric layers formed by impurities of the dielectric medium field concentration on geometrical micro inhomogenities of electrode surface supply of micro tip explosion products of the electrode material to discharge gap The influence of electrode processes on breakdown and the prevailing role of one process or another depends on the dielectric medium and breakdown conditions (voltage type, temperature, inter-electrode gap length etc.,). For gas, liquid and solid dielectric breakdown, the role of electrode processes increases with decreasing discharge gap length, more homogeneous field and high purity of the dielectric medium. Many parameters of the electrode material like work function of the electrons, mechanical, thermal and physical properties, oxidizability and quality of surface treatment of the electrode influence its discharge characteristics. The dependence of the electric strength of low-pressure gases on the work function of the cathode material is well understood by the dependence of the second Townsend coefficient ( ) on the cathode material and surface. When gas pressure rises, the relative contribution of micro geometry, electrode surface and gas impurities significantly increases; on the

4 20 contrary, the relative contribution of emission processes to discharge initiation and evolution decreases. The higher the pressure and strength of the electric field applied to the gap, the greater the influence of the material (Coocson, 1970). In many theories of liquid dielectric conductivity and breakdown, it is assumed that electrons are emitted in the same way as in vacuum and the influence of liquid is taken into account only through the corresponding correction factor for the permittivity of the medium. As seen from Table 2.1, the difference in electric strength (E s ) can even reach 50% depending on the electrode material (Swan, Lewis, 1960). Table 2.1 Effect of electrode material on breakdown strength of gaseous (Liquified state) insulation Electrode material E s (kv/mm) (gap distance, d = 50 m and electrode diameter D = 5 mm) Ar O 2 N 2 Stainless steel Brass Copper Gold Platinum As the electrode material has a tremendous impact in breakdown voltage of the dielectric medium especially at lower electrode gaps, a single electrode material-brass is chosen in this work to study the breakdown behavior of air, oil and OIP dielectrics. With brass, the shapes of the electrodes are designed to simulate the extreme field conditions in power apparatus.

5 EFFECT OF ELECTRODE GEOMETRY AND GAP DISTANCE ON BREAKDOWN VOLTAGE Electrode geometry is an important parameter in deciding the breakdown voltage of a particular gap distance. Literatures show that there are many physical and empirical approaches adopted in the past to define breakdown voltage in terms of the maximum electric field. One of the physical approaches adopted by Meek (1940 and 1942), for a slightly non-uniform field (Figure 2.1) is based on Meek s criterion for streamer growth x ( ) x exp ( ) dx kex( x / n) 0.5 (2.1) 0 where is Townsend primary ionisation coefficient, is electron attachment coefficient, E x is electric field at the point of x, n is gas density and k is a constant. Meek has used this equation to calculate V s of air for sphere gaps of various electrode diameters and gaps in the order of centimeter. Waters and Stark (1975) have defined an empirical approach to represent the field strength (E s ) for a hyperbolic field for air and gap distance in the order of centimeters as E s kv. cm 0.4 r (2.2) where r is the radius of the tip of the electrode.

6 22 These are successful in calculating the sparkover voltages with reasonable accuracy for configurations with a slight non-uniformity of electric field. Lau (1957) has averaged the breakdown voltages obtained by several authors for air for rod-plane gaps with mm gap distance and reports that the averaged results lie within +1% of values given by Vs 24.4 d 6.53 d (2.3) where V s - is the breakdown voltage in kv, d is the gap length in cm and the air density correction factor p t 273 (2.4) where p is atmospheric pressure in mbar t is dry bulb temperature in C Kuffel et. al., (1983), have highlighted the use of the utilisation factor approach for all field configurations. Utilisation factor ( ) can be expressed as the ratio of average electrical field (E mean = V/d) to the maximum electrical field (E max ) in a system. = E mean /E max (2.5)

7 23 Figure 2.1 Rod-to-plane electrode configuration with different utilisation factors (Kuffel, Zaengl, 1983) Sparkover occurs when the maximum field (here at the electrode surface in Figure 2.1), equals or exceeds critical field strength (E s ) of the insulating medium (E max > E s ) and is given by V s = E s d (when E max = E s ) (2.6) Utilisation factor ( ) is unity or 100 per cent for uniform field (when D tends to infinity) and it approaches zero for sharp electrode (when D is reduced to zero). For the same gap distance and dielectric medium, change in electrode configuration changes utilisation factor ( ) greatly, necessitating a study on the influence of electrode dimensions on breakdown voltage.

8 DESIGN OF ELECTRODES In actual transformers, the dielectric materials are stressed under different electrical fields. To consider the various field configurations present in actual transformers, the electrode configurations with highly uniform to non-uniform electric fields have been analysed. The electrodes considered are plane-plane, cone-cone, plane-needle and plane-cone. To analyse these for small gap distances in air and oil, the following electrode dimensions are considered and are as shown in the Figures 2.2 to 2.5. Figure 2.2 Plane-plane electrode configuration Figure 2.3 Plane-cone electrode configuration Figure 2.4 Plane-needle electrode configuration

9 25 Figure 2.5 Cone-cone electrode configuration For oil-impregnated paper insulating medium, separate sets of electrodes are chosen to emulate the actual working condition as shown in Figure 2.6. Figure 2.6 Typical transformer inter-disc winding insulation Electrode arrangement required for OIP insulation has been designed as per standard IS: and is shown in Figure 2.7. The electrodes are designed with a smooth surface and curved edges to avoid corona losses. The required thickness of paper is obtained by stacking the required number of layers.the insulation is kept in between the electrodes and made tight by a holding arrangement as shown in Figure 2.8, so that the specimen under study remains intact between electrodes and the test system is kept inside a container filled with transformer oil. Care has been taken while manually tightening the screws of holding arrangement that uniform pressure is applied to ensure the degree of compression of OIP system remain same in all the tests. Figures 2.9 (a) and 2.9 (b) show the photographs of the test cell with electrodes.

10 26 Figure 2.7 Electrode arrangements for OIP insulation test system Figure 2.8 OIP insulation test system

11 27 Figure 2.9 (a) Photograph of air and oil insulation test system with different types of electrodes Figure 2.9 (b) Photograph of insulation test system for OIP

12 ELECTROSTATIC FIELD ANALYSIS BY FEM The electrical field distribution across the insulation between different electrodes is computed using FEM. From the field plots, E max and ξ are calculated to analyse the electrode geometry effects on the breakdown characteristics of the given insulation. Two-dimensional Laplacian equation in electrostatic field is solved using Maxwell s FEM software from ANSOFT Corporation. The distance between the electrodes is varied from 1mm to 6mm in steps of 0.5 mm and the electrical field (E) along the shortest distance between the electrodes (line AB ) is plotted for each distance. The post processor of the FEM package is configured to contain 1000 elements and/or 3000 nodes for all simulations. Though the problem stated is 1D in nature, the analysis is performed in 2D to take account of the fringing effect. Figures 2.10 (a) and (b) show the equipotential plot and the field plot for plane-plane electrode for 1 mm gap distance in air. Figure 2.10(a) Equipotential plot of plane-plane electrode configuration for air with 1 mm gap distance

13 29 Figure 2.10(b) Electric field plot for plane-plane electrode configuration for air with 1 mm gap distance It is seen from Figure 2.10(b) that the maximum field occurs at both the electrode surfaces and E max is 1.085kV/mm (for an applied voltage of 1 kv). The maximum variation of field (E) with reference to E max is 13%. In case of plane-cone electrode configuration, E max occurs at the surface of the conical electrode and the maximum variation of field E with reference to E max is 85%. The equi-potential plot and the field plot are shown in Figure 2.11 (a) and 2.11 (b) respectively.

14 30 Figure 2.11(a) Equipotential plot of plane-cone electrode configuration for air with 1 mm gap distance Figure 2.11(b) Field plot for plane-cone electrode configuration for air with 1 mm gap distance

15 31 Similar analyses are performed for the plane-needle and cone-cone electrode configurations and the variations in field for gap distance of 1 mm are shown in Table 2.2. Table 2.2 Percentage variations of Electric field for different electrode configurations Electrode configuration E max (kv/mm) % Variation in E with reference to E max Utilisation factor Plane-plane % 0.92 Cone-cone % 0.52 Plane-cone % 0.36 Plane-needle % 0.30 It can be inferred from the Table 2.2 that the field is more uniform in plane-plane configuration and highly non-uniform in plane-cone configuration, which is also evident from the values of the utilisation factors. The same results are noted for oil insulating medium. Figure 2.12 shows the equi-potential plot for the OIP test system. It can be inferred that the potential is uniformly distributed in the OIP dielectric in-between the electrodes. It is found from the electric field plot that E is the same along the line AB, confirming the uniformity in E field as per the Standard IS 2584:1996.

16 32 Figure 2.12 Equipotential plot in the OIP electrode system for 1 mm gap distance Similar, analyses are carried out by varying the gap distance in steps of 0.5 mm for all electrode configurations CALCULATION OF THE UTILISATION FACTOR (ξ) The values of E max for each gap distance under plane-plane, plane-cone, cone-cone and plane-needle electrode configurations are shown in Figure 2.13 and the corresponding utilisation factors are calculated using equation 2.5. Figure 2.14 shows the utilisation factor for different gap distances.

17 33 Figure 2.13 E max as a function of gap distance for different electrode configurations Figure 2.14 Utilisation factor as a function of gap distance for different electrode configurations

18 34 It is seen from Figure 2.13 that for plane-cone electrode configuration E max varies from to kv/mm and for plane-plane configuration from to kv/mm. Based on the field uniformity, the electrode system can be ranked in the order mentioned in Table 2.3. The plane-plane and plane-cone configurations denote the extreme field configurations with utilization factors 0.92 (highly uniform) to (highly non-uniform). Hence these two electrodes are chosen for further analysis in air and transformer oil insulation. Table 2.3 E max and values for different electrode configurations Electrode configuration Range of E max (kv/mm) d = 1mm to 6 mm Range of Plane-plane to to 0.85 Cone-cone to to 0.20 Plane-Needle to to 0.12 Plane-cone to to In case of OIP electrode system, the variation of is to as shown in Figure It can be concluded that the OIP electrode system offers uniform field distribution for the entire range of paper thickness from 0.1 to 2.0 mm.

19 Utilisation Factor Gap Distance (mm) Figure 2.15 Utilisation factor for different thickness of OIP insulation 2.6 MEASUREMENT OF BREAKDOWN VOLTAGES Though literatures in the past have given many physical, chemical and analytical approaches to calculate the breakdown voltage, an experimental investigation on breakdown of small insulation gap has not been discussed in detail. Some of the similar works available in literature are outlined here. Feser (1970a) has reported the breakdown characteristics for rodplane and rod-rod gaps with different types of applied voltage. These are shown in Figures 2.16 and 2.17 respectively. For static voltages, the breakdown voltage V s is single-valued and is related to the gap distance d by an empirical equation either of the form given in Eqn. 2.7 or in Eqn V (2.7) 5.6 ( 130) 2 s d K Vs A Bd. (2.8)

20 36 V s in kv. The values of A, B and K are given in Table 2.4 for d in cm and Table 2.4 Values of constants for static breakdown voltages of Rodplane and rod-rod gaps in atmospheric air [Craggs and Meek, 1978] Gap HV Range of A B K geometry electrode d (cm) Rod-plane Negative Rod-plane Positive Rod-rod Negative Rod-rod Positive V s (kv) d (cm) Figure 2.16 Breakdown voltages of Rod-plane gaps in atmospheric air (Feser, 1970a)

21 37 Vs (kv) d (cm) Figure 2.17 Breakdown voltages of Rod-Rod gaps in atmospheric air (Feser, 1970a) Equations 2.7 and 2.8 serve as empirical formulae for the determination of the breakdown voltage for a particular electrode configuration and gap distance (in the order of tens of centimetres). The breakdown characteristics of oil gaps have impulse strength, which is greatly affected by slight changes in conditions of both insulation and electrodes. M.G. Danikas (1990) has presented the experimental results for breakdown voltages of small oil gaps (in cm) under AC excitation and has reported that impulse strengths are much higher than DC and AC strengths. Berg et. al., (1999) have recorded the discharge signatures of OIP insulation under AC excitation and have found that they depend to a great extent on applied voltage, time and moisture content of the insulation. Klein,

22 38 Hill and Dissado (1983) have proposed a theoretical model for the breakdown time lags of solid dielectric. Naidu.et. al., (1989) have suggested a model for the estimation of the probabilities of the breakdown time lags. However literatures describing breakdown voltage for small gaps are scarce. The average AC, DC (positive and negative) and 50% impulse (positive and negative) breakdown voltages are measured for air, oil and OIP insulating media under different electrode configurations. A 200kV MWB (Messwandler-Bau) high voltage test kit is used to generate AC, DC and impulse voltages as per standard IS: The measured AC breakdown voltages are in RMS, Lightning Impulse and DC voltages correspond to peak values. Relevant atmospheric correction factors are taken into account and all the voltages are measured with reference to standard temperature and pressure (STP). From the measured breakdown voltages data, the following observations are made for air insulation under plane-plane configuration: It can be observed from Figure 2.18(a) that AC breakdown voltages are less than DC breakdown voltages and which are in turn less than 50% impulse breakdown voltages. For both DC and impulse voltages, positive breakdown voltages are less than the negative breakdown voltages and the percentage differences are less than 3%. The difference between AC, DC and Impulse voltages increases with the gap distances. For example, for a 1mm gap, the percentage increase in DC breakdown voltage with respect to AC breakdown voltage is 10% and 31.5% for impulse breakdown voltage, against 54% and 63% for 5mm gap respectively.

23 39 The following observations are made for air insulation under planecone configuration: Though the same trend as in plane-plane is noticed, all breakdown voltages are lesser in plane cone than in plane-plane as shown in Figures 2.18(a) and 2.18 (b) Polarity effect is negligible The differences between AC, DC and Impulse voltages increase with gap distances and are more than the values obtained for plane-plane configuration. For example, for a gap of 1mm, the percentage increase in DC breakdown voltage with respect to AC breakdown voltage is 24% and 62% for impulse breakdown voltage, against 72% and 145% for 5mm gap respectively 25 A C 20 D C +ve D C -ve Voltage (kv) Imp ulse +ve Imp ulse -ve Dis tance (m m ) Figure 2.18(a) Breakdown voltage in air as a function of distance for plane-plane electrode configuration

24 40 20 Voltage (kv) AC DC +ve DC -ve Impulse +ve Impulse -ve Distance (mm) Figure 2.18(b) Breakdown voltage in air as a function of distance for plane-cone electrode configuration Voltage (kv) A C DC +ve DC -ve Im pulse +ve Im pulse -ve Distance (m m ) Figure 2.18(c) Breakdown voltage in oil as a function of distance for plane-plane electrode configuration

25 AC DC +ve DC -ve Impulse +ve Impulse -ve Voltage (kv) Distance (mm) Figure 2.18(d) Breakdown voltage in oil as a function of distance for plane-cone electrode configuration Figures 2.18 (c) and 2.18 (d) show the breakdown voltages for oil insulating media for plane-plane and plane-cone electrode configurations. It is observed from the graphs that, The difference between AC, DC and Impulse voltages are almost the same for all gap distances There is a maximum of 13% and 24% increase in the DC and impulse breakdown voltage compared to AC breakdown voltage for 5mm gap For plane-cone electrode configuration, the maximum increase is 12% and 107% in the DC and impulse breakdown voltage compared to AC breakdown voltage, at 5mm gap. The breakdown voltages have been determined for plane-needle and cone-cone configurations of air and oil insulations also and the results are shown in Appendix 1.

26 42 A similar trend as shown in Figure 2.18(e) is observed for OIP under uniform field configuration: AC DC +ve DC -ve Impulse +ve Voltage (kv) Distance (mm) Figure 2.18(e) Breakdown voltage in OIP as a function of distance The difference between AC, DC and Impulse breakdown voltages increase as the gap distance increases. For plane-plane configuration under 2mm OIP thickness, there is a maximum of about 8% increase in the DC breakdown voltage and 600% increase in impulse breakdown voltage when compared to AC breakdown voltage. From the measurement of breakdown voltages, definite trends of variation in breakdown voltages with respect to gap distance, electrode configurations, voltage waveshapes and insulating media are identified which could be modeled using an empirical approach. An attempt has been made to derive empirical equations for breakdown voltages in terms of maximum electrical field.

27 RELATIONSHIP BETWEEN BREAKDOWN VOLTAGE AND MAXIMUM ELECTRIC FIELD (E max ) In section 2.5, various electrode configurations have been considered and their maximum field (E max ) and utilisation factors (ξ) have been calculated using FEM. Experimental breakdown voltages for all electrodes have been determined as given in section 2.6. It is more useful if the experimentally measured breakdown voltage can be related to the E max value. Figures 2.19, 2.20 and 2.21 show the relationship between the calculated E max value and the measured breakdown voltage under plane-plane and plane-cone electrode configurations for air and oil. Regression analyses have been carried out on the E max values and breakdown voltages AC DC (+ve) Impulse (+ve) Voltage (kv) Emax (kv/mm) Figure 2.19 Breakdown voltage of air as a function of E max for planeplane electrode configuration

28 44 E max (kv/mm) Figure 2.20 Breakdown voltage of air as a function of E max for planecone electrode configuration Voltage (kv) Voltage (kv) E max (kv/mm) Figure 2.21 Breakdown voltage as a function of E max for oil for planeplane electrode configuration

29 45 Based on the non-linear regression analysis, the results show that the following empirical equation best describes the breakdown voltage (V s ) in terms of the E max value for air and oil insulation for all field configurations V s = A1 + A2 / E max + A3 / (E max ) 2 (2.9) where A1, A2 and A3 are constants and their values are given in Table 2.5. Table 2.5 Empirical constants for air and oil to estimate the breakdown voltage in terms of E max Dielectric medium Electrode system Type of Voltage A1 A2 A3 AC Plane-plane DC (+ve) Air Impulse (+ve) AC Plane-cone DC (+ve) Impulse (+ve) AC Plane-plane DC (+ve) Oil Impulse (+ve) AC Plane-cone DC (+ve) Impulse (+ve)

30 46 Similarly for OIP insulation, the following equation describes the breakdown voltage (V s ) as V s = B1 + B2* E max + B3 / E max (2.10) and Table 2.6 gives the values of constants B1, B2 and B3. Table 2.6 Empirical constants for OIP to estimate the breakdown voltage in terms of E max Dielectric medium OIP Type of Voltage B1 B2 B3 AC DC Impulse Based on experimental studies and from mathematical models proposed, the breakdown voltages can be predicted from the calculated E max value for gap distances ranging from 2 to 6 mm for air and oil and between 0.1 to 2 mm for OIP. The predicted voltages are compared with the actual voltages and the errors are found to be well within +5%. Also, the results can be extrapolated, for predicting the breakdown voltage for air and oil in lower gap distance of less than 1 mm. 2.8 CONCLUSIONS In this chapter, different factors viz. electrode material, electrode geometry and type of voltage (AC, DC or Impulse), which influences the breakdown in small insulation gaps, have been explained. In emphasising the simulation of the actual field pattern of the transformer, the small insulation

31 47 gaps from uniform to highly non-uniform electrode configurations have been considered. Plane-plane, plane-cone, cone-cone and plane-needle electrodes have been chosen for air and oil insulating media. A finite element analysis has been carried out with these electrode configurations, to calculate the maximum field and utilisation factor for different gap distances. The following conclusions have been drawn from the FEM analysis: The maximum percentage variation in electric field E, with respect to the E max has been observed to be 13% for planeplane configuration and 85% for plane-cone configuration. It has also been observed that for plane-plane electrode configuration ranges from 0.92 to 0.85 and for plane-cone configuration it ranges from 0.3 to The plane-plane and plane-cone configurations denote the extreme fields and hence are used for further analyses. In case of OIP test system, the variation of has been from to and thus offers uniform field distribution for the entire range of gap distance of 1 mm to 6 mm. Experimentations have been carried out to measure AC, DC and impulse breakdown voltages under different electrode configurations. Based on the measurement of breakdown voltages, the following conclusions have been drawn: For air, it can be observed that for both DC and impulse breakdown voltages, positive polarity breakdown voltages are lower when compared to negative polarity breakdown voltages and percentage differences are less than 3%. The differences between AC, DC and impulse voltages increase with the gap distance.

32 48 For oil, the analysis shows that the difference between AC, DC and impulse voltages are almost the same for all gap distances. For OIP, there is a maximum of 600% increase in impulse breakdown voltage when compared to AC breakdown voltage for 2 mm gap distance. The relationship between the computed E max and the breakdown voltage has been obtained (for 1 to 6 mm gap distances) as shown below. For air and oil insulation V s = A1 + A2 / E max + A3 / (E max ) 2 (2.9) For OIP insulation V s = B1 + B2* E max + B3 / E max (2.10) These equations have been validated with intermediate distances and results show that errors have been well within the limit. So far, only the magnitudes of the breakdown voltages have been considered. The voltage-time characteristic explaining the instant of breakdown on standard lightning impulse plays an important role in the insulation co-ordination of the entire power system and has been discussed in the following chapter.