MEASUREMENT OF THE INTERNAL INDUCTANCE OF IMPULSE VOLTAGE GENERATORS AND THE LIMITS OF LI FRONT TIMES

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1 The 20 th International Symposium on High Voltage Engineering, Buenos Aires, Argentina, August 27 September 01, 2017 MEASUREMENT OF THE INTERNAL INDUCTANCE OF IMPULSE VOLTAGE GENERATORS AND THE LIMITS OF LI FRONT TIMES W. Larzelere 1*, J. Hällström 2, A-P. Elg 3, A. Bergman 3, J. Klüss 4, Y. Li 5, and L. Zhou 6 1 Evergreen HV, USA 2 VTT Technical Research Centre of Finland Ltd, Centre for Metrology Mikes, Finland 3 SP-RISE Research Institutes of Sweden, Box 857, Boras, Sweden 4 Mississippi State University, USA 5 National Measurement Institute, Australia 6 Hua Gao, China * wel@ehvtest.com Abstract: The recent push to higher testing voltages for research and production tests on UHV system components rated above 800kV class has led to difficulties in achieving the standard waveshapes as required by IEC60060 Parts 1 and 2 and other existing IEC, IEEE/ANSI and other standards. One of the limiting components in achieving the maximum capacitive loading on an impulse generator for standard lightning impulse front times is the inductance of the circuit. The total inductance of the circuit is comprised of the internal inductance of the impulse generator and the inductance of the loop to connect to the load. The higher the voltage class of test objects, the larger the loop, yielding more inductance that in turn, reduces the test capacitance that can be connected and still remain inside the overshoot requirements of the standards. The internal inductance of the impulse generator is comprised of the wiring of the stages and the stage capacitor inductance and/or the inductance of the waveshaping resistors. This paper shows the results of methods to measure and calculate the internal inductance of several impulse generators and we review the formulas for calculating the maximum load of an impulse generator with a given internal inductance. We believe these methods give more realistic values than adding up nameplate inductance values from an impulse generator. The paper also reviews the pros and cons of higher stage capacitances in impulse generators to test larger loads that are ultimately limited by the circuit inductance value. The intent of this paper is to assist in the revision of future IEC and IEEE standards for impulse testing apparatus in the UHV range. 1 1 INTRODUCTION The internal inductance of an impulse generator is comprised of the internal inductance of the stage capacitor(s), the wiring of the stage components to the gap system and the inductance of the front resistors. The total inductance of the impulse test circuit is the sum of the internal inductance of the impulse generator plus the connections to the test object. See Figure 2. In the minimal case, the external circuit inductance can be simulated by using a wire connected in a rectangular loop. The loop dimensions are shown in Figure 6 and relate to the height of the impulse generator and based on a practical distance to keep adequate clearances to avoid voltage flashovers or streamers. The internal inductance of the impulse generator plus the inductance of the connections determines the maximum load capacitance that can be tested while staying within the tolerances of IE60060 Parts 1 and 2 [1,2] and IEEE Std. 4 [3] which require the overshoot on the peak of the waveform to be less than 10 %. This paper presents experimental data on measurements of inductance made on several impulse generators. While it is true that special circuits can be employed to increase the capacitive and inductive load range of a generator with a given inductance [6], it is useful to know the value of the internal inductance to make calculations of the intrinsic load range of a given generator without external HV circuit modifications. 2 LOAD RANGE The normal schematic diagram for common unipolar charging style Marx generators is shown in Figure 1. None of the individual components of inductance contributions to the circuit are shown.

2 resistance that can damp the oscillatory circuit with less than 10%. The minimum front resistance is estimated as: Where: R F 1.2 (L S /C L ) (4) R FT = the total front resistance (Ω) Figure 1: Basic impulse circuit. Figure 2 shows the various sources of series inductance added to an impulse circuit, where C G = impulse generator capacitance C L = load capacitance L R = front resistor inductance L C = stage capacitor inductance L ST = stage wiring inductance L E = external loop connection inductance L T = the inductance of the test object Then for n-stage generator the total internal generator inductance is L G =(L R + L C + L ST ) x n, (1) and the total circuit series connected inductance is: L s = L G +L E +L T (2) Ls = the total circuit inductance (µh) C L = the test load capacitance (µf) If we consider the slowest allowable front time to be 1.56µs, then the formula that can be used to calculate the value of front resistance for a given total circuit inductance (Ls) is: R FT = 3.37 x Ls (5) Where Ls is in uh It then follows that the maximum load (C Lmax ) that can be tested with the minimum total front resistance is: C Lmax = 624/R FT (6) where C Lmax is in nf As an example, a 10 stage, 1MV impulse generator with 20 µh internal generator inductance and 10 µh external loop inductance yields a maximum load of 6.1 nf. If the internal inductance of the impulse generator could be reduced from 20 to 15 µh the maximum load capacitance would increase to 7.4 nf for a gain of 20% in test load capacity. 3 IMPULSE GENERATOR ENERGY RATING Figure 2 Individual inductance components. For a maximum allowable front time of 1.56us according to international standards, the front time can be calculated from: T F 2.5 x (R FT ) x C L (3) It is seems logical that increasing the stage capacitance or energy rating of an impulse generator will increase the test load range. The formulas above show that inductance is the ultimate limiting factor in determining the capacitive load range. Increasing the capacitance or energy per stage of an impulse generator will increase the voltage efficiency but will not increase the test load range for the required (<10%) overshoot for the standardized front time since it is governed by the circuit inductance. An infinite stage capacitance cannot produce improvement in front time beyond what is determined by the circuit inductance. It should be noted that increasing the stage capacitance reduces the trigger range of an impulse generator as explained by Rodewald. (4) The capacitive load range of an impulse generator is determined by choosing the minimum front

3 4 MITIGATION TECHNIQUES In this paper we have looked at the inductance of the external loop and the internal wiring of the generator as a composite measurement. Of course the reduction of the length of the connections to and from the test object will lower the total circuit inductance. A value of approximately 1µH per meter can be realized. However for higher voltage tests, the minimum clearances cannot be easily reduced beyond a certain safe clearance level. In our analysis we try to determine the internal inductance value by subtracting the estimate of the external loop inductance. is stimulated with a variable frequency source. The output voltage and waveshape are measured on an oscilloscope and the self-resonant frequency f r is determined. With the value of stage capacitance known the total inductance can be calculate from: That is, fr =!!! L! C! (7) ω = 1/ LC (8) L = 1/ω! C (9) where C G is the generator capacitance. The reduction of the internal inductance of an impulse generator plays a key role in increasing the load range that can be tested without special efforts. It will be shown that not all impulse generators have the same value of internal inductance for a given output voltage. It should be noted that the inductance of the front resistors can vary, as does the inductance of the wiring of impulse generator stages. The front resistors have some inductance even with the best winding techniques [5]. In general the L/R time constant for front resistors should be under 100ns and inductance values <1 µh is easy to achieve. The measurements in this paper are with front resistors short-circuited to try to find the actual value of the wiring of the particular generator design. 5 EXPERIMENTAL SETUP To measure the inductance of low impedance components there are several possible methods. Figure 4: Mercury relay switch. Another method is shown in Figure 4. In this case a low voltage DC power supply is used to charge up the generator capacitance and a mercury wetted relay is used to short circuit the charged capacitor to ground through the inductance of the circuit. The voltage or current waveform can be measured to find the resonant frequency (Fig 5). Inductance is calculated as above. Figure 3: Variable frequency source. Figure 3 shows a circuit that places the inductance of the test circuit and the impulse generator capacitance in a series connection and the circuit Figure 5: Resonance Waveshape of 12 stages

4 6 TEST LAYOUTS In order to evaluate the inductance of the total circuit we arranged two different test layouts to give two different values of total inductance. In each case the entire impulse generator is connected by short-circuiting the front resistors and wiring all the stage capacitors in series by shortcircuiting the sphere gaps. This way all the connection inductance for each stage is included but not the inductance of the front resistors that will vary with ohmic value and design. [5] L E 2 x h (10) where inductance is given in µh and H is the height in meters. For a second test the following configuration was used. Figure 8: Reduced short circuit loop Figure 6: Shorted front resistor Laboratory Layouts In this case the external inductance can be estimated as L E h+2 (11) For this configuration the distance of the vertical connection was reduced to 1 meter. 7 TEST RESULTS Generator Tests The impulse generator evaluated is an ASEA generator from 1965 with 12 stages comprising of 4 capacitors 0.22µF/100kV in series-parallel connection giving a total capacitance of 18.3nF. Individual capacitor inductance has been measured as 1.1µH and the summed total capacitance is 1.1µF per stage. The external connections were made as short as possibleapprox. 0.5m. See Figure 9. Figure 7: Rectangular short circuit loop. For the first test configuration the short circuit loop height is the height of the impulse generator. The distance from the generator to the vertical connection is equal to one-half the height of the impulse generator. This would be a normal lead connection for most generators and would provide safety in voltage clearances and avoid proximity effects on the voltage divider. As an estimate we can say that the inductance of the external loop is:

5 7 CONCLUSIONS It is possible to measure the inductance of impulse capacitors and impulse generators by determining the self-resonant frequency of the L-C circuit. While there is some question about the actual value of inductance of simple wire connections per unit length in free space, the values estimated are reasonable. Future work will be to determine the maximum capacitive load that can be tested with different generators and keep within the 10% overshoot requirements of the standards while varying the external loop size and inductance. This will allow us to validate the estimates of circuit inductance. The authors believe that this simple test to determine the internal inductance of an impulse generator will help users to find the practical load range and determine the proper values for front resistances. Figure 9: 12 Stage Generator with Foil Loop. The complete stack with all 12 stages connected in series, short-circuited sphere gaps as well as short-circuited internal front resistors (charging resistors removed) showed an inductance of 47 µh. The generator is 8.3 m tall and the return loop from to top to the pulse generator was about 0.5 m from the sphere gaps and was made with a copper band 0.3 mm x 150 mm. Estimated conductor length for each stage is 3.8 m, lying horizontally. If the overall inductance measured for the loop is 47 µh and the loop distance is 10 meters then the internal inductance can be estimated as: L G = 37 µh (12) Since the front resistance inductance (L R ) is 0 and the stage capacitors L C is 1.1µH, we can estimate the stage inductance due to circuit design to be L S 37/ = 2 µh per stage (13) As a next step, verification of this estimate will be performed using a capacitive load calculated to have less than 10% overshoot. REFERENCES [1] IEC :2010, Ed.3.0, High-voltage test techniques-part 1, General Definitions and Test Requirements, [2] IEC :2010, Ed.3.0 High-voltage test techniques-part2, Measuring Systems. [3] IEEE Std "High Voltage Test Techniques" [4] A. Rodewald, "The Firing Probability of Coupling Spark Gaps of the Multiplying Circuit according to Marx" Haefely Publication Vol. 60(1969) P [5] Orsino Oliveira Filho, Fernando Chagas, Walter Cerqueira, Enio Alvarenga "Dynamic Behavior of Non Inductive Resistors for HV Impulse Applications, 9 th ISH 1995 Graz, Austria [6] Klaus Schwenk, Michael Gamlin, "Load range extension methods for lighting impulse testing with high voltage impulse generators" [7] K Schon, "High Impulse Voltage and Current Measurement Techniques" 2013 Springer The same impulse generator was measured but with only 6 stages with a height of 4 m. In this case: L G 23-6 = 17 uh (14) Calculating L S, L S 23/ uh per stage (15) Shows good agreement with the basic assumption of inductance in the external loop.