lightning impulse wave-shapes ion swaffield_ish_conference

Lightning impulse wave-shapes: defining the true origin and it’s impact on parameter evaluation

D.J.Swaffield1*, P.L.Lewin1, N.L.Dao1 and J.K.Hallstrom2 1University of Southampton, Southampton, Hampshire, SO17 1BJ, UK

2 Helsinki University of Technology, 02015 TKK, Finland *Email: [email protected]

Abstract: High-voltage testing of equipment is conducted in accordance with IEC 60060-1 which defines the parameters of full lightning impulse wave-shape and methods for generating and recording the test wave-shape. In the next revision of the standard it is proposed that the signal be digitally recorded and after suitable signal processing the parameter evaluation be implemented by a standardized algorithm. This paper examines two methods for parameter evaluation; firstly using a linear rising edge approximation and secondly a 3 standard deviations method. Obtained parameters are benchmarked against the IEC 61083-2 Test Data Generator and experimental results generated at the Tony Davies High Voltage Laboratory, University of Southampton. The sensitivity of the results to the method of implementation whilst using a double exponential function for the curve fitting is highlighted. The use of a separated double exponential function for curve fitting is proposed and shown to overcome this sensitivity.

1 INTRODUCTION

Standard high-voltage impulse testing requires the application of a specified wave-shape. IEC60060-1 and -2 are international standards that specify the high-voltage measuring techniques and measuring equipment to be used for testing [1]. With reference to Fig. 1, a full lightning impulse wave-shape is specified as having a front time (T1) of 1.2us ± 30% and a tail time (T2) of 50us ± 20%. Where

( ) sTsttT µµ 56.184.067.1 130901 ≤≤−= (1)

and

sTsttT µµ 6040 20502 ≤≤−= (2)

Where t0, t30 and t90 are the true origin of the

impulse, the time taken to reach U30, 30% of the peak voltage, and the time taken to reach U90 that is 90% of the peak voltage. Within the current standard the true origin can be calculated using

( )3090

3090

30300 tt

UU

Utt −

−−= (3)

The generation of impulse wave-shapes for testing generates disturbances in the measured signal including oscillations near the origin and overshoot. If the wave-shape is measured digitally it is desirable to remove the disturbances to the wave-shape where these do not have significant effect on the test result. Thus it is planned that within the next revision of the IEC60060-1 to include a suitable digital filtering technique for removal of disturbances to the recorded signal and method for parameter evaluation. This will offer an improvement over the loosely defined existing method and ensure a uniform approach is adopted worldwide.

In the next revision of IEC60060-1 it is proposed to filter either the whole of the recorded wave-form or just the oscillations and overshoot, known as the residual data. This residual is found by subtracting a curve of the double exponential (DE) form given in (4) and fitted using a least mean squares approach.

( )( ) ( )

−=

−−

−−

1

0

2

0

τταtttt

eetu (4)

The choice of a suitable digital filter, termed the K-factor, has been discussed elsewhere [2-7]. However it is important to also consider the method of parameter evaluation and specifically the method for defining the true origin as this will influence the recorded front and tail times (T1 and T2) using the parameter evaluation method currently specified by IEC60060-1. It has been proposed that defining the true origin using (3) be replaced by finding the time at which recorded data

Fig. 1. Definitions for calculation of lightning impulse voltage

waveform parameters.

Vol

tage

t0 t30 t50 t90 Time

UP

U90

U30

U50

rises above 3 standard deviations from the baseline data at the start of a recorded wave, where it is assumed this is time at which the wave-shape signal is greater than the level of background noise [5].

In this paper a series of experimental wave-shapes have been recorded and are filtered digitally using a non-causal zero-phase filter that matches the K-factor filter proposed for the next edition of IEC60060-1 [8]. Using this experimental data and waveforms obtained from the IEC 61083 -2 Test Data Generator; the influence of method used to define the true origin and the resultant impact on the front time and tail time recorded from the test wave-shapes is examined.

2 DEFINING THE TRUE ORIGIN

2.1. Method One – linear approximation

In the current version of IEC 60060-1 the true origin is defined using a linear approximation of the rising slope, this line is extended back to the point where it crosses the time axis to define the true origin, (3). If this technique is applied before a filter is applied to the raw data of a waveform noise, near the origin or on the rising slope, can cause the line to be plotted with an erroneous gradient. This may arise because the noise may cause a second value at which the signal is at 30 % of the peak voltage, for an example of this see Fig. 2(ii).

2.2. Method Two – 3 standard deviations

With reference to Fig 1. it is clear that even using a filtered signal a linear rising edge approximation may lead to a discrepancy between the true origin, if it is to be defined as the point at which the signal rises above the background noise compared to an estimate using (3). This has lead to the proposal of defining the true origin as the point when the signal rises above the noise using the point when the signal first rises above 3 standard deviations and the mean of the next five data points is also above the 5 standard deviation level.

The difficulty with this measure is that again electrical noise near the start of the impulse signal collected may contain oscillations greater than the background noise due for example to the firing of spark gaps, for an example see the experimental wave-shapes shown in Fig. 3. This may again lead to an incorrect estimation of the true origin.

3 TEST WAVE-SHAPES

Three cases from the IEC 61083-2 Test Data Generator have been used to test parameter evaluations, these are shown in Fig. 2. In addition to these the three evaluated experimentally generated wave-shapes with oscillations deliberately generated on the signal shown in Fig. 3 were also assessed.

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5

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tage

(V

)

(iii)

Fig. 2. IEC 601083-2 test data generator impulse waveforms:

(i) Case 08, (ii) Case 11, (iii) Case 14

4 RESULTS

It has been established from other studies [5,6,7] that the residual filtering method is more appropriate than global filtering for parameter evaluation of the measured impulse waveform and consequently only the

residual filtering approach has been implemented to assess the performance of the different methods for parameter evaluation.

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tage

(V

)

(iii)

Fig. 3. Experimentally generated impulse voltages

4.1. Double exponential function

Currently within IEC 60060-1 the formula used to define the curve of best fit is the double exponential (DE) of the form of (4), the best fit of which is found by employing a least mean squares curve fitting algorithm. Table 1 shows the resulting parameter evaluations using the DE form. What is immediately clear from this table is that the use of (3) the 30%-90% linear rising edge approximation to fit the curve and evaluate parameters leads to the greatest least mean square (LMS) errors. The reason for this error between the true data and the curve fit is down to a poor estimate of t0.

As an example Fig. 4 shows the original data, fitted curve and final curve after residual filtering has been applied for case 8 of the IEC 61083-2 Test Data Generator using both methods for defining t0. With reference to Fig. 4 it is clear that when using the DE curve form, selection of (3) or 3 standard deviations makes a difference to both the gradient of the rising edge of the fitted curve and also the shape near the origin. Considering the peaks shows that selecting (3) over the 3 standard deviations method leads to a sharper gradient (Fig. 4 (i) and (iii)), which in turn has the effect of causing a negative overshoot near the origin in Fig. 4(ii). A better curve fit, i.e. minimised error, results from selecting the 3 standard deviations method for this example. Table 1 shows that the error is reduced considerably and no significant change is seen in the error or parameters from selecting either method for parameter evaluation on the resultant wave-form, indeed these results fall within the IEC reference limits. However considering a case where there is noise near the origin further complicates the task of correctly selecting t0. As an example Fig. 5 shows the resultant plots of curves fitted to the experimentally generated waveform of Fig. 3 (ii). Fig. 5(ii) and (iv) show the region near the origin for curves fitted using the DE form by using (3) and the 3 standard deviations method respectively. This shows that whilst selecting the 3 standard deviations reduces the error significantly it is not as good as results later found from the separated double exponential (SDE) method. This is because without an exact definition of t0 there will be greater residual near the origin additional to the noise already present in this region. Thus after the residual is filtered and added back onto the fitted curve there is again a resultant negative overshoot near the origin.

4.2. Separated double exponential function

It is clear therefore from the proceeding results that the chief difficulty with employing the double exponential function is choosing the true origin. To overcome this apparent difficulty an alternative approach has been sought and the separated double exponential function has been proposed. Again this can be used to describe a wave-shape having two exponential components as is the case for the circuit

used to generate the impulse wave-shape. The form of the separated double exponential function is

−−−

−−=

1

02

2

01

)(exp

)(exp)(

ττtt

Att

Atu (5)

Where A1 and A2 replace the single constant α used in (4) and introduce an extra degree of freedom when fitting the curve. This makes the task of finding the best fit curve more difficult and requires careful choice of the curve fitting algorithm to ensure solver stability. To fit curves of both DE and SDE forms the same Levenberg-Marquardt least mean squares curve fitting algorithm has been applied. Despite the extra variable in the SDE form, there is no noticeable difference in computation time when running demonstration algorithms on a desktop computer to find solutions for each of the two curve forms. Both the DE and SDE methods take 2-3 seconds per curve. Additionally computation times maybe extended up to three times longer if a poor choice for origin is selected for the DE method.

Table 1 shows that the results when using the SDE function produces a lower least mean square (LMS) error for all the example wave-shapes examined. Investigation of the variation of the parameters evaluated, peak voltage, front and tail time with respect to a change in the initial estimate of the origin time is shown for DE and SDE curves, Fig. 7 an Fig. 8 respectively. From Fig. 7 there is a clear minimum in the error results, signifying the sensitivity of a good fit of the DE function to a good choice of t0. Conversely Fig. 8 shows that there is very little change in any of the evaluated parameters across a range twice as large as that of Fig. 7. What is in evidence at this scale is a small instability in the estimation of the parameters, which arises due to instability in solving for the variables of the SDE.

An investigation of the variation of the LMS error against a poor estimate of t0, Fig. 6, demonstrates how insensitive a good fit of the SDE is to the initial estimate. Indeed providing the estimate is within the flat region of the curve in this example from approximately -1.5 µs to +3 µs the error varies by only 0.028% this can be compared to 100% in the same region for the DE function. The variation of τ1 and τ2 when curve fitting a SDE is also small compared to the equivalent parameters for the DE; indicating that the front and tail shape and consequently front time parameter will also be less sensitive to a poor initial estimate of t0.

Disregarding the Tl-Tl result already discussed, for case 8 of the Test Data Generator (Fig. 2(i)) there is no difference in the Ts-Ts and Tl-Tl results of the DE when compared to the SDE curve fit (Table 1). The front and tail times fall within the reference limits provided by IEC 60183-2. However the peak is found to be just low

of the reference data for both curve fits. As has been discussed elsewhere [8] this is due a change in the treatment of oscillations superimposed onto the high-voltage test wave-form and their reduction by the application of digital filtering. The match in the results arises in this case because this wave-form is without large oscillations or noise at the origin and both DE and SDE curves provide a good fit when using the 3 standard deviation method to define an initial estimate of t0. The most notable change is in tail time between the different methods for front time evaluation; this is because tail time is sensitive to the selection of t0 as is seen from Fig. 1.

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datafit curvefinal curve

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x 10-6

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1x 105

time (s)

volta

ge (

V)


(vii) (viii)

Fig. 4. Plots of resultant curves for different curve fitting

methods and for DE and SDE forms applied to case 8 of IEC 60183-2 Test Data Generator; (i) and (ii) show the peak and

origin using (3) and DE, (iii) and (iv) show the peak and origin using 3 standard deviations and DE, (v) and (vi) show the

peak and origin using (3) and SDE, (vii) and (viii) show the peak and origin using 3 standard deviations and SDE

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(vii) (viii)

Fig.5. Plots of resultant curves for different curve fitting methods and for DE and SDE forms applied to the -150 kV experimental example (Fig. 3(ii)); (i) and (ii) show the peak and origin using (3) and DE, (iii) and (iv) show the peak and origin using 3 standard deviations and DE, (v) and (vi) show the peak and origin using (3) and SDE, (vii) and (viii) show

the peak and origin using 3 standard deviations and SDE

Fig.6. Error against drift from true origin when fitting the SDE curve form

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t tim

e (s

)

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x 10-6

4.75

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4.9 x 10-5

t0st0l

time(s)

tail

time

(s)

(iii) (iv)

Fig.7. DE variables against time, where t0l is the origin using (3), t0s is the origin using 3 standard deviations; (i) least mean square error against time, (ii) peak voltage against time, (iii)

front time against time, (iv) tail time against time.

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r

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9.99239.99249.99259.99269.99279.99289.9929

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1.1523 x 10-6

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t tim

e (s

)

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x 10-6

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4.8232

4.8233

4.8234

4.8235 x 10-5

t0s

t0l

time(s)

tail

time

(s)

(iii) (iv)

Fig.8. SDE variables against time, where t0l is the origin using (3), t0s is the origin using 3 standard deviations; (i) least mean square error against time, (ii) peak voltage against time,

(iii) front time against time, (iv) tail time against time.

5 CONCLUSIONS

It is argued that the SDE provides a more robust formula for curve fitting and negates the need to change the method used for parameter evaluation from (3) to a 3 standard deviation method. Although using the 3 standard deviations method to provide the initial estimate of t0 offers significant improvement when used for the DE curve, only a small gain may be found in using it at the initial curve fitting stage when using the SDE. However the DE curve fit never matches the performance of fitting an SDE curve. It is suggested that the SDE may provide a method worthy of adoption for the filtering of high-voltage full lightning impulse wave-shapes.

time

LMS

err

or

Table 1. Parameter evaluations for DE and SDE* DE curve fitting SDE curve fitting IEC reference Case08

Tl-Tl Ts-Ts Ts-Tl Tl-Tl Ts-Ts Ts-Tl LMS error 3.862 0.434 0.434 0.433 0.433 0.433

Low High

Peak(MV) 1.039 1.039 1.039 1.039 1.039 1.039 1.040 1.060 Front (µs) 1.737 1.603 1.603 1.603 1.603 1.603 1.600 1.700 Tail (µs) 47.56 47.16 47.49 47.49 47.25 47.49 45.00 49.00

DE curve fitting SDE curve fitting IEC reference Case11


Low High

Peak(MV) 0.955 0.955 0.955 0.955 0.955 0.955 0.940 0.960 Front (µs) 1.353 1.319 1.319 1.219 1.169 1.169 1.070 1.190 Tail (µs) 87.45 87.27 87.43 87.36 87.64 87.36 82.00 91.00

DE curve fitting SDE curve fitting IEC reference Case14


Low High

Peak(MV) -1.026 -1.028 -1.028 -1.028 -1.028 -1.028 -0.950 -0.970 Front (µs) 2.238 2.171 2.171 2.154 2.154 2.154 1.850 2.050 Tail (µs) 42.03 41.47 41.89 41.90 41.68 41.90 43.00 47.00

DE curve fitting SDE curve fitting Experiment

100kV Tl-Tl Ts-Ts Ts-Tl Tl-Tl Ts-Ts Ts-Tl LMS error 2.334 0.711 0.711 0.496 0.496 0.496 Peak(kV) 100.2 100.1 100.1 100 100 100 Front (µs) 1.436 1.336 1.336 1.269 1.269 1.269 Tail (µs) 45.87 45.64 45.86 45.85 46.29 45.85


-150kV Tl-Tl Ts-Ts Ts-Tl Tl-Tl Ts-Ts Ts-Tl LMS error 2.390 0.668 0.668 0.423 0.423 0.423 Peak(kV) -149.3 -149.2 -149.2 -149.1 -149.1 -149.1 Front (µs) 1.419 1.336 1.336 1.253 1.253 1.253 Tail (µs) 45.87 45.66 45.88 45.87 46.00 45.87


110kV Tl-Tl Ts-Ts Ts-Tl Tl-Tl Ts-Ts Ts-Tl LMS error 4.316 1.537 1.537 0.908 0.907 0.907 Peak(kV) 103.6 105 105 106.1 106.3 106.3 Front (µs) 0.751 0.601 0.601 0.434 0.401 0.401 Tail (µs) 39.21 38.38 38.48 37.78 38.23 37.66

*Notation: within Tab. 1. Tl-Tl signifies results obtained using the 30%-90% line approximation (3) to define t0 for the curve fitting algorithms and the subsequent use of the same approximation to evaluate T1 and T2 post filtering. Ts-Ts signifies the use of the 3 standard deviation method for an initial estimate of t0 for use by the curve fitting algorithms and then for parameter evaluation. Ts-Tl signifies the use of the 3 standard deviation method for an initial estimate of t0 for use by the curve fitting algorithms and then (3) to define t0 for parameter evaluation. REFERENCES

[1] IEC 60060-1:1989 “High Voltage Test Techniques” – Part 1 “General definitions and test requirement” published by the International Electrotechnical Commission

[2] J Rungis and Y Li “Precision Digital Filters for High Voltage Impulse Measurement Systems” IEEE Transactions on Power Delivery, vol.14, no.4, pp.1213-1220, 1999.

[3] K Hackemack, P Werle, E Gockenbach and H Borsi “A New Proposal for the Evaluation of Lightning Impulses” in Proceedings 6th International Conference on Properties and Applications of Dielectric Materials, Xi’an, China, pp.93-96, 21-26th June 2000.

[4] P Simon, F Garnacho, Berlijn and E Gockenbach “Determining the test voltage factor function for the evaluation of lightning impulses with oscillations and/or an overshoot” IEEE Transactions on Power Delivery, vol.21, no.2, pp. 560- 566, April 2006.

[5] J Hällström, S Berlijn, M Gamlin, F Garnacho, E Gockenbach, T Kato, Y Li and J Rungis “Applicability of Different Implementations of K-factor Filtering Schemes for the Revision of IEC60060-1 and -2” in Proceedings 14th International Symposium on High Voltage Engineering, Beijing, China, paper B-3, 25-29th August 2005.

[6] Y Li and J Rungis “Evaluation of Parameters of Lightning Impulses with Overshoot” in Proceedings 13th International Symposium on High Voltage Engineering, Delft, Netherlands, 25-29th August 2003.

[7] M Gamlin “Implementation of the K-factor for the Lightning Impulse Evaluation by means of Digital FIR Filtering” in Proceedings 14th International Symposium on High Voltage Engineering, Beijing, China, paper B-79, 25-29th August 2005.

[8] P Lewin, T Tran, D Swaffield and J Hällström “Zero phase Filtering for Lighting Impulse Evaluation: A K-factor Filter for the Revision of IEC60060-1 and -2” IEEE Transactions on Power Delivery in press.

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