05-03-2013, 10:34 AM
Lightning impulse wave-shapes: defining the true origin and it’s impact on parameter evaluation
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Abstract:
High-voltage testing of equipment is
conducted in accordance with IEC 60060-1 which
defines the parameters of full lightning impulse waveshape
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.
INTRODUCTION
Standard high-voltage impulse testing requires the
application of a specified wave-shape. IEC60060-1 and
-2 are international standards that specify the highvoltage
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%.
DEFINING THE TRUE ORIGIN
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).
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.
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.
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.