Electricity: measuring and testing – Measuring – testing – or sensing electricity – per se – Analysis of complex waves
Reexamination Certificate
1998-10-08
2001-12-11
Metjahic, Safet (Department: 2858)
Electricity: measuring and testing
Measuring, testing, or sensing electricity, per se
Analysis of complex waves
C324S076420, C324S076580, C702S075000
Reexamination Certificate
active
06329806
ABSTRACT:
FIELD OF THE INVENTION
The present invention relates to a process for determining harmonic oscillations of a fundamental component of an electrical signal.
BACKGROUND INFORMATION
The journal, “Elektronik”2, Jan. 23, 1987 pp. 89-96, in particular pp. 92-93, describes a process in which an electrical signal is sampled with a sampling rate corresponding to an integer multiple of the fundamental component's frequency after analog pre-filtering. According to an example given, sampling is performed at a sampling rate of 2.56 kHz, and the spectral lines up to the sixth harmonic oscillation are determined in addition to the spectral line of a 160 Hz fundamental frequency. The spectral lines of the higher harmonics are greater than half the sampling rate (Nyquist frequency) and for real input signals provide the same values as the first eight spectral lines due to mirroring on the Nyquist frequency. The spectral lines of the higher harmonics can not, therefore, be selected and determined with such a process for a sampling frequency of 2.56 kHz. If these spectral lines are also to be determined with this conventional method, a sampling frequency twice as high, i.e., a sampling frequency of 5.12 kHz, would be required.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a process for determining harmonic oscillations of a fundamental frequency of an electrical signal allowing relatively simple determination of even higher-order harmonics.
In accordance with the present invention, the signal is sampled with a sampling frequency corresponding to a non-integer multiple of the fundamental frequency. The sampled values of the signal are subjected, after analog-digital conversion, to a Discrete Fourier Transformation (DFT) to determine the harmonic oscillations. The DFT is performed by increasing the frequency resolution over several periods of the fundamental frequency to determine the harmonic oscillations.
The process of the present invention is based on the premise that, when sampling is performed with a non-integer multiple of the fundamental frequency, the higher harmonics are mirrored on a Nyquist frequency which does not coincide with a harmonic, but rather is located between two adjacent harmonics. Therefore, the higher harmonics mirrored on such a Nyquist frequency fall into the “gaps” between the lower-order harmonics and thus can be measured and selected. In order to obtain reproducible measuring results, it is necessary that the discrete Fourier transformation be carried out over a time interval corresponding to several periods of the fundamental frequency.
In general, it can be established that a sampling frequency f
ab
is used according to the present invention, which sampling frequency can be described by the following relationship (1):
f
ab
=N′*f
gr
. (1)
In equation (1), f
gr
denotes the frequency of the fundamental frequency of the electrical signal to be analyzed. N′ can be described by the following equation (2):
N′=M/L, (2)
where M is an odd integer and L is an integer≧1. For example, if M=21 and L=2 are selected, this means that a sampling frequency f
ab
will be used according to the present invention, which is equal to 10.5 times the fundamental frequency f
gr
. In this case, a discrete Fourier transformation must be performed over L periods, i.e., in the present case, over two periods.
One of the advantages of the process according to the present invention consists of the possibility of determining harmonic oscillations of a relatively high order by using a relatively low sampling frequency. This reduces the cost of measuring the harmonic or fundamental frequencies in an electrical signal. The longer measuring time over several periods of the fundamental frequency can often easily be taken into account, so that this does not represent a problem in most applications.
The frequency of the fundamental frequency of an electrical signal is often subject to fluctuations. This is true, for example, for electrical signals derived from the current or the voltage of an electric supply line. In order to also be able to use the process according to the present invention for such electrical signals and obtain accurate measurement results, in an improved version of the process according to the present invention, a measured value that provides the instantaneous frequency of the fundamental frequency of the electrical signal is obtained with a frequency measurement device supplied with the sampled values. The measured value is multiplied by a factor n to obtain a derived measured value, with factor n being equal to the quotient of a selected sampling frequency over the nominal frequency of the fundamental frequency of the electrical signal. The sampling is performed with a sampling frequency corresponding to the derived measured value.
Another advantage of this embodiment of the process according to the present invention is that, independently of the instantaneous frequency of the analog electrical signal analyzed, a sampling frequency corresponding to n times the instantaneous frequency of the electrical signal is used. This considerably increases the measurement accuracy, since the same number of samplings is always performed per period of the electrical signal, even for electrical signal frequencies that are different from the nominal frequency. Therefore, for this embodiment of the process according to the present invention, the sampling frequency is matched to the obtained frequency of the fundamental component.
Such a matching of the sampling frequency to the frequency of the fundamental component of an electrical signal is described in German Published Patent Application No. 43 30 179 A1.
In the process according to the present invention, the derived measured value can be supplied in various ways, e.g. directly, to the clock input of an analog-digital converter used for analog-digital conversion.
In another embodiment of the process according to the present invention, in order to obtain the highest possible accuracy, it is advantageous to form an intermediary value corresponding to the quotient of the magnitude of the clock frequency of a clock generator and the intermediary value providing the derived measured value in a quotient device, and to set the divider ratio of a frequency divider arranged between the clock generator and the clock input of an analog-digital converter used for analog-digital conversion so that the sampling frequency corresponding to the derived measured value is supplied to the clock input. In this way it is ensured that the sampling frequency is always derived anew from the clock frequency of the clock generator.
In order to achieve a smoothly operating process according to the present invention, it is also advantageous to modify the divider ratio as soon as possible after a few periods of the electrical signal have elapsed.
In the process according to the present invention the frequency measuring device can be a digital frequency meter in order to achieve the highest possible measurement accuracy.
REFERENCES:
patent: 4918381 (1990-04-01), Bender et al.
patent: 4928251 (1990-05-01), Marzalek et al.
patent: 4965757 (1990-10-01), Grassart
patent: 5099194 (1992-03-01), Sanderson et al.
patent: 5508605 (1996-04-01), Lo et al.
patent: 5889398 (1999-03-01), Reck et al.
patent: 5912829 (1999-06-01), Maier
patent: 5999573 (1999-12-01), Zangi
patent: 42 11 946 (1993-09-01), None
patent: 43 30 179 (1995-03-01), None
patent: 63101767 (1988-05-01), None
patent: WO 93/20454 (1993-10-01), None
K. Weignardt et al., “Elektronik” 2, Jan. 23, 1987, pp. 89-96.
J. Heydeman et al., “Microprocessor Based Underfrequency Relaying”, Delft University of Technology, the Netherlands, Third Internal Conference on Developments in Power System Protection, 1985, pp. 24-28.
Reck Thomas
Sezi Tevfik
Deb Anjan K
Kenyon & Kenyon
Metjahic Safet
Siemens AG
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