Method And Device For Determining Capacitive Component Parameters

Abstract

A method of determining the capacitance and loss-factor of each of a plurality of capacitive components of an electrical power device, wherein the method includes: a) obtaining for each capacitive component a respective capacitance value and loss-factor value, and b) processing the capacitance values and the loss-factor values, wherein the processing involves removing a common influence of temperature on the capacitance values from the capacitance values and removing a common influence of temperature on the loss-factor values from the loss-factor values to obtain for each capacitive component a temperature-compensated capacitance value and a temperature-compensated loss-factor value.

Claims

1. A method of determining the capacitance and loss-factor of each of a plurality of capacitive components of an electrical power device, wherein the method comprises: a) obtaining for each capacitive component a respective capacitance value and loss-factor value, and b) processing the capacitance values and the loss-factor values, wherein the processing involves removing a common influence of temperature on the capacitance values from the capacitance values and removing a common influence of temperature on the loss-factor values from the loss-factor values to obtain for each capacitive component a temperature-compensated capacitance value and a temperature-compensated loss-factor value, wherein the processing involves transforming by means of a first eigenvector matrix a capacitance vector for which each element is a respective one of the capacitance values, to obtain a transformed capacitance vector, and transforming back the transformed capacitance vector with the inverse of an adjusted first eigenvector matrix to obtain an adjusted capacitance vector, which as its elements contains the temperature-compensated capacitance values, wherein the adjusted first eigenvector matrix has the elements of one of the eigenvectors set to zero, wherein the eigenvector which has its elements set to zero is the eigenvector which corresponds to the largest eigenvalue, wherein the first eigenvector matrix contains the eigenvectors of a first covariance matrix of a learning-period capacitance matrix containing for each capacitive component a plurality of capacitance values obtained during a learning-period.

2. The method as claimed in claim 1, wherein the common influence of temperature on the capacitance values and loss-factor values of the plurality of bushings is obtained based on a learning-period in which a plurality of capacitance values of each capacitive component and a plurality of loss-factor values of each capacitive component have been collected.

3. The method as claimed in claim 2, wherein the common influence of temperature on the capacitance is obtained based on statistical correlation analysis of the plurality of capacitance values collected in the learning-period.

4. The method as claimed in claim 2, wherein the common influence of temperature on the loss-factor is obtained based on statistical correlation analysis of the plurality of loss-factor values obtained in the learning-period.

5. The method as claimed in claim 1, wherein the processing involves transforming by means of a second eigenvector matrix a loss-factor vector for which each element is a respective one of the loss-factor values to obtain a transformed loss-factor vector, and transforming back the transformed vector loss-factor vector with the inverse of an adjusted second eigenvector matrix to obtain an adjusted loss-factor vector, which as its elements contains the temperature-compensated loss-factor values.

6. The method as claimed in claim 5, wherein the second eigenvector matrix contains the eigenvectors of a second covariance matrix of a learning-period loss-factor matrix containing for each capacitive component a plurality of loss-factor values obtained during a learning-period.

7. The method as claimed in claim 5, wherein the adjusted second eigenvector matrix has the elements of one of the eigenvectors set to zero.

8. The method as claimed in claim 7, wherein the eigenvector which has its elements set to zero is the eigenvector which corresponds to the largest eigenvalue.

9. The method as claimed in claim 1, comprising providing a respective upper and lower threshold value for each capacitance and each loss-factor, and in case any of the temperature-compensated capacitance values or temperature-compensated loss-factor values is outside the corresponding upper or lower threshold, generating an alarm.

10. A computer program comprising computer-executable components which when run on processing circuitry of a capacitive component parameter determining device causes the capacitive component parameter determining device to perform the steps according to a method including: a) obtaining for each capacitive component a respective capacitance value and loss-factor value, and b) processing the capacitance values and the loss-factor values, wherein the processing involves removing a common influence of temperature on the capacitance values from the capacitance values and removing a common influence of temperature on the loss-factor values from the loss-factor values to obtain for each capacitive component a temperature-compensated capacitance value and a temperature-compensated loss-factor value, wherein the processing involves transforming by means of a first eigenvector matrix a capacitance vector for which each element is a respective one of the capacitance values, to obtain a transformed capacitance vector, and transforming back the transformed capacitance vector with the inverse of an adjusted first eigenvector matrix to obtain an adjusted capacitance vector, which as its elements contains the temperature-compensated capacitance values, wherein the adjusted first eigenvector matrix has the elements of one of the eigenvectors set to zero, wherein the eigenvector which has its elements set to zero is the eigenvector which corresponds to the largest eigenvalue, wherein the first eigenvector matrix contains the eigenvectors of a first covariance matrix of a learning-period capacitance matrix containing for each capacitive component a plurality of capacitance values obtained during a learning-period.

11. A computer program product comprising a storage medium including a computer program as claimed in claim 10.

12. A capacitive component parameter determining device configured to determine the capacitance and loss-factor of each of a plurality of capacitive components of an electrical power device, wherein the capacitive component parameter determining device includes: processing circuitry, and a storage medium including computer-executable components which when executed by the processing circuitry causes the capacitive component parameter determining device to perform the steps of the method including: a) obtaining for each capacitive component a respective capacitance value and loss-factor value, and b) processing the capacitance values and the loss-factor values, wherein the processing involves removing a common influence of temperature on the capacitance values from the capacitance values and removing a common influence of temperature on the loss-factor values from the loss-factor values to obtain for each capacitive component a temperature-compensated capacitance value and a temperature-compensated loss-factor value, wherein the processing involves transforming by means of a first eigenvector matrix a capacitance vector for which each element is a respective one of the capacitance values, to obtain a transformed capacitance vector, and transforming back the transformed capacitance vector with the inverse of an adjusted first eigenvector matrix to obtain an adjusted capacitance vector, which as its elements contains the temperature-compensated capacitance values, wherein the adjusted first eigenvector matrix has the elements of one of the eigenvectors set to zero, wherein the eigenvector which has its elements set to zero is the eigenvector which corresponds to the largest eigenvalue, wherein the first eigenvector matrix contains the eigenvectors of a first covariance matrix of a learning-period capacitance matrix containing for each capacitive component a plurality of capacitance values obtained during a learning-period.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The specific embodiments of the inventive concept will now be described, by way of example, with reference to the accompanying drawings, in which:

[0031] FIG. 1 schematically shows an example of a capacitive component parameter determining device;

[0032] FIG. 2 shows a flowchart of a method carried out by the capacitive component parameter determining device in FIG. 1;

[0033] FIG. 3 shows a measurement set-up for obtaining capacitance values and loss-factor values of capacitive components of an electrical power device;

[0034] FIGS. 4a-4b schematically show graphs of loss-factor values and capacitance values, respectively, with and without temperature-compensation, plotted over time; and

[0035] FIG. 5 schematically shows a graph of a bushing parameter, i.e. loss factor value or capacitance value, with upper and lower threshold values.

DETAILED DESCRIPTION

[0036] The inventive concept will now be described more fully hereinafter with reference to the accompanying drawings, in which exemplifying embodiments are shown. The inventive concept may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided by way of example so that this disclosure will be thorough and complete, and will fully convey the scope of the inventive concept to those skilled in the art. Like numbers refer to like elements throughout the description.

[0037] The present disclosure relates to a method of determining the capacitance and the loss-factor of a plurality of capacitances of a single electrical power device. Hereto, the method is especially suitable for capacitive component parameter determination of an electrical power device comprising a plurality of capacitive components. In particular, the electrical power device is advantageously a poly-phase electrical power device, i.e. an electrical power device comprising a plurality of capacitive components with each capacitive component being associated with a respective electric phase.

[0038] The method involves obtaining a capacitance value of each capacitive component and a loss-factor value of each capacitive component. There is hence obtained a plurality of capacitance values and a plurality of loss-factor values, each capacitance value being associated with a respective one of the capacitive components and each loss-factor value being associated with a respective one of the capacitive components.

[0039] The capacitance values and the loss-factor values are processed to obtain for each capacitive component a temperature-compensated capacitance value and a temperature-compensated loss-factor value. The processing involves removing a common influence of temperature on the capacitance values from the capacitance values and removing a common influence of temperature on the loss-factor values from the loss-factor values. In this manner, the temperature-compensated capacitance values and the temperature-compensated loss-factor values can be obtained.

[0040] Since all capacitive components are provided on the same electrical power device, there will be a common influence of temperature on all capacitance values obtained and a common influence of temperature on all the loss-factor values obtained. The common influences on the capacitance values is removed from the capacitance values and the common influence on the loss-factors is removed from the loss-factor values.

[0041] A capacitive component parameter determining device configured to perform the method as disclosed herein will now be described with reference to FIG. 1. The exemplified capacitive component parameter determining device 1 comprises processing circuitry 3 and a storage medium 5. The storage medium 5 comprises computer-executable components which when run on the processing circuitry 3 causes the capacitive component parameter determining device 1 to perform the method as disclosed herein.

[0042] The processing circuitry 3 uses any combination of one or more of a suitable central processing unit (CPU), multiprocessor, microcontroller, digital signal processor (DSP), application specific integrated circuit (ASIC), field programmable gate arrays (FPGA) etc., capable of executing any herein disclosed operations concerning bushing parameter determination.

[0043] The storage medium 5 may for example be embodied as a memory, such as a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), or an electrically erasable programmable read-only memory (EEPROM) and more particularly as a non-volatile storage medium of a device in an external memory such as a USB (Universal Serial Bus) memory or a Flash memory, such as a compact Flash memory.

[0044] A capacitive component as referred to herein may for example be a condenser core of a bushing of an electrical power device, or a capacitor of a capacitor bank.

[0045] FIG. 2 shows a method of determining the capacitance and loss-factor of each of a plurality of capacitive components of an electrical power device.

[0046] In a step a) for each capacitive component of the electrical device a respective capacitance value and a respective loss-factor value is obtained by the processing circuitry 3.

[0047] In case of a bushing provided with a condenser core, each capacitance value and loss factor value may for example be obtained based on measurements of the respective bushing terminal voltage and a respective bushing tap current. The capacitance values and the loss-factor values may be estimated based on the respective bushing terminal voltage and bushing tap current.

[0048] FIG. 3 shows an example of a set-up which provides measurement of a bushing terminal voltage V and bushing tap current I. The bushing terminal voltage V may for example be obtained using a voltage transformer. The complex admittance Y of a bushing is equal to the bushing tap current I divided by the bushing terminal voltage, i.e. Y=I/V, and each capacitance value may be estimated by dividing the imaginary part of the complex admittance with the angular frequency of the system, i.e. C=Im(Y)/. The loss-factor, or tan(), may be estimated by dividing the real part of the complex admittance with the complex part of the complex admittance, i.e. Re(Y)/Im(Y), which is equivalent to i.sub.r/i.sub.c, i.e. tan()=i.sub.r/i.sub.c.

[0049] In a step b) the capacitance values and the loss-factor values are processed by means of the processing circuitry 3. The processing involves removing a common influence of temperature on the capacitance values from the capacitance values and removing a common influence of temperature on the loss-factor values. In this manner, a temperature-compensated capacitance value and a temperature-compensated loss-factor value is obtained for each capacitive component.

[0050] According to one example the common influence of temperature on the capacitance values and the common influence of temperature on the loss-factor values are derived from plurality of capacitance values of each capacitive component and a plurality of loss-factor values of each capacitive component, collected during a learning-period before commencement of the present method. In particular, statistical correlation analysis may be carried out on this data set, i.e. on the capacitance values and loss-factor values collected in the learning-period, whereby the common influence of temperature on the capacitance values and the common influence of temperature on the loss-factor values may be determined. Hereto, the common influences on temperature are typically predetermined and are thus ready to be applied in step b).

[0051] According to one example, this statistical correlation analysis may involve using Principal Component Analysis (PCA) as will be described in more detail in the following. It should be noted that other statistical correlation analysis methods may alternatively be employed on the plurality of capacitance values and loss-factor values collected in the learning-period, for example statistical regression-based methods.

[0052] In the case of PCA, the processing in step b) involves transforming by means of a first eigenvector matrix V.sub.c a capacitance vector x.sub.c for which each element is a respective one of the capacitance values obtained in step a), to obtain a transformed capacitance vector y.sub.c. A transformation of the type V.sub.c*x.sub.c=y.sub.c is hence performed, where the columns of the first eigenvector matrix V.sub.c are eigenvectors of a first covariance matrix X.sub.cco of a learning-period capacitance matrix X.sub.c obtained during a learning-period. In particular, the learning-period capacitance matrix X.sub.c contains a plurality of capacitance values of each capacitive component, obtained during the learning-period. As an example, the first eigenvector matrix may be a 3*3 matrix V.sub.c=[V1c V2c V3c] in case the electromagnetic induction device has three electrical phases and thus three capacitive components, with V1c-V3c being the eigenvectors arranged as columns, and x=(c.sub.1, c.sub.2, c.sub.3) is a vector containing three components c1-c3 which are the three capacitance values obtained in step a).

[0053] The transformed capacitance vector y.sub.c is then transformed back with the inverse of an adjusted first eigenvector matrix V.sub.c to obtain an adjusted capacitance vector x.sub.c, which as its elements contains the temperature-compensated capacitance values. Hereto, a transformation (V.sub.c).sup.1y.sub.c=x.sub.c is performed where x.sub.c=(c.sub.1, c.sub.2, c.sub.3) contains the temperature-compensated capacitance values.

[0054] The adjusted first eigenvector matrix V.sub.c has the elements of one of the eigenvectors set to zero. In particular, the eigenvector which has its elements set to zero is the eigenvector which corresponds to the largest eigenvalue or singular value, so in the general n-capacitive component case the adjusted first eigenvector matrix is V.sub.c=(0 Vc2 . . . Vcn), and in the example with three capacitive components the adjusted first eigenevector matrix V.sub.c=(0 Vc2 Vc3).

[0055] Since the capacitance matrix X.sub.c is typically an m*n matrix, where mn, diagonalization of its covariance matrix, i.e. the first covariance matrix X.sub.cco, is not possible and to this end other factorization methods may be used to obtain the eigenvalues of the first covariance matrix X.sub.cco. Singular Value Decomposition (SVD) may for example be used to obtain the first eigenvector matrix V.sub.c.

[0056] As noted above, the learning-period capacitance matrix X.sub.c for the capacitance values contains a plurality of capacitance values of each capacitive component collected during the learning-period, and the capacitive component matrix may in the event of a three-phase system be of the form X.sub.c=(Xc1 Xc2 Xc3), and in more general X.sub.c=(Xc1 . . . Xcn), where Xck is a column vector with m elements, each being a capacitance value of the k:th capacitive component obtained during the learning-period.

[0057] It may also be noted that the learning-period capacitance matrix X.sub.c may be normalized and scaled before the first covariance matrix X.sub.cco is determined. The normalization may involve taking the mean of each column and subtracting the mean of a column from the elements of a column. The scaling may for example involve dividing the elements in each column with the standard deviation of the elements in the column.

[0058] The processing in step b) further involves transforming by means of a second eigenvector matrix V.sub.tan() a loss-factor vector x.sub.tan() for which each element is a respective one of the loss-factor values obtained in step a), to obtain a transformed loss-factor vector y.sub.tan(). A transformation of the type V.sub.tan()*x.sub.tan()=y.sub.tan() is hence performed, where the columns of the second eigenvector matrix V.sub.tan() are eigenvectors of a second covariance matrix X.sub.tan()co of a learning-period loss-factor matrix X.sub.tan() obtained during a learning-period. In particular, the learning-period loss-factor matrix X.sub.tan() contains a plurality of loss-factor values of each capacitive component, obtained during the learning-period. As an example, the second eigenvector matrix may be a 3*3 matrix V.sub.tan()=[V1.sub.tan() V2.sub.tan() V3.sub.tan()] in case the electromagnetic induction device has three electrical phases and thus three capacitive components, with V1.sub.tan()-V3.sub.tan() being the eigenvectors arranged as columns, and x.sub.tan()=(tan().sub.1, tan().sub.2, tan().sub.3) is a vector containing three components tan()1-tan()3 which are the three loss-factor values obtained in step a).

[0059] The transformed loss-factor vector y.sub.tan() is then transformed back with the inverse of an adjusted second eigenvector matrix V.sub.tan() to obtain an adjusted loss-factor vector x.sub.tan(), which as its elements contains the temperature-compensated loss-factor values. Hereto, a transformation (V.sub.tan()).sup.1y.sub.tan()=x.sub.tan() is performed where x.sub.tan()=(tan().sub.1, tan().sub.2, tan().sub.3) contains the temperature-compensated loss-factor values.

[0060] The adjusted second eigenvector matrix V.sub.tan() has the elements of one of the eigenvectors set to zero. In particular, the eigenvector which has its elements set to zero is the eigenvector which corresponds to the largest eigenvalue or singular value, so in the general n-capacitive component case the adjusted second eigenvector matrix is V.sub.tan()=(0 V tan()2 . . . V tan()n), and in the example with three capacitive components V.sub.tan()=(0 V tan()2 V tan()3).

[0061] Since the learning-period loss-factor matrix X.sub.tan() is typically an m*n matrix, where mn, diagonalization of its covariance matrix, i.e. the second covariance matrix X.sub.tan()co, is not possible and to this end other factorization methods may be used to obtain the eigenvalues of the second covariance matrix X.sub.tan()co. Singular Value Decomposition (SVD) may for example be used to obtain the second eigenvector matrix V.sub.tan().

[0062] As previously noted, the learning-period loss-factor matrix X.sub.tan() for the loss-factor values may contain a plurality of loss-factor value of each capacitive component collected during the learning-period, and the learning-period loss-factor matrix may in the event of a three-phase system be of the form X.sub.tan()=(X tan()1 X tan()2 X tan()3), and in more general X.sub.tan()=(X tan()1 . . . X tan()n), where X tan()k is a column vector with m items, each being a loss-factor value of the k:th capacitive component obtained during the learning-period.

[0063] It may also be noted that the learning-period loss-factor matrix X.sub.tan() may be normalized and scaled before the second covariance matrix X.sub.tan()co is determined. The normalization may involve taking the mean of each column and subtracting the mean of a column from the elements of the column. The scaling may for example involve dividing the elements in each column with the standard deviation of the elements in the column.

[0064] FIGS. 4a and 4b show examples of the temperature-compensated loss-factor values versus the non-compensated originally obtained loss-factor values, i.e. those obtained in step a) but without the processing of step b), and the temperature-compensated capacitance values versus the non-compensated capacitance values in the context of bushings.

[0065] In FIG. 4a the loss-factor values are shown in a graph for each of three bushings of an electromagnetic induction device. Curves 7a, 9a, and 11a show the temperature-compensated loss-factor values of three bushings over time, while curves 7b, 9b, and 11b show the corresponding non-compensated loss-factor values. As can be seen, the temperature-compensated loss-factor value curves 7a-11a are much less prone to fluctuations and provide a good measure of the actual absolute loss-factor values of the bushings. Similarly, in FIG. 4b, the capacitance values are shown in a graph for each of three bushings of an electrical power device. Curves 13a, 15a, and 17a show the temperature-compensated capacitance values of the three bushings over time, while curves 13b-17b show the corresponding non-compensated capacitance values.

[0066] Since the temperature-compensated loss-factor values and capacitance values provide accurate estimations of the loss factor and capacitance of the bushings, these values may be used to determine whether there is a capacitance fault or electrical power device fault present. Thus, according to one example, there may be provided a respective upper threshold value U and lower threshold value L for each capacitance and each loss-factor, as shown in FIG. 5 for only one capacitance parameter, i.e. plot 19 which shows one of the two capacitive component parameters discussed herein. The upper and lower threshold values U and L provide a range for each capacitive component and for each capacitive component parameter, within which the capacitance value or loss-factor is allowed to vary. In case any of the temperature-compensated capacitance values or temperature-compensated loss-factor values are outside the corresponding upper or lower threshold an alarm may be generated to thereby alert an operator that a fault is present.

[0067] The inventive concept has mainly been described above with reference to a few examples. However, as is readily appreciated by a person skilled in the art, other embodiments than the ones disclosed above are equally possible within the scope of the inventive concept, as defined by the appended claims.