Method for determining a relationship between two sinusoidally changing quantities and diagnostic device
Patent Information
- Authority / Receiving Office
- DE · DE
- Patent Type
- Patents
- Current Assignee / Owner
- FRIEDRICH ALEXANDER UNIV ERLANGEN NUERNBERG
- Filing Date
- 2012-02-27
- Publication Date
- 2026-07-09
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Abstract
Description
[0001] The invention relates to a method for determining a relationship between two variables that change periodically, essentially according to a sinusoid. It also relates to a diagnostic device for carrying out the method.
[0002] The motivation for providing the method comes from the field of measuring medium or high-voltage cables that are laid underground, ie underground cables. Here it is necessary to determine whether the cables have gone through an aging process and therefore need to be replaced. An essential variable here is the loss factor, which is referred to as tanδ. For this angular quantity δ, δ=π / 2−φ applies, where φ is the phase angle or the phase difference between an AC voltage applied to the cable and the AC current generated by the insulation. The AC voltage in the form of a sine wave is applied between the inner conductor and the outer conductor or the shield or between several inner conductors of the cable and possibly the shield. The outer conductor (sheath) is usually coupled to ground (earth). It is now a task to derive a corresponding relationship between the two electrical quantities present, even in real situations in which the AC voltage and the AC current are not ideally sinusoidally periodic.
[0003] A first starting point for determining how the relationship between two variables that essentially change periodically according to a sine curve can be found in the article by C. Freitag, I. Mladenovic and C. Weindl entitled “Fully Automated MV Cable Monitoring and Measurement System for Multi-Sample Acquisition of Artificial Aging Parameters” at the “International Conference on Renewable Energies and Power Quality (ICREPQ'10)”, Granada / Spain, which took place from March 23rd to 25th, 2010. In this article, the concept is presented that the first variable, which changes periodically according to the sine curve, at a plurality of times t k , k=1, k is measured. Each of the times t k a virtual imaginary part is now assigned, in which a measured value shifted by 90° (π / 2) in the period is used. If the assumption that a sinusoidal shape is present is correct, the actual measured value at a specific point in time t k form a 2-tuple as the real part and the added imaginary part, namely a complex number.
[0004] In the article by C. Freitag et al. assumed that every complex number is to be mapped in such a way that the time dependence with the fundamental frequency is no longer shown. It is therefore multiplied by a factor e –jωt multiplied, where j is the imaginary unit, ω is the (assumed) frequency of the sine wave (mains frequency) and t is the time of the respective measurement. The disadvantage here is that the uncertainties in the specification of the frequency immediately lead to measurement errors, and the times must also be determined precisely. In the mentioned article by C. Freitag et al. is multiplied by the factor e –jωt filtering is carried out and then a numerical value is calculated from which the phase shift between the two variables is deduced.
[0005] It is an object of the present invention that from the cited article by C. Freitag et al. to improve known methods and to ensure a high precision in determining the relationship between the two quantities which vary periodically essentially according to a sinusoid.
[0006] The task is solved by a method with the following steps: - measuring the first quantity at times t k , k=1,...,N, preferably over at least a quarter period, particularly preferably over at least one period; - measuring the second variable at the same times t k ; - for each of the times t k forming a 2-tuple from at least two values of the first variable measured at different points in time to indicate a respective complex number a[k]; – For each point in time t kforming a 2-tuple from at least two values of the second variable measured at different points in time to indicate a respective complex number b[k], marked by: - forming the ratio for all k; - from all ratios c[k] directly calculate a mean value c according to a mathematical calculation rule; – deriving a statement about the relationship from the mean value.
[0007] A first essential aspect of the invention is that the complex numbers a[k] and b[k] are not subject to a previous transformation (in the sense of a rotation with the factor e –jωt ) must be subjected before the actual calculation takes place. In this way, the individual ratios c[k] for different k reflect the respective one at time t k prevailing absolute phase in the sine curve. However, because an average value is then calculated directly (without additional steps), these values of the absolute phases balance each other out; the mean value c achieved therefore allows a good statement to be made about the actual value of some relationship variables.
[0008] As stated at the outset, the two variables are preferably electrical variables, in particular a voltage and an amperage.
[0009] It is preferred here that one variable is a voltage applied to an (underground) cable, in particular a medium or high-voltage cable, and the other variable is an amperage of a current flowing through the insulation of the cable.
[0010] The measured values obtained in the steps of measuring the first and second variables are preferably supplied to a computing device, optionally with their amplitude being transformed, so that they are present as small signals (between 0 and 12 V or between 0 and 5 V or the like).
[0011] A computing device can effectively process such small signals, so that the subsequent processing steps can be carried out digitally.
[0012] In this case, in order to form a 2-tuple for a variable, the computing device preferably links a first memory location for a measured value for the variable with a second memory location for a different measured value for the variable.
[0013] This linking can be done with the help of a pointer, for example, so that the 2-tuples do not have to be stored separately in addition to the measured values.
[0014] In a preferred embodiment of the invention, in the step of forming the ratio, arithmetic steps are carried out for dividing complex numbers, with the respective measured value from the first memory location being interpreted as the real part and the respective measured value from the second memory location being interpreted as the imaginary part, so that the ratio can be re-entered 2-tuple gets. This ensures that reliable statements can actually be derived from the ratio variables c[k] or their mean value c.
[0015] More preferably, it is provided that in the step of calculating the mean value, the 2-tuple of the ratio is linked using the calculation steps of an addition of complex numbers to form a new 2-tuple, with the addition of the first entry of the 2-tuple as a real part and the second entry of the 2-tuple can be interpreted as an imaginary part.
[0016] In the final step of the method, the phase φ=arg c (as an argument of c) and / or the absolute value |c| is preferably obtained from the 2-tuple c, which describes the mean value calculated, where the first entry of the 2-tuple for the mean is interpreted as the real part and the second entry of the 2-tuple for the mean is interpreted as the imaginary part, and where φ and / or |c| is or are used as a statement for the relationship of size.
[0017] The quantities φ and |c| are two very significant quantities from which further statements can also be derived. Thus, at least one of φ and |c| is also preferred another variable is calculated, in particular the loss factor tan(π / 2−φ), an impedance, admittance, resistance, conductance, the power factor cosφ, a dielectric constant of the cable, an apparent power, real power and / or reactive power is calculated. These are the variables with which statements can be made as to whether the examined cable is functional or not and can remain in the ground or has to be replaced.
[0018] In a preferred embodiment of the invention in all of the specified embodiments, the mean is the arithmetic mean, so that:
[0019] The arithmetic mean is particularly suitable for eliminating the same in the case of statistically distributed interference.
[0020] In a preferred embodiment of the invention, for the 2-tuple for a time t k one measured value at time t k used and one reading at a time t k' used, where the time t k' around 1 4 ± n, n ∊ Period durations T of the sine curve from time t k is spaced.
[0021] That the time t k' around 1 4 ± n Periods T is spaced apart in time, can alternatively be expressed in such a way that the point in time t k' around 3 4 ± n Period durations T of the sine curve from time t k is spaced.
[0022] In this way one obtains a particularly precise complex number that describes the sinusoidal oscillation particularly well.
[0023] In another aspect of the invention, the object is also achieved by a diagnostic device having the features of patent claim 13 .
[0024] The diagnostic device for determining a relationship between a voltage and a current, in particular in a medium or high-voltage cable, thus has a device for measuring N values of the voltage and a device for measuring N values of the current. Such measuring devices are known per se. For example, a device for measuring the voltage comprises a voltage divider with an impedance element, e.g. B. a resistor, and a measuring device for measuring the voltage drop across this impedance element. This measurement can initially take place in analog form and then be translated into digital values or determined directly by digital sampling. Likewise, the device for measuring N values of the current intensity preferably comprises a shunt resistor, through which the current whose current intensity is to be measured is passed, and a voltage drop across this shunt resistor is measured with a suitable voltmeter, which can be either analog works and then converts the analogue values into digital measured values, or works directly digitally.
[0025] The diagnostic device according to the invention also has a computing device which is designed to further process the N digital values obtained for the voltage and the N digital values for the current intensity by digital data processing. As a rule, the computing device will be a digital data processing device that is suitably programmed. This means that a program code is assigned to it, which is stored, for example, on a suitable memory device of the computing device and can be run (eg on a main memory of the computing device). The digital processing steps are intended to be the same as those mentioned above for the method according to the invention. steps (forming a 2-tuple for the voltage and for the current, forming the ratio for all k 2-tuples, immediately calculating a mean c from all the ratios c[k] and deriving a statement about the relationship from the mean c ).
[0026] A preferred embodiment of the invention is described in more detail with reference to the drawing in which
[0027] figure 1 is a flow chart for explaining an embodiment of the method according to the invention,
[0028] figure2a illustrates a measurement setup used to measure voltage and current over a medium or high-voltage cable, with the measurement taking place at medium or high-voltage potential,
[0029] figure 2b illustrates a measurement setup used to measure voltage and current over a medium or high-voltage cable, with the measurement taking place at ground potential,
[0030] figure 3a illustrates two sine curves, which are used to illustrate the concept of forming a 2-tuple in the method according to the invention,
[0031] figure 3b illustrates a corresponding representation of a curve in the complex plane,
[0032] figure 4a one of the figure 3b shows corresponding representation of noisy measured values of voltage and current,
[0033] figure 4b plots the voltage to current ratio as a complex number in a complex plane for a variety of values figure 4a illustrates and
[0034] figure 5 one of figure 4b is the corresponding representation in the event that the underlying sine wave is distorted.
[0035] In a method for determining a relationship between two quantities a(t) and b(t) that change periodically essentially according to a sine curve, N discrete values a[k] of quantity a(t) and N discrete values b[k] are first determined. of size b(t) recorded at the same times t k , for which synchronization takes place. The step of acquiring the discrete values a[k] is step S10, and that of acquiring the values b[k] is step S10'.
[0036] In the present example it is assumed that a test specimen P ( figure 2a and figure 2b) is an underground cable. In the simplest case, such a cable can be characterized by its resistance R Kabel and a capacitance C Kabel describe between the inner conductor and the metallic outer conductor. As the underground cable ages, its resistance and capacity change. This is reflected in the so-called loss factor tanδ. If this is to be measured, a test voltage u p (t) are applied and measured, and the current i p (t) of the electric current flowing here can be measured.
[0037] The measurement and evaluation is carried out with the aid of a diagnostic device D. The voltage is measured by dividing the voltage using a divider capacitance C Teiler and a divider resistor R Teiler , where the measurement of the voltage u(t) at the divider resistor R Teiler he follows. In series with the test cable is a shunt resistor R Shunt switched, across which a voltage drops, which is a measure of the current intensity i(t). The test voltage u can be calculated from u(t). p (t) can be derived, from i(t) the current intensity i p (t) are calculated.
[0038] figure 2a shows the measurement that is usually carried out at medium or high voltage potential. However, it can also be a measurement of earth potential in the manner of figure 2b take place.
[0039] A test voltage and p (t) now has an ideal amplitude, as shown by the curve 10 in figure 3a is shown. One can now give each point on this curve a value shifted by a quarter period according to the curve 12 assign and interpret this second value as an imaginary part. If you now plot the real part and imaginary part over time, you get according to figure 3b exactly one circle 14 . Certain calculations can be carried out more easily with the aid of such a circle or of measured values on such a circle, as will become clear below.
[0040] In step S12, the values a[k] are first auto-expanded to form N complex values a[k], where the following applies to the real part: Re a[k] = a[k ± m × N p ], where N p is the number of samples per period.
[0041] The following applies to the imaginary part of a[k]: in the [k] = a[k – 1 4 × N ± n × N p ]. The numbers m and n are integers here.
[0042] While the values a[k] are auto-expanded to the value a[k] in step S12, the corresponding auto-expanding is done in the values b[k] to the complex values b[k] in step S12'.
[0043] In a subsequent step S14, the ratio variable is calculated for all N values of k:
[0044] The invention lies in the fact that, in the present case, it is independent of the point in time t k for the measurement of the value a[k] and b[k] the ratio variable c[k] is formed. In particular, there is no mapping to eliminate the time dependency on the fundamental frequency (reverse rotation with mains frequency).
[0045] This calculation of N values for c[k] carried out in step S14 goes directly into step S16 of forming the mean value, in this case the arithmetic mean value. Instead of the arithmetic mean, a weighted mean can also be calculated using filtering. Thus, in step S16, the mean value calculated.
[0046] The phase can now be derived from this mean value c, namely the argument φ:=arg(c) is determined in step S18. Likewise, in step S20, the amount |c| be calculated. From these two variables φ and |c| calculated in steps S18 and S20 then other variables can be calculated, such as the loss factor tanδ = tan(π / 2 – φ), the active power, the reactive power, the impedance and much more. a. m.
[0047] The method according to the invention is used in the example as in figure 4a shown carried out: with the measurement setup according to figure 2a or figure 2b determined voltage U [V] is auto-extended to the complex number, so that the curve 16 is obtained, likewise the values for the stream are complex auto-extended, so that the curve 18 receives. By dividing the values from the curve 16 by the respectively assigned values from the curve 18 you now get a bunch of points 20 . How out figure 4b, these points are around a mean value 22 arranged around, which is calculated in step S16.
[0048] There may be a distortion in the sine shape of the curve, resulting in a ring-shaped distribution instead of a spot-like uniform distribution of the points, as in figure 5 shown. Calculate the mean here 22 , but this hits the desired actual value pretty much exactly, regardless of the distortion of the sine shape.
[0049] While steps S10 and S10 are carried out with the aid of measuring devices in diagnostic device D, the measured values are fed in the form of small signals to a computing device R in diagnostic device D, in which the measured values are stored in memory locations. With the help of a pointer (Pointers) can have two memory locations 24 and 26 or 24' and 26' are coupled together to form a complex number, such as the number a[k] or b[k].
[0050] The computing device R can also carry out the further steps of forming the ratio variables in step S14, forming the mean value in step S16 and the calculation steps S18, S20 and S22.
[0051] The output variables are output at an output A or on a screen B of the diagnostic device D in the form of small signals. Reference List P examinee D diagnostic device R computing device QUOTES INCLUDED IN DESCRIPTION
[0052] This list of documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Non-patent Literature Cited
[0053] C. Freitag, I. Mladenovic and C. Weindl with the title "Fully Automated MV Cable Monitoring and Measurement System for Multi-Sample Acquisition of Artificial Aging Parameters" at the "International Conference on Renewable Energies and Power Quality (ICREPQ'10)", Granada / Spain, March 23-25, 2010
[0003] C.Friday et al.
[0004] C.Friday et al.
[0005]
Claims
[1] Method for determining a relationship between two quantities (a(t), b(t)) which change periodically in an essentially sine curve, comprising the following steps: – Measuring (S10) the first quantity at a plurality of time points t k , k = 1, ..., N, – Measuring (S10') the second quantity at the same time points t k , – for each of the time points t k Forming (S12) a 2-tuple from at least two values of the first quantity measured at different times to specify a respective complex number a[k], – for each of the time points t k Forming (S12') a 2-tuple from at least two values of the second quantity measured at different times to specify a respective complex number b[k], characterized by – Forming (S14) the ratio for all k, – directly calculating (S16) a mean value c from all ratios c[k] according to a mathematical calculation rule, – Deriving a statement about the relationship from the mean (S18, S20, S22). [2] The method of claim 1, wherein the quantities are electrical quantities, in particular a voltage and a current. [3] Method according to claim 2, wherein one quantity is a voltage applied to a cable, in particular a medium or high voltage cable, and the other quantity is a current intensity of a current flowing through the insulation of the power cable. [4] Method according to claim 2 or 3, wherein measured values obtained in the steps of measuring the first and second quantities are supplied to a computing device (R). [5] Method according to claim 4, wherein the computing device (R) for forming a 2-tuple uses a first memory location ( 24 , 24') for a measurement of the size with a second memory location ( 26 , 26' ) linked to a different measurement for the size. [6] Method according to claim 5, wherein in the step of forming the ratio quantity computational steps for a division of complex numbers are carried out, wherein the respective measured value from the first storage location is interpreted as the real part and the respective measured value from the second storage location is interpreted as the imaginary part, so that a 2-tuple is obtained as the ratio quantity. [7] Method according to claim 6, wherein in the step of calculating the mean value the 2-tuples of the ratio quantity are combined to form a new 2-tuple using the computational steps of an addition of complex numbers, wherein for the addition the first entry of the 2-tuple is interpreted as a real part and the second entry of the 2-tuple as an imaginary part. [8] Method according to claim 7, wherein the phase φ = arg (c) is calculated as an argument of c and / or the magnitude |c| from the 2-tuple c describing the mean value, wherein the first entry of the 2-tuple is interpreted as the real part and the second entry of the 2-tuple as the imaginary part, and wherein φ and / or |c| are used as a statement for the relationship of the quantity. [9] Method according to claim 8, wherein from at least one of φ and |c| a further quantity is calculated, in particular the loss factor tan(π / 2 – φ), an impedance, admittance, resistance, conductance, the power factor cosφ, a dielectric constant of a cable, an apparent power, active power and / or reactive power. [10] A method according to any of the preceding claims, wherein the mean is the arithmetic mean, [11] Method according to one of the preceding claims, characterized in that the time points t kat equal intervals from the preceding or following time point. [12] Method according to one of the preceding claims, characterized in that for the 2-tuple at a time t k each measurement taken at time t k is used and a measurement is taken at a time t k ' is used, which is around 1 4 ± n, n ∊ Periods T of the sine curve in time from time t k is spaced apart. [13] Diagnostic device (D) for determining a relationship between a voltage and a current, in particular on a medium or high voltage cable (P), comprising: – an institution (R Teiler ) to measure N voltage values, – an institution (R Shunt ) for measuring N values of current intensity, – a computing device (R) which is designed to: a) Forming a 2-tuple from at least two voltage values measured at different times to specify a respective complex number a[k], k = 1, ..., N, b) Forming a 2-tuple from at least two current values measured at different times to specify a respective complex number b[k], k = 1, ..., N, c) Forming the ratio for all k, d) from all ratios c[k] directly calculate (S16) a mean value c according to a mathematical calculation rule, e) Deriving a statement about the relationship from the mean c. [14] Diagnostic device according to claim 13, designed to carry out the method according to any one of claims 2 to 12.