WIND TURBINE AND METHOD FOR DETECTING LOW-FREQUENCY OSCILLATIONS IN AN ELECTRICAL SUPPLY GRID

Abstract

A method for detecting low-frequency oscillations, in particular subsynchronous resonances, in a grid is provided. The method includes recording a series of measurements, having measurement points, of a grid variable over a measurement time period, for performing a frequency analysis and multiplying the series a time-dependent sinusoidal test function for the same measurement time period. The test function is characterized by a test frequency and a test angle as phase angle. The series for each measurement point is multiplied by the test function in order to obtain a test product for each measurement point. The method includes adding the test products taking into consideration the mathematical sign thereof to give a product sum, and evaluating, depending on the product sum, whether the series of measurements has a low-frequency oscillation having a frequency in the region of the test frequency and a phase angle in the region of the test angle.

Claims

1. A method for detecting low-frequency oscillations in an electrical supply grid having a line voltage and associated with a rated line frequency, comprising: recording at least one series of measurements having a plurality of measurement points of a grid variable over a measurement time period for performing a frequency analysis on the at least one series of measurements; multiplying each measurement point of the at least one series of measurements by a time-dependent sinusoidal test function for the measurement time period to obtain a product for each measurement point, wherein the test function has a test frequency and a test angle as phase angle; summing a plurality of products of the plurality of measurement points to produce a product sum, wherein summing the plurality of products includes retaining a plurality of signs of the plurality of products, respectively; and determining, based on the product sum, whether the at least one series of measurements has a low-frequency oscillation having an oscillation frequency in a region of the test frequency and a phase angle in a region of the test angle, wherein the oscillation frequency is below the rated line frequency.

2. The method as claimed in claim 1, comprising: repeating multiplying each measurement point of the at least one series of measurements by the test function and summing the plurality of products while varying the test frequency and/or varying the test angle to obtain a plurality of product sums; and determining whether the at least one series of measurements has the low-frequency oscillation depending on the plurality of product sums.

3. The method as claimed in claim 1, wherein: repeating multiplying each measurement point of the at least one series of measurements by the test function and summing the plurality of products while varying the test frequency and varying the test angle to obtain a product sum is each test pair formed by a test frequency value and a test angle value.

4. The method as claimed in claim 1, comprising: detecting the low-frequency oscillation based on the product sum by determining whether the product sum reaches at least a predetermined test amplitude.

5. The method as claimed in claim 1, comprising: repeating multiplying each measurement point of the at least one series of measurements by the test function and summing the plurality of products while varying the test frequency in a first test loop, wherein: the test frequency is varied within a first frequency range in the first test loop to detect the low-frequency oscillation having the oscillation frequency, and the oscillation frequency is detected with a first accuracy; and repeating multiplying each measurement point of the at least one series of measurements by the test function and adding the plurality of products while varying the test frequency in a second test loop, wherein: the test frequency is varied within a second frequency range in the second test loop; and the second frequency range is selected depending on the oscillation frequency detected in the first test loop to detect the oscillation frequency with a higher accuracy than in the first test loop.

6. The method as claimed in claim 5, comprising: repeating multiplying each measurement point of the at least one series of measurements by the test function and summing the plurality of products while varying the test angle in the first test loop, wherein: the test angle is varied within a first angle range, and the test angle is varied with a first angle increment; and repeating multiplying each measurement point of the at least one series of measurements by the test function and summing the plurality of products while varying the test angle in the second test loop, wherein: the test angle is varied within a second angle range, and the second angle range is selected depending on the phase angle of the low-frequency oscillation detected in the first test loop to detect the phase angle of the low-frequency oscillation with a higher accuracy than in the first loop.

7. The method as claimed in claim 5, wherein: in the first test loop, the test frequency is varied with larger frequency steps than in the second test loop, and/or in the first test loop, the test angle is varied with larger angle steps than in the second test loop.

8. The method as claimed in claim 1, comprising: recording a plurality of series of measurements of the grid variable, wherein: each series of measurements of the plurality of series of measurements is recorded for analyzing a respective frequency range, for each series of measurements of the plurality of series of measurements, a respective measurement time period is selected depending on the respective frequency range, for each series of measurements of the plurality of series of measurements, multiplying each measurement point of the series of measurements by the test function and summing the plurality products to produce the product sum is repeated while varying the test frequency and/or varying the test angle to obtain a respective plurality of product sums for each series of measurements, and for each series of measurements, the respective plurality of product sums are evaluated for detecting the low-frequency oscillation.

9. The method as claimed in claim 1, wherein: repeating multiplying each measurement point of the at least one series of measurements by the test function and summing the plurality of products to give the product sum while varying the test frequency, wherein: the test frequency is varied within at least one frequency range having an upper frequency value and a lower frequency value and using a frequency increment, and the frequency increment is set depending on the frequency range.

10. A wind power system for detecting low-frequency oscillations in an electrical supply grid having a line voltage and associated with a rated line frequency, the wind power system comprising: a controller configured to: record at least one series of measurements; having a plurality of measurement points of a grid variable over a measurement time period for performing a frequency analysis on the at least one series of measurements; multiplying each measurement point of the at least one series of measurements by a time-dependent sinusoidal test function for the measurement time period, wherein the test function has a test frequency and a test angle as phase angle; sum a plurality of products of the plurality of measurement points to produce a product sum, wherein summing the plurality of products includes retaining a plurality of signs of the plurality of products, respectively; and determining, based on the product sum, whether the at least one series of measurements has a low-frequency oscillation having a frequency in region of the test frequency and a phase angle in region of the test angle.

11. (canceled)

12. The method as claimed in claim 1, wherein the low-frequency oscillations are sub synchronous resonances.

13. The method as claimed in claim 1, wherein the oscillation frequency is 1 hertz (Hz) or less.

14. The method as claimed in claim 1, wherein the grid variable is the line voltage, an input current or a line frequency of the electrical supply grid.

15. The method as claimed in claim 2, comprising: when a first product sum has a maximum amplitude in relation to the plurality of product sums, detecting the low-frequency oscillation in the first product sum having an associated first frequency and an associated first phase of a first test frequency and a first test angle, and/or in response to detecting the low-frequency oscillation, detecting an amplitude of the low-frequency oscillation.

16. The method as claimed in claim 3, comprising: obtaining a curved area in three-dimensional space depending on test frequency values and test angle values for test pairs; and identifying the test frequency and phase angle of the low-frequency oscillation as a first test frequency value and a first test angle of the test pairs at which in relation the product sum has a maximum in relation to remaining product sums.

17. The method as claimed in claim 6, wherein the test angle is varied within the second angle range a second angle increment that is less than the first angle increment.

18. The method as claimed in claim 9, wherein the frequency increment is set depending on the frequency range such that: the frequency increment is less than the lower frequency value; and/or the frequency increment is less than a predetermined percentage value of the upper frequency value.

19. The method as claimed in claim 18, wherein the frequency increment is less than 10% of the lower frequency value and/or the predetermined percentage value is less than 1% of the upper frequency value.

20. The method as claimed in claim 9, wherein: the test frequency is varied within a plurality of frequency ranges, and frequency increments of different frequency ranges are different than each other, and each frequency increment is greater than a predetermined percentage of the respective lower frequency value of the respective frequency range.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0064] The invention will now be explained in more detail below by way of example with reference to the attached figures.

[0065] FIG. 1 shows a wind turbine in a perspective illustration.

[0066] FIG. 2 shows a wind farm in a schematic illustration.

[0067] FIG. 3 shows a flowchart for recording a plurality of product sums whilst varying a test frequency and varying a test angle.

[0068] FIG. 4 shows a flowchart for evaluating a plurality of product sums recorded in accordance with the flowchart shown in FIG. 3.

[0069] FIG. 5 shows, in a 3D graph, product sums depending on a varied test frequency and depending on a varied test angle.

[0070] FIG. 6 shows, schematically, a structure of a wind power system for detecting low-frequency oscillations.

DETAILED DESCRIPTION

[0071] FIG. 1 shows a wind turbine 100 comprising a tower 102 and a nacelle 104. A rotor 106 comprising three rotor blades 108 and a spinner 110 is arranged on the nacelle 104. The rotor 106 is set in rotary motion by the wind during operation and thereby drives a generator in the nacelle 104.

[0072] FIG. 2 shows a wind farm 112 comprising, by way of example, three wind turbines 100, which may be identical or different. The three wind turbines 100 are therefore representative of, in principle, any desired number of wind turbines in a wind farm 112. The wind turbines 100 provide their power, namely in particular the generated current, over an electrical farm grid 114. In this case, the respectively generated currents or powers of the individual wind turbines 100 are added, and usually a transformer 116 is provided, which steps up the voltage in the farm in order to then inject this into the supply grid 120 at the injection point 118, which is also generally referred to as the PCC. FIG. 2 is merely a simplified illustration of a wind farm 112, which does not show any control, for example, although naturally control is provided. For example, the farm grid 114 can also be configured differently by virtue of, for example, a transformer also being provided at the output of each wind turbine 100, to name but one other exemplary embodiment.

[0073] Both the wind turbine shown in FIG. 1 and the wind farm shown in FIG. 2 can each form a wind power system.

[0074] FIG. 3 shows a flowchart 300 for recording a plurality of product sums. In the start block 302, the signal to be investigated is recorded and further initialization is performed. The signal to be investigated may be a recorded time signal, which is sampled uniformly for investigation in the flowchart 300 with the time steps Δt. The signal to be investigated can also already be present in such a sampled form, but advantageously here the time increment is selected in order to thereby also fix the number of values to be investigated in total.

[0075] The signal y(t) to be investigated is therefore recorded or considered for a measurement time period and the measurement time period may extend from t=0 to t=t.sub.end. The measurement duration and therefore width of the measurement time period is therefore fixed by t.sub.end. For time t the following therefore applies:

t=0,1.Math.Δt,2.Math.Δt, . . . ,t.sub.end

[0076] Likewise, in the start block 302, the frequency range to be investigated from a start frequency f.sub.start up to an end frequency f.sub.end can be fixed. The increment Δf of the frequency investigation can be fixed depending on the start frequency f.sub.start and the end frequency f.sub.end and depending on the desired frequency step number n according to the following formula:

Δf=(f.sub.end−f.sub.start)/n

[0077] The increment of the phase angle investigation Δφ can likewise be fixed depending on a desired angle step number m according to the following formula:

Δφ=(2.Math.π)/m

[0078] These values, in particular the frequency step number n and the angle step number m and also the time step Δt can in principle be selected as desired, but it is proposed to draw a balance in the selection between accuracy and computational complexity.

[0079] In the first initialization block 304, the control variable i is initialized for an outer loop 306. The rate at which this outer loop 306 is executed corresponds to the frequency step number n and this is tested correspondingly in the first repetition request block 308, which follows the first increment block 310.

[0080] Within this outer loop 306 there is the second initialization block 312, in which the control variable j for an inner loop 314 is initialized. It is executed corresponding to the angle step number m, which is requested in the second repetition request 316, which follows the second increment block 318.

[0081] Finally, a calculation block 320 is provided, which is executed correspondingly (n×m) times. With each execution run, the reference frequency f.sub.ref is calculated, namely the frequency with respect to which in each case a sum product is calculated. This reference frequency f.sub.ref is calculated according to the following formula:

[00001]$f_{\mathrm{ref}}=f_{\mathrm{start}}+i.Math.\left(f_{end}-f_{\mathrm{start}}\right)/n$

[0082] At the same time, the respective reference angle θ.sub.ref is calculated, namely according to the following formula:

[00002]${\theta }_{\mathrm{ref}}=\left(j.Math.2.Math.\pi \right)/m$

[0083] Finally, the product sum is then calculated on the basis of these calculated values, i.e., for the value relevant in the execution run for the reference frequency f.sub.ref and the reference angle θ.sub.ref. The product sum can also be understood to mean the DC component, as has been explained above, with the result that the product sum here is denoted by DC.sub.prod. It is therefore calculated for the respective execution run i of the outer loop and the respective execution run j of the inner loop according to the following formula:

DC.sub.prod(i,j)=sum{y(t).Math.sin(2.Math.π.Math.f.sub.ref.Math.t+θ.sub.ref)}.Math.Δt/t.sub.end

[0084] Therefore, as the series of measurements, the signal y(t) to be investigated is multiplied by the sine function sin(2.Math.π.Math.f.sub.ref.Math.t+θ.sub.ref) and by this means the sum is formed. Therefore, a product is also formed here for each time point and these products are summated. This can be performed, for example, by a third innermost loop, in order to explain this illustratively, in which the time t increments from 0 to t.sub.end, namely in the time steps Δt. The result is also standardized by multiplication by the time step Δt and division by the end time t.sub.end, namely in such a way that the product sum DC.sub.prod is in principle independent of the time step Δt. The product sum is therefore in principle, in terms of its absolute value, independent of the number of summated products.

[0085] Once the inner loop 314 has been executed m times and the outer loop 306 has been executed n times, there are n×m individual product sums DC.sub.prod (i, j), which can be stored in a corresponding field and can then be investigated for further evaluation. For this purpose, the result of the flowchart 300 is passed on to the flowchart 400 in FIG. 4, which is indicated in the flowchart 300 by the block 400.

[0086] Correspondingly, FIG. 4 shows this block 400, namely the flowchart 400, and this builds upon the flowchart 300 in FIG. 3, which is indicated by the fact that the first block is denoted as flow block 300.

[0087] In the Max block 402, the product sum with the greatest value is sought from among all of the product sums which were calculated in the calculation block 320, namely taking into consideration the mathematical sign. If, in order to simplify or reduce the complexity, the test angle were not to be varied over 360°, but only over 180°—preferably it is also possible for it to be varied only over 90°—, it would also be possible here for the greatest value in terms of absolute value to be sought.

[0088] The search is performed for all of the product sums which in particular have been stored in a field, namely for each execution run of the outer loop 306 and the inner loop 314. These loops were namely executed with the outer control variable i and the inner control variable j, and these two control variables then here also serve to identify the maximum product sum, for example, in a data field. Correspondingly, in the identification block 404, an assignment of these two control variables is performed, namely according to which the control variables i and j in relation to which the maximum product sum was found in the Max block 402 are identified as selected outer and selected inner control variable i.sub.Max DC and j.sub.Max DC, respectively.

[0089] The maximum value of the product sums detected in block 402 belongs to these two selected control variables, namely the selected outer and the selected inner control variable i.sub.Max DC and j.sub.Max DC, respectively, and a reference frequency and a reference angle belong to said maximum value. The corresponding reference frequency and the corresponding reference angle can be calculated from the corresponding outer and inner control variable i,j, respectively. For this frequency and this angle, it is assumed that this is the corresponding frequency of a low-frequency oscillation and the corresponding angle of a low-frequency oscillation, respectively, with the result that this associated reference frequency is referred to as the frequency of the low-frequency oscillation f.sub.PSO, and the selected angle is referred to as the angle of the low-frequency oscillation θ.sub.PSO. These two values can be calculated according to the following equation:

[00003]$f_{\mathrm{PSO}}=f_{\mathrm{start}}+i.Math.\left(f_{\mathrm{end}}-f_{\mathrm{start}}\right)/n$${\theta }_{\mathrm{PSO}}=\left(j.Math.2.Math.\pi \right)/m$

[0090] And the frequency of the low-frequency oscillation f.sub.PSO and the angle of the low-frequency oscillation θ.sub.PSO are calculated when the corresponding selected control variable i.sub.Max DC and j.sub.Max DC, respectively, is used for the respective outer and inner control variable i, j. In this formula, the angle of the low-frequency oscillation θ.sub.PSO is given in rad and not in degrees.

[0091] In the calculation block 406, an amplitude of the low-frequency oscillation A.sub.PSO can also be calculated, namely according to the following equation:

[00004]$A_{\mathrm{PSO}}=\mathrm{Max}DC/\left(\mathrm{sum}\left\{\sin \left(2.Math.\pi .Math.f_{\mathrm{PSO}}.Math.t+{\theta }_{\mathrm{PSO}}\right).Math.\sin \left(2.Math.\pi .Math.f_{\mathrm{PSO}}.Math.t+{\theta }_{\mathrm{PSO}}\right)\right\}.Math.\Delta t/t_{\mathrm{end}}\right)$

[0092] The amplitude of the low-frequency oscillation therefore results from the fact that the detected maximum product sum is divided by a corresponding product sum of the reference signal multiplied by the reference signal for the entire investigated time range. Therefore, the product sum of the reference signal is determined by itself during the multiplication, which results in the maximum possible value because such a reference function correlates with itself to a maximum extent. It therefore remains a factor with respect to the less correlated product sum between the investigated signal and the reference signal. This amplitude A.sub.PSO is in this case likewise a standardized variable.

[0093] The results can therefore be output in the output block 408 and used further.

[0094] FIG. 5 illustrates, in a three-dimensional representation 500, the entirety of all of the product sums which were calculated in the calculation block 320 as a curved plane 502 as a function of the varied reference frequency f.sub.ref and the varied reference angle θ.sub.ref. The reference frequency f.sub.ref can also be referred to synonymously as test frequency, and the reference angle θ.sub.ref can also be referred to synonymously as test angle.

[0095] By way of example, a signal to be investigated has been selected which has a low-frequency oscillation with an oscillation frequency of 8.25 Hz (f.sub.PSO=8.25 Hz) at a phase angle of 90° (θ.sub.PSO=90°). For this purpose, a reference angle or test angle is varied from 0° to 360°, and a reference frequency or test frequency is varied from 0 to 25 Hz. It should be noted that for frequencies deviating severely from this oscillation frequency of 8.25 Hz, the product sums indicated in the curved plane 502 have substantially the value 0. In the vicinity of the oscillation frequency of 8.25 Hz, the amplitude increases in oscillatory fashion towards the oscillation frequency. However, it should also be noted that the reference angle or the test angle likewise plays a significant role. In the case of the oscillation frequency and the phase angle of the low-frequency oscillation, the absolute amplitude of the product sum is then also at a maximum and correspondingly the frequency of the low-frequency oscillation f.sub.PSO and the phase angle of the low-frequency oscillation θ.sub.PSO can be read from the graph or from the value field of the product sums.

[0096] The flowchart in FIG. 3 and indirectly also in FIG. 4 and also the graph in FIG. 5 relate to the case where the test frequency or reference frequency and also the test angle or the reference angle have each only been varied once, to be precise in each case with many values, but without repeating in particular the entire sequence of the outer and inner loop in accordance with the flowchart 300 with new values. This representation particularly in FIG. 3 to this extent serves an illustrative purpose and preferably in particular the entire sequence in accordance with the two flowcharts 300 and 400 is repeated with focused values for the range of the frequency to be investigated, i.e., for the frequency range to be investigated and also for new values for the angle range to be investigated. For this purpose, in the start block 302, correspondingly new values in the vicinity of the roughly identified maximum are determined, in particular on the basis of the values provided in the first execution run in the output block 408 for the frequency of the low-frequency oscillation f.sub.PSO and the phase angle of the low-frequency oscillation θ.sub.PSO.

[0097] FIG. 6 shows a wind power system 600, which is illustrated symbolically by a single wind turbine, but can also have a plurality of wind turbines. Said system is set up for detecting subsynchronous resonances in an electrical supply grid 602 into which the wind power system 600 injects.

[0098] A recording means (voltmeter, ammeter, multimeter, or oscilloscope) 604 for recording at least one series of measurements of a grid variable is provided which can detect a line voltage, an injected current or a line frequency. The series of measurements thus detected is passed on to a multiplication unit (controller) 606, which can perform a multiplication by a test function sin(t). This test function sin(t) is here to this extent only mentioned symbolically and is, as has also been described above, more complex than such a sine function, can be varied at least in respect of some input variables.

[0099] The result of this multiplication unit 606 is passed on to an addition unit (controller) 608, in which the test products which were generated in the multiplication unit 606 were added to give a product sum. Thus, a product sum is the result of the addition unit 608, and this is passed on to an evaluation device (controller) 610. The evaluation device in this case searches for a maximum of all of the product sums which it has obtained from the multiplication unit 606. For this purpose, a storage device (memory) 612 can be provided for recording a data field, which is here shown as part of the evaluation device 610. The result of the evaluation device is finally, if a low-frequency oscillation has been found, its oscillation frequency f.sub.PSO and its phase angle θ.sub.PSO. These values can then be further-processed by a further process control computer (controller) 614 in order, for example, to adapt an injection (converter or inverter) by the wind power system 600 into the electrical supply grid 602 in such a way that such a detected oscillation is counteracted. In addition, these two values, i.e., the frequency and the phase angle of the low-frequency oscillation, can be passed back to a synthesis block (controller) 616, which generates the already described test function, which is represented symbolically as sin(t), or adapts it in a further loop. In particular its input values are in this case adapted.

[0100] Therefore, particular consideration has been given to the fact that the detection of low-frequency oscillations (PSO/power system oscillations) and the parameters thereof can be a requirement. This is particularly because low-frequency oscillations generally have very low-frequency components. The problem consists not only in detecting whether an oscillation exists at all, but then also in identifying this oscillation, namely particularly identifying which frequency is present, which phase angle and which absolute value of the oscillation.

[0101] In principle, a known DFT method could be used. However, it has been identified that such a DFT method, depending on the sampling rate of the signal, provides information over a broad frequency range, which is not necessarily helpful. Furthermore, a DFT method requires a correspondingly long time window within the time range for finer resolution in the frequency range. In this case, it has been identified that the frequencies to be expected in the context of low-frequency oscillations are within a limited frequency range, and this can be utilized and other effective approaches which concentrate on such a limited frequency range may be helpful. It is also advantageous if corresponding approaches require a relatively short time window.

[0102] Energy systems are oscillatory systems, which have natural modes below and above the system frequency (50, 60 Hz). On excitation, such oscillations can impair the system stability if they are not sufficiently damped. Here, a new approach for detection of so-called power system oscillations (PSO) is now proposed. A possible precise identification of the frequency, the phase angle and the absolute value of power system oscillations (PSO) is intended to be achieved from a signal.

[0103] The monitoring of power system oscillations (PSO) may be helpful not only as a warning system for the operation of wind farms, but this information can also be used as a basis for a suitable generation of damping signals by wind turbines or wind farms for damping the power system oscillations.

[0104] It has also in particular been identified that the monitoring of power system oscillations (PSO), i.e., in particular low-frequency oscillations, may be an important component of a warning system also for the operation of wind farms. In addition, most approaches for damping PSO are based on a precise identification of an oscillation from a measurement.

[0105] The proposed method enables in particular the identification of PSO (or other types of oscillations) and their most important features (frequency, phase angle and absolute value).

[0106] The proposed, present method is aimed in particular at a possible precise identification of the frequency, the phase angle and the absolute value of an oscillation in a measured signal using as short a measurement window as possible. In this case, frequent restrictions of real systems such as computation capacity, storage space for the measured data, assumptions in respect of a constant working point are taken into consideration.

[0107] The proposed approach is based on the principle that the DC component of the product of the signal to be investigated having a sinusoidal reference signal which has the frequency f.sub.ref is only associated with the component of the signal in terms of frequency f.sub.ref. All of the other signal components which do not have this frequency of the reference signal virtually average one another out, expressed illustratively.

[0108] The basic concept can be summarized as follows. The signal to be investigated is multiplied by a sinusoidal reference signal. In the process, the phase angle of the reference signal is changed by m iterations in a loop in the complete range (0 up to 2π or 0° up to 360°). Furthermore, the frequency of the reference signal is changed in a further loop by n iterations in the frequency range to be investigated (f.sub.start up to f.sub.end). m×n products thus result. The frequency and the phase angle at which the DC component of the product is at its highest can be assumed to be the frequency and the phase angle of the low-frequency oscillation. By virtue of the knowledge of the frequency and the phase angle, the absolute value of the low-frequency oscillation can also be determined. This sequence is substantially illustrated in FIGS. 3 and 4.

[0109] The accuracy of the approach for a specific frequency range (f.sub.start to f.sub.end) can be improved by increasing the parameters m and n if, therefore, the two loops 306 and 314 shown in FIG. 3 are executed more often and with smaller steps. One possibility of optimizing the computation complexity involved is to implement the proposed approach shown in FIGS. 3 and 4 in two stages:

[0110] 1. The first stage has a rough resolution ((f.sub.end−f.sub.start)/n) and provides as a result a rough estimate of the frequency of PSO (f.sub.PSO1 below). For this purpose, the following values are recommended for the investigation parameters:

f.sub.start1=f.sub.start

f.sub.end1=f.sub.end

n.sub.1=the next integral number according to (f.sub.end−f.sub.start).Math.t.sub.end.Math.2

m.sub.1=36

[0111] 2. Then, the second stage investigates a smaller frequency range around the result of the first stage with a finer resolution. For this purpose, the following values are recommended for the investigation parameters:

f.sub.start2=f.sub.PSO1−1/(t.sub.end.Math.2)

f.sub.end2=f.sub.PSO1+1/(t.sub.end.Math.2)

n.sub.2:as high as possible(≥2)

m.sub.2:as high as possible(≥36)

[0112] n.sub.1 and n.sub.2 denote the first and second repetition number, respectively, of the loop for the frequency variation.

[0113] m.sub.1 and m.sub.2 denote the first and second repetition number, respectively, of the loop for the phase angle variation.

[0114] Advantages Over FFT and DFT (Standard Methods):

[0115] In the case of FFT and DFT, it is possible to identify only the oscillations with specific frequencies, namely: oscillations whose frequencies correspond to an integral multiple of 1/T (T: length of the investigation time window). Since the frequency of PSO is an unknown variable, it is very improbable that the frequency of PSO by chance corresponds to an integral multiple of 1/T. Therefore, when using FFT or DFT a certain degree of error in the determination of the frequency should always be expected. The error in the frequency determination impairs the determination of phase angle and absolute value. In contrast to FFT and DFT, in the proposed approach the frequency range can be investigated as finely as desired. In this case, it is merely necessary to find a compromise between the accuracy and the computation complexity. FFT provides, as a result, information on specific spectral lines. The number of spectral lines is linked to the number of measurement points of the signal to be investigated. In the case of FFT, it is not possible to investigate some of these spectral lines. In other words, there is no possibility for performing the FFT calculation for a limited frequency range. In contrast, the investigation range for the frequency in the proposed approach can be selected as desired. Furthermore, it is possible to select the computation complexity by selecting the investigation resolution appropriately for the computation capacity available.