WIND POWER PLANT AND METHOD FOR DETECTING LOW-FREQUENCY VIBRATIONS IN AN ELECTRICAL SUPPLY NETWORK

Description

[0001] The present invention relates to a method for detecting low-frequency vibrations, in particular subsynchronous resonances, in an electrical power supply network. The present invention also relates to a wind energy system, namely a wind turbine or a wind farm, for detecting low-frequency vibrations, in particular subsynchronous resonances, in an electrical power supply network.

[0002] Many electrical grids increasingly incorporate renewable energy generators, particularly wind turbines and wind farms. Their growing share in the grid means that it is becoming increasingly important to use wind turbines and wind farms to support the grid, or at least to take them into account.

[0003] One problem that can occur in the electrical power grid, which can also be referred to simply as the grid, is oscillations, specifically oscillations of the energy system, which can also be called "Power System Oscillations" (PSOs). Their causes can be very diverse, and a clear and simple example is that two directly coupled synchronous generators of conventional power plants, which feed into the grid, for example, more than 100 kilometers apart, oscillate against each other.

[0004] However, it is also possible that a single synchronous generator directly connected to the electrical grid could be excited to oscillate at its natural frequency due to a local excitation, such as a sudden change in the power consumption of connected loads. Conventional electrical grids regularly counteract such problems through appropriately stable control of the synchronous generators feeding directly into the grid. The high inertia of these synchronous generators, combined with damping characteristics inherent in their physical properties and / or their design, typically prevents excessive oscillations in conventional grids.

[0005] However, renewable energy sources, especially wind turbines or wind farms, do not inherently possess such properties. In particular, they have practically no physically determined properties that can counteract such low-frequency vibrations or prevent them from occurring in the first place.

[0006] Instead, modern wind turbines or wind farms now feed power into the electrical grid using frequency converters and a so-called full converter concept. Accordingly, the entire power input is fed into the grid by the inverter(s) according to precise specifications. These specifications primarily concern the amplitude, frequency, and phase of the injected electrical current, and these specifications can be set by a process computer. This leaves little room for physically determined reactions or adjustments to the injected current.

[0007] In order to react to phenomena in the electrical power grid, especially to low-frequency oscillations (PSOs), such oscillations would first need to be detected, ideally according to frequency, phase, and amplitude. Based on this, a desired response measure could then be calculated in the process computer and implemented by the inverter.

[0008] However, if such low-frequency oscillations are not detected with sufficient accuracy, any countermeasures taken may even worsen the situation. Detecting such low-frequency oscillations can be difficult because they are initially superimposed on the mains frequency, i.e., the 50 Hz or 60 Hz voltage signal in the electrical supply network, with a comparatively low amplitude. Especially when measuring voltage in the electrical supply network, interference and / or noise must be expected. Furthermore, such low-frequency oscillations fluctuate regularly. In particular, they occur weakly, strongly, or not at all, depending on the excitation.

[0009] Despite these measurement problems, rapid data acquisition is desirable. This, in turn, hinders longer-term analysis.

[0010] The problem is compounded by the fact that such low-frequency oscillations can lie in a frequency range of 0.05 Hz, or even lower, down to frequencies just below the mains frequency, i.e., on the order of 50 to 60 Hz, or even slightly higher. Due to purely physical reasons, detecting a sinusoidal oscillation requires a measurement lasting at least half a cycle of that cycle. Therefore, with a large frequency spectrum, capturing it necessitates a measurement duration of at least half a cycle of the oscillation with the lowest expected frequency.

[0011] The German Patent and Trademark Office has searched the following prior art in the priority application for the present application: DE 37 33 555 A1 and US 4,031,462 A.

[0012] The present invention is therefore based on the objective of addressing at least one of the aforementioned problems. In particular, a solution is to be proposed that enables the fastest possible detection of low-frequency vibrations, while simultaneously also being capable of detecting very low-frequency vibrations. At the very least, an alternative solution to previously known solutions is to be proposed.

[0013] According to the invention, a method according to claim 1 is proposed. This method serves to detect low-frequency oscillations in an electrical supply network, in particular to detect subsynchronous resonances in an electrical supply network. The method assumes an electrical supply network with a mains voltage and a nominal mains frequency, wherein the low-frequency oscillations to be detected preferably have a lower frequency than the nominal mains frequency. Here, a low-frequency oscillation is defined and considered as having a lower frequency than the nominal mains frequency. Preferably, the frequency of the low-frequency oscillations is assumed to be less than half the nominal mains frequency.

[0014] Low-frequency oscillations, in particular, can have values ​​of 1 Hz and below. However, they can also reach up to five times the nominal grid frequency. Here, low-frequency oscillations are defined as oscillations with a frequency of at most five times the nominal grid frequency, preferably with a frequency that is at most equal to the nominal grid frequency. Specifically, a low-frequency oscillation does not have a frequency that is a multiple of the nominal grid frequency. It should be noted that the investigation and consideration of low-frequency oscillations primarily serves to investigate or ensure the system stability of the electrical supply network. This differs from an assessment of the power quality or signal quality of the voltage signal in the electrical supply network, where harmonics, especially integer harmonics, are of particular importance.

[0015] The method proposes recording at least one measurement series with multiple measurement points over a measurement period in order to perform a frequency analysis based on these data. The measurement series therefore contains multiple measurement points or measured values ​​that are distributed over the measurement period or were recorded at different times over that period.

[0016] Network parameters include, in particular, the network voltage, an incoming current fed into the electrical supply network, or a network frequency.

[0017] For this series of measurements, it is proposed to multiply the measurement series by a time-dependent sinusoidal test function for the same measurement period. Such a sinusoidal test function can be provided as a function on a process computer. It is proposed that the test function be characterized by a test frequency and a test angle as the phase angle. The amplitude can also be predefined, but in practical implementation, normalizing the amplitude, e.g., to the value 1, is regularly considered. The peak value of the sinusoidal quantity can therefore, for example, assume the value 1, whereby the scaling in the process computer can be known.

[0018] The measurement series is multiplied by the test function as follows: for each measurement point, the measurement series is multiplied by the test function to obtain a test product for each point. In other words, a measured value at a given measurement point in the series is multiplied by the corresponding value of the test function, and this process is repeated for each measurement point. The test function is defined for a time period corresponding to the measurement period, or alternatively, the test function is determined for the measurement period. The multiplication then takes place at each point in time within the measurement period when a measured value is available. This measured value is then multiplied by the corresponding value of the test function for that same point in time.

[0019] The test products are now added together to form a product sum, taking their sign into account. Negative test products are therefore subtracted in absolute terms. Each test product can have a negative sign if either the corresponding measured value or the corresponding function value was negative.

[0020] Depending on the product sum, it is then assessed whether the measurement series exhibits a low-frequency vibration with a frequency in the range of the test frequency and a phase angle in the range of the test angle.

[0021] The underlying principle here is the following: If the test function and the measurement series are identical in terms of frequency and phase, each test product will exhibit a positive value, and consequently, the sum of the products will also be positive with a comparatively large amplitude. In this case, the measurement series represents a function that corresponds to the test function.

[0022] If the measurement series and the test function are identical but phase-shifted by 90°, the test products would result in a sinusoidal function (incidentally, with twice the frequency for the test function), without a DC component. The sum of the products would then be zero, at least if the test period corresponds to an integer multiple of the period of the signal under investigation. This phenomenon is known to electrical engineers as reactive power when current and voltage are shifted by 90° relative to each other. The first example without phase shift would correspond to a case involving only active power. This would result in a sinusoidal signal of double the frequency, shifted so significantly around the horizontal axis that only the smallest values ​​of the sine function would touch the horizontal axis. This shift can also be understood or described as the DC component. Here, the DC component would be very high, in fact, the highest.

[0023] However, frequency deviations between the measurement series and the test function can also lead to different DC components. The sum of these components, which can thus be interpreted as the DC component or be representative of it, can therefore also serve as a measure of the correlation between the measurement series and the test function. If the measurement series and the test function are completely uncorrelated, the DC component becomes zero, at least theoretically for an infinite measurement period.

[0024] However, even in practical application, the product sum is comparatively small if the measurement series and the test function are uncorrelated. If the measurement series and the test function are well correlated, and the phase angles of the measurement series and the test function also match, a high DC component or a large product sum results. From this, the presence of a low-frequency oscillation can be deduced in terms of frequency and phase. The low-frequency oscillation then has the frequency of the test function and a phase angle corresponding to the test angle of the test function.

[0025] Preferably, when detecting a low-frequency oscillation, the amplitude of the low-frequency oscillation is measured, particularly as a function of the product sum. It has been especially recognized that the amplitude can also be determined using the method for detecting a low-frequency oscillation based on frequency and phase.

[0026] Preferably, the method is carried out by repeating the multiplication of the measurement series by the test function and the summation of the test products to obtain a product sum, varying the test frequency and the test angle in order to generate several product sums. While it is also advantageous to vary only the test frequency or the test angle, as long as neither the frequency of the low-frequency signal to be detected nor its phase is known, it is usually advantageous to vary both the test frequency and the test angle. If both values ​​are varied, the result of the product sums can also be represented as a curved plane. In this case, the product sum would be shown as a function of the test frequency and the test angle. A local maximum would then be obtained at the test frequency and test angle at which there is the best agreement between the measurement series and the test function.

[0027] It is therefore proposed that the evaluation of whether the measurement series exhibits a low-frequency vibration be carried out based on the multiple product sums obtained. All the product sums obtained can thus be compared, and the presence of a low-frequency vibration can be determined from this, provided it has a frequency and a phase that are close to the test frequency and test angle, respectively.

[0028] In particular, a product sum with maximum amplitude relative to the other product sums is assumed to exhibit a low-frequency oscillation with the frequency and phase of the corresponding test frequency and test angle. For this evaluation of all product sums, it is not strictly necessary to choose the aforementioned three-dimensional representation. It is also possible to search only for maximum values ​​of the product sums, or, in the simplest case, for the maximum product sum.

[0029] It is therefore specifically proposed that the multiplication of the measurement series by the test function and the summation of the test products into a product sum be repeated while varying the test frequency and the test angle, so that a product sum is recorded for each test pair formed from a test frequency value and a test angle value. This is done in such a way that the recorded product sums, depending on the test frequency values ​​and the test angles, can be represented as a curved surface in three-dimensional space, although they do not necessarily have to be displayed.

[0030] For evaluation purposes, it is specifically suggested that if a product sum has the maximum amplitude relative to the other product sums, a low-frequency oscillation with the frequency and phase of the corresponding test frequency and test angle is assumed. Of course, interpolation is also a viable option if several adjacent product sums form a maximum, i.e., are equal or nearly equal in magnitude.

[0031] This makes fully automated evaluation programmable. Essentially, only the frequency range to be tested needs to be specified. Optionally, the step size for varying the test frequency can also be defined.

[0032] The test angle is preferably tested or varied from 0° to 360°. Alternatively, it may be considered to test it only from 0° to 180° and, when searching for the maximum product sum, to look for the product sum with the highest absolute value.

[0033] According to one embodiment, it is proposed that, to assume a low-frequency vibration of a product sum, it is checked exclusively or additionally whether the product sum reaches at least a predetermined test amplitude. This is based in particular on the assumption that, based on practical implementation alone, a maximum product sum can be expected in every case when, as described, test frequencies and test angles are varied. However, this would not necessarily imply that a low-frequency vibration, or a relevant low-frequency vibration, is actually present, since very small maxima can also be caused by measurement inaccuracies or other influences.

[0034] Checking whether the product sum has reached at least a predetermined test amplitude also makes it possible to detect multiple low-frequency vibrations, should they be present. In particular, to provide a clear explanation based on the curved surface of the product sum, checking for the achievement of a predetermined test amplitude can also reveal a local maximum within this curved surface.

[0035] Naturally, when several product sums are adjacent or at least close to each other with respect to frequency and phase angle, it is usually not assumed that multiple low-frequency vibrations are present. Such a cluster of large product sums then indicates a maximum, within which the maximum product sum is preferably chosen as the one whose test frequency and test angle can be assumed to be the frequency and phase of a detected low-frequency vibration.

[0036] According to one embodiment, it is proposed that in a first test loop, the multiplication of the measurement series by the test function and the summation of the test products are repeated while varying the test frequency. The test frequency is varied within a first frequency range to detect a low-frequency vibration with a specific oscillation frequency. The oscillation frequency is initially detected with a first level of accuracy. In a second test loop, the multiplication of the measurement series by the test function and the summation of the test products are repeated while varying the test frequency. During this repetition in the second test loop, the test frequency is then varied within a second frequency range. For this purpose, the second frequency range is selected based on the oscillation frequency detected in the first test loop in order to detect the oscillation frequency with higher accuracy than in the first loop.

[0037] The underlying principle here is that testing across numerous test frequencies and angles can lead to a high number of tests. Therefore, it is proposed to insert a first test loop that only varies the test frequency, possibly with an initial frequency step that is larger than the subsequent second frequency step used in the second test loop. Such a first test loop should produce an initial peak in magnitude, at least near the frequency of a low-frequency oscillation.

[0038] More precise testing can then be performed within this initial peaking range. For this purpose, a second frequency range is defined, which is smaller than the first frequency range and specifically lies within the first frequency range. The test angle can also be varied within this second test loop. This allows for high accuracy without requiring this high accuracy across the entire theoretical range resulting from the first frequency range and a full 360° range for the test angle.

[0039] Preferably, in the first test loop, the multiplication of the measurement series by the test function and the summation of the test products are repeated, additionally varying the test angle. Thus, both the test frequency and the test angle are varied. The test angle is varied within a first angular range, particularly from 0° to 360°, but preferably also limited to 0° to 180° or another 180° range. This is done to detect the low-frequency vibration along with its phase angle. Furthermore, even if the frequency of the low-frequency vibration and the test function closely match, the sum of the product values ​​can be small if the phase angle and the test angle differ significantly. In such a case, a low-frequency vibration could be missed.

[0040] Furthermore, it is proposed that the test angle be varied in a first angular increment, for example, in 5° steps. In the second test loop, the multiplication of the measurement series by the test function and the summation of the test products are repeated, again varying the test angle, this time within a second angular range. This variation is preferably performed with a second angular increment that is smaller than the first, for example, with a second angular increment of 1°. Specifically, the second angular range is selected based on the phase angle of the vibration detected in the first test loop, in order to capture the phase angle of the vibration with higher accuracy than in the first loop.

[0041] It is therefore proposed that in the first test loop, the test frequency and the test angle be varied to perform an initial coarse detection of at least one low-frequency oscillation, namely to determine an approximate value of the frequency and phase angle of the low-frequency oscillation. Within a range around this frequency and angle, the search can then be improved by testing the test frequency and angle within a smaller frequency and angle range.

[0042] According to one embodiment, it is proposed that in the first test loop, the test frequency is varied in larger frequency steps than in the second test loop, and alternatively, that the test angle is varied in larger angular steps in the first test loop than in the second. This allows a large frequency range to be tested in the first test loop with reasonable effort. A large angular range, in particular the complete angular range from 0 to 360°, or at least 0 to 180°, can also be tested. This enables an initial localization of a low-frequency vibration with reasonable effort. A more precise search with higher accuracy is then only required in the second test loop for a smaller range, namely both a smaller frequency range and a smaller angular range.

[0043] According to a further embodiment, it is proposed that multiple measurement series of the network parameters be recorded. This involves recording several measurement series, particularly of the network voltage, the feed-in current, and / or the network frequency. Each measurement series is intended for the analysis of a specific frequency range. For this purpose, a measurement period is selected for each series, depending on the frequency range being analyzed. Thus, different frequency ranges are investigated, and corresponding measurement series are recorded for each. It is specifically proposed that the measurement period for analyzing a low-frequency range be chosen to be long enough to capture even the lowest frequency within that range. Conversely, a shorter measurement period can be used for a higher-frequency range.Furthermore, it is preferably suggested that with correspondingly long measurement periods, the measurement times should be further apart than with a shorter measurement period.

[0044] It is therefore proposed that, especially for a total frequency range to be investigated, such as 0.1 Hz or below down to 50 Hz or even 250 Hz, a division into at least two measurement ranges should be made, specifically a low-frequency range and a high-frequency range. Thus, a division into a first and a second frequency range is made, and possibly further frequency ranges. A series of measurements is recorded for each frequency range to be analyzed—that is, to continue the example, for the low-frequency range and the high-frequency range. Therefore, in the aforementioned example, two series of measurements are recorded.

[0045] For each measurement series, the multiplication of the measurement series by the test function and the summation of the test products are repeated, varying the test frequency and, alternatively, the test angle, to obtain multiple product sums for each measurement series. Furthermore, it is proposed that for each measurement series, the product sums of the respective measurement series be evaluated to detect low-frequency vibrations.

[0046] This is based in particular on the understanding that different measurement times, or measurement periods, are required for investigating a low-frequency range on the one hand and a higher-frequency range on the other, and these should be considered in a meaningful way. Conversely, such a long measurement period for a low-frequency oscillation with a comparatively high frequency may be too long to detect this low-frequency oscillation in time.

[0047] For example, the first frequency range, which can also be called the low-frequency range, can extend from 0.02 to 2 Hz. To detect a low-frequency oscillation of 0.02 Hz, a measurement period of at least 50 seconds (the reciprocal of the first frequency range) should be used. The second frequency range, which can also be called the higher-frequency range, could then extend, for example, from 2 Hz to 250 Hz. Here, even to detect the lowest frequency of 2 Hz, a measurement period of 0.2 seconds is sufficient. An oscillation in such a second, higher-frequency range might, however, be detected within the 50-second test period of the first frequency range.significantly increase, in extreme cases leading to a resonance catastrophe or at least a situation where the amplitude of the low-frequency oscillation has become so large that initial damage can occur or initial shutdown processes can be initiated.

[0048] To address this dilemma, it is proposed here to at least divide the data into two frequency ranges and, in particular, to perform the analyses independently of each other in time.

[0049] According to one embodiment, it is proposed that the multiplication of the measurement series by the test function and the summation of the test products to obtain a product sum are repeated under a specific variation of the test frequency. The test frequency is varied within at least one frequency range, which has an upper and a lower frequency value, using a frequency step size, and the frequency step size is adjusted depending on the frequency range. This is done, in particular, such that the frequency step size is smaller than the lower frequency value, especially less than 10% of the lower frequency value. Alternatively, it is proposed that the frequency step size be smaller than a predetermined percentage, especially less than 1%, and more specifically less than 0.2%, of the upper frequency value.

[0050] Preferably, the test frequency is varied across several frequency ranges, and the frequency step size of different frequency ranges is set differently from one another. Preferably, each frequency step size is set larger than a predetermined percentage of the respective lower frequency value of the frequency range in question.

[0051] The test frequency is varied according to the respective frequency step size within the given frequency range. The frequency step size is set depending on the frequency range and is primarily based on the lowest frequency value within that range. This can be a percentage value relative to the lower frequency value. Alternatively, the frequency step size can be based on the upper frequency value, but it will be considerably smaller relative to the upper frequency value of the relevant frequency range. This approach ensures that the variation of the test frequency is clearly defined and can be selected differently for different frequency ranges. This allows the testing effort, specifically the effort required for varying the frequency, to be adapted to the respective frequency range. These specifications also enable automated testing routines.

[0052] The invention also proposes a wind energy system. Such a wind energy system can be a single wind turbine or a wind farm with multiple wind turbines. This wind energy system feeds power into an electrical supply network. It is designed to detect low-frequency oscillations, in particular subsynchronous resonances, in the electrical supply network. The electrical supply network has a network voltage with a nominal network frequency. The wind system comprises A recording device for recording at least one series of measurements of a network quantity, in particular the network voltage, a feed-in current or a network frequency, with several measurement points, over a measurement period, for carrying out a frequency analysis; a multiplication unit for multiplying the series of measurements with a time-dependent sinusoidal test function for the same measurement period, wherein the test function is characterized by a test frequency and a test angle as the phase angle, and the series of measurements is multiplied with the test function for each measurement point in order to obtain a test product for each measurement point; an adding unit for adding the test products, taking into account their sign, to a product sum; and an evaluation device for evaluating, depending on the product sum, whether the series of measurements exhibits a low-frequency oscillation with a frequency in the range of the test frequency and a phase angle in the range of the test angle.

[0053] Such a wind energy system can feed into the electrical grid and preferably also performs support functions to stabilize the grid. Such support functions can be particularly necessary or at least advantageous when distributed generators, such as a wind energy system, feed a significant portion of their power into the electrical grid or a relevant section thereof. Various support functions can arise, one of which may be to react to low-frequency oscillations. Preferably, however, such low-frequency oscillations are first detected, as precisely as possible according to frequency and phase, and possibly also amplitude. Then, a response can be implemented.

[0054] Preferably, the wind energy system is equipped to implement at least one method according to the embodiments described above. In particular, the wind energy system includes a process computer equipped to implement such a method. Specifically, the method is implemented on the process computer. The implementation of the method may include the acquisition of measurement points or a series of measurements, or multiple series of measurements, by the process computer receiving corresponding values ​​as measurement points or measured values, and / or by the process computer controlling the recording device to acquire the at least one series of measurements.

[0055] The acquisition device can be, for example, a sensor that measures voltage or current. The multiplication unit can also be implemented in the same or a different process computer. The same applies to the addition unit, although these units can also be implemented in different device units. The evaluation unit can also be implemented in the same process computer or be provided as a separate element.

[0056] The invention will now be explained in more detail using examples and with reference to the accompanying figures. Figure 1 shows a wind turbine in a perspective view. Figure 2 shows a wind farm in a schematic representation. Figure 3 shows a flowchart for recording multiple product sums while varying a test frequency and a test angle. Figure 4 shows a flowchart for evaluating multiple measurements according to the flowchart of Figure 3Recorded product sums. Figure 5 shows in a 3D diagram product sums as a function of a varied test frequency and as a function of a varied test angle. Figure 6 schematically shows a structure of a wind energy system for detecting low-frequency vibrations.

[0057] Figure 1 Figure 1 shows a wind turbine 100 with a tower 102 and a nacelle 104. A rotor 106 with three rotor blades 108 and a spinner 110 is mounted on the nacelle 104. During operation, the wind sets the rotor 106 into rotation, thereby driving a generator in the nacelle 104.

[0058] Figure 2Figure 112 shows a wind farm with three exemplary wind turbines 100, which can be identical or different. The three wind turbines 100 thus represent, in principle, any number of wind turbines in a wind farm 112. The wind turbines 100 supply their power, namely the generated electricity, via an electrical park grid 114. The currents or power outputs of the individual wind turbines 100 are added together, and a transformer 116 is usually provided to step up the voltage in the park in order to feed it into the supply grid 120 at the feed-in point 118, which is also generally referred to as PCC. Figure 2This is only a simplified representation of a wind farm 112, which, for example, does not show a control system, although a control system is of course present. The park network 114 can also be designed differently, for example, by including a transformer at the output of each wind turbine 100, to name just one other example.

[0059] Both the wind energy plant according to Figure 1 as well as the wind farm according Figure 2 Each can form a wind energy system.

[0060] Figure 3Figure 300 shows a flowchart for recording multiple product sums. In the start block 302, the signal to be examined is recorded and further initializations are performed. The signal to be examined can be a recorded time signal that, for the purpose of analysis in flowchart 300, is sampled uniformly with time steps Δt. The signal to be examined can also already be in such a sampled form; however, it is advantageous here to choose the time step size in order to also determine the total number of values ​​to be examined.

[0061] The signal y(t) under investigation is thus recorded or considered for a measurement period, and this measurement period can range from t = 0 to t = tend. The measurement duration, and therefore the width of the measurement period, is thus determined by tend. For time t, the following applies: t = 0 , 1 ⋅ Δ t , 2 ⋅ Δ t , … , t end

[0062] The frequency range to be investigated can also be defined in starting block 302, from a starting frequency fstart to an ending frequency fend. The step size Δf of the frequency analysis can be determined depending on the starting frequency fstart and the ending frequency fend, as well as depending on the desired number of frequency steps n, according to the formula: Δ f = f end − f start / n

[0063] The step size of the phase angle analysis Δϕ can also be determined depending on a desired number of angular steps m, according to the formula: Δ φ = 2 ⋅ π / m

[0064] These values, especially the number of frequency steps n and the number of angle steps m and also the time step Δt, can in principle be chosen arbitrarily, but it is suggested to weigh the choice between accuracy and computational effort.

[0065] In the first initialization block 304, the loop variable i is initialized for an outer loop 306. The frequency of iterations of this outer loop 306 corresponds to the frequency step count n, and this is checked accordingly in the first repetition query block 308, which follows the first increment block 310.

[0066] Within this outer loop 306 is the second initialization block 312, in which the loop variable j is initialized for an inner loop 314. It is iterated over according to the number of angular steps m, which is checked in the second repetition query 316, which follows the second increment block 318.

[0067] Finally, a calculation block 320 is provided, which is executed a corresponding (nxm) times. In each iteration, the reference frequency fref is calculated, namely the frequency at which each sum product is calculated. This reference frequency fref is calculated according to the formula: f ref = f start + i ⋅ f end − f start / n

[0068] At the same time, the respective reference angle θ ref is calculated, namely according to the formula: θ ref = j ⋅ 2 ⋅ π / m

[0069] Finally, based on these calculated values—that is, for the reference frequency fref and the reference angle θref relevant in the iteration—the product sum is calculated. As explained above, the product sum can also be understood as the DC component, so it is referred to here as DCprod. It is calculated for each iteration i of the outer loop and each iteration j of the inner loop according to the formula: DC prod i j = Summe y t ⋅ sin 2 ⋅ π ⋅ f ref ⋅ t + θ ref ⋅ Δ t / t end

[0070] The signal y(t) to be investigated is therefore measured as a series of measurements using the sine function sin(2 · π · ). f ref · t + θ ref ) The products are multiplied and then summed. So, a product is created for each point in time, and these products are summed. This can be illustrated, for example, by a third innermost loop in which time t increments from 0 to t end, in time steps Δt. The result is further normalized by multiplying by the time step Δt and dividing by the final time t end, such that the product sum DC prod is essentially independent of the time step Δt. Therefore, the absolute value of the product sum is fundamentally independent of the number of products summed.

[0071] After the inner loop has been executed 314m times and the outer loop 306n times, there are nxm individual product sums DC prod (i, j) that can be stored in a corresponding field and then examined for further evaluation. For this purpose, the result of flowchart 300 is transferred to flowchart 400. Figure 4 passed, which is indicated in flowchart 300 by block 400.

[0072] Accordingly, it shows Figure 4 This block 400, namely flowchart 400, builds upon flowchart 300 of the Figure 3 , which is indicated by the fact that the first block is designated as process block 300.

[0073] In the Max block 402, the product sum with the largest value is selected from all the product sums calculated in calculation block 320, taking the sign into account. If, to simplify or reduce the effort, the test angle were varied not over 360° but only over 180° – preferably also over 90° – the value with the largest absolute value could also be sought here.

[0074] The search is performed for all product sums that have been specifically stored in a field, namely according to the iteration of the outer loop 306 and the inner loop 314. These loops were traversed using the outer loop variable i and the inner loop variable j, and these two loop variables are then used here to identify the maximum product sum, for example, in a data field. Accordingly, an assignment of these two loop variables is made in the identification block 404; thus, the loop variables i and j, for which the maximum product sum was found in the Max block 402, are identified as the selected outer and selected inner loop variables i MaxDC and j MaxDC, respectively.

[0075] The maximum value of the product sums identified in Block 402, along with a reference frequency and a reference angle, are associated with these two selected running variables, namely the selected outer and inner running variables iMaxDC and jMaxDC, respectively. The corresponding reference frequency and reference angle can be calculated from the corresponding outer and inner running variables i and j, respectively. This frequency and angle are assumed to be the corresponding frequency and angle of a low-frequency oscillation, respectively. Therefore, this assigned reference frequency is referred to as the frequency of the low-frequency oscillation fPSO, and the selected angle is referred to as the angle of the low-frequency oscillation θPSO. These two values ​​can be calculated using the following equation: f PSO = f start + i ⋅ f end − f start / n θ PSO = j ⋅ 2 ⋅ π / m

[0076] The frequency of the low-frequency oscillation f PSO and the angle of the low-frequency oscillation θ PSO are calculated by substituting the corresponding selected running variable i MaxDC or j MaxDC for the respective external or internal running variable i, j. In this formula, the angle of the low-frequency oscillation θ PSO is given in radians and not in degrees.

[0077] In calculation block 406, the amplitude of the low-frequency oscillation A PSO can also be calculated, namely according to the equation: A PSO = MaxDC / Summe sin 2 ⋅ π ⋅ f PSO ⋅ t + θ PSO ⋅ sin 2 ⋅ π ⋅ f PSO ⋅ t + θ PSO ⋅ Δ t / t end

[0078] The amplitude of the low-frequency oscillation is thus obtained by dividing the measured maximum product sum by a corresponding product sum of the reference signal, multiplied by the reference signal for the entire investigated time interval. This determines the product sum of the reference signal when multiplied by itself, resulting in the maximum possible value because such a reference function is maximally correlated with itself. Therefore, a factor remains relative to the less correlated product sum between the investigated signal and the reference signal. This amplitude, APSO, is also a normalized quantity.

[0079] The results can therefore be output in output block 408 and used further.

[0080] Figure 5Figure 500 illustrates in a three-dimensional representation the entirety of all product sums calculated in calculation block 320 as a curved plane 502 as a function of the varied reference frequency f ref and the varied reference angle θ ref. The reference frequency f ref can also be referred to synonymously as test frequency, and the reference angle θ ref can also be referred to synonymously as test angle.

[0081] As an example, a signal was chosen for investigation that exhibits a low-frequency oscillation with a frequency of 8.25 Hz (f PSO = 8.25 Hz) at a phase angle of 90° (θ PSo = 90°). For this purpose, a reference angle or test angle was varied from 0° to 360°, and a reference frequency or test frequency was varied from 0 to 25 Hz. It can be seen that for frequencies deviating significantly from this oscillation frequency of 8.25 Hz, the product sums plotted in the curved plane 502 essentially have the value 0. Near the oscillation frequency of 8.25 Hz, the amplitude increases oscillatively towards the oscillation frequency. However, it is also evident that the reference angle or test angle plays a significant role. At the oscillation frequency and phase angle of the low-frequency oscillation, the absolute amplitude of the product sum is also at its maximum, and accordingly, the diagram can be used to determine...The frequency of the low-frequency oscillation f PSO and the phase angle of the low-frequency oscillation θ PSO can be read from the value field of the product sums.

[0082] The flowchart of the Figure 3 and indirectly also the Figure 4 and also the diagram of Figure 5 This concerns the case where the test frequency or reference frequency and also the test angle or reference angle were each varied only once, albeit with many values, but without specifically repeating the entire sequence of the outer and inner loop according to flowchart 300 with new values. This representation particularly of the Figure 3This serves for illustrative purposes, and preferably the entire process according to the two flowcharts 300 and 400 is repeated with focused values ​​for the frequency range under investigation, i.e., for the frequency range under investigation, and also for new values ​​for the angle range under investigation. For this purpose, corresponding new values ​​are determined in the starting block 302 near the roughly identified maximum, in particular based on the values ​​for the frequency of the low-frequency oscillation f PSO and the phase angle of the low-frequency oscillation θ PSO provided in the first iteration in the output block 408.

[0083] Figure 6Figure 600 shows a wind energy system, symbolically illustrated by a single wind turbine, but which can also include several wind turbines. This system is equipped to detect subsynchronous resonances in an electrical supply network 602 into which this wind energy system 600 feeds.

[0084] A recording device 604 is provided for recording at least one series of measurements of a network quantity, which can detect a network voltage, an injected current, or a network frequency. The measurement series thus recorded is fed to a multiplication unit 606, which can perform a multiplication by a test function sin(t). This test function sin(t) is referred to here only symbolically and, as also described above, is more complex than such a sine function and can be varied at least with respect to some input quantities.

[0085] The result of this multiplication unit 606 is fed to an adding unit 608, in which the test products generated in the multiplication unit 606 are summed to form a product sum. Thus, a product sum is the result of the adding unit 608 and is fed to an evaluation unit 610. The evaluation unit searches for the maximum of all product sums it received from the multiplication unit 606. For this purpose, a storage unit 612 can be provided to hold a data field, which is shown here as part of the evaluation unit 610. Finally, if a low-frequency oscillation is detected, the result of the evaluation unit is its oscillation frequency fPSO and its phase angle θPSO. These values ​​can then be further processed by another processing unit 614, for example, to...The feed-in of the wind energy system 600 into the electrical supply network 602 is adjusted to counteract any detected oscillation. Furthermore, these two values—the frequency and the phase angle of the low-frequency oscillation—can be fed back to a synthesis block 616, which generates the previously described test function, symbolically represented as sin(t), or adjusts it in a further loop. In particular, its input values ​​are modified.

[0086] Therefore, particular attention was paid to the fact that detecting low-frequency oscillations (PSOs / Power System Oscillations) and their parameters can be challenging. This is primarily because low-frequency oscillations typically have very low-frequency components. The problem lies not only in recognizing that an oscillation exists, but also in identifying it, specifically its frequency, phase angle, and amplitude.

[0087] In principle, a known DFT method could be applied. However, it was recognized that such a DFT method, depending on the signal's sampling rate, provides information over a broad frequency range, which is not necessarily helpful. Furthermore, a DFT method requires a correspondingly long time window in the time domain for finer resolution in the frequency domain. It was then discovered that the expected frequencies within low-frequency oscillations lie within a limited frequency range, and that this can be exploited. Other effective approaches that focus on such a limited frequency range can be helpful. It is also advantageous if such approaches require a shorter time window.

[0088] The invention is also based on the understanding that energy systems are oscillatory systems that possess natural modes below and above the system frequency (50, 60 Hz). When excited, such oscillations can impair system stability if they are not sufficiently damped. Here, a new approach for the detection of so-called power system oscillations (PSOs) is proposed. The aim is to achieve a possible precise identification of the frequency, phase angle, and magnitude of power system oscillations (PSOs) from a signal.

[0089] The observation of power system oscillations (PSO) can not only be helpful as a warning system for the operation of wind farms, but this information can also be used as a basis for the suitable generation of damping signals by wind turbines or wind farms to dampen the power system oscillations.

[0090] It was also recognized that the monitoring of power system oscillations (PSOs), especially low-frequency vibrations, can be an important component of a warning system, including for the operation of wind farms. Furthermore, most approaches to PSO damping are based on the precise identification of a vibration through measurement.

[0091] The proposed method particularly enables the identification of PSO (or other types of vibrations) and their main characteristics (frequency, phase angle and magnitude).

[0092] The proposed method aims specifically at the precise identification of the frequency, phase angle, and magnitude of an oscillation in a measured signal using the shortest possible measurement window. This takes into account common limitations of real-world systems, such as computing capacity, storage space for measurement data, and assumptions regarding a constant operating point.

[0093] The proposed approach is based on the principle that the DC component of the product of the signal under investigation and a sinusoidal reference signal with frequency fref is only related to the component of the signal at frequency fref. All other signal components, which do not have this frequency of the reference signal, essentially average out, to illustrate the point.

[0094] The underlying idea can be summarized as follows. The signal under investigation is multiplied by a sinusoidal reference signal. The phase angle of the reference signal is varied by m iterations in a loop across the entire range (0 to 2π or 0° to 360°). Furthermore, the frequency of the reference signal is varied by n iterations in another loop across the frequency range under investigation (f start to f end). This results in m x n products. The frequency and phase angle at which the DC component of the product is highest can be assumed to be the frequency and phase angle of the low-frequency oscillation. Knowing the frequency and phase angle, the magnitude of the low-frequency oscillation can also be determined. This process is essentially illustrated in Figures 3 and 4.

[0095] The accuracy of the approach for a specific frequency range (f start to f end) can be improved by increasing the parameters m and n, i.e., if the two loops 306 and 314 according to Figure 3 The process should be repeated more frequently and in smaller steps. One way to optimize the computational effort is to implement the proposed approach according to... Figure 3 and 4 to be implemented in two stages: 1. The first stage has a coarse resolution ((f end - f start ) / n) and provides a rough estimate of the frequency of PSO (hereinafter f PSO1). The following values ​​are recommended for the investigation parameters: f start 1 = f start f end 1 = f end n 1 = die nächste ganzzahlige Zahl nach f end − f start ⋅ t end ⋅ 2 m 1 = 36 2. Subsequently, the second stage examines a smaller frequency range around the result of the first stage with finer resolution. The following values ​​are recommended for the examination parameters: f start 2 = f PSO 1 − 1 / t end ⋅ 2 f end 2 = f PSO 1 + 1 / t end ⋅ 2 n 2 : Möglichst hoch ≥ 2 m 2 : Möglichst hoch ≥ 36

[0096] n 1 and n 2 denote the first and second number of repetitions of the loop for frequency variation, respectively.

[0097] m1 and m2 denote the first and second repetition number of the loop for phase angle variation, respectively.

[0098] Advantages over FFT and DFT (standard methods): With FFT and DFT, it is only possible to identify oscillations with specific frequencies, namely: oscillations whose frequencies correspond to an integer multiple of 1 / T (T: length of the investigation time window). Since the frequency of PSO is an unknown quantity, it is highly improbable that its frequency would coincidentally correspond to an integer multiple of 1 / T. Therefore, when applying FFT or DFT, a certain error in frequency determination must always be expected. This error in frequency determination affects the determination of the phase angle and magnitude. In contrast to FFT and DFT, the proposed approach allows for arbitrarily fine-grained investigation of the frequency range. Here, a compromise is simply made between accuracy and computational effort. FFT provides information about specific spectral lines as its result.The number of spectral lines is related to the number of measurement points of the signal under investigation. With the FFT, it is not possible to examine only a portion of these spectral lines. In other words, there is no way to perform the FFT calculation for a limited frequency range. In contrast, the frequency range under investigation can be chosen arbitrarily with the proposed approach. Furthermore, it becomes possible to adjust the computational effort by selecting the appropriate resolution for the analysis, matching it to the available computing power.

Claims

1. A method for detecting low-frequency oscillations, in particular subsynchronous resonances, in an electrical supply grid, wherein the electrical supply grid has a line voltage with a rated line frequency, comprising the steps of - recording at least one series of measurements, having a plurality of measurement points, of a grid variable, in particular the line voltage, an input current or a line frequency, over a measurement time period, for performing a frequency analysis, - multiplying the series of measurements by a time-dependent sinusoidal test function for the same measurement time period, wherein - the test function is characterized by a test frequency and a test angle as phase angle, and - the series of measurements for each measurement point is multiplied by the test function in order to obtain a test product for each measurement point, - 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.

2. The method as claimed in claim 1, characterized in that - the multiplication of the series of measurements by the test function and the addition of the test products to give a product sum is repeated whilst varying the test frequency and / or whilst varying the test angle in order to obtain a plurality of product sums, and - the evaluation to ascertain whether the series of measurements has a low-frequency oscillation is performed depending on the plurality of product sums thus obtained, in particular in such a way that - in the case of a product sum with a maximum amplitude in relation to the remaining product sums, a low-frequency oscillation having the frequency and the phase of the associated test frequency and the associated test angle is assumed, and / or that - on identification of a low-frequency oscillation, an amplitude of the low-frequency oscillation is detected, in particular depending on the product sum.

3. The method as claimed in claim 1 or 2, characterized in that - the multiplication of the series of measurements by the test function and the addition of the test products to give a product sum is repeated whilst varying the test frequency and whilst varying the test angle so that - a product sum is recorded for each test pair formed from a test frequency value and a value for the test angle, wherein in particular - the recorded product sums can be represented, depending on the test frequency values and depending on the test angles, as a curved area in a three-dimensional space, and wherein - a test frequency value and a test angle of a test pair in relation to which the product sum forms a maximum with respect to the remaining recorded product sums is assumed as the frequency and phase angle of a low-frequency oscillation.

4. The method as claimed in one of the preceding claims, characterized in that in order to assume a low-frequency oscillation of a product sum, a test is exclusively or additionally performed to ascertain whether the product sum reaches at least a predetermined test amplitude.

5. The method as claimed in one of the preceding claims, characterized in that - in a first test loop, the multiplication of the series of measurements by the test function and the addition of the test products is repeated whilst varying the test frequency, wherein - the test frequency is varied within a first frequency range in order to detect a low-frequency oscillation having an oscillation frequency, wherein - the oscillation frequency is detected with a first accuracy, and - in a second test loop, the multiplication of the series of measurements by the test function and the addition of the test products is repeated whilst varying the test frequency, wherein - the test frequency is varied within a second frequency range, and - the second frequency range is selected depending on the oscillation frequency detected in the first test loop in order to detect the oscillation frequency with a higher accuracy than in the first loop.

6. The method as claimed in claim 5, characterized in that - in the first test loop, the multiplication of the series of measurements by the test function and the addition of the test products is additionally repeated whilst varying the test angle, wherein - the test angle is varied within a first angle range, in particular within the range of from 0 to 360°, wherein - the test angle is varied with a first angle increment, and - in the second test loop, the multiplication of the series of measurements by the test function and the addition of the test products is additionally repeated whilst varying the test angle, wherein - the test angle is varied within a second angle range, in particular with a second angle increment which is less than the first angle increment, and - the second angle range is selected depending on the phase angle of the oscillation detected in the first test loop in order to detect the phase angle of the oscillation with a higher accuracy than in the first loop.

7. The method as claimed in claim 5 or 6, characterized in that - 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 one of the preceding claims, characterized in that - a plurality of series of measurements of the grid variable, in particular the line voltage, the input current or the line frequency is recorded, wherein - each series of measurements is intended for analyzing a frequency range, - for each series of measurements, a measurement time period is selected depending on the frequency range to be analyzed, and - for each series of measurements, the multiplication of the series of measurements by the test function and the addition of the test products to give a product sum is repeated whilst varying the test frequency and / or whilst varying the test angle in order to obtain a plurality of product sums for each series of measurements, and - for each series of measurements, in each case the product sums of the relevant series of measurements are evaluated for detecting a low-frequency oscillation.

9. The method as claimed in one of the preceding claims, characterized in that - the multiplication of the series of measurements by the test function and the addition of the test products to give a product sum is repeated whilst varying the test frequency, wherein - the test frequency is varied within at least one frequency range having an upper and a lower frequency value with a frequency increment, and - the frequency increment is set depending on the frequency range, in particular in such a way that - the frequency increment is less than the lower frequency value, in particular less than 10% of the lower frequency value, and / or that - the frequency increment is set to be less than a predetermined percentage value, preferably less than 1%, in particular less than 0.2% of the upper frequency value, - wherein, preferably, the test frequency is varied within a plurality of frequency ranges, and the frequency increments of different frequency ranges are set to be different than one another, wherein, preferably, each frequency increment is in each case set to be greater than a predetermined percentage of the respective lower frequency value of the relevant frequency range.

10. A wind power system, namely a wind turbine or wind farm, for detecting low-frequency oscillations, in particular subsynchronous resonances, in an electrical supply grid, wherein the electrical supply grid has a line voltage with a rated line frequency, and the wind system comprises - a recording means for recording at least one series of measurements, having a plurality of measurement points, of a grid variable, in particular the line voltage, an input current or a line frequency, over a measurement time period, for performing a frequency analysis, - a multiplication unit for multiplying the series of measurements by a time-dependent sinusoidal test function for the same measurement time period, wherein - the test function is characterized by a test frequency and a test angle as phase angle, and - the series of measurements for each measurement point is multiplied by the test function in order to obtain a test product for each measurement point, - an addition unit for adding the test products taking into consideration the mathematical sign thereof to give a product sum, and - an evaluation device for 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.

11. The wind power system as claimed in claim 10, characterized in that it is set up to perform a method as claimed in one of claims 1 to 9, wherein the wind power system, for this purpose, preferably has a process control computer, on which the method, at least part thereof, is implemented.