METHOD AND DEVICE FOR DETECTING AN ELECTRICAL VOLTAGE IN A SUPPLY NETWORK

Description

[0001] The following invention relates to a method for feeding electrical current into a three-phase electrical supply network. The present invention also relates to a wind turbine in which such a method is implemented.

[0002] To feed electrical power into an electrical supply network, which is typically three-phase, it is necessary to measure the voltage in terms of magnitude and phase, which also implies measuring or knowing the frequency. The requirements for measuring such voltages are becoming increasingly stringent, particularly with regard to the speed at which changes can be detected. For example, a method for fast and accurate measurement of voltage in terms of magnitude and phase is described in US Patent 8,981,755.

[0003] Furthermore, it is particularly possible with wind turbines that operate with a full converter concept, i.e., feed the electrical power of the wind turbine completely into the grid via an inverter, to specifically adjust the quality of the fed-in electrical power to imbalances in the grid.

[0004] An example of feeding in an unbalanced three-phase current is described in US patent application US 2013 / 0141951. This application uses the method of symmetrical components. Current components of the positive-sequence system and current components of the negative-sequence system are generated independently of each other and then superimposed to create the desired unbalanced current before being fed into the grid.

[0005] The quality of such a feed-in ultimately depends on the quality of imbalance detection. It should be noted that, until now, the concept in power grids has functioned as follows: large power plants with dominant, grid-connected synchronous generators have essentially determined the quality, and especially the symmetry, of the voltage through the dominance of the synchronous generator's current. While there have been initial considerations for some time regarding the targeted compensation of imbalances, as can be seen, for example, in US patent 6,924,627, the principle described above has nevertheless been maintained, not least because the synchronous generators of the large power plants described above can only provide such compensation passively through their design, and not through active control.

[0006] Furthermore, in modern energy systems, generation units and consumers are increasingly connected to the transmission or distribution network via frequency converters or rectifiers. The switching components of these power electronic systems introduce harmonic distortion into the ideally sinusoidal 50 Hz or 60 Hz alternating current by harmonics in the frequency range up to approximately 10 kHz. These harmonics put a strain on various components within the energy systems and are therefore attenuated by active or passive filters when their levels become too high.

[0007] Wind turbines already provide a significant portion of the generated energy in some energy systems. Often, and sometimes predominantly, they are connected to the grid via frequency converters and thus, in the worst case, also contribute to harmonics in the grid.

[0008] Document WO 2009 / 056158 A1 describes a method for estimating an alternating voltage. The magnitude and phase of a sine function with a fundamental frequency and at least one harmonic are estimated using an adaptive filter or an observer. The method can be applied separately to all three phases of the mains voltage.

[0009] Document US 2012 / 150468 A1 describes a method for estimating the three-phase voltage for synchronization with the power grid.

[0010] The German Patent and Trademark Office has identified the following prior art in the priority application for the present PCT application: DE 100 32 447 A1, US 2012 / 0150468 A1, US 2014 / 0307488 A1, EP 2 223 405 B1, Azam Bagheri et al. "Detection of Grid Voltage Fundamental and Harmonic Components Using Kalman Filter and Generalized Averaging Method", Ming Sun et al. "Extended Kalman Filter Based Grid Synchronization in the Presence of Voltage Unbalance for Smart Grid" and Robert R. Bitmead et al. "A Kalman Filtering Approach to Short-Time Fourier Analysis".

[0011] The present invention is therefore based on the objective of addressing at least one of these aforementioned problems, and in particular of proposing improvements. Specifically, a solution is to be proposed that creates possibilities for network improvement, including compensation of harmonics in the network. At the very least, an alternative solution to previously known solutions is to be proposed.

[0012] According to the invention, a method according to claim 1 is proposed. Accordingly, the electrical voltage in the three-phase electrical supply network is measured with respect to magnitude and phase for a fundamental frequency and at least one harmonic. An electrical supply network can also be understood to be, for example, an electrical distribution network. It is essentially an electrical network to which many electricity generators and consumers are connected.

[0013] First, an electrical, three-phase voltage from the supply network is measured.

[0014] The measured three-phase electrical voltage is then transformed into polar coordinates, resulting in a rotating voltage phasor for the fundamental frequency. This is referred to as the measured reference phasor and is used accordingly in subsequent analysis. The transformation can be performed, for example, as described in US patent 8,981,755.

[0015] Furthermore, the values ​​of at least one voltage vector for the fundamental frequency and at least one voltage vector of a harmonic to be measured are observed using a state observer. This is referred to as a state observer in the control engineering sense. The observed values ​​are then tracked as a function of the measured reference vector.

[0016] In other words, an observer model is used that represents the mains voltage using at least one fundamental frequency and at least one harmonic, and employs at least one voltage phasor for each. The measured system is represented by a voltage phasor for the fundamental frequency, whereby the magnitude and phase of this voltage phasor can also change through continuous measurement and transformation.

[0017] The comparison to the observer's tracking is made in particular by comparing this measured value in polar coordinates, i.e. the values ​​of this one rotating voltage vector from the measurement with the sum of all voltage vectors that the observer uses as a basis.

[0018] Preferably, the state observer operates based on a detected mains frequency, which is input into the state observer as an input variable. It is therefore proposed that the state observer does not observe the mains frequency as a state to be monitored and potentially tracked, but rather accepts the detected and inputted frequency value as given and uses it as its basis. This allows for improved stability, or in other words, a stabilization of the observation, because this frequency, which affects every circulating observed voltage phasor or is a characteristic parameter of such a voltage phasor, represents a fixed value. The observer can then concentrate on the magnitude and phase of the observation, thus eliminating any potentially disruptive or even stability-threatening interaction between frequency on the one hand and magnitude and phase on the other.

[0019] According to one embodiment, it is proposed that the state observer monitors the values ​​of the voltage vectors using a current observer matrix, and that the current observer matrix is ​​selected from several pre-calculated observer matrices depending on the detected mains frequency. It should be noted that the terms matrix and matrix are used synonymously here. Such an observer matrix represents a known component in an observer structure and essentially has the task of tracking the observed states based on comparative measurements. The reference vector serves as the comparative measurement. To account for varying frequencies during observation, the calculation of frequency-dependent observer matrices can be very computationally intensive. The computational effort may exceed the available processing capacity of a microcontroller in a given time step, making calculation impossible at the required clock rate.This effort can be reduced by using pre-calculated observer matrices, which are then selected based on frequency, specifically on the currently recorded frequency. In some cases, this is the only way to make such consideration of frequency variation possible in the first place. For frequencies for which no predetermined observer matrix exists (which is also a question of frequency acquisition accuracy), it can be determined by interpolation between two observer matrices.

[0020] Preferably, a Kalman filter is used as the state observer. In this respect, the observation of the states can also be described as filtering, and the state observer can be referred to as a filter. The use of a Kalman filter makes the observation and filtering particularly well-suited to taking disturbances, especially measurement noise, into account, namely filtering them out.

[0021] According to one embodiment, it is proposed that the state observer detects a DC component, and for the fundamental frequency and for each harmonic of the electrical voltage to be measured, a positive-sequence system and a negative-sequence system. This allows the state observer to also consider and detect any asymmetry in the three-phase voltage. Even if no significant asymmetry is present, which need not be known before the measurement, such detection of a negative-sequence system can still be performed. The negative-sequence component may then be correspondingly small. This detection of positive-sequence and negative-sequence systems thus follows the method of symmetrical components.

[0022] Preferably, one voltage phasor is used for the DC component, and two voltage phasors are used for the fundamental frequency and for each harmonic to be detected, and their values ​​are observed, so that one voltage phasor is assumed for a positive-sequence system and one for an negative-sequence system. It can also be advantageous to assume two values ​​for the DC component, namely the real and imaginary parts of the voltage phasor, because a phasor can be calculated here, at least formulaically, when applying the method of symmetrical components. Preferably, a very large number of harmonics are detected, for example, 25 harmonics, i.e., detection up to the 25th harmonic. In this case, if the first harmonic is the fundamental frequency, 51 phasors result, and thus 102 values.

[0023] According to one embodiment, the method for detecting the electrical voltage is characterized in that the measurement of the three-phase electrical voltage of the supply network is carried out at a transformer connected to the electrical supply network, which is often simply referred to as a transformer. Measurements can be taken at such a transformer, particularly one through which electrical current is fed into the electrical supply network, in a simple and reliable manner.

[0024] Measuring at such a transformer is particularly advantageous when electrical current is fed into the grid via this transformer and the feed-in takes into account the measurement or recording of the electrical voltage of the supply network. Especially when a current that at least partially compensates for the observed harmonics is fed into this transformer, distortions can be avoided.

[0025] Preferably, the measurement is taken on the side of the transformer that is electrically connected to a wind turbine which feeds power into the electrical grid via this transformer. This allows the wind turbine to take these measured voltage values, especially observed harmonics, into account and adjust the power feed-in accordingly. In particular, it can shape the incoming power feed-in in such a way as to compensate for, or at least reduce, observed harmonics in the grid voltage.

[0026] According to the invention, the measured voltage is transformed into polar coordinates using the Clarke transformation, assuming the voltage is zero-system free. This corresponds to the transformation described in the aforementioned US document (US 8,981,755). It is assumed that no zero system is present, which is also a common assumption when applying the theory of symmetrical components. However, the assumption of zero-system free does not necessarily imply the absence of DC components. Rather, different DC components can be present in each phase of a three-phase network, so that these are also reflected in the positive- and negative-sequence components after the transformation.

[0027] In the method according to the invention, electric current is fed into an electrical, three-phase supply network and this method also includes the following step: Generating an electric current for feeding into the electrical supply network, wherein the electric current includes a compensation current component to reduce the at least one detected harmonic.

[0028] The method therefore initially requires a three-phase electrical supply network, which also forms the basis of the method described above for measuring electrical voltage in such a three-phase electrical supply network. This can also include an electrical distribution network, to name just one example.

[0029] Thus, the electrical voltage is also measured using the method described above. This includes the measurement, specifically the observation, of values ​​for at least one harmonic of the voltage. This provides a value, namely the amplitude and phase, for such a harmonic, which can then be used to at least reduce, or ideally completely compensate for, the measured harmonic. The injected electrical current therefore includes a compensation current component, which thus contains at least one harmonic. In particular, the current includes a fundamental component or fundamental frequency, in order to feed the corresponding power into the electrical supply network. A compensation current component is then superimposed on this fundamental frequency, i.e., this idealized waveform, and thus added to it in an electrical sense.This compensation current component is intended to reduce the detected harmonics, or at least a portion of them.

[0030] According to one embodiment, it is proposed that the compensation current component has at least one current harmonic, and that each current harmonic is defined by its amplitude and phase, depending on the observed harmonics of the detected voltage. The observation of the voltage harmonics thus provides information, specifically a clearly defined description of this harmonic or harmonics. The compensation current component is then preferably structured similarly. For example, the compensation current component has a corresponding current harmonic for each detected voltage harmonic. The amplitude of the current harmonic can be in a predetermined ratio to, or at least related to, the voltage harmonic. Furthermore, the phase is adjusted accordingly so that compensation, or at least reduction, can be achieved.

[0031] Preferably, when measuring the voltage, a positive-sequence and a negative-sequence component are recorded for each harmonic. Similarly, the corresponding current harmonic preferably also has a positive-sequence and a negative-sequence component. Here, too, an amplitude and phase can be determined for each current harmonic. However, it is also possible to consider only the positive-sequence component, and in particular, it is also possible for the compensation current component to determine only one component for each current harmonic, thereby disregarding the asymmetry underlying the consideration of the symmetrical components. The rationale behind this is that considering both the positive-sequence and negative-sequence components can be beneficial for the observer in order to ensure the overall functionality, quality, and accuracy of the measurement.However, it is often sufficient to consider only the component of the system and generate it during feed-in.

[0032] It should be noted again here that both the harmonic and the current harmonic each refer to a harmonic of one order, and multiple harmonics each refer to a harmonic but with different frequencies.

[0033] Another embodiment proposes adjusting the amplitude of a current harmonic at the compensation current component via a controller. The controller receives as its input signal a control difference between the voltage setpoint and the observed actual voltage of the relevant harmonic of the detected voltage. In the simplest case, this means that the voltage setpoint has the value 0, since the harmonic is to be reduced to 0. In certain cases, it may of course be advantageous not to set the value 0. This difference, referred to here as the control difference, is then applied to the controller between the voltage setpoint and the actual voltage of the relevant harmonic. This could be, for example, a PID controller, a PI controller, or a PD controller.In the simplest case, a proportional (P) controller is used, and the detected voltage difference then leads to an amplitude of the current harmonic corresponding to this factor, which naturally also takes into account the different units of voltage and current. Therefore, with a pure proportional (P) controller, the relevant voltage harmonic will probably not be completely eliminated.

[0034] To completely eliminate this voltage harmonic, a PID controller is suggested, for example. However, it is important to ensure beforehand that sufficient actuator power is available. With sufficient actuator power, it may be possible to completely or almost completely eliminate the voltage harmonic. If insufficient actuator power is available, the controller could then enter a limiting mode.

[0035] If necessary, a PD controller can create dynamics without claiming to provide complete control.

[0036] Furthermore, a wind turbine according to the second independent claim is proposed, which includes an inverter. With this wind turbine, such current can then be fed into the grid, thus not only supplying energy to the electrical supply network but also compensating for or reducing voltage harmonics. The wind turbine is designed accordingly to carry out this method. Moreover, the method described above for determining harmonics of the grid voltage can also be used analogously for determining harmonics in the electric current. This is hereby also proposed according to the invention.

[0037] The invention will now be explained in more detail below using exemplary embodiments and with reference to the accompanying figures. Figure 1 schematically shows a wind turbine in a perspective view. Figure 2 shows a simplified structure to illustrate a method for detecting electrical voltage according to one embodiment. Figure 3 shows a functional block of the Figure 2 in a more detailed structure. Figure 4 schematically shows an arrangement for feeding electrical current into an electrical supply network by means of a wind turbine according to an embodiment of the invention.

[0038] Figure 1Figure 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.

[0039] Figure 2 Figure 1 shows a measuring arrangement 201 for detecting an electrical voltage in a three-phase electrical supply network 202, which is shown schematically. Accordingly, the electrical voltage U1,2,3 is measured three-phase using a sensor 204. The measurement is performed at each sampling step of the subsequent evaluation. The measured voltage is fed to a transformation unit 206, which transforms these three measured voltage values ​​into polar coordinates, here denoted as Uα, β.

[0040] The measured voltage is also fed into a frequency determination block 208, which determines the frequency f, namely the mains frequency of the supply network 202, from the measured voltage values. The frequency is thus determined by this frequency determination block 208 using an algorithm independent of the Kalman filter. For example, a filter for determining the mains frequency from a space vector voltage angle can be used. Preferably, alternatively, a discrete Fourier transform of the three voltage values ​​is used to determine a filtered angle of the mains voltage. A frequency signal can then be extracted from this by suitable filtering. The advantage of using the angle obtained from the DFT compared to using the space vector angle is the filtering effect on integer harmonics of the fundamental frequency.

[0041] It should be noted that this block representation of the Figure 2and also the Figure 3 and partly the Figure 4 This serves to illustrate the method used. The individual functions of the depicted blocks do not necessarily have to be performed in such a separate block, but can also be implemented together in a microprocessor or other computing unit.

[0042] In any case, the transformed polar coordinates Uα, Uβ and the measured mains frequency f are input into the Kalman filter block 210. The Kalman filter block 210 is thus a filter that determines and outputs the measured states x as its output. These measured states, represented here by this state vector x, can include, in particular, values ​​of voltage phasors for a DC component, a positive and negative system of the fundamental frequency, and a positive and negative system of each measured harmonic. If, for example, the voltage is considered up to the 25th harmonic, where the first order would be the fundamental frequency, this state vector x can comprise 102 values. This number results from two values ​​for the DC component, namely the real and imaginary parts, which are denoted as uαDC and uβDC.For the fundamental frequency and each overtone, two values ​​are obtained for the positive-sequence system and two for the negative-sequence system, namely the real and imaginary parts of the phasor. For the fundamental frequency, as the first order, these are then the values ​​u α(1+) and u β(1+) for the positive-sequence system and, correspondingly, the values ​​u α(1-) and u β(1-) for the negative-sequence system. Similarly, four values ​​can be provided for each subsequent order.

[0043] These values, i.e., this state vector thus recorded, can then be used for power generation to feed electrical current into the supply network 202.

[0044] Details of the Kalman filter block 210 are in Figure 3 Explained schematically. Figure 3 This shows this Kalman filter block 210, and it receives, as already mentioned... Figure 2The input variables are the measured voltage Uα, β, transformed into polar coordinates, and the mains frequency f, determined by frequency determination block 208. Depending on this determined mains frequency f, the observer matrix K is determined in observer matrix block 302 and output accordingly as observer matrix K(f). Observer matrix block 302 determines this observer matrix K by retrieving the corresponding observer matrix K from a table, depending on the frequency f. If no observer matrix K is stored for the exact frequency, it can be determined by interpolation from observer matrices of adjacent frequencies.

[0045] The system matrix A(f) is also determined as a function of the frequency in system matrix block 304. In system matrix block 304, the system matrix is ​​calculated in a known manner.

[0046] The system states x to be recorded are essentially constantly recalculated in update block 306. This update block 306 behaves somewhat like a system-describing model, taking into account the currently measured voltage U α, β, transformed into polar coordinates, for tracking or adjustment, to put it more simply.

[0047] Furthermore, the observer matrix K(f) is also required, which update block 306 always receives from observer matrix block 302. A matrix describing the system. C is also required and is therefore shown for illustrative purposes as the input to update block 306.

[0048] Furthermore, the updated state vector x (k+1) is required. This updated state vector x (k+1) is derived from the last state vector x(k) and the system matrix A(f) in state block 308 is calculated. State block 308 requires the system matrix A(f) for this, which it receives from system matrix block 304. The old state vector x (k) State block 308 currently receives from update block 306.

[0049] The updated state vector x (k+1) is therefore also considered, as described above, as an input for update block 306. This updated state vector is particularly useful for starting the process. x (k+1) an initialization is performed in the initialization block 310.

[0050] Thus, the Kalman filter 210 can now detect the respective state vector. x (k) output as state vector x. If necessary, this can be subjected to a transformation, possibly only in the sense of multiplication by a constant factor in transformation block 312. In that case, the in Figure 3The represented state vector x is derived from the internal state vector. x (k) differentiate accordingly.

[0051] This state vector x It can now contain values ​​for the DC component, the fundamental frequency phasor, and the harmonic phasors, which can be used to determine the required input currents. This is in the Figure 4 illustrated. Figure 4 This is illustrated for a Wind Energy Plant 400, but other feed-in devices can also record such measurements and use them for power control, namely the amount of power to be fed in.

[0052] The structure in Figure 4Figure 402 illustrates a power supply network into which electricity is fed via a transformer 404. For this purpose, the wind turbine 400 generates electrical current with a generator 406, which can be rectified in a rectifier 408 and fed to an inverter 410. Such an inverter 410 is also frequently referred to as an inverter 410.

[0053] This inverter 410 generates a three-phase current i 1,2,3 which can be fed into the supply network 402 via this transformer 404.

[0054] It is now proposed to use a symbolically represented sensor 412 to detect voltage and frequency and to feed this data to a measuring block 414. The measuring block 414, together with the sensor 412, can be connected to the measuring arrangement 201 of the Figure 2 The frequency f would then be determined from the measured voltage in measuring block 414, but for illustration purposes, in Figure 4The frequency f is also shown as an input variable for measuring block 414.

[0055] The measuring block 414 can then output the state vector x as an output variable, which can contain values ​​for the DC component, fundamental frequency and harmonic, in particular also for the positive- and negative-sequence systems, as above. Figure 2 was explained.

[0056] These values, i.e., the state vector x These values ​​can then be entered into control block 416, which may contain, for example, a controller. In this control block 416, adjustments can also be made based on the detected voltage values, which are represented in the state vector. xThe system contains data on the frequency, and deviations are calculated for each harmonic, from which the corresponding current values ​​can be determined. Specifically, a compensation current component is determined for each harmonic based on these deviations or other factors related to the measured voltage harmonics. This compensation current component, or these multiple compensation current components, are then superimposed on the current value for the fundamental frequency, which is used to supply electrical power, and potentially reactive power.

[0057] The control block 416 then finally determines the current setpoints. i These current setpoints are entered into the inverter 410. They take into account the current to be fed in, including superposition, i.e., fundamental frequency and harmonic(s). The inverter 410 can then operate based on these current setpoints. ito generate the corresponding current values. Alternatively, it can be provided to generate the fundamental frequency of the incoming current and the at least one harmonic to be superimposed separately and then superimpose them, i.e., add them together. For this purpose, it is proposed to provide several inverters, at least one of which generates the fundamental frequency or a part thereof, and at least one other of which generates the at least one harmonic or a part thereof.

[0058] The invention is therefore characterized in particular by the following.

[0059] In modern energy systems, generation units and consumers are increasingly connected to the transmission or distribution network via frequency converters or rectifiers. The switching components of these power electronic systems introduce harmonic distortion into the ideally sinusoidal 50 Hz or 60 Hz alternating current by harmonics in the frequency range up to approximately 10 kHz. These harmonics put a strain on various components within the energy systems and are therefore attenuated by active or passive filters when their levels become too high.

[0060] Wind turbines already provide a significant portion of the generated energy in some energy systems. They are predominantly connected to the grid via frequency converters and, in the worst case, can therefore also contribute to harmonics in the grid.

[0061] The invention described here relates to a method for detecting and compensating harmonics in the grid voltage of a power system by means of a wind turbine connected to this system via a full converter. The wind turbine is thus enabled to feed current into the grid to reduce voltage harmonics or opposing system voltages. These can be caused, for example, by other generating units or consumers.

[0062] For this purpose, the following procedure is particularly proposed: 1. Measurement of the terminal voltages on the wind turbine side at the system transformer. 2. Conversion of the three terminal voltages into a rotating voltage phasor using the Clarke transform, assuming zero-sequence isolation of the voltages, where the voltage phasor is defined by its magnitude and phase. 3. Application of a filter to observe the DC component, as well as positive- and negative-sequence voltages of multiples of the grid frequency from the first order (i.e., the fundamental frequency) up to a defined highest possible harmonic order. An additional input to the filter is a grid frequency defined by another method. The filter can be designed as a state monitor, in particular a Kalman filter. 4. Calculation of a desired compensation current in harmonic orders selected for compensation using a control law. Preferably, the adjustment is made via a proportional factor ki, which is used for the i.The voltage order defines a compensation current of ki A per V of voltage harmonic amplitude. Another preferred method for calculating the compensation current involves applying a PID controller to the difference between a target voltage, e.g., 0 V, and the actual voltage of the corresponding component. With sufficient current-controlling capability of the inverter, complete regulation of harmonic or negative system voltages can thus be achieved—ideally. 5. Setting the compensation current in addition to the desired active and reactive current in the fundamental frequency via a current control method. Preferably, a hysteresis current controller, also known as a tolerance band controller, is used, as this allows for very fast response times and high robustness against changing network parameters.

[0063] Particular attention must be paid to the appropriate filtering of the voltage vectors for the quick and precise determination of correct voltage amplitudes in the various frequency ranges, namely DC voltages, fundamental frequency and harmonics.

[0064] Existing methods for determining harmonic components in voltage are often based on recursively formulated discrete Fourier transforms of the measured quantities. These are characterized by high numerical robustness. However, the filter quality is only guaranteed if the sampling frequency is an integer multiple of the fundamental frequency of the measured signal or the interval between two frequency components to be identified. Since the mains frequency in a power system is generally subject to slight fluctuations, and since the applicability of a method in systems with different nominal frequencies (e.g., 50 and 60 Hz) is advantageous, high filter quality at different mains frequencies and a constant sampling rate is of great importance for the widest possible application.

[0065] Several solutions to this problem are known, but all have significant drawbacks. One possibility is to change the sampling rate of the algorithm depending on the mains frequency, as described in reference [1]. However, such a change in the sampling rate is often undesirable because other algorithms are executed on the processing unit for which a fixed sampling rate is important, as is the case, for example, with a discrete-time controller. Another possibility is to implement a phase or frequency control loop, as described in reference [2].However, these algorithms either exhibit insufficient filtering in abnormal network conditions, especially in connection with a phase-locked loop, or significant stability problems are observed in the digital implementation, particularly at low sampling rates, especially in connection with a frequency-locked loop.

[0066] A third solution category consists of Kalman filters, which are designed based on state-space models of the network voltage dynamics. A distinction can be made between filters for constant network frequency, as described in reference [3], which exhibit linear dynamics, and filters for variable network frequency, as described in reference [4], which are based on nonlinear differential equations. The latter filters recursively calculate the optimal observer matrix under the given noise parameters by using a state-space description based on the current state variables in the synthesis equations at each time step. With appropriate parameterization, this results in excellent filter properties even with varying network frequencies and under abnormal network conditions, such as...asymmetrical or heavily harmonic stresses, since all these effects can be taken into account in the state space description of the system.

[0067] A disadvantage of the extended Kalman filter method for observing state variables of a nonlinear system is the recursive calculation of the observer matrix. This requires multiple multiplications in each computation step of the state-space description matrices with each other and with vectors of the measured and state variables. With a large filter dimension to account for numerous harmonic orders, this negatively impacts the required computation time. With limited computing capacity, execution within the cycle time limited by the sampling rate may no longer be possible.

[0068] In contrast, assuming a constant mains frequency, it is possible to pre-calculate the observer matrix for the Kalman filter by solving an algebraic Riccati equation, due to the time-invariant and linear system equations in this case, as can be seen in reference [3]. According to at least one embodiment, pre-calculating the observer matrix for different mains frequencies is proposed here.

[0069] According to reference [3], the following frequency-dependent system of difference equations is used as the basis for deriving the observer implementation: x k + 1 = A f x k y k = Cx k A f = A 1 f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 A 2 f ⋯ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⋮ ⋱ ⋮ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ⋯ A N f 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 A i f = cos 2 πT s if − sin 2 πT s if sin 2 πT s if cos 2 πT s if 0 0 cos 2 πT s if sin 2 πT s if − sin 2 πT s if cos 2 πT s if C = 1 0 0 1 1 ⋯ 1 0 0 1 N + 1 x k = x 1 k x 2 k … x N k u DCα k u DCβ k T x i k = u i 1 α k u i 1 β k u i 2 α k u i 2 β k y k = u α k u β k T

[0070] In these equations, k denotes the current execution step, T s the sampling time of the discrete implementation of the algorithm, f the mains frequency, i an index that takes values ​​from 1 up to the number of the highest harmonic order N calculated in the observer, u DCα (k) / u DCβ (k) the alpha and beta DC voltage components, ui(1)α (k) / ui(1)β (k) the alpha and beta positive-sequence voltage components of the 1st order (i.e., for i = 1 fundamental frequency, for i > 1 harmonic components), and ui(2)α (k) / ui(2)β (k) the alpha and beta negative-sequence voltage components of the 1st order.

[0071] Based on these equations, an observer matrix K can be calculated for each network frequency f, which can then be used in a standard observer implementation to observe the states. The equation for calculating the Kalman observer matrix using the state and measurement signal noise covariance matrices Q and R is known, e.g., from reference [6].

[0072] Using matrix K, the state estimation is updated at each time step according to the known equation. x k k = x k k − 1 + K ∗ y k − C ∗ x k k − 1

[0073] Here, x(k|k) denotes the state estimate from the current time step and x(klk-1) denotes the state estimate for the current time step from the last time step.

[0074] According to the invention, at least according to one embodiment, the observer matrix, also referred to synonymously as the observer matrix, is pre-calculated for a given state-space description and defined measurement and state noise levels for various mains frequencies encompassing the entire desired operating range. At execution time, the frequency is determined by an algorithm independent of the Kalman filter. Such an algorithm can be implemented by a frequency determination block, as shown in the figures. Here, for example, a suitable filter can be used to determine the mains frequency from a space vector voltage angle. This frequency signal serves to select an observer matrix that matches this frequency. To increase the resolution, interpolation can be performed between different stored observer matrices at different frequencies.

[0075] This method thus enables a precise and rapid calculation of numerous harmonics of the mains voltage in positive- and negative-sequence systems with significantly reduced computational effort compared to the nonlinear, extended Kalman filter. Unlike the application of frequency control loops, as described, for example, in reference [5] using a Kalman filter, the algorithm described here does not use a closed loop to determine the mains frequency, which, due to its difficult-to-analyze nonlinear dynamics, always poses a stability risk to the filter algorithm. Instead, the mains frequency is determined separately and used only for selecting the observer matrix.

[0076] Furthermore, the method described above can also be used to determine harmonics in the current.

[0077] The references mentioned above are as follows: [1] B. P. McGrath, D. G. Holmes, J. Galloway: Improved Power Converter Line Synchronisation using an Adaptive Discrete Fourier Transform (DFT). Proceedings of IEEE 33rd Annual Power Electronics Specialists Conference, 2002, Bd. 2, S. 821-826. [2] R. Teodorescu, M. Liserre, P. Rodriguez: Grid Converters for Photovoltaic and Wind Power Systems. John Wiley & Sons, Chichester, 2011. [3] R. R. Bitmead, A. C. Tsoi, P. J. Parker: A Kalman Filtering Approach to Short-Time Fourier Analysis. IEEE Transactions on Acoustics, Speech and Signal Processing, Bd. ASSP-34(6), Dezember 1986, S. 1493- 1501. [4] B. La Scala, R. R. Bitmead: Design of an Extended Kalman Filter Frequency tracker. IEEE Transactions on Signal Processing, Bd. 44(3), März 1996, S. 739-742. [5] M. S. Reza, M. Ciobotaru, V. G. Agelidis: Instantaneous Power Quality Analysis Using Frequency Adaptive Kalman Filter Technique. Proceedings of 7th International Power Electronics and Motion Control Conference, Harbin, China, Juni 2012, S.81-87. [6] T. Glad, L. Ljung: Control Theory. Taylor & Francis, London, 2000.

Claims

1. Method for feeding electrical current into an electrical three-phase supply network, comprising the steps of: recording the magnitude and phase of a electrical three-phase voltage in the supply network for a fundamental and at least one harmonic, comprising the steps of: - measuring the electrical three-phase voltage of the supply network, - transforming the measured voltage values into polar coordinates using a rotating voltage phasor for the fundamental as a measured reference phasor, - wherein the measured voltage is transformed into polar coordinates with the aid of the Clarke transformation assuming that the voltage is free of the zero-sequence system, - respectively observing values of at least one voltage phasor for the fundamental and of at least one voltage phasor for at least one harmonic to be recorded with the aid of a state observer, and - tracking the observed values on the basis of the measured reference phasor and - producing an electrical current for feeding into the electrical supply network, the electrical current comprising a compensation current component in order to reduce the at least one recorded harmonic.

2. Method according to Claim 1, characterized in that the state observer operates on the basis of a recorded network frequency and the recorded network frequency is input to the state observer as an input variable.

3. Method according to Claim 1 or 2, characterized in that the state observer observes the values of the voltage phasors with the aid of an up-to-date observer matrix and the up-to-date observer matrix is selected from a plurality of pre-calculated observer matrices on the basis of the recorded network frequency.

4. Method according to one of the preceding claims, characterized in that a Kalman filter is used as the state observer.

5. Method according to one of the preceding claims, characterized in that a positive-sequence system and a negative-sequence system are respectively recorded by the state observer for the fundamental and for each harmonic to be recorded, and in that a DC component is optionally recorded.

6. Method according to one of the preceding claims, characterized in that a voltage phasor for a positive-sequence system and a voltage phasor for a negative-sequence system are respectively taken as a basis for the fundamental and for each harmonic to be recorded and their values are observed, and in that a voltage phasor is optionally taken as a basis for a DC component and its values are recorded.

7. Method according to one of the preceding claims, characterized in that the electrical three-phase voltage of the supply network is measured at a transformer connected to the electrical supply network, in particular on that side of the transformer which electrically faces a wind power installation which feeds the electrical supply network via this transformer.

8. Method according to one of the preceding claims, characterized in that the compensation current component has at least one current harmonic and a current harmonic is respectively determined by an amplitude and a phase and on the basis of the observed harmonics of the recorded voltage.

9. Method according to one of the preceding claims, characterized in that an amplitude of a current harmonic of the compensation current component is respectively adjusted using a controller, and the controller receives, as an input signal, a control difference between the desired voltage value and the observed actual voltage value of the relevant harmonic of the recorded voltage.

10. Method according to Claim 9, characterized in that, as the controller, a controller is selected from the list comprising - PID controller, - PI controller, - P controller, and - PD controller.

11. Method according to one of the preceding claims, characterized in that the compensation current component respectively takes into account current harmonics as positive-sequence system and negative-sequence system components.

12. Wind power installation having an inverter for producing an electrical current to be fed into a three phase electrical power supply system wherein the wind power installation is prepared to carry out a method according to one of Claims 1 to 11.