DAMPING HIGHER ORDER HARMONICS IN AVERAGE DC LINK VOLTAGES

Abstract

A converter system includes at least two branches, where each branch includes an AC-to-DC converter and a DC link cascade connected with each other. A method includes: determining at least two AC-side currents, each of which is input into one of the AC-to-DC converters; determining from the AC-side currents, a voltage reference for each of the AC-to-DC converters; determining a DC link ripple indicator; determining a converter reference correction from the DC link ripple indicator, such that a higher order harmonic in the average DC link voltage is damped; determining corrected voltage references for the AC-to-DC converter by adding the converter reference correction to the voltage references of the AC-to-DC converters or by adding the converter reference correction to an average current reference for the AC-to-DC converters; and controlling the AC-to-DC converters with the respective corrected voltage references.

Description

TECHNICAL FIELD

The present disclosure relates to a method, computer program, computer-readable medium and controller for controlling a converter system. The disclosure furthermore relates to the converter system and in particular to a converter system of a wind energy conversion system.

BACKGROUND

In gearless wind energy conversion systems with a permanent magnet synchronous generator, the back electromotive force (BEMF) harmonics of the generator may cause low frequency oscillation of the DC link voltage. This oscillation is transferred to the transformer primary, where it appears as voltage and current interharmonics or even harmonics depending on the generator fundamental frequency. Since the related grid standards are very stringent on the maximum acceptable values of interharmonics and even harmonics, the respective limits may be violated for high values of the modulation index.

Furthermore, the grid-side harmonics may coincide with resonance frequencies of the grid impedance and may cause stability issues. Adding a passive filter to damp the resonance would increase the wind park cost.

In general, when possible, it is desirable to damp oscillations by control of a converter system, such that passive filters, which are expensive and bulky components, can be omitted. Additionally, further losses may be generated by passive filters.

SUMMARY

It is an objective of the present disclosure to provide a control method for damping oscillations in paralleled converter branches. It is a further objective to provide an economic converter system for converting voltages from a generator, which observes grid standards of a grid, which is supplied by the converter system.

These objectives are achieved by the subject-matter of the independent claims. Further exemplary embodiments are evident from the dependent claims and the following description.

A first aspect of the disclosure relates to a method for controlling a converter system. The converter system may be adapted for converting an AC current from a generator, such as a wind turbine generator, into an AC current to be supplied to an electrical grid, which may be a large scale grid. In general, the converter system may be adapted for interconnecting a rotating electrical machine, which also may include a motor, with the electrical grid. The converter system may be a medium voltage system, adapted for converting voltages and currents of more than 1000 V and/or more than 100 A.

The converter system comprises at least two branches, wherein each branch comprises an AC-to-DC converter and a DC link cascade connected with each other. Each of these branches may be an AC-to-AC conversion branch comprising the AC-to-DC converter, the DC link and a DC-to-AC converter cascade connected with each other. AC means alternating current, DC means direct current.

Each branch may be associated with a stator winding system of the rotating electrical machine. The rotating electrical machine may comprise at least two stator winding systems. On a side of the electrical machine (which may be seen as machine side, motor side or generator side), each branch and in particular each AC-to-DC converter is connected with one of the stator winding systems.

The AC-side currents of the AC-to-DC converter may be phase-shifted with respect to each other. This may be due to the stator winding system configuration of the rotating electrical machine.

On the other side (which may be seen as grid-side), the branches may be coupled via a common transformer. Each branch and in particular each DC-to-AC converter may be connected to a transformer winding system of the common transformer.

It has to be understood that the converter system may be a three-phase system. Each of the stator winding systems and the transformer winding systems may comprise three windings. Furthermore, each of the currents and voltages described in the following may have three phases.

In general, the method may be performed automatically by a controller of the converter system. The method comprises: determining at least two AC-side currents, each of which is input into one of the AC-to-DC converters; and determining from the AC-side currents, a voltage reference for each of the AC-to-DC converters, such that the AC-side current follows a current reference for the respective AC-to-DC converter.

The AC-side currents may be stator currents from the rotating electrical machine. Analogously, the voltage references may be used for controlling the AC-side voltages, which may be stator voltages of the rotating electrical machine. The AC-side currents may be measured at the AC-side of the AC-to-DC converters and/or may be estimated from other quantities measured in the converter system. The AC-side currents may be seen as winding currents. The AC-side currents may be current vectors. Each of the AC-side currents may have two components (such as alpha, beta). The two components may be obtained from two or more phase currents by an appropriate transformation.

The controller may have sub-controllers, which may be seen as current controllers, into which the AC-side currents are input and which determine the voltage references. Besides the AC currents, also current references and a torque reference may be input into the current controllers. Standard dq-frame current controllers may be used for this. In general, when there are N branches and/or N stator winding systems and/or N secondary transformer winding systems, there may be N current controllers.

The method further comprises: determining a DC link ripple indicator, which DC link ripple indicator is an average DC link voltage of the DC links, an average DC link current of the DC links and/or an average active power input into the at least two branches.

The DC link voltage of each DC link may be measured and/or estimated. Then, the average DC link voltage may be determined therefrom, wherein the average DC link voltage is the average of the DC link voltages of the DC links of the branches. Here and in the following, the average of several quantities may be the sum of these quantities optionally divided by the number of these quantities.

The DC link current of each DC link may be measured and/or estimated. Then, the average DC link current may be determined therefrom, wherein the average DC link current is the average of the DC link currents of the DC links of the branches.

Alternatively or additionally, the active power input into each branch and/or processed by each AC-to-DC converter may be estimated. This may be done based on the AC-side current and the AC-side voltage of the AC-to-DC converter, which may be measured and/or estimated, for example, at the converter terminals. It also is possible that the active power of an AC-to-DC converter is estimated by the product of the converter switching function with the AC-current. Then, the average active power may be determined therefrom, wherein the average active power is the average of the active powers of the AC-side currents.

All the afore mentioned quantities, the average DC link voltage, the average DC link current and the average active power are an indicator for a ripple in the average DC link voltage. In general, the DC link voltage should be constant. The DC link ripple may be the deviation from the constant DC link voltage reference.

The method further comprises: determining a converter reference correction from the DC link ripple indicator, such that a higher order harmonic in the average DC link voltage is damped. The DC link ripple is composed of several higher order harmonics, which may be determined relative to the fundamental frequency of the AC-to-DC converter. The fundamental frequency may be also a fundamental frequency of the rotating electrical machine, i.e. the speed of the rotor.

The average DC link ripple may be particularly relevant for grid-side harmonics, for example harmonics that are present on a grid-side and/or primary side of a transformer, to which the branches are coupled on a secondary side. With the method, a specific higher order harmonic in the average DC link voltage is damped. It may be that solely the average ripple is seen at the output and/or primary side of the transformer. In this case, the specific higher order harmonic is removed or damped in the output of the transformer.

The DC link ripple indicator may be filtered with respect to the higher order harmonic and/or may be phase-shifted to generate a reference signal adapted for damping the higher order harmonic in the AC-to-DC converter.

The controller of the converter system may comprise a sub-controller, which determines the converter reference correction. This sub-controller may be seen as a DC link ripple controller. The DC link ripple controller may be a resonant controller with a resonance frequency equal to the one of the DC link ripple indicator.

The method further comprises: determining corrected voltage references for the AC-to-DC converter by adding the converter reference correction to the voltage references of the AC-to-DC converters or by adding the converter reference correction to an average current reference for the AC-to-DC converters.

The converter reference correction may be either added to an average current reference, which is input into the current controllers as described above or it may be added to the voltage references output by the current controller. In both cases, corrected voltage references are fed to the converter modulator.

The method further comprises: controlling the AC-to-DC converters with the respective corrected voltage references. From the corrected voltage references, switching signals for each AC-to-DC converter may be determined and semiconductor switches of the AC-to-DC converter may be switched in accordance with the switching signals.

According to an embodiment of the disclosure, the converter reference correction is determined with respect to a rotating reference frame rotating with a fundamental frequency of the AC-side currents. It may be that the DC link ripple indicator is based on quantities, such as the average DC link voltage and the active power, which have been estimated in the rotating reference frame rotating with a fundamental frequency of the AC-side currents. Such a rotating reference frame may be the dq reference frame.

In this case, the converter reference correction may have to be transformed into a stationary reference frame of the respective AC-side current considering the phase-shift of the AC-side currents. Such a transformation may comprise a rotation matrix based on the fundamental frequency and the respective phase-shift.

According to an embodiment of the disclosure, the converter reference correction is determined from the DC link ripple indicator with a second order generalized integrator (SOGI) with a central frequency at the higher order harmonic. A second order generalized integrator may have the following transfer function

$k_r\frac{s\cos \left({\phi }_c\right)-{\omega }_r\sin \left({\phi }_c\right)}{s^2+{\left({\omega }_r\right)}^2}$

where k_r is a gain factor, φ_c is a compensation angle and or is the resonance frequency of the second order generalized integrator, which in the present case is the frequency of the higher order harmonic.

According to an embodiment of the disclosure, the DC link ripple indicator is transformed into a rotating reference frame rotating with the frequency of the higher order harmonic. The second order generalized integrator can be implemented with complex valued quantities, when the corresponding quantities are processed in the rotating reference frame rotating with the frequency of the higher order harmonic.

Then, the converter reference correction may be determined from the DC link ripple indicator by multiplying a gain factor to the DC link ripple indicator, integrating it and adding a compensation angle to a phase of the output of the integrator.

After that, the converter reference correction may be transformed back into a rotating reference frame rotating with a fundamental frequency of the AC-side currents. In such a way, the converter reference correction can be further processed together with quantities that are in the rotating reference frame rotating with a fundamental frequency of the AC-side currents, such as the current references and/or the voltage references.

According to an embodiment of the disclosure, the higher order harmonic is the 6^th order harmonic with respect to a fundamental frequency of the AC-side currents. Such harmonics may be problematic in the context of a wind turbine generator system with a permanent magnet synchronous machine. A back electromotive force induced in the stator winding systems due to the rotation of the permanent magnets placed in the rotor may generate a DC link ripple at 6 times the generator frequency, which in the case of a wind turbine may be about 6·8 Hz=48 Hz. Considering the product of this harmonic with the grid-side converter fundamental component, a voltage harmonic component with a frequency of 50+48=98 Hz may appear on the grid-side, which may be higher than the limit defined in relevant grid standards.

According to an embodiment of the disclosure, each voltage reference for an AC-to-DC converter is determined with a current controller for the respective AC-to-DC converter. When the number of AC-to-DC converters is N, then also the number of current controllers may be N.

According to an embodiment of the disclosure, the method further comprises: determining an average current, which is the average of the AC-side currents; and determining a differential current for each pair of branches, which differential current is the difference of the AC-side currents for the respective pair of branches. Before the average current and the differential currents are determined, a phase-shift of the AC-side currents may have to be compensated.

According to an embodiment of the disclosure, the method further comprises: determining an average voltage reference from the average current with an average current controller, such that the average current follows an average current reference; and determining a differential voltage reference for each differential current with a differential current controller, such that the differential current follows a differential current reference for the respective pair of branches.

For N branches (i.e. N stator winding systems, N AC-to-DC converters, N DC links, etc.), one average current and one average voltage reference as well as N−1 differential currents and N−1 differential current references are determined. The average voltage reference may be determined with an average current controller. Each differential current reference may be determined with a differential current controller. The average current controller and/or the differential current controllers may be standard dq-frame current controllers.

According to an embodiment of the disclosure, the method further comprises: determining the voltage reference for each branch from the average voltage reference and the differential voltage references. The AC-side currents have been transformed with a specific transformation into the average and differential currents. The voltage references for the AC-to-DC converters are determined with the inverse transformation, which is applied to the average voltage reference and the differential voltage references.

According to an embodiment of the disclosure, the converter reference correction is added to the average voltage reference. It is not necessary to correct the differential voltage references, since the corresponding voltages do not affect the average voltage of the coupled branches. Thus, it is possible to add the converter reference correction solely to the average voltage reference.

According to an embodiment of the disclosure, the converter reference correction is added to the average current reference. A further possibility is to already correct the average current reference, which is input into the average current controller. In this way, the average voltage reference is corrected indirectly, while the differential voltage references are not affected. Thus, it is possible to add the converter reference correction to the solely average current reference.

It has to be noted that the converter reference correction may have to be converted from a first system, in which it has been calculated (such as complex numbers) into a second system (such as a two-component vectors), in which the voltage references and/or current references, in particular the average voltage reference and/or the average current reference, are calculated.

According to an embodiment of the disclosure, the AC-side currents are transformed in a rotating reference frame, which rotates with a fundamental frequency of the AC-side currents and which eliminates a phase-shift of the AC-side current, before the voltage references are determined. In this reference frame the considered machine inductances have a constant value, even for electrical machines with saliency (e.g. permanent magnet generators). Furthermore, the current controllers also may be implemented easily in this reference frame.

According to an embodiment of the disclosure, the voltage references are transformed back to a stationary reference frame of the respective AC-side current considering the phase-shift of the AC-side current introduced by the geometrical displacement angle of the different winding systems and/or by the windings connection. After the voltage references have been determined by the current controllers and have been corrected with the help of the DC link ripple controller, the voltage references can be transformed back into a reference frame, in which the switching signals for the AC-to-DC converters can be determined.

According to an embodiment of the disclosure, the converter reference correction is added to the voltage references, before the voltage references are transformed back to a stationary reference frame of the respective AC-side current considering the phase-shift of the AC-side current. The converter reference correction may be determined in the same rotating reference frame as the voltage references and in particular the average voltage reference.

A further aspect of the disclosure relates to a computer program, which, when being executed on at least one processor of a converter system, is adapted for performing the method of one of the previous claims. A control system of the converter system may comprise one or more processors, which perform the method.

A further aspect of the disclosure relates to a computer-readable medium in which such a computer program is stored. A computer-readable medium may be a hard disk, an USB (Universal Serial Bus) storage device, a RAM (Random Access Memory), a ROM (Read Only Memory), an EPROM (Erasable Programmable Read Only Memory) or a FLASH memory. A computer-readable medium may also be a data communication network, e.g. the Internet, which allows downloading a program code. In general, the computer-readable medium may be a non-transitory or transitory medium. For example, a memory of the controller or the control system may be such a computer-readable medium.

A further aspect of the disclosure relates to a controller for a converter system, which is adapted for performing the method as described above and below. It has to be noted that the controller also may be at least partially implemented in hardware, for example with an FPGA and/or a DSP.

As described above, the controller may comprise sub-controllers. In particular, the controller may comprise a DC link ripple controller for determining the converter reference correction and/or at least two current controllers for determining the voltage references.

A further aspect of the disclosure relates to a converter system, which is controlled as described above and below.

The converter system comprises at least two branches, each branch comprising an AC-to-DC converter and a DC link cascade connected with each other; and a controller adapted for performing the method as described above and below.

Each AC-to-DC converter may be composed of NPC (neutral point clamped) half-bridges, in particular 3LNPC (three-level neutral point clamped) half-bridges.

The DC links of the branches may be split DC links, i.e. they may comprise two series-connected capacitors providing a positive, negative and neutral point (NP) to be connected to the AC-to-DC converter.

According to an embodiment of the disclosure, the converter system further comprises a rotating electrical machine. The rotating electrical machine may comprise at least two stator winding systems, each of which is connected to one of the AC-to-DC converters. There may be a branch for each stator winding system.

According to an embodiment of the disclosure, the rotating electrical machine is a generator and/or motor. The rotating electrical machine is a permanent magnet synchronous machine. Each branch may be adapted for a power transfer from the rotating electrical machine to an electrical grid and vice versa.

According to an embodiment of the disclosure, the converter system further comprises a transformer with at least two secondary winding systems, each secondary winding system connected to an DC-to-AC converter cascade connected with a DC link of the branches.

The branches of the converter system may be coupled via the transformer.

The secondary winding systems may be differently designed to have a phase-shift with respect to each other, such as a star-connected secondary winding system and a delta-connected secondary winding system.

Each DC-to-AC converter may be composed of NPC (neutral point clamped) half-bridges, in particular 3LNPC (three-level neutral point clamped) half-bridges.

The transformer furthermore may comprise a primary winding system connected to an electrical grid.

It has to be understood that features of the method as described in the above and in the following may be features of the computer program, the computer-readable medium, the controller and the converter system as described in the above and in the following, and vice versa.

These and other aspects of the disclosure will be apparent from and elucidated with reference to the embodiments described hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject-matter of the present disclosure will be explained in more detail in the following text with reference to exemplary embodiments which are illustrated in the attached drawings.

FIG. 1 schematically shows a converter system according to an embodiment of the disclosure.

FIG. 2 illustrates the definition of reference frames used in some embodiments of the disclosure.

FIG. 3 schematically shows a converter used in some embodiments of the disclosure.

FIG. 4 shows a block diagram of a controller according to an embodiment of the disclosure.

FIG. 5 shows a block diagram of a controller according to a further embodiment of the disclosure.

FIG. 6 shows a block diagram of an embodiment of a sub-controller of the controllers of FIGS. 4 and 5.

FIG. 7 shows a block diagram of a further embodiment of the sub-controller of FIG. 6.

The reference symbols used in the drawings, and their meanings, are listed in summary form in the list of reference symbols. In principle, identical parts are provided with the same reference symbols in the figures.

DETAILED DESCRIPTION

FIG. 1 shows a wind energy conversion system (WECS) 10 with a wind turbine 12 and a converter system 14. The converter system 14 comprises a generator 16, at least two conversion lines and/or AC-to-AC conversion branches 18, which interconnect the generator 16 with a transformer 20. The transformer 20 is connected to an electrical grid 22.

The generator 16 or more general rotating electrical machine 16 comprises at least two stator winding systems 24, which will be explained in more detail with respect to FIG. 2.

Each branch 18 is composed of a machine-side AC-to-DC converter 26, a DC link 28 and a grid-side DC-to-AC converter 30, which are cascade connected. The converters 26, 28 will be described in more detail with respect to FIG. 3. The machine-side AC-to-DC converters 26 may be modulated with either CB-PWM (Carrier-Based Pulse Width Modulation) or OPPs (Optimized Pulse Patterns). The grid-side DC-to-AC converters 30 may be modulated with OPPs.

Each of the converters 30 is connected to a secondary winding system 32 of the transformer 20, which may have a delta-wye configuration. The primary winding system 34 of the transformer 20, which is connected to the grid 22, may be in a wye configuration.

FIG. 1 also shows a controller 36 of the converter system 14, which is designed to control the branches 18 and in particular the converters 26, 30.

FIG. 2 shows the rotating electrical machine 16 in more detail. The rotating electrical machine 16 comprises a stator 38 with two or more stator winding systems 24, 24_I, 24_II and a rotor 40. In the case of the rotating electrical machine 16 being a permanent magnet synchronous generator, the rotor 40 may comprise permanent magnets. In another possible configuration the winding systems may be in the rotor and the permanent magnet in the stator.

In each stator winding system 24_I, 24_II, a generator current or AC-side current i_I^s, i_II^s from the point of view of the converters 26 is induced. The AC-side currents i_I^s, i_II^s rotate with respect to a stationary reference frame with the rotor electrical speed OR (for example in rad/s). This is the derivative of the rotor electrical angle θ_R (for example in rad). The stator winding systems 24_I, 24_II have a geometrical displacement, which results in an electrical displacement angle β, which also causes a phase shift −β between the AC-side currents i_I^s, i_II^s.

FIG. 3 shows a schematic circuit diagram of the converter 26 and/or the converter 30, which may be designed equally. Each converter 26 is connected between the DC link 28 and one of the stator winding systems 24. Each converter 30 is connected between the DC link 28 and one of the secondary winding systems 32. Each of the converters 26, 28 may be a back-to-back 3LNPC converter with three NPC half-bridges 42. The DC link 28 is a split DC link with two series-connected capacitors C.

In the case of the AC-to-DC converters 26, the components i_a, i_b, i_c of the AC current i are the components i_Ia^s, i_Ib^s, i_Ic^s of the machine-side AC current i_I^s of the first (I) branch 18 or the components i_IIa^s, i_IIb^s, i_IIc^s of the machine-side AC current i_II^s of the first (II) branch 18. These are the AC-side currents of the AC-to-DC converters 26.

FIGS. 4 and 5 show block diagrams of parts of the controller 36, which are used for controlling the AC-to-DC converters 26. The diagrams also illustrate methods for controlling the converter system 14.

At first, at least two AC-side currents i_I^s, i_II^s (here two) are determined, each of which is input into one of the AC-to-DC converters 26. For example, the AC-side currents i_I^s, i_II^s may be measured or otherwise estimated.

In general, the control of the currents i_I^s, i_II^s of the generator-side converters 46 takes place in a rotating reference frame which is aligned to the rotor permanent magnet flux. In their original form, the currents i_I^s, i_II^s are in a stationary reference frame and may have three components for each phase. In blocks 52, the AC-side currents i_I^s, i_II^s are transformed in a rotating reference frame (such as a dq reference frame), which rotates with a fundamental frequency OR of the AC-side currents i_I^s, i_II^s. Furthermore, a phase-shift −β of the AC-side current i_II^s is eliminated.

From the AC-side currents i_I^s, i_II^s, in the rotating reference frame, an average current i_av, which is the average of AC-side currents i_I^s, i_II^s, and a differential current i_diff is determined. In the case of more than two branches 18, a differential current i_diff is determined for each pair of branches 18.

A decoupling of quantities of the at least two winding systems 24 and/or the at least two branches 18 is achieved by considering the average and differential quantities. For a quantity x, the corresponding average and differential quantities can be calculated as follows:

$\begin{array}{cc}{x}_{\mathrm{av}}=\frac{x_I+x_{\mathrm{II}}}{2}& \left(1\right)\end{array}$ $\begin{array}{cc}{x}_{\mathrm{diff}}=\frac{x_I-x_{\mathrm{II}}}{2},& \left(2\right)\end{array}$

where the indices I and II correspond to the different winding systems 24 and/or branches 18.

The average current i_av is the sum of all AC-side currents i_I^s, i_II^s, optionally divided by the number of branches 18. The differential current i_diff is the difference of the AC-side currents i_I^s, i_II^s for a pair of branches 18, optionally divided by the number of branches 18.

The average current i_av is input into an average current controller 46, which determines an average voltage v_av^ref from the average current i_av. Also an average current reference i_av^ref is input into the average current controller 46 and the average voltage v_av^ref is determined, such that the average current i_av follows the average current reference i_av^ref. The average current reference i_av^ref may be provided by a superordinated controller.

The differential current i_diff (or each of the differential currents) is/are input into a differential current controller 46, which determines a differential voltage reference v_diff^ref for each differential current i_diff. Also a differential current reference i_diff^ref is input into the differential current controller 46 and the differential voltage reference v_diff^ref is determined, such that the differential current i_diff follows the differential current reference i_diff^ref for the respective pair of branches 18. The differential current reference i_diff^ref may be provided by the superordinated controller.

From the average voltage reference v_av^ref and the one or more differential voltage references v_diff^ref, the voltage references v_I^ref, v_II^ref for the branches 18 and in particular for the controllers 46 are determined. This can be done be the inverse transformation as defined in (1) and (2) above.

As will be explained in detail below, a converter reference correction 44 is determined by a DC link ripple controller 50. The converter reference correction 44 is determined, such that a higher order harmonic in the average DC link voltage v_dc,av is damped.

As shown in FIG. 4, the converter reference correction 44 may be added to the average voltage reference v_av^ref before the calculation of the voltage references v_I^ref, v_II^ref takes place. Alternatively, the average voltage reference v_av^ref is added to every voltage reference v_I^ref, v_II^ref after the back transformation from the average/differential system.

As shown in FIG. 5, the converter reference correction 44 may be added to the average current reference i_av^ref.

In blocks 54, the voltage references v_I^ref, v_II^ref are transformed back to the stationary reference frame of the respective AC-side current i_I^s, i_II^s considering the phase-shift −β of the AC-side current i_I^s, i_II^s. The phase-shift −β of the AC-side currents i_II^s is reproduced in the respective voltage reference v_II^ref.

In general, the converter reference correction 44 is added to the voltage references v_I^ref, v_II^ref or to the average current reference i_av^ref, before the voltage references v_I^ref, v_II^ref are transformed back to the stationary reference frame of the respective AC-side current i_I^s, i_II^s.

The overall result of the control are the corrected voltage references v_I^{s ref}, v_II^{s ref} for the AC-to-DC converter 26, which are used to control the AC-to-DC converters 26. From the corrected voltage references v_I^{s ref}, v_II^{s ref}, a converter switching function u_x∈{−1,0,1} (see FIG. 3) for each phase x∈{a, b, c} is determined for each converter 46 and applied to the respective converter 46.

In FIGS. 4 and 5, for simplicity, the symbol “+” in case of addition of two quantities is omitted. Only the symbol “−” is shown in case of subtraction. The symbol “{circumflex over ( )}” is used for the estimated quantities. Because of the considered asymmetry in the d- and q-axis inductances, matrix notation is used instead of space vector notation. Note that the AC-side/stator currents of each winding are in advance transformed into two-component quantities

$\begin{array}{cc}{i}_I^s=\left[\begin{array}{c}{i}_{I,\alpha }\\ i_{I,\beta }\end{array}\right]& \left(3\right)\end{array}$ $i_{\mathrm{II}}^s=\left[\begin{array}{c}{i}_{\mathrm{II},\alpha }\\ i_{\mathrm{II},\beta }\end{array}\right]$

The frame transformations in the two-component system are based on

$\begin{array}{cc}J=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]& \left(4\right)\end{array}$ $e^{J{\hat{\theta }}_R}=\left[\begin{array}{cc}\cos {\hat{\theta }}_R& -\sin {\hat{\theta }}_R\\ \sin {\hat{\theta }}_R& \cos {\hat{\theta }}_R\end{array}\right].$

In the present context, the motivation for determining and adding the converter reference correction 44 is the reducing of higher order harmonics in the output voltage of the converter system 14 at the primary winding system 34. The root cause of the harmonics is that the voltages induced in the generator stator winding systems 24 by the permanent magnet flux of the rotor (typically referred to as back electromotive force, BEMF) are not sinusoidal. They include harmonics at multiples of the fundamental frequency. The most important of them appear at 3, 5 and 7 times the fundamental frequency. The 5^th and 7^th order BEMF harmonics cause current harmonics at the same frequency, which in turn cause a ripple of the total DC link voltage v_dc at a frequency of 6f_G, where f_G is the fundamental frequency of the generator 16. The total DC link voltage v_dc for one of the DC links 28 is the sum of the voltages of the two halves of the DC link 28.

The oscillating part of the total DC link voltage v_dc can be expressed as follows:

$\begin{array}{cc}{v}_{\mathrm{dc}}\left(t\right)=-\frac{3}{2}\frac{1}{C}\int \mathrm{Re}\left\{{\overrightarrow{u}}_0\sum {\overrightarrow{i}}_h^{*}+\sum {\overrightarrow{u}}_h{\overrightarrow{i}}_0^{*}\right\}\mathrm{dt},& \left(5\right)\end{array}$

where î₀ and {right arrow over (u)}₀ are the space vectors that correspond to the fundamental harmonics of the current and the converter switching function respectively in the rotating reference frame. The integrand is the oscillating part of the DC link current i_dc. The quantities {right arrow over (i)}_h and {right arrow over (u)}_h are the space vectors that correspond to the rest of the switching function and current harmonics. The real part of a space vector is equal to the d-axis component of the corresponding quantity. The imaginary part of a space vector is equal to the q-axis component of the corresponding quantity.

Considering a constant ratio of the switching function to the output voltage {right arrow over (v)}₁/{right arrow over (u)}₁=v_dc/2, we can rewrite (5) as

$\begin{array}{cc}{v}_{\mathrm{dc}}\left(t\right)=-\frac{3}{2}\frac{1}{C}\frac{2}{v_{\mathrm{dc}}}\int \mathrm{Re}\left\{{\overrightarrow{v}}_0\sum {\overrightarrow{i}}_h^{*}+\sum {\overrightarrow{v}}_h{\overrightarrow{i}}_0^{*}\right\}\mathrm{dt}& \left(6\right)\end{array}$

The integrand in (6) is the oscillating part active power.

The generator-side induced DC link ripple harmonics appear also on the grid-side voltage and current. This happens because via the modulation process, they are multiplied with the grid-side converter switching function. For an OPP-modulated grid-side converter 30, the switching function contains all harmonics with orders that are not multiples of 2 or 3. The following harmonic transfer rules have been derived:

If the DC link voltage harmonic components in the branches 18 have a phase difference of 0, then sidebands around the grid-side switching function harmonics with orders v∈(12k±1), k∈₀ (1, 11, 13, 23, 25, . . . ) appear on the grid-side. The sidebands around the grid-side harmonic orders v∈(2k+1)·6±1, k∈₀ (5, 7, 17, 19, . . . ) are cancelled out between the converters 30, if the branches 18 and the transformer windings 32 are symmetrical.

If the DC link voltage harmonic components in the branches 18 have a phase difference of π, then sidebands around the grid-side switching function harmonics with orders v∈(2k+1)·6±1, k∈₀ (5, 7, 17, 19, . . . ) appear on the grid-side. The sidebands around the grid-side harmonic orders v∈(12k+1), k∈₀ (1, 11, 13, 23, 25, . . . ) are cancelled out between the converters 30, if the branches 18 and the transformer windings 32 are symmetrical.

If the DC link voltage harmonic components have an arbitrary phase difference, which is neither 0 nor π, then sidebands around all possible grid-side switching function orders v∈|1±6k|, k∈₀ (1, 5, 7, 11, 13, 17, 19, . . . ) appear on the grid-side.

From the above harmonic transfer rules it becomes apparent that the strongest possible harmonic components on the grid-side will appear as sidebands around the grid fundamental frequency, if the harmonic components of the DC link voltages v_dc have zero phase difference. In other words, the ripple that appears in the sum of the DC link voltages v_dc of the branches 18 is the most relevant quantity for the grid-side harmonics, since the product of this ripple with the fundamental component of the grid-side converter switching function generates strong grid-side voltage harmonics.

In general, a DC link ripple indicator, which is indicative of the average ripple in the DC links 28, may be used to control and reduce the average DC link ripple and in particular higher order harmonics in the ripple. For example, the sum and/or average value v_dc,av of the measured and/or estimated DC link voltages v_dc and/or the sum and/or average value i_dc,av of the measured and/or estimated DC link current i_dc and/or the sum and/or average value p_av of the measured and/or estimated active powers in each generator winding system 24 may be used as a DC link ripple indicator.

As described, the control of the converter system 14 and in particular the AC-to-DC converters 26 may be done via an average/differential current controller 46, 48. These controllers may be standard dq frame controllers and/or resonant controllers.

Therefore, it is convenient to also use a resonant controller for the DC link ripple controller 50, in which the DC link ripple indicator, such as the average DC link voltage v_dc,av and/or the average DC link current i_dc,av and/or the average active power p_av, is input.

In space vector notation, a resonant controller for the estimated average power p_av may be described by the following equation:

$\begin{array}{cc}\begin{array}{c}{\overrightarrow{v}}_{\mathrm{av},\mathrm{res}}=F_{r6,\mathrm{av}}\left(s\right)\left(-j{\hat{p}}_{\mathrm{av}}\right)\\ =k_{r6,\mathrm{av}}\left(\frac{e^{i{\phi }_{c6,\mathrm{av}}}}{s-j6{\omega }_R}+\frac{e^{-i{\phi }_{c6,\mathrm{av}}}}{s+j6{\omega }_R}\right)\left(-\mathrm{jRe}\left\{{\overrightarrow{\hat{v}}}_{\mathrm{av}}{{\overrightarrow{i}}_{\mathrm{av}}^{*}}_{}\right\}\right)\\ =2k_{r6,\mathrm{av}}\frac{s\cos \left({\phi }_{c6,\mathrm{av}}\right)-6{\omega }_R\sin \left({\phi }_{c6,\mathrm{av}}\right)}{s^2+{\left(6{\omega }_R\right)}^2}\left(\mathrm{jRe}\left\{{\overrightarrow{\hat{v}}}_{\mathrm{av}}{{\overrightarrow{i}}_{\mathrm{av}}^{*}}_{}\right\}\right),\end{array}& \left(7\right)\end{array}$

where {right arrow over (i)}*_av is the space vector of the average measured current and {circumflex over ({right arrow over (v)})}_av is the space vector of the estimated average converter output voltage. F_r6,av(s) is the transfer function of a SOGI (second order generalized integrator).

The estimated average active power p_av=Re{{circumflex over ({right arrow over (v)})}_av,{right arrow over (i)}*_av} that appears in the above equation can be replaced by the measured and/or estimated average DC link current i_dc,av:

$\begin{array}{cc}\begin{array}{c}{\overrightarrow{v}}_{\mathrm{av},\mathrm{res}}=F_{r6,\mathrm{av}}\left(s\right)\left(-j{î}_{\mathrm{dc},\mathrm{av}}\right)\\ =k_{r6,\mathrm{av}}\left(\frac{e^{i{\phi }_{c6,\mathrm{av}}}}{s-j6{\omega }_R}+\frac{e^{-i{\phi }_{c6,\mathrm{av}}}}{s+j6{\omega }_R}\right)\left(-\mathrm{jRe}\left\{{\overrightarrow{\hat{u}}}_{\mathrm{av}}{{\overrightarrow{i}}_{\mathrm{av}}^{*}}_{}\right\}\right)\\ =2k_{r6,\mathrm{av}}\frac{s\cos \left({\phi }_{c6,\mathrm{av}}\right)-6{\omega }_R\sin \left({\phi }_{c6,\mathrm{av}}\right)}{s^2+{\left(6{\omega }_R\right)}^2}\left(\mathrm{jRe}\left\{{\overrightarrow{\hat{u}}}_{\mathrm{av}}{{\overrightarrow{i}}_{\mathrm{av}}^{*}}_{}\right\}\right),\end{array}& \left(8\right)\end{array}$

In (8) the voltage space vector {circumflex over ({right arrow over (v)})}_av has been replaced by the switching function space vector {circumflex over ({right arrow over (u)})}_av.

The estimated average active power can be also replaced by the measured and/or estimated average DC link voltage v_dc,av:

$\begin{array}{c}\left(9\right)\end{array}$ ${\overrightarrow{v}}_{\mathrm{av},\mathrm{res}}=F_{r6,\mathrm{av}}\left(s\right)\left(-{\mathrm{jv}}_{\mathrm{dc},\mathrm{av}}\right)=2k_{r6,\mathrm{av}}\frac{s\cos \left({\phi }_{c6,\mathrm{av}}\right)-6{\omega }_R\sin \left({\phi }_{c6,\mathrm{av}}\right)}{s^2+{\left(6{\omega }_R\right)}^2}\left(-{\mathrm{jv}}_{\mathrm{dc},\mathrm{av}}\right)$

The average DC link voltage v_dc,av and/or the average DC link current i_dc,av and/or the average active power p_av may be calculated from the respective quantities of each converter 26 as follows (see (1) above):

$\begin{array}{cc}{v}_{\mathrm{dc},\mathrm{av}}=\frac{v_{\mathrm{dc},I}+v_{\mathrm{dc},\mathrm{II}}}{2},& \left(10\right)\end{array}$ $i_{\mathrm{dc},\mathrm{av}}=\frac{i_{\mathrm{dc},I}+i_{\mathrm{dc},\mathrm{II}}}{2},$ $p_{\mathrm{av}}=\frac{p_I+p_{\mathrm{II}}}{2}$

FIGS. 6 and 7 show two possible implementations of a DC link ripple controller 50. FIG. 6 shows a general SOGI (Second Order Generalized Integrator), while FIG. 7 shows a specific implementation of a SOGI.

In general, the DC link ripple indicator may be input to one or more SOGIs (Second Order Generalized Integrators) with a central frequency at the higher order harmonic. For example, the central frequencies may be at 6kf_G, k∈. For the BEMF harmonics considered above (5^th and 7^th), one SOGI at a frequency of 6f_G (6^th higher order harmonic of the fundamental frequency) may suffice.

The converter reference correction 44 may be determined from the DC link ripple indicator v_dc,av, i_dc,av, p_av with a second order generalized integrator with a central frequency at the higher order harmonic. The higher order harmonic may be the 6^th order harmonic.

In both implementations in block 56, the DC link ripple indicator v_dc,av, i_dc,av, p_av is provided as complex value. It has to be noted that the converter reference correction 44 may be provided with respect to a rotating reference frame rotating with a fundamental frequency of the AC-side currents i_I^s, i_II^s. In a first step the DC link ripple indicator v_dc,av, p_av is rotated by 90° by multiplication with −j, the imaginary unit. This rotation can be incorporated in the compensation angle φ_c6,av.

In the implementation of FIG. 6, in block 58, the SOGI is applied directly, such as described with respect to formulas (7)-(9) above. k_r,av is the gain of SOGI and φ_c6,av is the compensation angle of the SOGI. Instead of 6ω_R, other multiples k of k^th higher harmonic can be multiplied with the rotor electrical speed ω_R.

In the implementation of FIG. 7, in blocks 60, the DC link ripple indicator v_dc,av, i_dc,av, p_av is transformed into a rotating reference frame rotating with the frequency of the higher order harmonic, here with 6{circumflex over (θ)}_R or more general k{circumflex over (θ)}_R, where {circumflex over (θ)}_R is the estimated rotor angle. The rotation is performed with positive and negative angle, so that both sine and cosine terms are covered.

In blocks 62, a gain factor k_r6,av is multiplied with the transformed DC link ripple indicator v_dc,av, i_dc,av, p_av and in blocks 64, a compensation angle φ_c6,av is added to the phase of the transformed DC link ripple indicator 44 and the converter reference correction 44 is formed in this way. The compensation angle φ_c6,av may be 0, if the DC link ripple indicator is the average DC link voltage v_dc,av, and may be π/2, if the DC link ripple indicator is the average active power p_av or the average DC link current i_dc,av. This may mean that the output of the DC link ripple controller 50 has only an imaginary part in the former and only a real part in the two latter cases.

In blocks 66, the converter reference correction 44 is transformed back in the rotating reference frame rotating with a fundamental frequency of the AC-side current i_I^s, i_II^s by applying the inverse transformation of blocks 60.

In both implementations, in block 68, the complex-valued converter reference correction 44 is split up into real part and imaginary part to form a two-component vector, which can be added to the respective reference i_av^ref, v_av^ref. Together with this reference, the converter reference correction 44 is transformed in the end into a stationary reference frame of the respective AC-side current i_I^s, i_II^s considering the phase-shift −β of the AC-side current i_I^s, i_II^s (see FIGS. 4 and 5).

While the disclosure has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the disclosure is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art and practicing the claimed disclosure, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single processor or controller or other unit may fulfil the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope.

Claims

1. A method for controlling a converter system, the converter system comprising at least two branches, wherein each branch comprises an alternating current to direct current (AC-to-DC) converter and a DC link cascade connected with each other, and wherein the method comprises: determining at least two AC-side currents, each of which is input into one of the AC-to-DC converters;determining from the AC-side currents, a voltage reference for each of the AC-to-DC converters, such that the AC-side current follows a current reference for the respective AC-to-DC converter;determining a DC link ripple indicator, wherein the DC link ripple indicator is an average DC link voltage of the DC links, and/or an average DC link current of the DC links and/or an average active power input into the at least two branches;determining a converter reference correction from the DC link ripple indicator, such that a higher order harmonic in the average DC link voltage is damped;determining corrected voltage references for the AC-to-DC converter by adding the converter reference correction to the voltage references of the AC-to-DC converters or by adding the converter reference correction to an average current reference for the AC-to-DC converters; andcontrolling the AC-to-DC converters with the respective corrected voltage references.

2. The method of claim 1, wherein; the converter reference correction is determined with respect to a rotating reference frame rotating with a fundamental frequency of the AC-side currents, andthe converter reference correction is transformed into a stationary reference frame of the respective AC-side current considering the phase-shift of the AC-side current.

3. The method of claim 1, wherein; the converter reference correction is determined from the DC link ripple indicator with a second order generalized integrator with a central frequency at the higher order harmonic.

4. The method of claim 1, wherein: the DC link ripple indicator is transformed into a rotating reference frame rotating with the frequency of the higher order harmonic,the converter reference correction is determined from the DC link ripple indicator by multiplying a gain factor by the DC link ripple indicator, integrating it and/or adding a compensation angle to a phase of the DC link ripple indicator and/or to a phase of the output of the integrator, andthe converter reference correction is transformed back in a rotating reference frame rotating with a fundamental frequency of the AC-side current.

5. The method of claim 1, wherein the higher order harmonic is the 6th higher order harmonic.

6. The method of claim 1, further comprising: determining an average current, which is the average of AC-side currents, and a differential current for each pair of branches, which differential current is the difference of the AC-side currents for a pair of branches;determining an average voltage from the average current with an average current controller, such that the average current follows an average current reference;determining a differential voltage reference for each differential current with a differential current controller, such that the differential current follows a differential current reference for the respective pair of branches; anddetermining the voltage reference for each branch from the average voltage reference and the differential voltage references.

7. The method of claim 6, wherein the converter reference correction is added to the average voltage reference.

8. The method of claim 6, wherein the converter reference correction is added to the average current reference.

9. The method of claim 1, wherein: the AC-side currents are transformed in a rotating reference frame, which rotates with a fundamental frequency of the AC-side current and which eliminates a phase-shift of the AC-side current, before the voltage references are determined, andthe voltage references are transformed back to a stationary reference frame of the respective AC-side current considering the phase-shift of the AC-side current.

10. The method of claim 1, wherein the converter reference correction is added to the voltage references, before the voltage references are transformed back to a stationary reference frame of the respective AC-side current considering the phase-shift of the AC-side current.

11. A computer program, which, when being executed by at least one processor of a converter system, the at least one processor is configured to perform the method of claim 1.

12. A non-transitory computer-readable medium on which a computer program according to claim 11 is stored.

13. A controller for a converter system, which is adapted for performing the method of claim 1, wherein the controller comprises: a DC link ripple controller for determining the converter reference correction; andat least two current controllers for determining the voltage references.

14. A converter system, comprising: at least two branches, each branch comprising an AC-to-DC converter and a DC link cascade connected with each other; anda controller adapted for performing the method of claim 1.

15. The converter system of claim 14, further comprising: a rotating electrical machine,wherein the rotating electrical machine comprises at least two stator winding systems, each of which is connected to one of the AC-to-DC converters.

16. The converter system of claim 15, wherein; the rotating electrical machine is a generator and/or a motor, andthe rotating electrical machine is a permanent magnet synchronous machine.

17. The converter system of claim 14, further comprising: a transformer with at least two secondary winding systems, each secondary winding system connected to a DC-to-AC converter, which is cascade connected with a DC link of the branches,wherein the transformer comprises a primary winding system connected to an electrical grid