WO2015155183A1

WO2015155183A1 - Active damping control of an electrical converter with a resonant output filter

Info

Publication number: WO2015155183A1
Application number: PCT/EP2015/057512
Authority: WO
Inventors: Silvia Mastellone; Tobias Geyer; Gregory Stephen LEDVA
Original assignee: Abb Technology Ag
Priority date: 2014-04-09
Filing date: 2015-04-07
Publication date: 2015-10-15
Also published as: EP2992596A1

Abstract

An electrical converter (10) comprises at least one output phase (16) connected via a electrical filter (20) with an electrical grid (22) or an electrical machine. A method for controlling the electrical converter (10) comprises: receiving a control reference (24) for the electrical converter; determining voltages and/or currents (26) in the electrical converter; determining switching positions (u) for semiconductor switches (14) of the electrical converter from the control reference (24) and the determined voltages and/or currents, based on model predictive direct control (32) such that a deviation from the control reference is minimized; and actively damping oscillations in the at least one output phase caused by the electrical filter.

Description

Active damping control of an electrical converter with a resonant output filter FIELD OF THE INVENTION

The invention relates to the field of active damping control of medium and high power converters. In particular, the invention relates to a method and a controller for actively damping the oscillations in an electrical converter. BACKGROUND OF THE INVENTION

Electrical converters are used for supplying an electrical motor with electrical power, for supplying the electrical power generated by a generator or solar cells into an electrical grid and for interconnecting two electrical grids. Examples are solar power generation, wind power generation, regenerative braking in rail systems, interfaces between high voltage DC grids and AC transmission systems, and flexible AC transmission system devices.

In an electrical converter, power electronics is used to produce waveforms and frequencies that are suitable for the specific application. In particular, an electronic controller measures currents and voltages in the converter and produces switching commands to switch power semiconductors such that the converter output follows specific references. For reducing oscillations and/or harmonics in the output current, a series inductor, or L- filter, may be used as the interface between the output of the converter and the connection with the grid. When using an L-filter, achieving acceptable harmonic content within the injected current usually requires high switching frequencies. Because the switching frequency is proportionally related to the switching losses of the power converter, a major part of the overall losses of the converter, any reduction of the switching frequency may have a significant impact on the operational cost of the converter and may increase the overall robustness and reliability.

Replacing the L-filter with an LCL-filter allows better attenuation of the high-frequency oscillations, which allows decreased switching frequencies and reduced switching losses. Using an LCL-filter, however, introduces difficulties into the control scenario: a resonant frequency within the system and a delay between the input and output of the LCL-filter. These difficulties result in waveform properties that are not suitable for injection into the grid when using a standard control structure. Extending the control to include active damping has been shown to provide suitable performance in the given control scenario. A control method for controlling the converter may be model predictive direct current control, as described in more detail in Ramirez Martinez, Juan C; Kennel, R.M.; Geyer, T., "Model predictive direct current control," Industrial Technology (ICIT), 2010 IEEE International Conference, pp.1808, 1813, 14-17 March 2010 and as described in EP 1 670 135 A1.

Active damping in model predictive direct current control is addressed in Scoltock, James; Geyer, Tobias; Madawala, Udaya, "Model Predictive Direct Current Control for a grid-connected converter: LCL-filter versus L-filter, "Industrial Technology (ICIT), 2013 IEEE International Conference, 576-581 , 2013, IEEE.

EP 2 546 979 A1 relates to a method for controlling harmonics and resonances in an inverter controlled by model predictive direct torque control.

LINDGREN M ET AL: "Control of a voltage-source converter connected to the grid through an LCL-filter-application to active filtering", POWER ELECTRONICS SPECIALISTS CONFERENCE, 1998. PESC 98 RECORD. 29TH A NNUAL IEEE FUKUOKA, JAPAN 17-22 MAY 1998, NEW YORK, NY, USA, IEEE, US, vol. 1 , 17 May 1998 (1998-05-17), pages 229-235, shows a controller, in which a difference of a measured capacitor voltage and a reference capacitor voltage is used for modifying a reference current.

SERPA L A ET AL: "A Modified Direct Power Control Strategy Allowing the Connection of Three-Phase Inverters to the Grid Through Filters", IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, IEEE SERVICE CENTER, PISCATAWAY, NJ, US, vol. 43, no. 5, 1 September 2007 (2007-09-01 ), pages 1388-1400, shows a controller, in which a reactive power of a capacitor of a filter is determined from a capacitor current (see page 1390, Fig. 3).

HOFF BJARTE ET AL: "Cascaded model predictive control of voltage source inverter with active damped LCL filter", 2013 IEEE ENERGY CONVERSION CONGRESS AND EXPOSITION, IEEE, 15 September 2013 (2013-09-15), pages 41 19-4125, shows a controller based on model predictive control, in which also current in an LCL filter are considered (see, for example, Fig. 1 and equations (7) to 13).

GEYER T ET AL: "Model Predictive Direct Torque Control-Part I: Concept, Algorithm, and Analysis", IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, IEEE SERVICE CENTER, PISCATAWAY, NJ, USA, vol. 56, no. 6, 1 June 2009 (2009-06-01 ), pages 1894- 1905, relates to model predictive control based on torque for a converter without considering an electrical filter. DESCRIPTION OF THE INVENTION

It is an objective of the present invention to reduce losses and therefore to reduce costs of power converters. In particular, an overall performance for grid-connected, medium voltage power converters may be improved.

These objectives may be 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 invention relates to a method for controlling an electrical converter, the electrical converter comprising at least one output phase connected via a (for example resonant) electrical filter with an electrical grid or an electrical machine. The electrical grid may be a large scale distribution grid, for example a medium or high voltage grid. The electrical machine may be a generator or a motor.

Usually, the electrical converter, the grid and the electrical machine may comprise three phases and the electrical filter may comprise three filter branches connected in parallel. The electrical filter or each of its branches may comprise at least one inductor and at least one capacitor.

In the case, the converter comprises at least two output phases, the filter may comprise at least one inductor for each phase interconnecting the converter with the grid or machine and/or at least one capacitor for each phase interconnecting the output phase with a grounding point.

According to an embodiment of the invention, the method comprises receiving a control reference for the electrical converter, determining voltages and/or currents in the electrical converter, determining switching positions for semiconductor switches of the electrical converter from the control reference and the determined voltages and/or currents, based on model predictive direct control such that a deviation from the control reference is minimized, and actively damping oscillations in the at least one output phase caused by the electrical filter. The oscillations may be based on current and/or voltage harmonics caused by the electrical filter.

In other words, based on a control reference (as a rule, a stream of reference values) and for example measured currents and/or voltages of the inverter, switching positions may be determined by a controller, which is based on model predictive direct control. Oscillations in the output phase or output phases are actively damped by the controller, for example in an outer control loop or inside the model predictive direct control scheme. The control reference may be at least one of a torque reference, a flux reference, a current reference. The control reference may be derived from other references, such as a reactive power reference and/or an active power reference.

According to the invention, the oscillations are actively damped by including a reference correction to a bound and/or constraint of the model predictive direct control and/or in a cost function of the model predictive direct control. The model predictive control method is based on a set of equations modelling the dynamic behaviour of the inverter and optionally the interconnected grid or machine, a cost function which may model the switching losses of the converter and constraint equations, for example modelling physical limits of the components of the converter. In these equations, the control reference may be replaced with a corrected control reference, which may be the sum of the control reference and a reference correction.

Furthermore, an additional term based on a control reference error is added to the cost function when the control reference error exceeds a predefined bounding value. In such a way, model predictive direct control provides incentives on candidate sequences that satisfy predefined active damping bounds.

The reference correction may be based on a difference between future values of future states of the converter and future reference values, which are determined in model predictive direct control. For example, the equations used for calculating the reference correction with the aid of a virtual voltage source and/or with a feedback matrix may be used in every time step of the model predictive control.

According to an embodiment of the invention, the reference correction is included in every future time step that is determined in model predictive control. Contrary to the approaches with the reference correction generated in the outer control loop, the reference correction may be calculated and used for every future time step considered by the model predictive direct control.

According to an embodiment of the invention, the constraint modified with the reference correction limits a control reference error to an interval. Thus, the limited control reference error, that is used for selecting and discarding candidate sequences, may be based on a difference between a future control variable and a future control reference corrected with the reference correction.

According to an embodiment of the present disclosure, the oscillations are actively damped by adding a reference correction to the control reference, wherein the reference correction is based on a difference between a measured voltage of a capacitor of the electrical filter and a capacitor voltage reference determined from a further control reference of the electrical converter. For example, the reference correction may be calculated in an outer control loop, wherein in the inner control loop, the switching positions are determined on model predictive direct control, which is based on the corrected control reference. According to an embodiment of the invention, the reference correction is determined based on a virtual circuit comprising a virtual resistor and a virtual voltage source connected in parallel to the capacitor of the electrical filter. The virtual voltage source may provide the capacitor voltage reference. In case, the reference correction is a current reference correction, it may be proportional to the difference between the measured capacitor voltage and the capacitor voltage reference divided by the virtual resistance.

According to an embodiment of the invention, the capacitor voltage reference is determined from a reference active power and/or a reference reactive power.

Both reactive powers may relate to the product of capacitor current and capacitor reference voltage. With the actual or reference phase of the output current, the capacitor reference voltage may be calculated from these two reference powers.

The reference powers also may be used in an outer control loop for determining the control reference, such as a current reference.

According to an embodiment of the present disclosure, the oscillations are actively damped by adding a reference correction to the control reference, wherein the reference correction is calculated via a feedback matrix, which is multiplied by a vector formed of current and voltage correction terms determined from voltages and currents measured in the electrical filter.

Alternatively or additionally, the reference correction provided by an outer control loop may be calculated directly from the currents and/or voltages measured in the circuitry of the electric filter. For example, the voltages and currents measured in the electrical filter may comprise at least a capacitor voltage and a grid current. The reference correction may depend linearly on these currents and/or voltages.

According to an embodiment of the invention, the feedback matrix is calculated offline from a model of the electrical filter by solving a linear-quadratic regulator, which is based on a mathematical model of the electrical filter. For example, the linear-quadratic regulator may comprise a first set of equations quadratic in the oscillations and a second set of linear equations modelling the dynamic behaviour of the electrical filter.

According to an embodiment of the invention, the current and voltage correction terms are determined by subtracting a fundamental frequency from the voltages and currents measured in the electrical filter. For example, the fundamental frequency may be determined from a grid frequency of a grid connected to the inverter and/or by a frequency analysis of the voltages and currents measured in the electrical filter.

In the approaches with the virtual voltage source and the feedback matrix, the reference correction may be determined in an outer control loop and the switching positions are determined in an inner control loop. However, it is also possible that the active damping is performed inside the model predictive direct control, i.e. in the inner control loop.

According to an embodiment of the invention, the model predictive direct control is model predictive direct current control, model predictive direct torque control or model predictive direct power control.

According to an embodiment of the invention, the model predictive direct control comprises determining candidate sequences of future states of the electrical converter based on the determined actual voltages and/or currents and on an actual switching state of the converter, wherein the sequences are determined from a mathematical model of the converter, determining a cost value for each candidate sequence by applying a cost function to the candidate sequence, the cost function modelling switching losses of the converter, determining the switching positions from a next future state of a candidate sequence with a smallest cost value.

A further aspect to the invention relates to a controller for an electrical converter adapted for performing the steps of the method as described in the above and in the following. It has to be understood that features of the method as described in the above and in the following may be features of the controller as described in the above and in the following and vice versa.

The method may be implemented in the controller as software running on a processor or may be at least partially implemented in hardware. It may be implemented in a FPGA and/or a DSP.

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

BRIEF DESCRIPTION OF THE DRAWINGS

The subject-matter of the invention 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 with a controller according to an embodiment of the invention.

Fig. 2 shows a flow diagram for a control method according to an embodiment of the invention. Fig. 3 shows schematically a filter with a virtual voltage source for a control method according to an embodiment of the invention.

Fig. 4 shows a control diagram for a control method according to an embodiment of the invention.

Fig. 5 shows a control diagram for a control method according to an embodiment of the invention.

Fig. 6 shows a control diagram for a control method according to an embodiment of the invention.

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 OF EXEMPLARY EMBODIMENTS

Fig. 1 schematically shows an electrical converter 10, comprising a DC link 12 and semiconductor switches 14 that are adapted for connecting the output phases 16 of the converter with DC+, DC- and a neutral point. The switch positions u_a, Ub, and u_c of the switches 14 within the converter 10 are assumed to be controlled by model predictive direct control by a controller 18. The switch positions u_a, Ub, and u_c induce the phase currents i_a, ib, and i_c in the converter-side of an LCL-filter 20.

Fig. 1 shows a neutral point clamped, three-phase, three-level converter, however, every type of converter may be used in the following.

The converter 10 is connected via the LCL-filter 20 with an electrical grid 22, which is indicated as three voltage sources. However, the converter 10 also may be connected to an electrical machine instead of the grid 22.

For each phase, the LCL-filter 20 comprises a converter-side inductance L, a converter- side resistance R, a filter capacitor C, a grid-side resistance R_g, and a grid-side inductance L_g, which may also be provided by physical resistors, inductances and capacitors. The phase branches of the filter 18 are star-connected via the filter capacitors C.

Via the filter 20, the converter 10 injects grid currents i_ga, igb, and i_gc into the grid 22. These injections are opposed by the ideal, AC voltage sources V_ga, V_gb, V_gc in each phase that represents the phase voltages of the grid 22.

In the physical system if Fig. 1 , there may be the difficulty that the LCL-filter 20 renders the grid injections not directly controllable. Specifically the LCL-filter 20 may cause significantly slower dynamics on the grid-side than on the converter-side of the system. This means that effective regulation of the injected grid currents i_ga, igb, igc may be no longer achievable by model predictive control not considering the filter 20. Furthermore, the LCL- filter 20 contains resonant frequencies, which may imply that a regulation of the filter output is necessary to produce suitable injections into the grid 22.

A specific resonance of interest is the resonance between the converter-side and grid- side currents. This resonance amplifies the oscillations produced within the converter 10 and may result in large amounts of distortion within the injected grid currents i_ga, igb, igc The resonance can be calculated as:

= ¹ where L_g corresponds to the grid-side inductance and C corresponds to the filter capacitor. The resonance f_res may induce oscillations in the grid currents i_ga, igb, and i_gc that may have to be actively damped.

Fig. 2 shows a flow diagram for a method for controlling the converter 10 with model predictive direct control.

In step S10, a control reference 24 for the electrical converter is received in the controller 18. For example, the control reference 24 may be a current reference i_ref(k). As may be seen from the time-step parameter k, the control reference 24 may be time-depended.

In steps S12, voltages and/or currents 26 of the electrical converter 10 and the electrical filter 20 are determined, for example measured or calculated from other measurement values. In particular, the currents i_ga, igb, i_gc and the capacitor voltages V_ca, V_Cb, V_cc may be measured. These values may be summarized as actual state x(k).

In step S14, the next switching positions u(k) for the semiconductor switches 14 are determined from the control reference 20, the determined voltages and/or currents 26 and the actual switching positions u(k-1 ).

Step S14 is based on model predictive direct control, which is explained with respect to substep S14a to S14c of step S14.

In substep S14a, candidate sequences s'(k) of future states of the electrical converter 10 are determined based on the determined actual voltages and/or currents 26 (or more general the actual state x(k)) and on the actual switching state u(k-1 ) of the converter 10. The sequences s'(k) are determined from a mathematical model of the converter 10, which comprises dynamic equations and constraints modeling the converter 10 and optionally the filter 20. In substep S14b, a cost value c' is determined for each candidate sequence s'(k) by applying a cost function to the candidate sequence. For example, the cost function may model switching losses of the converter 10 and may be quadratic in the future states.

In substep S14c, the next switching positions or next switching state u(k-1 ) is determined from the first future state of the candidate sequence with the smallest cost value.

In the following, three solutions are described that allow reduced harmonic distortion while requiring less switching effort from the converter 10.

In general, each of the presented active damping methods may achieve an undistorted error, or ripple, signal by calculating reference values for the measured quantities. The reference values represent the desired value of the measurements and by subtracting the reference from the measurement, an undistorted signal composed of the unwanted oscillations is achieved.

The reference values may be constructed using steady-state analysis of the system (i.e. converter 10 and filter 20) and the assumption that the desired power injection set-points are known. This assumption is valid as these define the desired performance of the control system. The required current injection may be calculated using the desired power injection and the measured or estimated voltage and frequency of the grid 20. The impedances of each branch within the LCL-filter can be calculated using the measured or estimated frequency, and values can then be generated for the desired capacitor voltage and converter current. Furthermore, these references may be projected forward in time using the expected angle of the grid voltage. Each of the active damping methods described below may implement this technique.

Virtual Voltage Source

In the first method, as indicated in Fig. 3, damping effects are simulated by placing an virtual resistor 28, RVR and a virtual voltage source 30, Vc^ref within the branch of the filter 30.

Fig. 3 shows a branch or a single phase of the system of converter 10, filter 20 and grid 22 and indicates the location of the simulated virtual resistor 28 and virtual voltage source 30 within the filter 20.

The virtual voltage source 30 injects a voltage into the virtual resistor 28 that opposes the physical voltage V_c across the capacitor C. By simulating a voltage Vc^ref equal to the capacitor's reference voltage, only the unwanted ripple in the capacitor voltage V_c induce a current through the virtual resistor 28. The resulting change in the control reference 24 may be based solely on ripple quantities within the system, and so only unwanted oscillations may be damped. The fundamental components may be unaffected and no additional measures must be taken to ensure the desired power injections are achieved.

Fig. 4 shows that this alternative may be implemented in an inner control loop 32 that performs the model predictive direct control (for example as described with respect to Fig. 2) and an outer control loop 34 that performs the calculation of a reference correction 36, such as a current reference correction Ai_ref(k).

The inner control loop 32 receives a corrected control reference 38 (here a corrected current reference f(k)), which is the sum of control reference 24 and reference correction 38, and determines the next switching positions u(k) from actual states x(k) and actual switching position u(k-1 ). The switching positions u(k) are applied to the physical system of converter 10 and filter 20.

The outer control loop 34 comprises a reference calculation unit 40 that receives the grid voltage V_g(k) and further references 42, such as an active power reference P^ref(k) and a reactive power reference Q^ref(k) from which the actual capacitor voltage reference Vc^ref(k) is calculated. The actual capacitor voltage reference Vc^ref(k) is subtracted from the actual measured capacitor voltage Vc^ref(k) and the result is divided by the virtual resistance RVR, which yields the current reference correction Ai_ref(k).

Summarized, the oscillations are actively damped by adding a reference correction 36 to the control reference 24, wherein the reference correction 36 is based on a difference between a measured voltage V_c of a capacitor C of the electrical filter 20 and a capacitor voltage reference Vc^ref determined from a further control reference 42 of the electrical converter.

Overall, this control method provides improved stability in the control algorithm, reduces complexity of the required control algorithm, and provides reductions in the required switching frequency for a given level of harmonic distortion.

Linear-Quadratic Regulator

Fig. 5 shows a diagram analogously to Fig. 4. However, the outer control loop 34 comprises an active damping unit 44 that determines the reference correction 36 directly from the actual state x(k) of the system 10, 20.

Similarly to Fig. 4, the reference correction 36 is added to the control reference 24, before it is provided to the inner control loop 32. However, the reference correction 36 is calculated via a feedback matrix as described below, which is multiplied by a vector formed of current and voltage correction terms determined from voltages and currents, such as V_c and i_g (which are a part of the actual state x(k)) measured in the electrical filter 20. It has to be understood that the linear-quadratic regulator method and/or control of Fig. 5 may be combined with the virtual voltage source method and/or control of Fig. 4.

The method of Fig. 4 may perform active damping based solely on the measured, existing ripple within the one point of the system. The linear-quadratic regulator method uses a dynamic model of the system 10, 20 to predict future oscillations within the system, and cancels them using a reference correction 36 that may be optimal over an infinite horizon.

The general formulation of the linear-quadratic regulator scheme may be summarized as: minimize = x Ί / 1 O ,r{ I )— t ff ) J? u(l)

P M

i=k

subject to x(l + 1) = , x(l) + B u(l).

The linear-quadratic regulator scheme is initialized using the present state x(k) of the system 10, 20, and determines optimal control actions u(l), that drive the future states x(l), to zero with minimal cost over an infinite horizon of predictions. The states are constrained by a dynamic model of the system 10, 20 that updates the value from a given prediction time-step, x(l), to the next prediction time-step, x(l+1 ), based on the control action u(l) taken, and a mathematical representation of the dynamic system. This representation is concisely described as the A and B matrices where the A matrix describes the interaction of the states and the B matrix describes the influence of the system input.

The costs are determined based on the Q and R matrices, which define costs for each element in x and u that differ from 0. This means that penalties are accrued for any errors in the states as well as any necessary control effort. These matrices may be tuned by the user to achieve a desired performance. The solution of the linear-quadratic regulator formulation may be solved offline (i.e. before the converter 10 is operating, for example while programming the controller 18), and results in a feedback matrix K that determines the optimal control action at the present time based solely on the present state of the system:

Ai^ref(k) = K x'(k) k e 1₊

Here, the values x'(k) are the oscillations of the respective state variables x(k).

One of the major benefits of this method is that the K matrix is pre-computed offline based solely on the underlying model of the system and the user-defined Q and R matrices. This leads to a very simple, yet highly effective algorithm for determining reference changes. The active damping method performed by the active damping unit 44 may be described as follows:

In a first step, receive the measure states x(k) of the system 10, 20, including the voltage Vc across the capacitor and the grid current and i_g.

In a second step, determine the ripple components (i.e. oscillations and/or harmonics) of the measurements. The oscillations may be determined based on the corresponding calculated voltage and current references by subtracting the measured values from the reference values. It may also be possible to determine the oscillations by a frequency analysis (such as a Fourier analysis) and by discarding the fundamental frequency components.

In a third step, use the ripple measurements and the optimal K matrix to determine an optimal control reference 36.

Using linear-quadratic regulator based decisions for active damping reference corrections 36 allows the incorporation of model-based predictions of oscillations within the decision. Furthermore, the reference corrections 36 are based on optimal control techniques, which results in reduced switching frequencies in the converter 10. A linear- quadratic regulator based active damping method also leads to more stable control within the converter 10, meaning that model predictive control 32 does not result in as many deadlocks.

Integrated active damping

As a further alternative, a method for integrating active damping into the model predictive direct control inner loop 32 is provided. Fig. 6 shows a diagram similar to diagrams 4 and 5 illustrating this method.

The outer loop methods of Fig. 4 and 5 may exclude valuable, known information about the future reference changes when selecting a switch position within the model predictive direct control method. These reference changes are known because once the system state is measured, estimated, or predicted for a given time, the reference change is based on a deterministic control law that depends only on the new value of the system states.

Furthermore, an outer loop may be eliminated and the reference changes can be directly determined within the model predictive direct control method. However, it may also be possible to combine this method with the methods of Fig. 4 and/or 5. To implement these changes in the model predictive direct control method, an additional constraint is added to update the reference currents within the model predictive direct control method algorithm and an additional cost term is added to the objective function.

The new constraint is used for calculating reference corrections at all time-steps within the prediction horizon. This constraint can be summarized as follows:

Ai^rei(V) = - K (x(l) - ^ref( ) I = k + 1. - - · . k + N_p x(l + 1) = A x(l) + B u(l) I = k, -^■■ , k + N_p - l

Here, the first equation determines a change in reference based on the measured or predicted states and the state references. The reference corrections may accommodate either the virtual voltage source or linear-quadratic regulator scheme described above. However, the reference corrections now occur at each time-step within the model predictive direct control method.

The second equation is usually already present within the model predictive direct control method. However, it is provided here to show how state predictions are updated, which then leads to updated reference corrections.

For incorporating the reference corrections into the model predictive direct control method, two separate references, i.e. a power reference and an active damping reference, are defined.

The power reference is externally provided based on the power set-points. An active damping update is calculated at the initial time-step of the prediction horizon, and this constant value for the reference correction is applied at all prediction time-steps. The model predictive direct control candidacy definition is applied to this reference.

The power reference implements a reference change based solely on the measured system quantities, and this change mirrors active damping operating in an outer loop. The power reference can be summarized as:

-<¾ < *( - (i^ref ( + Δΐ"^!ί (k)) < ¾ I = k + 1 , - - · , k + V„. .

where Ai^ref(k) is a reference change based on the measured system state.

The active damping reference is a current reference for active damping. It is constructed from modifications to the power reference after each state prediction.

The active damping reference is then used to incorporate a new cost in the objective function. The additional cost can be summarized as: ^ref(I) +

Here, an error is defined as the converter current's deviation from the active damping reference. A penalty is applied for any time-step where the error exceeds a predefined limit. This is then summed over the horizon and normalized by the horizon length. This provides incentives to trajectories that satisfy the active damping bounds and are valid for longer periods.

Summarized, with this method, actively damping may be performed by including a reference correction to a constraint of the model predictive direct control and/or in a cost function of the model predictive direct control. The reference correction is based on a difference between future values of future states of the converter and future reference values, which are determined in model predictive direct control.

With this method, active damping may be accounted for at all time-steps within the prediction horizon.

Including active damping described above with respect to the Fig. 3 to 6 allows reductions in switching frequency and system distortion by anticipating the active damping control actions. Furthermore, including this information also allows the stability of the control scheme to be improved by implementing switch positions that better satisfy the future bounds.

While the invention 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 invention 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 practising the claimed invention, 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. LIST OF REFERENCE SYMBOLS

10 converter

12 DC link

14 semiconductor switches

16 phase output

18 controller

20 filter

22 grid

24 control reference

26 voltages and currents

28 virtual resistor

30 virtual voltage source

32 inner control loop

34 outer control loop

36 reference correction

38 corrected control reference

40 reference calculation unit

42 further control reference

44 active damping unit

Claims

1. A method for controlling an electrical converter (10), the electrical converter (10) comprising at least one output phase (16) connected via a electrical filter (20) with an electrical grid (22) or an electrical machine, wherein the method comprises:

receiving a control reference (24) for the electrical converter;

determining voltages and/or currents (26) in the electrical converter;

determining switching positions (u) for semiconductor switches (14) of the electrical converter from the control reference (24) and the determined voltages and/or currents, based on model predictive direct control (32) such that a deviation from the control reference is minimized;

wherein the model predictive control is based on a set of equations modelling the dynamic behaviour of the converter, a cost function and constraint equations;

actively damping oscillations in the at least one output phase caused by the electrical filter by:

adding an additional term based on a control reference error to the cost function, when the control reference error exceeds a predefined value.

2. The method of claim 1 ,

wherein a constraint of the model predictive control limits the control reference error to an interval.

3. The method of claim 1 or 2,

wherein the control reference error is based on a difference between a future control variable and a future control reference corrected with the reference correction.

4. The method of one of the preceding claims,

wherein the control reference (24) includes at least a torque reference, a flux reference, a current reference.

5. The method of one of the preceding claims, wherein the model predictive direct control is model predictive direct current control or model predictive direct power control.

The method of one of the preceding claims, wherein the model predictive direct control comprises:

determining candidate sequences (S') of future states of the electrical converter (10) based on the determined actual voltages and/or currents and on an actual switching state of the converter, wherein the sequences are determined from a mathematical model of the converter;

determining a cost value (c') for each candidate sequence (S') by applying a cost function to the candidate sequence, the cost function modeling switching losses of the converter;

determining the switching positions (u) from a next future state of a candidate sequence (S') with a smallest cost value (c').

A controller (28) for an electrical converter (10) adapted for performing the steps of the method of one of claims 1 to 6.