Model Predictive Pulse Mode Control Based on Small Signal Pulse Mode Optimization

Abstract

A method for controlling an electrical converter system (10) comprises determining a nominal pulse pattern (t * p,i ,Δu * p,i ) and a reference trajectory (x) of at least one electrical quantity of the electrical converter system (10) * ), where the nominal pulse mode (t * p,i ,Δu * p,i ) and the reference trajectory (x * ) is determined from the optimized pulse pattern table, the nominal pulse pattern (t * p,i ,Δu * p,i ) includes a switching transition (Δu) between the output voltages of the electrical converter (12) of the electrical converter system (10) * p,i ), and the reference trajectory (x * ) indicates the expected future development of the power of the converter system (10); determining the small signal pulse mode by minimizing the cost function. The cost function includes a small signal error, which is based on the reference trajectory (x * ) and the predicted trajectory (x), where the pulse intensity of the small signal pulse mode (λ p,i ) in nominal pulse mode (t * p,i ,Δu * p,i ), and wherein the predicted trajectory (x) is obtained from the measured values ​​(i,v c ,i g ) and the model of the converter system (10) are determined within the range, the nominal pulse mode (t * p,i ,Δu * p,i ) and the sum of the small-signal pulse patterns are input to the model; by shifting the nominal pulse pattern (t * p,i ,Δu * p,i ) to determine the modified pulse pattern (t opt,p,i ,Δu p,i ), where the switching transition is shifted by a time interval such that the time interval multiplied by the direction of the switching transition equals the pulse intensity (λ p,i ) to encode a voltage-time value at a nominal switching transition; and to convert at least the modified pulse pattern (t opt,p,i ,Δu p,i) is applied to the electrical converter system (10).

Description

Technical Field

[0001] The present invention relates to the field of control of electrical converters. In particular, the present invention relates to a method, a computer program, a computer-readable medium and a controller for controlling an electrical converter system. Additionally, the present invention relates to an electrical converter system. Background Art

[0002] Optimized pulse mode (OPP) is particularly suitable for medium voltage converters because they have low total harmonic distortion (THD) at low switching frequencies. In order to achieve fast closed-loop control and suppress disturbances, model predictive control (MPC) methods are promising in power electronics applications. Specifically, model predictive pulse mode control (MPC) 3 C) can be seen as an adaptation of the MPC principle to the OPP control problem. 3 C controls the stator flux vector of the motor along its nominal trajectory by manipulating the switching moments of the OPP. For example, EP 2 469 692 A1 describes such a method, in which the switching moments of an optimized pulse pattern are modified to reduce the flux error.

[0003] However, MP 3 C is usually only applicable to first-order systems, such as motors. For these, the stator flux in the orthogonal coordinate system is the integral of the applied converter voltage (when neglecting the voltage drop due to the stator resistance). When considering higher-order systems, such as converters with LC filters, MP 3 The internal model of C may not capture the resonant behavior of the power converter circuit. To account for this, MP 3 C may need to have an additional damping term added to its cost function, or an external damping loop must be added. While these approaches may be effective during steady-state operation, performance during large transients may be quite poor. More specifically, to avoid exciting the filter resonance too strongly, large reference step changes may have to be filtered by a slope limiter, resulting in a slow step response.

[0004] WO 2016 / 134874 A1 relates to an optimized time shifting of the switching instants of a pulse mode. The time shifting is accomplished using model predictive control, where an objective function based on the flux error is minimized.

[0005] The following articles deal with converter control based on model predictive control and mention the linearization of the optimization problem:

[0006] Quevedo et al., “Model Predictive Control for Power Electronics Applications,” Springer International Publishing, Handbook of Model Predictive Control, pp. 551–580, November 30, 2018 (2018-11-30)

[0007] Geyer et al., “Hybrid Model Predictive Control of the Step-Down DC-DC Converter,” IEEE Transactions on Control Systems Technology, Vol. 16, No. 6, pp. 1112–1124, IEEE Service Center, New York, NY, November 1, 2008.

[0008] Cairano et al., “Model predictive controller matching: Can MPC enjoy small signal properties of my favorite linear controller?” IEEE 2009 European Control Conference (ECC), August 23, 2009, pp. 2217–2222. Summary of the Invention

[0009] It is an object of the present invention to provide a controller for an electrical converter based on an optimized pulse pattern, which has good performance also during transient operation and / or can be used in converter systems as higher-order physical systems.

[0010] This object is achieved by the subject-matter of the independent claims. Further exemplary embodiments are apparent from the dependent claims and the following description.

[0011] One aspect of the present invention relates to a method for controlling an electrical converter system. Specifically, the method can be applied to a converter system comprising an electrical converter and other components powered by the converter, such as a motor, a resonant subsystem, and / or a high-impedance cable. The resonant subsystem can be a filter, such as an LC or LCL filter. As already mentioned, LC filters can produce higher-order mathematical models, which can be addressed using the present method. The method can be automatically executed by a controller of the converter system.

[0012] According to an embodiment of the invention, the method comprises: determining a nominal pulse pattern and a reference trajectory of at least one electrical quantity of the electrical converter system within a range of future sampling instants, wherein the nominal pulse pattern and the reference trajectory are determined from an optimized pulse pattern table, the nominal pulse pattern comprising switching transitions between output voltages of an electrical converter of the electrical converter system, and the reference trajectory is indicative of an expected future development of the electrical quantity of the converter system;

[0013] The pulse pattern may comprise the switching moments and the output levels of the phases of the converter at the switching moments.The pulse pattern and all quantities mentioned below may be polyphase quantities, ie may have a value for each phase of the converter system.

[0014] A switching instant can be the time at which a converter is switched. A sampling instant can be the time at which a future quantity in a controller is calculated. For example, the sampling instants can be equidistant from one another. A switching instant can be located between two sampling instants.

[0015] The nominal pulse pattern may be determined online by the controller using a lookup table of offline optimized pulse patterns, which may have been determined with respect to an optimization target for steady-state operation.

[0016] Furthermore, a reference trajectory can be determined for one or more electrical quantities of the converter system. Electrical quantities can include converter current, grid current, filter capacitor voltage, etc. Typically, the electrical quantity can be a current and / or voltage and / or flux of a component of the converter system.

[0017] This can be done by extrapolating these quantities into the future from their actual values, which may have been determined from measurements. The extrapolation can be done using a mathematical model of the converter, which may include differential equations for these quantities. The reference trajectory may also have been determined offline for the optimized pulse pattern and read from a lookup table.

[0018] According to an embodiment of the present invention, the method further comprises determining a small-signal pulse pattern by minimizing a cost function including a small-signal error based on the difference between a reference trajectory and a predicted trajectory. The small-signal pulse pattern can encode a transient voltage-time pulse at each switching transition of the nominal pulse pattern. The temporal position of the pulse is given by the switching instant, while the amplitude or intensity of the pulse is related to the voltage-time area when modifying the switching transition. The predicted trajectory can be determined within a range from measurements in the converter system and a model of the converter system, with the sum of the nominal pulse pattern and the small-signal pulse pattern being input to the model and / or serving as an input.

[0019] The cost function may be a function of the small signal pulse pattern, in particular it may be a function of the instantaneous voltage-time pulse, which may be encoded by a set of voltage-time values. The cost function may be a quadratic function of these voltage-time values.

[0020] The small signal error can be determined by the difference between the reference trajectory and the predicted trajectory. More specifically, the difference between the values ​​of these trajectories at future time steps is determined, and the weighted norm of these differences is used to quantize the result into a scalar. A cost function can be determined to output the small signal error.

[0021] The model, which can be considered a mathematical and / or physical model of the converter system, can model differential equations for quantities of the converter system, such as converter currents, capacitor voltages, grid currents, machine currents, fluxes, etc. The differential equations can be treated as differential equations. Typically, these quantities can include currents and / or voltages and / or fluxes of components of the converter system. The cost function can be composed of quantities determined based on the mathematical model. These quantities can be assembled into matrices and / or vectors, which are used in the cost function.

[0022] All of these quantities can be viewed as trajectories over time. For each quantity, a sequence of values ​​over time (ie, a trajectory) can be determined.

[0023] Prediction and / or optimization may occur relative to constraints, such as minimum and maximum voltages and / or currents of specific components of the converter, such as the DC link voltage, the magnitude of the output current, and / or the output voltage of the converter.

[0024] Prediction and / or optimization may result in a quadratic procedure implemented in the controller. In this case, the controller solves equations for previously populated matrices and vectors based on previous measurements, reference trajectories, and / or small-signal pulse patterns.

[0025] According to an embodiment of the present invention, the method further comprises determining a modified pulse pattern by shifting a switching transition of the nominal pulse pattern, wherein the switching transition is shifted by a time interval such that the time interval multiplied by the direction of the switching transition equals the voltage-time value at the switching transition. In other words, the intensity of the pulse is equal to the voltage-time area added to the nominal pulse pattern to obtain the modified pulse pattern. Here, the direction of the switching transition may refer to a voltage difference and / or the sign of the voltage difference defined by the switching transition.

[0026] In this way, it is not the pulse pattern itself that is optimized, but rather the small-signal pulse pattern that is optimized, which can significantly simplify the computational burden when solving the optimization problem. Basically, using a small-signal pulse pattern can be viewed as a linearization around the nominal switching instant.

[0027] According to an embodiment of the present invention, the method further comprises applying at least the next switching transition of the modified pulse pattern within the sampling interval to the electrical converter system. A fallback range strategy may be implemented by the controller, i.e., the modified pulse pattern and / or the small-signal pulse pattern is determined within a range of more than one sampling instant, and only the next switching transition or the switching transition up to the next sampling instant is applied to the converter.

[0028] In general, the method can be applied to any linear converter system with multiple state variables and integer switch positions, which is modulated by an optimized pulse pattern. Continuous and discontinuous switching angles can be used. The method can adjust the converter system state along their reference trajectory, can manipulate the converter's switch positions (or, effectively, the switching moments and switching transitions), and can modulate the converter with a modified optimized pulse pattern. The modification to the pulse pattern can be approximated by the intensity of the voltage-time pulse, i.e., the normalized volt-second contribution of the pulse. These pulses may be referred to herein as voltage-time pulses. Their intensity may be referred to as voltage-time value.

[0029] The use of small-signal pulse patterns can be viewed as a linearization around the switching instant. Therefore, the evolution of the state error can be described by a set of linear difference equations. The optimization problem, encoded by a cost function and optional other constraints, penalizes tracking errors and, optionally, deviations from the unmodified switching instant. It is important to note that the optimization problem can be formulated as a convex quadratic program and, therefore, can be computationally relatively easy to solve.

[0030] On the other hand, during steady-state operation, the optimized pulse mode can achieve excellent harmonic performance. In addition, during transients, disturbances, and / or faults, a fast response can be achieved. An example of this could be excellent low voltage ride-through capability.

[0031] Electrical resonances in the converter system may not be excited and / or any associated oscillations may be actively damped.

[0032] The method may be insensitive to measurement and observer noise and may be robust with respect to parameter uncertainties, such as unknown variations in system parameters. Examples of this may include variations in the inductor and / or capacitor of the converter system.

[0033] According to an embodiment of the present invention, a switching transition of a modified pulse pattern during an actual and / or current sampling interval is applied to an electrical converter system. The small-signal pulse pattern and the modified pulse pattern can be determined during an actual and / or current sampling interval spanning more than one future sampling interval. Only the switching transition of the modified pulse pattern during the current sampling interval can be applied to the converter system.

[0034] According to an embodiment of the present invention, during the current sampling interval, the small-signal pulse pattern and the modified pulse pattern are again determined within a range starting from the next sampling interval. In other words, a fallback range strategy can be applied. Within a range longer than one sampling interval, the small-signal pulse pattern and the modified pulse pattern can be determined at each sampling interval.

[0035] According to an embodiment of the present invention, the cost function is a quadratic function of the voltage-time values, which is arranged as a vector of voltage-time values. The cost function may include a quadratic term having a model matrix multiplied on both sides by the vector of voltage-time values ​​and a linear term having a model vector multiplied by the vector of voltage-time values. The structure of the model matrix and model vector may be determined offline and / or online by inputting the measured values, reference trajectory, and small-signal pulse pattern into a mathematical model of the electrical converter.

[0036] According to an embodiment of the present invention, a model matrix and a model vector are determined from measurements, a reference trajectory, and a small-signal pulse pattern in a converter, such that a cost function encodes small-signal errors. By utilizing the known structure of the model matrix and the model vector, the entry values ​​of the model matrix and the model vector can be determined online from the measurements, the reference trajectory, and the small-signal pulse pattern in the converter system.

[0037] According to an embodiment of the present invention, the cost function additionally minimizes the amplitude of the voltage-time pulse, i.e., the voltage-time value. For example, the cost function may include a quadratic term having a penalty matrix that is multiplied on both sides by the vector of voltage-time values. The penalty matrix may be a positive semidefinite matrix that penalizes voltage-time values ​​that deviate from zero.

[0038] According to an embodiment of the present invention, the small signal pulse pattern is determined by minimizing a constrained cost function. These constraints may include constraints on the voltage and / or current in the converter system, specifically that these voltage and / or current do not leave a boundary interval. The boundary interval may be defined by a constant minimum value and a constant maximum value.

[0039] According to an embodiment of the present invention, the voltage-time values ​​of the small-signal pulse pattern are constrained so that the modified switching transitions in the phases maintain the original order.

[0040] According to an embodiment of the present invention, the optimal small-signal pulse pattern is determined by solving a quadratic program, wherein the small-signal pulse pattern, the reference trajectory, and the measured values ​​are input to and / or used as inputs to the quadratic program. The quadratic program can be based on a quadratic cost function in voltage-time values ​​(such as described above) and optional constraints (such as those mentioned above). At each sampling time, the quadratic program can be numerically solved by the controller to determine the voltage-time value.

[0041] According to an embodiment of the invention, the method further comprises determining an existing pulse pattern within the range, wherein the existing pulse pattern comprises the modified switching transitions determined at a previous sampling instant and the remaining switching transitions up to the nominal pulse pattern of the range.

[0042] When the method has determined a modified pulse pattern, the existing pulse pattern can be used instead of the nominal pulse pattern to optimize the voltage-time value of the small-signal pulse pattern. To improve the accuracy of the approximation, the linearization of subsequent time steps can be performed around the modified switching instants calculated at the previous time step, rather than around the switching instants of the nominal pulse pattern.

[0043] Specifically, the predicted trajectory can be determined by a model of the converter system, with the sum of the existing pulse pattern and the small-signal pulse pattern as input to the model. The model matrix and model vector used to form the quadratic cost function can be determined from the reference trajectory, the measured values, and the small-signal pulse pattern.

[0044] According to an embodiment of the present invention, the small-signal pulse pattern encodes a transient voltage-time pulse at each switching transition of the existing pulse pattern, which can be encoded by the pulse intensity. In other words, the instantaneous voltage-time pulse of the small-signal pulse pattern is shifted to the instantaneous voltage-time pulse of the existing pulse pattern (rather than the nominal pulse pattern). This can improve the accuracy of the linear approximation around the switching instants.

[0045] According to an embodiment of the present invention, a differential pulse pattern is determined that encodes at least one rectangular voltage-time region to compensate for the difference between the nominal pulse pattern and the existing pulse pattern. The differential pulse pattern may encode a rectangular voltage-time region at some or all switching transitions of the existing switching pattern. In order to resolve the difference between the nominal pulse pattern and the existing pulse pattern, the rectangular voltage-time region may be included together with the small signal pulse pattern. The differential pulse pattern may be the difference between the nominal pulse pattern and the existing pulse pattern determined at a previous sampling instant. The voltage-time region at the switching transition may be equal to the difference between the moments of the nominal pulse pattern and the existing pulse pattern multiplied by the direction of the switching transition. It must be noted that the rectangular voltage-time region representing the modification of the previous switching instant is not optimized, but is used to compensate for the difference between the nominal pulse pattern and the existing pulse pattern.

[0046] According to an embodiment of the present invention, an optimized pulse pattern and reference trajectory are determined offline and stored in a lookup table. An optimized pulse pattern can be determined for each modulation index and each pulse number used in the converter system. The actual modulation index and pulse number can be determined using actual reference values ​​and / or measurements in the converter system.

[0047] The optimized pulse pattern may have been calculated off-line with respect to a specific optimization goal, such as minimum total demand distortion of current during steady-state operation.The optimized pulse pattern may be stored in a lookup table in the controller.

[0048] One or more reference trajectories may also have been determined offline for the optimized pulse pattern.The values ​​of these reference trajectories may also be stored in a lookup table in the controller.

[0049] Other aspects of the invention relate to a computer program which, when executed by a processor, is adapted to carry out the method described above and below, and to a computer-readable medium in which such a computer program is stored. The method may be implemented in software and may be run on a controller having a processor and a memory in which the computer program is stored.

[0050] The computer-readable medium may be a floppy disk, a hard disk, a 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. The computer-readable medium may also be a data communication network, such as the Internet, which allows program code to be downloaded. In general, the computer-readable medium may be a non-transitory or transient medium.

[0051] Yet another aspect of the invention relates to a controller for an electrical converter, the controller being adapted to perform the above and following methods.It has to be noted that the method may also be implemented at least partially in hardware, such as a DSP or FPGA.

[0052] Yet another aspect of the invention relates to a converter system comprising an electrical converter interconnected to an electrical grid and a controller as described above and below.

[0053] According to an embodiment of the present invention, the converter system further includes a resonant subsystem comprising at least one of an inductor and a filter. For example, the resonant subsystem may be an LC filter or a cable, which may have a high impedance. The model of the converter system used during cost function optimization may include models of the electrical converter and the resonant subsystem. Specifically, the resonant subsystem may result in higher-order difference equations.

[0054] It has to be understood that features of the method described above and below may be features of the converter system, the computer program, the computer-readable medium and the controller described above and below, and vice versa.

[0055] 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

[0056] The subject matter of the invention will be explained in more detail hereinafter with reference to exemplary embodiments illustrated in the drawings.

[0057] Figure 1 A converter system according to an embodiment of the invention is schematically shown.

[0058] Figure 2 A block diagram of a controller according to an embodiment of the present invention is shown.

[0059] Figure 3A and 3B A pulse pattern used in a method according to an embodiment of the invention is shown.

[0060] In principle, identical parts are provided with the same reference symbols in the figures. DETAILED DESCRIPTION

[0061] Figure 1 A converter system 10 is shown that includes an electrical converter 12 and an LC filter 14 coupled to an electrical grid 16 . Figure 1 Other corresponding quantities shown are listed at the end of this description. Figure 1 Also shown is a controller 18 , which is suitable for executing the method for controlling the converter system 10 , as described herein.

[0062] The LC filter 14 may include a filter inductor L and a filter resistor R connected between the converter 12 and the grid 16 and a filter resistor R connected to the interconnection between the converter 12 and the grid 16. C and filter capacitor C.

[0063] As shown, the electrical converter 12 may be a mid-point clamped converter having a mid-point clamped phase leg 20 for each output phase. Other converters 12, such as a T-type converter, a modular multi-level converter, and / or a converter with a flying capacitor, may be used as a multi-level converter 12. Also, a two-level converter may be used.

[0064] Figure 2 is another diagram of the system 10 , in which the controller 18 is shown in more detail. The controller 18 includes a pulse pattern selector 20 , a reference trajectory generator 22 , a small signal optimizer 24 , an existing pulse pattern determiner 26 , and a Clarke transform block 28 .

[0065] A method for controlling the converter system 10 , which may be automatically performed by the controller 18 , will be explained below with respect to the different blocks 20 , 22 , 24 , 26 , 28 .

[0066] In the first step, depending on the grid voltage v g , grid current reference I * gand grid phase reference φ * g , the appropriate optimized divided pulse pattern is selected by the pulse pattern selector 20. The pulse pattern selector 20 then provides the nominal switching instant t of the nominal pulse pattern * p,i and nominal switching transition Δu * p,i .

[0067] The offline OPP calculation is a specific pulse-width modulation (PWM) method. Unlike carrier-based PWM or space vector modulation, OPP abandons the concept of a fixed modulation interval, with one switching transition per phase and modulation (half) interval. Eliminating these restrictions facilitates the calculation of the optimal switching angle to minimize harmonic current distortion for a given switching frequency.

[0068] Assuming quarter-wave and half-wave symmetry and a 120° phase shift between the three phases, the switching moments and switch positions of the OPP are usually calculated for one phase within a quarter of the fundamental period.

[0069] In the second step, the optimal state reference trajectory x * The reference trajectory generator 22 generates the nominal pulse pattern t * p,i ,Δu * p,i generate.

[0070] In summary, the nominal pulse mode t of the electrical converter system 10 * p,i ,Δu * p,i and its corresponding reference trajectory x * is determined within the future sampling time range, where the nominal pulse pattern t * p,i ,Δu * p,i and the corresponding reference trajectory x * Determined by the optimized pulse pattern table. Nominal pulse pattern t * p,i ,Δu * p,i The switching transition Δu between the output voltages of the electrical converter 12 of the electrical converter system 10 is included. * p,i , and the reference trajectory x * Indicates the expected future development of the charge of the converter system 10 .

[0071] Optimized pulse pattern and optional reference trajectory x * It may be determined off-line and stored in lookup tables in blocks 20 and 22, respectively.

[0072] In a third step, the small signal optimizer 24 receives measurements such as the converter current i, the filter capacitor voltage v c and grid current i g , which have been measured in the system 10 and have been Clarke transformed by block 28 .

[0073] Clarke transform

[0074] ξ αβ =Kξ abc (1)

[0075] Any variable ξ in the abc plane is transformed by the following transformation matrix abc =[ξ a ξ b ξ c ] T The two-dimensional vector ξ mapped to the αβ plane αβ =[ξ α ξ β ] T

[0076]

[0077] In this paper, all variables in the abc plane are denoted by their corresponding subscripts, while the subscripts are dropped for variables in the αβ plane.

[0078] From the measured values, the small signal optimizer 24 calculates the initial small signal error, Then it constructs the Hessian matrix H with the help of (44), see below, and the model vector c is constructed with the help of (50) and (51). By solving QP (61), the optimal pulse intensity vector Λ opt was found.

[0079] Can be used as the optimal pulse intensity vector Λ opt Small signal pulse mode provided It is determined by minimizing a cost function that includes the small signal error, which is based on the reference trajectory x * The difference between the predicted trajectory x and the predicted trajectory x. Small signal pulse mode The pulse intensity λ p,i In nominal pulse mode t * p,i ,Δu * p,i The voltage-time value λ at each switching transition p,i is encoded, and where the predicted trajectory x is the measured values ​​i,v from the converter system c ,i gand the model of the converter system 10 is determined within the range, the nominal pulse pattern t * p,i ,Δu * p,i and small signal pulse mode The sum of is fed into the model and / or used as input.

[0080] Thereafter, in the fourth step, the intensity λ p，i The small signal optimizer 24 converts it back into the switching time modification Δt opt,p,i , which is then added to the switching instant t of the nominal pulse mode * p,i Or the switching time t' of the existing pulse mode p,i (see below) to determine the modified switching instant t of the modified pulse pattern according to (63) opt,p,i .

[0081] Modified pulse mode t opt,p,i ,Δu p,i By shifting the nominal pulse pattern t * p,i ,Δu * p,i The switching transition is determined by shifting the switching transition by a time interval such that the time interval multiplied by the direction of the switching transition equals the pulse intensity λ p,i The voltage-time value encoded at the nominal switching transition.

[0082] Then, only the modified pulse pattern within the sampling interval t opt,p,i ,Δu p,i The switching transitions are applied to the electrical converter 12 .

[0083] Optionally, the method can also use the existing pulse mode t' p,i ,Δu p,i Instead of the nominal pulse mode in the small signal optimizer 24.

[0084] In this case, modify the switching time t' p,i and the switching transition Δu determined at the sampling instant p,i Stored as the current pulse pattern by block 26. Current pulse pattern t' p,i ,Δu p,i Updated at each sampling moment. At subsequent sampling moments, the existing switching mode t' p,i ,Δu p,i is the input into the optimizer 24 (instead of the nominal pulse pattern).

[0085] In summary, the existing pulse mode t' p,i ,Δu p,iDetermine in the range where the existing pulse pattern t' p,i ,Δu p,i including the modified switching transition t determined at the previous sampling instant opt,p,i and nominal pulse mode up to the range t * p,i ,Δu * p,i The remaining switching transitions. In the optimizer 24, the predicted trajectory x is determined by the model of the converter system 10, the existing pulse pattern t' p,i ,Δu p,i and small signal pulse mode The sum of is the input to the model.

[0086] The above steps may be repeated at each sampling instant. Note that if the operating conditions of the converter system 10 change, only the first two steps may be required.

[0087] In this method, several types of pulse modes are used, such as Figure 3A and 3B shown.

[0088] Nominal pulse mode u * The three-phase nominal pulse pattern is determined by the optimized pulse pattern calculated offline. * abc (t) indicates that its switching transition occurs at time t * p,i .

[0089] The existing pulse pattern u can be used by the controller 18 as a starting point, ie a pulse pattern whose switching transitions are to be modified. The three-phase existing pulse pattern is represented by u abc (t) indicates that its switching transition occurs at t' p,i .

[0090] Small Signal Pulse Mode Pulse intensity (or voltage-time value) λ p,i Optimized by the small signal optimizer 24. Small signal pulse mode It consists of a series of Dirac delta functions (also called pulses) that are switched at the switching time t' p,i With pulse intensity λ p,i .

[0091] Modified pulse mode u mod is generated by the optimizer and its first part (within the sampling interval) is applied to the converter 12. The three-phase modified pulse pattern is given by u mod,abc (t) indicates that its switching transition occurs at t p,i =t' p,i +Δt' p,i .

[0092] like Figure 3A and Figure 3B As shown, the controller 18 takes discrete time steps kT s Operation, where And T s is the sampling interval, such as 25 μs. Note that even if the controller 18 s Operations, switching time modifications can also be formulated in the continuous time domain. This means that the modified switching time is a real-valued quantity.

[0093] Pulse mode u * , u and is determined only for the prediction horizon 22. In the prediction horizon 22, only the modified switching instants within the current sampling interval are applied, i.e. within kT s and (k+1)T s Then, at each subsequent sampling instant, the modified switching instant from the previous sample (now the existing switching instant) is re-optimized based on the new information. This can be called a fallback horizon strategy, which provides feedback and can make the controller robust to disturbances and modeling errors.

[0094] Converter system

[0095] Consider a converter system 10 that includes linear elements and switching elements. The switch positions of the switching elements can be described by integer variables. Typical linear elements are voltage and current sources, ohmic resistors, capacitors, and inductors. Because inductors and ohmic resistors are building blocks of transformers and rotating electrical machines, they can also be part of converter system 10.

[0096] The converter system 10 with linear elements and integer inputs can be described by a continuous-time state-space representation

[0097]

[0098] in and are the state and parameter vectors in the αβ reference frame, and Input vector are the three-phase switch positions. Finally, F, G, and P are the state, input, and parameter matrices that characterize the converter system 10.

[0099] The formulation in (2) is general enough to include any converter topology, including dc / ac, ac / dc, dc / dc and ac / ac converters, two-level, three-level and universal multilevel converters and voltage source and current source converters. By adapting the input vector u abcDue to the dimensions, converters with a wide range of phase configurations can be handled, including single-phase, three-phase and multi-phase converters.

[0100] As an example, consider an NPC converter 12 connected to a grid 16 via an LC filter 14, such as Figure 1 As shown. The phase voltage is given by v p Assume that the dc link capacitor has infinite capacitance and the midpoint N is fixed, and the dc link voltage V is d Evenly divided across the dc link capacitors. Each phase leg can synthesize three voltage levels: Therefore, the output voltage for a particular phase is given by

[0101]

[0102] where u p ∈{-1, 0, 1} represents the switch position of a specific phase.

[0103] Assume that the three-phase grid voltage is symmetrical and its phase voltages are offset by 120° relative to each other in positive phase sequence. The stationary orthogonal reference frame can be defined by the grid voltage

[0104]

[0105] Where V g,LL is the root mean square (rms) line-to-line grid voltage, and ω1 is the fundamental angular frequency.

[0106] There is also a three-phase converter current i abc =[i a i b i c ] T , LC filter three-phase capacitor voltage v c，abc =[v c，a v c，b v c，c ] T and three-phase grid current i g，abc =[i g，a i g，b i g，c ] T These quantities are transformed into a stationary orthogonal reference frame using the Clarke transformation (1).

[0107] Based on this, the state vector is defined as

[0108] x(t)=[i α (t) i β (t) i g，α (t) i g，β (t) vc，α (t) v c，β (t)] T

[0109] And the converter system can be written in continuous-time state-space form (2). The corresponding matrix is ​​given as

[0110] and

[0111] Here, I2 represents the 2x2 identity matrix, and 0 2×2 is a 2x2 zero matrix. The grid voltage v g is considered as a time-varying parameter of the system. Note that the input u abc In the three-phase abc framework, the state vector x and the parameter vector v are given. g It is given in the stationary orthogonal αβ reference frame.

[0112] Control issues

[0113] The control problem at hand is to follow the appropriate state reference x * The state variables x of the power converter system (2) are regulated. Typically, the state variables include the voltage, current, flux and power of the converter, filter, load, grid or motor. In doing so, the active and reactive power of the converter, its dc link voltage or current, internal converter quantities (such as midpoint potential or flying capacitor voltage) and the grid or load can be controlled. Typical load quantities to be controlled are the electromagnetic torque and magnetization of the motor, the phase current of the load or the active and reactive power of the load. Any converter topology can be considered, including single-phase, three-phase, multi-phase, dc / ac, ac / dc, dc / dc and ac / ac converters. Two-level, three-level and general multi-level converters can be addressed, and voltage source and current source converters can be considered.

[0114] To minimize harmonic distortion and switching frequency, an optimized pulse pattern (OPP) with discrete switching angles can be used to modulate the converter switches. OPP lacks a fixed modulation interval. Therefore, there are no regularly spaced points in time when the ripple on the state variable is zero, and therefore no sampling instants. This means that when the state variable is sampled at regularly spaced instants, the sum of the fundamental component and its ripple component is measured. This significantly complicates controller design.

[0115] The present control method described herein regulates the state of a linear multi-input multi-output system with integer inputs along its reference trajectory, manipulates the switch positions of the converter, modulates the converter using OPP during steady-state operation to achieve excellent harmonic performance at low switching frequencies, achieves fast response with little overshoot during reference step changes, and rejects unmeasured disturbances.

[0116] Small signal modification at OPP switching time

[0117] small signal correction

[0118] First, only Figure 3A is considered. To simplify notation, the phase p is dropped from the variables. The nominal pulse pattern is denoted by u * (t) represents the nominal pulse mode with the switching time t * i ,i=1,…,n * Occurrence of n * switching transitions and can be expressed as

[0119]

[0120] where h(t) is the Heavyside step function, and u * 0 is the initial (nominal) switch position.

[0121] The pulse pattern that can be optimized (ie, the pulse pattern whose switching transition is modified) is called the existing pulse pattern and is denoted by u(t). The existing pulse pattern can be represented as

[0122]

[0123] where the switching transition t' i is called the existing switching moment.

[0124] The pulse mode will be applied to the power converter with u mod (t) is denoted and is referred to as the modified pulse pattern. The modified pulse pattern has n switching transitions occurring at modified switching instants

[0125] t i =t' i +Δt i (6)

[0126] For i=1,…,n, and where Δt i is the time modification. It can be observed that the i-th switching moment modification is associated with the following region

[0127] λ i =-Δt i Δu i (7)

[0128] It is removed or added to the existing pulse pattern. The area is proportional to the voltage-time area. The modified pulse pattern can be represented by

[0129]

[0130] Recall that the time derivative of the step function h(t) is the Dirac delta function, or simply the impulse δ(t). By using the time derivative of the step function h(t) around the existing switching instant t' i The first-order Taylor series expansion of the step function of (8) can be approximated by

[0131]

[0132] Using the definitions of (5) and (7), (9) is simplified to

[0133]

[0134] The (linearized) modified pulse pattern in (10) consists of two terms. The first is the (unmodified) existing pulse pattern u(t), while the second expression is

[0135]

[0136] These modifications are to the existing switching instant t' i A pulse with intensity λ i , and the intensity can be viewed as representing the (rectangular) voltage-time area.

[0137] This generates a series of voltage-time pulses that will become the input to the small signal model, as described below. Based on this model, the model predictive controller of the optimizer 24 will adjust the pulse intensity λ of the small signal pulse pattern as needed. i By rewriting (7), the pulse intensity can be converted into a switching moment modification

[0138]

[0139] The conversion from pulse intensity to switching instant modification is based on the linearization in (10). More specifically, Figure 3A and Figure 3B The (shaded) rectangular voltage-time region in the figure is approximated by the intensity of the voltage-time pulse. The narrower the voltage-time region, the better the approximation.

[0140] Update existing switching time

[0141] Since the modification of the pulse pattern of (10) is based on approximating the rectangular voltage-time region with the pulse intensity, the effect of the modification on the system state behavior is generally accurate only for small modifications to the switching instants (i.e., small pulse intensities). However, using the pulse intensity to model the correction will cause the underlying optimization problem of the control algorithm to become a convex QP. If the pulse intensity is not used to model the correction, and therefore the linearization step is not used, then the solution of the optimization problem will be substantially more difficult and time-consuming. To address this issue, the optimization problem is formulated around the switching instants calculated at the previous time step, rather than the nominal switching instants. This ensures a convex QP and highly accurate prediction during steady-state operation within a few sampling instants after the step transient.

[0142] The small signal input is defined as the difference between the modified pulse pattern and the nominal pulse pattern,

[0143]

[0144] Small signal input Includes two items.

[0145] Item 1 It is the difference between the existing pulse pattern and the nominal pulse pattern. This term is called the small-signal differential pulse pattern or small-signal differential input, and / or may consist of voltage-time domains.

[0146] Item 2 Refers to a series of voltage-time pulses, which can be called small signal pulse mode.

[0147] exist Figure 3A In the process, the switching time between the nominal pulse mode and the existing pulse mode is equal (t' i =t * i ). This results in the small signal input consisting only of the definition in (11) and Figure 3A The voltage-time pulse depicted in The controller 18 then calculates the pulse intensity, which is then converted into a modified switching instant t (of the modified pulse pattern) using (6) and (12). i .

[0148] exist Figure 3B In the subsequent steps in the existing switching time t' i Use the modified switching time t calculated at the previous time step k-1 i Update (ie, Figure 3A The small-signal input now contains the additional term (i.e., the actual (rectangular) voltage-time area from the previous correction) as well as the voltage-time pulse, i.e.,

[0149]

[0150] This is Figure 3B Note that except for the last term, all terms in (15) refer to the small signal differential pulse mode.

[0151] Three-phase situation

[0152] The previous section is generalized to the three-phase case. The modification to the i-th switching instant in phase p (where p∈{a, b, c}) is defined as

[0153] Δt p,i =t p,i -t' p,i , (16)

[0154] where t p,i Indicates the modification switching time, and t' p,i is the existing switching moment. The corresponding switching transition is defined as

[0155] Δu p,i =u p,i -u p,i-1 (17)

[0156] From u p,i-1 to u p,i , where u p,i-1 and Extending (7), the intensity of the i-th pulse in phase p is defined as

[0157] λ p,i =-Δt p,i Δu p,i (18)

[0158] Consider the time interval t∈{0, T p The modified three-phase pulse mode u mod,abc (t), where T p is the prediction range of the controller to be designed. Following the principle derived in (10), the modified pulse pattern is defined as the superposition of the existing three-phase pulse pattern

[0159]

[0160] The existing three-phase pulse mode is

[0161]

[0162] and a three-phase modification in the form of a series of weighted voltage-time pulses (i.e., a three-phase small signal pulse pattern)

[0163]

[0164] Here, n p is introduced as the phase p falls within the range T p The number of switching transitions within, and λ p,i As the intensity of the i-th pulse in this phase. Note that the existing switching time t' p,i It is defined relative to the current time step t0 = 0. Range T p The total number of switching transitions within the three phases is given by n sw =n a +n b +n c express.

[0165] Internal dynamic model

[0166] Recall the difference equations of the power converter system in (2). The modified three-phase pulse mode u mod,abc (t) is used as the input of the system. By integrating (2), at time t∈{0, T p The future state vector of} is

[0167]

[0168] where x0 is the initial state at time t0 = 0. Similarly, the optimal state reference trajectory during steady-state operation is derived from the nominal pulse mode

[0169]

[0170] where x * 0 is the optimal initial state, and

[0171]

[0172] The error between the actual state and its reference

[0173]

[0174] is the so-called small signal error, By inserting (22) and (23) and (19) into (25), the expression

[0175]

[0176] was obtained, of which is the initial small signal error. Since expression (19) is only approximately true, the small signal error in (26) is also an approximation. Note that the state error is the pulse intensity λ p,iis a function of , which models the modification of the existing pulse pattern. The grid voltage is not part of the small signal model in (26), but it will be required by the controller when choosing an appropriate pulse pattern.

[0177] State error in vector form

[0178] The small signal error (26) can be written in a compact form. To this end, in (26), the small signal pulse pattern is rearranged, see (21), resulting in

[0179]

[0180] in

[0181]

[0182] Operations involving Γ(t) are moved to Appendix A. By using the well-known offset property of pulses,

[0183]

[0184] The integral in (27) becomes

[0185]

[0186] Among them G a =G

[100] T , G b =G

[010] T , and G c =G

[001] T .

[0187] The small signal error can now be written in vector form as

[0188]

[0189] in is the input matrix,

[0190]

[0191] and is introduced as the pulse intensity vector,

[0192]

[0193] n sw Pulse intensity in the range T p Note that Γ(t) captures the behavior of the previous correction. It will be shown below that it can be ignored at the expense of accuracy.

[0194] Control methods

[0195] In this section, the controller 18 and the control method performed by the controller are described in more detail. The controller 18 and the control method are based on the small signal error expression (30).

[0196] Objective function

[0197] Objective function

[0198]

[0199] Use positive semidefinite penalty matrix The penalty length is T p The integral of the small signal error within the prediction range of . The second term in (33) penalizes the intensity of the voltage-time pulse to prevent unnecessary large modifications to the existing pulse pattern. The corresponding penalty matrix Need to be positive semidefinite.

[0200] The first term can be expanded to

[0201]

[0202] in

[0203] Υ(t)=2Φ(t) T QΦ(t), (35)

[0204]

[0205] and

[0206]

[0207] Consider n in (35) sw ×n sw The (i', j')th entry of the matrix Y. Assume that the i'th entry corresponds to the phase p1∈{a, b, c} and the i-th switching transition in that phase. For a given j', the quantities p2 and j are defined accordingly. The (i', j')th entry of Y can then be written as

[0208]

[0209] where t′ ij =max{t′ p1，i , t′ p2，j}. The integral of (38b) leads to

[0210]

[0211] It is not easy to calculate the integral of the exponential product of two non-commutative matrices. According to the theorem, the integral

[0212]

[0213] can be calculated as

[0214] Ξ(t)=M(t) T N(t), (41)

[0215] in

[0216]

[0217] Next, the integral in (39) is rewritten into the form of (40) so that (41) and (42) can be used to solve it:

[0218]

[0219] By time-shifting the integrand by t' ij , the integral becomes

[0220]

[0221] n in (36) sw The dimension column vector Θ(t) is split into two terms

[0222] Θ(t) T =Θ0(t) T +Θ Γ (t) T (45)

[0223] in

[0224]

[0225] Θ Γ (t) T =2(Γ(t)) T QΦ(t). (47)

[0226] Consider Θ0(t) T The i'th entry of and assume that it corresponds to phase p and the i-th switching transition in that phase. Using (31),

[0227]

[0228] Its integral

[0229]

[0230] It can also be written in the form of (40) so that (41) and (42) can be used to solve it. p,i Afterwards, the integral becomes

[0231]

[0232] The calculation of the second term in (45) involves

[0233]

[0234] Moved to Appendix B.

[0235] Then the i'th entry of vector c is given by

[0236] c i ′=c 0，i ′+c Γ，i '. (52)

[0237] Note that θ(t) in (34) is not a function of the pulse intensity vector Λ. Therefore, it is just a constant in the cost function and has no effect on the solution of the optimization problem to be derived. This fact allows us to omit θ(t) from now on.

[0238] The first term J1 of the objective function that minimizes the small signal error can now be written as

[0239]

[0240] The second term of the objective function that penalizes the entries of the pulse intensity vector Λ is

[0241]

[0242] The vector form objective function is a quadratic function

[0243]

[0244] where H = V + R is called the Hessian matrix and contains the second order partial derivatives of J(Λ), and c is a vector with linear coefficients.

[0245] In the above, the matrix V is also called the model matrix, and the vector c is called the model vector. The matrix R is called the penalty matrix.

[0246] constraint

[0247] To enforce an ascending order on the modified switching moments in each phase, the constraint set

[0248]

[0249] This must be enforced for each phase p. The switching instant cannot be shifted into the past and cannot be outside the prediction horizon T p Alternatively, the nth phase pA switching transition can be exceeded by the next existing switching transition As the upper limit.

[0250] With the help of (16) and (18), the constraint set (56) can be calculated based on the pulse intensity λ p,i To recast:

[0251]

[0252] Applying (57) to phases a, b, and c, the constraints

[0253] AΛ≤B (58)

[0254] Appears in matrix form, relative to

[0255] in

[0256] and

[0257] in

[0258] Additional constraints can be added to the controller formulation. For example, The state constraint (time is t∈[0, T p ]) can be added to (61b), see below. Assuming that the constraint set X is a polyhedron, the following optimization problem (61) is still a convex QP.

[0259] Secondary Program

[0260] Minimizing the objective function (55) while respecting the constraints (58) leads to the quadratic program (QP)

[0261]

[0262] With the constraint AΛ≤B. (61b)

[0263] The pulse intensity vector Λ is the decision (or optimization) variable, and Λ opt is the optimal solution to QP. The latter cannot be solved algebraically; instead, numerical optimization techniques must be employed, such as gradient methods or interior point methods.

[0264] Note that problem (61) is convex because the constraints are linear and the objective function is quadratic in the decision variables, with a positive semidefinite Hessian matrix H. It can be shown that this follows from the fact that the penalty matrices Q and R are positive semidefinite. If R is positive definite, then the Hessian matrix H is also positive definite.

[0265] Optimal switching time

[0266] After solving QP(61), the optimal pulse intensity vector Λ opt Use (18) to convert it into the optimal switching time advance or delay

[0267]

[0268] By adding these modifications to the existing switching moments of the pulse mode, the optimal switching moments are obtained

[0269]

[0270] Among them (16) are used.

[0271] Standard controller

[0272] If the switching instant update step is omitted (ie the linearization is always performed around the nominal switching instant), the computational burden of the control algorithm can be reduced. This means that the existing pulse mode u abc (t) is nominal pulse mode u * abc (t) is replaced. Since the existing pulse pattern and the nominal pulse pattern are then equal, the small signal error in (30) is reduced to

[0273]

[0274] The i'th entry of the linear term in the cost function (see (52)) is then reduced to c i ′=c 0，i ′.

[0275] The accuracy of small signal error prediction may be degraded. Recall that Figure 3A The voltage-time region in the y-axis approximates the intensity of the corresponding pulse. Small modifications accurately represent small voltage-time regions with small pulse intensities, but larger modifications may introduce certain errors. These errors can manifest themselves as inaccurate predictions. However, these inaccuracies can be compensated by the controller due to the backoff range policy.

[0276] Appendix A

[0277] The expression Γ(t) defined in (28) appearing in (30) can be rearranged as

[0278]

[0279] The integral involving the step function used is

[0280]

[0281] Here, has been introduced.

[0282] (65) is decomposed into three terms

[0283] Γ(t)=Γ′(t)-Γ * (t)+Γ0(t), (66)

[0284]

[0285]

[0286] Γ0(t)=(e Ft -I)F -1 GΔu abc，0 (69)

[0287] Appendix B

[0288] The equations involving the integral of (66) are evaluated. The integrals of the terms in (48) are considered separately,

[0289]

[0290] in

[0291]

[0292]

[0293]

[0294] First, (71) is further decomposed into each phase individually

[0295]

[0296] where p2 is the specific phase of (67), and t′ ij =max{t′ p，i , t′ p2，j}. Note Θ Γ′，i′ (t) = Θ Γ′，a，i′ (t)+Θ Γ′，b，i′ (t)+Θ Γ′，c，i′ (t). Its integral is split into two parts

[0297]

[0298] And shift forward in time t' ij , and using algebraic manipulation similar to the derivation of (44), becomes

[0299]

[0300] where Ξ(t) is defined in (40). The second integral can be calculated using

[0301]

[0302] in

[0303]

[0304] Using (77), (76) becomes

[0305]

[0306] Next consider (72), which has the same structure as (71) and, following the same derivation used for the latter calculation, can be stated as

[0307]

[0308] in

[0309] Finally, consider (73), which can be rewritten as

[0310]

[0311] Its integral is also split into two parts

[0312]

[0313] And shift forward in time t p,i becomes

[0314]

[0315] Using (41) and (77), (83) becomes

[0316]

[0317] symbol

[0318] t time,

[0319] k discrete time steps,

[0320] d number of pulses,

[0321] m modulation index, m∈[0, 4 / π]

[0322] p is a specific phase, p∈{a,b,c}

[0323] u p,i The i-th single-phase switch position of phase p, u p，i ∈{-1, 0, 1}

[0324] Δu p,i The i-th switching transition of phase p, Δu p，i ∈{-1, 1}

[0325] λ p,i The intensity of the i-th pulse of phase p (also called the voltage-time value),

[0326] The vector of pulse intensities within the range Λ (also called the vector of voltage-time values),

[0327] t * p,i The i-th nominal switching time of phase p

[0328] t' p,i The i-th existing switching moment of phase p

[0329] t p,i The i-th modification switching moment of phase p

[0330] Δt p,i The i-th switching moment modification of phase p, Δt p,i =t p,i -t' p,i

[0331] u * abc (t) Three-phase nominal pulse mode

[0332] u abc (t) Three-phase existing pulse mode

[0333] u mod,abc (t) Three-phase modified pulse mode

[0334] The three-phase small signal pulse mode is defined as

[0335] The three-phase differential pulse mode is defined as

[0336] x(t) state vector

[0337] x * (t) Optimal (reference) trajectory of the state vector

[0338] The small signal error, defined as

[0339] T pTime prediction range,

[0340] T s The sampling interval of the controller,

[0341] n p The number of switching transitions in phase p occurring within the range

[0342] n sw Total number of switching transitions in the range, n sw =n a +n b +n c

[0343] F is the system matrix in the continuous time domain

[0344] G is the input matrix in the continuous time domain.

[0345] P parameter matrix in the continuous time domain

[0346] Hessian Matrix in H QP

[0347] c Column vector in QP

[0348] variable

[0349] z(t) is a scalar in the continuous time domain.

[0350] z refers to a column vector, such as a three-phase quantity

[0351] abbreviation

[0352] ac alternating current

[0353] dc direct current

[0354] MPC Model Predictive Control

[0355] MP 3 C-model predictive pulse mode control

[0356] NPC Midpoint Clamp

[0357] OPP Optimized Pulse Mode

[0358] PWM Pulse Width Modulation

[0359] QP Quadratic Program

[0360] rms root mean square

[0361] Although 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 of the disclosed embodiments may be understood and implemented by those skilled in the art by studying the drawings, the disclosure and the appended claims, and practicing the claimed invention. 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 perform the functions of several items listed in the claims. The fact that certain measures are listed 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 an electrical converter system (10), the method comprising: Determine the nominal pulse pattern within the future sampling time range (t * p,i ,Δu * p,i ) and a reference trajectory (x * ), where the nominal pulse mode (t * p,i ,Δu * p,i ) and the reference trajectory (x * ) is determined from the optimized pulse pattern table, the nominal pulse pattern (t * p,i ,Δu * p,i ) includes a switching transition (Δu) between the output voltages of the electrical converter (12) of the electrical converter system (10) * p,i ), and the reference trajectory (x * ) indicating an expected future development of the electrical quantity of said converter system (10); Determine the small signal pulse pattern by minimizing the cost function The cost function includes a small signal error, which is based on the reference trajectory (x * ) and the predicted trajectory (x), where the small signal pulse pattern The pulse intensity (λ p,i ) in the nominal pulse mode (t * p,i ,Δu * p,i ) and wherein the predicted trajectory (x) is obtained from the measured values ​​(i,v c ,i g ) and the model of the converter system (10) are determined within the range, the nominal pulse pattern (t * p,i ,Δu * p,i ) and the small signal pulse mode The sum of is input into the model; By shifting the nominal pulse pattern (t * p,i ,Δu * p,i ) to determine the modified pulse pattern (t opt,p,i ,Δu p,i ), wherein the switching transition is shifted by a time interval such that the time interval multiplied by the direction of the switching transition is equal to the pulse intensity (λ p,i ) in the nominal pulse mode (t * p,i ,Δu * p,i ) of the voltage-time value encoded at the nominal switching transition of ; At least the modified pulse pattern (t opt,p,i ,Δu p,i ) is applied to the electrical converter system (10).

2. The method according to claim 1, wherein during the current sampling interval, the modified pulse pattern (t opt,p,i ,Δu p,i ) is applied to the electrical converter system (10); During the current sampling interval, the small signal pulse mode and the modified pulse pattern (t opt,p,i ,Δu p,i ) is determined again within the range of the start of the next sampling interval.

3. The method according to claim 1 or 2, The cost function is the pulse intensity (λ p,i ), said quadratic functions being arranged as a pulse intensity vector (Λ); wherein the cost function comprises a quadratic term with a model matrix (V) multiplied on both sides by the pulse intensity vector (Λ) and a linear term with a model vector (c), wherein the model matrix (V) is multiplied on both sides by the pulse intensity vector (Λ); wherein the model matrix (V) and the model vector (c) are derived from the measured values ​​(i, v c ,i g ), the reference trajectory (x * ) and the small signal pulse mode Determining such that the cost function encodes the small signal error.

4. The method according to claim 1 or 2, The cost function additionally makes the pulse intensity (λ p,i ) is minimized.

5. The method according to claim 1 or 2, Wherein the cost function comprises a quadratic term with a penalty matrix (R) which is multiplied on both sides by a pulse strength vector (Λ).

6. The method according to claim 1 or 2, The small signal pulse mode determining by minimizing said cost function subject to constraints; The small signal pulse mode The pulse intensity (λ p,i ) are constrained so that the modified switching transitions in the same phase maintain the original order.

7. The method according to claim 1 or 2, The small signal pulse mode Determine by solving the quadratic program, the reference trajectory (x * ), the measured value (i,v c ,i g ) and the small signal pulse mode is input into the secondary program.

8. The method according to claim 1 or 2, further comprising: Determine the current pulse mode (t' p,i ,Δu p,i ), wherein the existing pulse mode (t' p,i ,Δu p,i ) includes the modified switching transition (t opt,p,i ) and the nominal pulse mode (t * p,i ,Δu * p,i ) of the remaining switching transitions; The predicted trajectory (x * ) is determined from the model of the converter system (10), the existing pulse pattern (t' p,i ,Δu p,i ) and small signal pulse mode The sum of is input into the model.

9. The method according to claim 8, The small signal pulse mode The pulse intensity (λ p,i ) in the existing pulse mode (t' p,i ,Δu p,i ) at each switching transition; The differential pulse mode is determined, the differential pulse mode At least one rectangular voltage-time region is encoded to compensate for the nominal pulse pattern (t * p,i ,Δu * p,i ) and the existing pulse mode (t' p,i ,Δu p,i ) between .

10. The method according to claim 1 or 2, wherein the optimized pulse pattern and / or the at least one reference trajectory (x * ) are determined offline and stored in a lookup table.

11. A computer program product adapted to perform the method of any one of claims 1 to 10 when executed by a processor.

12. A computer-readable medium on which the computer program product according to claim 11 is stored.

13. A controller (18) for an electrical converter, adapted to perform the method of any one of claims 1 to 10.

14. A converter system (10), comprising: an electrical converter (12) interconnected with a power grid (16); The controller (18) of claim 13, configured to control the electrical converter (12).

15. The converter system (10) of claim 14, further comprising: A resonant subsystem (14) comprising at least one of an inductor and a filter; The model of the converter system (10) used during optimization of the cost function includes models of the electrical converter (12) and the resonant subsystem (14).

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