Model predictive pulse mode control based on optimized average switch position sequence

Abstract

A method for controlling an electrical converter system (10), comprising: determining a switching signal (u*) within a range of future sampling instants abc ) and a reference trajectory (Y*) of at least one electrical quantity of the electrical converter system (10) αβ ), where the switching signal (u* abc ) and the reference trajectory (Y* αβ ) is determined from the optimized pulse pattern (A*, U*) table, the switching signal (u* abc ) includes switching transitions between output levels of the electrical converters of the electrical converter system (10), and a reference trajectory (Y* αβ ) indicates a desired future trajectory of at least one electrical quantity of the converter system (10); from a switching signal (u* abc ) generates the average switch position (V* abc ) sequence, where the switching signal (ua* bc ) is divided into sampling intervals, the average switch position (V* abc ) sequence includes the average switch position (V* abc ), the average switch position is defined by the switching signal (u* abc ) is determined by averaging; by abc ) to determine the optimal average switch position (V* abc ) of the optimized average switch position (V abc ) sequence, the cost function (J) includes the reference trajectory (Y* αβ ) and the predicted trajectory, wherein the predicted trajectory is determined from a model of the converter system within the range, into which the modified average switching position sequence of the converter system and the measurement results are input; by shifting the switching signal (u* abc ) to determine the optimal switching signal (u abc ), so that in the current sampling interval, the switching signal (u abc ) is equal to the average value of the optimized switch position (v abc ); and the optimized switch signal (u abc ) 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] A few years ago, MP was introduced 3 C (Model Predictive Pulse Mode Control) to control the electrical converter. 3 C, the offline optimized pulse pattern can be modified online to control it in a closed loop to better achieve the control target.

[0003] For example, EP 2 469 692 A1 describes a method in which the switching moments generated from an optimized pulse pattern are modified (or shifted) to reduce flux errors.

[0004] MP 3 The concept of C is usually limited to control systems whose dynamics can be described by first-order differential equations. For example, first-order dynamic systems arise when controlling the virtual converter flux vector of a grid-tied converter or when controlling the stator flux vector of an electric motor.

[0005] Because the LC filter adds more than two state variables on each axis of the orthogonal coordinate system, a third-order system may appear when an LC filter is added to a converter system.

[0006] In the presence of LC filters, standard MP 3 C, and the number of virtual filters can be controlled instead of the number of grids or machines. Specifically, the virtual converter flux vector can be controlled. In this way, the current through the inductor of the LC filter can be controlled instead of the grid current or the stator current of the machine. As a result, the control system is a first-order system and can use standard MPLS. 3 C.

[0007] However, the closed-loop behavior of this type of control can be slow. More importantly, poorly damped resonant peaks in the circuit can cause oscillations in the presence of LC filters and / or long cables. In the absence of passive damping, active damping methods may be required to avoid large oscillations. These may require the addition of an active damping control loop.

[0008] WO 2016 / 134874 A1 relates to the time shifting of the switching moments of an optimized pulse pattern. The time shifting is accomplished using model predictive control, where an objective function based on the flux error is minimized.

[0009] EP 3 496 261 A1 mentions that averaging of switching signals can be used to hide the switching properties of a power converter. Quevedo et al. also make this statement in “Model Predictive Control for Power Electronics Applications”, Springer International Publishing, November 30, 2018, pp. 551-580. Summary of the Invention

[0010] It is an object of the present invention to provide a controller for an electrical converter system based on an optimized pulse pattern, which controller has good performance also during transient operation and / or can be used for the converter system as a higher order physical system.

[0011] 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.

[0012] 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 power grid, a resonant subsystem, and / or a high-impedance cable. The resonant subsystem can be a filter, such as an LC filter or an LCL filter. As already mentioned, LC filters can produce higher-order mathematical models, which can be addressed by the present method. The method can be automatically executed by a controller of the converter system.

[0013] According to an embodiment of the invention, the method comprises determining a reference trajectory of a switching signal and of at least one electrical quantity of the electrical converter system within a range of future sampling instants, wherein the switching signal and the reference trajectory are determined from an optimized pulse pattern table, the switching signal comprising and / or defining switching transitions between output levels of an electrical converter of the electrical converter system, and the reference trajectory indicating an expected future trajectory of the at least one electrical quantity and / or an expected future development of the electrical quantity of the converter system.

[0014] The switching signal may include the switching instant and the switch position at the switching instant. The switching signal and all quantities mentioned below may be polyphase quantities, i.e., may have a value for each phase of the converter system. The switch position may be the output level of the electrical converter.

[0015] A switching instant can be the time at which a semiconductor switch of a converter is turned on and off. A sampling instant can be the time at which a measurement and / or estimate is obtained and used to calculate future quantities in a controller. For example, the sampling instants can be equidistant from one another. A switching instant can be located between two sampling instants.

[0016] The controller may determine the switching signal online based on an offline calculated lookup table of optimized pulse patterns, which may have been determined with respect to an optimization target for steady-state operation.

[0017] Furthermore, a reference trajectory may be determined for one or more electrical quantities of the converter system. Electrical quantities may include converter current, grid current, filter capacitor voltage, stator current, stator flux, etc. Generally speaking, electrical quantities may be currents, voltages, and / or fluxes of components of the converter system.

[0018] This can be done by predicting the future quantity from actual values ​​that may have been determined based on measurements. The prediction can be done using a mathematical model of the converter, which may include differential equations for the quantity. The reference trajectory for the optimized pulse pattern may also have been determined offline and read from a lookup table.

[0019] According to an embodiment of the present invention, the method further comprises generating a sequence of nominal (discrete-time) average switch positions based on the nominal (continuous-time) switching signal within the range, wherein the switching signal is divided into sampling intervals and the average switch position is determined by averaging the switching signal in a sampling interval defined by the time instants and the switch positions in the sampling interval. The sequence of nominal average switch positions that can be determined for each phase of the converter system can be interpreted as a step function that changes only at the sampling instants. The sampling interval can be the interval between two consecutive sampling instants. The averaging can be performed such that, in a sampling interval, the average switch position is an accurate representation of the average switching signal in that sampling interval.

[0020] Due to the use of the average switch position, in the following steps of the method, the predicted future value can be determined solely for the sampling instant (and not additionally for the switching instant). This can significantly simplify the controller problem and / or calculations.

[0021] According to an embodiment of the present invention, the method comprises determining an optimized average switching position sequence by optimizing a cost function based on the average switching position sequence, the cost function comprising an error term having a difference between a reference trajectory and a reference trajectory, the reference trajectory and the predicted trajectory both being trajectories of at least one output variable, wherein the predicted trajectory is determined within the range based on a model of the converter system, the modified average switching position sequence of the converter system and the measurement results being input to the model.

[0022] 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 current, capacitor voltage, grid current, machine current, machine flux, etc. The differential equations can be processed in the form of difference equations applicable to the sampling instants. Generally speaking, these quantities can include currents, voltages, and / or fluxes of components of the converter system.

[0023] All of these quantities can be considered as trajectories over time. For each quantity, a sequence of values ​​at sampling moments (i.e., a trajectory) can be determined. When the predicted closed-loop performance becomes optimal, the average switch position sequence is optimized via a cost (or objective) function, into which the reference trajectory and the predicted trajectory are input, and which is optimized (minimized or maximized).

[0024] Prediction and / or optimization may occur relative to constraints such as minimum and maximum voltages, currents, and / or fluxes of specific components of the converter, such as capacitor voltages, current amplitudes, and / or output voltages of the converter.

[0025] The optimization can be performed using quadratic programming implemented in the controller. In this case, the controller solves a previously populated matrix equation based on measurements and / or estimates, reference trajectories and / or switching signals.

[0026] According to an embodiment of the present invention, the method further includes determining an optimized switching signal for the current sampling interval by shifting the switching transitions of the switching signal such that, in the current sampling interval, the average value of the switching signal with the modified switching transitions equals the optimized average switching position. Based on the optimized average switching position optimized by optimizing the cost function, the optimized switching signal and / or at least one optimized switching signal until the next sampling instant can be determined. This can be considered the inverse of the operation described above, in which the average switching position is determined from the optimized pulse pattern.

[0027] According to an embodiment of the present invention, the method further comprises applying the switching signal to the electrical converter at least before the next sampling instant of the optimized switching signal. A rolling range strategy may be implemented by the controller, i.e., determining an optimized average switch position sequence within a range of more than one sampling instant and the optimized switching signal at least before the next sampling instant, and applying only the optimized switching signal before the next sampling instant to the converter.

[0028] In summary, for converter systems with higher-order physical behavior, this method can manipulate the switching moments of a pre-calculated optimized pulse pattern to achieve the following goals:

[0029] Output variables can be regulated along their respective reference trajectories. These might include converter current, capacitor voltage, and grid current for a grid-connected converter with an LC filter. For a converter system with a motor and an LC filter, the output quantities might be electromagnetic torque, stator flux amplitude, stator flux vector, rotor flux, and / or motor speed, as well as inductor current and / or capacitor voltage of the LC filter.

[0030] During steady-state operation, excellent harmonic performance is achieved with optimized pulse mode. Due to the high bandwidth of the controller, disturbances such as DC-link voltage ripple are completely suppressed.

[0031] During transients, disturbances and / or faults, a fast response can be achieved. An example might be excellent low voltage ride-through capability.

[0032] Electrical resonances in the converter system may not be excited and / or any associated oscillations may be actively damped.

[0033] The method may be insensitive to measurement and observer noise and may be robust 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.

[0034] According to an embodiment of the present invention, sampling intervals without switching transitions are discarded, and only the average switch position is optimized for sampling intervals that include at least one switching transition. This can reduce the complexity of the required difference equations. For example, the resulting quadratic program may consist of a matrix of smaller size and dimension, without entries for the discarded sampling intervals. The switching times and / or switching transitions from the discarded sampling intervals of the original switching signal can be interpolated into the optimized switching signal.

[0035] According to an embodiment of the present invention, the optimized average switch position sequence is determined by solving a quadratic program, into which the average switch position sequence, the reference trajectory, and the system model are input. This may result in a cost function equation with a Hessian matrix, which is multiplied by the two input variable vectors. The Hessian matrix of the quadratic program may be time-independent and can be pre-computed, for example, when all sampling intervals are considered in the optimization of the cost function.

[0036] According to an embodiment of the invention, the cost function further comprises a term with the difference of the nominal average switching position and the optimized average switching position.This may lead to an optimization goal that the switching moments are modified as little as possible.

[0037] According to an embodiment of the present invention, the optimized average switch position is determined by optimizing a cost function subject to constraints. As already mentioned, these constraints can include constraints on the voltage, current, and / or flux in the converter system, such that these voltages, currents, and / or fluxes do not leave boundary intervals. The boundary intervals can be defined by constant minimum values ​​and / or constant maximum values.

[0038] According to an embodiment of the present invention, the average switch position in the average switch position sequence is constrained so that the modified switch transition remains within the corresponding sampling interval. This can be achieved by determining the minimum and maximum values ​​of the average switch position for each sampling interval. The minimum value can be the lowest switch position of the nominal switch signal in the sampling interval. Similarly, the maximum value can be the highest switch position of the nominal switch signal in the sampling interval.

[0039] According to an embodiment of the present invention, the average switch positions in the average switch position sequence are constrained so that the modified switch transitions remain in the original order. In this case, the switch transitions may be moved outside their original sampling instants.

[0040] According to an embodiment of the present invention, for each sampling interval, the modified switching transitions of the optimized switching signal are determined by solving a linear programming program with an additional cost function that minimizes the difference between the nominal switching transitions and the corresponding modified switching transitions, and constrains the modification of the switching transitions to be equal to the modification of the average switch position in the sampling interval. The linear programming program can also constrain the modified switching transitions to remain in their respective sampling intervals and original order. In the case where there may be multiple switching transitions between two sampling instants, the modification of the switching transitions can be performed according to the optimization goal of modifying the switching instants as little as possible. This optimization can be performed independently of the optimization of the error between the reference trajectory and the predicted trajectory and / or the average switch position.

[0041] According to an embodiment of the present invention, the reference trajectory includes a converter contribution determined by an optimized pulse pattern and / or a grid contribution determined by an estimated sinusoidal grid voltage. When the converter is connected to the grid, the reference trajectory may be the sum of the reference trajectory with the converter contribution and the reference trajectory with the contribution from the grid voltage. The influence of the converter and the grid on the reference trajectory can be divided into the contribution from the converter and the contribution from the grid.

[0042] The reference trajectory for each respective quantity may be the sum of the converter contribution and the grid contribution of the respective quantity. The converter contribution may be determined from an optimized pulse pattern, for example, offline, and / or may be stored in a lookup table. The grid contribution may be determined from measurements, and the grid voltage may be assumed to be a sinusoidal quantity.

[0043] According to an embodiment of the present invention, the converter contribution to the reference trajectory is determined at support points, which may be spaced differently from the controller sampling instants, and the value of the reference trajectory at the sampling instants is determined by interpolation. For example, the reference trajectory may have support points at the switching instants of the switching signal. Linear interpolation may be performed between these points.

[0044] According to an embodiment of the present invention, the converter contribution of an optimized pulse pattern to a reference trajectory is determined offline and stored in a lookup table. The optimized pulse pattern can be determined for each modulation index and each number of pulses used in the converter system. The actual modulation index and number of pulses can be determined based on actual reference values ​​and / or measured values ​​in the converter system.

[0045] The optimized pulse pattern may have been calculated offline with respect to a specific optimization objective such as minimum total required distortion of current during steady state operation.The optimized pulse pattern may be stored in a lookup table of the controller.

[0046] One or more reference trajectories may also have been determined offline from the optimized pulse pattern. The values ​​of these reference trajectories may also be stored in a lookup table in the controller. These reference trajectories may individually provide a converter contribution to the total reference trajectory, to which the grid contribution may be added.

[0047] Other aspects of the present invention relate to a computer program adapted to perform the method described above and below when executed by a processor, and to a computer-readable medium having such a computer program stored therein. The method may be implemented in software and run on a controller having a processor and a memory having the computer program stored therein.

[0048] 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 medium or a transient medium.

[0049] Another aspect of the invention relates to a controller for an electrical converter, the controller being adapted to perform the method as described above and below. It must be noted that the method can also be implemented at least partially in hardware, for example in a DSP or FPGA.

[0050] Another aspect of the invention relates to a converter system comprising an electrical converter connected to an electrical grid and a controller as described above and below.

[0051] According to an embodiment of the present invention, the converter system further includes a resonant subsystem comprising at least one of the following: an inductor, a capacitor, a filter, and / or a transformer. For example, the resonant subsystem may be an LC filter or a cable having a high impedance. The model of the converter system used during the optimization of the cost function may include models of the electrical converter and the resonant subsystem. In particular, the resonant subsystem may generate higher-order differential equations.

[0052] It has to be understood that features of the method as described above and below may be features of the converter system, the computer program, the computer readable medium and the controller as described above and below, and vice versa.

[0053] These and other aspects of the invention are apparent from and will be elucidated with reference to the embodiments described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The subject matter of the invention is explained in more detail hereinafter with reference to exemplary embodiments illustrated in the drawings.

[0055] FIG1 schematically shows a converter system according to an embodiment of the present invention.

[0056] FIG2 schematically shows a model of the converter system of FIG1 in αβ coordinates.

[0057] FIG. 3 shows a schematic circuit diagram of an electrical converter for use in the converter system of claims 1 and 2 .

[0058] FIG4 shows a block diagram of a controller according to an embodiment of the present invention.

[0059] FIG. 5 shows a block diagram of a portion of the controller of FIG. 4 .

[0060] FIG. 6 shows a block diagram of a portion of the controller of FIG. 4 .

[0061] FIG7 shows a graph with an optimized pulse pattern.

[0062] FIG. 8 shows a graph with reference trajectories used during the method performed by the controller of FIG. 4 to FIG. 6 .

[0063] FIG. 9 shows a diagram explaining the determination of an angle during the method performed by the controller of FIG. 4 to FIG. 6 .

[0064] 10a to 10d illustrate switch signals and average switch positions used during the method performed by the controller of FIG. 4 to FIG. 6 .

[0065] 11 a and 11 b show switch signals and average switch positions used during the method performed by the controller of FIG. 4 to FIG. 6 .

[0066] In principle, identical components are provided with the same reference symbols in the various figures. DETAILED DESCRIPTION

[0067] FIG1 shows a converter system 10 comprising an electrical converter 12, an LC filter 14, and a transformer 16, which are coupled to an electrical grid 18 via a point of common coupling PCC. The converter 12 and the electrical grid 18 are depicted by an equivalent circuit. The corresponding quantities shown in FIG1 are listed at the end of this description.

[0068] Furthermore, FIG1 shows a controller 20 adapted to perform the method for controlling the converter system 10 as described herein.

[0069] The LC filter 14 may include a filter inductor L1 and a filter resistor R2 connected between the converter 12 and the transformer 16 , and a filter resistor R2 and a filter capacitor C2 connected between the converter 12 and the transformer 16 .

[0070] FIG2 shows a more abstract equivalent single-line circuit for the converter system 10 of FIG1. ​​The transformer 16 is connected to the transformer leakage inductance L t and the transformer series resistor R t substituted. The LC filter and transformer are represented by an equivalent circuit of a resonant subsystem 21, which is connected between converter 12 and grid 18. The corresponding quantities shown in FIG2 have been transformed from a three-phase abc system to a stationary orthogonal αβ system using a Clarke transformation (see below). The corresponding quantities are listed at the end of this specification.

[0071] 3 shows an example of an electrical converter 12, which may be a neutral-point clamped converter having a neutral-point clamped phase leg 22 for each output phase. Other converters 12, such as a T-type converter, a modular multilevel converter, and / or a converter with flying capacitors, may be used as the multilevel converter 12.

[0072] System Model

[0073] In the controller 20, a mathematical system model and / or a physical system model is used, which describes a system 10 having a three-level NPC converter 12 connected to a grid 18 via an LC filter and a transformer, as shown in Figures 1 to 3. As previously mentioned, the filter 14 may include components L1 and C2 and their respective series resistances R1 and R2. The transformer 16 may be characterized by its leakage inductance L t and series resistor R t The grid 18 can be represented by a three-phase grid voltage v g,abc(t), grid inductance L g and the grid resistance R g The exact grid parameters may be unknown.

[0074] The converter system 10 can be connected to the grid 18 at the point of common coupling (PCC). At this point, harmonic grid codes may apply. To simplify the problem at hand, it can be assumed that the grid voltage and parameters are known. All quantities refer to the secondary side of the transformer 16.

[0075] Three-phase converter current i c,abc (t), capacitor voltage v cap,abc (t), grid current i g,abc (t), grid voltage v g,abc (t) and the converter voltage v c,abc (t) is transformed into the stationary orthogonal αβ reference frame by Clarke transformation (6, see below). The system model is shown in FIG2 in αβ coordinates.

[0076] From this, the following dynamic equations of the system 10 in the stationary orthogonal reference frame are derived:

[0077]

[0078]

[0079]

[0080] Converter voltage

[0081]

[0082] Equal to the DC link voltage V dc The three-phase switching signal u is scaled to half of abc (t). Note that the three-phase switching signal is defined as u abc (t)=[u a (t) u b (t) u c (t)] T For a three-level converter, the switch positions are constrained to be the set u abc ∈[-1, 0, 1] 3 .

[0083] Select the state vector

[0084]

[0085] And the grid voltage is introduced as an additional state variable into the system 10. Then, the model of the converter system 10 in the αβ framework is as follows:

[0086]

[0087]

[0088] System output

[0089]

[0090] Including converter current, capacitor voltage and grid current. The dimensions of state vector, input vector and output vector are represented by n x 、n u and n y The following derives the system matrix Input Matrix and the output matrix

[0091] The controller at discrete time t = kT s Operation, where Transform the continuous-time dynamic system (4) into a system with sampling interval T s The discrete time domain is completed by the exact discretization of the system:

[0092] x αβ (k+1)=Ax αβ (k)+Bv abc (k)

[0093] y αβ (k) = Cx αβ (k), (5)

[0094] in and matrix is of size n x ×n x The unit matrix of the three-phase input signal υ abc (k)=[υ a (k) υ b (k) υ c (k)] T is a real-valued approximation of the switching signal in the discrete time domain. We refer to this as the average switch position. This variable will be explained in detail below.

[0095] Clarke transform

[0096] Clarke transform is used to transform three-phase quantities from the abc system to a stationary orthogonal reference system. More specifically, Clarke transform transforms the three-phase quantities ξ into abc =[ξ a ξ b ξ c ] T Transformed into vector ξ αβ=[ξ α ξ β ] T ,vice versa:

[0097] ξ αβ =K αβ ξ abc and

[0098] where K αβ and is the transformation matrix given by:

[0099]

[0100] The scaling factor 2 / 3 is needed to ensure constancy of amplitude.

[0101] Continuous-time system models

[0102] Substituting (2) into (1), the notation is simplified by combining the inductance and resistance of the grid and transformer into

[0103] L3=L t +L g And R3=R t +R g

[0104] This yields:

[0105]

[0106]

[0107]

[0108] When assuming that the grid voltages are perfectly sinusoidal, they can be expressed in a stationary orthogonal coordinate system as follows:

[0109]

[0110] in is the amplitude of the grid voltage, ω g =2πf g is the grid angular frequency, θ g is the phase angle. The derivative of the grid voltage is as follows:

[0111]

[0112] Using the definition of the state vector (3) written in vector notation (8) we directly derive the compact continuous-time model (4) with the system matrix, input matrix, and output matrix

[0113]

[0114] and C=[I6 0 6×2 ].

[0115] Note that I2 and O2 are the identity matrix and zero matrix, respectively, of size 2 × 2. The identity matrix I6 is of size 6 × 6.

[0116] Overall control method

[0117] FIG4 shows a block diagram of a controller 20 for executing the method described above and below. The controller includes a converter voltage determination block 24, a mode and reference trajectory loader block 26, a switching table determination block 28, a reference trajectory determination block 30, and a pulse pattern controller block 32. These blocks, as well as the blocks described with respect to the following figures, may be modules of a computer program executed in the controller 20 and / or may be hardware blocks suitable for performing the corresponding functions.

[0118] In the converter voltage determination block 24, the magnitude of the grid voltage is obtained from the absolute value of the measured grid voltage. * and Q * , the required load angle γ can be obtained * This can be done with the help of phasor analysis using the system model shown in Figure 2. The phasor analysis also provides the required converter voltage, which can be calculated using the measured dc link voltage V dc Mapped to the necessary modulation index m.

[0119] The modulation index m is passed to the reference and pattern loader 26 together with the specified number of pulses d. Based on these two parameters, the required OPP is loaded from the lookup table. The OPP is determined by the single-phase vector A * and U * The former maintains a switching angle on a basic waveform, while the latter maintains the corresponding single-phase switch position.

[0120] Corresponding reference trajectory with converter contribution Also loaded from a lookup table that provides a reference for the output variable when OPP is applied and when zero grid voltage is assumed. Reference trajectory provided

[0121] In the switching table determination block 28, the switching table holds the next n p (where p∈{a, b, c}) switching transitions. To calculate the entries in the switching table corresponding to the switching signal, according to the single-phase vector A * and U *Create a three-phase pulse pattern. The desired angular position on the pulse pattern With the help of the voltage grid angle θ at the current sampling time g The switching angle is converted into the switching moment by the following formula:

[0122]

[0123] where ω g represents the angular grid frequency. It can be seen from (11) Finally, the switching transitions that fall within the prediction range are selected and these switching transitions are consistent with their and Nominal switching time in and switch position are stored together.

[0124] In the reference trajectory determination block 30 , a reference trajectory of at least one electrical quantity of the converter system 10 is determined. The contributions of the converters and other quantities are based on the reference trajectory To determine the reference trajectory of offline calculation Maybe just a support point During online operation, the desired angular position on the trajectory can be determined as And the reference vector of the next N sampling moments can be selected by interpolation Calculate grid voltage related trajectories And superimpose the two trajectories. This will be described in more detail with reference to Figure 5. The resulting reference trajectory within the prediction range is transmitted to the pulse mode controller 32 .

[0125] The pulse mode controller 32 described in more detail with respect to FIG. 6 receives the switch table at the current sampling moment, wherein the table entry is and The reference trajectory is and the measured (estimated) state vector is x αβ (k). After transforming the switching signal into the discrete time domain and generating the average switch position After the sequence, the quadratic program is solved as described below to obtain the optimal average switch position V abc (k) sequence. The average switch position modifications are thus determined. These average switch position modifications are converted back into switching moment modifications in continuous time and used to update the nominal OPP switching moment. The modified continuous-time switching signal u is thus determined abc (t), and applies it to the converter within the current sampling interval (i.e., before the next sampling instant).

[0126] Typically, the switching instants within the current sampling interval are provided to the converter along with the new switch positions. This concept can be based on a timestamp. Alternatively, a single switch position can be calculated, for example, by rounding the average switch position to the nearest integer switch position.

[0127] Number of pulses, switching signals and optimized pulse patterns

[0128] For the converter 12 of FIG. 1 to FIG. 3 , a fundamental voltage component is generated at each terminal.

[0129]

[0130] Where p∈{a, b, c} represents the phase, V dc is the total dc link voltage, m∈[0,4 / π] is the modulation index, ω1=2πf1 represents the angular fundamental frequency, and is the time. Number of pulses

[0131]

[0132] is defined as the switching frequency f of a semiconductor switch sw The ratio between the fundamental frequency f1.

[0133] In order to characterize the general periodic switching signal, it is assumed that the basic period is 2π. The 2π periodic switching signal u with the number of pulses d * (θ) is given by the 4d switching angle where i∈{1,...,4d} and 4d+1 switch positions where i∈{0,...,4d} Definition, see Figure 7. The i-th switching angle corresponds to the i-th switching transition

[0134]

[0135] Multilevel converters usually prohibit switching more than one level up or down; this constrains the switching transitions to Furthermore, for a three-level converter, the switch positions are constrained to

[0136] FIG. 7 shows an example of an optimized pulse pattern from which the switching signal can be derived.

[0137] Optimized pulse mode A * 、U * It may be a solution to the optimization problem subject to constraints. According to the definition of the switching signal, there are two sets of optimization variables in the optimization problem: the switching angle set and switch position set The switch position set also includes an initial switch position.

[0138] Typically, for optimized pulse mode A * 、U * The cost function J(A * ,U * ) can capture the total demand distortion (TDD) of the current, which is either the grid current of the grid-tied converter or the stator current of the machine-side inverter.

[0139]

[0140] is the amplitude of the nth order current harmonic relative to the nominal (or rated) current The square root of the sum of squares, where I nom is the rms value of the nominal current.

[0141] Usually the OPP optimization problem is to subject the objective function J(A * , U * )Minimum:

[0142] The dc component of the switching signal is zero;

[0143] The phase of the fundamental component is zero;

[0144] Amplitude of the fundamental component Equal to the modulation index m;

[0145] Switch angles are arranged in ascending order; and

[0146] Switch transition is limited to ±1.

[0147] This leads to a general OPP optimization problem of the following form:

[0148]

[0149] Subject to a0=0,a1=0,b1=m (16)

[0150]

[0151]

[0152] Where a0, a1 and b1 are the switching signals u * Fourier coefficients of (θ).

[0153] Reference trajectory

[0154] The reference trace can be the steady-state waveform of the nominal output variable over one fundamental cycle. These steady-state waveforms are directly derived from the nominal OPP (assuming no disturbances, no dc link voltage ripple, no ripple on the neutral point potential, etc.). Note that the output variable is a subset of the state.

[0155] To calculate the reference trajectory, the converter and grid voltage can be considered as inputs to the system using the concept of superposition. In this way, the grid voltage can be removed from the state vector and a definition with The reduced state vector of the state variables.

[0156]

[0157] Corresponding to the continuous-time state-space model

[0158]

[0159]

[0160] The grid voltage is considered as a time-varying parameter. In this model, the state variable and the output variable are the same; this implies that

[0161] To calculate the matrix of the reduced state space model (17a), the grid voltage can be considered as a parameter instead of a state variable. The new system matrix It can be derived from F by removing the seventh and eighth dimensions:

[0162]

[0163] The input matrix G can be replaced by two new input matrices:

[0164]

[0165] Reference trajectory calculation

[0166] The controller needs the reference vector for the next N sampling moments

[0167]

[0168] By using the superposition method, the converter voltages are calculated separately and grid voltage Contribution to the reference trajectory. This is shown in more detail in Figure 5. First, the output trajectory as a function of the converter voltage can be calculated; this calculation can be done offline for all required modulation indices and pulse numbers. The pattern loader 34 can load the optimized pulse pattern A * 、U * Thus, the reference trajectory within one fundamental period can be determined in the reference calculation block 36 These trajectories contain freely chosen reference sampling instants The reference vector and the optimized pulse pattern A * 、U * During online operation, the trajectory within one basic cycle calculated offline is stored in the lookup table. and the reference sampling vector can be loaded by the reference and pattern loader 26. Thus, the reference selector block 38 can select the appropriate reference vector for the next N sampling instants as The output trajectory as a function of the grid voltage for the next N sampling instants can also be calculated online in the reference selector block 38 The two output trajectories are then superimposed to produce the overall output vector trajectory.

[0169] Converter Contribution Trajectory Calculation (Block 36)

[0170] Consider a nominal OPP with modulation index m and pulse number d, where the switching angle vector is A * And the switch position vector is U * Based on these, the three-phase switching signal can be constructed The three-phase switching signal There are 4d switching transitions in each of the three phases. A single switching angle vector is created containing the switching angles in ascending order α = [α0 α1 α2 ... α n+1 ] T Arranged n = 3·4d switch angles. New names are assigned to the switch angles according to their sorted position. Note that the initial angle α0 = 0 and the final angle α n+1 =2π is to simplify the calculation within a basic period of 2π.

[0171] It can be switched at two consecutive switching angles α i and α i+1 Determine the constant three-phase switch position between Given α i The state vector at Use (17a) to calculate the next switching angle α i+1 The state vector at which the grid voltage v g,αβ is set to zero:

[0172]

[0173] in

[0174] and

[0175] and i∈{0, 1, 2, ..., n+1}. Now, we can recursively substitute into (20) to calculate the state vector at the switching angle within the entire basic period:

[0176]

[0177]

[0178]

[0179]

[0180]

[0181] The matrix product can be simplified by noting that:

[0182]

[0183] The first term in (25) is further reduced as follows:

[0184]

[0185] Through (26) and (27), (25) can be rewritten as follows:

[0186]

[0187] Due to the periodicity,

[0188]

[0189] By substituting (28) into (29), the initial state vector is derived as a function of the switching signal:

[0190]

[0191] Since α0 = 0 and (17b), (30) represents the nominal output vector at the beginning of the fundamental period Where θ=0.

[0192] In the following, the evolution of the nominal output vector over the fundamental period is calculated. For this purpose, the angular interval Δθ is used * Angles between 0 and 2π are meshed and the reference angle is calculated using the reduced system model (17a) The output vector at :

[0193]

[0194] Reference sampling time within a basic cycle and the resulting trajectory of the nominal output vector

[0195]

[0196] This can be done for each pulse number and modulation index.

[0197] Reference selector (block 38)

[0198] The reference selector 38 can be loaded with a pre-calculated output trajectory for the appropriate pulse number d and modulation index m The reference vector for the next N sampling moments can be selected from these output trajectories in the following manner, see also Figure 8. First, the grid voltage angle θ is obtained according to the following formula g and the load angle γ* determine the angular position of the converter voltage

[0199]

[0200] The load angle depends on the active power reference P * and reactive power reference Q * In Figure 9, examples of converter and grid voltages are shown in a stationary quadrature reference frame.

[0201] Nominal output vector within the prediction horizon N

[0202]

[0203] Can be calculated by interpolation.

[0204] Grid Contribution Trajectory Calculation (Block 40)

[0205] For the online calculation of the output trajectory as a function of the grid voltage, the converter voltage in (17a) can be set to zero and a perfectly sinusoidal grid voltage can be assumed. The corresponding state vector is The grid voltage is given by the following formula in the stationary orthogonal αβ coordinates:

[0206]

[0207] in is the amplitude of the grid voltage, ω g =2πf g is the grid angular frequency, and θ g It can be seen that all state variables are the grid frequency θ g Then, each pair of state variables in stationary orthogonal coordinates can be described by:

[0208]

[0209] And it evolves according to the differential equation:

[0210]

[0211] The derivatives of the state vector can be determined in an explicit manner, and (17a) can be rewritten as follows:

[0212]

[0213] Note that 02 is a 2×2 zero matrix. By rearranging (37), we can obtain the nominal output vector as a function of the grid voltage

[0214]

[0215] (17b) has been used. The matrix is ​​as follows:

[0216]

[0217] Superposition of reference trajectories

[0218] By superposition, the resulting overall output trajectory of the system is derived as follows:

[0219]

[0220] The resulting overall output trajectory contains the output vectors for the next N sampling moments, i.e.,

[0221]

[0222] This trajectory includes the contribution from the OPP calculated offline and the contribution from the grid voltage calculated online. It can be used by the controller 20 as a reference for the output variable within the prediction horizon.

[0223] Pulse Mode Controller

[0224] FIG6 shows the pulse mode controller of FIG4 in more detail. In the pulse mode controller, in order to achieve optimal trajectory tracking, the continuous time OPP is converted into a discrete time average switch position sequence, so that the controller 20 can use the discrete time model for prediction. The switch signal conversion block 42 will be composed of a and The switch table defines the switch signal Converted into optimized average switching position sequence, the optimized average switch position The sequence is optimized by the optimizer block 44 to an optimized average switch position V abc (k) Sequence. Modify ΔV by optimizing the average switch position. abc (k) sequence, determining the switch signal in block 46 The time shift Δt of the switching moment abc , these time offsets are used to update the data with entries in block 48 and In block 50, the optimized switching signal u for the current sampling interval is determined from it. abc (t), the optimized switching signal u abc (t) can be applied to the converter 12.

[0225] In particular, at the sampling time kT s , with entries and The switch table contains the current time kT s and prediction horizon (k+N)T s The nominal three-phase switch positions and the nominal switching moments of the continuous time OPP between the end of the period. Thus, the nominal average switch position is generated within the prediction range by the switching signal transformation explained below. A real-valued discrete time series.

[0226] Switch signal conversion (block 42)

[0227] Block 42 converts the continuous time switch signal Converted to discrete time average switch position This is done for each phase individually. Discrete value switching signal becomes the real-valued average switch position where p∈{a, b, c} and t∈[kT s , (k+1)T s ], the real-valued average switch position The k-th sampling interval has the same average switch position.

[0228] Figures 10a to 10d show, as an example, the mutually determined single-phase nominal switching signals Single-phase average switch position Optimize single-phase average switch position and optimize the single-phase switching signal u p (t).

[0229] Single-phase switching signal By having entry and The nominal switch table is constructed according to the prediction range (k+N)T s The current sampling time kT at the end of s Define the switch signal. The switch signal approximation (average switch position) is obtained by calculating the kth sampling interval [kT s , (k+1)T s] is averaged to derive the continuous-time switching signal within:

[0230]

[0231] Let n pk is the number of switching transitions occurring in phase p during the kth sampling interval

[0232]

[0233] To simplify the export, the interval limits are renamed as follows:

[0234]

[0235] Switching signal at the switching moment and With constant switch position between Through this constant switch position (41) By splitting the integral into n constant switch positions pk +1 interval to solve, which yields:

[0236]

[0237] Define the i-th time interval of constant switch position

[0238] where i = 0, 1, ..., n pk , (45)

[0239] (44) can be further simplified as follows:

[0240]

[0241] This equation illustrates the general transformation of a single-phase switching signal into an average switch position in the k-th sampling interval (ie, the k-th average switch position), where n pk A switch change.

[0242] When n pk = 0, which means that there is no switch transition in the kth sampling interval, as defined in (45) for the time interval τ of the constant switch position. p0 as follows:

[0243]

[0244] Substituting (47) into (46) yields:

[0245]

[0246] This implies that the average switch position corresponds to the switch position of the nominal OPP during the sampling interval.

[0247] The nominal average switch position of each phase in the kth sampling interval is summarized in the three-phase nominal average switch position vector The average switch position sequence can include the sequence from the current sampling time kT s Until in the range (k+N)T s The average switch position at the end of

[0248]

[0249] Constraints on average switch positions

[0250] The three-phase average switch positions within the prediction horizon can be the manipulated variables of the controller. Their sequence can be defined as the vector

[0251]

[0252] Consider phase p and assume that n pk A switch transition. Let t pi represents the i-th modified switching time, where i∈{1, 2, ..., n pk}. The order of switching times is required to remain unchanged in each phase. To achieve this, the constraint

[0253]

[0254] Applied to the modified switching times. This is done for each phase separately. No constraints are applied between these phases.

[0255] Let v p (k) represents the modified average switch position in phase p and the kth sampling interval. This variable is operated by the controller within the limits

[0256]

[0257] in u p (k) is the manipulated variable v p (k) is the lower limit, and is its upper bound. To derive these bounds, note that the continuous-time switching signal The minimum (maximum) value of is given by the lowest (highest) switch position in the sampling interval, where t∈[kT s , (k+1)T s ]. The lower and upper limits are as follows:

[0258] and

[0259] These definitions hold independent of the number of switching transitions in the sampling interval.

[0260] In the sampling interval where no switching transition occurs, that is, where n pk = 0, the average single-phase switch position remains equal to the nominal switch signal at the kth sampling moment Right now,

[0261]

[0262] By the constraints described above, the switching moments cannot move outside their respective sampling intervals, see (51). This implies that the lower and upper constraints on the average switch position are determined by the minimum and maximum switch positions that can be synthesized within the sampling interval.

[0263] In order to relax the constraints imposed by the sampling interval, we can give Δv p,max To relax the limit, it is allowed to move the switching moment outside its corresponding sampling interval.

[0264] Alternatively, the sampling interval constraint can be removed entirely. Consider a phase p, where p∈{a, b, c}, and consider its n within the prediction range p Then, constraint (51) is extended to the entire prediction range, i.e.,

[0265]

[0266] kT s The lower constraint at (k+N)T ensures that the switching instant does not move into the past. s The upper limit constraint at the last switching moment The constraint in (55) can be transformed into an equivalent constraint on the average switch position in the discrete time domain υ p (l), where l∈{k, k+1, ..., k+N}. These constraints can be added for each phase p. Coupling constraints between the three phases may not be required.

[0267] Optimization phase (block 44)

[0268] In block 44, the method implements trajectory tracking by modifying the average switch position sequence so that the prediction tracking error within the prediction range is minimized at the sampling instant. The required input is the measured (or estimated) state vector x αβ (k), reference trajectory Nominal average switch position The sequence and discrete-time system models (5) are used to predict the tracking error at each sampling instant within the prediction horizon. The controller manipulates the average switch position V defined in (50) abc (k) Sequence.

[0269] Cost function

[0270] The cost function of the optimization problem can be defined as follows:

[0271]

[0272] The cost function is the average switch position V within the prediction range abc (k) Function of the sequence. Tracking error is the optimal steady-state reference trajectory calculated in (39) and the optimal steady-state reference trajectory calculated using V abc (k) is the difference between the output predictions obtained as input from the discrete-time system model (5). The positive penalty matrix Q adjusts the weight of the tracking error of each output variable. Note that

[0273] The control effort corresponds to the degree to which the mean switch position is corrected. It can be defined as the difference between the nominal mean switch position and the modified mean switch position. The control effort is based on the scalar weight λ υ >0 is the cost.

[0274] constraint

[0275] For each phase and sampling interval, the constraints on the average switch position (52) can be derived through Algorithm 1.

[0276] Algorithm 1 Average switch position constraint

[0277]

[0278] The upper limit of the average switch position is summarized in the following formula:

[0279]

[0280] Thus, the lower bounds are summarized in the vector V abc (k). This gives the general formula for the constraint:

[0281] GV abc (k)≤g, (58)

[0282] in

[0283] and

[0284] Note, I3N Represents the identity matrix of size 3N×3N.

[0285] One of the main benefits of MPC is its ability to impose constraints on state, input, and output variables. It can be beneficial to impose constraints on output (or controlled) variables to limit overshoot during transients and faults. By limiting converter currents and capacitor voltages to their safe operating regions with output constraints, damage to the converter and its passive components can be avoided.

[0286] Based on the current state vector x αβ (k) and future operation variable V abc (k) sequence, which can predict the future output variable Y αβ (k). It is simple to impose upper and lower constraints on these output variables. To ensure that a solution to the quadratic program always exists, that is, to ensure that the manipulated variable V can be calculated for a given state vector and OPP in all cases abc (k) sequences, it is proposed to impose constraints on the output variables as soft constraints. These introduce slack variables in the inequality constraints, which are heavily penalized in the addition of terms to the objective function. Doing so, it is possible to (minor) violate the output constraints, albeit at the cost of a large penalty in the objective function.

[0287] Quadratic Programming

[0288] The cost function J in (56), the inequality constraints (58) and the discrete-time system model (5) form the basis for formulating the optimization problem that forms the basis of the present method. The following optimization problem can be formulated:

[0289]

[0290] Subject to x αβ (1+1)=Ax αβ (l)+Bv abc (l) (60)

[0291] y αβ (1+1)=Cx αβ (l+1)

[0292] GV abc (k)≤g.

[0293] To solve this problem, it can be reformulated into a traditional quadratic programming (QP) form.

[0294] At the current sampling time kT s The sequence of predicted output variables within the forecast horizon calculated at is as follows:

[0295]

[0296] It can be derived by recursively substituting into (5) as a function of the current state vector and the modified average switch position sequence. This yields:

[0297]

[0298] Recall that V abc (k) is the modified average switch position sequence defined in (50). Define the penalty matrix:

[0299]

[0300] in With this definition and (62), the cost function (56) can be rewritten as follows:

[0301]

[0302] Finally, the cost function is as follows:

[0303]

[0304] in

[0305]

[0306]

[0307]

[0308] Note that during optimization, the term θ(k) remains constant and can therefore be ignored in the cost function.

[0309] In summary, quadratic programming (QP)

[0310]

[0311] Subject to GV abc (k)≤g

[0312] Generate, where the Hessian matrix H and parameter vector Θ(k) are defined in (65) and (66), respectively. By solving QP at time step k, the optimal average three-phase switch position V within the prediction range can be obtained abc (k) Sequence.

[0313] By subtracting the nominal average switch position sequence, the optimal average switch position modified sequence

[0314]

[0315] These modifications are proportional to the volt-second modifications that are applied to each sampling interval and each phase within the prediction horizon.

[0316] Low-dimensional quadratic programming

[0317] The proposed control method can be extended in various ways. Due to the three phases and the prediction horizon N, the optimization vector V of QP abc The dimension of (k) is 3N. The time required to solve the QP depends largely on V abc (k) dimension. To speed up the computation, the problem dimensionality can be easily reduced. Recall that the controller 20 can be allowed to modify the average switch position only in sampling intervals where at least one switching transition occurs. In contrast, in this case, the average switch position cannot be manipulated in sampling intervals without switching transitions; therefore, the average switch position in these sampling intervals is fixed and can be removed as a degree of freedom. This means that the dimensionality of the optimization vector can be reduced accordingly. However, the Hessian matrix then becomes a time-varying matrix.

[0318] Switching moments as decision variables

[0319] In the alternative problem formulation, the switching time of the switching transition is modified by Δt pi can be used as a decision variable. As mentioned before, the average switch position v p (k) is used as input to the discrete-time system model (5). However, the average switch position V abc The (k) sequence (see (50)) is now considered as an auxiliary variable rather than a decision variable. The mean switch position is derived from the nominal mean switch position according to (46) and the average switch position modification Δv p (k) obtaining:

[0320]

[0321] At each time step l∈{k, k+1, ..., k+N} within the prediction horizon and for each phase p, where p∈a,b,c, an equality constraint of the form:

[0322]

[0323] The form of these equality constraints is the same as in (78, see below).

[0324] The switching timing modifications in the three phases within the prediction horizon are summarized in the vector:

[0325]

[0326] The following QP can be derived: The cost function is the same as that in (68). An additional equality constraint of the form (70) is added. With the help of Constraint (55) is added as an inequality constraint. The decision variables for solving QP are the vector ΔT as defined in (71).

[0327] Inverse Transform (Blocks 46, 48, and 50)

[0328] Average switch position modification ΔV in the discrete time domain abc (k) The sequence can be converted back to the continuous time domain to modify the switching moments:

[0329]

[0330] This can be done separately for each phase and each sampling interval within the prediction range. Let Δv p (k) represents the kth sampling interval and n pk Average switch position modification in phase p where a switching transition occurs. Average switch position modification Δv p (k) must be equal to n in the sampling interval and phase pk Modify Δt by the switching moment pi , where p∈{a, b, c} and i∈{1, 2, ..., n pk}.

[0331] Consider the single-phase average switch position modification in the k-th sampling interval:

[0332]

[0333] where v p (k) is the modified average switch position in the kth sampling interval. Recall that n pk represents the number of nominal switching transitions in the kth sampling interval, and the sampling interval limits are renamed according to (43). In (73), Replace with (44); v p (k) can be replaced by the equivalent equation without the superscript *. This yields:

[0334]

[0335] Note that according to (43), the first and last switching instants of the modified average switching position and the nominal average switching position are equal, since they correspond to the sampling interval limits

[0336] and

[0337] Furthermore, the i-th switching moment modification in phase p is defined as:

[0338]

[0339] As the modified switching time t pi With nominal switching time The difference between . Through (75) and (76), the sum in (74) is reduced to:

[0340]

[0341]

[0342] By switching in (14) The definition of (77) is simplified as follows:

[0343]

[0344] Therefore, the relationship

[0345]

[0346] The volt-second modification in the kth sampling interval is retained.

[0347] To calculate the switching moment modifications, a linear optimization problem, also known as linear programming (LP), can be solved:

[0348]

[0349] subject to

[0350]

[0351] The goal is to modify the switching instants as little as possible. This can be achieved by using a 1-norm to penalize the switching instant modifications. Recall the constraint (51) on the modified switching transitions, which ensures that the order of the switching transitions remains unchanged and the switching instants are constrained to the sampling interval. With the help of Constraint (80c) follows directly. Solving LP yields the vector modified at the switching moment

[0352] Rolling Range Strategy

[0353] The controller 20 can be operated in a rolling range manner, as shown in the single phase case in Figures 11a and 11b. Figure 11a shows the time step kT s The modified switching signal u in the continuous time domain at p and the modified average switch position u in the discrete time domain p; Figure 11b shows the time step (k+1)T s Both figures show the nominal OPP in the past 52, the predicted range 54 and the out-of-range 56.

[0354] At time kT s At this point, the controller determines the optimal average switch position V within the prediction range of N steps. p (k)[υ p (k)υ p (k+1)...υ p (k+N-1)] T , sequence, see Figure 11a. The average switch position sequence is converted from the discrete time domain to a modified switch signal in the continuous time domain. Only the switch signal (i.e., u) in the current sampling interval (i.e., before the next sampling instant) is p (t)) can be applied to the converter system 10, where t∈[kT s , (k+1)T s ].

[0355] At the next sampling time (k+1)T s At , the controller 20 receives the new reference value and the new state vector. Based on these, a new optimization problem is formulated and solved. The solution to this problem is the modified average switch position V p (k+1) sequence, see Figure 11b. p (k+1) may be different from [υ p (k+1) υ p (k+2)...υ p (k+N-2)] T This can be significantly different, especially during large disturbances and transients.

[0356] In general, rolling range strategies can provide feedback and a high degree of robustness in the presence of unmodeled disturbances and inaccuracies in the model.

[0357] symbol

[0358] t time,

[0359] k discrete time steps,

[0360] l is the number of discrete time steps within the forecast horizon, l∈[k, k+1, ..., k+N]

[0361] d number of pulses,

[0362] m modulation index, m∈[0, 4 / π]

[0363] Nominal i-th switching angle,

[0364] Nominal i-th single-phase switch position, e.g.,

[0365] Nominal i-th switching transition,

[0366] Continuous-time three-phase nominal switching signals, e.g.

[0367] v g,αβ (t) Grid voltage in stationary orthogonal αβ coordinates

[0368] i g,αβ (t) Grid current in stationary orthogonal αβ coordinates

[0369] v cap,αβ (t) Capacitor voltage in stationary orthogonal αβ coordinates

[0370] v c,αβ (t) Converter voltage in stationary orthogonal αβ coordinates

[0371] i c,αβ (t) Converter current in stationary orthogonal αβ coordinates

[0372] x αβ (t) State variables in stationary orthogonal αβ coordinates

[0373] y αβ (t) Output variable in stationary orthogonal αβ coordinates

[0374] E, System matrix in the continuous time domain

[0375] G, Input matrix in continuous time domain

[0376] A, System Matrix in Discrete Time Domain

[0377] B, Input matrix in discrete time domain

[0378] C Output matrices in the continuous-time and discrete-time domains

[0379] ω g Basic grid frequency

[0380] θg Grid voltage phase angle

[0381] N is the prediction horizon,

[0382] The sampling angle is calculated based on the reference trajectory of the converter voltage,

[0383] In a basic period of stationary orthogonal αβ coordinates The sampled reference trajectory based on the converter voltage,

[0384] The time kT in the stationary orthogonal αβ coordinates s Reference trajectory contribution from the converter voltage calculated at

[0385] The time kT in the stationary orthogonal αβ coordinates s The contribution from the reference trajectory of the grid voltage within the range calculated at

[0386] The time kT in the stationary orthogonal αβ coordinates s The reference trajectory of the controller within the range calculated at

[0387] t pi The modified i-th switching instant of the phase,

[0388] Δt pi Switching moment correction in phase p of the i-th switching transition,

[0389] T s Sampling interval,

[0390] n p The number of switching transitions in phase p occurring within the prediction horizon,

[0391] n pk The number of switching transitions in phase p in the kth sampling interval,

[0392] v abc (k) The modified average switch position of the three phases in the kth sampling interval, u abc ∈[-1, 1] 3

[0393] The nominal three-phase average switch position sequence within the range starting from the kth sampling interval,

[0394] V abc (k) The modified (or optimized) three-phase average switch position sequence within the range starting from the kth sampling interval, V abc ∈[-1, 1] 3N

[0395] Δv p (k) Correction of the average switch position in phase p in the k-th sampling interval,

[0396] ΔV abc (k) the three-phase average switch position modification sequence within the range starting from the kth sampling interval,

[0397] Hessian Matrix in H QP

[0398] variable

[0399] z(t) is a scalar in the continuous time domain.

[0400] z(k) is a scalar in the discrete-time domain

[0401] z refers to the column vector of the three-phase quantity, for example

[0402] Z is a scalar or vector sequence or a column vector of a matrix at multiple time moments

[0403] superscript

[0404] i * ,u * Current reference or nominal switching signal

[0405] Reduced dimensionality state vector

[0406] z T Row vector

[0407] The amplitude of the nth switching signal harmonic

[0408] abbreviation

[0409] dc direct current

[0410] LP linear programming

[0411] MPC Model Predictive Control

[0412] MP 3 C-model predictive pulse mode control

[0413] MP 3 C+ Generalized Model Predictive Pulse Mode Control

[0414] NPC Neutral Point Clamp

[0415] OPP Optimized Pulse Mode

[0416] PCC Point of Common Coupling

[0417] QP Quadratic Programming

[0418] rms root mean square

[0419] TDD Total Demand Distortion

[0420] 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 switching signal within the future sampling time range and a reference trajectory of at least one electrical quantity of the electrical converter system (10) The switching signal and the reference trajectory From the optimized pulse mode (A * ,U * ) table to determine, the switch signal comprising switching transitions between output levels of the electrical converter of the electrical converter system (10), and the reference trajectory indicating a desired future trajectory of the at least one electrical quantity of the converter system (10); According to the switching signal within the range Generate average switch position sequence, in which the switching signal is divided into sampling intervals, the average switch position The sequence consists of the average switch position for each sampling interval The average switch position is obtained by defining the switch signal at the switching moment and the output level in the sampling interval. Averaging is performed to determine; By based on the average switch position The cost function (J) is optimized to determine the optimal average switch position (v abc ) of the optimized average switch position (V abc ) sequence, the cost function (J) includes the reference trajectory and the predicted trajectory, and the cost function also includes an error term having the average switch position and the optimized average switch position (v abc ), wherein the predicted trajectory is determined within the range based on a model of the converter system, the modified average switching position sequence of the converter system and the measurement results being input to the model; By moving the switch signal The optimal switching signal (u abc ), so that in the current sampling interval, the switching signal (u abc ) is equal to the average value of the optimized average switch position (v abc ); The optimized switch signal (u abc ) is applied to the electrical converter system (10).

2. The method according to claim 1, The sampling interval in which there is no switch transition is from the average switch position The average switch position is only optimized in the sampling interval including the switching transitions.

3. The method according to claim 1 or 2, The optimized average switch position (V abc ) sequence is determined by solving quadratic programming, the average switch position, the reference trajectory and the predicted trajectory is input into the quadratic programming.

4. The method according to claim 1 or 2, The optimized average switch position (V abc ) a sequence is determined by optimizing said cost function subject to constraints; The average switch position (v abc ) is constrained so that the modified switching transition stays in the corresponding sampling interval.

5. The method according to claim 1 or 2, The optimized average switch position (V abc ) a sequence is determined by optimizing said cost function subject to constraints; The average switch position (v abc ) are constrained so that the modified switch transitions remain in the original order.

6. The method according to claim 1 or 2 The reference trajectory With converter contribution The converter contributes The optimized pulse mode (A * ,U * )Sure; The reference trajectory Contribute to the power grid The grid contribution Determined by estimating the sinusoidal grid voltage; The reference trajectory is the converter contribution and the grid contribution The sum of .

7. The method according to claim 1 or 2, For a reference trajectory within a basic cycle The converter contribution of is determined at support points that have a different spacing from the controller sampling instants, and the reference trajectory The value at the controller sampling instant is determined by interpolation.

8. The method according to claim 1 or 2, The optimized pulse mode (A * ,U * ) and the reference trajectory Converter contribution is determined offline and stored in a lookup table.

9. The method according to claim 1 or 2, The optimized switching signal (u abc ) are determined by solving a linear program with a further cost function, which minimizes the difference between the unmodified switching transitions and the corresponding modified switching transitions.

10. A computer program product comprising a computer program adapted to perform the method according to any one of claims 1 to 9 when the computer program is executed by a processor.

11. A computer-readable medium having stored thereon the computer program product according to claim 10.

12. A controller (20) for an electrical converter, adapted to perform the method according to any one of claims 1 to 9.

13. A converter system (10), comprising: an electrical converter (12) interconnected with an electrical grid (18); The controller (20) of claim 12, configured to control the electrical converter.

14. The converter system (10) of claim 13, further comprising: a resonant subsystem (21) comprising at least one of an inductor, a filter (14) and / or a transformer (16); 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 (21).

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