Method and control unit for controlling an electric converter and converter system

Abstract

A method for controlling an electric converter (16) is provided. The electric converter (16) is coupled to a DC energy source and to an electrical grid and is configured for converting a DC voltage from the DC energy source into an AC voltage and feeding the AC voltage into the electrical grid. The method comprises the following steps: receiving a grid current signal representing a grid current of the electrical grid and a grid voltage signal representing a grid voltage of the electrical grid; determining grid current harmonics of the grid current and grid voltage harmonics of the grid voltage from the grid voltage signal and the grid current signal (see equation (I)); determining an optimized pulse pattern (see equation (II)) for driving the electric converter (16) from the determined grid current harmonics, the determined grid voltage harmonics (see equation (I)) and a given fundamental grid current setpoint (see equation (III)), wherein the optimized pulse pattern (see equation (IV)) comprises switching angles (see equation (V)) of the electric converter (16) for a next modulation period of the electric converter (16); and applying at least one next switching angle determined from the optimized pulse pattern to the electric converter (16).

Description

Technical Field

[0001] This invention relates to the field of high-power converter control. Specifically, this invention relates to a method and a control unit for controlling an electric converter, as well as a converter system including the control unit and the electric converter. Background Technology

[0002] It is known to drive electric converters using pulse modes, such as Selective Harmonic Elimination (SHE) or Optimized Pulse Mode (OPP), which can be determined offline independently of the converter's operation. These pulse modes can be stored in a lookup table and used to drive the converter, and it is also known to modify these predetermined pulse modes online when driving the converter.

[0003] However, such pulse patterns used to drive electric converters do not inherently have a modulation period of fixed length. Therefore, unlike carrier-based methods, it is impossible to distinguish the fundamental component and its harmonic content from a single, fixed-rate ripple current sample. Given a sinusoidal current setpoint at the fundamental frequency, controlling such pulse patterns with a linear controller when feeding back this ripple current sample will be difficult. Harmonics will be interpreted as tracking errors, and depending on the design, the controller will attempt to eliminate them.

[0004] Taking SHE as an example, this objective leads to poor harmonic performance. For OPP, the objective is to minimize a wider harmonic spectrum, not just eliminate a few selected harmonics. When a linear controller controls OPP, its bandwidth must be strictly limited to maintain OPP's superior harmonic performance. This limits the controller's inherent tendency to eliminate harmonics when feeding back current samples with high ripple components.

[0005] The paper "Grid integration improvement for single-phase inverters of small wind turbines under distorted voltage conditions" published by Nguyen Thah Hai et al. in the *International Journal of Electrical Power & Energy Systems* (Jordan Hill, Oxford, GB, vol. 87, 14 November 2016, pp. 144-153, XP029868528, ISSN: 0142-0615, DOI:10.1016 / J.IJEPES.2016.11.003) describes a method for grid-connected single-phase inverters in small wind turbines based on PMSG (Permanent Magnet Synchronous Generator) under distorted grid voltage conditions. The inverter is connected to both DC power and the grid. Current is injected into the grid, referred to as grid current. A composite observer used to extract the fundamental and harmonic components of the grid voltage and current facilitates current control operation and synchronizes the inverter with the grid. The harmonic components of grid voltage and current are used as state variables in the composite observer model to perform pulse width modulation.

[0006] The paper "Optimized Pulse Patterns for the 5-Level ANPC Converter for HighSpeed ​​High Power Applications" published by Jorg Meili et al. at IEEE Industrial Electronics, IECON 2006 - 32nd Annual Meeting, IEEE, Piscataway, NJ, USA, November 1, 2006, pp. 2587-2592, XP031077188, ISBN: 978-1-4244-0135-2 describes the total harmonic distortion (THD) analysis of an active midpoint clamped five-level converter (ANPC5L) for high-speed, high-power applications, comparing different optimized pulse patterns with the traditional pulse width modulation (PWM) method. Summary of the Invention

[0007] The object of this invention is to provide a method and control unit for controlling an electric converter, which contributes to high-quality output voltage of the electric converter, is compatible with a variety of optimized pulse modes, and / or enables low total harmonic distortion (THD). Furthermore, the object of this invention is to provide a converter system including the control unit and the electric converter.

[0008] These objectives are achieved through the subject matter of the independent claims. Further exemplary embodiments will become apparent from the dependent claims and the following description.

[0009] One aspect of the present invention relates to a method for controlling an electric converter. The electric converter is coupled to a DC power source and a power grid. The electric converter is configured to convert a DC voltage from the DC power source into an AC voltage and feed the AC voltage into the power grid. The method includes the steps of: receiving a grid current signal representing a grid current and a grid voltage signal representing a grid voltage; determining grid current harmonics of the grid current and grid voltage harmonics of the grid voltage based on the grid voltage signal and the grid current signal; determining an optimized pulse pattern for driving the electric converter based on the determined grid current harmonics, the determined grid voltage harmonics, and a given fundamental grid current setpoint, wherein the optimized pulse pattern includes the switching angle of the electric converter in the next modulation cycle of the electric converter; and applying at least the next switching angle determined from the optimized pulse pattern to the electric converter.

[0010] Another aspect of the invention relates to a control unit for controlling an electric converter. The control unit includes: a harmonic observer electrically coupled to a power grid and configured to receive a grid current signal representing a grid current and a grid voltage signal representing a grid voltage, and to determine, based on the grid voltage signal and the grid current signal, a grid current harmonic of the grid current and a grid voltage harmonic of the grid voltage; and a harmonic controller electrically coupled to the harmonic observer and the power grid and configured to determine, based on the determined grid current harmonic, the determined grid voltage harmonic, and a given fundamental grid current setpoint, an optimized pulse pattern for driving the electric converter, wherein the optimized pulse pattern includes the switching angle of the electric converter in the next modulation cycle of the electric converter, and applies at least the next switching angle determined from the optimized pulse pattern to the electric converter.

[0011] Another aspect of the present invention relates to a converter system. The converter system includes: an electric converter coupled to a DC power source and a power grid, configured to convert a DC voltage from the DC power source into an AC voltage and feed the AC voltage into the power grid; and a control unit as described above and below, coupled to the electric converter and configured to control the electric converter according to the methods described above and below.

[0012] This invention embodies a novel concept of Linear Quadratic Gaussian Selective Harmonic Control (LQG-SHC) proposed in this paper. The basic idea of ​​the proposed method (which can be embodied as a control algorithm) is to regulate selected grid current harmonics and suppress their corresponding grid voltage harmonics. By decoupling these components, a high-bandwidth linear controller for optimized pulse modes is designed. In particular, by employing a decoupled system modeling approach, the method described in this paper can extract individual harmonics from a fixed-rate ripple current sample. This allows for the design of high-bandwidth linear control units for any optimized pulse mode without compromising their expected steady-state harmonic performance. Input disturbances, such as grid voltage harmonics, are also modeled and can therefore be suppressed. This innovative control method is independent of the optimized pulse mode or corresponding harmonic target used. With its general formulation, it can be extended to any application using an optimized pulse mode simply by changing the setpoint for each harmonic.

[0013] This method can be executed by a control unit coupled to the electric converter. The grid current signal can be received by the control unit from a current sensor coupled to the grid (or simply "grid"). The current sensor measures the grid current and generates a grid current signal accordingly. The grid voltage signal can be received by the control unit from a voltage sensor coupled to the grid. The voltage sensor measures the grid voltage and generates a grid voltage signal accordingly. The DC energy source can be, for example, a battery system, a DC link consisting of capacitor storage elements, or a photovoltaic system. The electric converter can be an inverter, particularly a grid-connected inverter.

[0014] The control unit may include a processor configured to perform the methods described above and below, and a memory communicatively coupled to the processor and configured to store one or more lookup tables including one or more optimized pulse patterns, each optimized pulse pattern including a corresponding switching angle.

[0015] Grid current harmonics and grid voltage harmonics can be determined through estimation. Switching angles can be converted into switching times, which can be determined by multiplying them by the fundamental frequency of the angle. The next modulation period can be the fundamental period, i.e., the reciprocal of the fundamental frequency, or it can be a part of or an integer multiple of the fundamental period.

[0016] According to one embodiment, a state harmonic setting value and an input harmonic setting value are determined based on a determined grid voltage harmonic and a given fundamental grid current setting value. An optimized pulse pattern is then determined based on the determined state harmonic setting value, the determined input harmonic setting value, and the grid current harmonic. This allows for the adjustment of individual grid current harmonics, thereby suppressing their corresponding grid voltage harmonics.

[0017] According to one embodiment, the state harmonic setting and input harmonic setting are determined based on the determined grid voltage harmonics and a given fundamental grid current setting. The modulation index is then determined based on this modulation index, followed by the determination of the switching angle of a predetermined optimized pulse pattern stored in a lookup table. The state harmonic setting and input harmonic setting are then determined based on the determined switching angle. This facilitates the very precise determination of the state harmonic setting and input harmonic setting, thereby effectively (e.g., optimally) suppressing their corresponding grid voltage harmonics.

[0018] According to one embodiment, Fourier coefficients are determined based on a determined switching angle; the amplitude and phase of the corresponding harmonics are determined based on the determined Fourier coefficients; the input harmonic setpoint is determined based on the amplitude and phase; and the state harmonic setpoint is determined based on the input harmonic setpoint and the grid voltage harmonics. Thus, the state harmonic setpoint and the input harmonic setpoint are determined based on the determined switching angle. This facilitates the simple determination of the harmonic grid current setpoint and the harmonic input setpoint.

[0019] According to one embodiment, an optimized pulse pattern is determined by determining input harmonic commands for the electric converter and by determining an optimized pulse pattern based on determined state harmonic settings, determined input harmonic settings, and grid current harmonics. This enables the electric converter to be driven such that corresponding grid voltage harmonics are suppressed.

[0020] According to one embodiment, an optimized pulse mode is determined based on a determined harmonic input command by determining the switching angle of the optimized pulse mode. This can facilitate driving the electric converter in a simple manner.

[0021] According to one embodiment, grid voltage harmonics are determined based on grid voltage signals, grid current signals, and optimized pulse patterns, and / or grid current harmonics are determined based on grid current signals, switching angles, and grid voltage harmonics. This helps to accurately determine grid current and grid voltage harmonics.

[0022] According to one embodiment, grid voltage harmonics are estimated by a first Kalman filter; and / or grid current harmonics are estimated by a second Kalman filter. Each Kalman filter can be a steady-state Kalman filter (SSKF). This helps to determine grid voltage and current harmonics in a simple and / or efficient manner.

[0023] According to one embodiment, the harmonic controller includes a harmonic setpoint generator for determining state harmonic setpoints and input harmonic setpoints based on a given fundamental grid current setpoint and a determined grid voltage harmonic.

[0024] According to one embodiment, the harmonic controller includes a linear quadratic regulator (LQR) coupled to the harmonic controller and configured to determine input harmonic commands for the electric converter based on a fundamental grid current setpoint, a state harmonic setpoint, and an input harmonic setpoint.

[0025] According to one embodiment, the harmonic controller includes an optimized pulse-mode QP solver coupled to the LQR and is configured to determine the switching angle of the optimized pulse mode based on the input harmonic command.

[0026] According to one embodiment, the harmonic controller includes a modulator coupled to an optimized pulse-mode QP solver and configured to apply a pulse mode determined based on a switching angle to the electrical converter. Quantization errors in the applied switching angle can degrade the harmonic performance of any optimized pulse mode. Therefore, sampling the optimized pulse mode at the highest possible rate may be advantageous. However, this contrasts with the sampling rate of advanced digital control algorithms, such as harmonic controllers, which should be executed at the lowest acceptable rate to reduce computational burden and thus the processing power required for hardware implementation. This trade-off between reducing quantization error and computational burden can be addressed by executing the modulator independently of the harmonic controller at a much higher rate, as further described below.

[0027] According to one embodiment, the harmonic observer includes: a first Kalman filter configured to estimate grid voltage harmonics based on a grid voltage signal, a grid current signal, and an optimized pulse pattern; and a second Kalman filter configured to estimate grid current harmonics based on a grid current signal, a switching angle, and grid voltage harmonics.

[0028] Another aspect of the invention relates to a computer program for controlling an electric converter, which, when executed by a processor (e.g., the processor of a control unit), is adapted to perform the steps of the methods described above, and to a computer-readable medium on which the computer program is stored. Both the harmonic observer and the harmonic controller can be executed as software on one or more processors (e.g., the processor of a control unit), or can be embodied as hardware (e.g., the hardware of the control unit), or a corresponding combination of software and hardware. The computer-readable medium can be a floppy disk, hard disk, USB storage device, RAM, ROM, EPROM, or flash memory. The computer-readable medium can also be a data communication network, such as the Internet, which allows the download of program code. Typically, the computer-readable medium can be a non-transitory or transient medium.

[0029] In general, it must be understood that the features of the methods described above and below can be the features of the computer programs, computer-readable media, control units, and converter systems described above and below, and vice versa.

[0030] These and other aspects of the invention will become apparent and will be illustrated by the embodiments described below. Attached Figure Description

[0031] The subject matter of the invention will be explained in more detail below with reference to exemplary embodiments shown in the accompanying drawings.

[0032] Figure 1 A block diagram of a converter system according to an embodiment of the present invention is shown.

[0033] Figure 2 It shows according to Figure 1 Block diagram of the harmonic controller of the converter system.

[0034] Figure 3 It shows that according to Figure 1 Block diagram of the harmonic observer of the converter system. Detailed Implementation

[0035] Figure 1 A block diagram of a converter system 10 according to an embodiment of the present invention is shown. The converter system 10 includes an electric power converter system 14 and a control unit 12.

[0036] The power converter system 14 includes an electric converter 16 coupled to a DC power source (not shown). The electric converter 16 is configured to convert a DC voltage from the DC power source into an AC voltage and feed that AC voltage into the power grid. The electric converter 16 has an RL output impedance 20 that couples it to an AC grid voltage 18.

[0037] The converter 16 can be a grid-connected three-phase converter, as is well known in the art. Therefore, the system to be modeled is a grid-connected three-phase converter. The converter's RL output impedance 20 typically represents the transformer, filter, and grid impedance. These are combined to form the RL output component 20, such as... Figure 1 As shown.

[0038] exist abc The state, input, and disturbance vectors in the coordinate system are:

[0039] Assuming a three-level pulse mode is used, therefore .

[0040] The system is modeled using a decoupling method within a stationary αβ coordinate system. This generates a unique model for each harmonic, with no cross-coupling between them.

[0041]

[0042] The number of positive and negative non-triple odd harmonics modeled in (1.2) depends on the selected harmonic set. h sel The highest order harmonic selected is n sel For the sake of brevity, and subscript h This represents a vector composed of these selected harmonics.

[0043] To discretize the system model, a zero-order hold (ZOH) is applied to (1.2):

[0044] in,

[0045] And the state, input, perturbation, and output vectors are respectively,

[0046] Essentially, this linear time-invariant (LTI) system plus the input perturbation (1.3) is modeled as a sum of non-triple odd harmonics, truncated to n. sel This is reflected in the output. In this case, the sample of the ripple current is decomposed into the sum of its selected harmonics. However, the Fourier series stipulates that an infinite number of harmonics are required to obtain it. This infinite harmonic and the residual harmonic h introduced res The concept is cleverly accomplished using a pair of states.

[0047] Control unit 12 is configured to control electrical converter 16. Control unit 12 includes harmonic observer 22 and harmonic controller 24.

[0048] Harmonic observer 22 is electrically coupled to the power grid. Harmonic observer 22 is configured to receive grid current representing the power grid. The grid current signal and the grid voltage representing the grid The grid voltage signal, and the method for determining the grid current based on the grid voltage signal and the grid current signal. Power grid current harmonics and grid voltage Grid voltage harmonics Grid current and grid voltage It can be measured.

[0049] Harmonic controller 24 is electrically coupled to harmonic observer 22 and the power grid. Harmonic controller 24 is configured to adjust the harmonics based on determined grid current harmonics. Determined grid voltage harmonics and the given fundamental grid current setpoint To determine the optimal pulse mode for driving the electric converter 16. Optimized pulse pattern Including the switching angle of the electrical converter 16 in the next modulation cycle of the electrical converter 16 And used to at least determine the optimized pulse pattern Determined next switching angle The modulation period is applied to the electrical converter 14. The next modulation period can be the fundamental period, i.e., the reciprocal of the fundamental frequency, or it can be a fraction or integer multiple of the fundamental period.

[0050] The control unit 12 may include a processor (not shown) configured to perform the methods described above and below, and a memory (not shown) communicatively coupled to the processor and configured to store one or more lookup tables that include optimized pulse patterns. One or more of them, where each optimized pulse mode Including the corresponding switching angle Harmonic observer 22 and harmonic controller 24 can each be embodied as software stored in memory and / or executed by a processor. Alternatively, harmonic observer 22 and harmonic controller 24 can each be embodied as hardware contained in or coupled to a processor. Alternatively, harmonic observer 22 and harmonic controller 24 can each be embodied as a corresponding combination of hardware and software.

[0051] Harmonic observers will measure grid current and grid voltage It is decomposed into estimated values ​​of its corresponding harmonics, i.e., grid current harmonics. and grid voltage harmonics Then, the harmonic controller 24 optimizes the Fourier coefficients to design an optimized pulse mode. This mode tracks the fundamental grid current setpoint. And the selected harmonics, to achieve any desired goal.

[0052] Figure 2 It shows that according to Figure 1 A block diagram of the harmonic controller 24 of the converter system 10. The harmonic controller 24 may have a harmonic setpoint generator 30 for generating a harmonic setpoint based on a given fundamental grid current setpoint. and determined grid voltage harmonics Determine the state harmonic setpoint and input harmonic setting value The harmonic controller 24 may have a linear quadratic regulator LQR coupled to the harmonic controller 24 and configured to adjust the state harmonic setpoint. Input harmonic setting value Harmonics with grid current To determine the input harmonic command for the electric converter 16. The harmonic controller 24 may have an optimized pulse-mode QP solver coupled to the LQR and is configured to respond to input harmonic commands. To determine the optimal pulse mode Switching angle The harmonic controller 24 may have a modulator 36 coupled to an optimized pulse-mode QP solver 34 and is configured to adjust the frequency according to the switching angle. Determined optimized pulse mode It is applied to the electrical converter 14.

[0053] Given the fundamental grid current setpoint And the estimated values ​​from harmonic observer 22, state harmonic setpoint and input harmonic setting value These can be created by the harmonic setpoint generator 30. These can be fed into the LQR for harmonic-based tracking. Then, the input command for the selected harmonic, in other words, the harmonic input command... It can be optimized to a switching angle by an optimized pulse-mode QP solver 34. Its goal is to adjust the pre-calculated pulse pattern to reflect the input harmonic command. The Fourier coefficients. Then, the modulator 36 can be executed at an accelerated rate to decouple the execution of the harmonic controller 24 and the determined optimized pulse pattern applied to the electrical converter 16. The resolution. Harmonic setting value

[0054] The concept of Linear Quadratic Gaussian Selective Harmonic Control (LQG-SHC), embodied and / or executed by control unit 12, is independent of the optimized pulse pattern used, particularly the pre-calculated optimized pulse pattern. The structure remains unchanged regardless of whether it is SHE, OPP, or SHM. Different optimized pulse patterns are simply understood as different states or input setpoints for each harmonic. To reiterate, any feasible setpoint for any harmonic can be given. This generalized formula enables LQG-SHC to perform well in many challenging grid-connected applications, such as active power filters or STATCOM. For example, if the pre-calculated optimized pulse pattern is constrained by the IEEE-519 grid specification, these constraints do not need to be reflected in the LQG-SHC. They are only included in the harmonic setpoint. As long as the harmonic setpoint is tracked, all constraints of the pre-calculated optimized pulse pattern are implicitly satisfied.

[0055] In subsequent chapters, the equilibrium point of the system model (1.3) will first be derived. This equilibrium point is evaluated to ensure the state harmonic setpoint in steady state. With input harmonic setting value This is consistent. Subsequently, a step-by-step method for generating a complete set of harmonic setpoints using pre-calculated optimized pulse modes will be presented: Equilibrium point

[0056] For the grid-connected inverter, which functions as converter 16, the system setpoints are active and reactive power. Focusing on the grid current control loop (presented here), these system setpoints are interpreted as the amplitudes of the grid current harmonics in the αβ coordinate system. and phase angle Setting value:

[0057] The reciprocal of (3.1.1) is:

[0058] For each harmonic, the equilibrium point is then found. This is the input setting. It attracts the system model (1.2) to the given state setpoint. :

[0059] in,

[0060] The equilibrium point (3.1.3) can be solved to obtain the input or state setpoint. , It also fundamentally explains grid voltage harmonics. As input interference. Recall that the positive and negative harmonics rotate in opposite directions, and the sign of each consecutive non-third odd harmonic n alternates (1.2).

[0061] To suppress or track harmonics in any phase, half-wave symmetry must be applied to pre-calculated optimized pulse patterns. The switching angles of these optimized pulse patterns are indexed by their modulation indices and then stored in a lookup table (LUT). New optimized pulse patterns can be optimized online to replace this LUT, as explained at the end of this specification. For example, if harmonics are present in the mains voltage, the LQG-SHC can switch to a new set of harmonic settings to suppress these input disturbances.

[0062] Pre-calculated optimized pulse patterns with quarter-wave or half-wave symmetry can be stored in this LUT. For example, the step-by-step procedure for obtaining harmonic setpoints from a QW LUT is as follows:

[0063] 1. Evaluate the balance point of the fundamental input setpoint:

[0064] 2. Calculate the modulation index:

[0065] 3. Extract the switching angle from the LUT:

[0066] 4. For each harmonic, calculate the amplitude and phase of its Fourier coefficients:

[0067] 5. Then, compensate for grid voltage harmonics to obtain a new input setting value for the tracking state setting value:

[0068] 6. Based on the equilibrium point, calculate the state setpoint for each harmonic:

[0069] By setting harmonic setpoints based on pre-calculated optimized pulse patterns (3.1.6), they are consistent in steady state. However, given arbitrary harmonic setpoints, they may become inconsistent if no corresponding optimized pulse pattern exists. This imposes a backward constraint on the control law, since it is unknown what harmonic setpoints are feasible before attempting to design a corresponding optimized pulse pattern. This significantly degrades controller performance because unknown nonlinearities are introduced into the controller's actuators—the optimized pulse patterns.

[0070] Nevertheless, the LUT used for LQG-SHC is a simple inclusion that ensures the harmonic setpoints and the optimized pulse mode applied are consistent in steady state. For transient states, the maximum permissible deviation of this pre-calculated optimized pulse mode is constrained, as described below.

[0071] It is important to note that optimized pulse pattern lookup tables (LUTs) typically assume the mains voltage. This is the ideal voltage. Therefore, if the grid voltage... If distortion occurs, then the LUT is suboptimal. This applies to various types of grid voltage harmonics. Storing LUTs is not feasible because their size would increase dramatically, becoming a burden. The following section will provide a method for handling grid voltage distortion. Here are some technically feasible suggestions for optimizing harmonic performance. Harmonic-based LQR control

[0072] In steady state, we expect the input setpoint to be applied by the control unit 12. To this end, we first redefine the state vector and input vector based on the error with the corresponding setpoint. Then, by subtracting the input disturbance term, we obtain the error space model of the LTI system:

[0073] For this LTI MIMO system (3.2.1), a full-state feedback controller is preferred; it is the simplest topology capable of regulating many states. In this error space form, the state feedback control rule applies the setpoint input while tracking error decay:

[0074] For the state feedback gain K, a linear quadratic regulator (LQR) is designed by minimizing the discrete-time algebraic Riccati equation (DARE):

[0075] The trade-off between tracking error and control effort is determined by the state penalty Q and the input penalty R, respectively. The design of these matrices will be described in a later subsection.

[0076] Input harmonic commands They cannot be applied directly by the electrical converter 16. Instead, they must be converted to switching angles by the optimized pulse-mode QP solver 34. As described below, this design embodies the Fourier coefficients. The optimized pulse pattern is obtained. Furthermore, as described below, the harmonic observer 22 can use a steady-state Kalman filter (SSKF) to estimate the individual current harmonics. Therefore, the state vector in control rule (3.2.2) is the estimated value. By combining LQR with SSKF, a linear quadratic Gaussian (LQG) controller for selective control of harmonics was created; therefore, the control algorithm is denoted as LQG-SHC. Status penalty

[0077] From the perspective of tracking error, changes in the fundamental setpoint are the most significant because they will have the largest amplitudes. Therefore, during transients, we focus less on optimizing harmonic performance and more on tracking the fundamental. To reflect this in the state penalty Q, it is designed as an identity matrix with added weighting factors. Tracking biased towards the fundamental frequency: (3.2.4) Input penalty

[0078] The power grid has extremely high inductance. Therefore, as the harmonic order increases, concerns about injected voltage harmonics decrease. This is reflected in the OPP formula, where the Fourier coefficients of each harmonic are weighted by the reciprocal of the square of its order.

[0079] The system model (1.3) does not reflect the decreasing importance of higher-order harmonics. Therefore, it is sensible to incorporate the above knowledge into the LQR to penalize lower-order input harmonics, since they are more significant. To this end, we revisit the equilibrium point (3.1.3), but neglect the resistance R (because R << ωL And grid voltage disturbances. Then, inspired by the LQR cost function (3.2.3), a quadratic term with scalar penalty is created:

[0080] Extending (3.2.5) to all modeled harmonics yields an analytical input penalty, which is then weighted by an intuitive weighting factor for tuning the closed-loop bandwidth. : (3.2.6)

[0081] Similar to OPP, (3.2.6) intuitively biases the input penalty towards lower harmonics by using the inverse square of the order. Recommendations for weighting factors are given below. Optimized pulse-mode QP solver 34

[0082] Given a set of input harmonic commands (3.2.2) The goal of the optimized pulse mode QP solver 34 can be to adjust the pre-calculated optimized pulse mode (3.1.6) to minimize the quadratic difference of the Fourier coefficients of each harmonic.

[0083] First, input commands for each harmonic can be provided. Perform the Park transform. This transforms the rotation vector into two scalars. After a simple coordinate axis realignment, these scalars become the Fourier coefficients of the harmonic, as described below.

[0084] Then, a small-angle approximation can be applied to linearize the Fourier coefficients of the pre-calculated pulse mode (3.1.6). This allows the nonlinear objective function used for design optimization of the pulse mode to be reformulated as a quadratic programming problem for efficient solution, as described below. The optimization variable of this QP is Δα, which is the adjustment amount of the switching angle of the pre-calculated pulse mode. Fourier coefficient transform

[0085] To design optimized pulse modes with the desired amplitude and phase for each harmonic, Fourier coefficients are required: in .

[0086] Reviewing the control rule (3.2.2), the input commands for each harmonic are expressed as a rotating vector. Given in the form of. In order to extract αβ The direct and quadrature axis scalar magnitudes of the components can be obtained by first applying the Park transform:

[0087] in

[0088] fundamental wave It is accelerated, therefore it is related to harmonics. Synchronization. Similar to PLLs, their phase shifts... Then it becomes constant.

[0089] Then, in order to complete the transformation to Fourier coefficients, the cross-axis components must be flipped so that they are aligned with those from (3.3.1). b n alignment:

[0090] In summary, in order to extract the Fourier coefficients of the input command Perform the Park transform (3.3.2) on each harmonic, and then flip the cross-axis component (3.3.3). objective function

[0091] Given a set of Fourier coefficients The nonlinear objective function used to optimize the pulse mode of the equivalent optimization can be:

[0092] Subject to

[0093] in

[0094] It can include the inverse square of the harmonic order to bias towards a more accurate fit to lower-order harmonics. Using the switching angle from a pre-calculated optimized pulse mode (3.1.6), the nonlinear Fourier coefficients can then be linearized by applying a small-angle approximation:

[0095] For small switching angle adjustments Δα, these linearized Fourier coefficients can approximate their nonlinear equivalents:

[0096] Substituting the linearized Fourier coefficients (3.3.5) into the nonlinear objective function (3.3.4), we now obtain the weighted least squares (WLS) objective function: Subject to in

[0097] Suggestions for defining matrices C, d, and W are given at the end of this specification. The first constraint ensures that the adjusted switching angles do not overlap. The second constraint introduces the parameter Δ. α max This protects the accuracy of our small-angle approximation by imposing a box constraint on the maximum permissible deviation from the pre-calculated optimized pulse pattern.

[0098] Model predictive control (MPC) demonstrates the potential for real-time, fast solution of quadratic programming (QP). To improve the technical feasibility of implementing LQG-SHC on commercial hardware, the WLS objective function (3.3.7) can be transformed into QP: Subject to in

[0099] Previous solution Δα(k-1) It can be added to pre-calculated optimized pulse patterns α LUT （k） In this way, the linearization point α is moved. ¯LUT Since Δ can now be performed α =Δ α max In two consecutive steps, the search space is effectively doubled. This allows for larger switching angle adjustments without reducing the accuracy of our linearized Fourier coefficients. To obtain the optimal switching angle for the electric converter 14... Add the solution of (3.3.8) to the linearization point:

[0100] The above method is inspired by Sequential Quadratic Programming (SQP). By utilizing pre-computed optimized impulse patterns, the nonlinear objective function (3.3.4) can be simplified to a QP subproblem (3.3.8). MPC examples demonstrate that QP is particularly well-suited for real-time solutions. Furthermore, as mentioned earlier, all constraints of the pre-computed optimized impulse patterns are implicitly satisfied. Except for the constraints on Δ... α max Aside from the simple box-type constraints, no additional constraints are required regardless of the harmonic objective. This is particularly important when introducing constraints from power grid standards such as IEEE-519. As described at the end of this specification, this introduces quadratic constraints, increasing the difficulty of optimizing the objective function for the optimized impulse mode. modulator

[0101] Applied switching angle Quantization errors degrade the harmonic performance of any optimized pulse mode. Therefore, it should be sampled at the highest possible rate. This contrasts with the sampling rate of advanced digital control algorithms, such as harmonic controllers, which should be executed at the lowest acceptable rate to reduce computational burden and thus reduce the processing power required for hardware implementation. The trade-off between reducing quantization errors and computational burden can be resolved by executing the modulator 36 independently of the harmonic controller 24 at a much higher rate, as exemplified below.

[0102] Figure 3 It shows that according to Figure 1 A block diagram of the harmonic observer 22 of the converter system 10 is shown. The harmonic observer 22 includes a first Kalman filter 40 and a second Kalman filter 42. Each Kalman filter 40, 42 can be a steady-state Kalman filter (SSKF). Alternatively, the grid voltage harmonics can be independent of the optimized pulse mode. The first Kalman filter 40 can be configured to determine the pulse pattern based on the grid voltage signal, the grid current signal, and the optimized pulse pattern. To estimate grid voltage harmonics The second Kalman filter 42 can be configured to adjust based on the grid current signal and switching angle. and grid voltage harmonics To estimate grid current harmonics Before proceeding, a brief background on SSKF 40 and 42 will be provided below, and the concept of residual harmonics will be introduced. Steady-state Kalman filter

[0103] To decompose a periodic signal into its Fourier coefficients, the Discrete Fast Fourier Transform (DFFT) is typically used. However, this method requires a large sampling window for the time-domain data and introduces unstable delays into high-bandwidth control loops. The Sliding Discrete Fourier Transform (SDFT) uses a smaller sliding window to slightly reduce the delay. Another method for extracting signal harmonics is to use resonators; however, these filters quickly become cumbersome because a filter must be tuned for each harmonic. LQG-SHC can use the SSKF. Compared to DFFT, SDFT, and resonators, the SSKF is able to quickly decompose a signal into estimates of many harmonics with negligible delay. background

[0104] A common assumption in optimal linear estimation is that modeling and measurement errors corrupt the LTI system through white Gaussian processes and output noise.

[0105] The covariances of the process and output noise are Q, respectively. f and Rf In practice, process covariance is difficult to quantify and is treated as a tuning parameter, while output covariance can be directly measured from the output sensor.

[0106] To estimate the state of this noisy LTI system (4.1.1), the Luenberger observer can be used:

[0107] The estimation rule (4.1.2) is precisely a combination of the prediction and update steps of the Kalman filter. In steady state, this recursive algorithm converges to the optimal estimated gain L. Since the system model (4.1.1) is LTI, the SSKF can be designed offline by solving for the steady-state value of L. To do this, we first review the duality between control and estimation: Control  Estimation

[0108] Then we design the covariance matrix R. f and Q f The former is the covariance of the output sensor, which can be measured. The latter is an estimate that includes any process errors that might corrupt the system model, such as parameter variations or unmodeled dynamics. For Q... f The intuitive understanding is that it is positively correlated with the estimated gain L. When Q f When the element ≠ 0, SSKF biases towards our model's prediction. However, when Q... f When the element ∞, it biases our measurement by adding the corresponding element of the estimated gain L.

[0109] After substituting the substitutions from (4.1.3) into DARE (similar to LQR), we solve it to obtain the optimal estimated gain: Residual harmonics

[0110] Recalling the concept of a Fourier series, an infinite number of harmonics can be accumulated to form any periodic signal. However, if this Fourier series is truncated, the signal will be partially reconstructed and incomplete. For SSKF, this means that any unmodeled harmonic will truncate the Fourier series and exhibit a permanent output estimation error. Fortunately, there is a simple and elegant remedy for the Fourier series of a signal. The residual harmonics are the complete signal minus its selected harmonics. h sel The remaining part. An intuitive explanation of this concept is that it refers to the part that comes from... n sel <n<∞Frequency banding states are added to the harmonics within the range. As will be shown below for each of SSKF40 and 42, a single residual harmonic state can be attached to the model of the selected harmonics, thereby generating a complete model for all harmonics. Second SSKF 42 Input harmonics

[0111] In order to optimize the switching angle of the pulse mode for the application Converted to each selected harmonic The input is used to reconstruct the Fourier coefficients for the optimized HW pulse mode:

[0112] Then, until n sel The Fourier coefficients of each harmonic are converted to αβ Rotation vector in the coordinate system:

[0113] This process is the same as the method described above regarding harmonic setpoints, except that it uses... replace α LUT Then, the concept of residual harmonics is applied to obtain the remaining input harmonic setpoint. This is the complete input. With the selected input harmonic setting value (not exceeding nsel) ） The difference between them, until n sel : System model for the second SSKF 42

[0114] Designing an SSKF requires a state-space representation of the LTI system. However, the system model (1.3) includes input disturbances, namely grid voltage harmonics. Essentially, perturbations are merely additional inputs, and therefore can be used to augment the input:

[0115] Then, residual harmonic states can be added to generate all grid current harmonics. Complete system model:

[0116] The system output is decomposed into a complete Fourier series:

[0117] Note that (4.3.6) is not truncated like (1.3b). n sel By applying the concept of residual harmonics, a single pair of additional states... Ensured It always holds true, regardless of the selected harmonics. h sel how. Regarding the process covariance of the second SSKF 42

[0118] From the grid current sample, higher-order harmonics and their ripples are gradually attenuated. This concept can be incorporated into the process covariance estimation by weighting the harmonics with the reciprocal of the square of their order.

[0119] Introducing two tuning parameters q f,i and q f,i;res To make SSKF i It leans towards prediction or measurement. As mentioned above, the following section provides recommendations for weighting factors. First SSKF 40

[0120] For state feedback controllers, the Internal Model Principle (IMP) can be satisfied simply by eliminating input disturbances in the control rules. Referring back to (3.2.2), this can be achieved by including the input setpoint (3.1.3) which incorporates the input disturbances. To estimate grid voltage harmonics... The first SSKF 40 can be designed as a disturbance observer. The first SSKF 40 system model

[0121] The input disturbance is modeled as αβ The first in the coordinate system n Secondary grid voltage harmonics:

[0122] ± depends on whether the non-third odd harmonic is positive or negative, as defined in (1.2). This simple grid voltage harmonic disturbance model can be extrapolated to model all selected harmonics, with residual states added to accumulate the remaining harmonics. These multiple disturbance states can be represented by a single state with grid current. αβ To augment the state model:

[0123] Comparing (4.4.2) and (1.3), the input disturbance is decomposed into a complete sum of its harmonics. (Choose...) h resThis is not important, as the process covariance can be simply adjusted to accumulate the remaining harmonics. Note that in other possible embodiments, the grid current state in (4.4.2) can be omitted to generate a system model without inputs, as described above. Regarding the process covariance of the first SSKF 40

[0124] The harmonic weights in (4.3.7) can be removed because the inductor network may not attenuate grid voltage harmonics:

[0125] Similar to the second SSKF 42, two tuners can be introduced. Parameter q f,v and q f,v;res This is to bias the first SSKF 40 towards prediction or measurement. Recommended weighting factors are given further below. The first identity matrix of (4.4.3) contains the process covariance of the grid current model, which can be biased accordingly by adjusting the two tuning parameters. Compensation for grid voltage harmonics Optimized Pulse mode

[0126] Currently, all commercially available optimized pulse modes are designed under the assumption of an ideal grid voltage. While simplistic, this assumption is reasonable given the stochastic nature of grid voltage harmonics. Pre-calculating optimized pulse modes to compensate for grid voltage harmonics is impractical because the possible combinations of their amplitude and phase appear to be infinite. Therefore, existing optimized pulse mode design methods unfortunately exhibit zero-input disturbance suppression capability against grid voltage harmonics.

[0127] As described below, optimized pulse modes for compensating for grid voltage harmonics have the potential to further reduce THDi and ensure performance under realistic conditions (i.e., distorted grid voltage). It robustly complies with power grid specifications.

[0128] Typically, power grid voltage harmonics The amplitude and phase evolve slowly compared to the sampling rate of the control algorithm. This allows sufficient time to estimate and optimize new, compensated pulse patterns online. .

[0129] Since LQG-SHC essentially estimates grid voltage harmonics It is ideal for online optimization and tuning of pulse patterns. This is to suppress these input disturbances. A separate thread can execute the less time-constrained task and then apply the newly optimized pulse pattern. Provided to the LQG-SHC thread for adjustment. Selected harmonics

[0130] Reasonable upper limit of the selected harmonics n sel It could be a quarter cycle for an optimized pulse pattern. k The selected switching angle The number of [factors]. This ensures that the optimized pulse-mode QP solver 34 has sufficient degrees of freedom to optimize the Fourier coefficients for each harmonic.

[0131] With the help of residual harmonics h sel The harmonic observer 22 can always model all harmonics. Therefore, the number of harmonics selected for control may be independent of its estimation accuracy. Weighting factor

[0132] By employing a controller based on the LQG (Linear Quadratic Gaussian Calculator), tuning is intuitive and familiar to those skilled in its design. A good baseline for the LQG-SHC is set... and The process covariance of the residual grid voltage harmonic state is intentionally larger because we want it to accumulate residual harmonics of different frequencies. Sampling rate

[0133] To avoid overburdening the algorithm with its single most complex task, sampling rates can be decoupled. This allows the most demanding parts to execute at the slowest speed, while the simpler parts can execute faster. Furthermore, decoupling sampling rates offers exciting opportunities for parallelizing the algorithm to achieve efficient implementation.

[0134] In the entire LQG-SHC control algorithm proposed in this paper, the optimized pulse-mode QP solver likely has the highest computational burden. Therefore, to allow implementation on feasible and inexpensive hardware, it can be executed at the lowest possible sampling rate. Other functions, such as the harmonic observer 22 and / or the modulator 36, can be simpler and can be executed at higher sampling rates. For example, for k=5, a good and technically feasible sampling rate for the harmonic controller 22 and the harmonic observer (optionally including the modulator) could be 10 kHz and 100 kHz, respectively. To ensure the ability to control and estimate higher-order selected harmonics, all sampling rates must also satisfy the Nyquist criterion. Optimized pulse mode (OPP-HW-DG+C) for constrained distorted power grids

[0135] Used to optimize new grid voltage harmonics Compensation is required and the current is limited by grid current harmonics. Constrained half-wave (HW) optimized pulse mode The objective function can be: Subject to in,

[0136] Examine (A.1) and (A.1a). a n and b n This includes the difference between the Fourier coefficients of the input and grid voltages. Any mismatch between them will be affected by the familiar 1 / n 2 The weighting penalty is applied because it is assumed that there is an RL output impedance of 20. And... Constraints will affect each grid current harmonic amplitude I g;n Limited to fundamental load current The percentage of, of V i,n Similarly, the difference lies between the Fourier coefficients of the input and grid voltage harmonics, because this is applied to the output admittance. T o （s） The voltage on it.

[0137] The probability of finding a feasible solution (A.1) is mainly affected by the switching angle. number k The frequency response of the output filter and the stringency of the mains current harmonic limits have an impact. Appropriate limits can be derived from IEEE-519.

[0138] Therefore, in steady state, a novel method is proposed for designing optimized pulse modes that are robust to distorted grid voltage. This method, denoted as OPP-HW-DG+C, incorporates grid voltage harmonics. (Such as harmonics estimated by the first SSKF 40) are incorporated into the objective function. This allows for the creation of new, optimized pulse modes. Input disturbance suppression capability. Linear weighted least squares matrix

[0139] The parameters of the linear weighted least squares objective function from (3.3.7) can be:

[0140] Although the invention has been illustrated and described in detail in the accompanying drawings and foregoing description, such illustrations and descriptions should be considered illustrative or exemplary rather than restrictive; the invention is not limited to the disclosed embodiments. Those skilled in the art, by studying the drawings, disclosure, and appended claims, can understand and implement other variations of the disclosed embodiments when practicing the claimed invention. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite articles "a" or "an" do not exclude multiple. A single processor or controller or other unit can implement several functions recited in the claims. The fact that certain measures are recited in mutually different dependent claims does not mean that a combination of these measures cannot be used advantageously. Any reference numerals in the claims should not be construed as limiting the scope. Reference Symbol List 10. Converter System 12 Control Units 14 Electric Power Converter System 16 Electric converter 18 AC grid voltage 20 RL output impedance 22 Harmonic Observer 24 Harmonic Controller 26 External Units 30 Harmonic Setpoint Generator 34 Pulse Mode QP Solver 36 Modulator 40 First Kalman Filter 42 Second Kalman Filter LQR linear quadratic regulator Grid current Grid voltage Power grid current harmonics Grid voltage harmonics Optimize pulse mode Switching angle State Harmonic Setting Value Input harmonic setting value Fundamental power grid current setting value Modulation index Switch angle from lookup table Input harmonic commands

Claims

1. A method for controlling an electrical converter (16) coupled to a DC power source and a power grid, and configured to convert a DC voltage from the DC power source into an AC voltage and feed the AC voltage into the power grid, the method comprising the steps of: Receive grid current representing the grid The grid current signal and the grid voltage representing the grid. The grid voltage signal; The grid current is determined based on the grid voltage signal and the grid current signal. Power grid current harmonics and the grid voltage Grid voltage harmonics ; According to the determined power grid current harmonics The determined grid voltage harmonics and the given fundamental grid current setpoint Determine the optimized pulse mode for driving the electric converter (16). The optimized pulse mode Including the switching angle of the electrical converter (16) in the next modulation cycle of the electrical converter (16). ; as well as At least by the optimized pulse pattern The determined next switching angle It is applied to the electrical converter (16).

2. The method according to claim 1, wherein: The optimized pulse pattern is achieved through the following methods. According to the determined power grid current harmonics The determined grid voltage harmonics and the given fundamental grid current setpoint And determined: by the determined grid voltage harmonics and the given fundamental grid current setpoint Determine the state harmonic setpoint and input harmonic setting value And by determining the state harmonic setting value. and the determined input harmonic setpoint and the power grid current harmonics To determine the optimized pulse mode .

3. The method according to claim 2, wherein: The state harmonic setpoint is obtained in the following manner. and the input harmonic setting value According to the determined grid voltage harmonics and the given fundamental grid current setpoint And determined: by the determined grid voltage harmonics and the given fundamental grid current setpoint Determine the modulation index By according to the modulation index To determine the switching angle of the predetermined optimized pulse pattern stored in the lookup table. And by determining the switching angle Determine the state harmonic setpoint and the input harmonic setting value .

4. The method according to claim 3, wherein: The state harmonic setpoint is obtained in the following manner. and the input harmonic setting value Based on the determined switching angle And determined: by according to the determined switching angle Determine the Fourier coefficients By using the determined Fourier coefficients To determine the amplitude of the corresponding harmonic. and phase and by means of the amplitude and the phase Determine the input harmonic set value and according to the input harmonic setting value and the grid voltage harmonics Determine the state harmonic setpoint .

5. The method according to any one of claims 2 to 4, wherein: The optimized pulse pattern is achieved through the following methods. Based on the determined state harmonic setting value The determined input harmonic setpoint and the power grid current harmonics And determined by: determining the input harmonic command for the electrical converter (16) And by means of the determined input harmonic command To determine the optimized pulse mode .

6. The method according to claim 5, wherein: The optimized pulse pattern is achieved through the following methods. According to the determined input harmonic command And determined: by according to the determined input harmonic command To determine the optimized pulse mode The switching angle .

7. The method according to any one of the preceding claims, wherein: The power grid voltage harmonics Based on the grid voltage signal, the grid current signal, and the optimized pulse pattern And determined, and / or The power grid current harmonics Based on the power grid current signal and the switching angle and the grid voltage harmonics And thus confirmed.

8. The method according to claim 7, wherein: The power grid voltage harmonics Estimated by the first Kalman filter (40); and / or The power grid current harmonics It is estimated by the second Kalman filter (42).

9. A control unit (12) for controlling an electric converter (16), wherein the electric converter (16) is coupled to a DC power source and a power grid, and is configured to convert a DC voltage from the DC power source into an AC voltage and feed the AC voltage into the power grid, the control unit (12) comprising: The harmonic observer (22) is electrically coupled to the power grid and is configured to receive the grid current representing the power grid. The grid current signal and the grid voltage representing the grid. The grid voltage signal, and the method for determining the grid current based on the grid voltage signal and the grid current signal. Power grid current harmonics and the grid voltage Grid voltage harmonics ; as well as The harmonic controller (24) is electrically coupled to the harmonic observer (22) and the power grid, and is configured to adjust the harmonics of the determined power grid current according to the harmonics. The determined grid voltage harmonics and the given fundamental grid current setpoint Determine the optimized pulse mode for driving the electric converter (16). The optimized pulse mode Including the switching angle of the electrical converter (16) during the next modulation cycle of the electrical converter (16). ; The harmonic controller (24) is configured to at least reduce the optimized pulse mode. The next switching angle is determined. It is applied to the electrical converter (16).

10. The control unit (12) according to claim 9, wherein: The harmonic controller (24) includes a harmonic setpoint generator (30) for generating a harmonic setpoint based on a given fundamental grid current setpoint. and the determined grid voltage harmonics Determine the state harmonic setpoint and input harmonic setting value .

11. The control unit (12) according to claim 9, wherein: The harmonic controller (24) includes a linear quadratic regulator (LQR) coupled to the harmonic controller (24) and configured to adjust the state harmonic setpoint. The input harmonic setting value and the power grid current harmonics To determine the input harmonic command for the electric converter (16) .

12. The control unit (12) according to claim 11, wherein: The harmonic controller (24) includes an optimized pulse-mode QP solver (34) coupled to the linear quadratic Gaussian modulator (LQR) and configured to respond to the input harmonic command. To determine the optimized pulse mode The switching angle .

13. The control unit (12) according to claim 12, wherein: The harmonic controller (24) includes a modulator (36) coupled to the optimized pulse-mode QP solver (34) and configured to control the switching angle. The determined optimized pulse mode It is applied to the electrical converter (16).

14. The control unit (12) according to any one of claims 9 to 13, wherein the harmonic observer (22) comprises: The first Kalman filter (40) is configured to adjust the pulse pattern according to the grid voltage signal, the grid current signal, and the optimized pulse pattern. To estimate the grid voltage harmonics ; and / or The second Kalman filter (42) is configured to adjust the switching angle according to the grid current signal and the switching angle. and the grid voltage harmonics To estimate the harmonics of the grid current .

15. A converter system (10), comprising: An electric converter (16) is coupled to a DC power source and a power grid, and is configured to convert a DC voltage from the DC power source into an AC voltage and feed the AC voltage into the power grid; as well as The control unit (12) according to any one of claims 9 to 14 is coupled to the electric converter (16) and configured to control the electric converter (16) by any one of claims 1 to 8.

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