Three-phase MMC current modeling method and device, computer equipment, storage medium and program product

Abstract

The invention relates to a three-phase MMC current modeling method and device, computer equipment, a storage medium and a program product. The method comprises the following steps: establishing a full-state space modeling equation of three-phase MMC current; converting the full-state space modeling equation into a matrix form modeling equation, wherein a plurality of vector and coefficient matrixes corresponding to the full-state space modeling equation are constructed in the matrix form modeling equation; performing row step simplification on the coefficient matrix to obtain a simplified matrix; and based on the simplified matrix, carrying out independent state variable extraction on the matrix form modeling equation to obtain a dimensionality-reduced state space model. By adopting the method, the modeling difficulty can be reduced, and the calculated amount is small.

Description

Technical Field

[0001] The present application relates to the technical field of power electronic converters, and in particular to a three-phase MMC current modeling method, apparatus, computer equipment, storage medium, and program product. Background Art

[0002] As a key component in power electronics converter technology, three-phase modular multilevel converters (MMCs) are widely used in high-voltage direct current (HVDC) and flexible alternating current (FAC) transmission systems due to their high efficiency, high power quality, and flexible scalability. Accurate current modeling is essential to fully tapping the performance potential of three-phase MMCs and ensuring their stable and efficient operation.

[0003] However, traditional modeling methods face challenges with complex electrical components and current dynamics within three-phase MMCs. Because the state space representation of a three-phase MMC involves numerous variables, the model dimensions are too high. Consequently, traditional modeling methods suffer from modeling difficulties and high computational complexity. Summary of the Invention

[0004] Based on this, it is necessary to provide a three-phase MMC current modeling method, device, computer equipment, storage medium and program product that can reduce the difficulty of modeling and have small calculation amount to address the above technical problems.

[0005] In a first aspect, the present application provides a three-phase MMC current modeling method, comprising the following steps:

[0006] Establish the full state space modeling equations of three-phase MMC current;

[0007] Converting the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation;

[0008] Performing row echelon simplification on the coefficient matrix to obtain a simplified matrix;

[0009] Based on the simplified matrix, independent state variables are extracted from the matrix form modeling equation to obtain a state space model after dimensionality reduction.

[0010] In a second aspect, the present application further provides a three-phase MMC current modeling device, comprising:

[0011] Establishing a module for establishing full state space modeling equations of three-phase MMC current;

[0012] a conversion module, configured to convert the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation;

[0013] A simplification module, configured to perform row echelon simplification on the coefficient matrix to obtain a simplified matrix;

[0014] A dimensionality reduction module is used to extract independent state variables from the matrix form modeling equation based on the simplified matrix to obtain a state space model after dimensionality reduction.

[0015] In a third aspect, the present application further provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0016] Establish the full state space modeling equations of three-phase MMC current;

[0017] Converting the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation;

[0018] Performing row echelon simplification on the coefficient matrix to obtain a simplified matrix;

[0019] Based on the simplified matrix, independent state variables are extracted from the matrix form modeling equation to obtain a state space model after dimensionality reduction.

[0020] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the following steps are implemented:

[0021] Establish the full state space modeling equations of three-phase MMC current;

[0022] Converting the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation;

[0023] Performing row echelon simplification on the coefficient matrix to obtain a simplified matrix;

[0024] Based on the simplified matrix, independent state variables are extracted from the matrix form modeling equation to obtain a state space model after dimensionality reduction.

[0025] In a fifth aspect, the present application further provides a computer program product, comprising a computer program, which, when executed by a processor, implements the following steps:

[0026] Establish the full state space modeling equations of three-phase MMC current;

[0027] Converting the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation;

[0028] Performing row echelon simplification on the coefficient matrix to obtain a simplified matrix;

[0029] Based on the simplified matrix, independent state variables are extracted from the matrix form modeling equation to obtain a state space model after dimensionality reduction.

[0030] The above-mentioned three-phase MMC current modeling method, device, computer equipment, storage medium and program product establish a full state space modeling equation for the three-phase MMC current; convert the full state space modeling equation into a matrix form modeling equation, in which multiple vectors and coefficient matrices corresponding to the full state space modeling equation are constructed; the coefficient matrix is ​​row-step simplified to obtain a simplified matrix; based on the simplified matrix, independent state variables are extracted from the matrix form modeling equation to obtain a reduced-dimensional state space model. By combining the modeling of the three-phase MMC state space model with dimensionality reduction technology, high-precision, low-complexity MMC dynamic modeling is achieved, and key state variables are included in the modeling process, which simplifies the model while ensuring that the reduced-dimensional state space model can still accurately reflect the core dynamic characteristics of the MMC. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0032] Figure 1 A diagram illustrating an application environment of a three-phase MMC current modeling method according to an embodiment;

[0033] Figure 2 1 is a flow chart of a three-phase MMC current modeling method according to an embodiment;

[0034] Figure 3 Schematic diagram of the structure of a three-phase MMC in one embodiment;

[0035] Figure 4 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0036] Figure 51 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0037] Figure 6 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0038] Figure 7 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0039] Figure 8 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0040] Figure 9 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0041] Figure 10 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0042] Figure 11 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0043] Figure 12 A schematic diagram of control logic for controlling a three-phase MMC in one embodiment;

[0044] Figure 13 Schematic diagram of the AC output voltage and current of the MMC and the upper and lower bridge arm currents in inverter mode and rated power in one embodiment;

[0045] Figure 14 Schematic diagram of the AC side voltage and current and upper and lower arm currents of the MMC in rectification mode and rated power in one embodiment;

[0046] Figure 15 1 is a flow chart of a three-phase MMC current modeling method according to another embodiment;

[0047] Figure 16 FIG. 4 is a structural block diagram of a three-phase MMC current modeling device in one embodiment. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0049] As a key component in power electronics converter technology, three-phase modular multilevel converters (MMCs) are widely used in high-voltage direct current (HVDC) and flexible alternating current (FAC) transmission systems due to their high efficiency, high power quality, and flexible scalability. Accurate current modeling is essential to fully tapping the performance potential of three-phase MMCs and ensuring their stable and efficient operation.

[0050] However, traditional modeling methods have the following problems when dealing with the complex electrical components and current dynamic behaviors within three-phase MMCs:

[0051] (1) Current modeling: To fully realize the potential of three-phase MMC, accurate modeling is crucial. Traditional modeling methods have difficulty in systematically describing the dynamic behavior of the internal current of three-phase MMC. For example, three-phase MMC contains many complex electrical components, and its internal current dynamics are complex, and existing methods cannot adapt well to this complexity. At the same time, the state space representation of three-phase MMC often involves a large number of variables, resulting in a model with too high a dimension. This not only increases the difficulty of modeling and poses a challenge to modeling accuracy, but also affects the effectiveness of subsequent control strategies. High-dimensional models significantly increase the amount of calculations, making it difficult to process quickly and effectively in practical applications.

[0052] (2) Control: An effective control strategy is required to ensure the stable and reliable operation of three-phase MMC. Existing control strategies are insufficient in dealing with the complex operating characteristics of three-phase MMC. For example, it is difficult to achieve minimum steady-state error and excellent dynamic performance while ensuring fast transient response. There are complex interactions between the branch currents of three-phase MMC, which increases the computational requirements and difficulty of control. Existing control strategies have difficulty in handling such interactions well and cannot fully optimize the performance of three-phase MMC. In addition, under different operating conditions, the dynamic response of three-phase MMC needs to ensure the quality of power, but existing control strategies are not adaptable enough in this regard.

[0053] Based on this, the present application proposes a three-phase MMC current modeling method, apparatus, computer equipment, storage medium and program product that can reduce the difficulty of modeling and have a small amount of calculation.

[0054] The three-phase MMC current modeling method provided in the embodiment of the present application can be applied to Figure 1The computer device shown in FIG. The computer device includes a processor, memory, an input / output interface, a communication interface, a display unit, and an input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are connected to the system bus via the input / output interface. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with external terminals via wired or wireless communication, and the wireless communication can be achieved via Wi-Fi, a mobile cellular network, NFC (near-field communication), or other technologies. When executed by the processor, the computer program implements a control method for an MMC-DES integrated system. The display unit of the computer device is used to produce a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covering the display screen, or a button, trackball or touchpad set on the computer device casing, or an external keyboard, touchpad or mouse.

[0055] Those skilled in the art will understand that Figure 1 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific terminal may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0056] In one embodiment, Figure 2 As shown in the figure, a three-phase MMC current modeling method is provided, which is applied to Figure 1 The computer device in the example is used to illustrate the process, including the following steps:

[0057] S201, establish a full state space modeling equation for the three-phase MMC current.

[0058] Among them, the full state-space modeling equation of the three-phase MMC circuit is an expression used to describe the dynamic change process of the electromagnetic energy inside the three-phase MMC. The full state-space modeling equation includes the rate of change of state variables over time, as well as the current state of the three-phase MMC current and the precise relationship between external inputs. State variables include current, capacitor voltage, etc., and external inputs include control signals, grid voltage, DC voltage, etc.

[0059] In an embodiment of the present application, each phase of a three-phase MMC has an upper bridge arm and a lower bridge arm. The upper and lower bridge arms of each phase are connected to the AC grid or load through a circuit node. Each bridge arm consists of N submodules connected in series and a bridge arm inductor. The positive and negative poles of the DC bus are respectively connected to the common circuit node of the three-phase upper bridge arm and the common circuit node of the lower bridge arm. The full state space modeling equation of the three-phase MMC current can be constructed based on the connection relationship between the bridge arms in the three-phase MMC, the current direction between the circuit nodes, the voltage between the bridge arms, and other circuit parameters.

[0060] In the embodiment of the present application, the three-phase MMC topology diagram is as follows: Figure 3 As shown, the three-phase output voltages on the AC side are defined as v a 、v b 、v c , the DC bus voltage is V dc The three-phase voltages of the upper and lower bridge arms are v ua 、v ub 、v uc 、v la 、v lb 、v lc The inflow currents corresponding to the voltage sources are i va 、i vb 、i vc 、i Vdc 、i vua 、i vub 、i vuc 、i vla 、i vlb 、i vlc The three-phase output inductance and bridge arm inductance are: L a , L b , L c , L ua , L ub , L uc , L la , L lb , L lc The corresponding inductor current is i a 、i b 、i c 、i ua 、i ub 、i uc 、i la 、i lb 、i lc The reference direction of voltage and current is as follows: Figure 1 As shown. The three-phase MMC has a total of 15 circuit nodes, such as Figure 3As shown, the 15 circuit nodes can be represented as node 0, node 1, ..., node 14. Define the voltage of node 0 as zero, and the voltages of the remaining nodes are defined as v1, v2, v3, v4, v5, v6, v7, v8, v9, v 10 、v 11 、v 12 、v 13 、v 14 , Figure 3 The SM in FIG is a submodule connected to the bridge arm inductor.

[0061] S202, converting the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with multiple vectors and coefficient matrices corresponding to the full state space modeling equation.

[0062] In an embodiment of the present application, the matrix form conversion of the full state-space modeling equations can be completed through structured encapsulation. Optionally, all differential equations describing the dynamics of the bridge arm current and capacitor voltage can be systematically reorganized into a state-space expression framework, wherein all state variables including the upper and lower bridge arm currents of each phase and the total capacitor voltage are integrated into a single multidimensional state vector, and the external input quantities including the insertion index, AC voltage and DC voltage constitute the input vector.

[0063] S203, performing row echelon simplification on the coefficient matrix to obtain a simplified matrix.

[0064] In the embodiments of the present application, a stepwise simplification operation is performed on the coefficient matrix, gradually eliminating linearly dependent rows in the matrix through elementary row transformations, and converting the original coefficient matrix into a simplified form with a trapezoidal structure. The stepwise arrangement of the trapezoidal matrix can clearly expose the hidden linear dependencies in the state equation, explicitly identify redundant differential equations, and thus reveal the true number of independent degrees of freedom inherent in the system.

[0065] S204 , extracting independent state variables from the matrix modeling equation based on the simplified matrix to obtain a state space model after dimensionality reduction.

[0066] In an embodiment of the present application, independent state variables are extracted based on a simplified ladder matrix. By identifying the pivot columns and their corresponding state variables in the ladder structure, a minimum set of independent state variables that can fully characterize the core dynamics of the system is directly screened out. State variables not selected by the pivot are identified as redundant variables, and their dynamic behavior can be fully reconstructed through linear combinations of the independent variables. This establishes a reduced-dimensional state space model: this model retains only the independent state variables and their corresponding simplified differential equations, while simultaneously reconstructing the reduced-dimensional system matrix and input matrix.

[0067] In the above-mentioned three-phase MMC current modeling method, a full state-space modeling equation for the three-phase MMC current is established; the full state-space modeling equation is converted into a matrix-form modeling equation, in which multiple vectors and coefficient matrices corresponding to the full state-space modeling equation are constructed; the coefficient matrix is ​​row-step simplified to obtain a simplified matrix; based on the simplified matrix, independent state variables are extracted from the matrix-form modeling equation to obtain a reduced-dimensional state-space model. By combining the modeling of the three-phase MMC state-space model with dimensionality reduction technology, high-precision, low-complexity MMC dynamic modeling is achieved. Key state variables are included in the modeling process, simplifying the model while ensuring that the reduced-dimensional state-space model still accurately reflects the core dynamic characteristics of the MMC.

[0068] In one embodiment, an implementation of the above S201 is provided, such as Figure 4 As shown, the above-mentioned “establishing the full state space modeling equation of the three-phase MMC current” includes:

[0069] S301 : Determine a first relationship between a node voltage at two end nodes of an inductor and an inductor current in a three-phase MMC.

[0070] In the embodiment of the present application, the state of the three-phase MMC is determined by 9 inductor current variables, i a 、i b 、i c 、i ua 、i ub 、i uc 、i la 、i lb 、i lc , according to Figure 3 The topology shown determines the first relationship between the node voltage across the inductor and the inductor current as shown in Equation 1:

[0071] (Formula 1)

[0072] Among them, the 9 relations in formula 1 are i a 、i b 、i c 、i ua 、i ub 、i uc 、i la 、i lb 、i lc A first relationship between the node voltage at both ends and the inductor current.

[0073] S302 : Determine a second relationship between the voltage of the voltage source and the node voltage in the three-phase MMC.

[0074] In the embodiment of the present application, the input of the three-phase MMC is determined to be 10 voltage sources, namely v a 、v b 、v c 、v dc 、v ua 、v ub 、v uc 、v la 、v lb 、v lc , according to Figure 3 The topology shown determines the second relationship between the voltage source power and the node voltage as shown in Equation 2:

[0075] (Equation 2)

[0076] Among them, the 10 relations in formula 2 are v a 、v b 、v c 、v dc 、v ua 、v ub 、v uc 、v la 、v lb 、v lc and a second relationship between the node voltage.

[0077] S303 : Determine a third relationship between the inflow current and the outflow current at the nodes at both ends of the inductor in the three-phase MMC.

[0078] In the embodiment of the present application, the relationship between the current inflow and outflow of each node is described according to Kirchhoff's current law, as shown in Formula 3:

[0079] (Formula 3)

[0080] S304 : Based on the first relationship, the second relationship, and the third relationship, a full state space modeling equation of the three-phase MMC current is obtained.

[0081] As an optional implementation, the first relationship, the second relationship, and the third relationship may be determined as a full state-space modeling equation of the three-phase MMC current.

[0082] As another optional implementation, the first relationship, the second relationship, and the third relationship may be combined simultaneously to obtain a full state-space modeling equation for the three-phase MMC current.

[0083] In the above-mentioned application embodiment, the full state space modeling equation of the three-phase MMC current is constructed from three perspectives: the relationship between the node voltage at both ends of the inductor and the inductor current, the relationship between the voltage source power supply and the node voltage, and the relationship between the current inflow and outflow of each node, so that the full state space modeling equation of the three-phase MMC current is more comprehensive and accurate.

[0084] In one embodiment, an implementation of the above S202 is provided, such as Figure 5 As shown, the above “converting the full state space modeling equation into a matrix modeling equation” includes:

[0085] S401 , defining a state vector including 9 inductor currents, an input vector including 10 voltage sources, a current vector including 10 voltage source currents, and a voltage vector including 14 node voltages at both ends of the inductor.

[0086] In the embodiment of the present application, Figure 3 The three-phase MMC topology shown in the figure contains 9 state vectors of inductor currents, which can be expressed as x=[i a ,i b ,i c ,i ua ,i ub ,i uc ,i la ,i lb ,i lc ]', the current vector containing 10 voltage source currents can be expressed as i u =[i va ,i vb ,i vc ,i Vdc ,i vua ,i vub ,i vuc ,i vla ,i vlb ,i vlc ]', the voltage vector containing the node voltages of the 14 inductor nodes can be expressed as v=[v1, v2, v3, v4, v5, v6, v7, v8, v9, v 10 , v 11 , v 12 , v 13 , v 14 ]'.

[0087] S402, construct four coefficient matrices.

[0088] In an embodiment of the present application, based on the current vector of the voltage source current and the voltage vector of the node voltage, a full state vector z representing the coupling relationship between the node voltage and the voltage source current is constructed as shown in Formula 4, and the dimension of the full state vector is 14+10=24.

[0089] (Formula 4)

[0090] In the embodiment of the present application, for 9 inductor currents and 14 nodes, the sub-matrix element corresponding to the inductor current flowing into the node is defined as 1, and the sub-matrix element corresponding to the inductor current flowing out of the node is defined as −1. The coefficient matrix corresponding to the dynamic characteristics of the inductor current is formed as shown in Equation 5:

[0091] (Formula 5)

[0092] In the embodiment of the present application, the coefficient matrix corresponding to the algebraic constraint equation can describe the coupling relationship between the input quantity and the node. For 10 voltage sources and 14 nodes, according to the reference direction, the sub-matrix element corresponding to the node connected to the positive pole of the voltage source is defined as −1, and the sub-matrix element corresponding to the node connected to the negative pole of the voltage source is defined as 1. The coefficient matrix corresponding to the algebraic constraint equation is shown in Equation 6:

[0093] (Equation 6)

[0094] In the embodiment of the present application, the system matrix corresponding to the input vector influence can describe the relationship between the circuit nodes and the voltage source current. For the 14 nodes, the sub-matrix elements corresponding to the voltage source current flowing into these nodes are defined as −1, and the sub-matrix elements corresponding to the voltage source current flowing out of these nodes are defined as 1. The system matrix corresponding to the input vector influence is formed as shown in Equation 7:

[0095] (Equation 7)

[0096] S403 , obtaining a matrix modeling equation based on the state vector, the input vector, the current vector, the voltage vector, and four coefficient matrices.

[0097] In the embodiment of the present application, a matrix modeling equation is constructed based on the state vector, input vector, current vector, voltage vector and four coefficient matrices: ,in As shown in formula 8, As shown in formula 9, As shown in formula 10:

[0098] (Equation 8)

[0099] Among them, G 11 , G 21 , G 32 They are the coefficient matrices corresponding to the dynamic characteristics of the inductor current, the algebraic constraint equations, and the input vector influence, G 12 , G 22 , G31 are all zero matrices.

[0100] (Equation 9)

[0101] (Equation 10)

[0102] in, Submatrix A x1 、A x2 are all zero matrices, submatrix A x3 It consists of a 9-dimensional identity matrix and a 5*9 zero matrix: . Submatrix B u1 、B u3 are all zero matrices, submatrix B u2 is the 10-dimensional identity matrix.

[0103] In the above application embodiment, the three-phase MMC current model is described by four coefficient matrices and a state vector, an input vector, a current vector, and a voltage vector, thereby improving the accuracy and reliability of the matrix form modeling equation.

[0104] In one embodiment, an implementation of the above S203 is provided, such as Figure 6 As shown, the above-mentioned "performing row echelon simplification on the coefficient matrix to obtain a simplified matrix" includes:

[0105] S501: horizontally concatenate the four coefficient matrices into a combined matrix.

[0106] In the embodiment of the present application, the four coefficient matrices are horizontally spliced ​​into a combined matrix [G, Adx, Ax, Bu], laying the foundation for subsequent step-by-step simplification.

[0107] S502 , performing row echelon simplification on the combined matrix to extract a simplified matrix consisting of three sub-matrices.

[0108] In the embodiment of the present application, the Gauss-Jordan elimination method is used to perform row echelon simplification on the combined matrix, extract key sub-matrices, and eliminate redundant variables. Specifically, the simplification process can be shown as Formula 11:

[0109] (Equation 11)

[0110] Furthermore, let E=M 22 ×E dx , A=-M 23 , B=-M 24 , the simplified matrix can be expressed as: , where the three sub-matrices are E, A, and B.

[0111] In an embodiment of the present application, row echelon simplification is performed on the coefficient matrix to convert the matrix into the simplest row echelon form, directly revealing all key variables and free variables, and the complete simplified information can be obtained without back substitution.

[0112] In one embodiment, an implementation of the above S204 is provided, such as Figure 7 As shown, the above “based on the simplified matrix, extracting independent state variables from the matrix form modeling equation to obtain a state space model after dimensionality reduction” includes:

[0113] S601: Determine the target number of independent state variables according to the rank of the simplified matrix.

[0114] In the embodiment of the present application, the rank of the simplified matrix is ​​the matrix M 22 The rank of M is 5, which is less than the dimension of the state 9. Then the target number of independent state variables is 5, M 22 There are 9-5=4 rows of zero vectors in , so E, A, and B can be further decomposed. The combination of sub-matrices is decomposed as shown in Equation 12:

[0115] (Equation 12)

[0116] S602 , based on the target number, reducing the original state variables in the matrix modeling equation by null space mapping to obtain a target number of independent state variables.

[0117] In the embodiment of the present application, in order to extract the independent state from Equation 12, the transfer matrix is ​​defined as The null space of the matrix [A2, B2] is: . Further, according to the transfer matrix , state vector x, input vector u determine the independent state vector x b and independent input vector u b As shown in formula 13:

[0118] (Equation 13)

[0119] S603: Generate a state space model after dimensionality reduction based on the target number of independent state variables.

[0120] In the embodiment of the present application, the coefficient matrix of the target number of independent state variables, that is, the coefficient matrix of 4 independent state variables, is determined according to Formula 13, as shown in Formula 14:

[0121] (Equation 14)

[0122] Furthermore, according to Equation 14, the state space model after dimensionality reduction is generated: , where the independent state vector is x b =[i ub ,i uc ,i la ,i lb ,i lc ], the coefficient matrix of the independent state vector is Equation 15-Equation 18:

[0123] (Equation 15)

[0124] (Equation 16)

[0125] (Equation 17)

[0126] (Equation 18)

[0127] In the above application embodiment, by determining independent variables based on matrix rank and using null space mapping for state reduction, the dimension of the state space model is significantly reduced, thereby reducing the computational burden while maintaining the core dynamic characteristics of the model.

[0128] In one embodiment, Figure 8 As shown, the above three-phase MMC current modeling method further includes:

[0129] S205 , based on the state space model, reconstructing the input vector into a controlled power input vector and a disturbance input vector to obtain a reduced-dimensional state space equation.

[0130] In an embodiment of the present application, the input vector is reconstructed, the AC side voltage and the DC side voltage are regarded as disturbance inputs, and the bridge arm voltage is used as the control input to generate a state space equation after dimensionality reduction.

[0131] S206, determining a cost function of the dimension-reduced state space equation.

[0132] In an embodiment of the present application, a cost function is designed based on state variables and control inputs. For example, a mathematical optimization objective can be constructed by the sum of the weighted squares of the state variables and the weighted squares of the control input energies.

[0133] Optional, such as Figure 9 As shown, the above “cost function for determining the dimensionality reduction state space equation” includes:

[0134] S701, obtaining independent state variables in the reduced-dimensional state space equation and a controlled power input vector.

[0135] In an embodiment of the present application, independent state quantities are extracted from the original high-order model of the three-phase MMC, such as the circulating component of the bridge arm current, the fluctuating component of the sub-module capacitor voltage, the AC side current tracking error, etc.; and the physical quantities directly corresponding to the active control degrees of freedom are determined, such as the modulation signal of the upper / lower bridge arm insertion voltage, or the dq-axis components of the equivalent bridge arm voltage.

[0136] S702, based on the independent state variable and the controlled power input vector, construct a cost function including tracking error and control amount size, wherein the tracking error is the tracking error between the independent state variable and the preset current reference value, and the control amount size is the control amount for the controlled power input vector.

[0137] In the embodiment of the present application, the cost function may be a linear quadratic regulator (LQR) cost function. For example, the LQR cost function is shown in Formula 19:

[0138] (Equation 19)

[0139] Among them, Q is the weight matrix of independent state variables, R is the weight matrix of control variables, and x ss is the system state of the three-phase MMC current model in steady state, u ss is the system input of the three-phase MMC current model in steady state; is the tracking error, To control the size.

[0140] S207 , calculating the optimal feedback gain matrix corresponding to the reduced-dimensional state space equation based on the cost function.

[0141] In the embodiment of the present application, the optimal feedback gain matrix corresponding to the reduced-dimensional state space equation can be determined by minimizing the cost function.

[0142] Optionally, minimize the cost function and calculate the optimal feedback gain matrix corresponding to the reduced-dimensional state space equation based on the Riccati equation.

[0143] Among them, the Riccati equation is a steady-state algebraic equation, and the Riccati differential equation is the core mathematical tool for solving the optimal feedback gain matrix. This equation can be recursively or directly analyzed to obtain a symmetric positive definite matrix by integrating the structural parameters of the dimensionality-reduced state space model and the cost function weight matrix. Its steady-state solution directly generates the optimal feedback gain. In the embodiment of the present application, the optimal feedback gain matrix Klqr is obtained by solving the Riccati equation, so that the optimal control input .

[0144] For example, the cost function of the linear quadratic regulator (LQR) control algorithm designed according to the system rated power and rated voltage effective value can be expressed as Equation 20:

[0145] (Equation 20)

[0146] Where J represents the cost function; v n Indicates the effective value of three-phase AC voltage; S n Indicates rated power; Represents the sum of the squares of the three-phase output currents, that is ; represents the sum of the squares of the six bridge arm currents, that is, ; Represents the sum of the squares of the six bridge arm voltages, that is .

[0147] Furthermore, the cost function is converted into a matrix form, and the optimal feedback gain matrix Klqr is calculated according to the Riccati equation as Equation 21:

[0148] (Equation 21)

[0149] S208 , controlling the three-phase MMC based on the optimal feedback gain matrix.

[0150] In an embodiment of the present application, key operating state quantities of the three-phase MMC are acquired in real time, including the upper and lower bridge arm currents of each phase, the collective mean and fluctuating components of the sub-module capacitor voltage, and the AC output current. After signal conditioning and coordinate transformation, a state vector consistent with the dimension of the reduced-dimensional state space equation is formed. Based on the real-time state vector and the optimal feedback gain matrix, an incremental instruction of the controlled power input vector is generated, and the three-phase MMC is controlled using the incremental instruction.

[0151] Optionally, the real-time state vector is multiplied by the optimal feedback gain matrix to generate an incremental instruction for the controlled power input vector, and the incremental instruction is superimposed on the steady-state operating point reference to generate a final controlled power input vector. This signal is converted into a switching sequence of the power semiconductor device by the pulse width modulation (PWM) unit, directly driving the switching action of the bridge arm sub-module.

[0152] In the above-mentioned application embodiment, a dimensionality reduction model with clear physical meaning is established by separating the controlled input and the disturbance input, and the balance relationship between the tracking error and the control quantity is quantified based on the cost function, thereby achieving high-precision, high-efficiency, and highly robust real-time control of the three-phase MMC.

[0153] In one embodiment, an implementation of the above S205 is provided, such as Figure 10As shown, the above “based on the state space model, the input vector is reconstructed into a controlled power input vector and a disturbance input vector to obtain a reduced-dimensional state space equation” includes:

[0154] S801: Define the upper and lower arm voltages in the three-phase MMC as controlled inputs, and define the AC side three-phase voltage and the DC bus voltage as disturbance inputs.

[0155] In the embodiment of the present application, based on equation 12, the input vector u is reconstructed and split into the controlled power input vector u cs = [v ua , v ub , v uc , v la , v lb , v lc ]′ and the disturbance input vector u es = [v a , v b , v c , V dc ]′.

[0156] S802 , based on the state space model, separating the controlled input coefficient matrix and the disturbance input coefficient matrix, forming a reduced-dimensional state space equation in which the control input and the disturbance input are separated.

[0157] In the embodiment of the present application, y is defined to represent the output of the system, and a state-space current model that can be directly used to design the LQR is constructed based on the control input and the disturbance input:

[0158] (Equation 22)

[0159] Among them, the controlled input coefficient matrix For Equation 21, the disturbance input coefficient matrix Formula 23:

[0160] (Equation 23)

[0161] (Equation 24)

[0162] In the above application embodiment, by separating the coefficient matrices of the controlled input and the disturbance input, a clear model foundation is laid for the subsequent design of a controller that can accurately track the controlled input and effectively suppress the voltage disturbances on the AC and DC sides.

[0163] In one embodiment, an implementation of the above S208 is provided, such as Figure 11 As shown, the above-mentioned “controlling three-phase MMC based on optimal feedback gain matrix” includes:

[0164] S901 , collecting deviations between independent state variables in the dimension-reduced state space equation and preset current reference values ​​in real time.

[0165] In the embodiment of the present application, the preset current reference value can be determined based on user input data, or can be determined based on the current usage scenario of the three-phase MMC. In the embodiment of the present application, monitoring values ​​corresponding to independent state variables in the three-phase MMC are collected in real time to determine the deviation between the independent state variables and the preset current reference value.

[0166] In the embodiment of the present application, the output y of the system should be equal to the current reference value r calculated by the power controller. ss To achieve this goal, Figure 12 As shown, define x ss = N x × r ss + N dx ×u e s and u ss = N u × r ss + N du ×u es , where u es is the disturbance input vector, N x 、N dx 、N u 、N du The transfer matrix can be constructed by the coefficient matrix B bc 、B be and C b To express it. Wherein, the transfer matrix is ​​shown in Equation 25:

[0167] (Equation 25)

[0168] S902 : Generate a bridge arm voltage control variable based on the deviation, the optimal feedback gain matrix, and the disturbance input vector defined in the reduced-dimensional state space equation.

[0169] In the embodiment of the present application, x ss with x b The difference is input into the optimal feedback gain matrix to obtain the optimal feedback gain, and the optimal feedback gain is combined with u ss Input into the state space model shown in Equation 22 to generate the bridge arm voltage control quantity.

[0170] S903 , driving the power devices of the three-phase MMC based on the bridge arm voltage control amount to adjust the upper and lower bridge arm voltages.

[0171] In an embodiment of the present application, the bridge arm voltage control quantity is converted into a specific gate drive signal of the power semiconductor switching device, and the drive signal is used to directly control the input and output states of the neutron modules in the upper and lower bridge arms of each phase, thereby accurately adjusting the instantaneous output voltage of each bridge arm.

[0172] Optionally, the effect achieved by adopting this technical solution can be verified by simulation of a three-phase MMC. The simulation model parameters are shown in Table 1:

[0173] Table 1

[0174]

[0175] For example, in Figure 12 Under the regulation of the MMC current controller shown, the MMC AC output voltage and current and the upper and lower bridge arm currents in inverter mode and rated power are as follows: Figure 13 The characteristics of these waveforms show that the AC current exhibits a highly standard sinusoidal shape and maintains a precise in-phase relationship with the AC voltage. Even at a switching frequency of only 500 Hz, the total harmonic distortion (THD) of the AC current in the inverter mode system is only 0.32%. Figure 14 The AC side voltage and current, as well as the upper and lower bridge arm currents, are displayed for the MMC in rectifier mode at rated power. The AC current is 180 degrees out of phase with the AC voltage. Compared to inverter mode, the bridge arm currents show an overall downward trend. In this mode, total harmonic distortion is only 0.41%, demonstrating the effectiveness and robust performance of the control system under diverse operating conditions. Figure 13 and Figure 14 Here, current represents current, kA represents kiloampere, Voltage represents voltage, and kV represents kilovolt.

[0176] In the above application embodiment, the upper and lower bridge arms of the three-phase MMC are controlled by reducing the dimension of the state space equation, thereby ensuring the stability, fast response, low overshoot and low control energy consumption of the MMC.

[0177] In one embodiment, a complete three-phase MMC current modeling method is provided, such as Figure 15 As shown, the method includes:

[0178] S1 , determining a first relationship between a node voltage at two end nodes of an inductor and an inductor current in a three-phase MMC.

[0179] S2, determining a second relationship between the voltage of the voltage source and the node voltage in the three-phase MMC.

[0180] S3, determining a third relationship between the inflow current and the outflow current at the nodes at both ends of the inductor in the three-phase MMC.

[0181] S4. Based on the first relationship, the second relationship, and the third relationship, a full state space modeling equation of the three-phase MMC current is obtained.

[0182] S5, defining a state vector including 9 inductor currents, an input vector including 10 voltage source currents, a current vector including 10 voltage source currents, and a voltage vector including 14 node voltages at both ends of the inductor.

[0183] S6, construct four coefficient matrices to describe the coupling relationship between node voltage and voltage source current, the dynamic characteristics of inductor current, the algebraic constraint equation and the influence of input vector.

[0184] S7, based on the state vector, input vector, current vector, voltage vector and four coefficient matrices, obtain the matrix form modeling equation.

[0185] S8, horizontally concatenate the four coefficient matrices into a combined matrix.

[0186] S9, performing row echelon simplification on the combined matrix to extract a simplified matrix consisting of three sub-matrices.

[0187] S10, determining the target number of independent state variables according to the rank of the simplified matrix.

[0188] S11, based on the target number, the original state variables in the matrix form modeling equation are reduced by null space mapping to obtain the target number of independent state variables.

[0189] S12, based on the target number of independent state variables, generates a reduced-dimensional state space model.

[0190] In step S13, the upper and lower bridge arm voltages in the three-phase MMC are defined as controlled inputs, and the three-phase voltages on the AC side and the DC bus voltage are defined as disturbance inputs.

[0191] S14, based on the state space model, separate the controlled input coefficient matrix and the disturbance input coefficient matrix to form a reduced-dimensional state space equation in which the control input and the disturbance input are separated.

[0192] S15, obtain the independent state variables in the reduced-dimensional state space equation and the controlled power input vector.

[0193] S16, based on the independent state variable and the controlled power input vector, construct a cost function including tracking error and control amount size, wherein the tracking error is the tracking error between the independent state variable and the preset current reference value, and the control amount size is the control amount for the controlled power input vector.

[0194] S17, minimize the cost function and calculate the optimal feedback gain matrix corresponding to the reduced-dimensional state space equation based on the Riccati equation.

[0195] S18, collecting in real time the deviation between the independent state variables in the reduced-dimensional state space equation and the preset current reference value.

[0196] S19, generates a bridge arm voltage control variable based on the deviation, the optimal feedback gain matrix, and the disturbance input vector defined in the reduced-dimensional state space equation.

[0197] S20: driving the power devices of the three-phase MMC based on the bridge arm voltage control amount to adjust the upper and lower bridge arm voltages.

[0198] In the above-mentioned three-phase MMC current modeling method, a full state-space modeling equation for the three-phase MMC current is established; the full state-space modeling equation is converted into a matrix-form modeling equation, in which multiple vectors and coefficient matrices corresponding to the full state-space modeling equation are constructed; the coefficient matrix is ​​row-step simplified to obtain a simplified matrix; based on the simplified matrix, independent state variables are extracted from the matrix-form modeling equation to obtain a reduced-dimensional state-space model. By combining the modeling of the three-phase MMC state-space model with dimensionality reduction technology, high-precision, low-complexity MMC dynamic modeling is achieved. Key state variables are included in the modeling process, simplifying the model while ensuring that the reduced-dimensional state-space model still accurately reflects the core dynamic characteristics of the MMC.

[0199] It should be understood that, although the various steps in the flowcharts involved in the various embodiments described above are displayed in sequence according to the instructions of the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a portion of the steps in the flowcharts involved in the various embodiments described above can include multiple steps or multiple stages, and these steps or stages are not necessarily executed and completed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a portion of steps or stages in other steps.

[0200] Based on the same inventive concept, embodiments of the present application further provide a three-phase MMC current modeling device for implementing the three-phase MMC current modeling method described above. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations in one or more embodiments of the three-phase MMC current modeling device provided below can be found in the limitations of the three-phase MMC current modeling method described above and will not be repeated here.

[0201] In one embodiment, Figure 16As shown, a three-phase MMC current modeling device is provided, comprising: an establishment module 10, a conversion module 11, a simplification module 12 and a dimension reduction module 13, wherein:

[0202] Establishing module 10, for establishing full state space modeling equations of three-phase MMC current;

[0203] A conversion module 11 is used to convert the full state space modeling equation into a matrix form modeling equation, in which a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation are constructed;

[0204] A simplification module 12 is used to perform row echelon simplification on the coefficient matrix to obtain a simplified matrix;

[0205] The dimension reduction module 13 is used to extract independent state variables from the matrix modeling equation based on the simplified matrix to obtain a state space model after dimension reduction.

[0206] Each module in the three-phase MMC current modeling device can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in hardware form, or can be stored in a memory in the computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0207] In one embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0208] In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0209] In one embodiment, a computer program product is provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0210] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above-mentioned embodiments. In particular, any reference to memory, database, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may be, but are not limited to, general-purpose processors, central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), programmable logic devices (PLDs), data processing logic devices based on quantum computing, and the like.

[0211] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0212] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A three-phase MMC current modeling method, characterized in that: The following steps are involved: Establish the full state space modeling equations of three-phase MMC current; Converting the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation; Performing row echelon simplification on the coefficient matrix to obtain a simplified matrix; Based on the simplified matrix, independent state variables are extracted from the matrix form modeling equation to obtain a state space model after dimensionality reduction.

2. The method according to claim 1, characterized in that The full state space modeling equation for establishing the three-phase MMC current includes: Determining a first relationship between a node voltage at two end nodes of an inductor and an inductor current in the three-phase MMC; determining a second relationship between a voltage of a voltage source in the three-phase MMC and the node voltage; determining a third relationship between an inflow current and an outflow current at two end nodes of an inductor in the three-phase MMC; Based on the first relationship, the second relationship and the third relationship, a full state-space modeling equation of the three-phase MMC current is obtained.

3. The method according to claim 1, characterized in that The converting of the full state space modeling equation into a matrix form modeling equation comprises: A state vector including 9 inductor currents, an input vector including 10 voltage source currents, a current vector including 10 voltage source currents, and a voltage vector including 14 node voltages at both ends of the inductor are defined; Construct 4 coefficient matrices; The matrix form modeling equation is obtained based on the state vector, the input vector, the current vector, the voltage vector and the four coefficient matrices.

4. The method according to claim 3, characterized in that The performing row echelon simplification on the coefficient matrix to obtain a simplified matrix includes: horizontally concatenate the four coefficient matrices into a combined matrix; Performing row echelon simplification on the combined matrix to extract a simplified matrix consisting of three sub-matrices.

5. The method according to claim 1, wherein The step of extracting independent state variables from the matrix modeling equation based on the simplified matrix to obtain a state space model after dimensionality reduction includes: determining a target number of independent state variables according to the rank of the simplified matrix; Based on the target number, reducing the original state variables in the matrix form modeling equation by null space mapping to obtain the target number of independent state variables; Based on the target number of independent state variables, a state space model after dimensionality reduction is generated.

6. The method according to any one of claims 1 to 5, characterized in that The method further comprises: Based on the state space model, the input vector is reconstructed into a controlled power input vector and a disturbance input vector to obtain a reduced-dimensional state space equation; determining a cost function for the reduced-dimensional state-space equation; Based on the cost function, calculating the optimal feedback gain matrix corresponding to the reduced-dimensional state-space equation; The three-phase MMC is controlled based on the optimal feedback gain matrix.

7. The method according to claim 6, characterized in that Based on the state space model, the input vector is reconstructed into a controlled power input vector and a disturbance input vector to obtain a reduced-dimensional state space equation, including: The upper and lower bridge arm voltages in the three-phase MMC are defined as controlled inputs, and the three-phase voltages on the AC side and the DC bus voltage are defined as disturbance inputs; On the basis of the state space model, a controlled input coefficient matrix and a disturbance input coefficient matrix are separated to form the reduced-dimensional state space equation in which the control input and the disturbance input are separated.

8. The method according to claim 6, characterized in that Determining the cost function of the reduced-dimensional state space equation includes: Obtaining the independent state variables in the reduced-dimensional state space equation and the controlled power supply input vector; Based on the independent state variable and the controlled power input vector, a cost function including a tracking error and a control amount size is constructed, wherein the tracking error is a tracking error between the independent state variable and a preset current reference value, and the control amount size is a control amount for the controlled power input vector.

9. The method according to claim 6, characterized in that The calculating, based on the cost function, an optimal feedback gain matrix corresponding to the reduced-dimensional state-space equation includes: The cost function is minimized, and an optimal feedback gain matrix corresponding to the reduced-dimensional state space equation is calculated based on the Riccati equation.

10. The method according to claim 6, characterized in that The controlling the three-phase MMC based on the optimal feedback gain matrix includes: real-time acquisition of deviations between independent state variables in the reduced-dimensional state space equation and preset current reference values; generating a bridge arm voltage control variable based on the deviation, the optimal feedback gain matrix, and the disturbance input vector defined in the reduced-dimensional state space equation; The power devices of the three-phase MMC are driven based on the bridge arm voltage control amount to adjust the upper and lower bridge arm voltages.

11. A three-phase MMC current modeling device, characterized in that: include: Establishing a module for establishing full state space modeling equations of three-phase MMC current; a conversion module, configured to convert the full state space modeling equation into a matrix form modeling equation, wherein the matrix form modeling equation is constructed with a plurality of vectors and coefficient matrices corresponding to the full state space modeling equation; A simplification module, configured to perform row echelon simplification on the coefficient matrix to obtain a simplified matrix; A dimensionality reduction module is used to extract independent state variables from the matrix form modeling equation based on the simplified matrix to obtain a state space model after dimensionality reduction.

12. A computer device, characterized in that: include: A memory and a processor, wherein the memory stores a computer program, and the processor implements the method according to any one of claims 1 to 10 when executing the computer program.

13. A computer-readable storage medium, characterized in that A computer program is stored thereon, and when the computer program is executed by a processor, the method according to any one of claims 1 to 10 is implemented.

14. A computer program product, characterized in that The computer program product includes a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 10 is implemented.

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