M3c impedance modeling method and device based on hss method

Abstract

The application provides an M3C impedance modeling method and device based on an HSS method, and relates to the technical field of automatic control. The method comprises the following steps: obtaining a power frequency bridge arm current reference value matrix model of a current inner loop controller, a low frequency bridge arm current reference value matrix model of the current inner loop controller, a power frequency control equation of the current inner loop controller, a low frequency control equation of the current inner loop controller, a first transformation equation small signal model and a second transformation equation; obtaining an equation relationship between port voltage and bridge arm current in a dq0 coordinate system in an M3C small signal model; obtaining a relationship formula between M3C port voltage and M3C port current according to the equation relationship; and performing harmonic state space method processing on the relationship formula to obtain an impedance model of M3C full frequency domain impedance characteristics. The method and device provided in the application embodiment are helpful to further analyze and improve the stability of a low frequency power transmission system.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and specifically to an M3C impedance modeling method and apparatus based on the HSS method. Background Technology

[0002] In recent years, numerous large-scale wind power bases have been built and put into operation. As an emerging technological solution, wind power aggregation and transmission technology based on low-frequency transmission systems (LFTS) has received widespread attention. Modular multilevel matrix converters (M3Cs) are the core equipment for realizing low-frequency transmission. Compared with frequency converters using other topologies, M3Cs have outstanding technical advantages such as high reliability, high power quality, and controllable power factor, and are considered to be the frequency converter topology with the broadest application prospects. Due to the numerous degrees of control freedom and complex low-frequency coupling characteristics of M3Cs, the lack of efficient and high-precision control schemes has been a key factor limiting the widespread application of M3Cs for a long time. Existing technology proposes a novel M3C control scheme using a decoupled control strategy, achieving relatively independent control of different physical quantities and significantly improving the performance of M3Cs. M3Cs using the decoupled control strategy have already been applied in some low-frequency transmission engineering demonstration projects.

[0003] The harmonic state-space (HSS) method is a concise and efficient approach for modeling and analyzing the dynamic characteristics of systems in the frequency domain. This method can construct models based on multidimensional harmonic transfer functions, characterizing the multi-frequency responses of various dynamic variables in the system. Furthermore, the state variables, inputs, and outputs in the HSS model are all in frequency-domain state-space form. This representation not only facilitates the extension of the model to harmonics of arbitrary orders but also allows for rapid computation in a computer.

[0004] The basic mathematical model of the HSS method will be briefly introduced below: For any periodic time-domain variable x(t), it can be expanded into the following Fourier series form: (1-1) In the formula, ω for x ( t The fundamental angular frequency of ) X k This is the Fourier coefficient. X k The calculation formula is as follows: (1-2) The time-domain state equation of a control system can be expressed in the following form: (1-3) Where x(t) and u(t) are the state vector and input vector in the time domain, respectively, and A(t) and B(t) are the corresponding coefficient matrices. Performing a Fourier transform on the above equation, the state equation in the frequency domain is obtained as follows: (1-4) The specific expressions for each quantity in the equation are shown below: (1-5) In the formula, X k , U k , A k , B k They are respectively x ( t ), u ( t ), A ( t ), B ( t )of k Fourier coefficients of subharmonics I Dimension and time-domain vector x ( t An identity matrix with the same dimension as the given matrix. m It is the highest harmonic order considered in the model.

[0005] The main advantage of the HSS method is that it can clearly characterize the dynamic characteristics of various physical quantities in the frequency domain, providing a mathematical foundation for modeling and analyzing systems with complex frequency characteristics. Currently, this method has been applied in the modeling and research of various power electronic converters, including buck-boost converters, thyristor-controlled reactors, single-phase and three-phase two-level converters, and modular multilevel converters (MMCs).

[0006] Impedance analysis (IMS) is a modeling and analysis method with clear physical meaning, which facilitates intuitive revelation of the oscillation mechanism of power systems. Compared to the state-space method, IMS does not rely on the internal structure and parameters of each component in the system, thus greatly reducing the dimensionality of the system model. This method has been widely used in stability studies of power systems containing a high proportion of power electronic devices. Accurate impedance modeling of converters is fundamental and crucial for analyzing the stability of power systems based on IMS. In recent years, research on impedance modeling of AC / DC converters such as two-level converters and MMCs has received widespread attention. Existing techniques use the HSS method to model the impedance of MMCs and apply the impedance model for system stability analysis. Some scholars have also conducted research on the impedance model of AC / AC converters, providing general ideas and methods for impedance modeling of AC / AC converters.

[0007] The impedance model of AC-AC inverters, including the M3C, describes the electrical characteristics and coupling effects of the inverter's high-frequency and low-frequency ports. Its general form is as follows: Define the harmonic voltage phasors and harmonic current vectors at the common coupling point on both sides of the inverter's high-frequency and low-frequency ports as follows: u p dS u p qS u p dL u p qL] T and[ i p dS i p qS i p dL i p qL] T The admittance of the frequency converter can then be defined as: (1-6) In the formula, Y AC-AC It is a four-dimensional square matrix, which is the admittance matrix characterizing the low-frequency coupling characteristics of the electrical quantities at the inverter ports. It can be further divided into four two-dimensional sub-matrices; sub-matrices Y SS , Y SL , Y LS , Y LL These can represent the self-admittance of the inverter's power frequency port, the coupling admittance of the low-frequency port to the power frequency port, the coupling admittance of the power frequency port to the low-frequency port, and the self-admittance of the low-frequency port, respectively.

[0008] In existing research on M3C impedance models, researchers have proposed harmonic impedance models for M3Cs based on a dual αβ transform control strategy. This model meticulously establishes the coupling and transmission relationships of major harmonic components among various electrical quantities based on the distribution and transmission characteristics of different harmonic components within the M3C. Then, small-signal analysis is used to analyze the response characteristics of small-frequency disturbances in the main circuit and control system. Finally, the relationship between the voltage and current small-signal vectors at the external ports of the M3C under small-signal excitation is obtained through computation and processing.

[0009] The advantage of this technical solution is that it fully considers the coupling harmonics inside the M3C and provides a relatively complete characterization of the distribution characteristics of harmonics at each frequency, thereby giving the obtained impedance model relatively high calculation accuracy.

[0010] A significant drawback of impedance models based on harmonic characteristic analysis is the difficulty in extending the model to higher-order harmonic components. This modeling method relies on detailed harmonic characteristic analysis, which not only leads to an exponential increase in the amount of analysis required as the coupling order of the harmonics being analyzed increases, but also makes it difficult to implement the harmonic analysis process using a computer. Furthermore, even subtle changes in the control system topology can affect the distribution and transmission characteristics of harmonics, resulting in relatively poor scalability of this impedance model.

[0011] Furthermore, compared to the decoupled control strategy in a synchronous rotating coordinate system, the M3C control strategy based on dual αβ transformation involves the control of mixing AC quantities, making it difficult to guarantee accuracy. Therefore, M3C using a decoupled control strategy has broader application prospects in engineering practice; however, impedance modeling methods for M3C with this control mode are still rarely reported. Summary of the Invention

[0012] To address the problems in the prior art, embodiments of the present invention provide an M3C impedance modeling method and apparatus based on the HSS method, which can at least partially solve the problems existing in the prior art.

[0013] On the one hand, this invention proposes an M3C impedance modeling method based on the HSS method, comprising: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0014] The bridge arm parameters include the power frequency bridge arm current, the low frequency bridge arm current, and the bridge arm equivalent module capacitor voltage; the electrical parameters include the power frequency three-phase voltage and the low frequency three-phase voltage. Correspondingly, based on the bridge arm parameters and electrical parameters of the M3C control system and the M3C main circuit, the power frequency bridge arm current reference value matrix model and the low frequency bridge arm current reference value matrix model of the current inner loop controller are obtained, including: The power frequency three-phase voltage is transformed into the dq0 coordinate system to obtain the power frequency voltage matrix of the M3C port; the low frequency three-phase voltage is transformed into the dq0 coordinate system to obtain the low frequency voltage matrix of the M3C port. The power frequency bridge arm current and the low frequency bridge arm current are transformed in the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low frequency bridge arm current transformation matrix. The equivalent module capacitor voltage of the bridge arm is transformed in the αβ0 coordinate system to obtain the transformation matrix of the equivalent module capacitor voltage of the bridge arm. The power frequency bridge arm current reference matrix and the low frequency bridge arm current reference matrix are determined based on the M3C control system. The low-frequency bridge arm current reference value matrix model is obtained based on the low-frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the low-frequency bridge arm current transformation matrix, the M3C port power frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the first preset control loop transfer function. The low-frequency bridge arm current reference value matrix model of the current inner loop controller is obtained based on the power frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current transformation matrix, the M3C port low-frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the second preset control loop transfer function.

[0015] The bridge arm parameters include the power frequency bridge arm current, the low frequency bridge arm current, the power frequency bridge arm average switching function, and the low frequency bridge arm average switching function. Based on the bridge arm parameters of the M3C control system and the M3C main circuit, the power frequency control equation and the low frequency control equation of the current inner loop controller are obtained, including: The power frequency bridge arm current and the low frequency bridge arm current are transformed in the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low frequency bridge arm current transformation matrix. The average switching function of the power frequency bridge arm and the average switching function of the low frequency bridge arm are transformed into the dq0 coordinate system to obtain the transformation matrix of the average switching function of the power frequency bridge arm and the transformation matrix of the average switching function of the low frequency bridge arm. The power frequency bridge arm current reference matrix and the low frequency bridge arm current reference matrix are determined based on the M3C control system. The low-frequency control equation of the current inner loop controller is obtained based on the transformation matrix of the average switching function of the low-frequency bridge arm, the transformation matrix of the αβ0 coordinate system, the reference value matrix of the low-frequency bridge arm current, and the first preset control parameter matrix. The power frequency control equation of the inner loop controller is obtained based on the power frequency bridge arm average switching function transformation matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current reference value matrix, and the second preset control parameter matrix.

[0016] The bridge arm parameters include the bridge arm average switching function, the voltage across the equivalent module, the current flowing through the equivalent module, and the capacitor voltage of the bridge arm equivalent module. Correspondingly, the small-signal model of the first transformation equation is obtained based on the bridge arm parameters of the M3C's main circuit, including: The voltage equation relationship of the bridge arm equivalent module is determined based on the voltage across the equivalent module, the average switching function of the bridge arm, and the capacitor voltage of the bridge arm equivalent module. The bridge arm current equation relationship is determined based on the bridge arm average switching function, the bridge arm equivalent module capacitor voltage, and the current flowing through the equivalent module. The voltage equation and current equation of the bridge arm equivalent module are transformed into dq0 coordinate system at power frequency and low frequency to obtain the first transformation equation. The time domain variables in the first transformation equation are taken as small signals to obtain the small signal model of the first transformation equation.

[0017] The bridge arm parameters include bridge arm inductance, bridge arm current, bridge arm voltage, and the equivalent resistance of each bridge arm. The electrical parameters include low-frequency three-phase voltage, power-frequency three-phase voltage, and the voltage difference between the neutral points on the low-frequency and power-frequency sides. Correspondingly, the second transformation equation is obtained based on the bridge arm parameters and electrical parameters of the M3C's main circuit, including: Based on the low-frequency three-phase voltage, the power frequency three-phase voltage, the voltage difference, the bridge arm inductance, the bridge arm current, the bridge arm voltage, and the equivalent resistance of each bridge arm, and using Kirchhoff's voltage law, the voltage and current relationship of M3C is obtained. The voltage and current relationship of the M3C is transformed into the dq0 coordinate system at power frequency and low frequency to obtain the second transformation equation.

[0018] The step of obtaining the equation relationship between the port voltage and bridge arm current in the dq0 coordinate system of the M3C small-signal model includes: The matrix dimension transformation is performed on the M3C small-signal model. Before the power frequency side variables of the M3C control system are used for the calculation of the M3C small-signal model, a transformation based on the phase-locked loop mapping function is performed. All equations of the M3C small-signal model are transformed and the system of equations is solved to obtain the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system.

[0019] On one hand, this invention proposes an M3C impedance modeling device based on the HSS method, comprising: The first acquisition unit is used to acquire the following based on the bridge arm parameters and electrical parameters of the M3C control system, the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. The second acquisition unit is used to acquire the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system in the M3C small signal model. The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. The modeling unit is used to obtain the relationship between the M3C port voltage and the M3C port current according to the equation, and to process the relationship using the harmonic state-space method to obtain the impedance model of the M3C full-frequency impedance characteristics.

[0020] In another aspect, embodiments of the present invention provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the following method: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0021] This invention provides a computer-readable storage medium, comprising: The computer-readable storage medium stores a computer program that, when executed by a processor, implements the following method: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0022] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the following method: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0023] The M3C impedance modeling method and apparatus based on the HSS method provided in this invention obtains the following matrix models based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C: the power frequency bridge arm current reference matrix model of the current inner loop controller, the low frequency bridge arm current reference matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation; and obtains the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system in the M3C small-signal model; wherein, the M3C small-signal model is composed of current... The following equations are constructed: the reference value matrix model of the power frequency bridge arm current of the inner loop controller, the reference value matrix model of the low frequency bridge arm current of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. Based on these equations, the relationship between the M3C port voltage and the M3C port current is obtained. This relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics. Establishing an accurate and easily expandable M3C impedance model helps to further analyze and improve the stability of the low-frequency transmission system. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a flowchart illustrating an M3C impedance modeling method based on the HSS method provided in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the main circuit structure of the M3C provided in an embodiment of the present invention.

[0026] Figure 3 This is a schematic diagram of the control system structure of M3C using a decoupling control strategy provided in an embodiment of the present invention.

[0027] Figure 4 This is a schematic diagram of the structure of an M3C impedance modeling device based on the HSS method provided in an embodiment of the present invention.

[0028] Figure 5 This is a schematic diagram of the physical structure of a computer device provided in an embodiment of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other.

[0030] Figure 1 This is a flowchart illustrating an embodiment of the M3C impedance modeling method based on the HSS method provided by the present invention, as shown below. Figure 1 As shown, the M3C impedance modeling method based on the HSS method provided in this embodiment of the invention includes: Step S1: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, obtain the following matrix models: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation.

[0031] Step S2: Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation.

[0032] Step S3: Obtain the relationship between the M3C port voltage and the M3C port current based on the equation, and process the relationship using the harmonic state-space method to obtain the impedance model of the M3C full-frequency impedance characteristics.

[0033] In step S1 above, the device obtains the following matrix models based on the M3C control system, the bridge arm parameters of the M3C main circuit, and the electrical parameters: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. The device can be a computer device that executes this method. The acquisition, storage, use, and processing of data in this application's technical solution all comply with relevant regulations.

[0034] Frequency domain impedance modeling provides a concise and efficient method for analyzing the frequency domain dynamic characteristics of the M3C. Next, this invention will establish mathematical models of the main circuit and control system of the M3C employing a decoupled control strategy, derive the relationships between electrical quantities at its low-frequency ports, and establish its frequency domain impedance model based on the HSS method.

[0035] like Figure 2 As shown, u a , u b , u c This indicates the three-phase voltage on the low-frequency side. u u , u v , u w This represents the three-phase voltage on the power frequency side. The three-phase input and three-phase output are connected through nine bridge arms, each consisting of... N A series full-bridge submodule and an inductor L Composition, the structure of a single full-bridge submodule in Figure 2 As shown in the lower left corner. Each bridge arm is named after the two phases it connects to, such as bridge arm au, which represents the bridge arm connecting the low-frequency side phase a and the power frequency side phase u.

[0036] Assuming that the voltage of each submodule within the same bridge arm remains equal, and the switching cycle of the modules is much shorter than the power frequency cycle, the average equivalent model of M3C can be used to convert the series submodule group in each bridge arm into a full-bridge submodule. The capacitance of the equivalent module is... C = C 0 / N , C 0 represents the capacitor of the submodule. N This represents the number of submodules in one bridge arm. The average switching function for the bridge arm xy is defined as follows: (2-1) In the formula, Represents the submodules in the bridge arm xy i The switching function can take values ​​of 0, 1, or -1. Let...u xy , i xy , v xy Let the voltage across the equivalent module of the bridge arm xy be the voltage across the equivalent module, the current flowing through the equivalent module be the current through the equivalent module, and the voltage across the capacitor of the equivalent module be the voltage across the equivalent module. These physical quantities satisfy the following equation: (2-2) (2-3) (2-4) In the formula, Represents the submodules in the bridge arm xy i The capacitor voltage.

[0037] According to Kirchhoff's voltage law, the voltage and current relationship of M3C is as follows: (2-5) In the formula, R It is the equivalent resistance of each bridge arm. u NO It is the voltage difference between the neutral points on the low-frequency side and the power frequency side, because u NO Since it is controllable and usually set to 0 in the control loop, the last term of equation (2-5) will be ignored in the derivation below. L is the bridge arm inductance. For the bridge arm current, For bridge arm voltage, It is a low-frequency three-phase voltage. The term "power frequency three-phase voltage" refers to the following: "Based on the low-frequency three-phase voltage, the power frequency three-phase voltage, the voltage difference, the bridge arm inductance, the bridge arm current, the bridge arm voltage, and the equivalent resistance of each bridge arm, and using Kirchhoff's voltage law, the voltage and current relationship of M3C is obtained."

[0038] The control system architecture of M3C employing a decoupled control strategy is as follows: Figure 3 As shown in the figure. In the control loop, it is necessary to map the electrical quantities in the abc coordinate system to the αβ0 coordinate system or the dq0 coordinate system. The mapping matrices are shown in equations (2-6) and (2-7), respectively. The dq0 coordinate system is also called the synchronous rotating coordinate system, and the transformation matrix shown in equation (2-7) is the Park transformation matrix.

[0039] (2-6) (2-7) A certain physical quantity of the nine bridge arms or bridge arm equivalent modules. xArranged in a certain order, they are written in matrix form as shown in equation (2-8), and marked with corresponding uppercase letters. X This matrix is ​​represented, and its notation is further defined by equation (2-9). X abc , X uvw , X αβ0 In this paper, physical quantities x The bridge arm current can be obtained. i Bridge arm average switching function s Equivalent module voltage u or equivalent module capacitor voltage v .

[0040] (2-8) (2-9) In the formula, ω S and ω L They are power frequency f S and low frequency f L The corresponding angular frequency. For ease of derivation later, a matrix is ​​defined to represent the port electrical quantities in the M3C synchronous rotating coordinate system. U S , I S , U L , I L As shown in equations (2-10) and (2-11); U S This refers to the M3C port power frequency voltage matrix. U L This is a low-frequency voltage matrix for the M3C port. I S This is the power frequency current matrix for the M3C port. I LThis refers to the low-frequency current matrix of the M3C port. Specifically, it explains that "the power frequency three-phase voltage is transformed using the dq0 coordinate system to obtain the power frequency voltage matrix of the M3C port; the low-frequency three-phase voltage is transformed using the dq0 coordinate system to obtain the low-frequency voltage matrix of the M3C port." Equation (2-9) explains that "the power frequency bridge arm current and the low-frequency bridge arm current are transformed using the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low-frequency bridge arm current transformation matrix," "the bridge arm equivalent module capacitor voltage is transformed using the αβ0 coordinate system to obtain the bridge arm equivalent module capacitor voltage transformation matrix," and "the power frequency bridge arm average switching function and the low-frequency bridge arm average switching function are transformed using the dq0 coordinate system to obtain the power frequency bridge arm average switching function transformation matrix and the low-frequency bridge arm average switching function transformation matrix."

[0041] (2-10) (2-11) Define matrix M xy Indicates only the first x Line number y A 3D square matrix with 1s in each column and 0s in the rest; matrix M all Let represent a 3D square matrix where all elements are 1. According to Kirchhoff's current law, the M3C port current and the bridge arm current satisfy the equation (2-12).

[0042] (2-12)

[0043] In the control system, the voltage / power outer loop controller is used to calculate the arm current reference value and apply it to the current inner loop controller. This illustrates that "the power frequency arm current reference value matrix and the low frequency arm current reference value matrix are determined according to the M3C control system". The process by which the controller obtains the power frequency side and the low frequency side arm current reference value matrices can be modeled as follows: (2-13) (2-14) In the formula, the superscript " “” represents the reference value of the corresponding variable. In equations (2-13) and (2-14), matrix “K” represents the matrix containing the transfer function of the control loop, and its specific expression is as follows: (2-15) in u s dS, u s qS and i s dS, is and qS are the steady-state values ​​of the power frequency side port voltage and current in the dq0 coordinate system, respectively. k object (s) represents the transfer function of the PI link in the control system, and "object" represents the control object of the controller in which the PI link is located. That is, K in equation (2-13) represents the transfer function of the first preset control link, and K in equation (2-14) represents the transfer function of the second preset control link. Equation (2-13) explains that "the power frequency bridge arm current reference value matrix model of the current inner loop controller is obtained based on the low frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the low frequency bridge arm current transformation matrix, the M3C port power frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix and the first preset control link transfer function".

[0044] Equation (2-14) explains that "the low-frequency bridge arm current reference value matrix model of the current inner loop controller is obtained based on the power frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current transformation matrix, the M3C port low-frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the second preset control loop transfer function".

[0045] The function of the current inner loop controller is to control the current of the nine bridge arms and obtain reference values ​​for the bridge arm voltages. The control equations of the low-frequency side current inner loop controller are as follows: (2-16) (2-17) In the formula, the matrix K S1 , K S2 , K L1 , K L2 The specific expression is as follows: (2-18) In equation (2-16), K is the first preset control parameter matrix, and in equation (2-17), K is the second preset control parameter matrix. Equation (2-16) explains that "the low-frequency control equation of the current inner loop controller is obtained based on the transformation matrix of the average switching function of the low-frequency bridge arm, the transformation matrix of the αβ0 coordinate system, the current reference value matrix of the low-frequency bridge arm, and the first preset control parameter matrix".

[0046] Equation (2-17) explains that "the power frequency control equation of the current inner loop controller is obtained based on the power frequency bridge arm average switching function transformation matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current reference value matrix, and the second preset control parameter matrix".

[0047] Considering that the diagonal voltage equalization controller in the inter-arm voltage equalization control is only intermittently activated during the steady-state operation of the M3C, and the switching frequency of the module voltage equalization controller within the bridge arm is much higher than the system frequency, it can be approximated that the voltages of each sub-module within the same bridge arm remain equal. Therefore, their impact on the frequency domain impedance of the M3C is very small, and they will be ignored in the modeling below.

[0048] Equation (2-2) illustrates the equation relationship of the voltage of the equivalent module of the bridge arm based on the voltage across the equivalent module, the average switching function of the bridge arm, and the capacitor voltage of the equivalent module of the bridge arm.

[0049] Equation (2-3) illustrates that "the bridge arm current equation relationship is determined based on the average switching function of the bridge arm, the equivalent module capacitor voltage of the bridge arm, and the current flowing through the equivalent module".

[0050] The equations (2-2) and (2-3) corresponding to the nine bridge arms are arranged into matrix form. The resulting matrix equations are then subjected to Park transforms at power frequency and low frequency, respectively, and the resulting equations are shown below: (2-19) (2-20) Equations (2-19) and (2-20) illustrate that "the voltage equation of the equivalent module of the bridge arm and the current equation of the bridge arm are transformed into the dq0 coordinate system at power frequency and low frequency to obtain the first transformation equation."

[0051] In the formula, the matrix P CS and P CL This is the coefficient matrix of the equation, and its specific expression is shown below: (2-21) For the sake of brevity, the expression will be... P ( ω S )diag( x xu , x xv , x xw ) P -1 ( ω S ) ( x =a,b,c) and P ( ω L )diag( x ay ,x by , x cy ) P -1 ( ω L ) ( y =u,v,w) are respectively represented by symbols X x and X y The superscripts "s" and "p" represent the steady-state and small-signal values ​​of the corresponding variables, respectively. Combining the commutative law of multiplication, taking the small-signal values ​​of the time-domain variables in equations (2-19) and (2-20), we obtain the small-signal models of the two equations as shown below: (2-22) (2-23) Equations (2-22) and (2-23) illustrate that "by taking the small signal of the time-domain variable in the first transformation equation, the small signal model of the first transformation equation is obtained".

[0052] Performing Park transforms on the M3C's KVL equation (2-5) at both power frequency and low frequency yields the following equations: (2-24) In the formula, the matrix P RLS and P RLL This is the coefficient matrix of the equation, and its specific expression is shown below: (2-25) Equation (2-24) explains that "the voltage and current relationship of the M3C is transformed into the dq0 coordinate system at power frequency and low frequency to obtain the second transformation equation".

[0053] In step S2 above, the device obtains the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system in the M3C small signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation.

[0054] The process of obtaining the equation relationship between port voltage and bridge arm current in the dq0 coordinate system of the M3C small-signal model includes: The matrix dimension transformation is performed on the M3C small-signal model. Before the power frequency side variables of the M3C control system are used for the calculation of the M3C small-signal model, a transformation based on the phase-locked loop mapping function is performed. All equations of the M3C small-signal model are transformed and the system of equations is solved to obtain the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system.

[0055] Since equation (2-24) is a linear equation, its small-signal model has the same mathematical form as the original equation. That is, the small-signal model of the equation can be obtained by simply taking the corresponding small-signal values ​​of the time-domain variables in the equation. Similarly, the equations (2-13), (2-14), (2-16), and (2-17) of the control system are also linear equations, and their small-signal models are all completely identical in mathematical form to the original equations.

[0056] Based on the M3C small-signal model constructed from the small-signal equations corresponding to equations (2-22), (2-23), (2-13), (2-14), (2-16), (2-17), and (2-24), the port voltage matrix in the dq0 coordinate system of the small-signal model can be derived. and With bridge arm current matrix and The equation relating the coefficient matrix and the variable matrix needs to be transformed into an equation involving the multiplication of a 3D coefficient matrix and a 3D variable matrix, which is equivalent to the multiplication of a 9D coefficient matrix by a 9D column vector. (2-26) This equivalent transformation unifies the mathematical form of each equation, solves the problem of adding like terms in the process of rearranging the original 3D matrix equations, and greatly simplifies the solution process of the system of equations.

[0057] It is worth noting that the power frequency-side synchronous rotating coordinate system in the control system differs from the power frequency-side synchronous rotating coordinate system of the M3C main circuit; the phase difference between the two is determined by the phase-locked loop. Therefore, the power frequency-side variables in the control system need to undergo the following function transformation before being used for small-signal model calculations: (2-27) g (·) denotes the mapping function determined by the phase-locked loop, which utilizes the port voltage on the M3C's power frequency side. U S To obtain the relative phase of the control system in the dq0 coordinate system on the power frequency side, and the corresponding variables in the main circuit and control system. X main _circuit and X control_systemEssentially, it is the projection of the same variable into two synchronously rotating coordinate systems with a certain phase difference.

[0058] Based on the equivalent mathematical transformation of equation (2-26), all equations of the M3C small-signal model are first transformed, and then the system of equations consisting of them is solved to eliminate equations that do not include port voltages. , and bridge arm current , The term. By rearranging the equations, the relationship between port voltage and bridge arm current can be quantitatively described in the following form: (2-28) In the formula, and All are 18-dimensional column vectors. The elements in the matrix are and The elements of a vector are arranged in a certain order; similarly, a vector... The elements in the matrix are and It is composed of the arrangement of elements. Y ap-18×18 It is an 18-dimensional admittance matrix composed of complex elements.

[0059] In step S3 above, the device obtains the relationship between the M3C port voltage and the M3C port current based on the equation, and processes the relationship using the harmonic state-space method to obtain the impedance model of the M3C full-frequency impedance characteristics.

[0060] According to equation (2-12), the M3C port current can be uniquely calculated from the bridge arm current. Therefore, there exists an 18-dimensional matrix. H 18×18 This makes the following equation true: (2-29) In the formula, the 18-dimensional vector The elements in the matrix are I p S and I The elements of pL are arranged in a permutation. Because of the vector... and Each of them contains only 4 distinct elements, and the vector and They are structurally identical, therefore an 18×4 matrix exists. H 18×4 This makes the following equation true: (2-30) Multiply both sides of equation (2-28) by the matrix on the left. H18×18 Substituting equations (2-29) and (2-30) into the equation, we obtain the following equation: (2-31) Construct a 4×18 matrix H 4×18 This makes the following equation true: (2-32) In the formula, I 4×4 It is a 4-dimensional identity matrix. Multiply both sides of equation (2-31) by the matrix on the left. H 4×18 The voltage and current relationship at the M3C port is shown below: (2-33) Equation (2-33) is the time-domain expression of the M3C impedance model. Applying the HSS model to equation (2-33) yields an impedance model describing the full-frequency impedance characteristics of the M3C: (2-34) Define the small-signal frequency and the system fundamental frequency as follows: f p and f The superscript "(h)" indicates a frequency of f p +hf The harmonic impedance model described above characterizes the spectrum of the current response generated under a certain voltage small-signal excitation. Clearly, the harmonic impedance is related to the frequency of the injected small signal. f p This indicates that the impedance characteristics of the M3C differ for disturbances of different frequencies.

[0061] The M3C impedance modeling method based on the HSS method provided in this invention constructs a frequency-domain small-signal impedance model for M3C. This method is based on the main circuit equations and control system equations of M3C, fully considering the influence of the control system structure and parameters on macroscopic impedance characteristics. This ensures the accuracy of the model and facilitates its extension to M3Cs employing other control strategies. The model, constructed based on the HSS method, clearly characterizes the excitation and response characteristics of M3C in the frequency domain, enabling the impedance model to be conveniently applied to the analysis and research of oscillation mechanisms in low-frequency transmission systems. This provides strong theoretical support for the targeted development of resonant stability enhancement measures for frequency-division transmission systems in engineering.

[0062] The M3C impedance modeling method based on the HSS method provided in this invention obtains the following matrix models based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C: the power frequency bridge arm current reference matrix model of the current inner loop controller, the low frequency bridge arm current reference matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation; and obtains the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system in the M3C small-signal model; wherein, the M3C small-signal model is composed of the current inner loop controller... The following equations are constructed: the reference value matrix model of the power frequency bridge arm current of the inner current controller, the reference value matrix model of the low frequency bridge arm current of the inner current controller, the power frequency control equation of the inner current controller, the low frequency control equation of the inner current controller, the small-signal model of the first transformation equation, and the second transformation equation. Based on these equations, the relationship between the M3C port voltage and the M3C port current is obtained. This relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics. Establishing an accurate and easily expandable M3C impedance model helps to further analyze and improve the stability of the low-frequency transmission system.

[0063] In the above optional embodiments, the bridge arm parameters include power frequency bridge arm current, low frequency bridge arm current, and bridge arm equivalent module capacitor voltage; the electrical parameters include power frequency three-phase voltage and low frequency three-phase voltage. Correspondingly, based on the bridge arm parameters and electrical parameters of the M3C control system and the M3C main circuit, the power frequency bridge arm current reference value matrix model and the low frequency bridge arm current reference value matrix model of the current inner loop controller are obtained, including: The power frequency three-phase voltage is transformed into the dq0 coordinate system to obtain the power frequency voltage matrix of the M3C port; the low frequency three-phase voltage is transformed into the dq0 coordinate system to obtain the low frequency voltage matrix of the M3C port; the above embodiments can be referred to for explanation, and will not be repeated here.

[0064] The power frequency bridge arm current and the low frequency bridge arm current are transformed in the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low frequency bridge arm current transformation matrix; the above embodiments can be referred to for explanation, and will not be repeated here.

[0065] The equivalent module capacitor voltage of the bridge arm is transformed using the αβ0 coordinate system to obtain the transformation matrix of the equivalent module capacitor voltage of the bridge arm; this can be referred to the above embodiment for explanation, and will not be repeated here.

[0066] The reference matrix for the power frequency bridge arm current and the reference matrix for the low frequency bridge arm current are determined according to the M3C control system; the above embodiments can be referred to for explanation, and will not be repeated here.

[0067] The low-frequency bridge arm current reference value matrix model is obtained based on the low-frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the low-frequency bridge arm current transformation matrix, the M3C port power frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the first preset control loop transfer function; the above embodiment can be referred to for explanation, and will not be repeated here.

[0068] The low-frequency bridge arm current reference value matrix model of the current inner loop controller is obtained based on the power frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current transformation matrix, the M3C port low-frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the second preset control loop transfer function. This can be referred to the above embodiment for further explanation and will not be repeated here.

[0069] In the above optional embodiments, the bridge arm parameters include power frequency bridge arm current, low frequency bridge arm current, power frequency bridge arm average switching function, and low frequency bridge arm average switching function; the power frequency control equation and the low frequency control equation of the current inner loop controller are obtained based on the bridge arm parameters of the M3C control system and the M3C main circuit, including: The power frequency bridge arm current and the low frequency bridge arm current are transformed in the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low frequency bridge arm current transformation matrix; the above embodiments can be referred to for explanation, and will not be repeated here.

[0070] The average switching function of the power frequency bridge arm and the average switching function of the low frequency bridge arm are transformed into the dq0 coordinate system to obtain the transformation matrix of the average switching function of the power frequency bridge arm and the transformation matrix of the average switching function of the low frequency bridge arm; this can be referred to the above embodiment for explanation, and will not be repeated here.

[0071] The reference matrix for the power frequency bridge arm current and the reference matrix for the low frequency bridge arm current are determined according to the M3C control system; the above embodiments can be referred to for explanation, and will not be repeated here.

[0072] The low-frequency control equation of the current inner loop controller is obtained based on the transformation matrix of the average switching function of the low-frequency bridge arm, the transformation matrix of the αβ0 coordinate system, the reference value matrix of the low-frequency bridge arm current, and the first preset control parameter matrix; the above embodiments can be referred to for explanation, and will not be repeated here.

[0073] The power frequency control equation of the inner loop controller is obtained based on the power frequency bridge arm average switching function transformation matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current reference value matrix, and the second preset control parameter matrix. This can be referred to the above embodiment for explanation, and will not be repeated here.

[0074] In the above optional embodiments, the bridge arm parameters include the bridge arm average switching function, the voltage across the equivalent module, the current flowing through the equivalent module, and the bridge arm equivalent module capacitor voltage; correspondingly, the small-signal model of the first transformation equation is obtained based on the bridge arm parameters of the M3C main circuit, including: The voltage equation relationship of the bridge arm equivalent module is determined based on the voltage across the equivalent module, the average switching function of the bridge arm, and the capacitor voltage of the bridge arm equivalent module; this can be referred to the above embodiment for explanation, and will not be repeated here.

[0075] The bridge arm current equation relationship is determined based on the average switching function of the bridge arm, the equivalent module capacitor voltage of the bridge arm, and the current flowing through the equivalent module; the above embodiments can be referred to for explanation, and will not be repeated here.

[0076] The voltage equations and current equations of the bridge arm equivalent modules are transformed using the dq0 coordinate system at power frequency and low frequency to obtain the first transformation equation. The time-domain variables in the first transformation equation are then converted to small-signal values ​​to obtain the small-signal model of the first transformation equation. This can be referred to the above embodiment for further explanation and will not be repeated here.

[0077] In the above optional embodiments, the bridge arm parameters include bridge arm inductance, bridge arm current, bridge arm voltage, and the equivalent resistance of each bridge arm; the electrical parameters include low-frequency three-phase voltage, power-frequency three-phase voltage, and the voltage difference between the neutral points on the low-frequency side and the power-frequency side; correspondingly, the second transformation equation is obtained based on the bridge arm parameters and electrical parameters of the M3C's main circuit, including: Based on the low-frequency three-phase voltage, the power frequency three-phase voltage, the voltage difference, the bridge arm inductance, the bridge arm current, the bridge arm voltage, and the equivalent resistance of each bridge arm, and using Kirchhoff's voltage law, the voltage and current relationship of M3C is obtained; please refer to the above embodiments for explanation, and will not be repeated here.

[0078] The voltage and current relationship of the M3C is transformed using the dq0 coordinate system for both power frequency and low frequency to obtain the second transformation equation. This can be referred to the above embodiment for further explanation and will not be repeated here.

[0079] In the above optional embodiments, obtaining the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system of the M3C small-signal model includes: The M3C small-signal model undergoes matrix dimension transformation. Before the power frequency side variables of the M3C control system are used for the calculation of the M3C small-signal model, a transformation based on the phase-locked loop mapping function is performed. This can be referred to the above embodiment for explanation, and will not be repeated here.

[0080] All equations of the M3C small-signal model are transformed and the system of equations is solved to obtain the equations between the port voltage and the bridge arm current in the dq0 coordinate system. This can be referred to the above embodiment for further explanation, and will not be repeated here.

[0081] Figure 4 This is a schematic diagram of the structure of an M3C impedance modeling device based on the HSS method provided in an embodiment of the present invention, as shown below. Figure 4 As shown, the M3C impedance modeling device based on the HSS method provided in this embodiment of the invention includes a first acquisition unit 401, a second acquisition unit 402, and a modeling unit 403, wherein: The first acquisition unit 401 is used to acquire the following data based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. The second acquisition unit 402 is used to acquire the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system of the M3C small-signal model. The M3C small-signal model is constructed from the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. The modeling unit 403 is used to acquire the relationship between the M3C port voltage and the M3C port current based on the equation relationship, and to process the relationship using the harmonic state-space method to obtain the impedance model of the M3C full-frequency impedance characteristics.

[0082] Specifically, the first acquisition unit 401 in the device is used to acquire the following matrix models based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. The second acquisition unit 402 is used to acquire the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system of the M3C small-signal model. The M3C small-signal model is constructed from the following matrix models: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. The modeling unit 403 is used to acquire the relationship between the M3C port voltage and the M3C port current based on the equation relationship, and to process the relationship using the harmonic state-space method to obtain the impedance model of the M3C full-frequency impedance characteristics.

[0083] The M3C impedance modeling device based on the HSS method provided in this invention obtains the following matrix models based on the bridge arm parameters and electrical parameters of the M3C control system, the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation: It also obtains the equation relationship between the port voltage and bridge arm current in the dq0 coordinate system of the M3C small-signal model; wherein, the M3C small-signal model is composed of the current inner loop controller... The following equations are constructed: the reference value matrix model of the power frequency bridge arm current of the inner current controller, the reference value matrix model of the low frequency bridge arm current of the inner current controller, the power frequency control equation of the inner current controller, the low frequency control equation of the inner current controller, the small-signal model of the first transformation equation, and the second transformation equation. Based on these equations, the relationship between the M3C port voltage and the M3C port current is obtained. This relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics. Establishing an accurate and easily expandable M3C impedance model helps to further analyze and improve the stability of the low-frequency transmission system.

[0084] The embodiments of the present invention provide an M3C impedance modeling device based on the HSS method, which can be used to execute the processing flow of the above-described method embodiments. Its functions will not be repeated here, but can be referred to the detailed description of the above-described method embodiments.

[0085] Figure 5 This is a schematic diagram of the physical structure of a computer device provided in an embodiment of the present invention, such as... Figure 5 As shown, the computer device includes: a memory 501, a processor 502, and a computer program stored in the memory 501 and executable on the processor 502. When the processor 502 executes the computer program, it implements the following method: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0086] This embodiment discloses a computer program product, which includes a computer program that, when executed by a processor, implements the following method: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0087] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the following method: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

[0088] Compared with existing technical solutions, the M3C impedance modeling method based on the HSS method provided in this invention obtains the following matrix models based on the bridge arm parameters and electrical parameters of the M3C control system, the power frequency bridge arm current reference value matrix model, the power frequency control equation, the low frequency control equation, the first transformation equation small-signal model, and the second transformation equation of the current inner loop controller, according to the bridge arm parameters and electrical parameters of the M3C main circuit. It also obtains the equation relationship between the port voltage and bridge arm current in the dq0 coordinate system of the M3C small-signal model. The M3C... The small-signal model is constructed from the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small-signal model of the first transformation equation, and the second transformation equation. Based on the aforementioned equations, the relationship between the M3C port voltage and the M3C port current is obtained. This relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics. Establishing an accurate and easily expandable M3C impedance model helps to further analyze and improve the stability of low-frequency transmission systems.

[0089] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0090] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0091] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0092] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0093] In the description of this specification, the references to terms such as "an embodiment," "a specific embodiment," "some embodiments," "for example," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0094] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An M3C impedance modeling method based on the HSS method, characterized in that, include: Based on the bridge arm parameters and electrical parameters of the M3C control system and the main circuit of the M3C, the following are obtained: the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. Obtain the equation relationship between port voltage and bridge arm current in the dq0 coordinate system in the M3C small-signal model; The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. Based on the aforementioned equation, the relationship between the M3C port voltage and the M3C port current is obtained. The relationship is then processed using the harmonic state-space method to obtain the impedance model of the M3C's full-frequency impedance characteristics.

2. The M3C impedance modeling method based on the HSS method according to claim 1, characterized in that, The bridge arm parameters include the power frequency bridge arm current, the low frequency bridge arm current, and the bridge arm equivalent module capacitor voltage; the electrical parameters include the power frequency three-phase voltage and the low frequency three-phase voltage. Correspondingly, based on the bridge arm parameters and electrical parameters of the M3C control system and the M3C main circuit, the power frequency bridge arm current reference value matrix model and the low frequency bridge arm current reference value matrix model of the current inner loop controller are obtained, including: The power frequency three-phase voltage is transformed into the dq0 coordinate system to obtain the power frequency voltage matrix of the M3C port; the low frequency three-phase voltage is transformed into the dq0 coordinate system to obtain the low frequency voltage matrix of the M3C port. The power frequency bridge arm current and the low frequency bridge arm current are transformed in the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low frequency bridge arm current transformation matrix. The equivalent module capacitor voltage of the bridge arm is transformed in the αβ0 coordinate system to obtain the transformation matrix of the equivalent module capacitor voltage of the bridge arm. The power frequency bridge arm current reference matrix and the low frequency bridge arm current reference matrix are determined based on the M3C control system. The low-frequency bridge arm current reference value matrix model is obtained based on the low-frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the low-frequency bridge arm current transformation matrix, the M3C port power frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the first preset control loop transfer function. The low-frequency bridge arm current reference value matrix model of the current inner loop controller is obtained based on the power frequency bridge arm current reference value matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current transformation matrix, the M3C port low-frequency voltage matrix, the bridge arm equivalent module capacitor voltage transformation matrix, and the second preset control loop transfer function.

3. The M3C impedance modeling method based on the HSS method according to claim 1, characterized in that, The bridge arm parameters include power frequency bridge arm current, low frequency bridge arm current, power frequency bridge arm average switching function, and low frequency bridge arm average switching function. Based on the bridge arm parameters of the M3C control system and the M3C main circuit, the power frequency control equation and the low-frequency control equation of the current inner loop controller are obtained, including: The power frequency bridge arm current and the low frequency bridge arm current are transformed in the dq0 coordinate system to obtain the power frequency bridge arm current transformation matrix and the low frequency bridge arm current transformation matrix. The average switching function of the power frequency bridge arm and the average switching function of the low frequency bridge arm are transformed into the dq0 coordinate system to obtain the transformation matrix of the average switching function of the power frequency bridge arm and the transformation matrix of the average switching function of the low frequency bridge arm. The power frequency bridge arm current reference matrix and the low frequency bridge arm current reference matrix are determined based on the M3C control system. The low-frequency control equation of the current inner loop controller is obtained based on the transformation matrix of the average switching function of the low-frequency bridge arm, the transformation matrix of the αβ0 coordinate system, the reference value matrix of the low-frequency bridge arm current, and the first preset control parameter matrix. The power frequency control equation of the inner loop controller is obtained based on the power frequency bridge arm average switching function transformation matrix, the αβ0 coordinate system transformation matrix, the power frequency bridge arm current reference value matrix, and the second preset control parameter matrix.

4. The M3C impedance modeling method based on the HSS method according to claim 1, characterized in that, The bridge arm parameters include the bridge arm average switching function, the voltage across the equivalent module, the current flowing through the equivalent module, and the bridge arm equivalent module capacitor voltage; correspondingly, the small-signal model of the first transformation equation is obtained based on the bridge arm parameters of the M3C main circuit, including: The voltage equation relationship of the bridge arm equivalent module is determined based on the voltage across the equivalent module, the average switching function of the bridge arm, and the capacitor voltage of the bridge arm equivalent module. The bridge arm current equation relationship is determined based on the bridge arm average switching function, the bridge arm equivalent module capacitor voltage, and the current flowing through the equivalent module. The voltage equation and current equation of the bridge arm equivalent module are transformed into dq0 coordinate system at power frequency and low frequency to obtain the first transformation equation. The time domain variables in the first transformation equation are taken as small signals to obtain the small signal model of the first transformation equation.

5. The M3C impedance modeling method based on the HSS method according to claim 1, characterized in that, The bridge arm parameters include bridge arm inductance, bridge arm current, bridge arm voltage, and the equivalent resistance of each bridge arm. The electrical parameters include low-frequency three-phase voltage, power-frequency three-phase voltage, and the voltage difference between the neutral points on the low-frequency and power-frequency sides. Correspondingly, the second transformation equation is obtained based on the bridge arm parameters and electrical parameters of the M3C's main circuit, including: Based on the low-frequency three-phase voltage, the power frequency three-phase voltage, the voltage difference, the bridge arm inductance, the bridge arm current, the bridge arm voltage, and the equivalent resistance of each bridge arm, and using Kirchhoff's voltage law, the voltage and current relationship of M3C is obtained. The voltage and current relationship of the M3C is transformed into the dq0 coordinate system at power frequency and low frequency to obtain the second transformation equation.

6. The M3C impedance modeling method based on the HSS method according to claim 1, characterized in that, The process of obtaining the equation relationship between port voltage and bridge arm current in the dq0 coordinate system of the M3C small-signal model includes: The matrix dimension transformation is performed on the M3C small-signal model. Before the power frequency side variables of the M3C control system are used for the calculation of the M3C small-signal model, a transformation based on the phase-locked loop mapping function is performed. All equations of the M3C small-signal model are transformed and the system of equations is solved to obtain the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system.

7. An M3C impedance modeling device based on the HSS method, characterized in that, include: The first acquisition unit is used to acquire the following based on the bridge arm parameters and electrical parameters of the M3C control system, the power frequency bridge arm current reference value matrix model of the current inner loop controller, the low frequency bridge arm current reference value matrix model of the current inner loop controller, the power frequency control equation of the current inner loop controller, the low frequency control equation of the current inner loop controller, the small signal model of the first transformation equation, and the second transformation equation. The second acquisition unit is used to acquire the equation relationship between the port voltage and the bridge arm current in the dq0 coordinate system in the M3C small signal model. The M3C small-signal model is constructed from the current inner loop controller power frequency bridge arm current reference value matrix model, the current inner loop controller low frequency bridge arm current reference value matrix model, the current inner loop controller power frequency control equation, the current inner loop controller low frequency control equation, the first transformation equation small-signal model, and the second transformation equation. The modeling unit is used to obtain the relationship between the M3C port voltage and the M3C port current according to the equation, and to process the relationship using the harmonic state-space method to obtain the impedance model of the M3C full-frequency impedance characteristics.

8. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 6.

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