Discrete state space model establishing method and device suitable for direct current three-port element

Abstract

In order to evaluate the stability of a high-proportion power electronic system, the discrete state space model establishing method and device suitable for the direct-current three-port element are provided on the basis of an original discrete state space modeling method, and the specific scene range of the discrete state space model is further expanded. The method comprises the following steps: firstly, deducing a direct current three-port element discrete state space model, establishing a direct current three-port element discrete equivalent circuit model, further establishing an alternating current and direct current hybrid system whole-network discrete state matrix containing the direct current three-port element, and verifying the correctness and practicability of the matrix. The small-signal model established by the method has relatively high expansibility, is convenient for subsequently establishing a full-system state space model connected with a large area containing a direct-current three-port element, and establishes a basis for researching the stability of the system.

Description

Technical Field

[0001] This invention relates to the field of power system small disturbance stability verification modeling, specifically a method and apparatus for establishing a discrete state-space model applicable to DC three-port components. Background Technology

[0002] In recent years, my country's new energy technologies have developed rapidly, with wind power and photovoltaic installed capacity increasing year by year. DC transmission equipment has also been widely used in power transmission, all relying on a large number of power electronic converters for grid connection. However, research shows that power electronic converters may experience oscillation and instability risks due to control interactions during actual operation. Subsynchronous oscillation accidents caused by new energy equipment have occurred in Texas, USA, and Guyuan, Hebei, my country. Therefore, small-disturbance stability verification of power systems is a crucial module for ensuring the safe and stable operation of power systems.

[0003] Currently, commonly used methods for small-disturbance stability analysis of high-proportion power electronic systems include electromagnetic transient analysis, impedance analysis, and eigenvalue analysis. Electromagnetic transient analysis can establish a time-domain simulation model of the system and visually observe system oscillations, but it lacks analysis of instability mechanisms and is time-consuming when analyzing large-scale power systems. Impedance analysis uses the Nyquist criterion to analyze system stability but lacks a specific quantitative description of the internal mechanisms of the power system. Eigenvalue analysis, based on the eigenvalues ​​of the system's linearized state-space matrix, determines system instability by whether the real parts of the eigenvalues ​​fall in the right half-plane. It has a rigorous mathematical foundation and can analyze the participation factors through the right eigenvectors of state variables, revealing key oscillation links, and has wide applications in the field of small-disturbance power systems.

[0004] Eigenvalue analysis (EVA) performs system stability analysis by establishing state-space equations. However, for large-scale power systems, the variety of components and the complexity of modeling make it difficult for traditional time-domain state-space equation establishment methods to construct matrices of thousands of orders. Some scholars have proposed a discretized state-space modeling method, which effectively solves the problem of the complexity of establishing state-space equations for large-scale power systems by establishing discrete state-space models of common power system components and constructing state-space matrices in the discrete domain. However, currently established discretized models mainly include single-port and two-port components. With the development of DC transmission technology, ultra-high voltage DC hierarchical access systems have been applied in large-scale power transmission. Therefore, the discretized model of DC three-port components, represented by these systems, and their access methods need further derivation, and the discretized component library needs further improvement. Summary of the Invention

[0005] The technical problem this invention aims to solve is to overcome the shortcomings of the existing technology and provide a method for establishing a discrete state-space model applicable to DC three-port components. To evaluate the stability of systems containing a high proportion of power electronics, this invention proposes a method for establishing a discrete state-space model applicable to DC three-port components, based on existing discretized state-space modeling methods, further expanding the scope of specific scenarios for discrete state-space models. This method first derives the discrete state-space model of the DC three-port component, establishes a discrete equivalent circuit model of the DC three-port component, and further establishes the discrete state matrix of the entire AC / DC hybrid system containing the DC three-port component, verifying its correctness and practicality. The small-signal model established by this method has strong scalability, facilitating the subsequent establishment of a full-system state-space model connecting large regions containing the DC three-port component, thus laying the foundation for studying system stability.

[0006] A method for establishing a discrete state-space model suitable for DC three-port components includes the following steps:

[0007] Step 1: Construct a discrete state-space model of a DC three-port component;

[0008] Step 2: Based on the discrete state-space model of the DC three-port element described in Step 1, construct the discretized equivalent circuit of the DC three-port element;

[0009] Step 3: Combine the discretized equivalent circuit of the DC three-port element obtained in Step 2 with the equivalent circuits of the other components in the system to construct a branch-node correlation matrix containing the DC three-port element.

[0010] Step 4: Based on the branch-node correlation matrix described in Step 3, construct the discrete state matrix of the entire AC / DC hybrid system containing DC three-port components. The discrete state matrix of the entire network is used for system eigenvalue calculation.

[0011] Furthermore, step one includes:

[0012] The DC three-port model is transformed from the continuous domain to the discrete domain, and the specific process is shown in equations (1) to (3):

[0013] Equation (1) is the continuous domain state-space model of a DC three-port element:

[0014] (1);

[0015] In the formula, X h U is the state vector of the continuous domain state-space equation for a three-port LCC. 1xy U 2xy and U 3xy These represent the input voltages of the three AC buses under the unified coordinate system of the entire network, i 1xy i2xy and i 3xy The output currents of the three AC buses in the unified coordinate system of the entire network are respectively determined by the coefficient matrix, which is determined by the linearized state-space equation of the specific DC three-port element.

[0016] Discretize the differential equation of equation (1) and define the historical current term h of the DC element. h The discretized equations are obtained, which yield the discrete state-space model of the DC three-port element, as follows:

[0017] (2);

[0018] The coefficient matrix in equation (2) is calculated from the coefficient matrix in equation (1);

[0019] (3);

[0020] In the formula, A d-h B d-h1 B d-h2 B d-h3 C d-h1 C d-h2 C d-h3 C d-h4 C d-h5 C d-h6 C d-h7 C d-h8 C d-h9 D d-h1 D d-h2 D d-h3 Both are coefficient matrices in the discrete domain, calculated from the coefficient matrices in equations (1) and (2).

[0021] Furthermore, step two specifically includes:

[0022] The discretized equations established in step one are used to establish an equivalent circuit model of a DC three-port element, represented by input voltage, output current, historical current terms, and node equivalent conductance. In equation (3), the three output currents are expressed from the input voltage, and the formula for the 3×3 order conductance matrix is:

[0023] (4);

[0024] In the formula, g 11 g 22 g 33 These represent the self-conductance of each node; g 12 g 13 g 21 g 23 g 31 g 32These represent the mutual conductance of each node;

[0025] Based on equation (4), the discretized equivalent circuit of the DC three-port element is established, thereby obtaining the basic discretized model of the DC three-port element.

[0026] Furthermore, step three specifically includes:

[0027] By combining the DC three-port element with the existing one-port and two-port elements, that is, setting the elements at the corresponding positions of the three nodes connected to the three-port element in the system branch-node correlation matrix to I2, and setting the elements at the remaining positions to 0, the voltage equation of the entire system discrete circuit network is obtained as follows:

[0028] (5);

[0029] In the formula, U node and i inject These are column vectors representing the system node voltages and node injected currents, respectively.

[0030] Formula (5) is the voltage equation that includes both AC and DC networks. Corresponding to the DC network equation (2) in step three, the main equation for the AC network is:

[0031] (6);

[0032] In the formula, h is the state vector of the entire system, and U branch For the branch voltages of single-port and AC two-port components, A d B d and D d It is a diagonal block matrix formed by the coefficient matrices in the discrete state-space equations of each component;

[0033] Thus, the discrete circuit network of the entire system containing DC three-port elements and the branch-node correlation matrix containing DC three-port elements are obtained.

[0034] Furthermore, step four specifically includes:

[0035] (1) Consistent with the AC system, the discrete state matrix of the system is generated according to the formula shown in equation (6). A is obtained from the voltage equation and branch-node correlation matrix of the discrete circuit network of the whole system. d L t and G;

[0036] (2) Since the diagonal matrix B is not required for DC components in the calculation, it is not necessary to use it for the time being. d and D d The element at the diagonal element corresponding to branch k is temporarily set to I2, and the other diagonal block elements are still generated according to the method in the communication system.

[0037] (3) Calculate 'B' separately. d L t =BL' and '-(L t ) T D d =LD';

[0038] (4) Use the coefficient matrix B in the discrete state-space model of DC components to represent the elements in the k-th row and m-th column of matrix BL. d-h1 Replace the elements in the k-th row and n-th column using the coefficient matrix B. d-h2 Replace the elements in the k-th row and f-th column using the coefficient matrix B. d-h3 replace;

[0039] (5) Use the coefficient matrix -D in the discrete state-space model of the DC element to represent the elements in the m-th row and k-th column of the matrix LD. d-h1 Replace the elements in the nth row and kth column using the coefficient matrix -D d-h2 Replace the elements in row f and column k using the coefficient matrix -D d-h3 Replacement; after the above steps, the state matrix A of the discrete state-space model of the entire system containing DC three-port components is obtained. D The expression is shown in equation (7), and it is used for eigenvalue calculation to verify system stability:

[0040] (7).

[0041] A device for establishing a discrete state-space model of a DC three-port component, comprising:

[0042] The model building module is used to build discrete state-space models of DC three-port components.

[0043] The equivalent circuit construction module is used to construct the discretized equivalent circuit of the DC three-port element based on the discrete state-space model of the DC three-port element.

[0044] The correlation matrix construction module is used to combine the obtained discretized equivalent circuit of the DC three-port element with the equivalent circuit of the other elements in the system to construct the discrete circuit network of the whole system containing the DC three-port element and the branch-node correlation matrix containing the DC three-port element.

[0045] The discrete state matrix construction module is used to construct the entire network discrete state matrix of the AC / DC hybrid system containing DC three-port components based on the branch-node correlation matrix. The entire network discrete state matrix is ​​used for system eigenvalue calculation.

[0046] Furthermore, the model building module is specifically used for:

[0047] The DC three-port model is transformed from the continuous domain to the discrete domain, and the specific process is shown in equations (1) to (3):

[0048] Equation (1) is the continuous domain state-space model of a DC three-port element:

[0049] (1);

[0050] In the formula, X h U is the state vector of the continuous domain state-space equation for a three-port LCC. 1xy U 2xy and U 3xy These represent the input voltages of the three AC buses under the unified coordinate system of the entire network, i 1xy i 2xy and i 3xy The output currents of the three AC buses in the unified coordinate system of the entire network are respectively determined by the coefficient matrix, which is determined by the linearized state-space equation of the specific DC three-port element.

[0051] Discretize the differential equation of equation (1) and define the historical current term h of the DC element. h The discretized equations are obtained, which yield the discrete state-space model of the DC three-port element, as follows:

[0052] (2);

[0053] The coefficient matrix in equation (2) is calculated from the coefficient matrix in equation (1);

[0054] (3);

[0055] In the formula, A d-h B d-h1 B d-h2 B d-h3 C d-h1 C d-h2 C d-h3 C d-h4 C d-h5 C d-h6 C d-h7 C d-h8 C d-h9 D d-h1 D d-h2 D d-h3 Both are coefficient matrices in the discrete domain, calculated from the coefficient matrices in equations (1) and (2).

[0056] Furthermore, the equivalent circuit construction module is specifically used for:

[0057] The discretized equations are used to establish an equivalent circuit model of a DC three-port element, represented by input voltage, output current, historical current terms, and node equivalent conductance. In equation (3), the three output currents are expressed from the input voltage, resulting in the 3×3 order conductance matrix formula:

[0058] (4);

[0059] In the formula, g 11 g 22 g 33 These represent the self-conductance of each node; g 12 g 13 g 21 g 23 g 31 g 32 These represent the mutual conductance of each node;

[0060] Based on equation (4), the discretized equivalent circuit of the DC three-port element is established, thereby obtaining the basic discretized model of the DC three-port element.

[0061] Furthermore, the association matrix construction module is specifically used for:

[0062] By combining the DC three-port element with the existing one-port and two-port elements, that is, setting the elements at the corresponding positions of the three nodes connected to the three-port element in the system branch-node correlation matrix to I2, and setting the elements at the remaining positions to 0, the voltage equation of the entire system discrete circuit network is obtained as follows:

[0063] (5);

[0064] In the formula, U node and i inject These are column vectors representing the system node voltages and node injected currents, respectively.

[0065] Formula (5) is the voltage equation that includes both AC and DC networks. Corresponding to the DC network equation (2) in step three, the main equation for the AC network is:

[0066] (6);

[0067] In the formula, h is the state vector of the entire system, and U branch For the branch voltages of single-port and AC two-port components, A d B d and D d It is a diagonal block matrix formed by the coefficient matrices in the discrete state-space equations of each component;

[0068] Thus, the discrete circuit network of the entire system containing DC three-port elements and the branch-node correlation matrix containing DC three-port elements are obtained.

[0069] Furthermore, the discrete state matrix construction module is specifically used for:

[0070] (1) Consistent with the AC system, the discrete state matrix of the system is generated according to the formula shown in equation (6). A is obtained from the voltage equation and branch-node correlation matrix of the discrete circuit network of the whole system. d L t and G;

[0071] (2) Since the diagonal matrix B is not required for DC components in the calculation, it is not necessary to use it for the time being. d and D d The element at the diagonal element corresponding to branch k is temporarily set to I2, and the other diagonal block elements are still generated according to the method in the communication system.

[0072] (3) Calculate 'B' separately. d L t =BL' and '-(L t ) T D d =LD';

[0073] (4) Use the coefficient matrix B in the discrete state-space model of DC components to represent the elements in the k-th row and m-th column of matrix BL. d-h1 Replace the elements in the k-th row and n-th column using the coefficient matrix B. d-h2 Replace the elements in the k-th row and f-th column using the coefficient matrix B. d-h3 replace;

[0074] (5) Use the coefficient matrix -D in the discrete state-space model of the DC element to represent the elements in the m-th row and k-th column of the matrix LD. d-h1 Replace the elements in the nth row and kth column using the coefficient matrix -D d-h2 Replace the elements in row f and column k using the coefficient matrix -D d-h3 Replacement; after the above steps, the state matrix A of the discrete state-space model of the entire system containing DC three-port components is obtained. D The expression is shown in equation (7), and it is used for eigenvalue calculation to verify system stability:

[0075] (7).

[0076] The advantages of the present invention are: (1) The discrete state space model established by the present invention based on the time-domain state space equation model of the DC three-port element can more accurately reflect the operating characteristics of the system after a small disturbance, and its eigenvalues ​​can correctly reflect the system state and oscillation frequency; (2) The discrete state space model of the DC three-port element established by the present invention can be well adapted to the original single-port element and two-port element, which facilitates the establishment of the discrete state space model of the whole system and the interaction analysis. Attached Figure Description

[0077] Figure 1 This is a structural diagram of the three-port LCC-HVDC DC transmission system of the present invention;

[0078] Figure 2 This is the discrete equivalent circuit model of the DC three-port element of the present invention;

[0079] Figure 3 This invention relates to a discrete circuit network for a system containing DC three-port components;

[0080] Figure 4 This is the branch-node correlation matrix form of the present invention containing DC three-port elements;

[0081] Figure 5 K is the DC current control loop of this invention. pconr The impact of parameters on system stability;

[0082] Figure 6 This is the oscillation waveform of the time-domain simulation system of this invention;

[0083] Figure 7 This is a structural diagram of the three-port LCC-HVDC access SVG system of the present invention;

[0084] Figure 8 This is a factor analysis diagram of the three-port LCC-HVDC access SVG system of the present invention.

[0085] Figure 9 This is a flowchart illustrating a method for establishing a discrete state-space model applicable to a DC three-port component, as described in an embodiment of the present invention. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0087] Please see Figure 9 This invention provides a method for establishing a discrete state-space model suitable for DC three-port components, comprising the following steps:

[0088] Step 1: Construct a discrete state-space model of a DC three-port component

[0089] Power systems mainly consist of single-port components, such as generators, wind turbines, and other power generation equipment, as well as loads and other power consumption equipment; AC two-port components, such as capacitors, resistors, and inductors; and DC two-port components, such as LCC-HVDC and VSC-HVDC transmission equipment. In recent years, three-port LCC-HVDC has been widely used in ultra-high voltage direct current (UHVDC) transmission. Unlike typical DC transmission models, it is connected to three separate buses in the system. The following section uses three-port LCC-HVDC as an example to introduce the method for establishing the discrete state-space equation model of DC three-port components.

[0090] A typical structure of a three-port LCC is as follows: Figure 1 As shown, it is connected to the AC system via three buses, PCC1, PCC2, and PCC3, respectively. Using the voltage and current of the three AC buses as input and output variables, respectively, its continuous linearized state-space equation can be expressed as:

[0091] (1)

[0092] Where, X h U is the state vector of the continuous domain state-space equation for a three-port LCC. 1xy U 2xy and U 3xy These represent the input voltages of the three AC buses under the unified coordinate system of the entire network, i 1xy i 2xy and i 3xy The output currents of the three AC buses are determined in the unified coordinate system of the entire system, and the other parameters can be determined by the linearized state-space equations of the specific DC three-port components.

[0093] To transfer the above equations to the discrete domain, consistent with single-port and two-port elements, a historical current term h can be introduced. h Discretizing equation (1) using the trapezoidal integral method yields the following discrete state-space model, where the coefficient matrix can be transformed from the continuous domain equation:

[0094] (2)

[0095] To obtain the complete input-output matrix of the system, substitute equation (2) into equation (1), that is, retain the historical current term h. h With output current i 1xy i2xy and i 3xy The discrete state-space model of the DC three-port port can be expressed as:

[0096] (3)

[0097] In the formula, A d-h B d-h1 B d-h2 B d-h3 C d-h1 C d-h2 C d-h3 C d-h4 C d-h5 C d-h6 C d-h7 C d-h8 C d-h9 D d-h1 D d-h2 D d-h3 Both are coefficient matrices in the discrete domain, calculated from the coefficient matrices in equations (1) and (2).

[0098] Step 2: Based on the discrete state-space model of the DC three-port element described in Step 1, construct the discretized equivalent circuit of the DC three-port element.

[0099] Based on the relationship between the AC voltage and AC current of the three-port LCC in the last two lines of equation (3), the discretized equivalent circuit model of the system can be obtained as follows: Figure 2 As shown, the discretized equivalent circuit model of a DC three-port element can be represented by the input voltage, output current, historical current term, and node equivalent conductance.

[0100] From equation (3), the equivalent conductance values ​​can be derived as follows:

[0101] (4)

[0102] Therefore, a basic discretized model of a DC three-port element can be established. Its main differences from AC elements are: (1) It has the asymmetric characteristics of DC elements, that is, the three terminals are connected by three historical current sources respectively; (2) It is consistent with DC two-port elements, with node self-conductance and mutual conductance. Its main differences from DC two-port elements are: (1) It is connected to an AC bus more than two-port elements, that is, there are three input voltages and output currents, and all three have an interaction relationship; (2) The conductance matrix is ​​a 3×3 matrix, which includes three self-conductances and six mutual conductances.

[0103] The above three-port DC components are based on three-port LCC-HVDC components, and the method can be extended to other three-port components, showing strong universality.

[0104] Step 3: Combine the discretized equivalent circuit of the DC three-port element obtained in Step 2 with the equivalent circuits of the other components in the system to construct a discrete circuit network of the entire system containing the DC three-port element and a branch-node correlation matrix containing the DC three-port element.

[0105] Since power systems contain components with different characteristics, determining how to combine these components is crucial for generating the discrete state-space matrix of the entire system. In the discretization model, the input voltage of each component can be eliminated by combining different component models, that is, all components can be represented in equivalent circuit form, as shown in the schematic diagram below. Figure 3 As shown. Figure 3 The main addition is the equivalent circuit diagram of a three-port DC component, which further expands the component library of the discretized model, making it suitable for more complex power systems.

[0106] To establish a discrete state-space model of the entire system, the first step is to establish the discrete circuit network of the system. According to discretization theory, for a discrete circuit network with p nodes and q branches, we can obtain a node conductance matrix G with dimension 2p×2p and a branch-node incidence matrix L with dimension 2q×2p. t The diagonal element values ​​of the conductance matrix G are G ii Equal to the sum of the equivalent conductances of all elements connected to node i, and the off-diagonal element G ij Equal to the negative of the equivalent conductance of the element directly connected between nodes i and j; the branch-node correlation matrix is ​​in the form of... Figure 4 As shown, rows represent branches and columns represent nodes. In the branch-node association matrix, the elements corresponding to the nodes connected to a single-port element are set to the identity matrix I2; the elements corresponding to the two nodes connected to an AC two-port element are set to I2 and -I2 respectively; the elements corresponding to the two nodes connected to a DC two-port element are both set to I2; and the elements at all other positions are set to 0. The same node matrix is ​​used for three-port elements, with the elements corresponding to the three nodes connected to the three-port element set to I2, and the elements at all other positions set to 0.

[0107] After establishing the conductance matrices of each node in the system, the discrete circuit network of the entire system is described by the following node voltage equations:

[0108] (5)

[0109] In the formula, U node (t) and i inject (t) represents the column vectors of system node voltage and node injected current, respectively.

[0110] For AC networks, it is necessary to calculate the voltage of each branch and ultimately represent it as a node voltage calculation matrix. The main equations are as follows:

[0111] (6)

[0112] In the formula, A d B d and D d All of these are diagonal block matrices composed of coefficient matrices in the discrete state-space equations of each component. Their arrangement order is the set node data of each type, which means that they can be solved by the determined discrete model of each type of component.

[0113] Thus, the discrete circuit network of the entire system containing DC three-port elements and the branch-node correlation matrix containing DC three-port elements are obtained.

[0114] Step 4: Based on the branch-node correlation matrix described in Step 3, construct the discrete state matrix of the entire AC / DC hybrid system containing DC three-port components. The discrete state matrix of the entire network is used for system eigenvalue calculation.

[0115] For DC component networks, the voltage of each node can be directly obtained from the voltage input term. Therefore, unlike AC components, branch voltages do not need to be calculated. From the branch-node correlation matrix and equation (6), it can be seen that the discretized state space matrix generation method of AC networks is not applicable to DC networks, that is, the coefficient matrix B in DC networks is not applicable to DC networks. d-h1 / B d-h2 and D d-h1 / D d-h2 Cannot be directly filled into diagonal block matrix B d and D d In this process, a storage module needs to be set up to store the voltage variables of the DC network nodes, and replacement and elimination should be performed after the AC network is solved.

[0116] For a three-port DC network, since it has three interfaces to external circuits, it cannot be directly considered as a branch. However, due to the independence of DC components, the relevant node voltages can be directly obtained. That is, the state-space model of the entire system can be completed using the same steps as for two-port DC components. Therefore, it can still be considered as a branch during calculation. Let the k-th component in the system be a three-port DC component, and the nodes it connects to be numbered m, n, and f. The specific steps for generating the state-space model of the entire system are as follows:

[0117] (1) Generate the discrete state matrix of the system according to the method shown in equation (6), and obtain A based on the voltage equation and branch-node correlation matrix of the discrete circuit network of the whole system. d L t and G;

[0118] (2) Since the diagonal matrix B is not required for DC components in the calculation, it is not necessary to use it for the time being. d and D dThe element at the diagonal element corresponding to branch k is temporarily set to I2, and the other diagonal block elements are still generated according to the method in the communication system.

[0119] (3) Calculate 'B' separately. d L t =BL' and '-(L t ) T D d =LD';

[0120] (4) Use the coefficient matrix B in the discrete state-space model of DC components to represent the elements in the k-th row and m-th column of matrix BL. d-h1 Replace the elements in the k-th row and n-th column using the coefficient matrix B. d-h2 Replace the elements in the k-th row and f-th column using the coefficient matrix B. d-h3 replace;

[0121] (5) Use the coefficient matrix -D in the discrete state-space model of the DC element to represent the elements in the m-th row and k-th column of the matrix LD. d-h1 Replace the elements in the nth row and kth column using the coefficient matrix -D d-h2 Replace the elements in row f and column k using the coefficient matrix -D d-h3 replace.

[0122] After the above steps, the state matrix A of the discrete state-space model of the entire system containing DC three-port components can be obtained. D It can also be used for eigenvalue calculation to verify system stability.

[0123] Calculation and application of eigenvalues ​​for DC three-port models:

[0124] By discretizing the state-space model of specific components using the above method, we can analyze whether there are characteristic roots crossing the real axis to determine whether the operating state is stable, and at the same time, read the oscillation frequency based on its imaginary part. Taking the three-port LCC-HVDC system as an example, we will establish the characteristic equation and perform eigenvalue analysis on this model.

[0125] Establish a three-terminal power supply system in the small-signal model and modify the LCC sending-end constant current control loop K. pconr Parameters, plotting the eigenvalue root locus as follows Figure 5 As shown. It can be seen that as K... pconr As the number of features increases, a pair of characteristic roots gradually approaches the imaginary axis and eventually crosses it.

[0126] In a time-domain simulation performed in PSCAD / EMTDC, the DC current control loop parameter Kp was increased from 1.0989 to 7.0989 after 3 seconds. The system then oscillated, as shown in the following results. Figure 6 As shown. When K pconrWhen = 7.0989, the oscillation frequency is approximately 76.67 Hz, corresponding to an eigenvalue of . As can be seen, the simulation results are almost identical to the calculation results.

[0127] To further demonstrate the efficiency of discretized state-space simulation in modeling, a design is presented as follows: Figure 7 As shown, the three-port LCC-HVDC converter has SVG connected to both sides of the sending end for voltage balancing. Based on the method described in this invention, a small-signal state-space model of the entire system is established. The model has 239 orders, where orders 1-15 are SVG1 state variables; orders 2-30 are SVG2 state variables; orders 31-222 are LCC filter and AC network circuit parameters; and orders 223-239 are three-port LCC-HVDC state variables. The method described in this paper can quickly establish this system model, and it can be used for factor analysis, such as... Figure 8 As shown, the interaction between the various modules of the system can be analyzed intuitively.

[0128] It is evident that the discrete state-space equation establishment method for DC three-port components established in this invention has strong applicability in the field of small disturbance analysis. By introducing a three-port component model, the original discretization model, which only includes single-port and two-port components, is extended, further broadening the applicable scenarios of the discretization method and exhibiting good adaptability to both single-port and two-port components.

[0129] This invention also provides a device for establishing a discrete state-space model of a DC three-port component, comprising:

[0130] The model building module is used to build discrete state-space models of DC three-port components.

[0131] The equivalent circuit construction module is used to construct the discretized equivalent circuit of the DC three-port element based on the discrete state-space model of the DC three-port element.

[0132] The correlation matrix construction module is used to combine the obtained discretized equivalent circuit of the DC three-port element with the equivalent circuit of the other elements in the system to construct the discrete circuit network of the whole system containing the DC three-port element and the branch-node correlation matrix containing the DC three-port element.

[0133] The discrete state matrix construction module is used to construct the entire network discrete state matrix of the AC / DC hybrid system containing DC three-port components based on the branch-node correlation matrix. The entire network discrete state matrix is ​​used for system eigenvalue calculation.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for establishing a discrete state-space model suitable for DC three-port components, characterized in that, Includes the following steps: Step 1: Construct a discrete state-space model of a DC three-port component; Step 2: Based on the discrete state-space model of the DC three-port element described in Step 1, construct the discretized equivalent circuit of the DC three-port element; Step 3: Combine the discretized equivalent circuit of the DC three-port element obtained in Step 2 with the equivalent circuits of the other components in the system to construct a branch-node correlation matrix containing the DC three-port element. Step 4: Based on the branch-node correlation matrix described in Step 3, construct the discrete state matrix of the entire AC / DC hybrid system containing DC three-port components. The discrete state matrix of the entire network is used for system eigenvalue calculation.

2. The method for establishing a discrete state-space model for a DC three-port component according to claim 1, characterized in that, Step one includes: The DC three-port model is transformed from the continuous domain to the discrete domain, and the specific process is shown in equations (1) to (3): Equation (1) is the continuous domain state-space model of a DC three-port element: （1）； In the formula, X h U is the state vector of the continuous domain state-space equation for a three-port LCC. 1xy U 2xy and U 3xy These represent the input voltages of the three AC buses under the unified coordinate system of the entire network, i 1xy i 2xy and i 3xy The output currents of the three AC buses in the unified coordinate system of the entire network are respectively determined by the coefficient matrix, which is determined by the linearized state-space equation of the specific DC three-port element. Discretize the differential equation of equation (1) and define the historical current term h of the DC element. h The discretized equations are obtained, which yield the discrete state-space model of the DC three-port element, as follows: （2）； The coefficient matrix in equation (2) is calculated from the coefficient matrix in equation (1); （3）； In the formula, A d-h B d-h1 B d-h2 B d-h3 C d-h1 C d-h2 C d-h3 C d-h4 C d-h5 C d-h6 C d-h7 C d-h8 C d-h9 D d-h1 D d-h2 D d-h3 Both are coefficient matrices in the discrete domain, calculated from the coefficient matrices in equations (1) and (2).

3. The method for establishing a discrete state-space model for a DC three-port component according to claim 2, characterized in that, Step two specifically includes: The discretized equations established in step one are used to establish an equivalent circuit model of a DC three-port element, represented by input voltage, output current, historical current terms, and node equivalent conductance. In equation (3), the three output currents are expressed from the input voltage, and the formula for the 3×3 order conductance matrix is: （4）； In the formula, g 11 g 22 g 33 These represent the self-conductance of each node; g 12 g 13 g 21 g 23 g 31 g 32 These represent the mutual conductance of each node; Based on equation (4), the discretized equivalent circuit of the DC three-port element is established, thereby obtaining the basic discretized model of the DC three-port element.

4. The method for establishing a discrete state-space model for a DC three-port component according to claim 1, characterized in that, Step three specifically includes: By combining the DC three-port element with the existing one-port and two-port elements, that is, setting the elements at the corresponding positions of the three nodes connected to the three-port element in the system branch-node correlation matrix to I2, and setting the elements at the remaining positions to 0, the voltage equation of the entire system discrete circuit network is obtained as follows: （5）； In the formula, U node and i inject These are column vectors representing the system node voltages and node injected currents, respectively. Formula (5) is the voltage equation that includes both AC and DC networks. Corresponding to the DC network equation (2) in step three, the main equation for the AC network is: （6）； In the formula, h is the state vector of the entire system, and U branch For the branch voltages of single-port and AC two-port components, A d B d and D d It is a diagonal block matrix formed by the coefficient matrices in the discrete state-space equations of each component; Thus, the discrete circuit network of the entire system containing DC three-port elements and the branch-node correlation matrix containing DC three-port elements are obtained.

5. The method for establishing a discrete state-space model for a DC three-port component according to claim 4, characterized in that, Step four specifically includes: (1) Consistent with the AC system, the discrete state matrix of the system is generated according to the formula shown in equation (6). A is obtained from the voltage equation and branch-node correlation matrix of the discrete circuit network of the whole system. d L t and G; (2) Since the diagonal matrix B is not required for DC components in the calculation, it is not necessary to use it for the time being. d and D d The element at the diagonal element corresponding to branch k is temporarily set to I2, and the other diagonal block elements are still generated according to the method in the communication system. (3) Calculate 'B' separately. d L t =BL' and '-(L t ) T D d =LD'; (4) Use the coefficient matrix B in the discrete state-space model of DC components to represent the elements in the k-th row and m-th column of matrix BL. d-h1 Replace the elements in the k-th row and n-th column using the coefficient matrix B. d-h2 Replace the elements in the k-th row and f-th column using the coefficient matrix B. d-h3 replace; (5) Use the coefficient matrix -D in the discrete state-space model of the DC element to represent the elements in the m-th row and k-th column of the matrix LD. d-h1 Replace the elements in the nth row and kth column using the coefficient matrix -D d-h2 Replace the elements in row f and column k using the coefficient matrix -D d-h3 Replacement; after the above steps, the state matrix A of the discrete state-space model of the entire system containing DC three-port components is obtained. D The expression is shown in equation (7), and it is used for eigenvalue calculation to verify system stability: （7）。 6. A device for establishing a discrete state-space model suitable for DC three-port components, characterized in that, include: The model building module is used to build discrete state-space models of DC three-port components. The equivalent circuit construction module is used to construct the discretized equivalent circuit of the DC three-port element based on the discrete state-space model of the DC three-port element. The correlation matrix construction module is used to combine the obtained discretized equivalent circuit of the DC three-port element with the equivalent circuit of the other elements in the system to construct the discrete circuit network of the whole system containing the DC three-port element and the branch-node correlation matrix containing the DC three-port element. The discrete state matrix construction module is used to construct the entire network discrete state matrix of the AC / DC hybrid system containing DC three-port components based on the branch-node correlation matrix. The entire network discrete state matrix is ​​used for system eigenvalue calculation.

7. The discrete state-space model establishment device for DC three-port components according to claim 6, characterized in that, The model building module is specifically used for: The DC three-port model is transformed from the continuous domain to the discrete domain, and the specific process is shown in equations (1) to (3): Equation (1) is the continuous domain state-space model of a DC three-port element: （1）； In the formula, X h U is the state vector of the continuous domain state-space equation for a three-port LCC. 1xy U 2xy and U 3xy These represent the input voltages of the three AC buses under the unified coordinate system of the entire network, i 1xy i 2xy and i 3xy The output currents of the three AC buses in the unified coordinate system of the entire network are respectively determined by the coefficient matrix, which is determined by the linearized state-space equation of the specific DC three-port element. Discretize the differential equation of equation (1) and define the historical current term h of the DC element. h The discretized equations are obtained, which yield the discrete state-space model of the DC three-port element, as follows: （2）； The coefficient matrix in equation (2) is calculated from the coefficient matrix in equation (1); （3）； In the formula, A d-h B d-h1 B d-h2 B d-h3 C d-h1 C d-h2 C d-h3 C d-h4 C d-h5 C d-h6 C d-h7 C d-h8 C d-h9 D d-h1 D d-h2 D d-h3 Both are coefficient matrices in the discrete domain, calculated from the coefficient matrices in equations (1) and (2).

8. The discrete state-space model establishment device for DC three-port components according to claim 7, characterized in that, The equivalent circuit construction module is specifically used for: The discretized equations are used to establish an equivalent circuit model of a DC three-port element, represented by input voltage, output current, historical current terms, and node equivalent conductance. In equation (3), the three output currents are expressed from the input voltage, resulting in the 3×3 order conductance matrix formula: （4）； In the formula, g 11 g 22 g 33 These represent the self-conductance of each node; g 12 g 13 g 21 g 23 g 31 g 32 These represent the mutual conductance of each node; Based on equation (4), the discretized equivalent circuit of the DC three-port element is established, thereby obtaining the basic discretized model of the DC three-port element.

9. The discrete state-space model establishment device for DC three-port components according to claim 6, characterized in that, The association matrix construction module is specifically used for: By combining the DC three-port element with the existing one-port and two-port elements, that is, setting the elements at the corresponding positions of the three nodes connected to the three-port element in the system branch-node correlation matrix to I2, and setting the elements at the remaining positions to 0, the voltage equation of the entire system discrete circuit network is obtained as follows: （5）； In the formula, U node and i inject These are column vectors representing the system node voltages and node injected currents, respectively. Formula (5) is the voltage equation that includes both AC and DC networks. Corresponding to the DC network equation (2) in step three, the main equation for the AC network is: （6）； In the formula, h is the state vector of the entire system, and U branch For the branch voltages of single-port and AC two-port components, A d B d and D d It is a diagonal block matrix formed by the coefficient matrices in the discrete state-space equations of each component; Thus, the discrete circuit network of the entire system containing DC three-port elements and the branch-node correlation matrix containing DC three-port elements are obtained.

10. The device for establishing a discrete state-space model of a DC three-port component according to claim 9, characterized in that, The discrete state matrix construction module is specifically used for: (1) Consistent with the AC system, the discrete state matrix of the system is generated according to the formula shown in equation (6). A is obtained from the voltage equation and branch-node correlation matrix of the discrete circuit network of the whole system. d L t and G; (2) Since the diagonal matrix B is not required for DC components in the calculation, it is not necessary to use it for the time being. d and D d The element at the diagonal element corresponding to branch k is temporarily set to I2, and the other diagonal block elements are still generated according to the method in the communication system. (3) Calculate 'B' separately. d L t =BL' and '-(L t ) T D d =LD'; (4) Use the coefficient matrix B in the discrete state-space model of DC components to represent the elements in the k-th row and m-th column of matrix BL. d-h1 Replace the elements in the k-th row and n-th column using the coefficient matrix B. d-h2 Replace the elements in the k-th row and f-th column using the coefficient matrix B. d-h3 replace; (5) Use the coefficient matrix -D in the discrete state-space model of the DC element to represent the elements in the m-th row and k-th column of the matrix LD. d-h1 Replace the elements in the nth row and kth column using the coefficient matrix -D d-h2 Replace the elements in row f and column k using the coefficient matrix -D d-h3 Replacement; after the above steps, the state matrix A of the discrete state-space model of the entire system containing DC three-port components is obtained. D The expression is shown in equation (7), and it is used for eigenvalue calculation to verify system stability: （7）。

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