A Distributed Stability Assessment Method for Multi-Converter Systems Based on XZ Diagrams

Abstract

This invention discloses a method based on x‑z A distributed stability assessment method for multi-converter systems is presented. The method involves first constructing the closed-loop characteristic equation of the system, then performing an equivalent transformation to decompose it into a diagonal block matrix composed of the equivalent admittance matrices of each converter and the extended admittance matrix of the power grid. Finally, the method verifies the performance of each converter individually. x‑z Is the diagram related to the power grid? x‑z The method of determining system stability by identifying disjoint graphs significantly simplifies the system stability analysis process, avoids the overall calculation of high-dimensional matrices, and allows the determination of system stability to be decomposed into independent verification of the external characteristics of each piece of equipment, thereby effectively solving the computational complexity problem in the analysis of large-scale heterogeneous multi-equipment systems.

Description

Technical Field

[0001] This invention belongs to the field of power system stability analysis, specifically relating to a method based on... x-z The figure shows a distributed stability assessment method for multi-converter systems. Background Technology

[0002] With the rapid development of new energy technologies such as wind power, photovoltaic power, DC transmission, and electrochemical energy storage, modern power systems exhibit a significant characteristic of coexisting high proportions of new energy sources and high proportions of power electronic equipment. Compared to traditional synchronous generators, power electronic equipment (mainly converters) lacks a physical rotor with large inertia; its dynamic characteristics are primarily determined by complex multi-timescale control systems, thus exhibiting dynamic behavior distinctly different from that of synchronous generators. Due to the different circuit topologies and control strategies of different types of power electronic equipment, significant differences exist in the dynamic characteristics of each device.

[0003] When massive amounts of heterogeneous power electronic equipment are interconnected through complex multi-port electrical networks, they form high-dimensional multi-input multi-output dynamic systems, posing a serious challenge to traditional stability assessment methods. Traditional state-space eigenvalue analysis methods require establishing a complete system state-space model and solving for eigenvalues. While this method can determine system stability, it is difficult to intuitively analyze and characterize the dynamic interactions between each piece of equipment and the grid, and their impact on system stability, since both equipment dynamics and grid dynamics are contained in a closed loop within the state matrix. Frequency-domain impedance analysis methods study system stability by establishing admittance models for each piece of equipment and the grid separately. Under single-machine system conditions, the system can be simplified to a single-input single-output transfer function, allowing for analysis using the Nyquist criterion. However, in multi-machine interconnected systems, simplification to a single-input single-output model is impossible, necessitating the use of the generalized Nyquist criterion. This method requires solving the determinant of the open-loop transfer function matrix, which is computationally complex and fails to intuitively reveal the dynamic interaction mechanisms between each piece of equipment and the grid, nor does it provide clear guidance for the rational design of equipment external characteristics.

[0004] Existing stability assessment methods suffer from the following technical problems: First, they cannot intuitively depict the dynamic interaction between multiple pieces of equipment and the power grid, and its decisive impact on system stability. Second, they struggle to establish a clear correspondence between the external characteristics of each piece of equipment and the overall stability of the system, thus failing to provide specific guidelines for equipment control design. Third, traditional analysis methods face the "curse of dimensionality" problem of high-dimensional matrix calculations when dealing with large-scale heterogeneous multi-equipment interconnected systems, lacking effective distributed analysis tools. Therefore, a new stability assessment method is needed that can intuitively depict the dynamic interaction between the "source and grid," establish a clear relationship between the external characteristics of equipment and system stability, and enable distributed analysis of large-scale systems. Summary of the Invention

[0005] To address the problems existing in the background art, the present invention provides a method based on... x-z This invention presents a distributed stability assessment method for multi-converter systems, addressing the technical challenges of existing technologies that struggle to intuitively characterize the dynamic interactions between multiple heterogeneous power electronic devices and the power grid, effectively perform distributed stability analysis on large-scale systems, and provide clear criteria for the design of external characteristics of equipment. The method utilizes complex matrices... x-z The diagram is used to analyze the dynamic interaction characteristics between the converter and the power network, that is, by verifying each converter individually. x-z Is the diagram related to the electrical network? x-z The stability of a system can be determined by whether the graphs intersect.

[0006] The technical solution adopted in this invention is: I. A method based on x-z The diagram illustrates a distributed stability assessment method for multi-converter systems: S1. Obtain grid information and equipment information of the multi-converter power system, and divide the system into grid and several converters.

[0007] S2. Based on the acquired information, establish the admittance matrix of each converter in the global dq coordinate system, and establish the admittance matrix of the power grid.

[0008] S3. Reduce the order of the power grid admittance matrix to obtain the equivalent power grid matrix that retains only the converter access nodes, and combine it with the admittance matrix composed of all converters to construct the closed-loop characteristic equation of the multi-converter system.

[0009] S4. Perform an equivalent transformation on the closed-loop characteristic equation, decomposing it into a diagonal block matrix composed of the equivalent admittance matrices of each converter and the extended admittance matrix of the power grid.

[0010] S5. For any frequency point, calculate the extended admittance matrix of the power grid. x-z The diagram shows the equivalent admittance matrix of each converter. x-z picture.

[0011] S6. For any frequency point, calculate the equivalent admittance matrix corresponding to each converter. x-z The diagram corresponds to the extended admittance matrix of the power grid. x-z The shortest distance between the graphs is used as the stability margin of the converters. It is determined whether the stability margin of all converters is greater than zero at all frequency points. If so, the multi-converter system is considered stable; otherwise, the multi-converter system is considered unstable.

[0012] The closed-loop characteristic equation of the multi-converter system in step S3 is set according to the following formula: ; in, To find the determinant; The admittance matrix of the power grid; This represents a diagonal matrix consisting of the ratio of the individual reference capacity of each converter to the global rated capacity. Indicates the Kronecker product; This represents the admittance matrix composed of all converters; The equivalent grid matrix that only retains the converter access node (after the Shure complement simplification, only the Thevenin equivalent admittance matrix of the grid for the equipment bus is retained). To achieve synchronous rotational speed; The line resistance-to-inductance ratio; s For the Laplace operator; This represents a 2-order identity matrix.

[0013] The closed-loop characteristic equation, after equivalent transformation, is set according to the following formula: in, The extended admittance matrix represents the power grid; This represents the equivalent admittance matrix corresponding to the admittance matrix composed of each converter.

[0014] The x-z The figure shows the DW shell of a complex matrix. x-z Two-dimensional projection on a plane.

[0015] Step S6 determines that the stability of the multi-converter system satisfies the following formula: ; in, i For indexing; The number of converters; j The imaginary unit; It is a frequency point, and ; Indicates the first i The stability margin of each converter; Let be the equivalent admittance matrix of the i-th converter; express The DW shell in x-z Two-dimensional projection on a plane; Represents the Nyquist operator; This represents a diagonal matrix consisting of the ratio of the individual reference capacity of each converter to the global rated capacity. Indicates the Kronecker product; The equivalent grid matrix retains only the converter access nodes; Indicates the shortest distance.

[0016] In step S6, when the multi-converter system is determined to be unstable, a specific converter with a stability margin less than or equal to zero is identified from all converters, and the control parameters of the identified specific converter are adjusted only. x-z The system can be restored to stability by adjusting the position of the converter until the stability margin of the specific converter is greater than zero at all frequency points.

[0017] 2. An electronic device, comprising: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor invokes the program data to execute the method described above.

[0018] 3. A computer-readable storage medium having program data stored thereon, wherein the program data, when executed by a processor, implements the above-described method.

[0019] The beneficial effects of this invention are: The method of this invention uses two dimensions x-z Analyzing the geometric separation characteristics of each piece of equipment (converter) and the electrical network on a planar plane significantly simplifies the system stability analysis process, avoids the overall calculation of high-dimensional matrices, and allows the judgment of system stability to be decomposed into independent verification of the external characteristics of each piece of equipment. This effectively solves the computational complexity problem in the analysis of large-scale heterogeneous multi-equipment systems. Simultaneously, the method of this invention can intuitively reveal the dynamic interaction relationship between each piece of equipment and the electrical network by examining the characteristics of each piece of equipment. x-z Is the diagram related to the electrical network? x-z Determining system stability by identifying non-intersecting graphs provides a clear analytical basis for identifying specific equipment that causes system instability, enabling system stability analysis and control to be carried out in a modular manner, and improving the practicality and engineering applicability of the analysis method. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method of the present invention.

[0021] Figure 2 This is a topology diagram of an embodiment of the present invention.

[0022] Figure 3 The curves show the stability margin of the three converters in Embodiment 3 of the present invention as a function of frequency.

[0023] Figure 4This is a magnified view of the stability margin curves of the three converters in Embodiment 3 of the present invention as a function of frequency within the range of 15-35Hz.

[0024] Figure 5 This is the simulation verification result of Embodiment 3 of the present invention. Detailed Implementation

[0025] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0026] Example 1: like Figure 1 As shown, the distributed stability assessment method for multi-converter systems in this embodiment includes the following steps: S1. Obtain grid information and equipment information of the multi-converter power system, and divide the system into grid and several converters.

[0027] S2. Based on the acquired information, establish the admittance matrix of each converter in the global dq coordinate system, and establish the admittance matrix of the power grid.

[0028] S3. Reduce the order of the power grid admittance matrix to obtain the equivalent power grid matrix that retains only the converter access nodes, and combine it with the admittance matrix composed of all converters to construct the closed-loop characteristic equation of the multi-converter system.

[0029] The closed-loop characteristic equation of the multi-converter system is set according to the following formula: ; in, To find the determinant; The admittance matrix of the power grid; This represents a diagonal matrix consisting of the ratio of the individual reference capacity of each converter to the global rated capacity. Indicates the Kronecker product; This represents the admittance matrix composed of all converters; The equivalent grid matrix that only retains the converter access node (after the Shure complement simplification, only the Thevenin equivalent admittance matrix of the grid for the equipment bus is retained). To achieve synchronous rotational speed; The line resistance-to-inductance ratio; s For the Laplace operator; This represents a 2-order identity matrix.

[0030] S4. Perform an equivalent transformation on the closed-loop characteristic equation, decomposing it into a diagonal block matrix composed of the equivalent admittance matrices of each converter and the extended admittance matrix of the power grid.

[0031] The closed-loop characteristic equation is set according to the following formula after equivalent transformation: in, The extended admittance matrix represents the power grid; This represents the equivalent admittance matrix corresponding to the admittance matrix composed of each converter.

[0032] S5. For any frequency point, calculate the extended admittance matrix of the power grid. x-z The diagram shows the equivalent admittance matrix of each converter. x-z picture.

[0033] x-z The figure shows the DW shell of a complex matrix. x-z Two-dimensional projection on a plane.

[0034] S6. For any frequency point, calculate the equivalent admittance matrix corresponding to each converter. x-z The diagram corresponds to the extended admittance matrix of the power grid. x-z The shortest distance between the graphs is used as the stability margin of the strain gauge.

[0035] Determine whether the stability margin of all converters is greater than zero at all frequency points. If so, the multi-converter system is considered stable; otherwise, the multi-converter system is considered unstable.

[0036] The following formula is used to determine the stability of a multi-converter system: ; in, i For indexing; The number of converters; j The imaginary unit; It is a frequency point, and ; Indicates the first i The stability margin of each converter; Let be the equivalent admittance matrix of the i-th converter; express The DW shell in x-z Two-dimensional projection on a plane; Represents the Nyquist operator; This represents a diagonal matrix consisting of the ratio of the individual reference capacity of each converter to the global rated capacity. Indicates the Kronecker product; The equivalent grid matrix retains only the converter access nodes; Indicates the shortest distance.

[0037] When a multi-converter system is determined to be unstable, a specific converter with a stability margin less than or equal to zero is identified from all converters, and the control parameters of the identified specific converter are adjusted only. x-z The system can be restored to stability by adjusting the position of the converter until the stability margin of the specific converter is greater than 0 at all frequency points.

[0038] This embodiment also provides an electronic device, including: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor calls the program data to execute the above-described method.

[0039] This embodiment also provides a computer-readable storage medium storing program data thereon, which, when executed by a processor, implements the method described above.

[0040] Specifically, the purpose of this invention is to analyze the relationship between each converter and the power grid. x-z By analyzing the geometric characteristics and separation relationships of the graph, a clear correspondence is established between the external characteristics of the equipment and the overall stability of the system. This enables a decentralized assessment of the stability of multi-equipment interconnected systems and provides specific geometric constraints for the optimized design of the external characteristics of the equipment.

[0041] Example 2: This embodiment first models the multi-converter power system. The system is divided into several converter modules and a grid module. Each converter is described using an admittance model in the global dq coordinate system. For the grid, a grid admittance matrix model is established, and an equivalent grid model retaining only the converter access nodes is obtained using the Kronen reduction method. Specifically, regardless of the control method and control parameters used, the first... i The admittance matrix model of a converter can always be expressed as: (1) in, and These are the port current vector and port voltage vector of the i-th converter port in the global dq coordinate system, respectively. It is the first i Admittance matrix of a converter It is the first i The ratio of the rated capacity of each converter to the total rated capacity. sAs a Laplace operator, extending equation (1) to all converters, its admittance matrix model can be expressed as: (2) in, yes n A diagonal block matrix consisting of the admittance matrices of each converter. yes n A diagonal matrix consisting of the ratios of the base capacity of each converter to the global rated capacity. Indicates the Kronecker product. .

[0042] The admittance matrix model of a power grid can be expressed as: (3) (4) in, After simplification, only the network Thevenin equivalent admittance matrix of the equipment bus is retained in the Shure complement. To synchronize rotation speed, This represents the line resistance-to-inductance ratio.

[0043] Combining equations (2) and (3), the closed-loop characteristic equation of the multi-converter system can be expressed as: (5) in, To find the determinant.

[0044] Secondly, the DW shell of complex matrices in three-dimensional space, and its... x-z Two-dimensional projection of a plane x-z picture.

[0045] 1) Define the Davis-Wielandt shell (DW) for complex matrices: For complex matrices , Represents the set of complex numbers. n Let DW be the dimension of the complex matrix, and its DW shell be denoted as DW( A ), defined as follows: in, Indicates taking the real part; and Let each represent a complex vector and its conjugate transpose; Indicates taking the imaginary part; Represents the l2 norm; For complex matrices The conjugate transpose of .

[0046] 2) Define the complex matrixx-z picture: Further define the DW shell of the complex matrix A in x-z Two-dimensional projection on a plane (say" x-z The image is: (6) Introducing based on x-z Graph-based distributed stability criterion: For the diagonal block transfer function considering open-loop stability and positive definite matrix Characteristic equation of closed-loop transfer function A sufficient condition for having no unstable poles can be expressed as: for any All conditions are met: (7) in, This represents the Nyquist operator.

[0047] Based on the distributed stability criterion shown in equation (7), a method for calculating the stability margin of frequency bands is further proposed: (8) in, This represents the shortest distance between set A and set B on a two-dimensional plane.

[0048] Applying the distributed stability criteria shown in equations (7) and (8) to a multi-converter system, we first perform an equivalent transformation on the closed-loop characteristic equation shown in equation (5), and we can obtain: (9) in, It is a diagonal block matrix composed of the equivalent admittance matrices of each converter. The equivalent admittance matrix of each converter is written as: . Let this be the extended admittance matrix of the power grid, which is a positive definite matrix. Substituting into equation (8), we can obtain the distributed stability criterion applicable to multi-converter systems: for open-loop stable systems In other words, if the system is at any frequency point... If all conditions are met as shown in equation (10), then the closed-loop system is stable.

[0049] (10) in, That is, the first... i Taiwan converter equipment in frequency place x-z Diagram and power grid x-z The shortest distance in the graph.

[0050] The stability criterion shown in equation (10) can be expressed as: In a multi-converter system, if for any frequency... Each converter x-z Images and networks x-z If all shortest distances in the graph are greater than 0, then the system is stable.

[0051] The method of this invention does not require overall calculation of the high-dimensional diagonal block matrix of the entire system, thus avoiding the computational complexity brought about by high-dimensional matrix analysis; x-z The diagram separation condition provides explicit geometric constraints for the design of equipment external characteristics, namely, the geometric separation conditions of each piece of equipment. x-z The diagram needs to be located in the electrical network. x-z On the right side of the figure, this explicit geometric separation requirement provides a concrete and visual verification standard for equipment control design and external characteristic optimization; simultaneously, through analysis of various equipment... x-z Diagrams and Electrical Networks x-z The relative positions of the components in the diagram can accurately identify specific equipment causing system instability, and allow for targeted adjustments to that equipment. x-z The instability problem can be solved by mapping the location, without requiring a unified control design for all equipment. In summary, based on... x-z The distributed stability assessment method for multi-converter systems provided by the figure offers a simple, efficient, and physically meaningful analytical approach for the stability analysis and control design of large-scale power electronic systems.

[0052] Example 3: like Figure 1 As shown, firstly, the network admittance matrix transfer function and the converter admittance matrix transfer function are obtained respectively, thus deriving the closed-loop characteristic equation of the system. Then, based on the data obtained from the power grid and various power electronic equipment at different frequency points... x-z The diagram is used to calculate the corresponding shortest distance as the stability margin. System stability is determined by whether the stability margin is greater than 0 across the entire frequency band.

[0053] This invention is built in the MATLAB / Simulink environment as follows Figure 2 The electromagnetic transient simulation model of the three-machine nine-node system of the multi-infeed converter system shown is used to verify the effectiveness of the proposed method for judging the small-signal stability of the system based on the numerical domain separation theory.

[0054] The control parameters and network parameters of each converter in this scenario are shown in Table 1 and Table 2.

[0055] Table 1 Parameters in Simulation Verification of the Example Table 2 Power Grid Parameters Simulations were performed on a 3-machine, 9-node system. All three converters were controlled by PLLs. Detailed parameters are shown in Table 1. Figure 3 The stability margin curves of each converter within the range of 0~100Hz are given. Figure 4 A magnified view of the stability margin curve within the 15-35Hz range is provided. It can be observed that converter 3 has a stability margin of 0 within the 20-30Hz range, indicating a risk of instability. Figure 5 As shown, a three-machine, nine-node electromagnetic transient simulation was built in MATLAB / Simulink. t At 0.2s, an infinite grid voltage was temporarily reduced by 0.05 pu and restored at 0.22s. It was observed that the active power output of the three converters exhibited constant-amplitude oscillations, indicating system instability. This is based on... x-z The graph-based stability margin method effectively identifies the risk of system instability.

[0056] The above embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method based on xz The distributed stability assessment method for multi-converter systems, characterized by the following features: Includes the following steps: S1. Obtain grid information and equipment information of the multi-converter power system, and divide the system into grid and several converters; S2. Based on the acquired information, establish the admittance matrix of each converter in the global dq coordinate system, and establish the admittance matrix of the power grid; S3. Reduce the order of the power grid's admittance matrix to obtain an equivalent power grid matrix that retains only the converter access nodes. Combine this with the admittance matrix of all converters to construct the closed-loop characteristic equation of the multi-converter system. S4. Perform an equivalent transformation on the closed-loop characteristic equation, decomposing it into a diagonal block matrix composed of the equivalent admittance matrices of each converter and the extended admittance matrix of the power grid. S5. For any frequency point, calculate the extended admittance matrix of the power grid. xz The diagram shows the equivalent admittance matrix of each converter. xz picture; S6. For any frequency point, calculate the equivalent admittance matrix corresponding to each converter. xz The diagram corresponds to the extended admittance matrix of the power grid. xz The shortest distance between the graphs is used as the stability margin of the strain gauge; Determine whether the stability margin of all converters is greater than zero at all frequency points. If so, the multi-converter system is considered stable; otherwise, the multi-converter system is considered unstable.

2. A method based on claim 1 xz The distributed stability assessment method for multi-converter systems, characterized by: The closed-loop characteristic equation of the multi-converter system in step S3 is set according to the following formula: ； ； ； in, To find the determinant; The admittance matrix of the power grid; This represents a diagonal matrix consisting of the ratio of the individual reference capacity of each converter to the global rated capacity. Indicates the Kronecker product; This represents the admittance matrix composed of all converters; The equivalent grid matrix retains only the converter access nodes; To achieve synchronous rotational speed; The line resistance-to-inductance ratio; s For the Laplace operator; Represents a second-order identity matrix; The closed-loop characteristic equation, after equivalent transformation, is set according to the following formula: ； ； in, The extended admittance matrix represents the power grid; This represents the equivalent admittance matrix corresponding to the admittance matrix composed of each converter.

3. A method based on claim 1 xz The distributed stability assessment method for multi-converter systems, characterized by: The xz The figure shows the DW shell of a complex matrix. xz Two-dimensional projection on a plane.

4. A method based on claim 1 xz The distributed stability assessment method for multi-converter systems, characterized by the following features: Step S6 determines that the stability of the multi-converter system satisfies the following formula: ； ； ； in, i For indexing; The number of converters; j The imaginary unit; It is a frequency point, and ; Indicates the first i The stability margin of each converter; Let be the equivalent admittance matrix of the i-th converter; express The DW shell in xz Two-dimensional projection on a plane; Represents the Nyquist operator; This represents a diagonal matrix consisting of the ratio of the individual reference capacity of each converter to the global rated capacity. Indicates the Kronecker product; The equivalent grid matrix retains only the converter access nodes; Indicates the shortest distance.

5. A method based on claim 1 xz The distributed stability assessment method for multi-converter systems, characterized by: In step S6, when the multi-converter system is determined to be unstable, a specific converter with a stability margin less than or equal to zero is identified from all converters, and the control parameters of the identified specific converter are adjusted only. xz The system can be restored to stability by adjusting the position of the converter until the stability margin of the specific converter is greater than zero at all frequency points.

6. An electronic device, characterized in that, include: A memory and a processor are coupled to each other, wherein the memory stores program data, and the processor invokes the program data to perform the method as described in any one of claims 1-5.

7. A computer-readable storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, the method as described in any one of claims 1-5 is implemented.

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