Microgrid dynamic model reduction method based on moment matching

Abstract

The application discloses a micro-grid dynamic model simplification method based on moment matching, which comprises the following steps: firstly, constructing a high-dimensional accurate dynamic model of the micro-grid, and establishing a linear mapping relationship between a group of intermediate variables and the output of the high-dimensional accurate model, and generating a signal generator according to the linear mapping relationship; secondly, expanding the signal generator, and establishing an extended linear mapping relationship between the expanded intermediate variables and the state variables of the high-dimensional accurate dynamic model, and estimating the moment of the accurate model of the micro-grid according to the extended linear mapping relationship; thirdly, establishing a low-dimensional simplified model, and making the low-dimensional simplified model satisfy the dynamic characteristics of the signal generator and have the same moment as the accurate model of the micro-grid, so as to determine the parameters of the simplified model and realize the simplification of the dynamic model of the micro-grid based on moment matching. The method can retain the dynamic characteristics of the micro-grid as much as possible, simplify the model to the maximum extent, ensure the accuracy of stability analysis and reduce the analysis difficulty, and the analysis result is used for guiding the structure and parameter setting of the micro-grid in actual engineering.

Description

Technical Field

[0001] This invention relates to a method for simplifying dynamic models of microgrids based on moment matching, and more specifically, to a model order reduction technique for microgrid stability analysis. Background Technology

[0002] Microgrid dynamic model simplification involves simplifying the complex dynamic model of a microgrid to facilitate stability analysis. The analysis results are then used to guide the microgrid's structure and control settings, improving the system's resistance to disturbances. Existing simplification methods for microgrid dynamic models mainly include singular perturbation methods, equivalent model methods, and dynamic vector methods. However, due to the large number of power electronic devices in a microgrid, its model is extremely complex, and existing simplification methods struggle to achieve a balance between simplification effectiveness and accurate preservation of characteristics.

[0003] Regarding the singular perturbation method, Meng Xiaoxiao et al., in their article "Meng Xiaoxiao, Zhou Niancheng, Wang Qianggang. Multi-timescale reduction-order analysis and stability consistency proof of inverter-based distributed power generation model [M] / / Proceedings of the Chinese Society for Electrical Engineering: Vol. 38. 2018:3813-3825.", used singular perturbation to treat 10 state variables related to electromagnetic transient characteristics in a 13th-order microgrid model as fast variables (fast variables are variables whose steady-state speed is much higher than the steady-state speed of the system), and set the rate of change of the fast variables to 0, thus simplifying the model to order 3. In their article "CADUFF I, MARKOVIC U, ROBERTS C, et al. Reduced-order Modeling of Inverter-based Generation using Hybrid SingularPerturbation [J / OL]. Electric Power Systems Research, 2021, 190: In 106773, the singular perturbation method was further improved by dividing the state variables into slow, fast, and rapid variables, and setting the rate of change and acceleration of the latter two to 0, which further improved the simplification capability. The singular perturbation method has good simplification performance, but it is based on the "quasi-steady state" assumption. The simplified model only describes the characteristics of the system when it is about to stabilize, which is difficult to meet the needs of stability analysis for a universal simplified model.

[0004] Regarding the equivalent model method, the article "RASHIDIRAD N, HAMZEH M, SHESHYEKANI K, et al. ASimplified Equivalent Model for the Analysis of Low-frequency Stability of Multi-bus DC Microgrids[J / OL]. IEEE Transactions on Smart Grid, 2018, 9(6):6170-6182." performs series and parallel equivalents on the device impedance to obtain an equivalent simplified model of the microgrid; the article "SHUAIZ, PENG Y, LIU X, et al. Dynamic Equivalent Modeling for Multi-microgrid basedon Structure Preservation Method[J / OL]. IEEE Transactions on Smart Grid, 2019, 10(4): 3929-3942." simplifies the model of unimportant network parts through the structure preservation method; Wu Zaijun et al. in the article "HU W, WU Z, LV X, et al. Robust Secondary Frequency Control for VirtualSynchronous Machine-based Microgrid Cluster" The paper "Using Equivalent Modeling [J / OL]. IEEE Transactions on Smart Grid, 2021, 12(4): 2879-2889" simplifies the model by equating the microgrid controlled by the virtual synchronous machine to a synchronous generator and integrating the error generated by the equivalence as an uncertain parameter. The equivalent model method has a smaller computational load and is compatible with various types of systems, but its accuracy is not high. The equivalence process suffers from the loss of dynamic characteristics, which may lead to inaccurate stability analysis conclusions.

[0005] Regarding the dynamic vector method, the article "LEVRON Y, BELIKOV J. Modeling Power Networks using Dynamic Phasors in the dq0 Reference Frame [J / OL]. Electric PowerSystems Research, 2017, 144: 233-242." uses Fourier decomposition of each signal in the state-space model to separate the characteristics at different frequencies, thereby establishing a dynamic vector model, and then further simplifies the model through Taylor series. In the article "WANG H, JIANG K, SHAHIDEHPOUR M, et al. Reduced-order State Space Model for Dynamic Phasors in Active Distribution Networks [J / OL]. IEEE Transactions on Smart Grid, 2020, 11(3): 1928-1941.", He Benteng et al. use the structure retention method to simplify the dynamic vector model, retaining a certain degree of accuracy. The advantage of the dynamic vector method is that it requires less computation. However, Fourier decomposition decouples the characteristics of different frequency bands, and the system characteristics determined by coupling will be ignored in the stability analysis, resulting in less convincing conclusions. Summary of the Invention

[0006] To overcome the shortcomings of the existing technology, this invention provides a method for simplifying the dynamic model of a microgrid based on moment matching. This method preserves the dynamic characteristics of the microgrid as much as possible while simplifying the model to the greatest extent, ensuring the accuracy of stability analysis and reducing the difficulty of analysis. The analysis results can then be used to guide the structure and parameter settings of microgrids in practical engineering.

[0007] To achieve its objectives, the present invention employs the following technical solution: This invention relates to a method for simplifying the dynamic model of a microgrid based on moment matching. The microgrid includes a power source, converter, filter, controller, and load. The method for simplifying the dynamic model of the microgrid is as follows: A high-dimensional accurate dynamic model of a microgrid is constructed, and a set of intermediate variables is set. A linear mapping relationship is established between the intermediate variables and the output of the high-dimensional accurate model. A signal generator is generated based on the linear mapping relationship. The signal generator is extended, and an extended linear mapping relationship is established between the extended intermediate variables and the state variables of the high-dimensional accurate dynamic model. The moments of the accurate model of the microgrid are estimated based on the extended linear mapping relationship. A low-dimensional simplified model is established to satisfy the dynamic characteristics of the signal generator, and the moments of the low-dimensional simplified model are set to be the same as the moments of the accurate microgrid model. The parameters of the simplified model are thus determined, thereby realizing the simplification of the microgrid dynamic model based on moment matching.

[0008] The simplified method for microgrid dynamic models based on moment matching in this invention is carried out according to the following steps: Step 1: Establish an accurate dynamic model of the microgrid as shown in the following formula. and : ; In equations (1.1) and (1.2): express n A column vector of dimension, which is: ; These are the state variables in the precise dynamic model of a microgrid. T Indicates transpose; express n A column vector of dimension, which is: , One-to-one correspondence The first derivative; express i A column vector of dimension, which is: , These are the input variables of the microgrid; express j A column vector of dimension, which is: , It is the output variable of the microgrid; Indicates will and Mapped to The set of functional relations, by n Composed of several functions, And: ; and They represent The linear and nonlinear parts; Indicates will Mapped to The set of functional relations, Depend on j Functions Composition, namely: ; Step 2: Set up the signal generator represented by equation (2), and use the signal generator to provide the signal generated by equation (2). r Dimensional intermediate variables The intermediate variable vector , Using linear transformation intermediate variable vector Mapped to The "." symbol represents the dot product operation of matrices. (2); In formula (2): S yes A 3D matrix is ​​used to store the intermediate variable vectors. linearly mapped to , ; One-to-one correspondence The first derivative, r < n ; L for i OK r A matrix of columns, used to... linearly mapped to ; Step 3: Transfer the intermediate variable vector Expand to vector and vector Approximately mapped to : Add to the signal generator characterized by equation (2) m - r An intermediate variable, Expand to ,in, Thus, the extended signal generator characterized by equations (3.1) and (3.2) is obtained: (3.1); (3.2); In equations (3.1) and (3.2): , Represents a diagonal matrix. for 3D matrix; for i OK m A matrix of columns, linearly mapped to ; Based on the formula (2) The relationship that has increased m - r The intermediate variable does not affect and The relationship between them; Through in Add one to the right side i OK m-r The zero matrix of columns What is obtained, that is ; And there are: ; Will Approximately linear mapping as Establish the relationship as described in equation (4): (4); In equation (4): It is a linear mapping obtained by solving equation (5). Characterized as n OK m A matrix of columns (5); In equation (5): symbol Represents the dot product of vectors; and They are respectively and The matrix of dimension is obtained by equations (6.1) and (6.2) respectively: (6.1); (6.2); In equations (6.1) and (6.2), with Solving under the constraints of zero state and zero input in a microgrid and ; It is In Take as , Take as ; Estimate the moment of the microgrid; because Will Approximately linear mapping as Therefore, In Take as , obtained As an estimate of the moment of the microgrid system; Step 4: Establish a simplified model of the microgrid; Step 4.1: Establish a simplified model of the microgrid system represented by equations (7.1) and (7.2): (7.1); Ψ (7.2); In equations (7.1) and (7.2): express r A column vector of dimension, which is: , These are the state variables in the simplified model of the microgrid; express r A column vector of dimension, which is: ; express j A column vector of dimension, which is: , These are the output variables of the simplified microgrid model; Indicates will and Mapped to The set of functional relations, Depend on r It consists of several functions, namely: And: = , = , Indicates will Mapped to The set of functional relations, by j It consists of several functions, namely: , Each function corresponds one-to-one with the function represented by equation (7.2); Step 4.2: Define the set of nonlinear functions , Depend on r Composed of several functions, Mapped to That is: , Represent each mapping function; make Satisfying equation (2) The relationship, and the relationship in equation (2) Replace with Equation (8) is obtained: (8); As shown in equation (8) r Solving the system of differential equations yields... ; Then simplify the model Calculated using equation (9): (9); Step 4.3: Match the moments by calculating equation (10) to complete the solution of equation (7.1) in the simplified model: (10); The moment is the output, and matching the output vector is called moment matching.

[0009] The simplified method of the microgrid dynamic model based on moment matching in this invention is as follows: In step 4.3, equation (4) is used in equation (1.2) to... Replace with Let the output vector Equals the simplified model's output vector and among them Replace with , thus obtaining equation (10).

[0010] Compared with existing technologies, the beneficial effects of this invention are reflected in: 1. The method of this invention relies on the merging of intermediate variables and the approximate expression of the system dynamic characteristics represented by multiple state variables, which effectively reduces the complexity of the microgrid dynamic model and the difficulty of stability analysis; 2. The merging of dynamic characteristics in the method of this invention is applicable to systems under any state, and there is no problem that traditional methods can only accurately describe system characteristics under specific states. Considering that stability analysis covers multiple complex processes of a stable system becoming unstable due to disturbances and then gradually stabilizing again, the method provided by this invention has higher accuracy than traditional model simplification methods and can provide more reliable stability analysis conclusions. Detailed Implementation

[0011] In this embodiment, a microgrid refers to a small network that includes power sources, converters, filters, controllers, and loads. The simplified microgrid dynamic model based on moment matching in this embodiment is performed according to the following steps: Step 1: Establish an accurate dynamic model of the microgrid as shown in the equation. and ; In equations (1.1) and (1.2): express n A column vector of dimension, which is: ; These are the state variables in the precise dynamic model of a microgrid. T Indicates transpose; express n A column vector of dimension, which is: , One-to-one correspondence The first derivative; express i A column vector of dimension, which is: , These are the input variables of the microgrid; express j A column vector of dimension, which is: , It is the output variable of the microgrid; Indicates will and Mapped to The set of functional relations, by n Composed of several functions, And: ; and They represent The linear part and the nonlinear part are defined as follows: the linear part refers to the part of the set of functional relationships that conforms to the superposition theorem, and the nonlinear part is the remaining part of the original functional relationship after removing the linear part.

[0012] Indicates will Mapped to The set of functional relations, Depend on j Functions Composition, namely: ; Step 2: Setting up the signal generator represented by equation (2) is to establish a set of intermediate variables as a medium. First, a linear mapping relationship is established with the output of the microgrid. Subsequently, another linear mapping relationship is established with the system's state variables through extension. The establishment of the two sets of linear relationships will retain the relationship between the system's output and state variables during the model simplification process, that is, the dynamic characteristic information of the system. The signal generator provides the signal generated by the microgrid. r Dimensional intermediate variables The intermediate variable vector , Using linear transformation intermediate variable vector Mapped to The "." symbol represents the dot product operation of matrices. (2); In formula (2): S yes A 3D matrix is ​​used to store the intermediate variable vectors. linearly mapped to The purpose of establishing this matrix is ​​to give the signal generator linear dynamic characteristics, which facilitates the simplification of subsequent models, where: ; One-to-one correspondence The first derivative, r < n ; L for i OK r A matrix of columns, used to... linearly mapped to ; Step 3: Transfer the intermediate variable vector Expand to vector and vector Approximately mapped to , expansion Because The number of variables is relatively small, and subsequent studies... Solving for the linear mapping parameters is difficult, but appropriate extensions can reduce this difficulty. Add to the signal generator characterized by equation (2) m - r An intermediate variable, Expand to ,in, Thus, the extended signal generator characterized by equations (3.1) and (3.2) is obtained: (3.1); (3.2); In equations (3.1) and (3.2): , Represents a diagonal matrix. for 3D matrix; for i OK m A matrix of columns, linearly mapped to ; Based on the formula (2) The relationship that has increased m - r The intermediate variable does not affect and The relationship between them; Through in Add one to the right side i OK m-r The zero matrix of columns What is obtained, that is ; And there are: ; Will Approximately linear mapping as Establish the relationship as shown in equation (4): (4); In equation (4): It is a linear mapping obtained by solving equation (5). Characterized as n OK m A matrix of columns, and (5); In equation (5): symbol Represents the dot product of vectors; and They are respectively and The matrix of dimension is obtained by equations (6.1) and (6.2) respectively: (6.1) (6.2) In equations (6.1) and (6.2), with Solving under the constraints of zero state and zero input in a microgrid and ; It is In Take as , Take as ; Estimate the moment of the microgrid; because Will Approximately linear mapping as Therefore, In Take as , obtained As an estimate of the moment of the microgrid system; Step 4: Establish a simplified model of the microgrid. The method for determining the parameters of the simplified model is to adapt the model to the dynamic characteristics of the signal generator and to ensure that the simplified model and the accurate model have the same output. Here, ensuring that the two models have the same output is called moment matching. Step 4.1: Establish a simplified model of the microgrid system represented by equations (7.1) and (7.2): (7.1); Ψ (7.2); In equations (7.1) and (7.2): express r A column vector of dimension, which is: , These are the state variables in the simplified model of the microgrid; express r A column vector of dimension, which is: ; express j A column vector of dimension, which is: , These are the output variables of the simplified microgrid model; Indicates will and Mapped to The set of functional relations, Depend on r It consists of several functions, namely: And: = , = , Indicates will Mapped to The set of functional relations, by j It consists of several functions, namely: , Each function corresponds one-to-one with the function represented by equation (7.2); Step 4.2: Define the set of nonlinear functions , Depend on r Composed of several functions, Mapped to That is: , Represent each mapping function; make Satisfying equation (2) The relationship, and the relationship in equation (2) Replace with Equation (8) is obtained: (8); As shown in equation (8) r Solving the system of differential equations yields... ; Then simplify the model Calculated using equation (9): (9); Step 4.3: Achieve moment matching through calculation formula (10), and complete the solution of formula (7.1) in the simplified model: In equation (1.2), use equation (4) to... Replace with Let the output vector Equals the simplified model's output vector and among them Replace with Equation (10) is obtained: (10); The moment is the output, and the matching of the output vector is moment matching. By solving equation (10), the expression of equation (7.2) in the simplified model is obtained, and the solution of the simplified model is completed.

[0013] The method of this invention has higher accuracy than traditional model simplification methods and can provide more reliable stability analysis conclusions.

Claims

1. A method for simplifying the dynamic model of a microgrid based on moment matching, wherein the microgrid includes a power source, a converter, a filter, a controller, and loads; characterized in that: The method for simplifying the microgrid dynamic model is as follows: A high-dimensional accurate dynamic model of the microgrid is constructed, and a set of intermediate variables is set. A linear mapping relationship is established between the intermediate variables and the output of the high-dimensional accurate model. A signal generator is generated based on the linear mapping relationship. The signal generator is extended, and an extended linear mapping relationship is established between the extended intermediate variables and the state variables of the high-dimensional accurate dynamic model. The moments of the accurate microgrid model are estimated based on the extended linear mapping relationship. A low-dimensional simplified model is established, such that the low-dimensional simplified model satisfies the dynamic characteristics of the signal generator. The moments of the low-dimensional simplified model are set to be the same as the moments of the accurate microgrid model, thereby determining the parameters of the simplified model and realizing the simplification of the microgrid dynamic model based on moment matching. The method for simplifying the microgrid dynamic model based on moment matching is characterized by the following steps: Step 1: Establish an accurate dynamic model of the microgrid as shown in equations (1.1) and (1.2): ； In equations (1.1) and (1.2): express n A column vector of dimension, which is: ; These are the state variables in the precise dynamic model of a microgrid. T Indicates transpose; express n A column vector of dimension, which is: , One-to-one correspondence The first derivative; express i A column vector of dimension, which is: , These are the input variables of the microgrid; express j A column vector of dimension, which is: , It is the output variable of the microgrid; Indicates will and Mapped to The set of functional relations, by n Composed of several functions, And: ； and They represent The linear and nonlinear parts; Indicates will Mapped to The set of functional relations, Depend on j Functions Composition, namely: ; Step 2: Set up the signal generator represented by equation (2), and use the signal generator to provide the signal generated by equation (2). r Dimensional intermediate variables The intermediate variable vector , Using linear transformation intermediate variable vector Mapped to The comma "." indicates the dot product operation of matrices. （2）； In formula (2): S yes A 3D matrix is ​​used to store the intermediate variable vectors. linearly mapped to , ; One-to-one correspondence The first derivative, r < n ; L for i OK r A matrix of columns, used to... linearly mapped to ; Step 3: Transfer the intermediate variable vector Expand to vector and vector Approximately mapped to : Add to the signal generator characterized by equation (2) m - r An intermediate variable, Expand to ,in, Thus, the extended signal generator characterized by equations (3.1) and (3.2) is obtained: （3.1）； （3.2）； In equations (3.1) and (3.2): , Represents a diagonal matrix. for 3D matrix; for i OK m A matrix of columns, linearly mapped to ; Based on the formula (2) The relationship that has increased m - r The intermediate variable does not affect and The relationship between them; Through in Add one to the right side i OK m-r The zero matrix of columns What is obtained, that is ; And there are: ; Will Approximately linear mapping as Establish the relationship as described in equation (4): （4）； In equation (4): It is a linear mapping obtained by solving equation (5). Characterized as n OK m A matrix of columns （5）； In formula (5): symbol Represents the dot product of vectors; and They are respectively and The matrix of dimension is obtained by equations (6.1) and (6.2) respectively: （6.1）； （6.2）； In equations (6.1) and (6.2), with Solving under the constraints of zero state and zero input in a microgrid and ; It is In Take as , Take as ; Estimate the moment of the microgrid; because Will Approximately linear mapping as Therefore, In Take as , obtained As an estimate of the moment of the microgrid system; Step 4: Establish a simplified model of the microgrid; Step 4.1: Establish a simplified model of the microgrid system represented by equations (7.1) and (7.2): （7.1）； P (7.2); In equations (7.1) and (7.2): express r A column vector of dimension, which is: , These are the state variables in the simplified model of the microgrid; express r A column vector of dimension, which is: ; express j A column vector of dimension, which is: ; These are the output variables of the simplified microgrid model; Indicates will and Mapped to The set of functional relations, Depend on r It consists of several functions, namely: And: = 、 = 、 Indicates will Mapped to The set of functional relations, by j It consists of several functions, namely: , Each of these corresponded to a function represented by equation (7.2); Step 4.2: Define the set of nonlinear functions , Depend on r Composed of several functions, Mapped to That is: ； Represent each mapping function; make Satisfying equation (2) The relationship, and the relationship in equation (2) Replace with Equation (8) is obtained: （8）； As shown in equation (8) r Solving the system of differential equations yields... ; Then simplify the model Calculated using equation (9): （9）； Step 4.3: Match the moments by calculating equation (10) to complete the solution of equation (7.1) in the simplified model: （10）； The moment is the output, and matching the output vector is called moment matching.

2. The method for simplifying the dynamic model of a microgrid based on moment matching according to claim 1, characterized in that: In step 4.3, equation (4) is used in equation (1.2) to... Replace with Let the output vector Equals the simplified model's output vector and among them Replace with , thus obtaining equation (10).

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