A method for stability evaluation of decentralized multi-inverter system based on hybrid gain and phase theorem

Abstract

The application discloses a kind of based on hybrid gain and phase theorem's dispersed multi-converter system stability evaluation method.Method includes first obtaining converter admittance matrix and grid admittance matrix, constructs the closed-loop characteristic equation of system, then carries out equivalent transformation and is decomposed into diagonal block matrix by the equivalent admittance matrix of each converter and the extended admittance matrix of grid;The gain and phase of the equivalent admittance matrix of each converter in diagonal block matrix are calculated, and the gain and phase of the extended admittance matrix of grid;In the preset frequency range, whether to meet the preset dispersed stability criterion is judged in frequency point, to evaluate the closed stability of multi-converter system at current frequency point.The method of the application can effectively evaluate large-scale, dynamic complex multi-converter power system, especially in the case of grid dynamic complexity, converter type diversification, still can provide accurate stability determination and design guidance.

Description

Technical Field

[0001] This invention belongs to the field of power system stability assessment, and specifically relates to a method for stability assessment of distributed multi-converter systems based on hybrid gain and phase theorem. Background Technology

[0002] With the widespread application of power electronic converters in modern power systems, especially in renewable energy, electric vehicles, energy storage systems, and high-voltage direct current transmission, the dynamic characteristics of power systems have undergone fundamental changes. As a key technology connecting the power grid to these new energy systems, the dynamic behavior of converters differs significantly from that of traditional synchronous generators. Unlike the relatively simple synchronous generator model in traditional power systems, converters exhibit more complex behavior within the power grid, and their control methods, communication protocols, and interactions with the grid all profoundly impact system stability. As a large number of converters are connected to the grid, traditional power system stability analysis and assessment methods are gradually revealing their limitations in addressing these complex dynamic behaviors.

[0003] Traditional stability analysis and evaluation methods, such as state-space analysis and impedance analysis, typically rely on global modeling, requiring detailed modeling and solving of the entire system. However, in multi-converter systems, especially when the system size increases and converter types become more diverse, traditional methods often suffer from excessive computational complexity and poor scalability. State-space analysis requires solving the state equations of the entire system and calculating its eigenvalues, which becomes extremely computationally intensive in multi-converter systems due to the dramatic increase in system dimensionality. On the other hand, while impedance analysis can provide some frequency response information, its accuracy and applicability are significantly reduced when dealing with complex large-scale systems, especially when the interaction between the power grid and converters is highly complex. Furthermore, these traditional methods usually assume that the system parameters are known, but in practical applications, the power grid topology and converter control parameters often exhibit uncertainties and dynamic changes, making it difficult for traditional methods to effectively address these uncertainties.

[0004] Therefore, although traditional state-space analysis and impedance analysis methods provide theoretical support for the stability of power systems to a certain extent, they face many problems such as large computational load, poor scalability, and excessive conservatism in modern complex multi-converter power systems. There is an urgent need for a new and more efficient stability analysis and evaluation method to adapt to the increasingly complex dynamic environment of current power systems. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention provides a stability evaluation method for distributed multi-converter systems based on hybrid gain and phase theorem, which solves the technical problems of computational complexity and scalability of traditional methods in multi-converter power systems.

[0006] The criterion proposed in this invention analyzes the dynamic behavior of each converter separately, combined with the network dynamics of the power grid, and employs a gain and phase analysis framework to achieve decentralized stability determination. Specifically, in a heterogeneous power system, the system is stable if the gain of each converter is always less than or equal to the gain of the power grid, or if the phase domain of each converter is contained within the phase domain of the power grid. This invention avoids detailed modeling of the global system state, instead achieving decentralized stability analysis of large-scale multi-converter power systems through local gain and phase analysis.

[0007] The technical solution adopted in this invention is: I. A stability evaluation method for distributed multi-converter systems based on hybrid gain and phase theorem: S1. Obtain grid information and equipment information of the multi-converter power system, and divide the system into grid and several converters.

[0008] 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.

[0009] 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.

[0010] 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.

[0011] S5. Calculate the gain and phase of the equivalent admittance matrix of each converter in the diagonal block matrix, as well as the gain and phase of the extended admittance matrix of the power grid.

[0012] S6. Within the preset frequency range, the multi-converter system is judged at each frequency point to determine whether it meets the preset distributed stability criterion: if for any frequency point, the multi-converter system satisfies at least one of the gain condition and the phase condition, then the closed-loop stability of the multi-converter system is evaluated and determined.

[0013] 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; 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.

[0014] The specific decentralized stability criterion in step S6 is as follows: If each converter satisfies at least one of the gain and phase conditions at a certain frequency point, then the multi-converter system is closed-loop stable at the corresponding frequency point; if the multi-converter system is closed-loop stable at all frequency points within a preset frequency range, then the closed-loop stability of the multi-converter system is evaluated and determined.

[0015] The specific conditions for a converter to satisfy the gain condition are as follows: No. i The admittance matrix of a converter and the equivalent admittance matrix of its transfer function. At frequency point The following conditions must be met: in, This represents the upper limit of singular values; This represents the lower bound of singular values; j The imaginary unit; This is a diagonal matrix composed of the ratios of the individual reference capacity of each converter to the global rated capacity; The equivalent grid matrix retains only the converter access nodes; The extended admittance matrix represents the power grid; Indicates the Kronecker product; This represents a 2-order identity matrix.

[0016] The converter satisfies the phase condition as follows: No. i Equivalent admittance matrix of a converter It is a sector matrix, and at the frequency point The following conditions must be met: in, and These represent the maximum and minimum phases, respectively. and These represent the indexes respectively. i Iterate through all cases and take the maximum and minimum values ​​of the expressions within the parentheses; j It is the imaginary unit.

[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 method described above.

[0019] The beneficial effects of this invention are: By introducing an improved decentralized stability criterion, this invention effectively addresses the computational complexity and scalability issues of traditional stability analysis methods in large-scale multi-converter power systems, making system stability analysis more efficient and flexible. Through an analysis framework based on the hybrid gain / phase theorem, this invention enables rapid assessment of the small-disturbance stability of multi-converter systems without the need for global modeling. Unlike traditional methods, this invention does not require constructing high-dimensional state-space models or complex impedance matrices; instead, it determines system stability through comparisons of local gains and phases, thereby significantly reducing computational load and model complexity.

[0020] Furthermore, this invention provides more accurate stability analysis results and can quantitatively assess the stability margin of the system. By combining gain and phase conditions, this invention not only improves the accuracy of stability analysis but also adapts to the heterogeneous control strategies and dynamic characteristics present in multi-converter systems. It exhibits excellent adaptability and robustness, particularly in complex scenarios such as weak grids and diverse converter control strategies. Simulation verification shows that this invention demonstrates stronger criterion applicability and engineering reliability in power systems with large-scale, high-proportion converter integration, providing more effective technical means and theoretical basis for the design, planning, operation, and control of multi-converter power systems. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the method of the present invention.

[0022] Figure 2 This is a topology diagram of an embodiment of the present invention.

[0023] Figure 3 This is a gain or phase curve diagram during the process of Embodiment 3 of the present invention.

[0024] Figure 4 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 stability evaluation method for a distributed multi-converter system in this embodiment is implemented according to 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] The power grid information includes the power grid topology and line impedance parameters; the equipment information includes the control strategies, control parameters, and rated capacity of each converter.

[0028] 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.

[0029] S3. Reduce the order of the power grid's admittance matrix to obtain an equivalent power grid model that retains only the converter access nodes. Combine the admittance matrix of all converters to construct the closed-loop characteristic equation of the multi-converter system.

[0030] 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.

[0031] 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.

[0032] The closed-loop characteristic equation is set according to the following formula after equivalent transformation: in, This is a diagonal matrix composed of the ratios of the individual reference capacity of each converter to the global rated capacity; The equivalent grid matrix retains only the converter access nodes; The extended admittance matrix represents the power grid; This represents the equivalent admittance matrix corresponding to the admittance matrix composed of each converter.

[0033] S5. Calculate the gain and phase of the equivalent admittance matrix of each converter in the diagonal block matrix, as well as the gain and phase of the extended admittance matrix of the power grid.

[0034] Gain is defined as the singular value of a matrix; phase is defined as the set of phases at all points in the numerical domain of the matrix.

[0035] S6. Within the preset frequency range, the multi-converter system is checked at each frequency point to determine whether the preset distributed stability criterion is met: If, for any frequency point, the multi-converter system satisfies at least one of the gain condition and the phase condition, then the closed-loop stability of the multi-converter system is evaluated and determined.

[0036] The specific stability criterion for distributed systems is as follows: If each converter satisfies at least one of the gain and phase conditions at a certain frequency point, then the multi-converter system is closed-loop stable at the corresponding frequency point; if the multi-converter system is closed-loop stable at all frequency points within a preset frequency range, then the closed-loop stability of the multi-converter system is evaluated and determined.

[0037] The converter satisfies the gain condition specifically as follows: i Equivalent admittance matrix of a converter At frequency point The following conditions must be met: in, This represents the upper limit of singular values; This represents the lower bound of singular values; j The imaginary unit; This is a diagonal matrix composed of the ratios of the individual reference capacity of each converter to the global rated capacity; The equivalent grid matrix retains only the converter access nodes; The extended admittance matrix represents the power grid; Indicates the Kronecker product; This represents a 2-order identity matrix.

[0038] The converter satisfies the phase condition specifically as follows: i The admittance matrix of a converter and the equivalent admittance matrix of its transfer function. It is a sector matrix, and at the frequency point The following conditions must be met: in, and These represent the maximum and minimum phases, respectively. and These represent the indexes respectively. i Iterate through all cases and take the maximum and minimum values ​​of the expressions within the parentheses; j It is the imaginary unit.

[0039] 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.

[0040] This embodiment also provides a computer-readable storage medium storing program data thereon, which, when executed by a processor, implements the above-described method.

[0041] Example 2: This invention first models a multi-converter power system. The system is divided into several converters and a power grid. Each converter is described using an admittance model in a global dq coordinate system. For the power grid, a power grid admittance matrix model is established, and an equivalent power grid model retaining only the converter access nodes is obtained through the Kron reduction method.

[0042] Specifically, regardless of the control method and control parameters used, the first i Admittance matrix model of a converter It can always be expressed as: (1) in, and They are the first iPort current vector and port voltage vector of each converter port in the global dq coordinate system. 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. s For the Laplace operator, equation (1) is extended to all converters, and its admittance matrix model is... It can be represented 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. .

[0043] Admittance matrix model of power grid It can be represented 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.

[0044] 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.

[0045] Secondly, two indices, gain and phase, of the complex matrix are introduced to describe the amplitude amplification capability and phase distribution characteristics of the multivariator system, respectively, thus providing a foundation for the subsequent construction of stability criteria. For any n complex matrix of order Its gain is defined as the singular value of the matrix: (6) in, This indicates finding the first element of the matrix. i There are 10 singular values. These singular values ​​are ordered as follows: (7) in, It is to find the maximum singular value of a matrix. This involves finding the minimum singular value of a matrix. Correspondingly, the phase of a matrix is ​​defined by its numerical field, which is defined as: (8) in, yes n dimensional vector, This indicates the 2-norm calculation. If the matrix... A The numerical domain does not include the origin, that is... Then the matrix is ​​called a matrix. A It is sector-shaped, and the phase of a sector matrix is ​​defined as the set of phases of all points within its numerical domain: (9) in, To find complex numbers z Phase, defined and They are matrices A The maximum and minimum phases. Based on equations (6) and (9), a hybrid gain or phase theorem for judging the stability of linear systems is introduced.

[0046] 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: (10) or: (11) By performing an equivalent transformation on the closed-loop characteristic equation shown in equation (5), we can obtain: (12) 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. Then the stability problem shown in equation (12) can be solved by the mixed gain or phase theorem shown in equations (10) and (11) to achieve distributed stability analysis. That is, for the open-loop stable equivalent admittance matrix In other words, if the system is at any frequency point... The following conditions must be met: (13) or: (14) The closed-loop system is then stable.

[0047] The above distributed stability criterion can be stated as follows: In a multi-converter system, if for any frequency... The gain of each converter is less than the gain of the network, or the phase domain of each converter is contained within the network. If the system is stable, then it is stable.

[0048] Compared with existing traditional stability analysis methods, this invention has significant advantages. First, the decentralized stability analysis method avoids the complexity of global modeling, allowing the stability assessment of each converter to be performed independently, thus significantly reducing the computational load. Second, by combining gain and phase conditions, this invention makes stability determination more flexible and accurate, adapting to the complex interactions between converters and the power grid. Particularly in large-scale systems, the scalability of this method is particularly outstanding, effectively handling the complex dynamic behavior of multi-converter systems. Furthermore, compared to traditional passivity theorems, the stability analysis conditions provided by this invention are more relaxed and practical, effectively avoiding overly conservative results. By introducing a hybrid gain / phase theorem, the system can satisfy stability conditions over a wider frequency range, thereby improving the flexibility and reliability of system design and control. Finally, this invention provides strong theoretical support for the planning and safe and stable operation of new power systems.

[0049] Example 3: like Figure 1 As shown, information on the power grid and equipment is obtained, including the network equivalent admittance matrix. and the equivalent transfer function of each converter and its corresponding capacity ratio And obtain the extended admittance matrix of the power grid.

[0050] Finally, calculate the equivalent transfer function of the converter. The gain and phase of each converter are analyzed to determine whether the gain of each converter is less than the gain of the grid, or whether the phase of each converter is contained in [-π, π].

[0051] This invention is built in the MATLAB / Simulink environment as follows Figure 2 The electromagnetic transient simulation model of the three-machine nine-node multi-feed converter system shown is used to verify the effectiveness of the proposed method for judging the small-signal stability of the system based on hybrid gain / phase theory.

[0052] The control parameters and network parameters of each converter in this scenario are shown in Table 1 and Table 2.

[0053] 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. Under these conditions, the network gain can be considered constant (network gain is 4.82), and the network phase domain is -180° to 180° at any frequency. Converter 3 has the highest sector switching frequency (26Hz). Above this frequency, the phase domains of all three converters are contained within the network's phase domain, satisfying the small phase condition. Before 14.4Hz, the gains of all converters are lower than the network's gain curve, satisfying the small gain theorem. However, between 14.4Hz and 26Hz... Figure 3 Within the gray region, neither the small gain theorem nor the small phase theorem can be satisfied, therefore the system is unstable.

[0054] like Figure 4 As shown, a three-machine, nine-node electromagnetic transient simulation was built in MATLAB / Simulink. At t=0.2s, an infinite grid voltage was set to temporarily drop by 0.05 pu and recover at 0.22s. It was found that the active power output of the three converters exhibited constant amplitude oscillations, indicating system instability. That is, the hybrid gain / phase theory effectively identified the system instability.

[0055] The method of this invention can effectively evaluate large-scale, dynamically complex multi-converter power systems, especially under conditions of complex grid dynamics and diverse converter types, still providing accurate stability assessments and design guidance. Furthermore, by reducing the conservatism of traditional methods, this invention makes stability analysis more relevant to practical applications, improving the practicality and reliability of system design and control.

[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 stability evaluation method for a distributed multi-converter system based on hybrid gain and phase theorem, characterized in that, 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. Calculate the gain and phase of the equivalent admittance matrix of each converter in the diagonal block matrix, and the gain and phase of the extended admittance matrix of the power grid. S6. Within the preset frequency range, the multi-converter system is checked at each frequency point to determine whether the preset distributed stability criterion is met: If, for any frequency point, the multi-converter system satisfies at least one of the gain condition and the phase condition, then the closed-loop stability of the multi-converter system is evaluated and determined.

2. The stability evaluation method for a distributed multi-converter system based on hybrid gain and phase theorem as described in claim 1, characterized in that: 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. The stability evaluation method for a distributed multi-converter system based on hybrid gain and phase theorem as described in claim 1, characterized in that, The specific decentralized stability criterion in step S6 is as follows: If each converter satisfies at least one of the gain and phase conditions at a certain frequency point, then the multi-converter system is closed-loop stable at the corresponding frequency point; if the multi-converter system is closed-loop stable at all frequency points within a preset frequency range, then the closed-loop stability of the multi-converter system is evaluated and determined.

4. The stability evaluation method for a distributed multi-converter system based on hybrid gain and phase theorem as described in claim 3, characterized in that, The specific conditions for a converter to satisfy the gain condition are as follows: No. i The admittance matrix of a converter and the equivalent admittance matrix of its transfer function. At frequency point The following conditions must be met: ； in, This represents the upper limit of singular values; This represents the lower bound of singular values; j The imaginary unit; This is a diagonal matrix composed of the ratios of the individual reference capacity of each converter to the global rated capacity; The equivalent grid matrix retains only the converter access nodes; The extended admittance matrix represents the power grid; Indicates the Kronecker product; This represents a 2-order identity matrix.

5. The stability evaluation method for a distributed multi-converter system based on hybrid gain and phase theorem as described in claim 3, characterized in that, The converter satisfies the phase condition as follows: No. i Equivalent admittance matrix of a converter It is a sector matrix, and at the frequency point The following conditions must be met: ； in, and These represent the maximum and minimum phases, respectively. and These represent the indexes respectively. i Iterate through all cases and take the maximum and minimum values ​​of the expressions within the parentheses; j It is the imaginary unit.

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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