A numerical range based multi-inverter system stability evaluation method

Abstract

The application discloses a kind of based on numerical range multi-converter system stability evaluation method.Method includes: whether the open loop stability condition is satisfied by the equivalent admittance matrix of the admittance matrix transfer function of the converter side of multi-converter system;The numerical range of the equivalent admittance matrix of the admittance matrix transfer function of the network side and the converter side of multi-converter system is established;When meeting the open loop stability condition, then whether the closed loop stability condition is satisfied by the numerical range of multi-converter system, if meeting, then evaluate multi-converter system stability.The application is based on numerical range analysis framework, without global modeling, can realize the fast evaluation of small signal stability of multi-converter system.The application shows stronger criterion applicability and engineering reliability in large-scale, high proportion converter access power system, provides more effective technical means and theoretical basis for the design, planning, operation and control of multi-converter power system.

Description

Technical Field

[0001] This invention relates to a method for evaluating the stability of a converter system, which relates to the field of power system stability control, and specifically to a method for evaluating the stability of a multi-converter system based on the numerical domain. 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 significant 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 strategies and interactions with the grid have a profound impact on system stability. As a large number of converters are connected to the grid, traditional power system stability analysis methods are gradually revealing their limitations in dealing with these complex dynamic behaviors.

[0003] Traditional generalized Nyquist methods typically rely on directly coupling the power grid and converters for holistic calculations. While this approach provides some theoretical basis for system stability, it struggles to reveal the deeper mechanisms underlying system stability. Specifically, the generalized Nyquist method analyzes stability by calculating the system's open-loop gain and phase response, but this requires global modeling of the complex interactions between the power grid and converters. This often leads to excessive computational complexity when dealing with multi-converter and large-scale power systems, and makes it difficult to effectively explain the dynamic interactions between the power grid and converters. Therefore, traditional methods cannot intuitively reveal the complex interactions between the power grid and converters and their contribution to system stability.

[0004] While traditional methods provide a theoretical framework for power system stability analysis, their limitations become increasingly apparent in modern multi-converter power systems, especially in the context of complex dynamic interactions. Traditional methods rely on global modeling by directly coupling the grid and converters, which, while providing stability analysis, struggles to reveal the system's stability mechanisms. Therefore, a new stability assessment method is urgently needed to more efficiently and deeply capture the complex dynamic interactions between the grid and converters, providing more accurate and effective stability analysis for modern power systems. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention provides a stability assessment method for multi-converter systems based on the numerical domain. This invention solves the problem that the traditional generalized Nyquist criterion in multi-converter power systems is computationally complex and lacks physical interpretability. The criterion utilizes the mathematical properties of the matrix numerical domain, equating the stability analysis of multi-machine systems to the separation of the numerical domains of the converter admittance matrix and the network admittance matrix. The numerical domain method can achieve "source-grid separation" stability analysis, providing a more intuitive description of the complex interaction between the grid and converters, and offering a more effective solution to cope with the increasingly complex dynamic environment of power systems. The method avoids the complex calculation of frequency-point eigenvalue decomposition of the global system admittance matrix, instead achieving stability analysis of multi-converter systems through the characteristics of each converter admittance matrix and its combination with the minimum eigenvalue of the system node admittance, thereby significantly reducing the computational burden.

[0006] This invention addresses the problem that the traditional generalized Nyquist criterion is computationally complex and fails to reveal the physical mechanisms in the analysis of multi-converter systems. The traditional generalized Nyquist criterion requires eigenvalue decomposition of the entire system admittance matrix at each frequency point. This method is computationally complex when there are many converters and the system is large in scale. Furthermore, because the eigenvalue decomposition lacks an analytical form, it is difficult to intuitively reveal the intrinsic mechanisms of the dynamic interaction between each converter and the power grid. This invention introduces a matrix numerical domain analysis method, transforming the stability analysis of multi-converter systems into a question of whether the numerical domains of the converter admittance matrix and the network admittance matrix intersect. By checking whether there are intersection points between the numerical domains of the converter admittance matrix and the network admittance matrix in the complex plane, the stability of the system can be determined. This avoids the need for complex eigenvalue calculations of the global system admittance matrix, providing a simpler and more physically meaningful analytical tool for the stability assessment and analysis of multi-converter power systems.

[0007] The technical solution adopted in this invention is:

[0008] The numerical domain-based stability assessment method for multi-converter systems of the present invention includes:

[0009] Step 1: Determine whether the open-loop stability condition is met by using the equivalent admittance matrix of the transfer function on the converter side of the multi-converter system.

[0010] Step 2: Establish the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function for the network side and converter side of the multi-converter system.

[0011] Step 3: When the open-loop stability condition is met, determine whether the multi-converter system meets the closed-loop stability condition by using the numerical domain of the equivalent admittance matrix on the network side and the converter side. If it is met, evaluate the stability of the multi-converter system.

[0012] In step 1, the open-loop stability condition is satisfied by determining the pole positions of the inverse of the equivalent admittance matrix of the admittance matrix transfer function on the converter side.

[0013] In step 1, the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function on the network side of the multi-converter system is as follows:

[0014]

[0015]

[0016]

[0017] in, For the numerical field; Let be the network-side admittance matrix, the equivalent admittance matrix of the transfer function, and s be the Laplace operator; For generalized Nyquist operators; A diagonal matrix formed by the ratio of the base capacity of each converter to the global capacity; The Thevenin equivalent admittance matrix of the network side of the multi-converter system, which is simplified to retain only the equipment bus after the Schul complement is used; For Kronecker product; It is a second-order identity matrix; and These are the x and y coordinates of a point in the numerical domain, respectively. This refers to the generalized short-circuit ratio on the network side. It is the smallest eigenvalue of the matrix.

[0018] In step 1, the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function on the converter side of the multi-converter system is as follows:

[0019]

[0020]

[0021] in, For the numerical field; Transfer function of admittance matrix on the converter side The equivalent admittance matrix, where s is the Laplace operator; The transfer function characterizes the dynamics of an electrical network line, where j represents the imaginary unit. For an n-dimensional vector, for The conjugate transpose of; This indicates the search for the 2-norm.

[0022] In step 3, if the device side is dynamic If the open-loop system is stable, then we will analyze the closed-loop stability of the multi-converter system. The specific closed-loop stability conditions are as follows:

[0023]

[0024] in, Let be the equivalent admittance matrix of the transfer function on the converter side, and s be the Laplace operator. The equivalent admittance matrix of the transfer function is the admittance matrix on the network side. It is an empty set.

[0025] When the multi-converter system is at the frequency point If the closed-loop stability condition is satisfied at any frequency point, then the multi-converter system is stable.

[0026] The electronic device of the present invention includes: 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.

[0027] The present invention provides a computer-readable storage medium having program data stored thereon, which, when executed by a processor, implements the method described above.

[0028] Compared with the traditional generalized Nyquist criterion, the numerical domain stability criterion proposed in this invention has significant advantages. The method does not require constructing and calculating the complete system admittance matrix and its frequency-wise eigenvalue decomposition; stability assessment can be performed solely based on the minimum eigenvalues ​​of the admittance matrices of each converter and the system node admittance matrices. This significantly reduces computational complexity and provides a clear theoretical foundation for the stability analysis of heterogeneous multi-converter systems.

[0029] The beneficial effects of this invention are:

[0030] This invention effectively addresses the limitations of the generalized Nyquist analysis method in large-scale multi-converter power systems by introducing a stability criterion based on the numerical domain, making system stability analysis more efficient and flexible. Unlike the traditional generalized Nyquist criterion, which relies on direct coupling of the power grid and converters for global modeling, making it difficult to effectively separate the dynamic characteristics of the source and network and reveal the deep mechanisms of system stability, this invention, based on a numerical domain analysis framework, enables rapid assessment of the small-disturbance stability of multi-converter systems without requiring global modeling. Determining system stability through local numerical domain calculations avoids the construction of high-dimensional state-space models or complex impedance matrices, thus significantly reducing computational load and model complexity. Simulation results demonstrate that this invention exhibits stronger criterion applicability and engineering reliability in large-scale, high-proportion converter-connected power systems, providing more effective technical means and theoretical basis for the design, planning, operation, and control of multi-converter power systems. Attached Figure Description

[0031] Figure 1 This is a schematic flowchart of the method of the present invention;

[0032] Figure 2 This is a topology diagram of an embodiment of the present invention;

[0033] Figure 3 This is a dynamic open-loop pole diagram on the device side in an embodiment of the present invention;

[0034] Figure 4 This is a numerical domain diagram in the implementation process of the present invention;

[0035] Figure 5 The figure shows the simulation verification results of an embodiment of the present invention. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] like Figure 1 As shown, the numerical domain-based stability evaluation method for multi-converter systems of the present invention is as follows:

[0038] Step 1: Determine whether the open-loop stability condition is satisfied by using the equivalent admittance matrix of the transfer function on the converter side of the multi-converter system. Determine the open-loop stability condition by finding the pole locations of the inverse of the equivalent admittance matrix of the transfer function on the converter side. Check whether the equivalent admittance matrix of the converter is open-loop stable, i.e. Whether it is stable in open loop can be determined by... calculate The inverse poles. The numerical domain of the equivalent admittance matrix of the network-side admittance matrix transfer function of the multivariator system is as follows:

[0039]

[0040]

[0041]

[0042] in, For the numerical field; Let be the network-side admittance matrix, the equivalent admittance matrix of the transfer function, and s be the Laplace operator; For generalized Nyquist operators; This is a diagonal matrix formed by the ratio of the base capacity of each converter to the global capacity. , is the ratio of the rated capacity of the i-th converter to the global reference capacity, and n is the total number of converters; The Thevenin equivalent admittance matrix of the network side of the multi-converter system, which is simplified to retain only the equipment bus after the Schul complement is used; For Kronecker product; It is a second-order identity matrix; and These are the x and y coordinates of a point in the numerical domain, respectively. This refers to the generalized short-circuit ratio on the network side. It is the smallest eigenvalue of the matrix.

[0043] Analyzing the numerical field of the equivalent admittance matrix, since the equivalent admittance matrix on the network side is positive definite, its numerical field is equal to the convex hull of its eigenvalues, and the smallest eigenvalue is a positive real number. Considering the operator... By utilizing this function, the numerical domain of the equivalent admittance matrix on the network side can be obtained.

[0044] The numerical domain of the equivalent admittance matrix of the admittance matrix transfer function on the converter side of a multi-converter system is as follows:

[0045]

[0046]

[0047] in, For the numerical field; Transfer function of admittance matrix on the converter side The equivalent admittance matrix, where s is the Laplace operator; The transfer function characterizes the dynamics of an electrical network line, where j represents the imaginary unit. For an n-dimensional vector, for The conjugate transpose of; This indicates the search for the 2-norm.

[0048] Step 2: Establish the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function for the network side and converter side of the multi-converter system.

[0049] Step 3: When the open-loop stability condition is met, determine whether the multi-converter system meets the closed-loop stability condition by using the numerical domain of the equivalent admittance matrices on the network side and the converter side. If it does, evaluate the stability of the multi-converter system. If the equipment side dynamics... If the open-loop system is stable, then we will analyze the closed-loop stability of the multi-converter system. The specific closed-loop stability conditions are as follows:

[0050]

[0051] in, Let be the equivalent admittance matrix of the transfer function on the converter side, and s be the Laplace operator. The equivalent admittance matrix of the transfer function is the admittance matrix on the network side. It is an empty set.

[0052] When the multi-converter system is at the frequency point If the closed-loop stability condition is satisfied at any frequency point, then the multi-converter system is stable.

[0053] This invention first acquires network information and converter information respectively, and then determines the network's admittance matrix and transfer function Y. grid (s) and the admittance matrix and transfer function Y of the i-th converter IBR,i (s), as follows:

[0054]

[0055] in, To synchronize rotation speed, The line resistance-to-inductance ratio; and These are the disturbances of the converter port current and voltage in the global xy coordinate system, respectively, where T is the transpose.

[0056] Combining the power grid and equipment side matrices, the characteristic equation of the system is obtained as follows:

[0057]

[0058]

[0059] in, To find the determinant; is the total admittance matrix transfer function of the converter.

[0060] Then it is further transformed as follows:

[0061]

[0062]

[0063]

[0064] in, It is a diagonal block matrix consisting of the equivalent admittance matrix of each converter.

[0065] Then, based on the definition of the numerical domain and the sufficient form of the generalized Nyquist curve, the stability criterion for closed-loop systems based on numerical domain separation is obtained as follows:

[0066] Define the numerical field of a complex matrix. For any complex matrix... , Let n be the set of complex numbers, and n be the dimension of the matrix. Its numerical field is defined as:

[0067]

[0068] in, For an n-dimensional vector, for The conjugate transpose of; This indicates the search for the 2-norm.

[0069] Based on the definition of the numerical field, we can obtain the following property: for non-singular matrices... In other words, if and If the numerical domains of the matrices do not intersect, then the matrix... The determinant of is also not 0, that is:

[0070]

[0071] We obtain a sufficient form of the generalized Nyquist criterion, that is, for an open-loop stable transfer function matrix... In other words, if the system is At any frequency point, the following condition is satisfied:

[0072]

[0073] in, is the identity matrix; j is the imaginary unit.

[0074] Then closed-loop system There are no unstable poles.

[0075] Will Substituting these values, and based on the properties of the numerical field and the sufficient form of the generalized Nyquist criterion, we can obtain the stability condition based on the separation of the numerical field, i.e., for an open-loop stable transfer function matrix... In other words, if the system is At any frequency point, the following condition is satisfied:

[0076]

[0077] Then closed-loop system There are no unstable poles.

[0078] Finally, we analyze whether the admittance matrix transfer function of the converter has open-loop poles. If it satisfies the open-loop stability condition, we use the numerical domain separation condition to analyze whether it is closed-loop stable.

[0079] like Figure 2 As shown, this invention constructs an electromagnetic transient simulation model of a three-machine, nine-node converter multi-infeed system in the MATLAB / Simulink environment to verify the effectiveness of the proposed method for determining the small-signal stability of the system based on numerical domain separation theory. The control parameters and network parameters of each converter in this scenario are shown in Tables 1 and 2.

[0080] Table 1 Parameters in Simulation Verification of the Example

[0081]

[0082] Table 2 Power Grid Parameters

[0083] Line number Line impedance <![CDATA[Z 1,4 ]]> 0.025+j0.25 <![CDATA[Z 4,9 ]]> 0.005+j0.05 <![CDATA[Z 8,9 ]]> 0.005+j0.05 <![CDATA[Z 2,8 ]]> 0.018+j0.18 <![CDATA[Z 7,8 ]]> 0.008+j0.08 <![CDATA[Z 6,7 ]]> 0.005+j0.05 <![CDATA[Z 4,5 ]]> 0.008+j0.08 <![CDATA[Z 5,6 ]]> 0.005+j0.05 <![CDATA[Z 3,6 ]]> 0.035+j0.35 <![CDATA[Z9]]> 0.0039+j0.039

[0084] This invention was simulated on a 3-machine, 9-node system. All three converters were controlled by a phase-locked loop (PLL), and detailed parameters are shown in Table 1. First, the open-loop stability of each converter was verified. The open-loop pole distribution of each converter is shown in Table 1. Figure 3 As shown, it can be seen that the open-loop poles of the converters are all located in the left half of the complex plane, therefore each converter is open-loop stable. Further analysis of the system's stability using numerical domain analysis reveals that the network's numerical domain is a straight line on the x-axis, ranging from [-∞, gSCR]. Figure 4 As shown, the numerical domain of the device-side dynamics within 0~100Hz is given. It can be found that it intersects with the numerical domain of the electrical network, thus failing to meet the stability condition.

[0085] like Figure 5 As shown, a three-machine, nine-node electromagnetic transient simulation was built in MATLAB / Simulink. At t=0.2s, the infinite grid voltage was set to temporarily drop by 0.05pu and recover at 0.22s. It was found that the active power output of the three converters exhibited constant amplitude oscillation, indicating that the system was unstable. That is, the numerical domain method effectively identified the instability risk of the system.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and not to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for stability evaluation of a multi-converter system based on the numerical domain, characterized in that, include: Step 1: Determine whether the open-loop stability condition is satisfied by using the equivalent admittance matrix of the transfer function on the converter side of the multi-converter system. Step 2: Establish the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function for the network side and converter side of the multi-converter system; Step 3: When the open-loop stability condition is met, determine whether the multi-converter system meets the closed-loop stability condition by using the numerical domain of the equivalent admittance matrix on the network side and the converter side. If it is met, evaluate the stability of the multi-converter system.

2. The method for stability evaluation of multi-converter systems based on the numerical domain according to claim 1, characterized in that: In step 1, the open-loop stability condition is satisfied by determining the pole positions of the inverse of the equivalent admittance matrix of the admittance matrix transfer function on the converter side.

3. The method for stability evaluation of multi-converter systems based on the numerical domain according to claim 2, characterized in that: In step 1, the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function on the network side of the multi-converter system is as follows: in, For the numerical field; Let be the network-side admittance matrix, the equivalent admittance matrix of the transfer function, and s be the Laplace operator; For generalized Nyquist operators; A diagonal matrix formed by the ratio of the base capacity of each converter to the global capacity; Here is the Thevenin equivalent admittance matrix on the network side of the multi-converter system; For Kronecker product; It is a second-order identity matrix; and These are the x and y coordinates of a point in the numerical domain, respectively. This refers to the generalized short-circuit ratio on the network side. It is the smallest eigenvalue of the matrix.

4. The method for stability evaluation of multi-converter systems based on the numerical domain according to claim 1, characterized in that: In step 1, the numerical domain of the equivalent admittance matrix of the admittance matrix transfer function on the converter side of the multi-converter system is as follows: in, For the numerical field; Transfer function of admittance matrix on the converter side The equivalent admittance matrix, where s is the Laplace operator; The transfer function characterizes the dynamics of an electrical network line, where j represents the imaginary unit. It is an n-dimensional vector. for The conjugate transpose of; This indicates the search for the 2-norm.

5. The method for stability evaluation of multi-converter systems based on the numerical domain according to claim 1, characterized in that: In step 3, the closed-loop stability condition is as follows: in, Let be the equivalent admittance matrix of the transfer function on the converter side, and s be the Laplace operator. The equivalent admittance matrix of the transfer function is the admittance matrix on the network side. It is an empty set; When the multi-converter system is at the frequency point If the closed-loop stability condition is satisfied at any frequency point, then the multi-converter system is stable.

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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