Geometrically decoupled small-signal stability assessment method for new energy power systems

Abstract

The application discloses a kind of new energy power system small disturbance stability evaluation methods based on geometric separation.Method includes: obtaining the geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function of the network side and the converter side of new energy power system, and then determining whether new energy power system and each converter meet closed loop stability condition by geometric separation method, if meet, then evaluate new energy power system stability.The method of the application supports the stability verification of massive heterogeneous power electronic equipment in a decentralized and modular manner, effectively avoiding the computational complexity caused by the growth of system dimension;At the same time, the proposed geometric separation condition provides a clear and operable guidance for the external characteristic specification of grid-connected equipment and controller design, which helps to achieve "plug and play" and high proportion of safe access of new energy power system.

Description

Technical Field

[0001] This invention relates to a method for assessing the stability of a power system, and to the field of power system stability control, specifically to a method for assessing the stability of a new energy power system with small disturbances based on geometric separation. Background Technology

[0002] With the large-scale integration of new energy sources such as wind power and photovoltaics, as well as power electronic equipment such as flexible DC transmission and electrochemical energy storage, modern power systems are exhibiting the "dual high" characteristics of "high proportion of renewable energy" and "high proportion of power electronic equipment." These power electronic devices (such as converters) typically employ complex multi-timescale control strategies, and their dynamic characteristics differ significantly from traditional synchronous generators. They also come in various types (such as grid-connected and grid-connected) with varying parameters. When a large number of heterogeneous power electronic devices are interconnected through the power grid, the entire system constitutes a high-dimensional, multiple-input multiple-output (MIMO) closed-loop dynamic system. This leads to frequent new stability problems, such as low-frequency oscillations in grid-connected converters under weak grid conditions, subsynchronous resonance between doubly-fed wind turbines and series compensation lines, and high-frequency resonance in flexible DC converter stations. The core of these problems lies in the mismatch between the dynamic characteristics of the "source-grid" relationship.

[0003] Currently, stability analysis of such systems mainly relies on two methods: eigenvalue analysis based on state-space models and impedance / admittance analysis based on frequency-domain models (such as the generalized Nyquist criterion). However, both methods have significant shortcomings. Eigenvalue analysis requires a detailed closed-loop state-space model of the entire interconnected system, with computational complexity increasing dramatically with the number of devices. Furthermore, it struggles to intuitively reveal the dynamic interaction mechanism between individual devices and the power grid, making it unsuitable for distributed evaluation of massive heterogeneous devices. While impedance analysis can establish external characteristic models for both devices and the power grid, it faces computational difficulties in multi-machine systems due to the need to handle the determinant of high-dimensional transfer function matrices. It also fails to provide a clear and intuitive physical picture to explain how the "source-grid" interaction determines system stability, and it cannot effectively guide the standardization of the external characteristics of individual devices to ensure global stability.

[0004] Furthermore, passive design, as a method for standardizing the external characteristics of equipment, requires the equipment to exhibit positive real characteristics across the entire frequency band, which is too demanding and often fails to meet the requirements in the low-frequency band, which includes synchronous dynamics, leading to an overly conservative design. Therefore, there is an urgent need for a new method that can intuitively depict the dynamic interaction between the source and the grid, support distributed stability assessment, and effectively guide the standardization of equipment external characteristics in order to address the increasingly severe stability challenges of new energy power systems. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention provides a method for small-disturbance stability assessment of new energy power systems based on geometric separation. This invention utilizes the geometric characteristics of complex matrices to characterize and analyze the dynamic interaction between the source and the grid. It proposes a hierarchical, frequency-band-specific stability criterion system to determine whether the external characteristics of the converter match the external characteristics of the network, and comprehensively derives a global small-disturbance stability conclusion. This invention aims to overcome the shortcomings of traditional state-space and frequency-domain criteria in high-dimensional, multi-type power electronic equipment interconnection scenarios, such as the "curse of dimensionality," lack of intuitive physical meaning, and difficulty in guiding equipment design. By constructing a geometrically validated stability criterion that can be distributed and verified, it achieves intuitive characterization, efficient assessment, and proactive control of the dynamic interaction between the source and the grid, supporting the modular and stable operation of large-scale new energy power systems.

[0006] The technical solution adopted in this invention is:

[0007] The present invention provides a method for evaluating the small-disturbance stability of a new energy power system based on geometric separation, comprising:

[0008] The geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function of the network side and converter side of the new energy power system are obtained. Then, the geometric separation method is used to determine whether the new energy power system and each converter meet the closed-loop stability condition. If they do, the stability of the new energy power system is evaluated.

[0009] The geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function include the DW shell, numerical domain, xz plot, gain, and phase. When the admittance matrix transfer function on the converter side is in open-loop stability, the overall stability of the new energy power system is evaluated using a geometric separation method based on the geometric characteristics of the equivalent admittance matrices on the network and converter sides. Furthermore, the stability of each converter is evaluated using the geometric separation method based on the geometric characteristics of its equivalent admittance matrix, thus achieving small-disturbance stability assessment of the new energy power system.

[0010] When evaluating the overall stability of a new energy power system using the geometric separation method, i.e., evaluating the closed-loop stability problem of the new energy power system, based on the geometric characteristics of each equivalent admittance matrix, when the new energy power system is at any frequency point... If any one of the following conditions a~e is met, the new energy power system is generally stable. The specific conditions a~e are as follows:

[0011] Condition a) The equivalent admittance matrix of the transfer function on the converter side. At frequency point The small gain theorem is satisfied at this location:

[0012]

[0013]

[0014] in, This represents the upper limit of singular values; j is the imaginary unit; This refers to the generalized short-circuit ratio on the network side. It is the smallest eigenvalue of the matrix; 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 new energy power system on the network side, which is simplified to retain only the equipment bus after Schulbu's work; Includes all converters.

[0015] b) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. It is a sector matrix, and the equivalent admittance matrix of the admittance matrix transfer function on the converter side. At frequency point The small phase theorem is satisfied at this point:

[0016]

[0017] in, and These represent the maximum and minimum phases, respectively.

[0018] c) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The numerical domain is separated at the specified location:

[0019]

[0020] in, For the numerical field; It is a generalized Nyquist operator.

[0021] d) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The xz graph is separated at the following location:

[0022]

[0023] in, This is an xz graph.

[0024] e) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The DW shell separation condition is satisfied:

[0025]

[0026] in, This indicates a DW shell.

[0027] When evaluating the stability of each converter, for each converter, based on the geometric characteristics of the converter's equivalent admittance matrix, when the new energy power system is at any frequency point... If any one of the following conditions a to c is met, the new energy power system will be generally stable. The specific conditions a to c are as follows:

[0028] Condition a) The admittance matrix of the i-th converter and the equivalent admittance matrix of its transfer function At frequency point The small gain theorem is satisfied at this location:

[0029]

[0030] in, This represents the upper limit of singular values; j is the imaginary unit; This represents the generalized short-circuit ratio on the network side.

[0031] Condition b) The equivalent admittance matrix of the transfer function of the i-th converter It is a sector matrix, and at the frequency point The small phase theorem is satisfied at this point:

[0032]

[0033] in, and These represent the maximum and minimum phases, respectively.

[0034] Condition c) The equivalent admittance matrix of the transfer function of the i-th converter At frequency point The xz graph is separated at the following location:

[0035]

[0036] in, For xz graphs; 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 for the network side of the new energy power system; For Kronecker product; It is a second-order identity matrix.

[0037] 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.

[0038] 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.

[0039] Compared with traditional stability criteria (such as the generalized Nyquist criterion and state-space eigenvalue analysis), the geometric stability criterion proposed in this invention has significant advantages. The method can intuitively characterize the dynamic interaction between massive heterogeneous converters and complex power networks, transforming the stability problem of high-dimensional multi-input multi-output (MIMO) systems into a separation judgment of the external characteristics of complex matrices in geometric space, significantly improving the visualization and physical interpretability of the analysis. Simultaneously, it supports decentralized and modular stability verification of each grid-connected device, effectively avoiding the "curse of dimensionality" problem caused by the surge in system dimensionality in traditional methods. Furthermore, it provides clear and operable design guidelines for the external characteristic specifications of power electronic equipment and the tuning of controller parameters, thereby supporting the safe, stable, and modular construction of new energy power systems under high-proportion access.

[0040] The beneficial effects of this invention are:

[0041] This invention introduces a geometric stability criterion, transforming the traditionally difficult-to-understand stability problem of high-dimensional systems into a visual relationship of the external characteristics of complex matrices in geometric space, significantly improving the clarity of understanding the dynamic interaction mechanism between the source and the grid. Compared with the generalized Nyquist criterion and state-space eigenvalue analysis, this method supports decentralized and modular stability verification of massive heterogeneous power electronic devices, effectively avoiding the computational complexity (i.e., the "curse of dimensionality") brought about by the growth of system dimensions. At the same time, the proposed geometric separation condition provides clear and operable guidance for the external characteristic specifications and controller design of grid-connected equipment, which helps to achieve "plug-and-play stability" and high-proportion safe access of new energy power systems. Attached Figure Description

[0042] Figure 1 This is a schematic flowchart of the method of the present invention;

[0043] Figure 2 This is a topology diagram of a single-machine grid connected to an infinite power grid, as shown in an embodiment of the present invention.

[0044] Figure 3 This is a gain and phase diagram of a single-machine system according to an embodiment of the present invention;

[0045] Figure 4 This is a numerical domain diagram of a single-machine system according to an embodiment of the present invention;

[0046] Figure 5 This is an xz diagram of a standalone system according to an embodiment of the present invention, wherein, Figure 5 (a) is the xz diagram of the stand-alone system before the changes in this embodiment of the invention. Figure 5 (b) is the modified xz diagram of the stand-alone system according to an embodiment of the present invention;

[0047] Figure 6 This is a DW shell diagram of a standalone system according to an embodiment of the present invention;

[0048] Figure 7 This is a simulation verification result diagram of a single-machine system in an embodiment of the present invention;

[0049] Figure 8 This is a topology diagram of a three-machine, nine-node system used in an embodiment of the present invention;

[0050] Figure 9 This is a gain and phase diagram of a three-machine system in an embodiment of the present invention;

[0051] Figure 10 This is an XZ diagram of a three-machine system according to an embodiment of the present invention, wherein, Figure 10 (a) is the xz diagram of converter 1 before the change in the embodiment of the present invention. Figure 10 (b) is the xz diagram of the converter 1 in the embodiment of the present invention after the change. Figure 10 (c) is the xz diagram of converter 2 in an embodiment of the present invention. Figure 10 (d) is the xz diagram of converter 3 in an embodiment of the present invention;

[0052] Figure 11 The figure shows the simulation verification results of the three-machine system in the embodiment of the present invention. Detailed Implementation

[0053] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] like Figure 1 As shown, the small-disturbance stability assessment method for new energy power systems based on geometric separation of the present invention is as follows:

[0055] The geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function of the network side and converter side of the new energy power system are obtained. Then, the geometric separation method is used to determine whether the new energy power system and each converter meet the closed-loop stability condition. If they do, the stability of the new energy power system is evaluated.

[0056] The geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function include the DW shell, numerical domain, xz plot, gain, and phase. When the admittance matrix transfer function on the converter side is in open-loop stability, the overall stability of the new energy power system is evaluated using a geometric separation method based on the geometric characteristics of the equivalent admittance matrices on the network and converter sides. Furthermore, the stability of each converter is evaluated using the geometric separation method based on the geometric characteristics of its equivalent admittance matrix, thus achieving small-disturbance stability assessment of the new energy power system.

[0057] The equivalent admittance matrices of the transfer functions on both the network and converter sides are complex matrices. The steps for analyzing matrix singularities based on the geometric properties of complex matrices are as follows:

[0058] 1) Define the Davis-Wielandt shell (DW) for complex matrices:

[0059] For complex matrices , Let represent the set of complex numbers, where n is the dimension of the complex matrix, and its DW shell is denoted as DW(A), defined as follows:

[0060]

[0061] In this case, the sign on the left of := is defined as the value on the right. Indicates taking the real part; and Let each represent a complex vector and its conjugate transpose; This indicates taking the imaginary part; Represents the l2 norm; For complex matrices The conjugate transpose of .

[0062] As can be seen, the DW shell is a geometric shape defined in three-dimensional space, and the coordinates of each point of this three-dimensional shape are... satisfy , , .

[0063] 2) Define the numerical field of a complex matrix:

[0064] For complex matrices Its numerical range is denoted as The definition is as follows:

[0065]

[0066] As can be seen, the numerical domain of a matrix is ​​a geometric figure defined on a two-dimensional plane, and the coordinates of each point on this two-dimensional figure are... satisfy , As can be seen from the above definition, a matrix numerical domain It is its three-dimensional DW shell Projection onto the xy two-dimensional plane.

[0067] 3) Define the xz plot of a complex matrix:

[0068] Further define the two-dimensional projection of the DW shell of the complex matrix A onto the xz plane. (Referring to the "xz diagram") is as follows:

[0069]

[0070] The coordinates of each point in the 2D xz graph satisfy , It can be seen that the xz diagram of the complex matrix is ​​the projection of the DW shell onto the xz plane.

[0071] 4) Define the gain and phase of the matrix:

[0072] For complex matrices Its gain can be obtained through the singular values ​​of matrix A. definition:

[0073]

[0074]

[0075] in, , … They represent singular value matrices respectively. The first, second, ..., nth singular value in the sequence; and They represent singular values ​​respectively. The upper and lower limits.

[0076] Maximum singular value of matrix A and minimum singular value These correspond to the maximum and minimum values ​​of its DW shell on the z-axis, respectively.

[0077] matrix The phase is defined by its numerical field. If the numerical field of matrix A does not include the origin, that is... Then matrix A is said to be sector-shaped. In this case, there exists a nonsingular matrix T and a diagonal matrix D such that... This refers to the sector decomposition of matrix A. Based on this sector decomposition, the phase of the sector matrix A can be defined as the phase of the n diagonal elements of matrix D. :

[0078]

[0079]

[0080] in, , … Representing the phase matrix respectively The first, second, ..., nth phase; and These are the maximum and minimum phases of matrix A, defined by the two tangents from the origin to the numerical domain of A, respectively. The other phase values ​​of matrix A are... It lies between these two tangents. When matrix A does not satisfy the sector characteristic, that is, its numerical domain includes the origin, then the phase of A is undefined, but its numerical domain and DW shell still exist.

[0081] 5) Obtain the geometric properties of the complex matrix:

[0082] For two non-singular complex matrices Specifically, the matrix is ​​valid when the following conditions are met. Non-singular.

[0083] i) DW shell separation: .

[0084] ii) Separation of numerical domain: .

[0085] iii) xz-plot separation: .

[0086] iv) Small Gain Theorem: .

[0087] v) Small Phase Theorem: .

[0088] The steps for analyzing the stability of a multi-input multi-output system using the geometric properties of complex matrices are as follows:

[0089] 1) Obtain a sufficient form of the generalized Nyquist criterion for complex matrices, i.e., for open-loop stable transfer function matrices. In other words, if the system is At any frequency point, the following condition is satisfied:

[0090]

[0091] Then closed-loop system There are no unstable poles.

[0092] 2) Using the geometric properties of complex matrices, based on the geometric properties of complex matrices and the sufficient form of the generalized Nyquist criterion, the geometric conditions for the stability of the closed-loop system can be obtained, that is, for the open-loop stable transfer function matrix... In other words, if the system is At any frequency point, any one of a~e is satisfied:

[0093] a) and The small gain theorem is satisfied at this frequency if the following condition is met:

[0094]

[0095] b) and All are sector matrices and the following condition holds, i.e., the small phase theorem is satisfied at this frequency point:

[0096]

[0097] c) and The following condition must be met for numerical domain separation to be achieved at this frequency point:

[0098]

[0099] in, It is a generalized Nyquist operator.

[0100] d) and The following condition must be met for xz-graph separation to be achieved at this frequency point:

[0101]

[0102] e) and The DW shell separation is satisfied at this frequency point if the following conditions are met:

[0103]

[0104] Then closed-loop system There are no unstable poles.

[0105] When evaluating the overall stability of a new energy power system using the geometric separation method, i.e., evaluating the closed-loop stability problem of the new energy power system, based on the geometric characteristics of each equivalent admittance matrix, when the new energy power system is at any frequency point... If any one of the following conditions a~e is met, the new energy power system is generally stable. The specific conditions a~e are as follows:

[0106] Condition a) The equivalent admittance matrix of the transfer function on the converter side. At frequency point The small gain theorem is satisfied at this location:

[0107]

[0108]

[0109] in, This represents the upper limit of singular values; j is the imaginary unit; This refers to the generalized short-circuit ratio on the network side. It is the smallest eigenvalue of the matrix; 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 new energy power system on the network side, which is simplified to retain only the equipment bus after Schulbu's work; Includes all converters.

[0110] b) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. It is a sector matrix, and the equivalent admittance matrix of the admittance matrix transfer function on the converter side. At frequency point The small phase theorem is satisfied at this point:

[0111]

[0112] in, and These represent the maximum and minimum phases, respectively.

[0113] c) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The numerical domain is separated at the specified location:

[0114]

[0115] in, For the numerical field; It is a generalized Nyquist operator.

[0116] d) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The xz graph is separated at the following location:

[0117]

[0118] in, This is an xz graph.

[0119] e) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The DW shell separation condition is satisfied:

[0120]

[0121] in, This indicates a DW shell.

[0122] When evaluating the stability of each converter, for each converter, based on the geometric characteristics of the converter's equivalent admittance matrix, when the new energy power system is at any frequency point... If any one of the following conditions a to c is met, the new energy power system will be generally stable. The specific conditions a to c are as follows:

[0123] Condition a) The admittance matrix of the i-th converter and the equivalent admittance matrix of its transfer function At frequency point The small gain theorem is satisfied at this location:

[0124]

[0125] in, This represents the upper limit of singular values; j is the imaginary unit; This represents the generalized short-circuit ratio on the network side.

[0126] Condition b) The equivalent admittance matrix of the transfer function of the i-th converter It is a sector matrix, and at the frequency point The small phase theorem is satisfied at this point:

[0127]

[0128] in, and These represent the maximum and minimum phases, respectively.

[0129] Condition c) The equivalent admittance matrix of the transfer function of the i-th converter At frequency point The xz graph is separated at the following location:

[0130]

[0131] in, For xz graphs; 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 for the network side of the new energy power system; For Kronecker product; It is a second-order identity matrix.

[0132] Since the admittance matrix transfer function of the converter is block diagonal, it satisfies , Let denot convex hull, and let DW shell of network admittance matrix be convex. Using the above properties, dispersion criteria based on DW shell separation can be derived.

[0133] Analyzing the DW shell parameters of the network admittance matrix The trajectory formed by the change is as follows:

[0134] First, we analyze the DW shell of the network admittance matrix. Since... It is positive definite, therefore its DW shell is:

[0135]

[0136] in, express The i-th eigenvalue.

[0137] The DW shell of the network-side admittance matrix is ​​a convex polygon, and the x-coordinates of the endpoints of the polygon are... The negative of the eigenvalues, with the ordinate at 0, and the squares of the z-axis and x-axis coordinates, meaning each endpoint lies on... superior.

[0138] Then consider the operators in the sufficient form of the generalized Nyquist criterion. , The function, It can be represented by a graph enclosed by two parabolas and a straight line:

[0139]

[0140]

[0141] ,

[0142] Where a represents the slope of the line, and k and b represent the slope and intercept of the line, respectively;

[0143] and They represent The minimum and maximum eigenvalues.

[0144] The method of this invention obtains the network admittance matrix transfer function and the converter admittance matrix transfer function respectively, and obtains the closed-loop admittance matrix model of the system. The steps are as follows:

[0145] First, obtain network information and determine the network admittance matrix Y. grid (s), as shown below.

[0146]

[0147] in, The transfer function characterizing the dynamics of the line; s is the synchronous rotational speed; s is the Laplace operator; This represents the line resistance-to-inductance ratio.

[0148] Then, information about each converter is obtained, including topology, operating parameters, and control parameters, to obtain n converter admittance matrices and transfer functions:

[0149]

[0150]

[0151] in, and These are the port current and voltage disturbance of the i-th converter in the global xy coordinate system, respectively, where T is the transpose; Y IBR,i (s) is the transfer function of the admittance matrix of the i-th converter.

[0152] Then, combining the power grid and equipment side matrices, the characteristic equation of the system is obtained, as shown below:

[0153]

[0154] in, This represents finding the determinant; further, it can be transformed into:

[0155]

[0156]

[0157]

[0158]

[0159] in, It is a diagonal block matrix composed of the equivalent admittance matrix of each converter.

[0160] Then, the DW shell, numerical domain, xz plot, gain, and phase of the complex matrix are defined. The singularity of the matrix is ​​analyzed using its geometric properties. The stability of a multi-input multi-output system is analyzed using these geometric properties, and the DW shell of the network admittance transfer function varies with parameters. The trajectory formed during the change is finally analyzed using a geometric separation method to disperse the stability of the system.

[0161] Specific embodiments of the present invention are as follows:

[0162] This invention is built in the MATLAB / Simulink environment as follows Figure 2 and Figure 8 The single-machine integrated infinite power grid system and the three-machine nine-node system shown are used to verify the effectiveness of the proposed small-disturbance stability method for new energy power systems based on geometric separation. Let be the equivalent admittance transfer function of the converter. L is the network equivalent transfer function. F1 and L F2 The filter inductors are located on the machine side and the network side, respectively, C F For the filter capacitor, the control parameters and network parameters of each converter in this scenario are shown in Tables 1 and 2. The phase-locked loop parameters of the grid-connected equipment in the single-unit infinite power grid system are 27+377 / s, and other parameters are consistent with those in Table 1.

[0163] Table 1 Parameters in Simulation Verification of the Example

[0164]

[0165] Table 2 Power Grid Parameters

[0166]

[0167] The small-disturbance stability analysis process of new energy power systems based on geometric separation first uses gain / phase. In frequency bands where the small gain and small phase conditions are not met, it then checks whether the two-dimensional xz graph separation or numerical domain separation is satisfied. At frequencies where the xz graph separation or numerical domain separation is not satisfied, the three-dimensional DW shell separation is finally checked, thereby reducing the computational load of checking the three-dimensional graph.

[0168] like Figure 3 As shown, the converter gain is less than the network gain at frequencies below 16Hz (the small gain theorem holds), while at frequencies above 50Hz, the converter's phase domain is contained within the network's phase domain (the small phase theorem holds). However, between 16Hz and 50Hz, the system does not satisfy either the small gain or small phase theorem. In this case, further verification of the numerical domain, xz plot, DW shell, and other characteristics is possible, and verification is only required for the frequency band where the small gain and small phase theorems are not satisfied, i.e., between 16Hz and 50Hz.

[0169] like Figure 4 As shown, the evolution of the numerical domains of the converter and the electrical network with frequency (between 16Hz and 50Hz) is presented. If the numerical domains of the converter and the electrical network are separated, the system closed-loop is stable. Figure 4 It can be seen that at any frequency, the numerical domain of the electrical network is a straight line on the real axis (x-axis), extending from -SCR to -∞ (considering...). The numerical domain of the converter is an ellipse, which is caused by the changes in the voltage (i.e., the voltage). As can be seen from the figure, although the numerical domain of the power network and the numerical domain of the converter are relatively close, they do not intersect, that is, they are "geometrically separated". Therefore, the numerical domain separation is valid between 16Hz and 50Hz, and the system is stable.

[0170] like Figure 5 (a) and Figure 5 As shown in (b), the evolution of the xz diagram of the converter and the power network with frequency (between 16Hz and 50Hz) is given. It can be seen from the figure that the xz diagrams of the converter and the power network do not intersect, that is, they are geometrically separated, thus satisfying the xz diagram separation condition.

[0171] like Figure 6 The figure shows the evolution of the DW shell of the converter and the power network with frequency (between 16Hz and 50Hz). At each frequency point, the DW shell of the converter is a hollow ellipsoid, and this ellipsoid moves in space as the frequency point changes. It can be seen from the figure that the DW shell of the power network and the DW shell of the converter are separated, satisfying the DW shell separation condition.

[0172] like Figure 7 As shown, an electromagnetic transient simulation of a single-machine system connected to an infinite grid was built in MATLAB / Simulink. At t=0.2s, the voltage of the infinite grid was set to drop by 0.05pu and recover at 0.22s. It was found that the active power output of the converter exhibited weakly damped oscillations and eventually recovered, thus indicating that the system was stable.

[0173] The process of distributed analysis of multi-machine systems based on geometric separation conditions first uses gain / phase, and then checks whether two-dimensional xz diagram separation is satisfied in frequency bands that do not meet the conditions of small gain and small phase.

[0174] like Figure 9 As shown, the gain and phase diagrams of the three converters and the power network are given. It can be seen that below 15Hz, the gain of the three converters is less than the gain of the power network, thus satisfying the small gain theorem; above 53Hz, the phase domains of the three converters are all contained within the phase domain of the power network, thus satisfying the small phase theorem.

[0175] like Figure 10 of (a) Figure 10 of (b) Figure 10 (c) and Figure 10 As shown in (d), the xz plots of the three converters and the power network are given between 15Hz and 53Hz. At each frequency point, the xz plot of the converter is an ellipse. The xz plots of converters 1 and 2 do not intersect with the xz plot of the power network, while the xz plot of converter 3 intersects with the xz plot of the power network, which indicates that the system is unstable.

[0176] like Figure 11 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 geometric separation method effectively identified the instability risk of the system.

[0177] 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 evaluating the small-disturbance stability of a new energy power system based on geometric separation, characterized in that, include: The geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function of the network side and converter side of the new energy power system are obtained. Then, the geometric separation method is used to determine whether the new energy power system and each converter meet the closed-loop stability condition. If they do, the stability of the new energy power system is evaluated.

2. The method for evaluating the small-disturbance stability of a new energy power system based on geometric separation according to claim 1, characterized in that: The geometric characteristics of the equivalent admittance matrix of the admittance matrix transfer function include the DW shell, numerical domain, xz plot, gain, and phase. When the admittance matrix transfer function on the converter side is in open-loop stability, the overall stability of the new energy power system is evaluated using a geometric separation method based on the geometric characteristics of the equivalent admittance matrices on the network and converter sides. Furthermore, the stability of each converter is evaluated using the geometric separation method based on the geometric characteristics of its equivalent admittance matrix, thus achieving small-disturbance stability assessment of the new energy power system.

3. The method for evaluating the small-disturbance stability of a new energy power system based on geometric separation according to claim 2, characterized in that: When evaluating the overall stability of a new energy power system using the geometric separation method, based on the geometric characteristics of each equivalent admittance matrix, the new energy power system at any frequency point... If any one of the following conditions a~e is met, the new energy power system is generally stable. The specific conditions a~e are as follows: Condition a) The equivalent admittance matrix of the transfer function on the converter side. At frequency point The small gain theorem is satisfied at this location: in, This represents the upper limit of singular values; j is the imaginary unit; This refers to the generalized short-circuit ratio on the network side. It is the smallest eigenvalue of the matrix; A diagonal matrix formed by the ratio of the base capacity of each converter to the global capacity; The Thevenin equivalent admittance matrix for the network side of the new energy power system; b) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. It is a sector matrix, and the equivalent admittance matrix of the admittance matrix transfer function on the converter side. At frequency point The small phase theorem is satisfied at this point: in, and These represent the maximum and minimum phases, respectively. c) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The numerical domain is separated at the specified location: in, For the numerical field; For generalized Nyquist operators; d) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The xz graph is separated at the following location: in, For xz graphs; e) The equivalent admittance matrix of the transfer function on the converter side and the equivalent admittance matrix of the network-side admittance matrix and transfer function. At frequency point The DW shell separation condition is satisfied: in, This indicates a DW shell.

4. The method for evaluating the small-disturbance stability of a new energy power system based on geometric separation according to claim 2, characterized in that: When evaluating the stability of each converter, for each converter, based on the geometric characteristics of the converter's equivalent admittance matrix, when the new energy power system is at any frequency point... If any one of the following conditions a to c is met, the new energy power system will be generally stable. The specific conditions a to c are as follows: Condition a) The admittance matrix of the i-th converter and the equivalent admittance matrix of its transfer function At frequency point The small gain theorem is satisfied at this location: in, This represents the upper limit of singular values; j is the imaginary unit; This represents the generalized short-circuit ratio on the network side; Condition b) The equivalent admittance matrix of the transfer function of the i-th converter It is a sector matrix, and at the frequency point The small phase theorem is satisfied at this point: in, and These represent the maximum and minimum phases, respectively. Condition c) The equivalent admittance matrix of the transfer function of the i-th converter At frequency point The xz graph is separated at the following location: in, For xz graphs; 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 for the network side of the new energy power system; For Kronecker product; It is a second-order identity matrix.

5. 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 1-4.

6. A computer-readable storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, it implements the method as described in any one of claims 1-4.

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