Robust stability analysis method for meshed grid-type hybrid multi-infeed system

Abstract

The application relates to a kind of robust stability quantitative evaluation methods of follow net network type hybrid multi-infeed system, comprising: S1, constructing hybrid multi-infeed system model;S2, equivalent hybrid multi-infeed system is equivalent to equivalent network subsystem and equivalent follow net subsystem, respectively calculate generalized short-circuit ratio as power grid intensity quantitative index;S3, select nominal system model, determine the critical value of nominal system small disturbance stability through dominant eigenvalue trajectory;S4, draw the frequency domain characteristic curve of uncertainty perturbation singular value, determine the upper bound of uncertainty perturbation;S5, draw the complementary sensitivity peak value curve of nominal system after decoupling when accessing different power grid intensity ac network, and combine the upper bound of uncertainty perturbation to quantify the critical value and margin of robust stability under the perspective of power grid intensity. Compared with the prior art, the application creatively proposes a robust small disturbance stability quantitative evaluation method, which can provide technical support for coordinated optimization configuration and safe and stable operation of high-proportion new energy grid-connected system.

Description

Technical Field

[0001] This invention relates to the field of new energy power systems, and in particular to a robust stability analysis method for a multi-infeed system with grid-connected structure. Background Technology

[0002] With the increasing penetration of new energy sources such as wind power and photovoltaics, the power system is transforming into a new type of power system dominated by power electronic devices. The control method of new energy grid-connected equipment (i.e., converters) using power electronics as the interface significantly affects system stability. Currently, most converters adopt grid-following (GFL) control, relying on phase-locked loops (PLLs) to track the AC voltage at the grid connection point for synchronization. When a grid-following converter operates in a weak grid with a low short-circuit ratio, the strong coupling between the PLL and the grid can easily lead to phase-lock failure, causing subsynchronous oscillation instability. In contrast, grid-forming (GFM) converters, which employ power synchronization strategies, can actively establish and support grid voltage and frequency, exhibiting good adaptability to weak grids. However, they may face low-frequency oscillation instability risks under strong grids with high short-circuit ratios. The gradual deployment of grid-forming converters will lead to the formation of hybrid multi-infeed systems combining grid and grid-forming converters. Studies have shown that configuring grid-forming converters can effectively improve the subsynchronous frequency band oscillation problem in hybrid multi-infeed systems, but it increases the risk of low-frequency oscillation instability.

[0003] In hybrid multi-infeed systems, the dynamic external characteristics of grid-connected and grid-connected equipment differ significantly, and the coupling mechanisms between equipment and between equipment and the AC grid are complex. Existing research often assumes that the external characteristics of grid-connected or grid-connected converters in hybrid multi-infeed systems are consistent. However, in reality, not only do converters with different control methods exhibit external characteristic differences (strong heterogeneity), but converters using the same control method are also typically "heterogeneous" (weak heterogeneity). It is necessary to combine the decoupling concept of the dominant oscillation mode of grid-connected / grid-connected converters with modern robust control theory to analyze the impact of uncertainties (perturbations) on the system that characterize the heterogeneous characteristics of the equipment. Furthermore, existing research on hybrid multi-infeed systems often neglects the impact of uncertainties, basing its theory on the assumption that the external characteristics of grid-connected (grid-connected) converters are similar.

[0004] Therefore, there is an urgent need for a robust stability quantitative evaluation method applicable to the complex dynamic characteristics of hybrid multi-feed systems. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a robust stability quantitative evaluation method for a multi-infeed system with grid-connected structure. It creatively proposes a robust small-disturbance stability quantitative evaluation method, which can provide technical support for the coordinated optimization configuration and safe and stable operation of high-proportion renewable energy grid-connected systems.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A method for quantitatively evaluating the robust stability of a multi-feed system with a mesh-like structure includes the following steps:

[0008] S1. Construct a multiplicative perturbation model for a hybrid multi-feed system;

[0009] S2. Equivalently convert the hybrid multi-feed system into an equivalent grid subsystem and an equivalent follow-up subsystem. Calculate the generalized short-circuit ratio of the equivalent grid subsystem and the equivalent follow-up subsystem respectively, and use the generalized short-circuit ratio as a quantitative indicator of grid strength.

[0010] S3. Select the nominal system model and determine the critical value for small disturbance stability of the nominal system by plotting the dominant eigenvalue locus.

[0011] S4. Plot the frequency domain characteristic curves of the singular values ​​of the uncertainty perturbation and determine the upper bound of the uncertainty perturbation;

[0012] S5. Plot the complementary sensitivity peak curves of the decoupled nominal system when connected to AC networks with different grid strengths, and combine the upper bound of uncertainty perturbation to quantify the critical value and margin of robust stability from the perspective of grid strength.

[0013] Preferably, the multiplicative perturbation model of the hybrid multi-feed system specifically includes:

[0014] Nominal system equipment side:

[0015]

[0016] Where: Y GFL (s) indicates the dynamics of the network device, Y PLL (s) represents the nominal admittance of the grid-connected converter, Y GFM (s) represents the dynamics of network-connected devices, Y GF (s) represents the nominal admittance of the grid-type converter, and S1 and S2 are diagonal matrices formed by the capacity ratios of the grid-type converter and the grid-connected converter, respectively. For the Kronecker product, e Jθ and e -Jθ θ is the coordinate transformation matrix between the global coordinate system and the local coordinate system, where θ represents the steady-state phase angle difference between the two coordinate systems.

[0017] Nominal system network side:

[0018]

[0019] Where: Y multi_grid(s) represents the network-side dynamics, B matrix is ​​the node admittance matrix of the AC network, N is the number of converter feed-in nodes (internal nodes in the network have been eliminated by Kron Reduction method), ω0 is the nominal frequency of the system, and τ is the R / L ratio of the line.

[0020] Uncertainty perturbation:

[0021]

[0022] Where Δ1(s) is the block diagonal matrix formed by the perturbations corresponding to n grid-type converters in the hybrid system, Δ2(s) is the block diagonal matrix formed by the perturbations corresponding to m grid-type converters in the hybrid system, and diag represents the block diagonal matrix. PLL,i (s)(i=1,K,n) represents the i-th perturbation corresponding to the mesh converter, Δ GF,j (s)(j=1,K,m) represents the perturbation corresponding to the j-th grid-type converter. Let be the device admittance matrix of the i-th grid-connected converter in the global coordinate system of the actual hybrid system. Let be the device admittance matrix in the global coordinate system of the j-th grid-type converter in the actual hybrid system.

[0023] Preferably, by segmenting the dynamics of the hybrid multi-infeed system equipment, the hybrid multi-infeed system is equivalent to an equivalent network subsystem and an equivalent tracking network subsystem, specifically:

[0024] The equivalent network subsystem The closed-loop dynamics are:

[0025]

[0026]

[0027]

[0028] in: To account for the admittance matrix of the grid-type converter, which takes into account uncertainties on the equipment side, B redv This is the equivalent network node admittance matrix after Krona reduction, where # indicates that a control loop is formed between the device dynamics on the left and the network dynamics on the right, and gSCR v For equivalent network subsystems The generalized short-circuit ratio describes the low-frequency grid strength of the hybrid system, and eig(·) is a function for calculating the eigenvalues ​​of the matrix ·.

[0029] The equivalent network subsystem The closed-loop dynamics are:

[0030]

[0031] B redp =B 11

[0032]

[0033] in: To account for the admittance matrix of the grid-connected converter, which takes into account uncertainties on the equipment side, B redp To delete the submatrices corresponding to the rows and columns of the network converter nodes in matrix B, gSCR p For equivalent network subsystem The generalized short-circuit ratio describes the grid strength in the subsynchronous frequency band of the hybrid system, and Δλ(s) is the perturbation caused by the dynamics of the grid-type converter in the equivalent network.

[0034] Preferably, the hybrid multi-feed system uses a robust stability criterion based on the small gain theorem to determine robust stability, specifically:

[0035] If the uncertainty perturbs Δ(s) H ∞ If the norm has an upper bound, then a sufficient condition for the robust stability of a hybrid multi-feed system is:

[0036] 1) The nominal system of the equivalent subsystem is stable with small disturbances, that is:

[0037]

[0038] Among them: gSCR v For equivalent network subsystems The generalized short-circuit ratio, CgSCR v gSCR is the critical value for small-interference stability of the nominal system in the low-frequency band. p For equivalent network subsystem The generalized short-circuit ratio, CgSCR p This is the critical value for the nominal system stability under small disturbances in the subsynchronous frequency band;

[0039] 2) The grid-connected / grid-connected converter's ability to support grid voltage meets the robust stability requirements:

[0040]

[0041] Among them: CRgSCR v For the critically robust generalized short-circuit ratio in the low-frequency band, CRgSCR p The critical robust generalized short-circuit ratio for the subsynchronous frequency band.

[0042] Preferably, the margin for robust stability under the power grid strength perspective, as quantified by the upper bound of the uncertainty perturbation, is specifically as follows:

[0043]

[0044] Where: η1 is the robust stability margin in the low-frequency band, η2 is the robust stability margin in the subsynchronous frequency band, and CRgSCR v For the critically robust generalized short-circuit ratio in the low-frequency band, CRgSCR p For the subsynchronous band critical robust generalized short-circuit ratio, gSCR v For equivalent network subsystems The generalized short-circuit ratio, gSCR p For equivalent network subsystem The generalized short-circuit ratio.

[0045] Preferably, the step of selecting a nominal system model and determining the critical value for small-disturbance stability of the nominal system by plotting the dominant eigenvalue trajectory specifically involves: selecting a nominal system model and determining the critical value CgSCR for small-disturbance stability of the nominal networked system by using the low-frequency dominant eigenvalue trajectory. v The critical value CgSCR for small-interference stability of the nominal tracking network system was determined by using the dominant eigenvalue trajectory of the subsynchronous frequency band. p .

[0046] Preferably, the use of the generalized short-circuit ratio (GSCR) as a quantitative indicator of grid strength specifically involves: based on the eigenvalue decoupling theory of the GSCR, a homogeneous N-infeed system is dynamically characterized by N independent single-infeed systems. The GSCR gSCR is used to characterize the grid strength of the weakest single-infeed system. For grid-connected systems, there is... For network-type systems, there are Among them, SCR i The short-circuit ratio corresponding to the i-th single-feed system.

[0047] Preferably, the step of plotting the frequency domain characteristic curve of the singular value of the uncertainty perturbation and determining the upper bound of the uncertainty perturbation specifically involves: plotting the frequency domain characteristic curve of the singular value of the uncertainty perturbation Δ(s) according to the maximum modulus theorem, and determining the H of the uncertainty perturbation Δ(s) through the peak value of the frequency domain characteristic curve. ∞ The upper bound of the norm is calculated as follows:

[0048]

[0049] Where, δ p δ is the reciprocal of the upper bound of the perturbation Δ1(s). v The upper bound of the perturbation Δ2(s) is the reciprocal, sup represents the maximum value, and σ is the maximum value. max [·] represents the maximum singular value of the matrix.

[0050] Preferably, the step of plotting the complementary sensitivity peak curves when the decoupled nominal system is connected to AC networks of different grid strengths includes:

[0051] Establish an explicit relationship between complementary sensitivity and short-circuit ratio (SCR):

[0052]

[0053] Where: Y C (s) represents the admittance matrix of grid-type and network-type converters in a unified manner. For matrix SB -1 The i-th eigenvalue corresponds to the reciprocal of the short-circuit ratio of the i-th single-feed system after decoupling; W is the eigenvector matrix, which undergoes a similar diagonal transformation: κ2(W) is the spectral condition number of matrix W, when SB -1 When it is a symmetric matrix, κ2(W) = 1;

[0054] Using the generalized short-circuit ratio gSCR to characterize the grid strength of the weakest single-infeed system, the explicit relationship between the generalized short-circuit ratio and the peak complementary sensitivity is as follows:

[0055]

[0056] Where gSCR is the generalized short-circuit ratio of a homogeneous multi-infeed system, and for a homogeneous multi-infeed grid system, For isomorphic multi-feed network systems

[0057] Preferably, the step of plotting the complementary sensitivity peak curves of the decoupled nominal system when connected to AC networks with different grid strengths, and combining the upper bound of uncertainty perturbation to quantify the critical value of robust stability from the perspective of grid strength, specifically includes:

[0058] Drawing the weakest single-infeed system after decoupling from the nominal and mesh system, connected to different generalized short-circuit ratios gSCR p The complementary sensitivity peak curves of the AC system, in which the critical robust generalized short-circuit ratio CRgSCR in the subsynchronous band is shown. p The corresponding ordinate is δ p / κ2(W p The generalized short-circuit ratio gSCR at that time p The value, and the corresponding calculation expression is:

[0059]

[0060] Among them: W p To extend the admittance matrix The eigenvector matrix.

[0061] Drawing the weakest single-infeed system after decoupling of the nominal network system connected to different generalized short-circuit ratios gSCR v The complementary sensitivity peak curves of the AC system, where the critical robust generalized short-circuit ratio CRgSCR in the low-frequency band is shown.v The corresponding ordinate is δ v / κ2(W v The generalized short-circuit ratio gSCR at that time v The value, and the corresponding calculation expression is:

[0062]

[0063] Among them: W v To extend the admittance matrix The eigenvector matrix.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] (1) This invention clearly presents the mechanism and analytical relationship between the generalized short-circuit ratio and the robust stability of the hybrid multi-infeed system. The larger the generalized short-circuit ratio of the equivalent grid subsystem, the stronger the grid converter's ability to support the grid voltage and the better the robust stability in the subsynchronous frequency band. Conversely, the smaller the generalized short-circuit ratio of the equivalent grid subsystem, the lower the risk of low-frequency oscillation. In other words, the proposed robust stability quantitative evaluation method is strictly based on mathematical derivation, calculation and simulation, and has higher reliability.

[0066] (2) The critical value for robust stability of the present invention is the short-circuit ratio of the weakest single-feed root network / network type system when considering uncertainty. Its calculation only involves 2×2 matrix operations, avoiding the "curse of dimensionality" problem caused by high-order matrix operations, and the calculation is more convenient.

[0067] (3) The present invention characterizes the differences in the external characteristics of each converter with multiplicative uncertainty perturbation. The relationship between the nominal system complementary sensitivity peak and the grid strength is usually only related to the control mode. It is also applicable to complex scenarios in which there are converters with different control parameters, control structures and operating modes in the system, and has a certain degree of universality. Attached Figure Description

[0068] Figure 1 This is a flowchart of the method of the present invention;

[0069] Figure 2 This is a flowchart illustrating a specific embodiment of the present invention;

[0070] Figure 3 This is a schematic diagram of a multi-converter grid-connected system in an embodiment of the present invention;

[0071] Figure 4 This is a schematic diagram of the multiplicative perturbation model of the hybrid multi-feed system in an embodiment of the present invention;

[0072] Figure 5 This is a schematic diagram illustrating the model deconstruction method of the hybrid multi-feed system in an embodiment of the present invention;

[0073] Figure 6 This is a comparison diagram of the low-frequency dominant eigenvalue trajectories of the hybrid multi-feed system and its equivalent network subsystem in this embodiment of the invention.

[0074] Figure 7 This is a comparison diagram of the dominant eigenvalue trajectories of the hybrid multi-feed system and its equivalent tracking network subsystem in the embodiments of the present invention in the subsynchronous frequency band.

[0075] Figure 8 This is a graph showing the distribution of uncertainty perturbation with frequency in an embodiment of the present invention;

[0076] Figure 9 This is a graph showing the relationship between the complementary sensitivity peak and gSCRp in an embodiment of the present invention.

[0077] Figure 10 This is a schematic diagram illustrating the critical robust stability of the equivalent root network subsystem in an embodiment of the present invention. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0079] Example

[0080] like Figure 1 As shown in the figure, this embodiment provides a method for quantitatively evaluating the robust stability of a multi-feed system with a mesh-type hybrid configuration. The method includes the following steps:

[0081] S1. Construct a multiplicative perturbation model of the hybrid multi-infeed system, and input the initial value of the rated capacity of the hybrid multi-infeed system and the original data such as the equivalent AC network line impedance;

[0082] S2. Equivalently convert the hybrid multi-feed system into an equivalent grid subsystem Σ1 and an equivalent follow-mesh subsystem Σ2, and calculate the generalized short-circuit ratio gSCR of the equivalent grid subsystem and the equivalent follow-mesh subsystem, respectively. v and gSCR p The generalized short-circuit ratio is used as a quantitative indicator of power grid strength.

[0083] S3. Select the nominal system model and determine the critical value for small-disturbance stability of the nominal system by plotting the dominant eigenvalue trajectory using MATLAB simulation. Specifically, determine the critical value CgSCR for small-disturbance stability of the nominal networked system by using the dominant eigenvalue trajectory in the low-frequency band. vThe critical value CgSCR for small-interference stability of the nominal tracking network system was determined by using the dominant eigenvalue trajectory of the subsynchronous frequency band. p ;

[0084] S4. Plot the frequency domain characteristic curves of the singular values ​​of the uncertainty perturbation to determine the upper bound of the uncertainty perturbation. Specifically, plot the frequency domain characteristic curves of the singular values ​​of the uncertainty perturbation Δ1(s) and Δ2(s) to determine the H of the perturbation. ∞ upper bound of norm δ p -1 and δ v -1 ;

[0085] S5. Plot the complementary sensitivity peak curves of the decoupled nominal system connected to AC networks with different grid strengths, and quantify the critical value and margin of robust stability from the perspective of grid strength in conjunction with the upper bound of uncertainty perturbation. Specifically, plot the peak curves of the decoupled nominal grid-type system connected to AC networks with different gSCRs. v The complementary sensitivity peak curves of the AC system are used to solve the critical robust generalized short-circuit ratio CRgSCR in the low-frequency band. v And robust stability margin η1; plot the decoupled nominal and network topology system accessing different gSCRs. p The complementary sensitivity peak curves of the AC system are used to solve the critical robust generalized short-circuit ratio CRgSCR in the subsynchronous band. p And robust stability margin η2.

[0086] The method of this embodiment will now be described in detail.

[0087] First, a multiplicative perturbation model of the hybrid multi-infeed system, taking into account equipment uncertainties, is established. Figure 3 The multi-converter grid-connected system shown includes n grid-connected converters (nodes 1 to n) and m network-connected converters (nodes n+1 to N). The dynamic external characteristics of each grid-connected converter and each network-connected converter are different. The differences mainly come from the different control parameters, control structures and operating modes used by the converters.

[0088] Using the perturbation Δ(s) to characterize the uncertainty on the equipment side, a multiplicative perturbation model for a hybrid multi-feed system can be obtained, such as... Figure 4 As shown, the model consists of the following three parts:

[0089] 1) Nominal system equipment side:

[0090]

[0091] Among them, Y GFL (s) indicates the dynamics of the network device, Y PLL (s) represents the nominal admittance of the grid-connected converter, YGFM (s) represents the dynamics of network-connected devices, Y GF (s) represents the nominal admittance of the grid-type converter, and S1 and S2 are diagonal matrices formed by the capacity ratios of the grid-type and grid-connected converters, respectively. Jθ and e -Jθ θ is the coordinate transformation matrix between the global coordinate system and the local coordinate system, where θ represents the steady-state phase angle difference between the two coordinate systems.

[0092] 2) Nominal system network side:

[0093]

[0094] Where: Y multi_grid (s) represents the network-side dynamics, ω0 is the nominal frequency of the system, and τ is the R / L ratio of the line. The B matrix is ​​the node admittance matrix of the AC network, which can be represented in blocks as follows:

[0095]

[0096] 3) Uncertainty perturbations:

[0097]

[0098] Where Δ1(s) is the block diagonal matrix formed by the perturbations corresponding to n grid-type converters in the hybrid system, Δ2(s) is the block diagonal matrix formed by the perturbations corresponding to m grid-type converters in the hybrid system, and diag represents the block diagonal matrix. PLL,i (s)(i=1,K,n) represents the i-th perturbation corresponding to the mesh converter, Δ GF,j (s)(j=1,K,m) represents the perturbation corresponding to the j-th grid-type converter. Let be the device admittance matrix of the i-th grid-connected converter in the global coordinate system of the actual hybrid system. Let be the device admittance matrix in the global coordinate system of the j-th grid-type converter in the actual hybrid system.

[0099] Then, the grid-type converter is dynamically merged into the equivalent network, such as... Figure 5 As shown, the hybrid multi-infeed system is decomposed into two subsystems on the equipment side, each dominated by a single type of converter. Since the closed-loop poles of the original hybrid multi-infeed system are the combination of the closed-loop poles of the two decomposed subsystems, it can be proven that the original hybrid multi-infeed system is stable if and only if the two subsystems are stable.

[0100] To make the robust stability analysis method based on the small gain theorem applicable to both subsystems, it is also necessary to construct an equivalent heterogeneous multi-infeed grid-connected / grid-connected system to approximate the dominant oscillation modes Σ2 and Σ1 of the two subsystems, and quantify the grid voltage support capability of the grid-connected / grid-connected converter for the hybrid multi-infeeded system from the perspective of grid strength.

[0101] The equivalent network subsystem is obtained by performing Kron reduction on the network side.

[0102]

[0103] in: To account for the admittance matrix of the grid-type converter, which takes into account uncertainties on the equipment side, B redv gSCR is the equivalent network node admittance matrix after Krona reduction; v For equivalent network subsystems The generalized short-circuit ratio is also a quantitative indicator of power grid strength in the low-frequency band.

[0104] Equivalent network subsystem The closed-loop dynamics are:

[0105]

[0106] B redp =B 11

[0107] gSCR p =min[eig(S1) -1 B redp )]+Δλ(s)

[0108] in: To account for the admittance matrix of the grid-connected converter, which takes into account uncertainties on the equipment side, B redp To delete the submatrices corresponding to the rows and columns of the network converter nodes in matrix B; gSCR p For equivalent network subsystem The generalized short-circuit ratio is also a quantitative indicator of the subsynchronous frequency band power grid strength; Δλ(s) is the perturbation caused by the dynamics of the grid-type converter in the equivalent network, which can be ignored since the grid-type converter usually has high admittance.

[0109] Figure 6 and Figure 7 The original hybrid multi-feed system and its equivalent subsystem obtained through MATLAB simulation are shown. The comparison of the dominant eigenvalue trajectories in the low-frequency / subsynchronous frequency bands shows that the dominant eigenvalue trajectories are approximately fitted, indicating that the robust stability of the hybrid multi-feed system is characterized by its equivalent subsystem.

[0110] To reduce the conservatism of the robust stability criterion, a follow-mesh / network-building device that minimizes perturbations is selected as the nominal model. Based on the characteristic equation of the "weakest" single-feed follow-mesh / network-building system after decoupling of the nominal follow-mesh / network-building system and gSCR... p / gSCR v Explicit relationships between them:

[0111] c(s) = det(Y) PLL (s)+gSCR p *F(s))

[0112] c(s) = det(Y) GF (s)+gSCR v *F(s))

[0113] Plot the dominant eigenvalue trajectories in the subsynchronous / low-frequency bands of the nominal network / networked system using MATLAB. When the real part of the dominant eigenvalue is 0, the system is considered critically stable under small disturbances, thus determining the critical value CgSCR for the nominal system's stability under small disturbances. p / CgSCR v .

[0114] The robust stability quantification evaluation process for the two equivalent subsystems is consistent. The following section uses the equivalent root network subsystem as an example. For example, its device uncertainty perturbation is expressed as:

[0115]

[0116] in: For equivalent network subsystem The device admittance matrix in the global coordinate system of the i-th converter, e Jθ Y PLL (s)e -Jθ This is the device admittance matrix in the nominal network system global coordinate system.

[0117] Analyze the above uncertainty perturbation and plot σ in MATLAB. max [Δ PLL,i The distribution curve of (jω) with frequency (e.g.) Figure 8 As shown), determine the peak value of the perturbation and its reciprocal δ. p .

[0118] The uncertainty perturbation Δ1(s) on the equipment side affects the critical value CgSCR of the nominal following mesh system's small disturbance stability. p By solving the following equations inversely, the critical robust generalized short-circuit ratio CRgSCR can be obtained. p Explicit expression:

[0119]

[0120] The above solution process is equivalent to plotting the "weakest" single-feed system after decoupling from the nominal mesh system in MATLAB, connected to different gSCRs. p The complementary sensitivity peak curve of the AC system (e.g.) Figure 9 As shown), CRgSCR p The corresponding ordinate is δ p / κ2(W p gSCR at ) p Value. Equivalent to a network subsystem. A schematic diagram of the critical robust stability is shown below. Figure 10 .

[0121] That is, the equivalent network subsystem based on the generalized short-circuit ratio is obtained. Robust stability and its critical value quantification evaluation index can define the robust stability margin of the system in the subsynchronous frequency band as:

[0122] η2=gSCR p -CRgSCR p

[0123] Similarly, the equivalent network subsystem can be calculated. Critically robust generalized short-circuit ratio CRgSCR v And quantify the robust stability margin of the system in the low-frequency band:

[0124] η1=CRgSCR v -gSCR v

[0125] Simulation results show that the equivalent subsystem model constructed in this embodiment can fit the dominant characteristic root trajectory of the original hybrid multi-feed system, simplifying the robust stability analysis of the complex system to the robust stability analysis of two subsystems. Furthermore, the robust stability quantification evaluation method that combines the generalized short-circuit ratio theory and the small gain theorem can not only take into account uncertainties, but also simplify the problem of solving high-order matrices to solving 2×2 matrices, greatly reducing the amount of computation and having application value in practical engineering.

[0126] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for quantitatively evaluating the robust stability of a hybrid multi-feed system with a network structure, characterized in that, Includes the following steps: S1. Construct a multiplicative perturbation model for a hybrid multi-feed system; S2. Equivalently convert the hybrid multi-feed system into an equivalent grid subsystem and an equivalent follow-up subsystem. Calculate the generalized short-circuit ratio of the equivalent grid subsystem and the equivalent follow-up subsystem respectively, and use the generalized short-circuit ratio as a quantitative indicator of grid strength. S3. Select the nominal system model and determine the critical value for small disturbance stability of the nominal system by plotting the dominant eigenvalue locus. S4. Plot the frequency domain characteristic curves of the singular values ​​of the uncertainty perturbation and determine the upper bound of the uncertainty perturbation; S5. Plot the complementary sensitivity peak curves of the decoupled nominal system when connected to AC networks with different grid strengths, and combine the upper bound of uncertainty perturbation to quantify the critical value and margin of robust stability from the perspective of grid strength. By segmenting the dynamics of the hybrid multi-infeed system devices, the hybrid multi-infeed system is equivalent to an equivalent network subsystem and an equivalent tracking network subsystem, specifically: The equivalent network subsystem The closed-loop dynamics are: in: The admittance matrix of the grid-type converter takes into account uncertainties on the equipment side; This is the equivalent network node admittance matrix after Krona reduction. This indicates that a control closed loop is formed between the dynamics of the devices on the left and the dynamics of the network on the right; The nominal frequency of the system. For the line R / L ratio; For Kronecker product; B Let be the node admittance matrix of the communication network. They are respectively B The parameters in the first row and first column, the first row and second column, the second row and first column, and the second row and second column; For equivalent network subsystems The generalized short-circuit ratio is used to describe the low-frequency grid strength of a hybrid system; A function for calculating the eigenvalues ​​of a matrix; A diagonal matrix formed by the capacity ratios of grid-type converters; The equivalent network subsystem The closed-loop dynamics are: in: To account for uncertainties on the equipment side, the admittance matrix of the grid-connected converter is... B redp To delete the matrix B Submatrices corresponding to rows and columns of nodes in a medium-grid converter; gSCR p For equivalent network subsystem The generalized short-circuit ratio is used to describe the subsynchronous frequency band grid strength of a hybrid system; The perturbation caused by the dynamics of the network converter in the equivalent network; This is a diagonal matrix formed by the ratio of the capacity of the grid converter; The hybrid multi-feed system employs a robust stability criterion based on the small gain theorem for robust stability determination, specifically: If uncertainty perturbation of If the norm has an upper bound, then a sufficient condition for the robust stability of a hybrid multi-feed system is: 1) The nominal system of the equivalent subsystem is stable with small disturbances, that is: in: For equivalent network subsystems The generalized short-circuit ratio, This is the critical value for small-interference stability of the nominal system in the low-frequency band. For equivalent network subsystem The generalized short-circuit ratio, This is the critical value for the nominal system stability under small disturbances in the subsynchronous frequency band; 2) The grid-connected / grid-connected converter's ability to support grid voltage meets the robust stability requirements: in, CRgSCR v For the critically robust generalized short-circuit ratio in the low-frequency band, CRgSCR p The critical robust generalized short-circuit ratio for the subsynchronous frequency band.

2. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure as described in claim 1, characterized in that, The multiplicative perturbation model of the hybrid multi-feed system specifically includes: Nominal system equipment side: in: This indicates the dynamic status of network-type devices. The nominal admittance of the grid-connected converter, Indicates the dynamics of network-type devices. The nominal admittance of the grid-connected converter. and These are diagonal matrices formed by the capacity ratios of the grid-type converter and the network-type converter, respectively. and This is the coordinate transformation matrix between the global coordinate system and the local coordinate system. This represents the steady-state phase angle difference between two coordinate systems; Nominal system network side: in: Indicates network-side dynamics. B The matrix is ​​the node admittance matrix of the communication network. This represents the number of feed nodes to the converter. Uncertainty perturbation: in: For hybrid systems n A block diagonal matrix consisting of perturbations corresponding to a grid converter. For hybrid systems m The block diagonal matrix formed by the perturbations corresponding to each grid-type converter. diag Represents a block diagonal matrix. For the first i A perturbation corresponding to a grid converter. For the first j The perturbation corresponding to a grid-type converter. For the actual hybrid system i The device admittance matrix in the global coordinate system of a grid converter. For the actual hybrid system j Device admittance matrix in the global coordinate system of a grid-type converter.

3. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure according to claim 2, characterized in that, The margin for robust stability under the uncertainty perturbation upper bound quantifies the power grid strength perspective, specifically as follows: in: For robust stability margin in the low-frequency band, For robust stability margin of subsynchronous frequency band, For the critically robust generalized short-circuit ratio in the low-frequency band, The critical robust generalized short-circuit ratio for the subsynchronous frequency band. For equivalent network subsystems The generalized short-circuit ratio, For equivalent network subsystem The generalized short-circuit ratio.

4. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure as described in claim 2, characterized in that, The selection of the nominal system model and the determination of the critical value for small-disturbance stability of the nominal system by plotting the dominant eigenvalue trajectory are specifically as follows: The nominal system model is selected, and the critical value for small-disturbance stability of the nominal networked system is determined by using the low-frequency dominant eigenvalue trajectory. CgSCR v The critical value for small-interference stability of the nominal tail network system is determined by the dominant eigenvalue trajectory in the subsynchronous frequency band. CgSCR p .

5. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure according to claim 2, characterized in that, The use of the generalized short-circuit ratio as a quantitative indicator of power grid strength specifically involves: based on the characteristic root decoupling theory of the generalized short-circuit ratio, isomorphic... N Dynamic feeding system N Characterized by an independent single-feed system, using the generalized short-circuit ratio Characterizing the grid strength of the weakest single-infeed system, for grid-connected systems, we have: For network-type systems, there are ,in, Corresponding to the The short-circuit ratio of a single-feed system.

6. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure according to claim 2, characterized in that, The step of plotting the frequency domain characteristic curves of the singular values ​​of the uncertainty perturbation and determining the upper bound of the uncertainty perturbation specifically involves: plotting the uncertainty perturbation according to the maximum modulus theorem. The frequency domain characteristic curve of singular values ​​is used to determine the uncertainty perturbation through the peak value of the frequency domain characteristic curve. of The upper bound of the norm is calculated as follows: in: For perturbation The reciprocal of the upper bound value, For perturbation The reciprocal of the upper bound value, where sup represents the maximum value. It is the largest singular value of the matrix.

7. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure according to claim 6, characterized in that, The process of plotting the complementary sensitivity peak curves of the decoupled nominal system when connected to AC networks of different grid strengths includes: Establish complementary sensitivity and short-circuit ratio Explicit relationship between them: in: To provide a unified representation of the admittance matrix for both grid-type and mesh-type converters, For matrix SB -1 The The eigenvalue corresponds to the after decoupling. The reciprocal of the short-circuit ratio of a single-feed system; Given an eigenvector matrix, there exists a similar diagonal transformation: ; For matrix W The spectral condition number, when When it is a symmetric matrix, ; With generalized short-circuit ratio Characterizing the grid strength of the weakest single-infeed system, the explicit relationship between the generalized short-circuit ratio and the peak complementary sensitivity is as follows: in: gSCR For a homogeneous multi-infeed system, the generalized short-circuit ratio is given by the following formula: (This is the generalized short-circuit ratio for a homogeneous multi-infeed grid system.) For isomorphic multi-feed network systems, .

8. The robust stability quantitative evaluation method for a hybrid multi-feed system with a mesh structure according to claim 7, characterized in that, The process of plotting the complementary sensitivity peak curves of the decoupled nominal system connected to AC networks of different grid strengths, and combining this with the upper bound of uncertainty perturbation to quantify the critical value of robust stability from the perspective of grid strength, specifically includes: Drawing the weakest single-infeed system with different generalized short-circuit ratios after decoupling the nominal and mesh systems The complementary sensitivity peak curves of the AC system, in which the critical robust generalized short-circuit ratio in the subsynchronous band is shown. The corresponding vertical axis is Generalized short-circuit ratio at time The value, and the corresponding calculation expression is: in: To extend the admittance matrix eigenvector matrix; Plot the weakest single-infeed system after decoupling of the nominal network system with different generalized short-circuit ratios. The complementary sensitivity peak curves of the AC system, where the critical robust generalized short-circuit ratio in the low-frequency band is shown. The corresponding vertical axis is Generalized short-circuit ratio at time The value, and the corresponding calculation expression is: in: To extend the admittance matrix The eigenvector matrix.

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