A method for calculating the nearest saddle-node bifurcation point based on direct current power space

Abstract

This invention discloses a method for calculating the nearest saddle-node bifurcation point based on DC power space, comprising: S1, constructing a power space algebraic equation characterizing the saddle-node bifurcation point of the DC multi-infeed system based on the generalized short-circuit ratio; S2, constructing the normal vector of the voltage stability boundary in the power space using the eigenvector corresponding to the generalized short-circuit ratio; S3, performing iterative calculation using the power space algebraic equation and the normal vector of the voltage stability boundary to obtain the shortest distance from the current operating point to the voltage stability boundary; S4, using the shortest distance in S3 as the distance from the current operating point to the nearest saddle-node bifurcation point. This invention, by constructing a set of power space algebraic equations characterizing the saddle-node bifurcation point of the system and combining them with the normal vector of the voltage stability boundary in the power space for iterative calculation of the nearest saddle-node bifurcation point, directly and accurately obtains the distance from the current operating point to the nearest saddle-node bifurcation point, enabling rapid and effective early warning of stability risks.

Description

Technical Field

[0001] This invention relates to the field of voltage saddle bifurcation technology, and in particular to a method for calculating the nearest saddle bifurcation point based on DC power space. Background Technology

[0002] Due to the geographical separation between my country's new energy power generation resources and load centers, large-scale DC transmission projects are used for long-distance power transmission. With the continuous increase in the scale of high-voltage DC transmission based on grid-connected converters, multi-infeed receiving-end systems face severe voltage stability challenges. In particular, due to the randomness and intermittency of new energy power generation, as well as fluctuations in the receiving-end grid load, the operating point of multi-infeed DC systems constantly changes. To ensure the safe and stable operation of the receiving-end grid, it is necessary to assess the voltage stability margin. For multi-infeed systems, there are three common short-circuit ratio indices: the multi-infeed short-circuit ratio proposed by the CIGRE DC Working Group, the equivalent effective short-circuit ratio proposed by Denis et al. of ETH Zurich, and the generalized short-circuit ratio proposed by Professor Xin Huanhai of Zhejiang University, representing network mode decoupling indices. However, these indices can only quantify the voltage stability margin of multi-infeed DC systems to a certain extent and cannot indicate the nearest saddle-node bifurcation point to the current operating point, making it difficult to provide dispatchers with more direct information on unstable operating points.

[0003] The "Method and Device for Judging Power System Stability Based on Generalized Operating Short-Circuit Ratio" disclosed in Chinese patent literature, publication number CN110137943B, published on 2020-10-23, includes inputting power flow information from the power system into a generalized operating short-circuit ratio (GOSCR) model; comparing the output value of the GOSCR model with the value 1; if the value is greater than 1, the power system is in a stable state; if the value is equal to 1, the power system is in a critical stable state; if the value is less than 1, the power system is unstable. This technology considers the influence of the synchronous machine and its excitation voltage control dynamic characteristics, and establishes a new generalized operating short-circuit ratio model, making the judgment of power system stability more accurate. At the same time, the low dimensionality of the power voltage sensitivity factor reduces the computational load of the model and makes the operation faster. However, this technology can only reflect whether the power system is stable, and cannot intuitively reflect the voltage stability margin more accurately through the distance between the current operating point and the nearest saddle-node bifurcation point, and cannot provide a fast and effective early warning of stability risks. Summary of the Invention

[0004] This invention aims to overcome the problem in existing technologies where the short-circuit ratio index of multi-infeed systems cannot fully quantify and determine the voltage stability margin of DC multi-infeed systems. It provides a method for calculating the nearest saddle-node bifurcation point based on DC power space. By constructing a set of power space algebraic equations characterizing the saddle-node bifurcation point of the system, and combining the normal vector of the voltage stability boundary in the power space, the nearest saddle-node bifurcation point is calculated iteratively. This allows for the direct and accurate determination of the distance from the current operating point to the nearest saddle-node bifurcation point, enabling rapid and effective early warning of stability risks.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for calculating the nearest saddle-node bifurcation point based on DC power space includes:

[0007] S1. Construct a power space algebraic equation characterizing the saddle junction bifurcation point of the DC multi-infeed system based on the generalized short-circuit ratio of the DC multi-infeed system.

[0008] S2. Construct the normal vector of the voltage stability boundary in the power space using the eigenvector corresponding to the generalized short-circuit ratio.

[0009] S3. Use the power space algebraic equation and the normal vector of the voltage stability boundary to perform iterative calculations to obtain the shortest distance from the current operating point to the voltage stability boundary;

[0010] S4. The shortest distance described in S3 is taken as the distance from the current running point to the nearest saddle junction bifurcation point.

[0011] This invention establishes a mathematical connection between saddle-node bifurcation and voltage stability boundary, and adopts the generalized short-circuit ratio index. When the generalized short-circuit ratio corresponding to the current operating point approaches its critical value, the power of the multi-infeed system will approach the voltage stability boundary in the power space. When a saddle-node bifurcation occurs in the DC multi-infeed system, a stability boundary surface will be generated in the power space, which is the voltage stability boundary. The current operating point can approach this surface in any direction, but it can only reach the surface fastest along the normal vector direction of the voltage stability boundary, i.e., the nearest saddle-node bifurcation point. This indicates that the normal vector direction is the direction with the worst voltage stability. Therefore, it is necessary to indicate the distance from the current operating point to the nearest saddle-node bifurcation point in a timely manner. The closer the distance, the closer it is to the critical point of voltage stability, thereby providing relevant personnel with a fast and effective early warning of stability risks.

[0012] Preferably, the construction steps of the power space algebraic equation include:

[0013] The minimum eigenvalue of the extended admittance matrix of the DC multi-infeed system is taken as the generalized short-circuit ratio gSCR;

[0014] The power space algebraic equations representing the saddle node bifurcation of the system are as follows:

[0015]

[0016] Where B is the nodal admittance matrix of the Thevenin equivalent circuit of the DC multi-infeed system, P is the diagonal matrix of the multi-infeed DC power transmission, and u∈R n Let be the right eigenvector corresponding to the zero eigenvalue of matrix B-gSCR×P.

[0017] In this invention, the distance from the current operating point to the nearest saddle-node bifurcation point is the distance to the voltage stability boundary in the power space; the point on the voltage stability boundary is the saddle-node bifurcation point. In the power space algebraic equations of this invention, when the generalized short-circuit ratio gSCR equals the critical generalized short-circuit ratio CgSCR, the power space algebraic equations have a solution, and the matrix B-gSCR×P is singular, indicating that the matrix B-gSCR×P has an eigenvalue of 0, which means that the current operating point coincides with the saddle-node bifurcation point, and the system will experience voltage instability. Therefore, the difference between the current system's generalized short-circuit ratio and the critical short-circuit ratio can reflect the distance from the current operating point to the voltage stability boundary, reflecting the voltage stability margin.

[0018] Preferably, the generalized short-circuit ratio is:

[0019] gSCR=minλ(J eq )

[0020] J eq ≈P -1 B

[0021] Where λ represents the eigenvalue of the matrix; J eq To extend the admittance matrix; B is the nodal admittance matrix of the Thevenin equivalent circuit of the DC multi-infeed system; P = diag(P1, ..., P n ), P i This represents the active power output at node i of the DC multi-infeed system.

[0022] In this invention, the extended admittance matrix in the generalized short-circuit ratio gSCR reflects the influence of DC output active power and network structure and parameters on the voltage stability margin of the multi-infeed system. Simultaneously, similar to the short-circuit ratio in AC / DC systems, the generalized short-circuit ratio gSCR has a critical generalized short-circuit ratio CgSCR, corresponding to the operating conditions where the Jacobian matrix of the DC multi-infeed system is singular or saddle-node bifurcation occurs. The distance between gSCR and CgSCR reflects the voltage stability margin of the multi-infeed system. Using the generalized short-circuit ratio, the saddle-node bifurcation problem of large-scale DC multi-infeed systems can be transformed into a saddle-node bifurcation problem with an extended admittance matrix for study, effectively reducing the matrix size and computational load. The critical generalized short-circuit ratio of the DC multi-infeed system is generally an empirical value, with CgSCR set to 3.

[0023] As a preferred option, v∈R nand u∈R n These are the left and right eigenvectors corresponding to the zero eigenvalues ​​of the generalized short-circuit ratio matrix B-gSCR×P, respectively; the normal vector of the voltage stability boundary is... This represents the element-wise product vector at corresponding positions between vectors. The matrix B-gSCR×P is a symmetric matrix, and the left eigenvector v is equal to the right eigenvector u; the normal vector of the voltage stability boundary is...

[0024] In this invention, the normal vector of the voltage stability boundary is used to provide the direction of power vector increase during the iterative calculation of the saddle-node bifurcation point. Since B-gSCR×P is a symmetric matrix, its left and right eigenvectors corresponding to its zero eigenvalue are equal. In this case, the normal vector can be uniformly represented by the right eigenvector. This facilitates subsequent iterative calculations.

[0025] Preferably, step S3 specifically includes the following steps:

[0026] S31. Obtain the Thevenin equivalent circuit node admittance matrix B of the DC multi-infeed system, and obtain the power vector p at the current operating point. i-1 ;

[0027] S32, Calculate the power vector p i-1 The generalized short-circuit ratio and its corresponding right eigenvector u at time i-1 ;

[0028] S33, Update Power Vector This is the normal vector of the voltage stability boundary at this point;

[0029] S34, p i Substituting the critical generalized short-circuit ratio CgSCR into the power space algebraic equations and solving for the distance l from the current operating point to the voltage stability boundary, we can obtain the distance l. i and the new right eigenvector u i ;

[0030] S35. Determine whether the eigenvectors satisfy the convergence criterion |u i -u i-1 | 2 If ≤ε, then let i = i + 1 and return to S32 for iterative calculation; if satisfied, then stop iterative calculation.

[0031] In this invention, the generalized short-circuit ratio represents the current operating point, and its corresponding right eigenvector can be used to construct the normal vector of the voltage stability boundary. The nearest saddle-node bifurcation point can be found along the direction of the normal vector. Therefore, a new power vector is generated along the normal vector, and the new power vector p iBy substituting the critical generalized short-circuit ratio CgSCR and the nodal admittance matrix B into the power space algebraic equations and solving them, the distance l from the current operating point to the voltage stability boundary can be obtained. i When the eigenvectors satisfy the convergence criterion, it means that the shortest distance from the current running point to the voltage stability boundary has been found. If the convergence criterion is not satisfied, it means that it is not the shortest distance and further iterative calculation is needed.

[0032] The present invention has the following beneficial effects: by constructing a power space algebraic equation system characterizing the saddle-node bifurcation point of the system, and combining the normal vector of the voltage stability boundary in the power space to perform iterative calculation of the nearest saddle-node bifurcation point, the distance from the current operating point to the nearest saddle-node bifurcation point can be obtained directly and accurately, enabling rapid and effective early warning of stability risks. Attached Figure Description

[0033] Figure 1 This is a flowchart of the method for calculating the nearest saddle-node bifurcation point in this invention;

[0034] Figure 2 This is the Thevenin equivalent diagram of the three-feed DC system in this embodiment of the invention;

[0035] Figure 3 This is the CIGRE classic DC model used in the embodiments of the present invention;

[0036] Figure 4 This is a flowchart of the saddle-node bifurcation point iterative algorithm in an embodiment of the present invention;

[0037] Figure 5 This is the iterative search process for the bifurcation point of the saddle-node in the three-feed system in this embodiment of the invention;

[0038] Figure 6 This is the iterative process of the distance from the current operating point to the voltage stability boundary in this embodiment of the invention. Detailed Implementation

[0039] The present invention will now be further described with reference to the accompanying drawings and specific embodiments.

[0040] like Figure 1 As shown, a method for calculating the nearest saddle-node bifurcation point based on DC power space includes:

[0041] S1. Construct the power space algebraic equation characterizing the saddle-junction bifurcation point of the DC multi-infeed system based on the generalized short-circuit ratio; the generalized short-circuit ratio is:

[0042] gSCR=minλ(J eq )

[0043] J eq ≈P -1 B

[0044] Where λ represents the eigenvalue of the matrix; J eq To extend the admittance matrix; B is the nodal admittance matrix of the Thevenin equivalent circuit of the DC multi-infeed system; P = diag(P1, ..., P n ), P i This represents the active power output at node i of the DC multi-infeed system.

[0045] The steps for constructing the power space algebraic equations include:

[0046] The minimum eigenvalue of the extended admittance matrix of the DC multi-infeed system is taken as the generalized short-circuit ratio gSCR;

[0047] The power space algebraic equations representing the saddle node bifurcation of the system are as follows:

[0048]

[0049] Where B is the nodal admittance matrix of the Thevenin equivalent circuit of the DC multi-infeed system, P is the diagonal matrix of the multi-infeed DC power transmission, and u∈R n Let be the right eigenvector corresponding to the zero eigenvalue of matrix B-gSCR×P.

[0050] S2. Construct the normal vector of the voltage stability boundary in the power space using the eigenvector corresponding to the generalized short-circuit ratio.

[0051] v∈R n and u∈R n These are the left and right eigenvectors corresponding to the zero eigenvalues ​​of the generalized short-circuit ratio matrix B-gSCR×P, respectively; the normal vector of the voltage stability boundary is... This represents the element-wise product vector between corresponding positions. The matrix B-gSCR×P is a symmetric matrix, with the left eigenvector v equal to the right eigenvector u; the normal vector of the voltage stability boundary is...

[0052] S3. Using the power space algebraic equation and the normal vector of the voltage stability boundary, perform iterative calculations to obtain the shortest distance from the current operating point to the voltage stability boundary; specifically including the following steps:

[0053] S31. Obtain the Thevenin equivalent circuit node admittance matrix B of the DC multi-infeed system, and obtain the power vector p at the current operating point. i-1 ;

[0054] S32, Calculate the power vector p i-1 The generalized short-circuit ratio and its corresponding right eigenvector u at time i-1 ;

[0055] S33, Update Power Vector This is the normal vector of the voltage stability boundary at this point;

[0056] S34, p i Substituting the critical generalized short-circuit ratio CgSCR into the power space algebraic equations and solving for the distance l from the current operating point to the voltage stability boundary, we can obtain the distance l. i and the new right eigenvector u i ;

[0057] S35. Determine whether the eigenvectors satisfy the convergence criterion |u i -u i-1 | 2 If ≤ε, then let i = i + 1 and return to S32 for iterative calculation; if satisfied, then stop iterative calculation.

[0058] S4. Use the shortest distance from the current operating point to the voltage stability boundary as the distance from the current operating point to the nearest saddle-node bifurcation point to perform stability risk warning.

[0059] This invention establishes a mathematical connection between saddle-node bifurcation and voltage stability boundary, and adopts the generalized short-circuit ratio index. When the generalized short-circuit ratio corresponding to the current operating point approaches its critical value, the power of the multi-infeed system will approach the voltage stability boundary in the power space. When a saddle-node bifurcation occurs in the DC multi-infeed system, a stability boundary surface will be generated in the power space, which is the voltage stability boundary. The current operating point can approach this surface in any direction, but it can only reach the surface fastest along the normal vector direction of the voltage stability boundary, i.e., the nearest saddle-node bifurcation point. This indicates that the normal vector direction is the direction with the worst voltage stability. Therefore, it is necessary to indicate the distance from the current operating point to the nearest saddle-node bifurcation point in a timely manner. The closer the distance, the closer it is to the critical point of voltage stability, thereby providing relevant personnel with a fast and effective early warning of stability risks.

[0060] In this invention, the distance from the current operating point to the nearest saddle-node bifurcation point is the distance to the voltage stability boundary in the power space; the point on the voltage stability boundary is the saddle-node bifurcation point. In the power space algebraic equations of this invention, when the generalized short-circuit ratio gSCR equals the critical generalized short-circuit ratio CgSCR, the power space algebraic equations have a solution, and the matrix B-gSCR×P is singular, indicating that the matrix B-gSCR×P has an eigenvalue of 0, which means that the current operating point coincides with the saddle-node bifurcation point, and the system will experience voltage instability. Therefore, the difference between the current system's generalized short-circuit ratio and the critical short-circuit ratio can reflect the distance from the current operating point to the voltage stability boundary, reflecting the voltage stability margin.

[0061] In this invention, the extended admittance matrix in the generalized short-circuit ratio gSCR reflects the influence of DC output active power and network structure and parameters on the voltage stability margin of the multi-infeed system. Simultaneously, similar to the short-circuit ratio in AC / DC systems, the generalized short-circuit ratio gSCR has a critical generalized short-circuit ratio CgSCR, corresponding to the operating conditions where the Jacobian matrix of the DC multi-infeed system is singular or saddle-node bifurcation occurs. The distance between gSCR and CgSCR reflects the voltage stability margin of the multi-infeed system. Using the generalized short-circuit ratio, the saddle-node bifurcation problem of large-scale DC multi-infeed systems can be transformed into a saddle-node bifurcation problem with an extended admittance matrix for study, effectively reducing the matrix size and computational load. The critical generalized short-circuit ratio of the DC multi-infeed system is generally an empirical value, with CgSCR set to 3.

[0062] When the minimum eigenvalue of the extended admittance matrix approaches the critical generalized short-circuit ratio, the DC output active power satisfies the following equation:

[0063]

[0064] Among them, I n Let CgSCR be an n-order identity matrix, and let CgSCR be the critical generalized short-circuit ratio determined by the DC system control and circuit parameters, u∈R. n For matrix J eq -CgSCR×I n The right eigenvector corresponding to the zero eigenvalue, which is also gSCR as matrix J eq The right eigenvectors corresponding to non-zero eigenvalues. Matrix J eq -CgSCR×I n If the eigenvalues ​​of the system of equations are all real numbers, then the matrix J is singular (matrix J). eq -CgSCR×I n There is a characteristic value of 0, at which point gSCR = CgSCR). The DC output active power P satisfies the system of equations. i The numbers i = 1, ..., n constitute the voltage stability boundary of the system.

[0065] In this invention, the normal vector of the voltage stability boundary is used to provide the direction of power vector increase during the iterative calculation of the saddle-node bifurcation point. Since B-gSCR×P is a symmetric matrix, its left and right eigenvectors corresponding to its zero eigenvalue are equal. In this case, the normal vector can be uniformly represented by the right eigenvector. This facilitates subsequent iterative calculations.

[0066] In this invention, the generalized short-circuit ratio represents the current operating point, and its corresponding right eigenvector can be used to construct the normal vector of the voltage stability boundary. The nearest saddle-node bifurcation point can be found along the direction of the normal vector. Therefore, a new power vector is generated along the normal vector, and the new power vector p iBy substituting the critical generalized short-circuit ratio CgSCR and the nodal admittance matrix B into the power space algebraic equations and solving them, the distance l from the current operating point to the voltage stability boundary can be obtained. i When the eigenvectors satisfy the convergence criterion, it means that the shortest distance from the current running point to the voltage stability boundary has been found. If the convergence criterion is not satisfied, it means that it is not the shortest distance and further iterative calculation is needed.

[0067] In embodiments of the present invention, for example... Figure 2 The Thevenin equivalent diagram of the three-infeed DC system is shown. A typical three-infeed DC system is built in MATLAB software. The DC system used in the specific implementation adopts the following... Figure 3 The standard model shown is the one proposed by the CIGRE DC Working Group in 1991. Figure 2 The rated voltage is 525kV, and the rated capacity of each of the three DC lines is 8000MW, with a critical short-circuit ratio CgSCR = 3. The initial operating point of each of the three DC lines is 1.0 pu of rated power. The corresponding Thevenin equivalent circuit node admittance matrix parameters are:

[0068]

[0069] like Figure 4 The diagram illustrates the process in this embodiment of calculating the distance from the current running point to the nearest saddle node bifurcation point using the nearest saddle node bifurcation point iterative algorithm:

[0070] The first step is to obtain the nodal admittance matrix B and the power vector p of the DC multi-infeed system. i-1 ;

[0071] The second step is to calculate the generalized short-circuit ratio gSCR and the corresponding right eigenvector u at this point. i-1 ;

[0072] The third step is to determine the right eigenvector u based on the current eigenvector. i-1 Update the power vector as Among them l i As an unknown quantity, it means the distance from the current operating point to the voltage stability boundary.

[0073] The fourth step is to update the power vector p. i Substituting the nodal admittance matrix B and the critical short-circuit ratio CgSCR into the power space algebraic equations and solving for l... i And the new right eigenvector u i ;

[0074] Step 5: Determine if the convergence criterion is satisfied |u i -u i-1 | 2If the condition is not met, then let i = i + 1 and return to the second step to update the power vector again, continuing the iteration process; if the condition is met, then exit the iteration process and output the distance l from the current running point to the voltage stability boundary. i This is the shortest distance from the current operating point to the voltage stability boundary. In this embodiment, since the point on the voltage stability boundary is the saddle-node bifurcation point, the distance from the current operating point to the nearest saddle-node bifurcation point is also l. i .

[0075] The iterative search process for the bifurcation points of the three DC power space saddles in a triple-feed DC system is as follows: Figure 5 As shown. In the iterative calculation, the initial direction is the direction in which the three DC lines increase their transmission power proportionally; that is, the predicted normal vector direction before iteration is [1, 1, 1]. T After five iterations, the normal vector converges, and the predicted normal vectors used in each iteration correspond to vectors n0 to n3 in the figure, respectively.

[0076] like Figure 6 As shown, during the iterative process of this embodiment, the distance from the current operating point to the voltage stability boundary gradually decreases. Observing the change in distance during the iteration process: In the first iteration, the distance from the current operating point to the voltage stability boundary is 0.78. As the number of iterations increases, this distance gradually decreases. By the fifth iteration, the distance from the current operating point to the voltage stability boundary, i.e., the nearest saddle-node bifurcation point, stabilizes at 0.65. It can be seen that with each iteration of the iterative algorithm, the distance from the current operating point to the voltage stability boundary gradually decreases, eventually yielding the optimal solution. In the first iteration of this embodiment, the predicted normal vector direction is used, and the obtained distance of 0.78 represents the distance from the current operating point to the voltage stability boundary along the predicted normal vector direction. However, the voltage stability boundary is a curved surface, and 0.78 is not necessarily the shortest distance from the current operating point to the surface. Therefore, it is necessary to search through an iterative process to find the distance from the current operating point to the nearest saddle-node bifurcation point.

[0077] The above embodiments are further elaborations and descriptions of the present invention to facilitate understanding, and are not intended to limit the present invention in any way. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the nearest saddle-node bifurcation point based on DC power space, characterized in that, include: S1. Construct a power space algebraic equation characterizing the saddle junction bifurcation point of the DC multi-infeed system based on the generalized short-circuit ratio of the DC multi-infeed system. S2. Construct the normal vector of the voltage stability boundary in the power space using the eigenvector corresponding to the generalized short-circuit ratio. S3. Calculate the shortest distance from the current operating point to the voltage stability boundary: S31. Obtain the Thevenin equivalent circuit node admittance matrix B of the DC multi-infeed system, and obtain the power vector at the current operating point. ; S32, Calculate the power vector The generalized short-circuit ratio and its corresponding right eigenvector at time ; S33, Update for , This is the normal vector at this time; S34, will Substituting the critical generalized short-circuit ratio CgSCR into the power space algebraic equations, the distance from the current operating point to the voltage stability boundary can be obtained. and the new right eigenvector ; S35, Judgment Does it meet the convergence criterion? If the condition is not met, let i = i + 1 and return to S32 for iterative calculation; if the condition is met, stop iterative calculation. S4. The shortest distance described in S3 is taken as the distance from the current running point to the nearest saddle junction bifurcation point.

2. The method for calculating the nearest saddle-node bifurcation point based on DC power space according to claim 1, characterized in that, The construction steps of the power space algebraic equation include: The minimum eigenvalue of the extended admittance matrix of the DC multi-infeed system is taken as the generalized short-circuit ratio gSCR; The power space algebraic equations representing the saddle node bifurcation of the system are as follows: ， Where B is the nodal admittance matrix of the Thevenin equivalent circuit of the DC multi-infeed system, and P is the diagonal matrix of the multi-infeed DC power transmission. For matrix The right eigenvector corresponding to the zero eigenvalue.

3. A method for calculating the nearest saddle-node bifurcation point based on DC power space according to claim 1 or 2, characterized in that, The generalized short-circuit ratio is: ， ， in Represents the eigenvalues ​​of a matrix; To extend the admittance matrix; B is the nodal admittance matrix of the Thevenin equivalent circuit of the DC multi-infeed system; , This represents the active power output at node i of the DC multi-infeed system.

4. A method for calculating the nearest saddle-node bifurcation point based on DC power space according to claim 1 or 2, characterized in that, and These are the matrices corresponding to the generalized short-circuit ratio. The left and right eigenvectors corresponding to the zero eigenvalues; the normal vector of the voltage stability boundary is... , This represents the element-wise product vector between corresponding positions of vectors.

5. The method for calculating the nearest saddle-node bifurcation point based on DC power space according to claim 4, characterized in that, The matrix The left eigenvector is a symmetric matrix. With the right feature vector Equal; the normal vector of the voltage stability boundary is .

6. A method for calculating the nearest saddle-node bifurcation point based on DC power space according to claim 1 or 5, characterized in that, The critical generalized short-circuit ratio CgSCR corresponds to the operating conditions of a DC multi-infeed system where the Jacobian matrix is ​​singular or a saddle-node bifurcation occurs.

7. The method for calculating the nearest saddle-node bifurcation point based on DC power space according to claim 6, characterized in that, The critical generalized short-circuit ratio of a DC multi-infeed system is 3.

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