A method and system for calculating load margin in a three-phase unbalanced distribution network

Abstract

This invention discloses a method and system for calculating the load margin of a three-phase unbalanced distribution network. First, the network topology is traversed to obtain line parameters and load access methods, establishing an initial semidefinite programming model of the three-phase unbalanced branch power flow and converting it to a sequence component framework. Next, a positive-sequence power flow Jacobian matrix is ​​constructed, and the minimum singular value lower bound constraint and delta-connected load power constraint are introduced using the matrix maximum convex subset construction method. Then, an iteratively optimized semidefinite relaxation-tightening constraint is established using a semidefinite programming method, forming the final load margin calculation model. Finally, the relaxation matrix result is obtained through iterative solving, and the load margin power flow result is output. This invention can accurately assess the load margin of a three-phase unbalanced distribution network, exhibiting good convergence and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of power system steady-state stability analysis technology, and in particular relates to a method and system for calculating the load margin of a three-phase unbalanced distribution network. Background Technology

[0002] In the field of load margin calculation for three-phase unbalanced distribution networks, the minimum singular value of the power flow Jacobian matrix is ​​often used to characterize the steady-state voltage stability margin and can be embedded in the optimal power flow model to depict the load growth boundary. However, in actual distribution networks, single-phase lines, two-phase lines, and single-phase, two-phase, and three-phase branches and delta-connected loads coexist. The traditional three-phase Jacobian matrix is ​​usually constructed based on a complete three-phase structure, which is prone to structural rank deficiency in the case of missing-phase branches. This makes it difficult for its singularity to accurately reflect the true voltage stability margin, thus affecting the reliability of the load margin calculation results.

[0003] In load margin calculation, existing methods are mostly based on continuous power flow methods or conventional optimal power flow models, which make it difficult to simultaneously consider unbalanced operating characteristics, modeling of missing-phase branches, and load constraints in delta connections. Although semidefinite programming relaxation methods can reduce the difficulty of solving the original non-convex power flow problem, the relaxation results usually cannot guarantee rank uniformity, and the obtained solution may not be able to be directly recovered from the feasible solution in the original AC power flow problem, thus limiting its application in load margin calculation of practical distribution networks.

[0004] In summary, there is an urgent need to propose a method for calculating the load margin of a three-phase unbalanced distribution network in order to solve the above-mentioned technical problems. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for calculating the load margin of a three-phase unbalanced distribution network, which realizes the coexistence of single-phase, two-phase, three-phase branches and delta-connected loads in the unbalanced distribution network, thereby improving the applicability and feasibility of load margin calculation.

[0006] To achieve the objectives of this invention, on the one hand, this invention provides a method for calculating the load margin of a three-phase unbalanced distribution network, comprising the following steps:

[0007] Step 1: Traverse the three-phase unbalanced distribution network topology to obtain its corresponding line parameters and load access methods;

[0008] Step 2: Based on the line parameters and load access method, establish an initial load margin calculation model using the three-phase unbalanced branch power flow semi-definite programming modeling method; transform the load margin calculation model into a sequence component framework through phase sequence transformation.

[0009] Step 3: Based on the ordered component framework, construct the positive-order power flow Jacobian matrix within the load margin calculation model using the Jacobian auxiliary matrix construction method;

[0010] Step 4: Using the positive-sequence power flow Jacobian matrix, construct a load margin calculation model with iterative optimization minimum singular value lower bound constraint and delta-connected load power constraint through the matrix maximum convex subset construction method;

[0011] Step 5: Based on the ordered component framework, establish a load margin calculation model with iterative optimization semidefinite relaxation-tightening constraints using a semidefinite programming method;

[0012] Step 6: The load margin calculation model with iteratively optimized minimum singular value lower bound constraint, delta-connected load power constraint, and iteratively optimized semidefinite relaxation-tightening constraint is solved iteratively to obtain the relaxation matrix result and output the load margin power flow result.

[0013] On the other hand, the present invention also provides a system for calculating the load margin of a three-phase unbalanced distribution network, comprising the following modules:

[0014] The topology parameter acquisition module is used to traverse the three-phase unbalanced distribution network topology and obtain its corresponding line parameters and load access methods.

[0015] The initial model building module is used to establish an initial load margin calculation model based on the line parameters and load access method using a three-phase unbalanced branch power flow semi-definite programming modeling method, and to convert the initial load margin calculation model to a sequence component framework through phase sequence transformation.

[0016] The positive-sequence power flow Jacobian matrix construction module is used to construct the positive-sequence power flow Jacobian matrix within the load margin calculation model based on the order component framework and using the Jacobian auxiliary matrix construction method.

[0017] The singular value lower bound constraint and delta connection load power constraint construction module is used to construct the minimum singular value lower bound constraint and delta connection load power constraint iteratively optimized within the load margin calculation model using the positive sequence power flow Jacobian matrix and the matrix maximum convex subset construction method.

[0018] The relaxation matrix tightening module is used to establish iteratively optimized semidefinite relaxation tightening constraints within the load margin calculation model based on the ordered component framework and through a semidefinite programming method, and to form the final load margin calculation model.

[0019] The iterative solution output module is used to obtain the relaxation matrix result through iterative solution using the final load margin calculation model, and output the network load margin power flow result.

[0020] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the load margin calculation method described above.

[0021] A non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the above-described load margin calculation method.

[0022] A computer program product includes computer program instructions that, when executed on a computer, cause the computer to perform the above-described load margin calculation method.

[0023] The significant advancement of this invention compared to existing technologies lies in:

[0024] (1) This invention utilizes the topology traversal of a three-phase unbalanced distribution network to obtain line parameters and load access methods, thereby improving the detail of distribution network modeling and reducing the problem of insufficient model description caused by complex topology and diverse load access methods;

[0025] (2) This invention utilizes the three-phase unbalanced branch power flow semidefinite programming modeling method and phase sequence transformation method to improve the load margin calculation model's ability to express the three-phase unbalanced characteristics, and reduce the problems of computational complexity and insufficient model adaptability of traditional three-phase modeling in unbalanced scenarios;

[0026] (3) This invention uses the Jacobi auxiliary matrix construction method under the order component framework to construct the positive order power flow Jacobi matrix, improves the applicability of the power flow stability criterion in phase-loss and unbalanced distribution networks, and reduces the risk of rank deficiency caused by phase-loss branches in the traditional three-phase Jacobi matrix.

[0027] (4) This invention uses the matrix maximum convex subset construction method to establish minimum singular value lower bound constraints and triangular connection load power constraints, thereby improving the stability and feasibility of load margin calculation results and reducing the computational difficulties caused by direct solution of non-convex constraints.

[0028] (5) This invention utilizes a semidefinite programming method under the order component framework to establish an iteratively optimized semidefinite relaxation and tightening constraint, thereby improving the approximation accuracy of the semidefinite relaxation solution to the original non-convex power flow model and reducing the risk of infeasible solutions caused by inaccurate relaxation.

[0029] (6) This invention uses the final load margin calculation model to perform iterative solution and output the relaxation matrix result and the network load margin power flow result, which improves the solution efficiency and result reliability of the load margin calculation of three-phase unbalanced distribution network and reduces the problem of heavy calculation burden of traditional continuous power flow method in complex unbalanced distribution network.

[0030] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0031] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0032] Figure 1 This is a flowchart illustrating the method described in this invention;

[0033] Figure 2 This is a schematic diagram of the three-phase unbalanced distribution network IEEE-13 of the present invention;

[0034] Figure 3 This is a schematic diagram showing the load growth ratio coefficient results corresponding to the load limit of this invention;

[0035] Figure 4 This is a schematic diagram of the voltage results corresponding to the load limit of the present invention; wherein Figure 4 (a) is the three-phase PV curve at node 4 of this invention, calculated using the continuous power flow method. Figure 4 (b) is the corresponding stability limit voltage diagram calculated based on the continuous power flow method of this invention. Figure 4 (c) is the steady-state limiting voltage diagram calculated by the method described in this invention; Figure 4 (d) Result diagram of failure calculation based on load margin at the same node using traditional optimization methods;

[0036] Figure 5 This is a schematic diagram illustrating the feasibility of the load margin power flow solution of the present invention; wherein Figure 5 (a) is the result diagram when the solution recovery method is not used in this invention. Figure 5 (b) is the result diagram after the solution recovery method of the present invention. Detailed Implementation

[0037] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] This invention provides a method for calculating the load margin of a three-phase unbalanced distribution network, combined with... Figure 1 This includes the following steps:

[0039] Step 1: Traverse the three-phase unbalanced distribution network topology to obtain its corresponding line parameters and load access methods; the line parameters include branch impedance parameters and branch phase information; the load access methods include the load access phase, wiring method, and active and reactive power parameters of each load node;

[0040] Step 2: Based on the line parameters and load access method, establish an initial load margin calculation model using the three-phase unbalanced branch power flow semi-definite programming modeling method; transform the load margin calculation model into a sequence component framework through phase sequence transformation.

[0041] Step 3: Based on the ordered component framework, construct the positive-order power flow Jacobian matrix within the load margin calculation model using the Jacobian auxiliary matrix construction method;

[0042] Step 4: Using the positive-sequence power flow Jacobian matrix, construct a load margin calculation model with iterative optimization minimum singular value lower bound constraint and delta-connected load power constraint through the matrix maximum convex subset construction method;

[0043] Step 5: Based on the ordered component framework, establish a load margin calculation model with iterative optimization semidefinite relaxation-tightening constraints using a semidefinite programming method;

[0044] Step 6: The load margin calculation model with iteratively optimized minimum singular value lower bound constraint, delta-connected load power constraint, and iteratively optimized semidefinite relaxation-tightening constraint is solved iteratively to obtain the relaxation matrix result and output the load margin power flow result.

[0045] The initial load margin calculation model in step 2 is shown in the following formula:

[0046] ;

[0047] in, It is node i. It is node j, set It is the set of load nodes excluding the balancing node 0; It is a collection of branches of the power distribution network. It is a branch that points from upstream node i to downstream node j; , and These are the load growth ratio coefficients for the 1st, 2nd, and 3rd phase loads at node j, respectively. , and These are the complex power of the 1st, 2nd, and 3rd phase loads at node j, respectively; It is the complex power vector of the three-phase load at node j; This is the phase sequence transformation matrix. yes The conjugate transpose of ; It is the sequence impedance between branches ij. yes Relaxed expression yes Relaxed expression yes The relaxed expression, in which It is the voltage vector of node i under the ordered component framework. yes The conjugate transpose of . It is the current vector between branches ij under the order component framework. yes The conjugate transpose of . It is the voltage matrix constant corresponding to the equilibrium node in the order component framework. It is an artificially defined constant of the equilibrium node voltage vector. yes The conjugate transpose of . It is the lower bound vector of the voltage at node j. yes The conjugate transpose of . It is the upper bound vector of the voltage at node j. yes The conjugate transpose of . It is the upper bound of the complex power of a single load; ordinary voltage vector. and ordinary current vector with vector and The specific relationship is shown in the following formula: ; ;in, ; It is a general impedance matrix, which is related to... The specific relationship is shown in the following formula: .

[0048] Step 3 involves constructing a positive-sequence power flow Jacobian matrix within the load margin calculation model using the Jacobian auxiliary matrix construction method.

[0049] First, a large voltage matrix constraint needs to be constructed, as shown in the following formula:

[0050] ;

[0051] in, It is a large voltage matrix under the order component framework. yes The relaxed expression, It is the ordered admittance matrix of the branch between node i and node j. It is by The corresponding node admittance matrix under the ordered component framework;

[0052] The power flow Jacobian matrix under the ordered component framework is specifically shown in the following formula:

[0053] ;

[0054] in, It is the partial derivative matrix of the active power function with respect to the voltage phase angle. It is the partial derivative matrix of the active power function with respect to the voltage amplitude. It is the partial derivative matrix of the reactive power function with respect to the voltage phase angle. It is the partial derivative matrix of the reactive power function with respect to the voltage amplitude;

[0055] Constructing the positive-order power flow Jacobian matrix requires first constructing a Jacobian auxiliary matrix and then constructing the Jacobian matrix under the order component framework based on the Jacobian auxiliary matrix:

[0056] The Jacobian auxiliary matrix is ​​specifically shown in the following formula:

[0057] ;

[0058] in, and They are respectively The real and imaginary parts;

[0059] The Jacobian matrix under the framework of constructing order components based on the Jacobian auxiliary matrix is ​​shown in the following equation:

[0060] ;

[0061] The positive-order quantities in the Jacobian matrix under the ordered component framework are extracted to construct the positive-order power flow Jacobian matrix:

[0062] ;

[0063] in, It is the zero-order Jacobian matrix block corresponding to node 1 and node 2. It is the orthogonal Jacobian matrix block corresponding to node 1 and node 2. It corresponds to the negative-order Jacobian matrix block of node 1 and node 2, and so on for other subscripts.

[0064] The load margin calculation model in step 4, which incorporates iterative optimization of the minimum singularity lower bound constraint and the delta-connected load power constraint, is shown in the following formula:

[0065] ;

[0066] in, It is the positive-order power flow Jacobian matrix of the t-th iteration step. Yes The rotation matrix constant obtained by polar decomposition. It is a lower bound of the minimum singular value that is set by the user; matrix It is the identity matrix;

[0067] The specific formula for constructing the triangular connection load power constraint is as follows:

[0068] ;

[0069] in, It is the complex power vector of the three-phase load connected in a triangle at node j. The combined load power of phases ab connected by the triangle at node j is the load power of phases ab. It is the combined load power of phase bc of the triangular connection at node j. The complex power of the load phase ca connected in the triangle at node j is the power of the load phase ca. yes Convex relaxation expression, yes The conjugate transpose of the matrix. yes The convex relaxation expression, in which, It is the current flowing through the delta-connected load itself. yes The conjugate transpose of . It is a star-triangular transformation matrix: .

[0070] The load margin calculation model with iteratively optimized semi-definite relaxation tightening constraints in step 5 specifically includes:

[0071] First, we need to construct the first tightening auxiliary matrix. Second tightening auxiliary matrix The specific formula is as follows:

[0072] ;

[0073] First tightening auxiliary matrix The corresponding tightening constraint is:

[0074] ;

[0075] in, subscript , Used for selection The rows and columns correspond to a second-order principal submatrix: Each 6x6 auxiliary matrix There is a corresponding The aforementioned tightening constraints and second-order principal submatrices; for vectors , From the previous iteration's optimization solution, It is the current optimization variable. It is a penalty variable; It is a nonconvex function constructed from the determinant of the second-order principal submatrix: ; Is the function about the vector gradient: ;

[0076] Finally, a corresponding penalty term needs to be added to the objective function: ,in, This is the weighting coefficient for the corresponding penalty item;

[0077] Similarly, the above formula is used to tighten the second auxiliary matrix. Construct its corresponding tightening constraints.

[0078] The relaxation matrix result and the output network load margin power flow result in step 6 are as follows:

[0079] First, the load margin calculation model with iterative optimization of minimum singular value lower bound constraints, delta-connected load power constraints, and iterative optimization of semidefinite relaxation-tightening constraints is iteratively solved to obtain the numerical result of the first tightening auxiliary matrix: Numerical results for the second compaction auxiliary matrix: ;

[0080] Then to Perform SVD decomposition:

[0081] ;

[0082] in, For the k-th singular vector, yes The conjugate transpose of . It is the k-th singular value;

[0083] When k=1, in the first singular vector The extracted load margin power flow result is as follows: The numerical result of the second tightening auxiliary matrix. The corresponding load margin power flow result extracted using the above formula is as follows: .

[0084] The system for calculating the load margin of a three-phase unbalanced distribution network according to the present invention includes the following modules:

[0085] The topology parameter acquisition module is used to traverse the three-phase unbalanced distribution network topology and obtain its corresponding line parameters and load access methods.

[0086] The initial model building module is used to establish an initial load margin calculation model based on the line parameters and load access method using a three-phase unbalanced branch power flow semi-definite programming modeling method, and to convert the initial load margin calculation model to a sequence component framework through phase sequence transformation.

[0087] The positive-sequence power flow Jacobian matrix construction module is used to construct the positive-sequence power flow Jacobian matrix within the load margin calculation model based on the order component framework and using the Jacobian auxiliary matrix construction method.

[0088] The singular value lower bound constraint and delta connection load power constraint construction module is used to construct the minimum singular value lower bound constraint and delta connection load power constraint iteratively optimized within the load margin calculation model using the positive sequence power flow Jacobian matrix and the matrix maximum convex subset construction method.

[0089] The relaxation matrix tightening module is used to establish iteratively optimized semidefinite relaxation tightening constraints within the load margin calculation model based on the ordered component framework and through a semidefinite programming method, and to form the final load margin calculation model.

[0090] The iterative solution output module is used to obtain the relaxation matrix result through iterative solution using the final load margin calculation model, and output the network load margin power flow result.

[0091] Example

[0092] like Figure 2 The diagram shows an IEEE-13 three-phase unbalanced power distribution network. In this embodiment, the number of nodes in the unbalanced power distribution network is N=13, and the 13 nodes are numbered as follows: 650, 632, 633, 634, 645, 646, 671, 680, 684, 611, 652, 692, and 675. The voltage regulator is located on the branch between nodes 650 and 632; the transformer is located on the branch between nodes 633 and 634; and the switch is located on the branch between nodes 671 and 692.

[0093] The detailed implementation steps are as follows:

[0094] 1) In the above three-phase unbalanced distribution network, the load of each node is set as PQ load, and the branch phase loss setting, delta-connected load, transformer and line voltage regulator and other equipment models in the original standard distribution network are retained to reflect the unbalanced operation characteristics, phase loss branch characteristics and voltage regulation characteristics in the actual distribution network.

[0095] 2) Construct an iterative calculation model for load margin (OPF method);

[0096] 3) Based on step 2), perform iterative optimization to obtain the maximum load results, as shown in Table 1:

[0097] Table 1 Maximum Load Results

[0098]

[0099] 4) Calculate the load margin based on the optimization results obtained in step 3), and compare it with a load margin power flow result calculated based on a continuous power flow method. This serves as a verification of the accuracy of the load margin calculation results of this method. The comparison results are shown in Table 2:

[0100] Table 2 Load Margin Power Flow Results and Comparison

[0101]

[0102] 5) Based on the optimization results obtained in step 3), the load growth ratio coefficient λ obtained by this invention is compared with the load growth ratio coefficient obtained by the continuous power flow method (CPF method) as a verification of the accuracy of the load margin calculation results of this method. Figure 3 As shown.

[0103] 6) Furthermore, a detailed comparative analysis of the IEEE-13 node three-phase unbalanced test network was conducted; such as... Figure 4 As shown, Figure 4 (a) The three-phase PV curve at node 4 is calculated using the continuous power flow method. Figure 4 (b) The corresponding stability limiting voltage calculated by the continuous power flow method is given; Figure 4 (c) The steady-state limiting voltage calculated by the method described in this invention is given; Figure 4 (d) gives the results of load margin calculation failure at the same node based on the traditional optimization method.

[0104] The above comparison shows that the method of the present invention can maintain consistency with the results of the standard continuous power flow method, while avoiding the calculation failure problem caused by the structural rank deficiency of the traditional three-phase Jacobian matrix in three-phase unbalanced distribution networks with missing phase branches, thereby improving the applicability and usability of the load margin calculation results.

[0105] 7) Recover the power flow solution using the relaxation matrix, and evaluate the feasibility of the recovered solution based on the power mismatch index. Specifically, for the numerical results obtained in step 3: and Singular value decomposition is performed, and the corresponding load margin power flow solution is obtained based on the decomposition results. To evaluate the feasibility of the recovered solution in the original non-convex power flow problem, a node power mismatch index is introduced:

[0106] ;

[0107] in, Represents a node The power balance deviation at that point. When and When the result is ideally rank-one, the voltage and current variables recovered from the principal eigenvectors satisfy the original power flow equations. At this point, the power mismatch index at any node... The power mismatch index is zero; when it is not zero, it indicates that the recovered solution is infeasible at the corresponding node. The closer the power mismatch index is to zero, the closer the recovered power flow solution is to the feasible solution of the original non-convex power flow problem, such as... Figure 5 As shown, this illustrates the power mismatch indicators for each node in an IEEE-13 distribution network: Figure 5 (a) shows the result without using the solution recovery method. Figure 5 (b) shows the result after using the solution recovery method.

[0108] Furthermore, to evaluate the overall infeasibility of the distribution network, the total power mismatch index is defined as: in, Let represent the set of nodes. By comparing the node power mismatch index and the total power mismatch index before and after introducing the solution recovery method, the improvement effect of the solution recovery method on power flow feasibility is determined. If the total power mismatch index of the distribution network is significantly reduced after introducing the solution recovery method, it indicates that the solution recovery method can improve the feasibility of the semi-definite relaxation result in the original three-phase unbalanced power flow problem. The weighting coefficient of the penalty term set in this invention for this distribution network is [missing information]. Table 3 compares the results with and without the solution recovery method in the left and right columns, respectively, thus verifying the effectiveness of the method:

[0109] Table 3 Comparison of the effects of different recovery methods

[0110]

[0111] In summary, the technical solution of this embodiment includes delta-connected load power constraints and semi-definite relaxation-tightening constraints, which can improve the feasibility of load margin calculation results in the original non-convex power flow problem. At the same time, considering the unbalanced operation characteristics of single-phase, two-phase, three-phase branches and delta-connected loads, by constructing a positive-sequence power flow Jacobian matrix, the calculation failure caused by the constant singularity of the traditional three-phase Jacobian matrix when there is a missing phase branch is avoided, and the calculation speed is improved, thereby improving the applicability and feasibility of load margin calculation.

[0112] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0113] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating load margin of a three-phase unbalanced distribution network, characterized in that, Includes the following steps: Step 1: Traverse the three-phase unbalanced distribution network topology to obtain its corresponding line parameters and load access methods; Step 2: Based on the line parameters and load access method, establish an initial load margin calculation model using the three-phase unbalanced branch power flow semi-definite programming modeling method; transform the load margin calculation model into a sequence component framework through phase sequence transformation. Step 3: Based on the ordered component framework, construct the positive-order power flow Jacobian matrix within the load margin calculation model using the Jacobian auxiliary matrix construction method; Step 4: Using the positive-sequence power flow Jacobian matrix, construct a load margin calculation model with iterative optimization minimum singular value lower bound constraint and delta-connected load power constraint through the matrix maximum convex subset construction method; Step 5: Based on the ordered component framework, establish a load margin calculation model with iterative optimization semidefinite relaxation-tightening constraints using a semidefinite programming method; Step 6: The load margin calculation model with iteratively optimized minimum singular value lower bound constraint, delta-connected load power constraint, and iteratively optimized semidefinite relaxation-tightening constraint is solved iteratively to obtain the relaxation matrix result and output the load margin power flow result.

2. The method of claim 1, wherein, The initial load margin calculation model in step 2 is shown in the following formula: ； in, It is node i. It is node j, set It is the set of load nodes excluding the balancing node 0; It is a collection of branches of the power distribution network. It is a branch that points from upstream node i to downstream node j; , and These are the load growth ratio coefficients for the 1st, 2nd, and 3rd phase loads at node j, respectively. , and These are the complex power of the 1st, 2nd, and 3rd phase loads at node j, respectively; It is the complex power vector of the three-phase load at node j; This is the phase sequence transformation matrix. yes The conjugate transpose of ; It is the sequence impedance between branches ij. yes Relaxed expression yes Relaxed expression yes The relaxed expression, in which It is the voltage vector of node i under the ordered component framework. yes The conjugate transpose of . It is the current vector between branches ij under the order component framework. yes The conjugate transpose of . It is the voltage matrix constant corresponding to the equilibrium node in the order component framework. It is an artificially defined constant of the equilibrium node voltage vector. yes The conjugate transpose of . It is the lower bound vector of the voltage at node j. yes The conjugate transpose of . It is the upper bound vector of the voltage at node j. yes The conjugate transpose of . It is the upper bound of the complex power of a single load; ordinary voltage vector. and ordinary current vector with vector and The specific relationship is shown in the following formula: ; ;in, ; It is a general impedance matrix, which is related to... The relationship is specifically shown by the following formula: .

3. The method for calculating the load margin of a three-phase unbalanced distribution network according to claim 2, characterized in that, Step 3 involves constructing a positive-sequence power flow Jacobian matrix within the load margin calculation model using the Jacobian auxiliary matrix construction method. First, a large voltage matrix constraint needs to be constructed, as shown in the following formula: ； in, It is a large voltage matrix under the order component framework. yes The relaxed expression, It is the ordered admittance matrix of the branch between node i and node j. It is by The corresponding node admittance matrix under the ordered component framework; The power flow Jacobian matrix under the ordered component framework is specifically shown in the following formula: ； in, It is the partial derivative matrix of the active power function with respect to the voltage phase angle. It is the partial derivative matrix of the active power function with respect to the voltage amplitude. It is the partial derivative matrix of the reactive power function with respect to the voltage phase angle. It is the partial derivative matrix of the reactive power function with respect to the voltage amplitude; Constructing the positive-order power flow Jacobian matrix requires first constructing a Jacobian auxiliary matrix and then constructing the Jacobian matrix under the order component framework based on the Jacobian auxiliary matrix: The Jacobian auxiliary matrix is ​​specifically shown in the following formula: ； in, and They are respectively The real and imaginary parts; The Jacobian matrix under the framework of constructing order components based on the Jacobian auxiliary matrix is ​​shown in the following equation: ； The positive-order quantities in the Jacobian matrix under the ordered component framework are extracted to construct the positive-order power flow Jacobian matrix: ； in, It is the zero-order Jacobian matrix block corresponding to node 1 and node 2. It is the orthogonal Jacobian matrix block corresponding to node 1 and node 2. It corresponds to the negative-order Jacobian matrix block of node 1 and node 2, and so on for other subscripts.

4. The method for calculating the load margin of a three-phase unbalanced distribution network according to claim 3, characterized in that, The load margin calculation model in step 4, which incorporates iterative optimization of the minimum singularity lower bound constraint and the delta-connected load power constraint, is shown in the following formula: ； in, It is the positive-order power flow Jacobian matrix of the t-th iteration step. Yes The rotation matrix constant obtained by polar decomposition. It is a lower bound of the minimum singular value that is set by the user; matrix It is the identity matrix; The specific formula for constructing the triangular connection load power constraint is as follows: ； in, It is the complex power vector of the three-phase load connected in a triangle at node j. The combined load power of phases ab connected by the triangle at node j is the load power of phases ab. It is the combined load power of phase bc of the triangular connection at node j. The complex power of the load phase ca connected in the triangle at node j is the power of the load phase ca. yes Convex relaxation expression, yes The conjugate transpose of the matrix. yes The convex relaxation expression, in which, It is the current flowing through the delta-connected load itself. yes The conjugate transpose of . It is a star-triangular transformation matrix: .

5. The method for calculating the load margin of a three-phase unbalanced distribution network according to claim 4, characterized in that, The load margin calculation model with iteratively optimized semi-definite relaxation tightening constraints in step 5 specifically includes: First, we need to construct the first tightening auxiliary matrix. Second tightening auxiliary matrix The specific formula is as follows: ； First Tightening Auxiliary Matrix The corresponding tightening constraint is: ； in, subscript , Used for selection The rows and columns correspond to a second-order principal submatrix: Each 6x6 auxiliary matrix There is a corresponding The aforementioned tightening constraints and second-order principal submatrices; for vectors , From the previous iteration's optimization solution, It is the current optimization variable. It is a penalty variable; It is a nonconvex function constructed from the determinant of the second-order principal submatrix: ; Is the function about the vector gradient: ; Finally, a corresponding penalty term needs to be added to the objective function: ,in, This is the weighting coefficient for the corresponding penalty item; Similarly, the above formula is used to adjust the second tightening auxiliary matrix. Construct its corresponding tightening constraints.

6. The method for calculating the load margin of a three-phase unbalanced distribution network according to claim 5, characterized in that, The relaxation matrix result and the output network load margin power flow result in step 6 are as follows: First, the load margin calculation model with iterative optimization of minimum singular value lower bound constraints, delta-connected load power constraints, and iterative optimization of semidefinite relaxation-tightening constraints is iteratively solved to obtain the numerical result of the first tightening auxiliary matrix: Numerical results for the second compaction auxiliary matrix: ; Then to Perform SVD decomposition: ； in, For the k-th singular vector, yes The conjugate transpose of . It is the k-th singular value; When k=1, in the first singular vector The extracted load margin power flow result is as follows: The numerical result of the second tightening auxiliary matrix. The corresponding load margin power flow result extracted using the above formula is as follows: .

7. The system for calculating the load margin of a three-phase unbalanced distribution network according to claims 1-6, characterized in that, Includes the following modules: The topology parameter acquisition module is used to traverse the three-phase unbalanced distribution network topology and obtain its corresponding line parameters and load access methods. The initial model building module is used to establish an initial load margin calculation model based on the line parameters and load access method using a three-phase unbalanced branch power flow semi-definite programming modeling method, and to convert the initial load margin calculation model to a sequence component framework through phase sequence transformation. The positive-sequence power flow Jacobian matrix construction module is used to construct the positive-sequence power flow Jacobian matrix within the load margin calculation model based on the order component framework and using the Jacobian auxiliary matrix construction method. The singular value lower bound constraint and delta connection load power constraint construction module is used to construct the minimum singular value lower bound constraint and delta connection load power constraint iteratively optimized within the load margin calculation model using the positive sequence power flow Jacobian matrix and the matrix maximum convex subset construction method. The relaxation matrix tightening module is used to establish iteratively optimized semidefinite relaxation tightening constraints within the load margin calculation model based on the ordered component framework and through a semidefinite programming method, and to form the final load margin calculation model. The iterative solution output module is used to obtain the relaxation matrix result through iterative solution using the final load margin calculation model, and output the network load margin power flow result.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method as described in any one of claims 1 to 6.

10. A computer program product comprising computer program instructions, characterized in that, When the computer program instructions are executed on a computer, the computer causes the computer to perform the method as described in any one of claims 1 to 6.

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