A power distribution network static voltage stability margin analysis method considering switch switching

Abstract

This application discloses a method for analyzing the static voltage stability margin (SVSM) of a distribution network considering line switching. The method includes constructing a distribution network SVSM model considering line switching, wherein the SVSM model aims to maximize load growth parameters. For the SVSM model, given the current limits of each line, the maximum number of network switching operations, and the corresponding switching operations when the current exceeds the limit for each line, the initial state of the line switches is taken as a corresponding constant representing the original distribution network topology. The SVSM model is solved to obtain the number of switching operations and the distribution network SVSM and the corresponding line switch states after switching and network topology. This method can optimize the power flow distribution of the distribution network, reduce the load level of critical lines, thereby effectively improving the distribution network SVSM and ensuring the safe and stable operation of the distribution network. Simultaneously, it achieves direct solution of the maximum load growth parameters under the condition that the distribution network can transfer power, greatly improving the solution efficiency.

Description

Technical Field

[0001] This invention relates to the field of power grid technology, and more specifically to a method for analyzing the static voltage stability margin of distribution networks considering switch switching. Background Technology

[0002] The static voltage stability margin (SVSM) of a distribution network reflects the maximum load increase that the current operating point of the distribution network can withstand. Existing SVSM analysis methods for distribution networks are mainly based on fixed network topologies, without considering the line power flow limit constraints during load growth, or the impact of actual engineering operations such as switching on and off distribution line switches when the power flow exceeds the limits during load growth on the SVSM calculation results.

[0003] Currently, the optimal power flow method is mainly used for SVSM analysis and calculation of distribution networks. However, if the switching and reconnection of distribution line switches due to power flow exceeding limits during load growth are considered, the optimal power flow model for SVSM calculation of distribution networks will become a nonlinear, non-convex mixed-integer nonlinear programming model containing discrete variables. Since mixed-integer nonlinear programming models belong to NP (non-deterministic polynomial) difficult problems, it is difficult to obtain the optimal solution, and the solution time is very long.

[0004] As loads continue to increase, some distribution lines may become overloaded, requiring switching operations to transfer power. Many existing studies on distribution network SVSM calculations do not consider this scenario, and the calculated SVSMs are often only theoretical results that do not reflect actual engineering conditions. They deviate significantly from the maximum load increase that the current operating point of the distribution network can withstand in real-world projects, thus failing to guarantee the safe and stable operation of the distribution network.

[0005] Since mixed-integer nonlinear programming problems are NP-hard, directly using commercial optimization solvers such as SBB can lead to high solution difficulty, long computation time, and difficulty in finding feasible or optimal solutions. In large-scale distribution networks or strongly nonconvex models, the efficiency and feasibility of solving these problems are severely limited. The same issues arise when applying this to SVSM (Switching and Transfer Mode) distribution network models that consider the switching and transfer of power supply during load growth. Specifically, the large number of discrete variables introduced by the switching and transfer of power supply and the constraints of the nonlinear extended power flow equations make the model solution time-consuming and difficult to converge. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for analyzing the static voltage stability margin of a distribution network considering switch switching, so as to adjust the topology of the distribution network, optimize the power flow distribution, reduce the load level of critical lines, thereby effectively improving the SVSM of the distribution network and ensuring the safe and stable operation of the distribution network.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows:

[0008] Methods for analyzing the static voltage stability margin of distribution networks considering switch switching include:

[0009] A distribution network SVSM model considering line switch switching is constructed, and the distribution network SVSM model aims to maximize the load growth parameter;

[0010] For the SVSM model of the distribution network, the current limit value of each line, the maximum number of network switch switching operations, and the corresponding switch switching operation when the current of each line exceeds the limit are given.

[0011] The initial state of the line switch is set to the corresponding fixed value representing the original topology of the distribution network;

[0012] Solve the SVSM model of the distribution network to obtain the number of switch switching operations and the line switch states corresponding to the SVSM and network topology of the distribution network after switch switching.

[0013] Compared with the prior art, the advantages of this invention are as follows:

[0014] (1) The method of the present invention constructs a distribution network SVSM model that considers switch switching, with the goal of maximizing the load growth parameter. For the distribution network SVSM model, given the current limit value of each line, the maximum number of network switch switching operations, and the switch switching operation corresponding to the current exceeding the limit of each line, when the current of a distribution line exceeds the safe operation limit as the load increases, the model will automatically act according to the pre-set switch switching operation, thereby changing the network topology, optimizing the power flow distribution, and ensuring that the current of all lines is maintained within the thermal stability allowable range after the switch is switched, thus ensuring the safe and stable operation of the distribution network. At the same time, it realizes the direct solution of the maximum load growth parameter under the condition that the distribution network can transfer power supply.

[0015] (2) This invention addresses the nonlinearity and nonconvexity of the SVSM model for distribution networks by proposing a linearization and convex relaxation method for the nonlinear constraints in the model, transforming the mixed-integer nonlinear programming model into a mixed-integer second-order cone programming model. While maintaining the computational accuracy of the SVSM model for distribution networks, this invention significantly reduces the difficulty of solving the problem, effectively shortens the computation time, and greatly improves the applicability and computational efficiency of the model in actual distribution network engineering. Attached Figure Description

[0016] Figure 1 The main flowchart of the distribution network static voltage stability margin analysis method considering switch switching provided in the embodiments of this application;

[0017] Figure 2 The feasible region is defined as the voltage of the photovoltaic power station after relaxation and its square relationship.

[0018] Figure 3 Improved IEEE-33 node distribution network wiring diagram Detailed Implementation

[0019] Example:

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] See Figure 1 As shown, the static voltage stability margin analysis method for distribution networks considering switch switching provided in this embodiment mainly includes the following steps:

[0022] 110. Construct a distribution network SVSM model that considers line switch switching, wherein the distribution network SVSM model aims to maximize load growth parameters;

[0023] 120. For the aforementioned SVSM model of the distribution network, the current limit values ​​for each line are given. The maximum number of network switch switching operations and the corresponding switch switching operations when the current of each line exceeds the limit.

[0024] 130, set the initial state α of the line switch. ij0 Take the corresponding constant value representing the original topology of the distribution network;

[0025] 140. Solve the SVSM model of the distribution network to obtain the number of switch switching operations and the line switch states corresponding to the SVSM and network topology of the distribution network after switch switching.

[0026] Therefore, this method constructs a distribution network SVSM model that considers switch switching, aiming to maximize the load growth parameter. For this distribution network SVSM model, given the current limit value of each line, the maximum number of network switch switching operations, and the corresponding switch switching operation when the current of each line exceeds the limit, when the current of a distribution line exceeds the safe operation limit as the load increases, the model will automatically act according to the pre-set switch switching operation, thereby changing the network topology, optimizing the power flow distribution, and ensuring that the current of all lines remains within the thermal stability allowable range after the switch switching, thus ensuring the safe and stable operation of the distribution network. At the same time, it realizes the direct solution of the maximum load growth parameter under the condition that the distribution network can transfer power supply.

[0027] In one specific embodiment, the distribution network SVSM model aims to maximize the load growth parameter as follows: (1)

[0028] In the formula, λ t This is a load growth parameter. The subscript t represents the variable after the t-th line switch switching operation, t=0, 1,2, 3, ..., n, where n is the maximum number of switch switching operations. The subscript t in the following formulas has the same meaning. It is stipulated that each switch switching operation only disconnects and closes one line switch.

[0029] In one specific embodiment, the constraints of the distribution network SVSM model include extended power flow equations, line thermal stability constraints, network switching constraints, and distributed photovoltaic power plant operation constraints.

[0030] The extended power flow equation constraints include:

[0031] Since distribution networks typically have a radial structure, branch-type power flow models exhibit better convergence than traditional nodal power flow models, making them more suitable for distribution network optimization calculations. Therefore, under a given distribution network topology, the branch-type extended power flow equations are as follows: (2) (3) (4) (5)

[0032] In the formula, k: j→k represents the set of terminal nodes k of the branch with node j as the starting point, P ijt and Q ijt R represents the active and reactive power at the beginning of branch ij, respectively. ij and x ij These are the resistance and reactance of branch ij, respectively. P represents the square of the current in branch ij. PVjt and Q PVjt P represents the active and reactive power outputs of the photovoltaic power station at node j, respectively. Lj0 and Q Lj0 These represent the active and reactive power absorbed by the load at node j, respectively. PLj and b QLj This indicates the growth pattern of active and reactive power at node j, typically represented by b. PLj =P Lj0 b QLj =Q Lj0 U it This represents the square of the voltage at node i.

[0033] In addition, during the operation of the distribution network, it is required that the current of each line be limited within the safe allowable range after the line switches are switched on, as follows: (6)

[0034] In the formula, This represents the maximum value of the square of the current ij in the line.

[0035] In the operation of a distribution network, considering the switching operations of distribution line switches as the load increases, a 0-1 variable α representing the state of the line switches is introduced. ijt The traditional branch-type extended power flow equations (2)-(5) are modified to obtain branch-type extended power flow equations applicable to the switching of distribution line switches, as shown in equations (7)-(10). Among them, equations (7)-(8) represent the active and reactive power balance equations for each node connecting all branches, and equations (9)-(10) represent the voltage drop equations for all closed branches and the expression for the relationship between branch current and power: (7) (8) (9) (10)

[0036] In the formula, S l Let α be the set of all branches in the distribution network. ijt α is a 0-1 variable representing the switching state of line ij. ijt =1 indicates that line ij is connected, α ijt =0 indicates that line ij is disconnected.

[0037] The operational constraints of this distributed photovoltaic power station include:

[0038] Reactive power-voltage control in distributed photovoltaic power plants typically employs droop control mode, with the following operating constraints: (11) (12) (13) (14)

[0039] In the formula, k qi V is the droop control coefficient for the photovoltaic power station at node i. PVit and U PVit Q represents the voltage and square of the photovoltaic power station at node i, respectively. PVit and Q PViNThese are the actual and rated reactive power outputs of the photovoltaic power station at node i, respectively, Q. PVimax and Q PVimin Q PVit The upper and lower limits of V PVimax and V PVimin V PVit The upper and lower limits.

[0040] The network switch switching constraints include:

[0041] In the operation of a distribution network, as the load increases, i.e., λ t As the current increases, the power flow in the distribution lines changes. When the current in a distribution line exceeds the limit, pre-set switching operations will be performed to adjust the distribution network topology and reduce the load level of critical lines to prevent them from exceeding the limit. If the current in a distribution line does not exceed the limit, the original state will be maintained. It is stipulated that each switching operation will only disconnect and close one line switch at a time.

[0042] First, introduce the 0-1 variable μ. ijt To determine whether the line current ij exceeds the limit, the line current constraint (6) can be transformed into the following inequality constraint: (15)

[0043] Where M is a positive number significantly larger than other relevant variables in the model, and ε is a positive number close to 0. When At that time, the line current ij did not exceed the limit, μ ijt =0; when When the line current ij exceeds the limit, μ ijt =1.

[0044] Next, based on the calculated μ ijt Perform line switch switching operations. Before the switch switching operations, based on the distribution network wiring diagram, node loads, and tie switch connection points, reasonably set the corresponding switch switching operations for each line when the current exceeds the limit, that is, which switch to close and open to transfer power. The expression for the switch switching operation is as follows: (16) (17) (18)

[0045] In the formula, o ijt and c ijt It is a 0-1 variable. ijt =0 indicates that the switching state of line ij remains unchanged, o ijt =1 indicates that the switch of line ij is open. ijt =0 indicates that the switching state of line ij remains unchanged, cijt =1 indicates that the switch of line ij is closed. If line lk is the line with the greatest current over-limit, then its switching operation is the corresponding o. abt The circuit breaker with value = 1 is open, c cdt The circuit switch for line =1 is closed; the corresponding o for the other lines... ijt =0 and c ijt =0, the switch state remains unchanged; based on this, the switch state α of each line after the switch switching operation can be obtained by equation (18). ij(t+1) If all line currents do not exceed the limit, then μ lkt =0, no switching operation occurs, and the power grid topology remains unchanged.

[0046] Then, introduce 0-1 variables x. t This indicates whether, after the t-th switching operation, there is still a situation where the line current exceeds the limit and a corresponding switching operation needs to be performed again: (19)

[0047] In the formula, when x t When =1, all lines o ijt =0 indicates that there is no line current exceeding the limit after the t-th switch switching; when x t When =0, there exists a line o. ijt =1 indicates that after the t-th switch switching, there is a situation where the line current exceeds the limit and the corresponding switch switching operation is executed, and it is assumed that only the line with the largest current exceeding the limit will execute the corresponding switch switching operation.

[0048] After switching operations are performed, the distribution network topology changes, and each topology corresponds to a set of branch-type extended power flow equations. Therefore, x is introduced into the objective function. t Let t = 0, 1, ..., n, representing the values ​​of λ after the t-th switching operation in sequence. t Maximum value. After the t-th switching operation, there is no line current exceeding the limit when solving the SVSM of the distribution network, i.e., x t If λ = 1, then the topology at this point is the final topology, λ t The maximum value is the final SVSM. At this point, relevant constraints need to be introduced as shown in equation (20), and the objective function needs to be modified to the form of equation (21). If x0=x1=...=x n =1, then the distribution network does not experience line current exceeding limits as the load increases, and no switching operations occur; if x0=0, x1=...=x n =1, then the distribution network experiences line current exceeding limits as the load increases. After performing a single switch switching operation, the line power flow and thermal stability constraints are satisfied. x0, x1, ..., x nThe meanings of other possible values ​​are similar: (20) (twenty one)

[0049] Since the maximum number of switching operations n at the current operating point of the distribution network cannot be known in advance as the load increases, based on the experience that the switching operations generally do not exceed 3 times under the condition of line current exceeding the limit in actual distribution network operation, in this embodiment, n=3 is assumed. Then, the constraint condition (20) and objective function (21) are in the form shown in equation (22): (twenty two)

[0050] Therefore, using equation (21) as the objective function and equations (7)-(20) as constraints, a distribution network SVSM model considering switch switching is formed. This model is a mixed integer nonlinear programming model. Solving this model will yield the distribution network SVSM considering switch switching, as well as the number of switch switching operations and the final topology of the distribution network at the static voltage stability limit point. However, since the mixed integer nonlinear programming model (7)-(21) is an NP-hard problem, it is difficult to obtain the optimal solution, and the solution time is very long. Therefore, this embodiment proposes a solution method that transforms the original model into a mixed integer second-order cone programming model.

[0051] Because mixed-integer nonlinear programming models contain a large number of discrete variables and nonlinear constraints, the solution speed is very slow and the computational efficiency is very low. Therefore, this embodiment proposes a linearization and convex relaxation method for the nonlinear elements in the model to transform the model into a mixed-integer second-order cone programming model, which can be solved efficiently to obtain the distribution network SVSM considering line switch switching.

[0052] The objective function is a function in which each term is the product of n+1 zero-1 variables and one continuous variable. It is transformed into a linear expression using two linearization methods.

[0053] ① Multiplying 0-1 variables

[0054] For a term multiplied by two 0-1 variables Given that A, B∈{0, 1}, introducing a 0-1 variable C, we can transform C=AB into the following linear inequality through equivalent transformation: (twenty three)

[0055] Next, this is generalized to multiple 0-1 variables. Multiplying (t = 0, 1, ..., n). Introducing a 0-1 variable X, we can achieve the following through equivalent transformation: This can be transformed into the following linear inequality: (twenty four)

[0056] Each term in the objective function (21) is multiplied by n+1 0-1 variables, because x t Since it is a 0-1 variable, 1-x t It is also a 0-1 variable. Therefore, for each of the n+1 0-1 variables multiplied, a 0-1 variable X is introduced. t By performing a process similar to equation (24) to transform it into a linear inequality, the objective function (21) can be transformed into the form of equation (25). The equation involving the multiplication of the introduced n+1 0-1 variables can be transformed into a linear inequality as shown in equation (26): (25)

[0057] In the formula, X0, X1, X2, ..., X t , ..., X n All are introduced 0-1 variables: (26)

[0058] ② Multiplying a 0-1 variable and a continuous variable

[0059] Introducing continuous variable ω t The big M method can be used to obtain ω t =X t λ t Transformed into a linear inequality constraint as shown in equation (27): (27)

[0060] Therefore, the objective function (21) can be further transformed into a linear expression as follows: (28)

[0061] The branch-type extended power flow equations (7)-(10) are nonlinear constraints, and equations (9)-(10) only apply to closed branches. First, by introducing linear inequality constraints, the active power, reactive power, and current of the disconnected line are made zero, and this constraint has no effect on closed branches: (29)

[0062] After introducing the linear inequality constraint (29), equations (7)-(8) can be transformed into linear constraints as follows: (30) (31)

[0063] Since equation (9) only applies to closed branches, the big M method can be used to further relax it, transforming it into linear inequality constraints of equations (32)-(33), and after the transformation, it is not necessary to introduce constraints that only apply to closed branches: (32) (33)

[0064] Due to the introduction of the linear inequality constraint (29), equation (10) becomes a non-convex quadratic equation applicable to all branches. A second-order cone relaxation is then applied to it, as follows: (34)

[0065] The non-convex quadratic equation (12) in the operational constraints of distributed photovoltaic power stations is relaxed using the convex hull relaxation method. First, the equality sign is relaxed, and the equation is written in the following second-order cone inequality constraint form: (35)

[0066] Since the convex relaxation here expands the feasible region, the following constraints are added: (36)

[0067] Among them, V PVimax / U PVimax and V PVimin / U PVimin Let be the upper and lower bounds of the voltage and its square of the distributed photovoltaic power station at node i, respectively. The feasible region of the voltage and its square relationship of the photovoltaic power station after convex relaxation is as follows: Figure 2 As shown in the shaded area.

[0068] Therefore, the SVSM model of the distribution network considering switch switching is transformed into a mixed integer second-order cone programming model, with the objective function being equation (28) and the constraints including equations (11), (13)-(20), (26)-(27), and (29)-(36). This model can be solved quickly and reliably using the CPLEX solver.

[0069] The following application scenario will be used to verify and illustrate the static voltage stability margin analysis method for distribution networks considering switch switching:

[0070] Taking a modified IEEE-33 node distribution network as an example, the correctness and effectiveness of the proposed static voltage stability margin analysis method considering switch switching are verified. The hardware environment of the test system for the example is an Intel(R) Xeon(R) E3-1270 CPU @3.50 GHz, 32G memory, Win10 64bit operating system, and programming in GAMS win64 41.5.0 software.

[0071] The revised wiring diagram of the IEEE-33 node distribution network is as follows: Figure 3 As shown in the diagram, the red dashed line represents the tie switches. The base power of the distribution network is 1 MVA, and the base voltage is 12.66 kV. Node 1 is the slack node, and node 16 is connected to a 300 kW photovoltaic power station. There are five tie switches in the distribution network, located at 8-21, 9-15, 12-22, 18-33, and 25-29.

[0072] First, under the original topology, without considering switch switching, the line currents are required to meet the safety limit constraints. At this time, the distribution network SVSM model is the traditional branch-type optimal power flow model (1)-(6), (11)-(14), without switch state changes, and is a continuous nonlinear programming model, which can be solved using the CONOPT solver. Solving this model, the distribution network SVSM without considering switch switching is 0.1760.

[0073] Next, based on the original topology of the distribution network, node loads, and tie switch connection points, the corresponding switch switching operations for each line when the current exceeds the limit are set, i.e., which switch is opened and closed respectively. A 0-1 variable α is introduced to represent the line switch status. ijtThe SVSM of the IEEE-33 node distribution network considering switch switching was calculated. Model 1 is a mixed integer nonlinear programming model (7)-(19), (22), which was solved using the BARON solver. Model 2 is a mixed integer second-order cone programming model (11), (13)-(20), (26)-(36) which is transformed by linearizing and convex relaxing the nonlinear constraints in Model 1 and solved using the CPLEX solver. Assuming that the maximum number of switch switching operations n=3, the calculation results of the SVSM of the distribution network considering switch switching are shown in Table 1. The switch switching corresponding to the solution results of the two models are as follows: the current of line 12-13 exceeds the limit, the switch of line 12-13 is opened, the switch of line 9-15 is closed, and the current of all lines does not exceed the limit after the switch switching. Calculation results show that switching operations to transfer power when the line current exceeds the limit can reduce the load level of the overloaded line, ensuring that the current of all lines remains within the safe operating range after the switching operation, and improving the distribution network SVSM. Furthermore, the switching schemes corresponding to the solutions obtained by the two methods are consistent, and the calculated distribution network SVSM considering switching is very similar, indicating that the transformed mixed-integer second-order cone programming model has high computational accuracy. In addition, the computation time of Model 2 is 385.312s, which is 95.23% less than that of Model 1 (8069.937s), indicating that transforming the model into a mixed-integer second-order cone programming model effectively reduces the solution difficulty and significantly reduces computation time. Therefore, the method proposed in this embodiment can significantly improve computational efficiency while maintaining the accuracy of distribution network SVSM calculation.

[0074] Table 1. Calculation results for the IEEE-33 node distribution network considering switch switching.

[0075] Then, the solution results of the mixed-integer second-order cone programming model were calculated and substituted into the deviations corresponding to the original nonlinear constraints to further verify the accuracy of Model 2 after relaxation. The deviations on both sides of the ≤ sign in the calculated second-order cone inequalities (34) and (35) are shown in Table 2. It can be seen that the deviations on both sides of the ≤ sign in inequalities (34) and (35) are relatively small, indicating that relaxing the nonlinear quadratic equations (10) and (12) into second-order cone inequalities (34) and (35) has high calculation accuracy and will not bring too much error to the SVSM calculation of the distribution network.

[0076] Table 2. Deviations of the second-order cone inequality

[0077] The above results demonstrate that the proposed distribution network SVSM analysis method considering switchover can initiate switchover operations when the distribution line current exceeds the safe operating limit as the load increases, thus maintaining the line current within the allowable safe operating range. The obtained SVSM is more consistent with the actual operation of the distribution network, ensuring its safe and stable operation. This verifies the correctness and effectiveness of the proposed model and solution method, and significantly improves computational efficiency. This invention provides an effective technical solution for SVSM evaluation of distribution networks in high-load and high-penetration distributed power generation scenarios.

[0078] In summary, the SVSM analysis method for distribution networks considering switch switching provided in this embodiment has the following technical advantages compared with the prior art:

[0079] (1) This invention constructs a distribution network SVSM model considering switch switching, with the goal of maximizing load growth parameters. For this distribution network SVSM model, the current limit values ​​of each line, the maximum number of network switch switching operations, and the corresponding switch switching operations when the current of each line exceeds the limit are given. When the current of a distribution line exceeds the safe operating limit as the load increases, the model will automatically act according to the pre-set switch switching operations, thereby changing the network topology, optimizing the power flow distribution, and ensuring that the current of all lines remains within the thermal stability allowable range after the switch switching, thus realizing the direct solution of the maximum load growth parameters under the condition that the distribution network can transfer power supply.

[0080] (2) This invention addresses the nonlinearity and nonconvexity of the SVSM model for distribution networks by proposing a linearization and convex relaxation method for the nonlinear constraints in the model, transforming the mixed-integer nonlinear programming model into a mixed-integer second-order cone programming model. While maintaining the computational accuracy of the SVSM model for distribution networks, this invention significantly reduces the difficulty of solving the problem, effectively shortens the computation time, and greatly improves the applicability and computational efficiency of the model in actual distribution network engineering.

[0081] The above embodiments are merely illustrative of the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made based on the essence of the content of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for analyzing the static voltage stability margin of a distribution network considering switch switching, characterized in that, include: A distribution network SVSM model considering line switch switching is constructed, and the distribution network SVSM model aims to maximize the load growth parameter; For the SVSM model of the distribution network, the current limit value of each line, the maximum number of network switch switching operations, and the corresponding switch switching operation when the current of each line exceeds the limit are given. The initial state of the line switch is set to the corresponding fixed value representing the original topology of the distribution network; Solve the SVSM model of the distribution network to obtain the number of switch switching operations and the line switch states corresponding to the SVSM and network topology of the distribution network after the switch switching. The SVSM model for the distribution network aims to maximize the load growth parameters. (1) In the formula, λ t For load growth parameters, the subscript t represents the variable after the t-th line switch switching operation, t=0, 1, 2, 3,..., n, where n is the maximum number of switch switching operations. It is stipulated that each switch switching operation only disconnects and closes one line switch respectively. The constraints of the distribution network SVSM model include extended power flow equations, which include: Under a certain distribution network topology, the branch-type extended power flow equations of the distribution network are as follows: (2) (3) (4) (5) In the formula, k: j→k represents the set of terminal nodes k of the branch with node j as the starting point, P ijt and Q ijt R represents the active and reactive power at the beginning of branch ij, respectively. ij and x ij These are the resistance and reactance of branch ij, respectively. P represents the square of the current in branch ij. PVjt and Q PVjt P represents the active and reactive power outputs of the photovoltaic power station at node j, respectively. Lj0 and Q Lj0 These represent the active and reactive power absorbed by the load at node j, respectively. PLj and b QLj Let b represent the growth pattern of active and reactive power of the load at node j. PLj =P Lj0 b QLj =Q Lj0 U it Represents the square of the voltage at node i; The extended power flow equations also include: In the operation of a power distribution network, the current in each line must be limited to a safe and permissible range after the line switches are switched on or off, as follows: (6) In the formula, The maximum value of the square of the line current ij; In the operation of a distribution network, considering the switching operations of distribution line switches as the load increases, a 0-1 variable α representing the state of the line switches is introduced. ijt Modify the power flow equations (2)-(5) to obtain the branch-type extended power flow equations applicable to the switching of distribution line switches, as shown in equations (7)-(10); Equations (7)-(8) represent the active and reactive power balance equations for each node connecting all branches, and equations (9)-(10) represent the voltage drop equations and the relationship between branch current and power for all closed branches: (7) (8) (9) (10) In the formula, S l Let α be the set of all branches in the distribution network. ijt α is a 0-1 variable representing the switching state of line ij. ijt =1 indicates that line ij is connected, α ijt =0 indicates that line ij is disconnected.

2. The method for analyzing the static voltage stability margin of a distribution network considering switch switching as described in claim 1, characterized in that, The constraints of the distribution network SVSM model also include operating constraints for distributed photovoltaic power plants, which include: The reactive power-voltage control of distributed photovoltaic power stations adopts a droop control mode, and the operating constraints are as follows: (11) (12) (13) (14) In the formula, k qi V is the droop control coefficient for the photovoltaic power station at node i. PVit and U PVit Q represents the voltage and square of the photovoltaic power station at node i, respectively. PVit and Q PViN These are the actual and rated reactive power outputs of the photovoltaic power station at node i, respectively, Q. PVimax and Q PVimin Q PVit The upper and lower limits of V PVimax and V PVimin V PVit The upper and lower limits.

3. The method for analyzing the static voltage stability margin of a distribution network considering switch switching as described in claim 2, characterized in that, The constraints of the distribution network SVSM model also include network switch switching constraints, which include: Introducing 0-1 variables μ ijt To determine whether the line current ij exceeds the limit, the line current constraint (6) is transformed into the following inequality constraint: (15) Where M is a positive number greater than other relevant variables in the model, and ε is a positive number close to 0; when At that time, the line current ij did not exceed the limit, μ ijt =0; when When the line current ij exceeds the limit, μ ijt =1; Based on the calculated μ ijt Perform line switch switching operations; before the switch switching operations, based on the distribution network wiring diagram, node load and tie switch connection point, set the corresponding switch switching operation when the current of each line exceeds the limit, that is, which switch to close and open to transfer power.

4. The method for analyzing the static voltage stability margin of a distribution network considering switch switching as described in claim 3, characterized in that, The expression for the switch-on / off operation is as follows: (16) (17) (18) In the formula, o ijt and c ijt For 0-1 variables; o ijt =0 indicates that the switching state of line ij remains unchanged, o ijt =1 indicates that the switch of line ij is open; c ijt =0 indicates that the switching state of line ij remains unchanged, c ijt =1 indicates that the switch of line ij is closed; if line lk is the line with the greatest current over-limit, then its switching operation is the corresponding o. abt The circuit breaker with value = 1 is open, c cdt The circuit breaker with value 1 is closed; the rest... The line corresponding to o ijt =0 and c ijt =0, the switch state remains unchanged; Based on this, the switching state α of each line after the switching operation can be obtained from equation (18). ij(t+1) If all line currents do not exceed the limit, then μ lkt =0, no switching operation occurs, and the power grid topology remains unchanged.

5. The method for analyzing the static voltage stability margin of a distribution network considering switch switching as described in claim 4, characterized in that, Introduce 0-1 variables x t This indicates whether, after the t-th switching operation, there is still a situation where the line current exceeds the limit and a corresponding switching operation needs to be performed again: (19) In the formula, when x t When =1, all lines o ijt =0 indicates that there is no line current exceeding the limit after the t-th switch switching; when x t When =0, there exists a line o. ijt =1 indicates that after the t-th switch switching, there is a situation where the line current exceeds the limit and the corresponding switch switching operation is executed, and it is assumed that only the line with the largest current limit exceedance will execute the corresponding switch switching operation; After switching operations are performed, the distribution network topology changes, and each topology corresponds to a set of branch-type extended power flow equations; x is introduced into the objective function. t Let t = 0, 1, ..., n, representing the values ​​of λ after the t-th switching operation in sequence. t Maximum value; after the t-th switching operation, there is no line current exceeding the limit when solving the distribution network SVSM, i.e., x t If λ = 1, then the topology at this point is the final topology, λ t The maximum value is the final SVSM; at this time, relevant constraints need to be introduced as shown in equation (20), and the objective function needs to be modified to the form of equation (21); if x0=x1=...=x n =1, then the distribution network does not experience line current exceeding limits as the load increases, and no switching operations occur; if x0=0, x1=...=x n =1, then the distribution network may experience line current exceeding the limit as the load increases. After performing a switch switching operation, the line power flow thermal stability constraint is satisfied. (20) (21) Assuming n=3, then the constraint (20) and objective function (21) are in the form shown in equation (22); (22)。 6. The method for analyzing the static voltage stability margin of a distribution network considering switch switching as described in claim 5, characterized in that, Solving the distribution network SVSM model includes: converting the distribution network SVSM model into a mixed integer second-order cone programming model for solution, including: Linearizing the objective function (21), the linearization of the objective function (21) includes: Multiplying 0-1 variables by 0-1 variables: For the product of two 0-1 variables, AB, where A, B ∈ {0, 1}, introducing the 0-1 variable C, we can transform C = AB into the following linear inequality through equivalent transformation: (23) Generalization to multiple 0-1 variables Multiplying (t = 0, 1, ..., n); introducing a 0-1 variable X, through equivalent transformation, can... This can be transformed into the following linear inequality: (24) Each term in the objective function (21) is multiplied by n+1 0-1 variables, and the objective function (21) is transformed into the form of (25): (25) In the formula, X0, X1, X2, ..., X t , ..., X n All are introduced 0-1 variables; (26) Multiplying a 0-1 variable with a continuous variable introduces the continuous variable ω. t ω is obtained through the big M method t =X t λ t Transformed into a linear inequality constraint as shown in equation (27): (27) The objective function (21) is transformed into a linear expression as follows: (28)。 7. The method for analyzing the static voltage stability margin of a distribution network considering switch switching as described in claim 4, characterized in that, The step of converting the distribution network SVSM model into a mixed integer second-order cone programming model for solution also includes: The branch-type extended power flow equations (7)-(10) are nonlinear constraints, and equations (9)-(10) only apply to closed branches; by introducing linear inequality constraints, the active power, reactive power, and current of the disconnected line are made zero, and this constraint has no effect on closed branches: (29) After introducing the linear inequality constraint (29), equations (7)-(8) are transformed into linear constraints as follows: (30) (31) Equation (9) is further relaxed using the Big M method, and transformed into the linear inequality constraints of Equations (32)-(33). After the transformation, there is no need to introduce constraints that only apply to closed branches. (32) (33) Due to the introduction of the linear inequality constraint (29), equation (10) becomes a non-convex quadratic equation applicable to all branches. A second-order cone relaxation is then applied to it, as follows: (34) The non-convex quadratic equation (12) in the operating constraints of distributed photovoltaic power stations is relaxed using the convex hull relaxation method; first, the equality sign is relaxed, and the equation is written in the following second-order cone inequality constraint form: (35) The following constraints are added: (36) Among them, V PVimax / U PVimax and V PVimin / U PVimin These are the upper and lower limits of the voltage and its square of the distributed photovoltaic power station at node i, respectively.

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