A method for solving power distribution system security region considering N-1 criterion

Abstract

The application discloses a kind of distribution system safety domain solving method considering N-1 criterion, belong to distribution system safety analysis and planning technical field, including the following steps: step 1: establish normal scene and N-1 fault scene set;Step 2: construct linear security constraint;Step 3: construct single scene initial outer approximation domain;Step 4: solve the most infeasible point and generate feasible cut;Step 5: obtain the intersection of all scene safety domains under N-1 criterion.To solve the problems that the safety boundary of the prior art distribution system is difficult to model uniformly, high-dimensional boundary is difficult to solve explicitly, and multi-scenario fault constraints are difficult to be uniformly included.The output result can directly serve the dispatch point fast safety check, boundary slice display, fault scenario risk analysis and subsequent dispatch optimization.The minimum value in the upper bound of each scene is obtained.

Description

Technical Field

[0001] This invention belongs to the field of power distribution system safety analysis and planning technology, specifically involving a method for solving the safety domain of a power distribution system considering the N-1 criterion, which is applicable to the characterization of the safety boundary, safety verification, safety domain analysis and safety margin assessment of power distribution systems. Background Technology

[0002] With the large-scale integration of distributed power sources, energy storage, and flexible loads, the operating state of power distribution systems exhibits characteristics such as multi-source disturbances, high-dimensional coupling, and complex boundaries. Traditional safety verification methods based on a single operating point can only determine whether a given state meets the operating constraints, making it difficult to reveal the overall safety boundary shape of the system in the multi-dimensional state space, and also making it difficult to provide explicit boundary information for scheduling optimization, risk warning, and safety margin analysis.

[0003] Current research on the security domain of power distribution systems still has the following shortcomings: (1) Most methods only consider normal operating conditions and do not uniformly incorporate the N-1 single component fault constraints into the definition of the safety domain, resulting in the safety domain not being able to directly reflect the operational range of the system after the fault.

[0004] (2) The power flow equations and operating constraints of the power distribution system are significantly nonlinear, and it is difficult to directly obtain the boundary of the high-dimensional safety domain. Traditional methods often rely on a large number of samples or numerical enumerations, which have problems such as large computational load and limited boundary accuracy.

[0005] (3) For the net injected state space of high-dimensional nodes, existing methods usually lack interpretable boundary representations, which is not conducive to subsequent scheduling point projection, boundary slice visualization and fast calculation of safety margin.

[0006] (4) When considering multiple scenarios, especially the N-1 fault scenario, the feasible domains under different scenarios need to be modeled and intersected in a unified manner. Existing methods still have room for improvement in terms of unified approximation and computational efficiency in multiple scenarios.

[0007] Therefore, there is an urgent need for a solution method for the security domain of power distribution systems that can simultaneously consider normal operating conditions and single fault conditions, explicitly characterize high-dimensional security boundaries, and has high solution efficiency. Summary of the Invention

[0008] To address the shortcomings and deficiencies in existing technologies, the present invention aims to provide a method for solving the security domain of a power distribution system that considers the N-1 criterion, thereby solving the problems in existing technologies such as the difficulty in uniformly modeling the security boundary of a power distribution system, the difficulty in explicitly solving high-dimensional boundaries, and the difficulty in uniformly incorporating fault constraints from multiple scenarios.

[0009] The technical problem solved by this invention is addressed by the following technical solution: A method for solving the security domain of a power distribution system considering the N-1 criterion includes the following steps: Step 1: Establish a set of normal and N-1 fault scenarios: Establish a unified definition model of the power distribution system security domain that considers normal and N-1 fault conditions. The unified definition model of the power distribution system security domain defines the power distribution system security domain as a set of state points that satisfy power flow equality constraints and operation inequality constraints. The state points of the power distribution system security domain are defined as the node net power limit vector. Step 2: Construct linear security constraints: Based on the unified definition model of the power distribution system security domain, the linearized DistFlow method is used to establish security constraint models for the normal scenario and the N-1 scenario. The feasible domain of the power distribution system in each scenario is written in a unified linear inequality form and mapped to the state variables corresponding to the security domain dimension. Step 3: Construct the initial outer approximation domain for a single scenario: Construct an initial outer approximation envelope containing the real safe domain for each scenario, and define the most infeasible point relative to the real safe domain in the current outer approximation domain; Step 4: Solve for the most infeasible point and generate feasible cuts: Use the binary boundary external approximation method to generate new linear feasible cuts for the most infeasible point, and iteratively update the scene external approximation domain until the external approximation domain converges to the boundary of the corresponding scene's true safe domain. Step 5: Find the intersection of the security domains of all scenarios under the N-1 criterion: Eliminate redundant constraints by using the umbrella constraint identification method, find the intersection of the single-scenario security domains obtained under normal operating conditions and all N-1 fault scenarios, and obtain the boundary expression of the power distribution system security domain that satisfies the N-1 criterion.

[0010] Furthermore, in step 1, the unified definition model for the power distribution system security domain is as follows: , In the formula, Π (c) For the scene c The security domain below, c For running scene indexing, oh For the security domain state vector, oh It consists of the net active power and net reactive power of each node. y (c) Let F be the vector of internal decision variables corresponding to scenario c. （c） Let c be the constraint matrix. f (c) For scenario c, there is a constant term. C It is a mapping matrix.

[0011] Furthermore, in step 2, the safety constraint models under normal and N-1 scenarios include: node power balance constraints, node voltage upper and lower limits constraints, line power flow capacity constraints, distributed power output constraints, and energy storage static operation constraints at a single moment. For the N-1 fault scenario, a constraint matrix corresponding to the fault scenario is formed by modifying the network topology matrix, branch capacity limits, and available control variables. F (c) and constant term f (c) .

[0012] Furthermore, in step 3, the state vector components in each dimension are calculated in the scene. c The upper and lower bounds below each dimension oh i Find its upper and lower bounds: , Construct the initial outer approximation envelope of the safety domain for this scene: , In the formula, n ω For the dimension of the security domain, The initial outer approximation envelope is a region that includes the real-world safety domain: .

[0013] Furthermore, in step 4, the new linear feasible cut: , In the formula, l (c)※ , m (c)※ The corresponding optimal dual solution. oh For the security domain state vector, f (c) This is the constant term corresponding to scenario c; Then, the outer approximation domain is gradually shrunk to approximate the boundary of the true safe region, where the boundary vector coefficients corresponding to the feasible cut are... m By introducing the binary boundary assumption, each boundary vector component takes only three values: {-1, 0, 1}, thus transforming the feasible cut generation process into a mixed-integer linear programming problem for solution.

[0014] Furthermore, step 4 also includes a safe domain characterization acceleration strategy, which includes: adopting a hierarchical expansion strategy for the boundary vector, gradually increasing the number of non-zero components to improve the efficiency of high-dimensional boundary search. , In the formula, It is a row vector. Let be the positive vector of the boundary normal vector of scene c. Let be the negative vector of the boundary normal vector of scene c. To simplify the counting of non-zero components in the normal vector; A symbolic decomposition strategy is adopted for the boundary normal vectors. The boundary vectors that are all non-negative and all non-positive are solved in parallel, and then the mixed positive and negative boundary vectors are solved to reduce the solution scale of mixed integer linear programming.

[0015] Furthermore, in step 5, The single-scenario security domain: , In the formula, For a single-scene security domain under scenario c, D(c) Let be the cutting plane coefficient matrix in scene c. d(c) This refers to the right-hand item in scenario c; Stack all single-scenario security domains: , In the formula, For a single-scene security domain under scenario N-1, D N-1 Let N be the cutting plane coefficient matrix for scene N-1. dN-1 This is the right-hand item under scenario N-.

[0016] Furthermore, the boundary of the power distribution system security domain satisfying the N-1 criterion is expressed as follows: , In the formula, u is the umbrella constraint set.

[0017] An electronic device includes at least one processor and at least one memory, wherein the processor may include one or more processing cores, the processor executes instructions, programs, code sets or instruction sets stored in the memory, and calls data stored in the memory to perform any of the methods described above.

[0018] A computer-readable storage device, wherein computer program instructions are permanently stored therein, and when the computer program instructions are invoked and loaded by a processor and executed, the method described in any of the preceding claims is performed.

[0019] Compared with the prior art, the present invention has the following beneficial effects: 1. By unifying the normal operating conditions and N-1 fault conditions into the definition of the safety domain, the resulting boundary can directly reflect the true safe operating range under fault constraints.

[0020] 2. The scenario-based modeling approach based on linearized DistFlow can balance physical meaning and solution efficiency, making it suitable for characterizing high-dimensional safety boundaries in power distribution systems.

[0021] 3. By adopting the binary boundary external approximation iterative method, the high-dimensional nonlinear security domain can be gradually transformed into an explicit hyperplane intersection form, which facilitates visualization, projection, and security margin calculation.

[0022] 4. By introducing the binary boundary assumption of direction vector and the acceleration strategy, the difficulty of boundary search in high-dimensional scenes can be effectively reduced and the efficiency of solving multiple scenes can be improved.

[0023] 5. The output results can directly serve for rapid safety verification of scheduling points, boundary slice display, fault scenario risk analysis, and subsequent scheduling optimization. The minimum value among the upper bounds of each scenario is taken. Attached Figure Description

[0024] Figure 1 This is the logic block diagram for this method. Detailed Implementation

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0026] A method for solving the security domain of a power distribution system considering the N-1 criterion is provided in the appendix. Figure 1 As shown, it includes: Step 1: Establish a set of normal operating conditions and N-1 fault scenarios. First, determine the dimensions of the security domain to be characterized, and construct a set of scenarios including normal operating conditions and all single component failure scenarios, including single line failure and single transformer failure.

[0027] A unified definition model for the safety domain of a power distribution system is established, considering both normal operating conditions and N-1 single-component fault conditions. The safety domain of a power distribution system is defined as a set of state points that satisfy power flow equality constraints and operational inequality constraints. The state points of the safety domain of a power distribution system are defined as the node net power limit vectors. The N-1 single-component fault scenario is also known as the N-1 fault scenario, hereinafter referred to as the N-1 scenario.

[0028] Unified definition of power distribution system security domain in N-1 scenario 1) Basic security domain definition Let the state vector of the power distribution system's security domain be...

[0029] in, n ω Let be the dimension of the safety region. If a general complex power safety region is used, then we can take .

[0030] If we only study the limit of net active power at the nodes, then let

[0031] The safety region is defined as the set of all operating points that satisfy the power flow equations and operational constraints; therefore, its general form can be written as:

[0032] In the formula, h ( oh )=0 indicates a power flow equality constraint. g ( oh )≤0 represents inequality constraints such as equipment capacity, voltage upper and lower limits, and converter station control. The boundary expression of the safety region is usually a high-dimensional nonlinear set. To simplify the calculation, it will be rewritten as a linear polyhedron in the following text.

[0033] 2) Definition of security domain for N-1 scenario remember c For running scene indexing, c =0 indicates normal operating conditions. c ∈ C ᴺ -1 This represents all single-component failure scenarios. For any scenario... c ,make y (c) Let be the vector of internal decision variables in this scenario, including branch power flow, node voltage, active and reactive power of the converter station, control variables, and necessary auxiliary variables. After linearization, the internal feasible region of this scenario can be uniformly written as:

[0034] Then use the mapping matrix C If we select the state variables corresponding to the security domain dimension from the internal variables, then we have

[0035] Therefore, the scene c The safe domain is the internal feasible set in the state space. oh Projection on:

[0036] Define the set of trusted single faults as

[0037] in, C ᴸ、 C ᵀ、 C ⱽ represent sets of single fault scenarios such as lines, transformers, and converters. According to the N-1 criterion, a given state vector... oh Only if it remains feasible under normal operating conditions and any single failure scenario does it belong to the N-1 safety domain.

[0038] The equivalent definition of the N-1 security region can be obtained.

[0039] The above formula shows that after considering the N-1 criterion, the safety domain is no longer a projection of a single scene, but rather "the intersection of multiple scene projection sets".

[0040] Step 2: Construct linear safety constraints For normal operating conditions and various N-1 fault scenarios, the linearized DistFlow method is used to establish safety constraint models under normal and N-1 scenarios. The feasible domain of the power distribution system under each scenario is written in a unified linear inequality form and mapped to the state variables corresponding to the safety domain dimension. These constraints include: node power balance constraints to ensure that the net injected power of each node and the power flow of adjacent branches are in a conservation relationship; node voltage relationship constraints to describe the linear approximate relationship between branch power and node voltage; node voltage upper and lower limit constraints to ensure that the voltage of each node is within the allowable range; line power flow capacity constraints to ensure that the power transmitted by the branch does not exceed the thermal stability limit; distributed generation output constraints to limit the upper and lower limits of the output of distributed generation; and energy storage single-moment static constraints to limit the boundary of energy storage charging and discharging power.

[0041] Linearized DistFlow Scenario-based Security Constraint Model First, linearized constraint models are established for both normal operating conditions and single-fault operating conditions. A linearized DistFlow power flow approximation is then used. For any scenario... c The node power balance can be written as:

[0042]

[0043] in, d ( j ) represents a node j The set of downstream branches. If the net injection of a node is defined as the combined result of distributed power sources, energy storage, and load, then:

[0044]

[0045] Using the linearized DistFlow model, the node voltage relationship can be written as:

[0046] The upper and lower limits of the voltage at each node are:

[0047] The power flow capacity constraint of the line can be written as:

[0048] The output constraints of distributed power sources are:

[0049]

[0050] Energy storage can be written as follows under static modeling at a single moment:

[0051] After transforming all the above equality constraints into a unified linear inequality through variable substitution or decomposition, the scenario can be obtained. c Compact matrix form:

[0052] For the N-1 fault scenario, the faulty line or device can be reflected by modifying the network topology matrix, capacity limit, and corresponding available control variables. Therefore, each fault scenario corresponds to a different set of... F (c) and f (c) .

[0053] Step 3: Construct the initial external approximation domain for a single scene For each scenario c Construct each containing the real security domain Π (c) The initial outer approximation envelope is determined, and the most infeasible point relative to the true safe region in the current outer approximation domain is defined, providing the initial boundary for subsequent iterative shrinkage.

[0054] Binary boundary approximation characterization method 1) Construction of the initial outer approximation safe region First, construct an initial outer envelope in the state space containing the real N-1 safety regions. For each dimension... oh i Find its upper and lower bounds:

[0055] Therefore, the scene can be obtained. c Initial outer approximation safe region:

[0056] The above equation is only a very rough estimate of the initial external approximation, and it is clear that:

[0057] Subsequently, through continuous searching The least feasible point is identified, and new feasible cuts are added, gradually shrinking the outer envelope.

[0058] Step 4: Solve for the most infeasible point and generate feasible cuts, introducing a binary boundary assumption and accelerating the solution. Specifically, the binary boundary external approximation method is used to generate new feasible cuts for the most infeasible point, and the external approximation domain of the scene is iteratively updated until the external approximation domain converges to the true safe domain boundary of the corresponding scene. For high-dimensional safe regions, the following acceleration strategies can be further adopted: hierarchical expansion strategy: first search for boundary normal vectors containing only a small number of non-zero components, and then gradually increase the number of non-zero components; symbol decomposition strategy: solve the three types of normal vectors in parallel: all non-negative, all non-positive, and mixed positive and negative.

[0059] 1) Generation of permissible cuts For a given state point oh 0 Define its context c The minimum infeasible distance is:

[0060] st

[0061]

[0062]

[0063] Among them, s + s - δ represents the positive and negative correction values ​​for each dimension of the state vector. c ( oh 0 If )=0, then oh 0 Belongs to Π (c) Inside or boundary; if d c ( oh 0 If )>0, then it means oh 0 In the scene c This approach is not feasible, and the larger the objective function value, the further it is from the true safe region.

[0064] Let the current scene be set. c The outer approximation is Then its relative real security domain Π (c) The most infeasible distance can be written as:

[0065] To solve the max-min problem:

[0066] st

[0067]

[0068]

[0069] Taking the dual of the inner minimization problem, we obtain the dual form:

[0070] st

[0071]

[0072]

[0073] Solve for the optimal solution given by the above equation. oh ※ This is the state point that is least feasible relative to the true safe region in the current external approximation. If =0, then it means Already with Π (c) overlap; if If the value is greater than 0, then a new effective tangent plane can be directly constructed based on the dual solution.

[0074] Let the optimal dual solution be . l (c)※ , m (c)※ Then, according to the weak duality relation, for the true security region Π (c) any point in the middle oh All of them are:

[0075] Therefore, it can be added to the current out-of-scene approximation as a new feasible cut to obtain the updated out-of-scene approximation:

[0076] That is, repeatedly performing the process of "finding the most infeasible point - constructing a feasible cut - updating the external approximation".

[0077] Bilinear terms in the dual problem m ᵀ oh This will affect the solution efficiency. Following the approach of the first paper, a binary boundary assumption is introduced for the boundary normal vector coefficients, so that each component only takes the values ​​of -1, 0, and 1:

[0078]

[0079]

[0080] The expression can then be transformed into a mixed-integer linear programming problem:

[0081] st

[0082]

[0083]

[0084]

[0085]

[0086] In this way, each iteration only needs to solve a mixed-integer linear programming problem to obtain the scenario. c The new security domain cutting plane is then defined.

[0087] 2) Security Domain Characterization Acceleration Strategy Hierarchical expansion strategy: If the dimension of the security region is high, a hierarchical expansion strategy and a symbolic decomposition strategy can be further adopted. The hierarchical expansion strategy searches step by step by controlling the number of non-zero normal vector coefficients:

[0088] The above formula means that we first search for the boundary with only one non-zero coefficient, and then gradually expand it to two or three coefficients until we get a sufficiently accurate boundary.

[0089] Symbolic decomposition strategy: For the three types of normal vectors, namely all non-negative, all non-positive, and mixed positive and negative, parallel solution can be used to generate the upper limit of energy, the lower limit of energy, and the climbing boundary, respectively, so as to reduce the size of the mixed integer linear programming problem.

[0090] Step 5: Find the intersection of the security regions of all scenarios under the N-1 criterion. Redundant constraints are eliminated by umbrella constraint identification method. The intersection of the single-scenario security domains obtained under normal operating conditions and all N-1 fault scenarios is obtained to obtain the boundary expression of the power distribution system security domain that satisfies the N-1 criterion. For normal operating conditions and all N-1 fault scenarios, repeat step 4 to obtain the safety domain Π(c) for each single scenario. Then, perform intersection calculations on all scenarios to obtain the final power distribution system safety domain that satisfies the N-1 criterion.

[0091] Solving the security domain of a power distribution system under the N-1 criterion Since the N-1 security domain is essentially the intersection of multiple scenario security domains, the most direct and safest approach is: First, calculate each scene c Single-scenario security domain:

[0092] Then stack all scenes:

[0093]

[0094]

[0095] Record the total number of constraints after stacking all scenes:

[0096] set up D N-1 The j Behavior , d N-1 The j The elements are The security domain of the power distribution system can then be written as:

[0097] Since the boundary hyperplanes obtained under different fault scenarios may have overlapping or inclusion relationships, the direct use of... As a final result, it often contains a large number of redundant constraints. Therefore, the umbrella constraint definition is introduced: if the first... j If the global feasible region changes after the constraint is applied, then the first constraint is called the first constraint. j A single constraint is called an umbrella constraint; the set of all umbrella constraints is called the umbrella constraint set.

[0098] For the j Constraints ,when When there exists a point on the y-th node that satisfies all other constraints, the y-th node... j The constraint is an umbrella constraint.

[0099] Design the following optimization problem to identify umbrella constraints:

[0100]

[0101]

[0102]

[0103] Therefore, when the optimal solution satisfies At that time, the first j The constraints are umbrella constraints. Extracting all umbrella constraints yields the umbrella constraint set:

[0104] After obtaining the umbrella constraint set u Then, extract the corresponding rows from the global stacked constraints and construct the redundant constraint matrix and right-hand side terms:

[0105]

[0106] The final security domain boundary of the power distribution system that satisfies the N-1 criterion can be written as:

[0107] The above is the expression of the boundary characterization result of the safety domain under the N-1 criterion: the final safety domain is still a hyperplane intersection, which can be directly used for safety verification, scheduling point projection, visualization slicing and safety margin analysis.

[0108] The core of this method includes: First, a unified expression for the safety domain of the power distribution system is established, unifying normal operating conditions and various single-component failure conditions into feasible domains under different scenarios. The safety domain is defined as a set of state points that satisfy power flow equations, node voltage constraints, line capacity constraints, distributed generation output constraints, and energy storage operation constraints. The state points in the power distribution system safety domain are the node net power limit vectors.

[0109] Secondly, a linearized DistFlow model is used to model the normal operating condition and the N-1 fault condition in a scenario-based manner, constructing the matrix form of the linear constraints under each scenario. Thirdly, an initial outer envelope of the safety domain is constructed. By solving for the most infeasible point, generating feasible cuts, and iteratively updating the outer approximation set, the safety domain boundary under a single N-1 fault scenario is gradually approximated. Simultaneously, the boundary vector binary assumption, hierarchical expansion strategy, and symbolic decomposition strategy are introduced to improve the efficiency of solving high-dimensional safety domains.

[0110] Finally, the safety domain expressions under normal operating conditions and all N-1 single fault scenarios are stacked, and redundant constraints are eliminated by umbrella constraint identification method to obtain the intersection of the safety domains under normal operating conditions and all N-1 single fault scenarios, thereby obtaining the boundary expression of the power distribution system safety domain that meets the N-1 safety verification requirements.

[0111] The serial numbers in the above embodiments are for descriptive purposes only and do not represent the chronological order of assembly or use of the components. Those skilled in the art will understand that the embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0112] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure one One or more processes and / or boxes Figure one A device that provides the functions specified in one or more boxes.

[0113] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0114] This application also provides an electronic device, which may include at least one processor and at least one memory. The processor may include one or more processing cores. The processor connects to various parts of the server using various interfaces and lines, and performs various functions of the server and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory, and by calling data stored in the memory.

[0115] This application also provides a computer-readable storage medium storing instructions. When executed by one or more processors, these instructions cause an electronic device to perform one or more of the methods described in the above embodiments.

[0116] Furthermore, the functional units in this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0117] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and the disclosure of practical truth. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for solving the security domain of a power distribution system considering the N-1 criterion, characterized in that, Includes the following steps: Step 1: Establish a set of normal and N-1 fault scenarios: Establish a unified definition model of the power distribution system security domain that considers normal and N-1 fault conditions. The unified definition model of the power distribution system security domain defines the power distribution system security domain as a set of state points that satisfy power flow equality constraints and operation inequality constraints. The state points of the power distribution system security domain are defined as the node net power limit vector. Step 2: Construct linear security constraints: Based on the unified definition model of the power distribution system security domain, the linearized DistFlow method is used to establish security constraint models for the normal scenario and the N-1 scenario. The feasible domain of the power distribution system in each scenario is written in a unified linear inequality form and mapped to the state variables corresponding to the security domain dimension. Step 3: Construct the initial outer approximation domain for a single scenario: Construct an initial outer approximation envelope containing the real safe domain for each scenario, and define the most infeasible point relative to the real safe domain in the current outer approximation domain; Step 4: Solve for the most infeasible point and generate feasible cuts: Use the binary boundary external approximation method to generate new linear feasible cuts for the most infeasible point, and iteratively update the scene external approximation domain until the external approximation domain converges to the boundary of the corresponding scene's true safe domain. Step 5: Find the intersection of the security domains of all scenarios under the N-1 criterion: Eliminate redundant constraints by using the umbrella constraint identification method, find the intersection of the single-scenario security domains obtained under normal operating conditions and all N-1 fault scenarios, and obtain the boundary expression of the power distribution system security domain that satisfies the N-1 criterion.

2. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 1, characterized in that, In step 1, the unified definition model for the security domain of the power distribution system is as follows: ， In the formula, Π (c) For the scene c The security domain below, c For running scene indexing, ω For the security domain state vector, ω It consists of the net active power and net reactive power of each node. y (c) Let F be the vector of internal decision variables corresponding to scenario c. （c） Let c be the constraint matrix. f (c) For scenario c, there is a constant term. C It is a mapping matrix.

3. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 2, characterized in that, In step 2, the safety constraint models under normal and N-1 scenarios include: node power balance constraints, node voltage upper and lower limit constraints, line power flow capacity constraints, distributed power output constraints, and energy storage static operation constraints at a single moment. For the N-1 fault scenario, a constraint matrix corresponding to the fault scenario is formed by modifying the network topology matrix, the branch capacity limit, and the available control variables. F (c) and constant term f (c) .

4. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 3, characterized in that, In step 3, the state vector components in each dimension are calculated in the scene. c The upper and lower bounds below each dimension ω i Find its upper and lower bounds: ， Construct the initial outer approximation envelope of the safety domain for this scene: ， In the formula, n ω For the dimension of the security domain, The initial outer approximation envelope is a region that includes the real-world safety domain: 。 5. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 4, characterized in that, In step 4, the new linear feasible cut: ， In the formula, λ (c)※ , μ (c)※ The corresponding optimal dual solution. ω For the security domain state vector, f (c) This is the constant term corresponding to scenario c; Then, the outer approximation domain is gradually shrunk to approximate the boundary of the true safe region, where the boundary vector coefficients corresponding to the feasible cut are... μ By introducing the binary boundary assumption, each boundary vector component takes only three values: {-1, 0, 1}, thus transforming the feasible cut generation process into a mixed-integer linear programming problem for solution.

6. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 5, characterized in that, Step 4 further includes a safe domain characterization acceleration strategy, which includes: adopting a hierarchical expansion strategy for the boundary vector, gradually increasing the number of non-zero components to improve the efficiency of high-dimensional boundary search. ， In the formula, It is a row vector. Let be the positive vector of the boundary normal vector of scene c. Let be the negative vector of the boundary normal vector of scene c. To simplify the counting of non-zero components in the normal vector; A symbolic decomposition strategy is adopted for the boundary normal vectors. The boundary vectors that are all non-negative and all non-positive are solved in parallel, and then the mixed positive and negative boundary vectors are solved to reduce the solution scale of mixed integer linear programming.

7. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 6, characterized in that, In step 5 The single-scenario security domain: ， In the formula, For a single-scene security domain under scenario c, D(c) Let be the cutting plane coefficient matrix in scene c. d(c) This refers to the right-hand item in scenario c; Stack all single-scenario security domains: ， In the formula, For a single-scene security domain under scenario N-1, D N-1 Let N be the cutting plane coefficient matrix for scene N-1. dN-1 This is the right-hand item under scenario N-.

8. The method for solving the security domain of a power distribution system considering the N-1 criterion according to claim 7, characterized in that, The boundary of the security domain of the power distribution system satisfying the N-1 criterion is expressed as follows: ， In the formula, u is the umbrella constraint set.

9. An electronic device, characterized in that, It includes at least one processor and at least one memory, wherein the processor may include one or more processing cores, the processor executes instructions, programs, code sets or instruction sets stored in the memory, and calls data stored in the memory to perform the method as described in any one of claims 1 to 8.

10. A computer-readable storage device, characterized in that, The storage device contains computer program instructions, which are invoked and loaded by the processor and executed to perform the method as described in any one of claims 1 to 8.

Images