Multi-objective oriented power distribution network security domain operating point screening method, medium and device
By constructing a static security domain for the distribution network and combining Monte Carlo sampling and non-dominated sorting, the Pareto optimal solution is selected, which solves the problem of difficulty in coordinating the optimization of economy and reliability in the distribution network and achieves efficient and accurate selection of operating points.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2026-02-04
- Publication Date
- 2026-06-05
AI Technical Summary
Existing technologies are insufficient for effectively coordinating and optimizing economy and reliability in power distribution networks. Traditional methods have low computational efficiency and poor convergence, making it difficult to meet the needs of real-time operation decision-making, and they lack comprehensive screening and optimization of multiple objectives.
A multi-objective distribution network safety domain operation point selection method is adopted. By establishing power flow equations and safety operation criteria, a static safety domain is constructed. Combined with Monte Carlo sampling and non-dominated sorting, fuzzy multi-attribute decision-making is used to select the optimal operation point, thereby achieving a unified optimization of economy and reliability.
It improves computational efficiency, ensures the physical authenticity and high fidelity of results, avoids the risk of misjudgment, and achieves a unified optimization of safety, economy and reliability. It is suitable for active distribution network dispatching and distributed power source coordination control.
Smart Images
Figure CN122159256A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power system operation and optimization control technology, and in particular to a method, medium and equipment for screening operating points in the safety domain of distribution networks for multiple objectives. Background Technology
[0002] With the increasing penetration of distributed generation in distribution networks, the operating characteristics of these networks are becoming increasingly complex. Traditional deterministic operation methods are struggling to adapt to the safety and economic challenges posed by their randomness and intermittency. The distribution network safety domain, as a systematic safety assessment tool, can characterize the system's safe operating boundary from the perspective of injected power space, providing operators with intuitive safety margin information. However, existing safety domain analysis methods mostly focus on static safety constraints and have not fully considered multi-objective collaborative optimization problems such as operational economy and power supply reliability.
[0003] Traditional safety domain analysis is mainly based on the optimal power flow feasible region model. It determines the system safety boundary by solving for the set of feasible points that satisfy the power flow equations and constraints. However, existing methods mostly remain at the level of a binary "safe / unsafe" division, lacking further screening and optimization of internal points.
[0004] In existing technologies, distribution network operation optimization typically employs single-objective or weighted multi-objective optimization methods, which struggle to effectively handle conflicts and trade-offs between objectives and are prone to getting trapped in local optima. Although multi-objective evolutionary algorithms have demonstrated good performance in multi-objective optimization problems, their application in distribution network security domain boundary selection remains limited. Furthermore, traditional methods often suffer from low computational efficiency and poor convergence when dealing with high-dimensional, nonlinear, and multi-constraint distribution network optimization problems, making it difficult to meet the needs of real-time operational decision-making.
[0005] In active distribution networks incorporating distributed generation (DG) such as solar and wind power, economic efficiency and reliability are often mutually constrained. Increasing voltage stability margin requires additional reactive power support or energy storage capacity, leading to increased investment and operating costs. Conversely, pursuing the lowest possible cost may push the system close to its operational limits, potentially triggering safety risks. Therefore, a multi-objective optimization method based on the safety domain is needed to automatically balance economic efficiency and reliability objectives while ensuring operational safety. Summary of the Invention
[0006] The main objective of this invention is to provide a method, medium, and device for screening operating points in the safety domain of a distribution network for multiple objectives, in order to solve existing technical problems.
[0007] To achieve the above objectives, the present invention provides a method for screening operating points in the security domain of a distribution network with multiple objectives, comprising the following steps; S1: Obtain information on distribution network nodes and branches, establish power flow equations, set constraints based on safe operation criteria, and construct the static security domain of the distribution network; S2: Based on the power vector injection direction characteristics of node distributed power sources, establish a safety domain boundary search model. Initially delineate the boundary using the initial direction, evaluate the error, and adaptively add new search directions until the boundary approximation accuracy meets the standard. S3: Monte Carlo sampling is used to generate candidate running points under safety constraints, economic and reliability indices are calculated, Pareto optimal solution set is obtained through fast non-dominated sorting, and comprehensive membership degree is calculated by combining fuzzy multi-attribute decision-making and objective weights to screen the optimal running point; S4: Initially sort the target running points according to the comprehensive membership degree, establish a multi-objective vector function and normalize it, set the weight vector according to the decision-maker's preference, calculate the comprehensive evaluation value, sort it and provide it to the upper-level decision-maker for selection.
[0008] Furthermore, S1 specifically includes; S1.1 Establish power flow equations for the distribution network based on line and node information. Combined with the safe operation criteria of the distribution network, set operation constraints and regard the set of operating points that satisfy the power flow equations and constraints as the static safety domain of the distribution network. Obtain information such as nodes and lines in the distribution network, and define the node set as... Where Nd is the number of nodes. If the first and last nodes of a line are i and j respectively, then the line is defined as... The set consisting of all lines can be defined as For any node i, construct the power flow equations for the distribution network:
[0009] (1) In the formula: and Let be the net injected active and reactive power at node i, respectively. and Let these be the active and reactive power outputs of the distributed power source at node i, respectively. and These represent the active and reactive loads of node i, respectively. and Let i and j be the voltage amplitudes at nodes i and j, respectively. The voltage phase angle difference between nodes i and j and The lines are respectively The electrical conductance and susceptance between them; S1.2. Based on the operational safety criteria of the distribution network, different constraints are set: (1) Node voltage constraints: (2) In the formula: and These are the upper and lower limits of the voltage amplitude at node i, respectively; (2) Branch flow constraints: (3) In the formula: This represents the complex power flowing from node i to node j. Indicates the line The limit of transmission power; (3) Output constraints of distributed power sources: (4) In the formula: and Let be the maximum and minimum active power output of the distributed power source at node i, respectively. and These are the maximum and minimum reactive power outputs of the distributed power source at node i, respectively. (4) Active and reactive power constraints of the load: (5) In the formula: and Let be the maximum and minimum active power demand of node i, respectively. and These are the maximum and minimum values of the reactive power demand of node i, respectively; (5) Constraints on phase angle difference between nodes: (6) In the formula: This represents the voltage phase angle difference between node i and node j. and This represents the maximum and minimum values of the voltage phase angle difference between nodes i and j; Suppose that there are Ng nodes in the system equipped with distributed generation, and the active and reactive power output vectors of the distributed generation are respectively... , ,in , These are the active and reactive power outputs of the kth distributed power source, respectively. Define the node-distributed power associativity matrix : (7) Therefore, we can conclude that: (8) Define the vector x consisting of system node voltages and phases as a state variable: (9) Define the node power injection vector u as a control variable: (10) The set of operating points that satisfy the power flow equations and safe operation constraints of the distribution network is constructed into the static security domain of the distribution network: (11) In the formula: f(x,u) is the power flow equation, and g(x,u) is the set that satisfies the above inequality constraints.
[0010] Furthermore, S2 specifically includes; S2.1 Assume a given baseline operating point and a power injection direction Find the maximum running point that satisfies the constraints in this direction, that is, solve for the maximum feasible distance α along this direction; At a given benchmark operating point Based on this, the first step is to select the set of nodes participating in the power injection change according to the distributed power source fluctuation. And according to the preset distributed power output change mode, for the collection Each node in the process is assigned a corresponding weight k. i ; Then, based on the power injection value P of each node at the reference operating point... i,0 and Q i,0 Construct the original power injection change vector : ;in: ; For nodes that do not participate in the change, set their power injection increment to zero, and normalize the original power injection change vector to obtain the unit power injection direction vector:
[0011] Known Based on the above analysis, the following optimization model is constructed: (12) Slack variables are introduced into the safety constraints of the initial model. Furthermore, by adding a penalty term for the slack variables to the objective function, the following improved "relaxation-penalty" robust optimization model can be obtained: (13) In the formula: f is the AC power flow equation, g is various inequality constraints, u0 is the control variable at the initial operating point, α is the scaling factor along the direction, and s is the slack variable. A sufficiently large penalty factor is used to ensure that the optimal solution tends to s≈0; The solution is obtained by using mature optimization software and iterating step by step. When the slack variables converge to zero, the solution obtained is the true boundary point of the safe region. S2.2. Search in each direction to obtain the boundary of the security domain and determine several injection directions. Solve the above maximization problem for each direction to obtain the corresponding... This yields a set of security domain boundary points. These points are then used to form a security domain boundary through piecewise interpolation, resulting in an approximate model.
[0012] Furthermore, S2.2 specifically includes; S2.2.1 Selecting Initial Directions: Select a set of sparse initial directions. Solving the robust optimization model for each direction yields a set of initial boundary points. ; S2.2.2, Connect adjacent boundary points p i and p i+1 Connect them into line segments: The normal distance between the midpoint of a line segment and the true boundary is used as an indicator of the approximation error of that segment. Calculate the midpoint of the chord: (14) In the formula: p i Let p be the coordinate vector of the i-th determined safety domain boundary point in the power injection space. i+1 Let be the coordinate vector of the (i+1)th adjacent security domain boundary point; Along the normal direction of the chord Perform a short-range boundary search to obtain the true boundary points. Calculation error: (15) In the formula: The initial and final coordinates are... The coordinates of the actual boundary endpoint; Calculate the index value corresponding to the line segment with the largest current error: (16) if Then a new search direction is generated at the point where the error is maximum. This direction points to the reference point and The direction of the connection will Add the direction set, return to step 2.2.1, and perform the iteration; Step 2.2.3, Convergence Criterion: When the approximation error of all segments... All less than the precision threshold The search process terminates when the maximum number of iterations is reached; the final set of boundary points constitutes a high-precision approximation of the safe region boundary, and the safe region boundary can be obtained by fitting the boundary points using the least squares method. (17).
[0013] Furthermore, S3 specifically includes; S3.1 For the security domain established above, its operating point can be represented as: For a running point u0, along a certain growth direction, the minimum scaling factor required to reach the safety boundary is calculated based on the continuous power flow method. ; Therefore, the reliability index function is selected as follows: (18) In the formula: For load margin; The economic indicator function is: (19) In the formula: For investment costs, For network loss costs, For operation and maintenance costs; Based on the optimal economic and reliability considerations of the operating points within the security domain, the following multi-objective optimization model is constructed: (20) In the formula: Let the objective function vector be... For the economic objective function, The reliability objective function; S3.2, From the security domain The method uses Monte Carlo sampling to sample a large number of running points and calculates the bi-objective value for each sampling point. and Then perform non-dominated sorting: if a point There are no other points. , making ≤ and ≥ If at least one of the inequalities is strictly true, then It is a Pareto optimal solution, and the set of all optimal solutions is the Pareto optimal solution set: (twenty one) Each solution corresponds to a running point. Assume that the Pareto solution set contains k solutions, and each solution contains two sub-objective function values. S3.3. Select the optimal solution in the Pareto solution set based on the fuzzy multi-attribute decision method; First, the Pareto solution set is standardized to establish a standardized decision matrix: (twenty two) In the formula: E is the standardized decision matrix, Let be the fuzzy membership function of the i-th solution in the Pareto solution set with respect to the j-th sub-objective. Let j be the sub-objective function value in the i-th scheme. , Let be the extreme value of the i-th sub-objective in the Pareto solution set; Based on standardized decision matrix First, determine the relative importance measure of the i-th solution under the j-th sub-objective among all solutions. : (twenty three) Subsequently, the information entropy value of the j-th sub-target is calculated. : (twenty four) Furthermore, the objective weights of each sub-indicator are determined based on the information entropy value. : (25) Calculate the overall membership degree of each option: (26) choose The largest solution is taken as the optimal target running point.
[0014] Furthermore, S4 specifically includes; according to Sort the run points in the Pareto solution set to obtain the set of candidate optimal run points: (27) The multi-objective vector function is established based on reliability and economic indicators as follows: (28) Normalize the multi-objective indicators: (29) Set the weight vector according to the decision-maker's preferences: (30) Calculate the overall evaluation value: (31) according to The data are sorted from highest to lowest, with key performance parameters highlighted for decision-makers to choose from.
[0015] In another aspect, the present invention also discloses a computer-readable storage medium for a multi-objective distribution network security domain operation point selection method, which stores a computer program. When the computer program is executed by a processor, the processor performs the steps of the method described above.
[0016] In another aspect, the present invention also discloses a computer device for a multi-objective distribution network security domain operation point screening method, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the above method.
[0017] The beneficial effects of this invention are reflected in: This invention optimizes based on a safety domain, strictly limiting the search space of the operating point to a feasible region that satisfies constraints such as voltage, power flow, and line flow. This method constructs a static safety domain based on an accurate AC power flow model, without linearizing or approximating voltage, reactive power, or line power flow, ensuring the physical authenticity and high fidelity of the results and avoiding the numerous infeasible solutions and misjudgment risks present in traditional DC or linearized models. Secondly, the invention employs a two-stage strategy of "approximate search + local correction," introducing directional search and piecewise hyperplane approximation mechanisms. This enables rapid location of potential boundary points in a high-dimensional control space, followed by precise correction through AC power flow and constraint verification. This significantly reduces the computational load of the full-domain simulation search, improving computational efficiency by more than an order of magnitude, meeting the requirements for real-time or near-real-time safety assessment.
[0018] This invention introduces a non-dominated ranking mechanism to automatically extract the Pareto front solution set. It does not rely on manually set weights, avoiding subjective biases caused by human intervention and ensuring the objectivity and diversity of the solution set. Compared to the traditional weighted sum method, it has a stronger multi-objective expressive capability. Finally, by introducing a fuzzy multi-attribute decision-making method, the Pareto solution set is subjected to secondary screening, comprehensively considering decision-maker preferences and indicator information entropy. This ensures that the final solution is both data-driven and reasonable, and possesses high decision interpretability and practical value.
[0019] This invention achieves unified optimization of "safety, economy, and reliability", and features high computational efficiency, strong robustness, and good embeddability. It can be applied to scenarios such as active distribution network scheduling, distributed power source coordination control, and energy storage configuration optimization, providing a scientific and feasible new method for intelligent decision-making in new power systems. Attached Figure Description
[0020] Figure 1 This is a schematic flowchart of a multi-objective distribution network security domain operation point selection method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the power distribution network structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram of boundary search and direction refinement according to an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the comprehensive evaluation and ranking of an embodiment of the present invention. Detailed Implementation
[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. 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.
[0022] Please see Figure 1-4 This invention provides a method for selecting operating points in the safety domain of a distribution network with multiple objectives, comprising the following steps: Step 1: Obtain information such as nodes and branches in the distribution network, establish distribution network power flow equations based on branch and node information, set safe operation constraints in combination with distribution network safe operation criteria, and construct the static safety domain of the distribution network based on the above power flow equations and safe operation constraints. Step 2: In the direction of power vector injection of the distributed power source at the node, as the load increases, the operating point will be located at the safety limit of a certain constraint. Based on this, a safety domain boundary search model can be established. Based on the safety domain model established in Step 1, the safety domain boundary can be roughly depicted with a small number of initial directions, and its error with the true boundary can be evaluated. New search directions are adaptively added in the direction with the largest error until the approximate accuracy of the entire boundary meets the requirements. Step 3: Based on the distribution network security domain model established in Step 1, a large number of candidate operating points satisfying security constraints are generated using the Monte Carlo sampling method. For each candidate operating point, the economic and reliability indices of the distribution network under that operating point are calculated. All candidate operating points are processed using a fast non-dominated sorting algorithm to select the Pareto optimal solution set where neither option is superior in terms of economy or reliability. Based on the fuzzy multi-attribute decision-making method, the comprehensive membership degree of each scheme in the Pareto solution set is calculated considering objective weights, and the scheme with the highest comprehensive membership degree is selected as the optimal operating point, achieving a comprehensive optimal decision considering safety, economy, and reliability. Step 4: Based on the comprehensive membership degree, the corresponding target operation points are initially ranked, and a multi-objective vector function composed of reliability and economic indicators is established. To eliminate the influence of different indicator dimensions, each indicator is normalized to obtain a standardized function. Weight vectors are set according to the actual operational preferences of the decision-makers, and the comprehensive evaluation value of each operation point is calculated. The candidate operation points are ranked from high to low according to the comprehensive evaluation value, and the ranking results are then provided to the upper-level decision-makers for selection.
[0023] The following are detailed explanations: Step 1 specifically includes: Step 1.1: Establish power flow equations for the distribution network based on line and node information. Combined with the safe operation criteria of the distribution network, set operating constraints and regard the set of operating points that satisfy the power flow equations and constraints as the static security domain of the distribution network. Obtain information such as nodes and lines in the distribution network, and define the node set as... Where Nd is the number of nodes. If the first and last nodes of a line are i and j respectively, then the line is defined as... The set consisting of all lines can be defined as For any node i, construct the power flow equations for the distribution network: (1) In the formula: and Let be the net injected active and reactive power at node i, respectively. and Let these be the active and reactive power outputs of the distributed power source at node i, respectively. and These represent the active and reactive loads of node i, respectively. and Let i and j be the voltage amplitudes at nodes i and j, respectively. The voltage phase angle difference between nodes i and j and The lines are respectively The electrical conductance and susceptance between them.
[0024] Step 1.2: Based on the operational safety criteria of the power distribution network, set different constraints: 1) Node voltage constraints: (2) In the formula: and These are the upper and lower limits of the voltage amplitude at node i, respectively.
[0025] 2) Branch flow constraints: (3) In the formula: This represents the complex power flowing from node i to node j. Indicates the line The limit of transmission power.
[0026] 3) Output constraints of distributed power sources: (4) In the formula: and Let be the maximum and minimum active power output of the distributed power source at node i, respectively. and These are the maximum and minimum reactive power outputs of the distributed power source at node i, respectively.
[0027] 4) Active and reactive power constraints of the load: (5) In the formula: and Let be the maximum and minimum active power demand of node i, respectively. and These are the maximum and minimum values of the reactive power demand of node i, respectively.
[0028] 5) Constraints on phase angle difference between nodes: (6) In the formula: This represents the phase angle difference between node i and node j. and This represents the maximum and minimum phase angle difference between nodes i and j.
[0029] Suppose that there are Ng nodes in the system equipped with distributed generation, and the active and reactive power output vectors of the distributed generation are respectively... , ,in , These represent the active and reactive power outputs of the k-th distributed power source, respectively.
[0030] Define the node-distributed power associativity matrix : (7) Therefore, we can conclude that: (8) Define the vector x consisting of system node voltages and phases as a state variable: (9) Define the node power injection vector u as a control variable: (10) The set of operating points that satisfy the power flow equations and safe operation constraints of the distribution network is constructed into the static security domain of the distribution network: (11) In the formula: f(x,u) is the power flow equation, and g(x,u) is the set that satisfies the above inequality constraints.
[0031] Step 2 specifically includes: Step 2.1: Assume a given baseline operating point. and a power injection direction Find the maximum running point that satisfies the constraints in this direction, that is, solve for the maximum feasible distance α along this direction; At a given benchmark operating point Based on this, the first step is to select the set of nodes participating in the power injection change according to the distributed power source fluctuation. And according to the preset distributed power output change mode, for the collection Each node in the process is assigned a corresponding weight k. i .
[0032] Then, based on the power injection value P of each node at the reference operating point... i,0 and Q i,0 Construct the original power injection change vector :
[0033] in:
[0034] For nodes that do not participate in the change, set their power injection increment to zero, and normalize the original power injection change vector to obtain the unit power injection direction vector:
[0035] Known Based on the above analysis, the following optimization model is constructed: (12) Non-negative relaxation variables are introduced into the safety constraints of the initial model. Furthermore, by adding a penalty term for the slack variables to the objective function, the following improved "relaxation-penalty" robust optimization model can be obtained: (13) In the formula: f is the AC power flow equation, g is various inequality constraints, u0 is the control variable at the initial running point, α is the scaling factor along the direction, and s is the non-slack variable. A sufficiently large penalty factor is used to ensure that the optimal solution tends to s ≈ 0.
[0036] The solution is obtained by using mature optimization software and iterating step by step. When the slack variables converge to zero, the solution obtained is the true boundary point of the safe region.
[0037] Step 2.2: Search in each direction to obtain the boundary of the security region and determine several injection directions. (Covering different nodes and different source load combinations), solve the above maximization problem for each direction to obtain the corresponding... This yields a set of security domain boundary points. These points are then used to form a security domain boundary through piecewise interpolation, creating an approximate model. Step 2.2.1: Select initial directions: Select a set of sparse initial directions. Solving the robust optimization model for each direction yields a set of initial boundary points. .
[0038] Step 2.2.2: Connect adjacent boundary points p i and p i+1 Connect them into line segments. The normal distance between the midpoint of a line segment and the true boundary is used as an indicator of the approximation error of that segment. Calculate the midpoint of the chord: (14) In the formula: p i Let p be the coordinate vector of the i-th determined safety domain boundary point in the power injection space. i+1 It is the coordinate vector of the (i+1)th adjacent security domain boundary point.
[0039] Along the normal direction of the chord Perform a short-range boundary search to obtain the true boundary points. Calculation error: (15) In the formula: The initial and final coordinates are... These are the coordinates of the actual boundary endpoint.
[0040] Calculate the index value corresponding to the line segment with the largest current error: (16) if (Accuracy threshold) then generates a new search direction at the point where the error is maximum. This direction points to the reference point and The direction of the connection will Add the direction set, return to step 2.2.1, and perform the iteration.
[0041] Step 2.2.3, Convergence Criterion: When the approximation error of all segments... All less than the precision threshold The search process terminates when the maximum number of iterations is reached. The final set of boundary points constitutes a high-precision approximation of the safe region boundary. The safe region boundary can be obtained by fitting the boundary points using the least squares method. (17) Step 3 specifically includes: Step 3.1: For the security domain established above, its operating point can be represented as follows: For a running point u0, along a certain growth direction, the minimum scaling factor required to reach the safety boundary is calculated based on the continuous power flow method. ; Therefore, the reliability index function is selected as follows: (18) In the formula: This represents the load margin.
[0042] The economic indicator function is: (19) In the formula: For investment costs, For network loss costs, For operation and maintenance costs.
[0043] Based on the optimal economic and reliability considerations of the operating points within the security domain, the following multi-objective optimization model is constructed: (20) In the formula: Let the objective function vector be... For the economic objective function, The objective function is the reliability objective function.
[0044] Step 3.2, from the security domain The method uses Monte Carlo sampling to sample a large number of running points and calculates the bi-objective value for each sampling point. and Then perform non-dominated sorting: if a point There are no other points. , making ≤ and ≥ If at least one of the inequalities is strictly true, then It is a Pareto optimal solution, and the set of all optimal solutions is the Pareto optimal solution set: (twenty one) Each solution corresponds to a running point. Assume that the Pareto solution set contains k solutions, and each solution contains two sub-objective function values.
[0045] Step 3.3: Select the optimal solution in the Pareto solution set based on the fuzzy multi-attribute decision method; First, the Pareto solution set is standardized to establish a standardized decision matrix: (twenty two) In the formula: E is the standardized decision matrix, Let be the fuzzy membership function of the i-th solution in the Pareto solution set with respect to the j-th sub-objective. Let j be the sub-objective function value in the i-th scheme. , Let be the extreme value of the i-th sub-objective in the Pareto solution set.
[0046] Based on standardized decision matrix First, determine the relative importance measure of the i-th solution under the j-th sub-objective among all solutions. : (twenty three) Subsequently, the information entropy value of the j-th sub-target is calculated. : (twenty four) The entropy value reflects the degree of dispersion of the indicator data. The lower the entropy value, the greater the amount of information provided by the sub-objective in the comprehensive evaluation, and the more prominent its importance.
[0047] Furthermore, the objective weights of each sub-indicator are determined based on the information entropy value. : (25) Calculate the overall membership degree of each option: (26) choose The largest solution is taken as the optimal target running point.
[0048] Step 4 specifically includes: according to Sort the run points in the Pareto solution set to obtain the set of candidate optimal run points: (27) The multi-objective vector function is established based on reliability and economic indicators as follows: (28) Normalize the multi-objective indicators: (29) Set the weight vector according to the decision-maker's preferences: (30) Calculate the overall evaluation value: (31) according to The data are sorted from highest to lowest, with key performance parameters highlighted for decision-makers to choose from.
[0049] The following are examples: Figure 2 The network topology of the test case in this study is shown. A typical 10-node radial distribution network is selected as the example system, with node 1 as the slack node and the rest as PQ nodes. The system contains three distributed generation sources, located at nodes 3, 6, and 9 respectively. The voltage constraints for each node are as follows:
[0050] The main line and node parameters are shown in Table 1:
[0051] The load and DG configuration of each node are shown in Table 2:
[0052] The AC power flow equations were solved using the Newton-Raphson method under the reference operating conditions (DG3=0.2 MW, DG6=0.3 MW, DG9=0.4 MW). The calculation results are as follows: Total network loss P loss = 0.083MW; Lowest node voltage U min =0.95 (node 8); The biggest trend on the side streets | S 8-9 | = 0.93 MVA.
[0053] The reference node voltages are shown in Table 3:
[0054] Constructing power flow equations With constraints Determine the static security domain of the distribution network, and set the reference operating point u0 and injection direction. A "relaxation-punishment" model was established, where the punishment factor λ=10. 5 Through iterative solutions, the maximum feasible scaling coefficients in each direction are obtained as shown in Table 4:
[0055] The direction refinement is achieved using the chord midpoint method, which converges when the error threshold τ = 0.01pu. Boundary search and direction refinement are as follows: Figure 3As shown.
[0056] Within the security domain, 1000 feasible points are randomly sampled, and their economic and reliability indices are calculated. Where ρ is the load margin, the results are shown in Table 5:
[0057] The Pareto front is obtained through non-dominated sorting. The Pareto solution set is then standardized, and its entropy and weights are calculated. Figure 4 The comprehensive evaluation ranking chart shown below yields the following calculation results: Entropy value: , ; Weight: , ; Final overall membership degree: .
[0058] The results show that scheme D has the highest overall membership degree. And the optimal solution is shown in Table 6:
[0059] As shown above, the constructed static safety domain accurately reflects the feasible region of the system under multiple constraints. The "relaxation-penalty" boundary search method converges quickly, requiring only two rounds of refinement, with an error of less than 0.01 pu. Multi-objective optimization achieves a balance between economy and reliability. Compared to the benchmark, the optimal solution (DG balanced output) reduces network losses by nearly 20%, increases load margin by approximately 8%, and comprehensively improves operating voltage. This method can be directly applied to small and medium-sized distribution network dispatching and safety assessment systems.
[0060] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.
[0061] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.
[0062] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute any of the mobile source emission prediction methods based on time-series feature migration described in the above embodiments.
[0063] It is understood that the systems, devices, and storage media provided in the embodiments of the present invention correspond to the methods provided in the embodiments of the present invention, and the explanations, examples, and beneficial effects of the relevant content can be referred to the corresponding parts of the above methods.
[0064] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (SSD)).
[0065] 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 a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0066] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.
[0067] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for selecting operating points in the security domain of a distribution network oriented towards multiple objectives, characterized in that: Includes the following steps; S1: Obtain information on distribution network nodes and branches, establish power flow equations, set constraints based on safe operation criteria, and construct the static security domain of the distribution network; S2: Based on the power vector injection direction characteristics of node distributed power sources, establish a safety domain boundary search model. Initially delineate the boundary using the initial direction, evaluate the error, and adaptively add new search directions until the boundary approximation accuracy meets the standard. S3: Monte Carlo sampling is used to generate candidate running points under safety constraints, economic and reliability indices are calculated, Pareto optimal solution set is obtained through fast non-dominated sorting, and comprehensive membership degree is calculated by combining fuzzy multi-attribute decision-making and objective weights to screen the optimal running point; S4: Initially sort the target running points according to the comprehensive membership degree, establish a multi-objective vector function and normalize it, set the weight vector according to the decision-maker's preference, calculate the comprehensive evaluation value, sort it and provide it to the upper-level decision-maker for selection.
2. The method for selecting operating points in a distribution network security domain oriented towards multiple objectives as described in claim 1, characterized in that: S1 specifically includes; S1.1 Establish power flow equations for the distribution network based on line and node information. Combined with the safe operation criteria of the distribution network, set operation constraints and regard the set of operating points that satisfy the power flow equations and constraints as the static safety domain of the distribution network. Obtain information such as nodes and lines in the distribution network, and define the node set as... Where Nd is the number of nodes; if the first and last nodes of the line are i and j respectively, then the line is defined as The set consisting of all lines can be defined as For any node i, construct the power flow equations for the distribution network: (1) In the formula: and Let be the net injected active and reactive power at node i, respectively. and Let these be the active and reactive power outputs of the distributed power source at node i, respectively. and These represent the active and reactive loads of node i, respectively. and Let i and j be the voltage amplitudes at nodes i and j, respectively. The voltage phase angle difference between nodes i and j and The lines are respectively The electrical conductance and susceptance between them; S1.
2. Based on the operational safety criteria of the distribution network, different constraints are set: (1) Node voltage constraints: (2) In the formula: and These are the upper and lower limits of the voltage amplitude at node i, respectively; (2) Branch flow constraints: (3) In the formula: This represents the complex power flowing from node i to node j. Indicates the line The limit of transmission power; (3) Output constraints of distributed power sources: (4) In the formula: and Let be the maximum and minimum active power output of the distributed power source at node i, respectively. and These are the maximum and minimum reactive power outputs of the distributed power source at node i, respectively. (4) Active and reactive power constraints of the load: (5) In the formula: and Let be the maximum and minimum active power demand of node i, respectively. and These are the maximum and minimum values of the reactive power demand of node i, respectively; (5) Constraints on phase angle difference between nodes: (6) In the formula: This represents the voltage phase angle difference between node i and node j. and This represents the maximum and minimum values of the voltage phase angle difference between nodes i and j; Suppose that there are Ng nodes in the system equipped with distributed generation, and the active and reactive power output vectors of the distributed generation are respectively... , ,in , These are the active and reactive power outputs of the kth distributed power source, respectively. Define the node-distributed power associativity matrix : (7) Therefore, we can conclude that: (8) Define the vector x consisting of system node voltages and phases as a state variable: (9) Define the node power injection vector u as a control variable: (10) The set of operating points that satisfy the power flow equations and safe operation constraints of the distribution network is constructed into the static security domain of the distribution network: (11) In the formula: f(x,u) is the power flow equation, and g(x,u) is the set that satisfies the above inequality constraints.
3. The method for selecting operating points in a distribution network security domain oriented towards multiple objectives as described in claim 1, characterized in that: S2 specifically includes; S2.1 Assume a given baseline operating point and a power injection direction Find the maximum running point that satisfies the constraints in this direction, that is, solve for the maximum feasible distance α along this direction; At a given benchmark operating point Based on this, the first step is to select the set of nodes participating in the power injection change according to the distributed power source fluctuation. And according to the preset distributed power output change mode, for the collection Each node in the process is assigned a corresponding weight k. i ; Then, based on the power injection value P of each node at the reference operating point... i,0 and Q i,0 Construct the original power injection change vector : ;in: ; For nodes that do not participate in the change, set their power injection increment to zero, and normalize the original power injection change vector to obtain the unit power injection direction vector: Known Based on the above analysis, the following optimization model is constructed: (12) Slack variables are introduced into the safety constraints of the initial model. Furthermore, by adding a penalty term for the slack variables to the objective function, the following improved "relaxation-penalty" robust optimization model can be obtained: (13) In the formula: f is the AC power flow equation, g is various inequality constraints, u0 is the control variable at the initial operating point, α is the scaling factor along the direction, and s is the slack variable. A sufficiently large penalty factor is used to ensure that the optimal solution tends to s≈0; The solution is obtained by using mature optimization software and iterating step by step. When the slack variables converge to zero, the solution obtained is the true boundary point of the safe region. S2.
2. Search in each direction to obtain the boundary of the security domain and determine several injection directions. Solve the above maximization problem for each direction to obtain the corresponding... This yields a set of security domain boundary points. These points are then used to form a security domain boundary through piecewise interpolation, resulting in an approximate model.
4. The method for selecting operating points in a distribution network security domain oriented towards multiple objectives as described in claim 3, characterized in that: S2.2 specifically includes; S2.2.1 Selecting Initial Directions: Select a set of sparse initial directions. Solving the robust optimization model for each direction yields a set of initial boundary points. ; S2.2.2, Connect adjacent boundary points p i and p i+1 Connect them into line segments: The normal distance between the midpoint of a line segment and the true boundary is used as an indicator of the approximation error of that segment. Calculate the midpoint of the chord: (14) In the formula: p i Let p be the coordinate vector of the i-th determined safety domain boundary point in the power injection space. i+1 Let be the coordinate vector of the (i+1)th adjacent security domain boundary point; Along the normal direction of the chord Perform a short-range boundary search to obtain the true boundary points. Calculation error: (15) In the formula: The initial and final coordinates are... The coordinates of the actual boundary endpoint; Calculate the index value corresponding to the line segment with the largest current error: (16) if Then a new search direction is generated at the point where the error is maximum. This direction points to the reference point and The direction of the connection will Add the direction set, return to step 2.2.1, and perform the iteration; Step 2.2.3, Convergence Criterion: When the approximation error of all segments... All less than the precision threshold The search process terminates when the maximum number of iterations is reached; the final set of boundary points constitutes a high-precision approximation of the safe region boundary, and the safe region boundary can be obtained by fitting the boundary points using the least squares method. (17)。 5. The method for selecting operating points in a distribution network security domain oriented towards multiple objectives as described in claim 1, characterized in that: S3 specifically includes; S3.1 For the security domain established above, its operating point can be represented as: For a running point u0, along a certain growth direction, the minimum scaling factor required to reach the safety boundary is calculated based on the continuous power flow method. ; Therefore, the reliability index function is selected as follows: (18) In the formula: For load margin; The economic indicator function is: (19) In the formula: For investment costs, For network loss costs, For operation and maintenance costs; Based on the optimal economic and reliability considerations of the operating points within the security domain, the following multi-objective optimization model is constructed: (20) In the formula: Let the objective function vector be... For the economic objective function, The reliability objective function; S3.2, From the security domain The method uses Monte Carlo sampling to sample a large number of running points and calculates the bi-objective value for each sampling point. and Then perform non-dominated sorting: if a point There are no other points. , making ≤ and ≥ If at least one of the inequalities is strictly true, then It is a Pareto optimal solution, and the set of all optimal solutions is the Pareto optimal solution set: (21) Each solution corresponds to a running point. Assume that the Pareto solution set contains k solutions, and each solution contains two sub-objective function values. S3.
3. Select the optimal solution in the Pareto solution set based on the fuzzy multi-attribute decision method; First, the Pareto solution set is standardized to establish a standardized decision matrix: (22) In the formula: E is the standardized decision matrix, Let be the fuzzy membership function of the i-th solution in the Pareto solution set with respect to the j-th sub-objective. Let j be the sub-objective function value in the i-th scheme. , Let be the extreme value of the i-th sub-objective in the Pareto solution set; Based on standardized decision matrix First, determine the relative importance measure of the i-th solution under the j-th sub-objective among all solutions. : (23) Subsequently, the information entropy value of the j-th sub-target is calculated. : (24)。 6. The method for selecting operating points in a distribution network security domain oriented towards multiple objectives as described in claim 5, characterized in that: The objective weights of each sub-indicator are determined based on the information entropy value. : (25) Calculate the overall membership degree of each option: (26) choose The largest solution is taken as the optimal target running point.
7. The method for selecting operating points in a distribution network security domain oriented towards multiple objectives as described in claim 6, characterized in that: S4 specifically includes; according to Sort the run points in the Pareto solution set to obtain the set of candidate optimal run points: (27) The multi-objective vector function is established based on reliability and economic indicators as follows: (28) Normalize the multi-objective indicators: (29) Set the weight vector according to the decision-maker's preferences: (30) Calculate the overall evaluation value: (31) according to The data are sorted from highest to lowest, with key performance parameters highlighted for decision-makers to choose from.
8. A readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it causes the processor to perform the steps of the method as described in any one of claims 1 to 7.
9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the computer program is executed by the processor, it causes the processor to perform the steps of the method as described in any one of claims 1 to 7.