Power distribution network differentiated reinforcement planning method based on improved NSGA-II algorithm and electronic equipment
By improving the NSGA-II algorithm and dynamic reassessment mechanism, and combining low-fidelity and high-fidelity models, differentiated reinforcement of distribution network branches was achieved, solving the problems of uneven resource allocation and heavy computational burden, improving power supply reliability and economy, and realizing rapid optimization and efficient evaluation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2026-05-12
- Publication Date
- 2026-06-12
Smart Images
Figure CN122198552A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of distribution network reinforcement planning, and in particular to a method and electronic equipment for differentiated reinforcement planning of distribution networks based on an improved NSGA-II algorithm. Background Technology
[0002] As the final link in the power supply chain, the reliability of the distribution network directly impacts the power quality for users. Statistics show that over 80% of power outages are attributed to distribution network faults. With the increasing dependence on electricity in modern society, ensuring the continuity of power supply from the distribution network has become a core task in power grid construction. Implementing targeted and differentiated hardening of the distribution network during the planning phase is a key strategy for improving system power supply reliability. However, achieving optimal differentiated hardening decisions requires not only establishing a scientific hardening plan but also matching it with an efficient reliability assessment model and a powerful multi-objective optimization algorithm to cope with increasingly complex power grid operating conditions.
[0003] However, existing technologies for distribution network reinforcement planning, reliability assessment, and optimization still have significant limitations in practical applications. In reinforcement planning, traditional techniques often employ uniform construction standards, failing to fully consider the differentiated impacts of varying environments and load importance on line fault risks. This leads to uneven allocation of reinforcement resources, making it difficult to maximize overall system reliability within a limited investment budget. In reliability assessment, traditional Monte Carlo simulation methods often face challenges in handling high-dimensional, low-probability fault scenarios, including large sample requirements and low computational efficiency, making it difficult to balance efficiency and accuracy in large-scale distribution network assessments. Regarding optimization of planning models, traditional multi-objective optimization algorithms require intensive full-scale reliability simulations for each candidate solution during the evolution process, resulting in a heavy computational burden, slow convergence, and difficulty in finding high-quality Pareto optimal solutions under limited computational resources.
[0004] Therefore, resolving the technical contradictions of blind resource allocation, redundant assessment calculations, and inefficient optimization searches in distribution network planning has become a critical issue that urgently needs to be addressed in the field of distribution network planning. A breakthrough in this area is of significant practical importance for promoting efficient and reliable distribution network planning and ensuring the continuity of power supply to users. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of existing technologies, such as uneven resource allocation in distribution network reinforcement planning, difficulty in balancing efficiency and accuracy in reliability assessment, heavy computational burden and slow convergence in multi-objective optimization, and to provide a distribution network differentiated reinforcement planning method and electronic equipment based on the improved NSGA-II algorithm.
[0006] In a first aspect, the present invention provides a method for differentiated reinforcement planning of distribution networks based on an improved NSGA-II algorithm, comprising:
[0007] S1: Obtain node information and branch information of the distribution network, select reinforcement strategies in combination with the differentiated reinforcement planning model of the overhead line of the distribution network, reinforce each branch in the distribution network, generate an initial reinforcement scheme, and construct the objective function corresponding to the initial reinforcement scheme. The objective function includes minimizing the expected value of power shortage and minimizing the comprehensive investment cost function. S2: Based on a preset low-fidelity model, calculate the expected value of power shortage for the initial reinforcement scheme, and simultaneously calculate the comprehensive investment cost of the initial reinforcement scheme; perform fast non-dominated sorting and congestion calculation on the initial reinforcement scheme according to the expected value of power shortage and the comprehensive investment cost, and obtain the non-dominated level label and congestion value of each initial reinforcement scheme. S3: Based on the preset dynamic re-evaluation ratio function, calculate the number of re-evaluation schemes in the initial reinforcement scheme, and select the corresponding number of schemes as re-evaluation schemes from the initial reinforcement scheme according to the non-dominated level label and congestion value. Use a high-fidelity model to calculate and update the expected value of power shortage of the re-evaluation scheme. S4: Based on the updated expected value of power shortage and comprehensive investment cost, perform fast non-dominated sorting and congestion calculation on the initial reinforcement scheme, and then generate offspring reinforcement schemes through selection, crossover and mutation operations. S5: Determine whether the current iteration optimization process meets the preset convergence criterion: If it does not meet the criterion, merge the initial reinforcement scheme and the offspring reinforcement scheme as the initial reinforcement scheme for the next iteration, and repeat S2–S4; if it meets the criterion, output the Pareto optimal solution set as the optimal reinforcement scheme.
[0008] Preferably, the node information includes node number, node type, and active and reactive load data corresponding to each node; the branch information includes the first node number, the last node number, the branch length, the branch impedance, the branch fault probability, and the branch switch status information for each branch.
[0009] Preferably, the reinforcement strategies of the differentiated reinforcement planning model for overhead power distribution lines include: no reinforcement, enhanced operation and maintenance, structural reinforcement, and equipment replacement. Different reinforcement strategies correspond to different failure probability reduction factors and reinforcement costs.
[0010] Furthermore, the overall investment cost includes reinforcement costs and operation and maintenance costs.
[0011] Furthermore, the low-fidelity model takes the fault location and reinforcement strategy of the distribution network as input and calculates the expected value of power shortage through the fault propagation method.
[0012] Preferably, the dynamic re-evaluation ratio function takes the minimum re-evaluation ratio benchmark in the initial stage, the maximum re-evaluation ratio peak allowed in the later stage of evolution, the current iteration number, the maximum iteration number, and the evolution accuracy adjustment index as inputs, outputs the ratio of the re-evaluation scheme to the initial reinforcement scheme, and then combines the ratio with the number of initial reinforcement schemes to determine the number of re-evaluation schemes.
[0013] Furthermore, the proportion of the re-evaluation scheme to the initial reinforcement scheme increases non-linearly with the number of iterations, and the growth rate is controlled by the evolution accuracy adjustment index.
[0014] Preferably, when selecting a reassessment scheme in S3, the initial reinforcement scheme with a smaller non-dominated level label number is preferred; within the same non-dominated level, the initial reinforcement scheme with a larger congestion value is preferred.
[0015] Preferably, the high-fidelity model uses an importance sampling method based on improved cross-entropy to calculate the expected value of power shortage.
[0016] In a second aspect, the present invention provides an electronic device including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the distribution network differentiated reinforcement planning method based on the improved NSGA-II algorithm as described in the first aspect.
[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention provides a differentiated reinforcement planning method for distribution networks based on an improved NSGA-II algorithm. By employing a differentiated reinforcement strategy, it achieves targeted reinforcement of distribution network branches, solving the problem of uneven resource allocation caused by traditional unified construction standards. This enables precise resource allocation and improves power supply reliability. The dynamic re-evaluation mechanism, combining low-fidelity and high-fidelity models, balances the efficiency and accuracy of reliability assessment, avoiding the computational drawbacks of traditional assessment methods. The improved NSGA-II algorithm reduces computational burden and accelerates convergence through a scientific optimization mechanism, while simultaneously using dual-objective optimization to balance power supply reliability and investment economy, addressing the core pain points of traditional planning. 2. This invention provides an electronic device that, through the synergistic effect of a memory and a processor, provides a reliable operating platform for the reinforcement planning method described in the first aspect, ensuring stable and efficient execution of the method, effectively solving the problems of heavy computational burden and slow convergence in power distribution network reinforcement planning optimization, and realizing the rapid output of the optimal reinforcement scheme. Attached Figure Description
[0018] Figure 1 This is a flowchart of the distribution network differentiated reinforcement planning method based on the improved NSGA-II algorithm in Example 1; Figure 2Here is a flowchart of the improved NSGA-II algorithm in Example 1; Figure 3 This is a diagram of the improved IEEE-33 system in Example 2; Figure 4 This is a diagram of the optimal reinforcement scheme in Example 2; Figure 5 This is a comparison chart of the results of various planning schemes in Example 2. Detailed Implementation
[0019] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.
[0020] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," and "outer," etc., used in the description of specific embodiments of the present invention to indicate orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.
[0021] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are arranged as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when arranged in "horizontal," "vertical," "suspended," "parallel," or "coaxial" directions, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.
[0022] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.
[0023] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.
[0024] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.
[0025] The distribution network differentiated reinforcement planning method and electronic equipment based on the improved NSGA-II algorithm provided in this invention can be applied to the planning and design of urban distribution networks, rural distribution networks, industrial park distribution networks, and other scenarios. For clarity, the following definitions apply: distribution network refers to the power network used to receive electrical energy and distribute it to end users; NSGA-II refers to Non-dominated Sorting Genetic Algorithm II; EENS refers to Expected Energy Not Supplied, used to quantify system reliability; reinforcement scheme refers to the combination of differentiated reinforcement strategies adopted for each branch in the distribution network. It should be noted that the reinforcement target of this invention is overhead lines. In the network topology, each overhead line corresponds to one branch. Therefore, in this invention, "branch" and "line" refer to the same physical object in technical terms and can be used interchangeably.
[0026] Example 1 Figure 1 This is a flowchart of the differentiated reinforcement planning method for distribution networks based on the improved NSGA-II algorithm provided in this embodiment. Figure 2 To improve the NSGA-II algorithm flowchart, the following section combines... Figure 1 The technical solution of this embodiment will be described in detail below.
[0027] S1: Obtain node information and branch information of the distribution network, select reinforcement strategies in combination with the differentiated reinforcement planning model of the overhead line of the distribution network, reinforce each branch in the distribution network, generate an initial reinforcement scheme, and construct the objective function corresponding to the initial reinforcement scheme. The objective function includes minimizing the expected value of power shortage and minimizing the comprehensive investment cost function. For example, the node information and branch information of the distribution network are first obtained. In one possible implementation, the node information includes, but is not limited to: node number, node type, and active and reactive load data corresponding to each node. The branch information includes, but is not limited to: the starting node number, ending node number, branch length, branch impedance, branch fault probability, and branch switch status information for each branch.
[0028] After obtaining the above information, and combining it with the differentiated reinforcement planning model for overhead power distribution lines, a corresponding reinforcement strategy is selected for each branch in the distribution network to generate an initial reinforcement scheme. Optionally, the reinforcement strategies in the differentiated reinforcement planning model for overhead power distribution lines include: no reinforcement, enhanced operation and maintenance, structural reinforcement, and equipment replacement. Different reinforcement strategies correspond to different failure probability reduction factors and reinforcement costs.
[0029] Specifically, considering the differences in the operating conditions of various lines in the distribution network, and within a limited investment budget, independent decisions are made regarding the reinforcement strategies for each line, prioritizing the improvement of the resilience of the system's critical paths. The differentiated strategies encompass three typical methods: enhanced operation and maintenance, structural reinforcement, and equipment replacement. As the reinforcement level increases, the initial construction cost increases accordingly, leading to a significant decrease in the probability of line failure. The reinforcement effect is characterized in the model by applying a graded reduction factor to the initial failure probability, as shown in Table 1.
[0030] Table 1 Differentiated reinforcement planning model for overhead lines of power distribution network
[0031] In the distribution network Fault probability after m-level reinforcement of the line for:
[0032] In the formula, For the first The initial fault probability of each line. It is an m-level reduction factor.
[0033] After generating the initial reinforcement scheme, a corresponding objective function is constructed. This objective function includes minimizing the expected value of power shortage and minimizing the overall investment cost. In one possible implementation, the overall investment cost includes reinforcement cost and operation and maintenance cost. For example, for a given reinforcement scheme, the reinforcement cost is the sum of the reinforcement costs of each branch, and the operation and maintenance cost is the repair cost after a line fault.
[0034] Specifically, minimizing the expected value function of insufficient electrical energy. and minimizing the overall investment cost function as follows:
[0035]
[0036] In the formula, x As decision variables, N The total number of randomly simulated scenarios. For the first k The sum of the amount of power not supplied at each load point in the system under each scenario. To reinforce investment costs, For operation and maintenance costs.
[0037] Among them, reinforcement investment costs and maintenance costs Further expansion yields:
[0038]
[0039] In the formula, x As decision variables, This is the initial reinforcement plan. The investment cost corresponding to the reinforcement level, For the line The reinforcement level decision variables, N The total number of randomly simulated scenarios. For the scene Central route The number of failures that occurred during the evaluation period. For the line The cost of a single repair.
[0040] The constraints are as follows:
[0041]
[0042]
[0043]
[0044]
[0045] In the formula, , These are the inflow and outflow nodes, respectively. The set of branch paths, For grid connection at nodes DG collection, , Scenes Lower branch road exist The active and reactive power flow of the line at any given time. , For the scene Distributed power supply Actual output , For the scene The next source node is in the node Injected power, , For the scene Next node The load at the location, , Scenes Distributed power supply The upper and lower limits of contribution. , Scenes Distributed power supply The upper and lower limits of reactive power output For the scene Lower branch road Current applied, , Branch roads The upper and lower limits of the current, For the scene Next node Voltage at point, , They are nodes The upper and lower limits of the voltage.
[0046] By constructing the dual objective function described above, this embodiment can take into account both power supply reliability and investment economy in the subsequent optimization process, thus solving the problem of resource allocation imbalance caused by single objective optimization in traditional planning methods.
[0047] S2: Based on a preset low-fidelity model, calculate the expected value of power shortage for the initial reinforcement scheme, and simultaneously calculate the comprehensive investment cost of the initial reinforcement scheme; perform fast non-dominated sorting and congestion calculation on the initial reinforcement scheme according to the expected value of power shortage and the comprehensive investment cost, and obtain the non-dominated level label and congestion value of each initial reinforcement scheme. For example, based on a pre-defined low-fidelity model, the expected value of power deficiency for the initial reinforcement scheme is calculated, and the overall investment cost of the initial reinforcement scheme is calculated simultaneously. In one possible implementation, the low-fidelity model takes the fault location and reinforcement strategy of the distribution network as input, and calculates the expected value of power deficiency using the fault propagation method. Specifically, the fault propagation method quickly determines the set of load nodes that have lost power due to the fault based on the fault location and system topology, and estimates the average repair time based on empirical load recovery rules, thereby calculating an approximate EENS.
[0048] Specifically, the low-fidelity model employs an approximate model based on fault propagation for rapid evaluation. This method avoids performing a complete power flow convergence and recovery simulation for each candidate solution. It utilizes topological fracture information obtained from fault propagation and empirical load recovery rules to quickly calculate the approximate EENS, achieving rapid evaluation of system reliability. In a given scenario... k The formula for calculating EENS under the low-fidelity model is as follows:
[0049] In the formula, For EENS in the low-fidelity model, x As decision variables, For power outage load aggregation, For load nodes The active load; This represents the estimated average repair time based on the fault location and hardening strategy.
[0050] After calculating the expected power shortage and overall investment cost, a rapid undominated ranking and congestion calculation are performed on the initial reinforcement schemes based on these two target values, yielding undominated level labels and congestion values for each initial reinforcement scheme. The undominated level labels are used to distinguish the Pareto superiority / inferiority relationship between schemes, while the congestion value measures the distribution density of schemes within the same undominated level. Through this process, this embodiment can quickly screen reinforcement schemes with potential advantages, providing a basis for subsequent high-fidelity evaluation.
[0051] S3: Based on the preset dynamic re-evaluation ratio function, calculate the number of re-evaluation schemes in the initial reinforcement scheme, and select the corresponding number of schemes as re-evaluation schemes from the initial reinforcement scheme according to the non-dominated level label and congestion value. Use a high-fidelity model to calculate and update the expected value of power shortage of the re-evaluation scheme. For example, based on a preset dynamic re-evaluation ratio function, the number of schemes requiring re-evaluation in the initial reinforcement scheme is calculated. In one possible implementation, the dynamic re-evaluation ratio function takes as input the minimum re-evaluation ratio benchmark in the initial stage, the maximum allowed peak re-evaluation ratio in the later stage of evolution, the current iteration number, the maximum iteration number, and the evolution accuracy adjustment index, and outputs the proportion of re-evaluated schemes to the initial reinforcement schemes. This proportion, combined with the number of initial reinforcement schemes, determines the number of re-evaluated schemes. Optionally, the proportion of re-evaluated schemes to the initial reinforcement schemes increases non-linearly with the number of iterations, and the growth rate is controlled by the evolution accuracy adjustment index.
[0052] Specifically, the dynamic re-evaluation ratio function The specific format is as follows:
[0053] In the formula, This serves as the minimum reassessment ratio benchmark in the initial stage. The maximum allowed re-evaluation ratio peak in the later stages of evolution, where y is the current generation. The maximum number of generations is preset. The evolution accuracy adjustment index is used to control the nonlinear rate of transition from low fidelity to high fidelity.
[0054] After determining the number of reassessment schemes, a corresponding number of schemes are selected from the initial reinforcement schemes as reassessment schemes based on the non-dominated level label and the congestion value. Optionally, when selecting reassessment schemes, priority is given to initial reinforcement schemes with smaller non-dominated level label numbers (i.e., schemes with better Pareto levels); within the same non-dominated level, priority is given to initial reinforcement schemes with larger congestion values (i.e., schemes with sparser distribution and greater representativeness).
[0055] After selecting a reassessment scheme, a high-fidelity model is used to calculate and update the expected value of the power shortage under the reassessment scheme, while keeping the overall investment cost unchanged. In one possible implementation, the high-fidelity model uses an importance sampling method based on improved cross-entropy (iCE-IS) to calculate the expected value of the power shortage.
[0056] Specifically, the high-fidelity reliability assessment model uses iCE to establish a bias distribution and performs importance sampling to obtain a high-precision estimate of the system's EENS, serving as an accurate source for the final result. Importance sampling based on cross-entropy is achieved by using a parameterized distribution family... h ( x ; υIn the original distribution, the Kullback-Leibler divergence with the optimal distribution is iteratively minimized to find an approximate optimal distribution. iCE-IS, on the other hand, achieves a smooth transition from the original distribution to the optimal distribution through a smooth intermediate objective, and uses weighted samples in each layer to robustly update parameters, thereby improving stability and convergence.
[0057] The intermediate target of iCE-IS is defined as follows:
[0058] In the formula, x As decision variables, For intermediate target distribution, For true edge joint distribution, For the limit state function, The standard normal cumulative distribution function is... is the smoothing parameter for the y-th generation.
[0059] make For the first The initial edge failure rate of the line, the overall random input vector of the system is Each component Description of the The state of each line, under the independent Bernoulli edge assumption, can be represented by the true joint edge distribution of the system as follows:
[0060] In the formula, x As decision variables, For true edge joint distribution, For the first The initial edge failure rate of each line, where n is the total number of lines. For the first The decision variables for each route.
[0061] Using this as the initial input, iCE-IS further iterates to obtain the reference edge failure rate vector in the reference distribution. The reference distribution thus constructed is:
[0062] In the formula, x As decision variables, For reference distribution, For the first The reference edge failure rate of each line, where n is the total number of lines. For the first The decision variables for each route.
[0063] Using the aforementioned reference distribution as the Monte Carlo sampling distribution, sample weights are constructed based on the ratio of the true distribution to the reference distribution. The unpowered quantities in the samples are then weighted and summed according to these weights. The resulting weighted average is the unbiased estimate of EENS. Importance Weights The formula for calculating EENS under the high-fidelity model is as follows:
[0064]
[0065] In the formula, For EENS in a high-fidelity model, x As decision variables, S This represents the number of samples. For the scene The sum of the unpowered quantities at each load point in the system. For true edge joint distribution, This is the reference distribution.
[0066] Through the aforementioned dynamic re-evaluation mechanism, this embodiment uses a low-fidelity model to quickly screen a large number of schemes in the early stage of evolution, and a high-fidelity model to accurately evaluate key schemes in the later stage of evolution. This balances computational efficiency and evaluation accuracy, and solves the computational redundancy problem caused by using high-precision evaluation for all schemes in traditional methods.
[0067] S4: Based on the updated expected value of power shortage and comprehensive investment cost, perform fast non-dominated sorting and congestion calculation on the initial reinforcement scheme, and then generate offspring reinforcement schemes through selection, crossover and mutation operations. For example, based on the updated expected power shortage and overall investment cost, a fast non-dominated sorting and congestion calculation are performed on the initial reinforcement scheme to obtain the updated non-dominated hierarchy and congestion distribution. Then, offspring reinforcement schemes are generated through selection, crossover, and mutation operations. Through the above genetic operations, this embodiment can continuously iterate and optimize the reinforcement scheme, gradually approaching the Pareto optimal front.
[0068] S5: Determine whether the current iteration optimization process meets the preset convergence criterion: If it does not meet the criterion, merge the initial reinforcement scheme and the offspring reinforcement scheme as the initial reinforcement scheme for the next iteration, and repeat S2–S4; if it meets the criterion, output the Pareto optimal solution set as the optimal reinforcement scheme.
[0069] For example, determine whether the current iterative optimization process meets the preset convergence criterion: if not, merge the initial reinforcement scheme and the offspring reinforcement scheme as the initial reinforcement scheme for the next iteration, and repeat S2–S4; if it meets the criterion, output the Pareto optimal solution set as the optimal reinforcement scheme. In one possible implementation, the convergence criterion could be reaching the maximum number of iterations, or the rate of change of the Pareto front for multiple consecutive generations being less than a preset threshold. After meeting the convergence condition, output the Pareto optimal solution set as the optimal reinforcement scheme. Optionally, all non-dominated solutions on the Pareto front can be directly output for planners to select according to budget and reliability requirements; or the knee solution (the optimal solution for the bi-objective trade-off) can be selected from the Pareto optimal solution set as the optimal reinforcement scheme.
[0070] This embodiment provides a differentiated reinforcement planning method for distribution networks based on an improved NSGA-II algorithm. By employing a differentiated reinforcement strategy, it achieves targeted reinforcement of distribution network branches, solving the problem of uneven resource allocation caused by traditional unified construction standards. This enables precise resource allocation and improves power supply reliability. The dynamic re-evaluation mechanism, combining low-fidelity and high-fidelity models, balances the efficiency and accuracy of reliability assessment, avoiding the computational drawbacks of traditional evaluation methods. The improved NSGA-II algorithm reduces computational burden and accelerates convergence through a scientific optimization mechanism, while simultaneously using dual-objective optimization to balance power supply reliability and investment economy, addressing the core pain points of traditional planning.
[0071] Example 2 To verify the effectiveness of the method described in Example 1, an improved IEEE-33 node distribution network test case was established, and the IEEE-33 system was improved as follows: Figure 3 As shown.
[0072] Based on the given differentiated reinforcement levels and cost parameters (see Table 2), this embodiment utilizes an improved NSGA-II algorithm for multi-objective optimization. To achieve the optimal balance between improving reliability and controlling investment, this embodiment selects the knee of the Pareto front as the optimal compromise solution for the optimal reinforcement scheme (e.g., ...). Figure 4 (As shown).
[0073] Table 2 Differentiated Reinforcement Levels and Costs for Overhead Lines
[0074] To comprehensively evaluate the effectiveness of the planning method proposed in this paper, a comparative analysis of five planning schemes is conducted: Option I: No reinforcement measures are taken, serving as the baseline option; Option II: Implement Level 1 reinforcement for all lines and transformers in the system; Option III: Implement Level 2 reinforcement for all lines and transformers in the system; Option IV: Implement Level 3 reinforcement for all lines and transformers in the system; Option V: The differentiated reinforcement planning scheme proposed in this embodiment; For example, each planning scheme Figure 5 As shown, from a reliability perspective, EENS exhibits a significant downward trend with increasing reinforcement level. Specifically, the EENS of Scheme IV is 65.7% lower than that of the baseline Scheme I. This indicates that physical reinforcement is a direct means of improving the reliability of the distribution network. However, the standardized reinforcement scheme demonstrates a significant diminishing marginal benefit; blindly investing in high-level reinforcement across the entire network can lead to severe resource redundancy and economic deterioration. In contrast, Scheme V proposed in this embodiment demonstrates superior cost-effectiveness and planning rationality. From a comprehensive cost perspective, Scheme V has the lowest total cost among all schemes, reducing the total cost by 10.5% compared to Scheme III while maintaining a roughly equal reliability level. Compared to Scheme IV, which has the best reliability index, Scheme V avoids excessive investment costs of 750,000 yuan while sacrificing some power outage risk.
[0075] In summary, the proposed scheme in Example 1 can accurately identify key nodes and weak branches that contribute significantly to overall reliability in the system, achieving optimal spatial allocation of limited reinforcement resources. This reinforcement strategy avoids over-reinforcement of insensitive branches at the end while ensuring sufficient disaster resistance for backbone feeders and high-load areas, thus minimizing the overall lifecycle cost while maintaining a high level of reliability. Simulation results strongly support the application value and scientific validity of the differentiated planning model presented in this paper in actual distribution network reinforcement projects.
[0076] Example 3 Based on the same inventive concept, this embodiment also provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the power distribution network differentiated reinforcement planning method based on the improved NSGA-II algorithm as described in Embodiment 1.
[0077] For example, a processor may include one or more processing units, such as a neural network processing unit (NPU), an application processor (AP), a modem processor, a graphics processing unit (GPU), an image signal processor (ISP), a controller, a digital signal processor (DSP), a baseband processor, etc. The different processing units may be independent devices or integrated into one or more processors. The controller can generate operation control signals based on the instruction opcode and timing signals to control instruction fetching and execution.
[0078] The memory can be used to store executable program code, including instructions. Internal memory may include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function, etc. The data storage area may store data created during the use of the electronic device (such as input data, output data, etc.). Furthermore, internal memory may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, universal flash storage (UFS), etc. The processor executes various functional applications and data processing of the electronic device by running instructions stored in the internal memory and / or instructions stored in memory located within the processor.
[0079] This embodiment provides an electronic device that, through the synergistic effect of memory and processor, provides a reliable operating platform for the reinforcement planning method described in Embodiment 1, ensuring stable and efficient execution of the method, effectively solving the problems of heavy computational burden and slow convergence in distribution network reinforcement planning optimization, and realizing the rapid output of the optimal reinforcement scheme.
[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A differentiated reinforcement planning method for distribution networks based on an improved NSGA-II algorithm, characterized in that, include: S1: Obtain node information and branch information of the distribution network, select reinforcement strategies in combination with the differentiated reinforcement planning model of the overhead line of the distribution network, reinforce each branch in the distribution network, generate an initial reinforcement scheme, and construct the objective function corresponding to the initial reinforcement scheme. The objective function includes minimizing the expected value of power shortage and minimizing the comprehensive investment cost function. S2: Based on a preset low-fidelity model, calculate the expected value of power shortage for the initial reinforcement scheme, and simultaneously calculate the comprehensive investment cost of the initial reinforcement scheme; perform fast non-dominated sorting and congestion calculation on the initial reinforcement scheme according to the expected value of power shortage and the comprehensive investment cost, and obtain the non-dominated level label and congestion value of each initial reinforcement scheme. S3: Based on the preset dynamic re-evaluation ratio function, calculate the number of re-evaluation schemes in the initial reinforcement scheme, and select the corresponding number of schemes as re-evaluation schemes from the initial reinforcement scheme according to the non-dominated level label and congestion value. Use a high-fidelity model to calculate and update the expected value of power shortage of the re-evaluation scheme. S4: Based on the updated expected value of power shortage and comprehensive investment cost, perform fast non-dominated sorting and congestion calculation on the initial reinforcement scheme, and then generate offspring reinforcement schemes through selection, crossover and mutation operations. S5: Determine whether the current iteration optimization process meets the preset convergence criterion: If it does not meet the criterion, merge the initial reinforcement scheme and the offspring reinforcement scheme as the initial reinforcement scheme for the next iteration, and repeat S2–S4; if it meets the criterion, output the Pareto optimal solution set as the optimal reinforcement scheme.
2. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 1, characterized in that, The node information includes node number, node type, and active and reactive load data corresponding to each node; the branch information includes the first node number, the last node number, the branch length, the branch impedance, the branch fault probability, and the branch switch status information for each branch.
3. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 1, characterized in that, The reinforcement strategies of the differentiated reinforcement planning model for overhead power distribution lines include: no reinforcement, enhanced operation and maintenance, structural reinforcement, and equipment replacement. Different reinforcement strategies correspond to different failure probability reduction factors and reinforcement costs.
4. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 3, characterized in that, The total investment cost includes reinforcement costs and operation and maintenance costs.
5. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 3, characterized in that, The low-fidelity model takes the fault location and reinforcement strategy of the distribution network as input and calculates the expected value of power shortage through the fault propagation method.
6. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 1, characterized in that, The dynamic re-evaluation ratio function takes the minimum re-evaluation ratio benchmark in the initial stage, the maximum re-evaluation ratio peak allowed in the later stage of evolution, the current iteration number, the maximum iteration number, and the evolution accuracy adjustment index as inputs, and outputs the ratio of the re-evaluation scheme to the initial reinforcement scheme. The number of re-evaluation schemes is then determined by combining the ratio with the number of initial reinforcement schemes.
7. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 6, characterized in that, The proportion of the re-evaluation scheme to the initial reinforcement scheme increases non-linearly with the number of iterations, and the growth rate is controlled by the evolution accuracy adjustment index.
8. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 1, characterized in that, When selecting a reassessment scheme in S3, the initial reinforcement scheme with the smaller label number at the non-dominated level is given priority; within the same non-dominated level, the initial reinforcement scheme with the larger congestion value is given priority.
9. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm according to claim 1, characterized in that, The high-fidelity model uses an importance sampling method based on improved cross-entropy to calculate the expected value of power shortage.
10. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements as described in claim 1. The method for differentiated reinforcement planning of distribution networks based on the improved NSGA-II algorithm as described in any one of the following 9.