A power distribution network multi-objective balanced investment decision-making method based on time sequence coupling

Abstract

The application discloses a kind of based on timing coupling's multi-objective equalization investment decision-making method of distribution network, belong to distribution network planning and investment decision-making technical field.Multiple dimensions of basic data of distribution network selected investment project are collected, and standardization processing is carried out;Static reference weight is constructed by using analytic hierarchy process and entropy weight method combination weighting, and dynamic weight correction mechanism is established in combination with planning year policy guidance and load demand change, and the dynamic comprehensive score of project is obtained;Project coupling relationship model is constructed based on the degree of overlap of project influence dimension, influence direction consistency and coupling relationship type;Differentiated risk loss function is established for safety type, benefit type and policy type project, and project investment risk value is calculated using Monte Carlo simulation and conditional risk value CVaR;Further, a multi-objective optimization model for maximizing comprehensive benefit, minimizing investment risk and minimizing life cycle cost is constructed, and an improved NSGA-II algorithm is used for solution, and the optimal result of distribution network project and construction timing arrangement are output.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning and investment decision-making technology, and more specifically to a multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling. Background Technology

[0002] With the deepening of energy transition and power system upgrades, the distribution network, as a crucial link connecting power sources and users, has seen its investment scale continuously expand and its technological complexity significantly increase, becoming a core support for the efficient operation of the power grid. Relevant guiding documents clearly state that distribution network investment must balance accuracy, efficiency, and security to achieve improved investment quality and efficiency. However, current distribution network investment decisions still face multiple technical bottlenecks, making it difficult to adapt to the development needs under the new circumstances.

[0003] First, traditional investment evaluation systems suffer from static limitations. Existing methods often employ single-dimensional evaluation models with fixed weights, failing to fully consider the dynamic changes in load demand and technical standards under different construction sequences. This leads to a disconnect between project prioritization and actual needs. For example, some projects, by neglecting the impact of construction timing on benefits, have experienced lower-than-expected returns on investment and resource imbalances, severely hindering the efficiency of distribution network investment. Second, the coupling relationships between projects are not effectively quantified. Distribution network projects exhibit complex interrelationships in terms of functional attributes, topology, and resource requirements, manifesting as various coupling relationships such as mutual assistance, constraint, dependence, and conflict. Traditional methods often evaluate individual projects in isolation, failing to incorporate coupling synergies or constraints into the optimization framework. This results in frequent engineering conflicts, resource waste, and benefit offsetting issues during the implementation of planning schemes, affecting the overall operational efficiency of the distribution network. Third, a balanced optimization mechanism for risk and benefit is lacking. Factors such as the high proportion of clean energy integration and the deepening of transmission and distribution price reforms expose distribution network investment to multiple risks, including market fluctuations and technological failures. Existing single-objective optimization models often focus on maximizing benefits but lack a scientific risk measurement and balancing mechanism. This leads to actual losses in some high-yield projects due to uncontrolled risks, or missed opportunities due to excessive risk avoidance. Finally, multi-objective optimization solutions are inefficient. Distribution network investment optimization involves multiple objectives such as benefits, costs, and risks. Traditional optimization algorithms suffer from slow convergence speeds and uneven Pareto solution distribution, making it difficult to quickly output feasible project combinations and time-series solutions under complex constraints. This fails to meet the precise and differentiated investment decision-making needs of power grid companies.

[0004] In summary, existing investment decision-making methods for distribution networks have significant shortcomings in dynamic evaluation, coupled quantification, risk balancing, and solution efficiency. There is an urgent need to construct an investment optimization method that can integrate temporal dynamics, coupled correlation, and risk-benefit-cost balance to provide decision support for efficient and scientific investment in distribution networks. Summary of the Invention

[0005] In view of the above problems, the present invention is proposed to provide a time-coupled multi-objective equilibrium investment decision-making method for distribution networks that overcomes or at least partially solves the above problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] S1. Collect multi-dimensional basic data of potential investment projects in the power distribution network, and standardize the multi-dimensional basic data to obtain standardized values ​​for each project in each data dimension. S2. Divide the planning period of the candidate investment projects into multiple planning years; determine the static benchmark weights of each data dimension; adjust the static benchmark weights year by year according to the policy guidance or load demand of each planning year to obtain the dynamic weights of each data dimension in each planning year; combine the standardized values ​​of each project with the dynamic weights of the corresponding planning year to obtain the dynamic comprehensive score of each project in each planning year. S3. Based on whether the project construction causes changes in the data dimension values, determine the subset of data dimensions affected by each project and the direction of change in each dimension; based on the degree of overlap of the affected dimension subsets of each pair of projects, the consistency of the direction of change in the common affected dimension, and the type of coupling relationship between the two, calculate the coupling strength coefficient between each pair of projects. S4. Classify each project into a preset risk type, and construct a corresponding profit and loss function for each risk type; calculate the loss value under each scenario by generating multiple risk scenarios, and calculate the investment risk value of each project based on the tail expectation of the loss value. S5. Set decision variables for each candidate investment project regarding whether it is selected and its construction year. Take the sum of the dynamic comprehensive scores of the projects indicated by the decision variables and the contribution of coupling strength as the comprehensive benefit objective, the sum of the investment risk values ​​of the projects indicated by the decision variables as the risk objective, and the total discounted value of the full life cycle cost of the projects indicated by the decision variables as the cost objective. Construct a multi-objective investment optimization model with preset constraints. S6. The multi-objective investment optimization model is solved using a multi-objective evolutionary algorithm. During the solution process, the population diversity maintenance strategy and crossover mutation probability are dynamically adjusted, and the Pareto optimal solution set is output, where each solution corresponds to a set of values ​​of the decision variables. S7. Select the optimal solution that meets the preset constraints and decision preferences from the Pareto optimal solution set, and output the optimal results and construction schedule of the power distribution network project.

[0008] Preferably, the static benchmark weights in step S2 are determined by a combination of the analytic hierarchy process (AHP) and the entropy weight method. The AHP is used to calculate the subjective weights of each data dimension, while the entropy weight method is used to calculate the objective weights based on the numerical distribution of each item in the data dimension. The subjective weights and objective weights are then weighted and summed to obtain the static benchmark weights.

[0009] Preferably, the method for calculating the dynamic comprehensive score in step S2 is as follows: the standardized values ​​of each project in each data dimension are weighted and summed with the dynamic weight of the corresponding planning year to obtain the dynamic comprehensive score of the project in the planning year; wherein, the dynamic weight of each planning year is obtained by normalizing the weight of the previous year after adding the weight increment, and the weight increment is determined according to the policy orientation or load demand of the planning year.

[0010] Preferably, the degree of overlap in step S3 is measured by Jaccard similarity, which is the number of intersection elements of the two items' influence dimension subsets divided by the number of union elements; the consistency of change direction is measured by consistency coefficient, which is the number of dimensions in which the two items have the same change direction in the common influence dimension divided by the total number of common influence dimensions; the coupling relationship types include mutual assistance, constraint, dependence, conflict, and coexistence, each type corresponding to a preset correction coefficient; the coupling strength coefficient is obtained by multiplying the Jaccard similarity, consistency coefficient, and correction coefficient.

[0011] Preferably, the correction coefficient is determined according to the coupling relationship type: positive for mutual assistance, negative for constraint, positive for dependency, negative for conflict, and positive for coexistence.

[0012] Preferably, the risk types mentioned in step S4 include safety-type, benefit-type, and policy-type; the revenue loss function of safety-type projects includes equipment failure rate, probability of natural disasters, and operation and maintenance cost fluctuation factors; the revenue loss function of benefit-type projects includes electricity sales price volatility, benefit achievement rate deviation, and environmental protection cost growth rate factors; the revenue loss function of policy-type projects includes subsidy standard adjustment factors and development planning matching degree deviation factors.

[0013] Preferably, the risk scenario in step S4 is generated by Monte Carlo simulation, and the probability distribution of each risk factor is fitted based on historical data, and multiple sets of scenario samples are randomly selected; the tail expectation of the loss value is calculated using conditional value at risk (CVaR). Under a preset confidence level, the conditional expectation of the loss value exceeding the value at risk (VaR) is calculated as the investment risk value of the project.

[0014] Preferably, the preset constraints in step S5 include: investment limit constraints, i.e., the total investment in each planning year and the entire planning period does not exceed the preset limit; resource supply constraints, i.e., the number of projects with different resource demand levels in the same planning year does not exceed the corresponding preset upper limit; coupling relationship constraints, i.e., logical restrictions imposed on decision variables according to the type of coupling relationship, including prohibiting the simultaneous selection of restrictive project pairs, the simultaneous or non-selection of mandatory coexistence project pairs, and requiring that subsequent projects can only be selected after the completion of the preceding project in a dependent project pair; and time sequence constraints, i.e., mandatory projects are selected at least once in the planning period, and a single project is selected at most once in multiple planning years.

[0015] Preferably, the multi-objective evolutionary algorithm in step S6 is an improved NSGA-II algorithm, and the dynamic adjustment strategy for maintaining population diversity includes: setting a dynamic crowding threshold that decays exponentially with the number of iterations, using a larger threshold in the early stage of iteration to maintain population diversity, and using a smaller threshold in the later stage of iteration to focus on the local optimal region. The dynamic adjustment of crossover and mutation probabilities includes: adaptively adjusting the crossover and mutation probabilities based on the comparison between individual fitness and the population average fitness, wherein individuals with fitness better than the average fitness are given lower crossover and mutation probabilities, and individuals with fitness worse than the average fitness are given higher crossover and mutation probabilities.

[0016] Preferably, step S7 specifically includes: The planning period is divided into several decision-making stages by year, and the set of completed projects, remaining investment amount, remaining resource capacity and coupling relationship status of each stage are defined. The stage state transition verification is performed on each candidate solution in the Pareto optimal solution set in turn, and candidate solutions with investment exceeding the limit, resource exceeding the capacity, dependency timing misalignment, conflicting construction at the same time or coexisting but not constructed synchronously are eliminated. For the candidate solutions that pass the verification, they are sorted according to the normalized closeness of comprehensive benefits, investment risk and whole life cycle cost, and the optimal solution is selected to determine the construction year of each project and output it.

[0017] The beneficial effects of the above-described technical solutions provided in the embodiments of the present invention include at least the following: (1) Construct a dynamic weight evolution mechanism so that the weight of the evaluation indicators can be dynamically adjusted with the planning year, policy orientation and load demand changes, thereby improving the matching degree between the project evaluation results and future development needs; (2) Establish a quantitative model of project coupling relationship and a differentiated risk assessment model to achieve unified quantitative analysis of project synergy, conflict relationship and investment risk, and improve the scientificity and reliability of investment decision-making; (3) Construct a comprehensive benefit, investment risk and full life cycle cost collaborative optimization model, and use the improved NSGA-II algorithm to solve it, so as to realize the collaborative decision-making of the optimal selection of distribution network investment projects and construction sequence, and improve investment benefits and resource allocation efficiency.

[0018] As can be seen from the above technical solution, compared with the prior art, the present invention constructs an integrated investment decision-making framework of "dynamic evaluation - coupling analysis - equilibrium optimization", which integrates the project time sequence characteristics, project correlation and investment risk factors into the optimization decision-making process, realizes the coordinated decision-making of power distribution network project selection and construction sequence, and improves the economy, safety and implementation rationality of investment schemes. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the overall process of a multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling, as provided in an embodiment of the present invention. Figure 2 This diagram illustrates a comparison of the convergence performance of the improved NSGA-II algorithm and the traditional NSGA-II algorithm provided in this embodiment of the 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention discloses a multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling: S1. Collect multi-dimensional basic data of potential investment projects in the power distribution network, and standardize the multi-dimensional basic data to obtain standardized values ​​for each project in each data dimension. S2. Divide the planning period of the candidate investment projects into multiple planning years; determine the static benchmark weights of each data dimension; adjust the static benchmark weights year by year according to the policy guidance or load demand of each planning year to obtain the dynamic weights of each data dimension in each planning year; combine the standardized values ​​of each project with the dynamic weights of the corresponding planning year to obtain the dynamic comprehensive score of each project in each planning year. S3. Based on whether the project construction causes changes in the data dimension values, determine the subset of data dimensions affected by each project and the direction of change in each dimension; based on the degree of overlap of the affected dimension subsets of each pair of projects, the consistency of the direction of change in the common affected dimension, and the type of coupling relationship between the two, calculate the coupling strength coefficient between each pair of projects. S4. Classify each project into a preset risk type, and construct a corresponding profit and loss function for each risk type; calculate the loss value under each scenario by generating multiple risk scenarios, and calculate the investment risk value of each project based on the tail expectation of the loss value. S5. Set decision variables for each candidate investment project regarding whether it is selected and its construction year. Take the sum of the dynamic comprehensive scores of the projects indicated by the decision variables and the contribution of coupling strength as the comprehensive benefit objective, the sum of the investment risk values ​​of the projects indicated by the decision variables as the risk objective, and the total discounted value of the full life cycle cost of the projects indicated by the decision variables as the cost objective. Construct a multi-objective investment optimization model with preset constraints. S6. The multi-objective investment optimization model is solved using a multi-objective evolutionary algorithm. During the solution process, the population diversity maintenance strategy and crossover mutation probability are dynamically adjusted, and the Pareto optimal solution set is output, where each solution corresponds to a set of values ​​of the decision variables. S7. Select the optimal solution that satisfies the preset constraints and decision preferences from the Pareto optimal solution set, and output the construction year of the selected project according to the values ​​of the decision variables in the solution.

[0023] Please refer to the following: Figure 1 The overall flowchart of the method shown below provides a further detailed description of the present invention.

[0024] The invention comprises a data acquisition and preprocessing module, a dynamic comprehensive evaluation module, a project coupling relationship quantification module, an investment risk measurement module, a multi-objective investment optimization combination module, and a time-series decision output module.

[0025] The process involves several steps: First, acquiring and standardizing the basic data of potential power distribution network investment projects. Then, using an AHP-entropy weighting and dynamic correction mechanism, the dynamic comprehensive score of each project in each planning year is calculated. Next, the coupling relationships between projects are identified, and a coupling relationship matrix is ​​constructed. Simultaneously, differentiated risk loss functions are established for different project categories, and project investment risk values ​​are obtained through risk scenario simulation. Based on this, a collaborative optimization model for comprehensive benefits, investment risk, and full life-cycle cost is constructed and solved using an improved NSGA-II algorithm. Finally, combining state transitions and constraint verification during the planning phase, the optimal investment projects and construction schedule for the year are output. Steps S1-S7 are described in detail below: Step S101: Data Acquisition and Preprocessing In one embodiment, the 110kV, 35kV, 10kV, and 380 / 220V distribution networks in Jincheng City, Shanxi Province, are taken as the research object, with a planning period from 2025 to 2030, totaling six planning years. Thirty potential investment projects are selected from this region, including 12 safety-related projects, 8 policy-related projects, and 10 benefit-related projects. Project types cover old line renovation, transformer capacity expansion, distributed photovoltaic access, energy storage collaborative construction, electric vehicle charging infrastructure, distribution automation upgrades, and flexible interconnection projects. Basic data comes from distribution automation systems, equipment operation and maintenance systems, marketing systems, and meteorological databases, including equipment status parameters, load demand data, distributed power supply access scale, investment costs, operation and maintenance expenses, policy subsidy information, and geographical topology information.

[0026] Specifically, we collected raw indicator data from all dimensions of 30 candidate projects, used the 3σ criterion to identify and remove outliers, and used linear interpolation to complete missing data to form a complete raw dataset. The evaluation indicators for power distribution networks are divided into positive benefit indicators (the larger the indicator value, the higher the project value) and negative cost indicators (the smaller the indicator value, the higher the project value). The range standardization method is used to make all indicators dimensionless.

[0027] Through the above range standardization process, all evaluation indicators are mapped to the [0,1] interval, and the transformed values ​​are uniformly aligned towards a benefit-oriented direction where larger values ​​are better. For example, the smaller the original value of the investment cost, the closer it is to 1 after standardization; the larger the original value of the improvement in power supply reliability, the closer it is to 1 after standardization. The resulting standardized values... By eliminating differences in dimensions and orders of magnitude, the project can be directly weighted and summed with the dynamic weights of subsequent indicators to calculate the dynamic comprehensive score of each project in each planning year. .

[0028] For positive benefit indicators (the higher the value, the better), the following approach is adopted:

[0029] For negative cost indicators (the smaller the value, the better), adopt...

[0030] in, This represents the original value of the k-th indicator for the i-th item. These are the maximum and minimum values ​​of the i-th indicator, respectively. These are the standardized values.

[0031] S102. Divide the planning period of the candidate investment projects into multiple planning years; determine the static benchmark weights of each data dimension; adjust the static benchmark weights year by year according to the policy orientation or load demand of each planning year to obtain the dynamic weights of each data dimension in each planning year; combine the standardized values ​​of each project with the dynamic weights of the corresponding planning year to obtain the dynamic comprehensive score of each project in each planning year. In one embodiment, the planning period for the selected investment projects is divided into six planning years from 2025 to 2030, denoted as follows: t =1,2,...,6, let the number of investment projects to be selected be... The number of evaluation indicators is , No. The project in the The standardized value of each evaluation indicator is denoted as . To avoid subjectivity or data volatility bias caused by a single weighting method, the Analytic Hierarchy Process (AHP) is used to calculate subjective weights, and the entropy weight method is used to calculate objective weights. The static baseline weights are obtained by weighting these weights together. Dynamic weights are obtained by combining annual policy and load demand adjustments, and finally, the annual comprehensive score of the project is calculated.

[0032] (1) Static benchmark weights First, the analytic hierarchy process (AHP) is used to calculate subjective weights. Based on the investment decision-making objectives of the power distribution network, the evaluation indicators are divided into dimensions such as safety benefits, economic benefits, social benefits, environmental benefits, policy compatibility, and investment costs. Experts then construct a judgment matrix based on the principle of "prioritizing power supply safety, ensuring policy and project support, and balancing economic benefits."

[0033] in, Indicates the first The first indicator is relative to the first The importance of the indicators. The geometric mean method is used to calculate the [number of indicators]. Subjective weights of indicators: Subjective weights are obtained using the Analytic Hierarchy Process (AHP).

[0034] Secondly, the objective weights are calculated using the entropy weight method. Based on the standardized values ​​of each candidate investment project on different indicators, the objective weights are calculated. The project is in The weighting of each indicator: Objective weights are calculated using the entropy weighting method.

[0035] Further calculation of the first Information entropy of each indicator:

[0036] when At that time, it was stipulated Therefore, we obtain the first... The objective weight of entropy weight for each indicator:

[0037] in, For the first Information entropy of each indicator The objective weights are obtained using the entropy weight method.

[0038] Finally, the subjective weights and objective weights are linearly combined to obtain the first... The static benchmark weights of each indicator:

[0039] in, and These represent the subjective weighting coefficient and the objective weighting coefficient, respectively, in this embodiment. Take 0.55, The value is 0.45. The static baseline weights for each indicator are then obtained.

[0040] (2) Dynamic weight adjustment The static baseline weights are adjusted annually based on policy guidance or load demand for each planning year. Let the... t The target indicator that needs to be weighted upwards this year is: k Its weight increment is At this point, it's important to note the weight increment. The determination is made by the power grid company's investment decision-making committee based on policy documents and load forecasting results. The recursive formula is as follows: First, update the target metrics. k：

[0041] Then, the other indicators are scaled proportionally to ensure that the sum of the weights of all indicators is 1.

[0042] in, , The first , Year The weights of each investment evaluation indicator; The weight increment of the target indicator is determined by the power grid company's investment decision-making committee based on policy documents and load forecast results; , The first , Year The weights of each investment evaluation indicator; For example, in the initial planning stage of 2025, the static benchmark weight of the distributed power absorption rate indicator was:

[0043] As the scale of distributed photovoltaic grid connection continues to grow, the pressure on new energy consumption is increasing year by year. Based on the annual new energy development plan, the power grid company's investment decision committee has decided to gradually increase the weight of this indicator starting in 2026.

[0044] Assume the annual weight increments from 2026 to 2030 are all taken as:

[0045] Then according to the formula

[0046] achievable

[0047]

[0048]

[0049]

[0050]

[0051] Therefore, the weight of this indicator will gradually increase from 0.084 in 2025 to 0.127 in 2030.

[0052] At the same time, according to the formula:

[0053] The weights of the remaining indicators are automatically reduced proportionally to ensure that the sum of the weights of all evaluation indicators always meets the following requirement:

[0054] This shows that as the penetration rate of new energy sources continues to increase, the importance of the distributed power generation absorption rate in the investment evaluation system is increasing year by year. This makes the optimization model more inclined to prioritize projects with strong new energy access capabilities and good absorption effects in the later stages of planning, so that the investment plan is more in line with the future development needs of the power distribution network.

[0055] (3) Overall weight and dynamic overall score The static benchmark weights and dynamic adjustment weights are combined to obtain the various indicators. k In the t Overall weighting for the year:

[0056] In this embodiment, the weighting coefficient We set it to 0.55, meaning the static part accounts for 55% and the dynamic part accounts for 45%.

[0057] Finally, a weighted summation is used to calculate the dynamic composite score for each project in each planning year:

[0058] in The total number of evaluation indicators, For the first The indicator in the first The overall weighting for the year The obtained standardized value.

[0059] S103. Based on whether the construction of the project causes changes in the data dimension values, determine the subset of data dimensions affected by each project and the direction of change in each dimension; based on the degree of overlap of the affected dimension subsets of each pair of projects, the consistency of the direction of change in the common affected dimension, and the type of coupling relationship between the two, calculate the coupling strength coefficient between each pair of projects. Specifically, after obtaining the dynamic composite score for each project, it is also necessary to consider the synergistic or conflicting relationships between the projects, as these directly affect the effectiveness of the overall investment plan. This step involves identifying and quantifying the coupling relationships between projects.

[0060] (a) Jaccard similarity (degree of overlap of indicators) By calculating the degree of overlap of the set of project impact indicators, the basic strength of the coupling relationship can be reflected.

[0061] Define Project The set of influencing indicators is ,project The set of influencing indicators is Then the Jaccard similarity is

[0062] in: This represents the number of elements in the intersection of the sets of indicators affected by the two projects, i.e., the number of indicators jointly affected by the two projects. The number of elements in the union represents the total number of metrics affected by the two projects.

[0063] The value ranges from [0,1] to [0,1]. The larger the value, the higher the degree of overlap between the two items' indicators.

[0064] (ii) Direction of influence and consistency coefficient To correct for the positive or negative nature of the coupling strength, it is necessary to determine whether the two projects have the same direction of influence on the common influencing index.

[0065] First, define the influence direction coefficient. For the project With indicators : If the project construction optimizes the indicators, then ; If the indicators worsen, then ; No effect .

[0066] For the two projects and The set of common influence indicators The consistency coefficient of a single indicator is defined as:

[0067] in: like This indicates that the two projects are related to the indicators. The direction of their impact is consistent (both are either optimizations or both are deteriorations); like This indicates that the two projects are related to the indicators. The effects are opposite (one improves, the other worsens); like This indicates that at least one item has no impact on the indicator (but since they are in the intersection, they are usually non-zero). Then, the average value of all indicators with common influence is taken to obtain the average consistency coefficient:

[0068] In the formula: For the project and The average consistency coefficient reflects the degree of consistency in the overall impact direction of two projects on all common indicators. A positive value indicates that the overall impact direction of the two projects on common indicators tends to be consistent, while a negative value indicates that they tend to be opposite.

[0069] (iii) Coupling Relationship Type Correction Coefficient Based on the actual relationships between projects, such as functional connections, resource competition, and construction dependencies, the coupling relationships are divided into five categories, each corresponding to a preset correction coefficient. .

[0070] 1) Mutual assistance type: Its core concept is that collaborative project construction can generate a benefit amplification effect of 1+1>2, improving the overall comprehensive score. The criterion for judgment is that when two projects are implemented together, the sum of the comprehensive benefit scores is ≥10% higher than when they are implemented alone. 2) Constraint type: The core concept is that the benefits of projects built simultaneously will be offset due to resource competition and functional conflicts, resulting in an overall score lower than the sum of the scores when implemented separately. The criterion for judgment is that when the two projects are implemented together, the sum of the comprehensive benefit scores is ≥5% lower than when implemented separately. 3) Dependency type: Its core meaning is that project B can only be implemented after project A is completed; otherwise, it cannot function or there will be contradictions in the engineering logic. The criterion for judgment is that the construction of project B must be based on the commissioning of project A. 4) Conflict type: The core meaning is that the construction of Project A and Project B at the same time will cause construction conflicts. The judgment criteria is that the overlap rate of the construction scope of the two projects is ≥30%, and the cross interference cannot be avoided by adjusting the construction plan. 5) Coexistence type: Its core meaning is that Project A and Project B must be constructed and put into operation simultaneously. Neither can achieve the core objective when implemented alone. The criterion for judgment is that when either project is put into operation alone, the comprehensive benefit score is lower than the threshold. Mutual assistance type is assigned 1.0, constraint type is assigned -0.8, dependency type is assigned 0.9, conflict type is assigned -0.9, and coexistence type is assigned 1.0.

[0071] (iv) Comprehensive Coupling Strength Coefficient Combining the above three factors, the final coupling strength coefficient is calculated:

[0072] in, For the project and The coupling strength coefficient has a value range of [-1, 1]; a positive value indicates positive coupling and cooperation, and a negative value indicates negative coupling and conflict; the larger the absolute value, the stronger the coupling strength, and 0 indicates no coupling.

[0073] Through the above steps, for all N candidate investment projects, each pair of projects... A coupling strength coefficient can be calculated from all of them. .all The N×N symmetric matrix that forms the coupling relationship is called the coupling relationship matrix. This matrix quantitatively characterizes the degree of synergy (positive value) or conflict (negative value) between any two projects, and serves as an important input for subsequent multi-objective investment optimization models.

[0074] S104. Divide each project into a preset risk type, and construct a corresponding profit and loss function for each risk type; calculate the loss value under each scenario by generating multiple risk scenarios, and calculate the investment risk value of each project based on the tail expectation of the loss value. In this example, after completing the dynamic comprehensive evaluation of the project and quantifying the project's coupling relationships, it is necessary to further assess the risk level that the project may face during planning, construction, and operation. Since different types of projects have significantly different construction goals, revenue realization methods, and external dependencies, their risk sources also differ. Using a uniform risk assessment model for calculation can easily mask the risk characteristics of different projects, leading to distorted risk assessment results. Therefore, this invention first classifies the selected projects by risk and extracts corresponding risk factors for different categories of projects to construct differentiated risk scenarios.

[0075] Projects are categorized into three types: safety-oriented, benefit-oriented, and policy-oriented. Safety-oriented projects primarily include the renovation of aging power lines, overload mitigation, distribution automation upgrades, grid reinforcement, and equipment replacement. The main objective of these projects is to improve power supply reliability and system operational safety. Their risks primarily stem from equipment operating conditions, the external natural environment, and subsequent operation and maintenance (O&M) processes. For example, increased equipment failure rates may lead to premature equipment retirement or additional investment; natural disasters may cause project damage and construction delays; and abnormal increases in O&M costs may result in project lifecycle costs exceeding expectations. Therefore, for safety-oriented projects, the focus is on extracting risk factors such as equipment failure rates, the impact of natural disasters, and the volatility of O&M costs, using these as important input variables for constructing subsequent risk scenarios.

[0076] Profit-oriented projects mainly include energy storage projects, charging infrastructure projects, power supply expansion and sales projects, and integrated energy utilization projects. The investment returns of these projects primarily come from market transaction revenue, increased user energy demand, and operational revenue; therefore, their risks are highly market-driven. In actual operation, fluctuations in electricity prices may lead to a decrease in project revenue, changes in user demand may cause the realized revenue level to deviate from the predicted results, and increases in environmental and operating costs may compress the project's profit margin. Therefore, for profit-oriented projects, it is crucial to extract risk factors such as electricity price volatility, revenue deviation rate, and environmental cost growth rate to reflect the impact of changes in the market environment on the project's investment returns.

[0077] Policy-driven projects mainly include distributed photovoltaic (PV) grid connection projects, new energy consumption projects, rural power grid consolidation and upgrading projects, and clean energy substitution projects. These projects typically aim to promote new energy consumption and drive green and low-carbon development, and their effectiveness is significantly influenced by the policy environment. For example, adjustments to subsidy policies may alter project profitability, changes in new energy development plans may affect project construction scale, and lower-than-expected regional load growth may reduce project utilization. Furthermore, changes in national and local energy policies may lead to adjustments in construction standards, grid connection requirements, and investment timing. Therefore, for policy-driven projects, it is crucial to extract risk variables such as subsidy adjustment impact factors, planning adjustment impact factors, and load growth deviation factors to reflect the uncertain impact of policy environment changes on project investment outcomes.

[0078] After identifying risk factors, risk factor sets were established for safety-oriented projects, benefit-oriented projects, and policy-oriented projects. Subsequently, based on historical operational data, market transaction data, equipment maintenance data, policy document data, and load forecasting results, the probability distribution characteristics of each risk factor were fitted, and multiple risk scenarios were randomly generated using the Monte Carlo method. Each risk scenario corresponds to a set of risk factor value combinations. By substituting this set of risk factors into the risk loss function corresponding to the project type, the potential loss value of the project under that scenario was calculated, thus forming the project's risk loss distribution and providing basic data for subsequent CVaR risk value calculation.

[0079] Using the same risk calculation method for all projects would mask these differences and lead to distorted risk estimates. Therefore, this invention constructs separate revenue and loss functions for the three types of projects.

[0080] For each type, construct a corresponding profit / loss function, and for the th For each scenario, substitute the corresponding project type's revenue / loss function to calculate the project... The loss value in this scenario; For safety-oriented projects, the risk loss function is defined as:

[0081] in, Indicates the equipment failure rate. Indicates the probability of natural disasters. This indicates the volatility of operation and maintenance costs.

[0082] For benefit-oriented projects, the risk loss function is defined as:

[0083] in, Indicates the volatility of electricity sales prices. Indicates the profit deviation rate. This indicates the growth rate of environmental protection costs.

[0084] For policy-driven projects, the risk loss function is defined as:

[0085] To reflect the uncertainty of risk factors, the Monte Carlo method is used to generate risk scenarios. First, the historical data for each risk factor is fitted with a probability distribution. Then, multiple risk scenarios are generated by randomly sampling according to the fitting results.

[0086] in,

[0087] Substituting the scene variables into the corresponding loss functions yields the total scene loss values:

[0088] At confidence level At a risk level of 95%, the investment risk value for each project is calculated using the discrete formula for Conditional Value at Risk (CVaR):

[0089] The project was finally obtained Investment risk value:

[0090] This risk value serves as the input to the risk objective function in the subsequent step S105.

[0091] S105. Set decision variables for each candidate investment project regarding whether it is selected and its construction year. Take the sum of the dynamic comprehensive scores of the projects indicated by the decision variables and the coupling strength contribution as the comprehensive benefit objective, the sum of the investment risk values ​​of the projects indicated by the decision variables as the risk objective, and the sum of the discounted total life cycle costs of the projects indicated by the decision variables as the cost objective. Construct a multi-objective investment optimization model with preset constraints. In one embodiment, after obtaining the dynamic composite score for each item... Coupling strength coefficient between projects and the investment risk value of each project Then, a multi-objective investment optimization model that comprehensively considers benefits, risks, and costs can be constructed to select the optimal project portfolio and construction sequence. After processing steps S102~S104, each candidate project forms the following set of characteristics:

[0092] For each candidate investment project ( ) and each planning year ( Define binary decision variables (corresponding to 2025-2030):

[0093] (2) Objective function This embodiment simultaneously optimizes the following three objectives 1) Maximizing overall benefits (including project-specific scores and synergistic effects): The objective function for maximizing overall benefits is as follows:

[0094] in, P represents the total number of projects, T In order to plan for studying, For the project exist The year's independent composite score; For the project and The coupling coefficient; Let be a binary decision variable, representing the items selected in year t. The first term represents the sum of the independent scores of all selected items. The second term represents the sum of the scores of all selected items against each other. The sum of coupling contributions, when two projects are selected at the same time, is added to their coupling strength coefficient (positive values ​​for synergistic effect, negative values ​​for conflict loss).

[0095] 2) The risk minimization objective function is as follows:

[0096] For all planning years and all projects Selected items Conditional Value at Risk Summation, For the confidence level, we use 0.95 in this example, which reflects the total tail risk of the portfolio.

[0097] 3) The objective function for minimizing the total lifecycle cost is as follows:

[0098] in, The objective function is the total lifecycle cost. This represents the total number of candidate items. For the planned annual total; As a decision variable, when the project In the The value is 1 if the year is selected for construction, otherwise it is 0. For the project The total life cycle cost; is the discount rate.

[0099] (3) Constraints To ensure the feasibility of the investment plan, the following constraints are set: 1) Investment limit constraints: Considering the limited actual investment capacity of power grid companies, the total investment amount of the selected investment project portfolio should not exceed the planned investment amount of the power grid company.

[0100]

[0101] In the formula: Annual limit; This is the total limit. Where: The benchmark discount rate is used.

[0102] 2) Resource Constraints: Within an investment decision year, due to limitations in human resources, equipment resources, and technological resources, the number of projects that can be constructed simultaneously is limited and cannot exceed a specific value, namely:

[0103] In the formula: , , These represent the number of projects selected for high, medium, and low resource requirements respectively that year; , , This represents the maximum allowed quantity for each category.

[0104] 3) Coupling relationship constraints (based on the five types of relationships mentioned above) Mutual assistance relationship type:

[0105] Constraint type:

[0106] Dependency type:

[0107] Coexistence type:

[0108] Conflict type:

[0109] 4) Timing constraints If the project is only constructed once, then The required projects meet the following requirements. .

[0110] The above three objective functions and constraints constitute a multi-objective investment optimization model.

[0111] S106. The multi-objective investment optimization model is solved using a multi-objective evolutionary algorithm. During the solution process, the population diversity maintenance strategy and crossover mutation probability are dynamically adjusted, and the Pareto optimal solution set is output, where each solution corresponds to a set of values ​​of the decision variables. In one embodiment, the multi-objective investment optimization model established in the previous step is characterized by nonlinearity (coupling terms contain the product of decision variables), discreteness (binary variables), and multiple constraints, belonging to a typical complex combinatorial optimization problem. Traditional multi-objective evolutionary algorithms such as NSGA-II, while capable of outputting the Pareto front, are prone to problems such as solution set clustering (uneven distribution) and slow convergence speed when dealing with large-scale, multi-constraint problems. Therefore, this invention introduces two improvements on the standard NSGA-II: a dynamic crowding threshold and an adaptive crossover mutation probability, to improve solution efficiency and solution set quality.

[0112] (1) Dynamic congestion threshold In standard NSGA In Part II, individuals within the same non-dominated layer maintain diversity by ranking them by crowding distance; however, a fixed crowding threshold easily leads to clustering of solutions in local regions. This invention sets a dynamic crowding threshold that decays exponentially with the number of iterations:

[0113] in, For the first The crowding threshold for the current iteration number; As the initial congestion threshold, this embodiment takes... ; The attenuation coefficient is set to 0.015 in this embodiment.

[0114] Early stage of iteration Smaller A larger value (approximately 1.0) allows for greater crowding distances between individuals, thus maintaining population diversity and facilitating global exploration; as the number of iterations increases, As the exponent decreases, the conditions for retaining individuals are gradually narrowed, prompting the algorithm to focus on the sparse region of the Pareto front, thereby improving the uniformity and accuracy of the final solution set.

[0115] (2) Adaptive crossover probability and mutation probability To avoid premature convergence or search stagnation caused by fixed genetic parameters, this invention dynamically adjusts the crossover probability and mutation probability based on individual fitness and the number of iterations.

[0116] The crossover probability is adaptively adjusted based on the relationship between the current individual fitness and the population fitness distribution:

[0117] in, For the first The fitness value of each individual (in multi-objective optimization, fitness is evaluated by a combination of non-dominated ranking and crowding distance). , These are the average fitness and maximum fitness of the current population, respectively. The baseline crossover probability is set to 0.85 in this embodiment.

[0118] When an individual's fitness is better than the population average (i.e. < )hour, The value is relatively large (the upper limit is close to the upper limit). This promotes genetic recombination between superior individuals and other individuals, further searching for better regions; when an individual's fitness is worse than average, The population should be reduced accordingly to protect the superior patterns already acquired within the population.

[0119] The mutation probability increases linearly with the number of iterations to enhance the ability to perform local perturbations in later stages and avoid getting trapped in local optima.

[0120] in: This represents the current iteration number; To determine the maximum number of iterations, this embodiment takes... =300; As the baseline mutation probability, this embodiment takes =0.08.

[0121] In the early stages of iteration , near The variation intensity is relatively small, which is conducive to accumulating excellent solutions; as iteration progresses, As the value increases linearly, the mutation intensity gradually strengthens, helping the algorithm escape local optima and improving the diversity of the solution set.

[0122] (3) Algorithm execution flow Based on the above improvements, NSGA is improved. The specific steps of Algorithm II are as follows: Step 1: Initialize the population and construct the investment plan code. Initialize the population. Parameters such as the maximum number of iterations, crossover probability, and mutation probability are set. For the power distribution network investment decision problem of this invention, project-year joint coding is performed on the individuals in the population:

[0123] Step 2: Calculate the fitness of investment schemes and verify the constraints. For each investment scheme in the population, calculate the project dynamic comprehensive score obtained in step S102, the project coupling strength coefficient obtained in step S103, and the project risk value obtained in step S104.

[0124] Step 3: Fast Non-Dominated Ranking. Based on the three objective functions of comprehensive benefits, investment risk, and total life cycle cost, all investment options are ranked quickly and non-dominated to obtain the Pareto grade for each investment option.

[0125] Step 4: Dynamic Crowding Distance Calculation and Solution Set Selection. For individuals within the same non-dominated layer, sort them according to their objective function values ​​and calculate the dynamic crowding distance, i.e. ,in It is the first Individual in the first Function values ​​on each target; , For the first layer The maximum and minimum values ​​of each objective are determined. Combined with a dynamic crowding threshold, individuals with crowding distances less than the threshold are filtered out, preserving the diversity of the solution set.

[0126] Step 5: Genetic Evolution Operations. Genetic operations are performed on the current population, including selection, crossover, and mutation. The crossover and mutation processes consider not only traditional genetic operators but also project construction timing constraints and coupling relationship constraints. This ensures that newly generated individuals always meet the practical requirements of the power distribution network investment planning problem in this invention.

[0127] Step 6: Merge and update the parent and offspring populations. Merge the parent and offspring populations, and perform fast non-dominated sorting and dynamic crowding screening again. Retain the investment scheme with better overall benefits, lower risk, lower cost, and that meets the constraints to form a new generation population. Then return to Step 2 for further iterative optimization.

[0128] Step 7: Output the Pareto optimal solution set and determine the final investment plan. If the maximum number of iterations is reached or the Pareto front shows no significant change after a certain number of iterations, terminate the iteration and output the Pareto optimal solution set.

[0129] Step 8: Planning Cycle Stage Division. After obtaining the Pareto optimal solution set, the entire planning cycle is divided into several decision stages according to the year, denoted as t=1,2,... Each stage corresponds to a planning year. The project construction results of the previous stage serve as the status input for the investment decision of the next stage, reflecting the continuity of the construction sequence of power distribution network investment projects.

[0130] Step 9: Define the stage state variables. (This refers to the definition of the stage state variables.) For each planning year, stage-specific state variables are defined to characterize the set of completed projects, remaining investment, remaining resource capacity, and satisfied coupling relationships prior to the start of that year. Their expression can be written as: , This indicates up to the [number]. A collection of projects completed before the end of the year; Indicates the remaining investment budget; Indicates the remaining resource constraint capacity; It indicates the state of satisfaction of inter-project dependencies, coexistence, mutual assistance, and conflict relationships.

[0131] Step 10: For each candidate investment plan in the Pareto optimal solution set, perform state transition verification sequentially according to the project construction year. If the project is in the... If selected in a given year, update the stage status: Soon The project is added to the set of completed projects, and the corresponding annual investment amount and resource usage are deducted, while the project coupling relationship status is updated simultaneously. If, after the state transition, there are situations such as annual investment exceeding the limit, resource constraints not being met, dependencies not being completed in advance, conflicting projects being constructed concurrently, or coexisting projects not being constructed synchronously, then the candidate solution is determined to not meet the timing constraints and is removed from the Pareto solution set.

[0132] Step 11: Optimal Solution Selection. For candidate solutions that pass state transition and constraint verification, a comprehensive ranking is further performed based on decision preferences. A normalized proximity evaluation method can be used to unify the three objectives—comprehensive benefits, investment risk, and life-cycle cost—into dimensionless indicators, and the distance between each candidate solution and the ideal solution is calculated. The comprehensive evaluation value can be expressed as: .in, For the first The comprehensive decision value of each candidate solution; , , These are the normalized overall benefits, investment risks, and total life-cycle costs, respectively. , , These represent the decision preference weights.

[0133] Step 12: Output the optimal project and timeline for the year. Based on the decision variables in the final recommended plan. The system selects values ​​to determine whether each project is selected and its construction year. The final output includes a list of optimal investment projects for the year, the project construction sequence, the annual investment scale, and corresponding benefit, risk, and cost evaluation results, forming a multi-objective equilibrium investment decision-making scheme for the power distribution network.

[0134] like Figure 2 As shown, a comparison of the convergence curves of the two algorithms is presented: the horizontal axis represents the number of iterations from 0 to 300, and the vertical axis represents the normalized objective function value (a weighted sum of the three objectives is used to illustrate the convergence process). The dashed line represents the traditional algorithm, and the solid line represents the algorithm of this invention.

[0135] The figure divides the algorithm into three regions: the global exploration phase (generations 0-100), the convergence acceleration phase (generations 100-200), and the stable convergence phase (generations 200-300). As shown in the figure, both algorithms gradually converge towards the Pareto optimal front as the number of iterations increases. However, the improved NSGA-II algorithm proposed in this invention, due to the introduction of a dynamic crowding threshold strategy and an adaptive crossover mutation mechanism, maintains better population diversity in the global exploration phase, rapidly approaches the optimal region in the convergence acceleration phase, and obtains a more uniform Pareto solution set in the stable convergence phase.

[0136] Compared with the traditional NSGA-II algorithm, the algorithm of this invention requires fewer iterations to reach a stable state and has a lower final comprehensive objective function value, indicating that the proposed algorithm can effectively improve the solution efficiency and solution set quality.

[0137] In order to verify the effectiveness of the present invention, the method of the present invention was compared with the traditional fixed weight + standard NSGA-II method, and the results are shown in Table 1.

[0138] Table 1

[0139] The results show that the method of the present invention is significantly better than the traditional method in terms of overall benefits, risk control, cost saving, reduction of engineering conflicts, algorithm convergence speed and solution set uniformity, which fully verifies the effectiveness and superiority of the present invention.

[0140] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0141] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling, characterized in that, Includes the following steps: S1. Collect multi-dimensional basic data of potential investment projects in the power distribution network, and standardize the multi-dimensional basic data to obtain standardized values ​​for each project in each data dimension. S2. Divide the planning period of the candidate investment projects into multiple planning years; determine the static benchmark weights for each data dimension; Based on the policy orientation or load demand of each planning year, the static benchmark weights are adjusted year by year to obtain the dynamic weights of each data dimension in each planning year. The standardized values ​​of each project are combined with the dynamic weights of the corresponding planning year to obtain the dynamic comprehensive score of each project in each planning year. S3. Based on whether the project construction causes changes in the data dimension values, determine the subset of data dimensions affected by each project and the direction of change in each dimension; based on the degree of overlap of the affected dimension subsets of each pair of projects, the consistency of the direction of change in the common affected dimension, and the type of coupling relationship between the two, calculate the coupling strength coefficient between each pair of projects. S4. Classify each project into a preset risk type, and construct a corresponding profit and loss function for each risk type; calculate the loss value under each scenario by generating multiple risk scenarios, and calculate the investment risk value of each project based on the tail expectation of the loss value. S5. Set decision variables for each candidate investment project regarding whether it is selected and its construction year. Take the sum of the dynamic comprehensive scores of the projects indicated by the decision variables and the contribution of coupling strength as the comprehensive benefit objective, the sum of the investment risk values ​​of the projects indicated by the decision variables as the risk objective, and the total discounted value of the full life cycle cost of the projects indicated by the decision variables as the cost objective. Construct a multi-objective investment optimization model with preset constraints. S6. The multi-objective investment optimization model is solved using a multi-objective evolutionary algorithm. During the solution process, the population diversity maintenance strategy and crossover mutation probability are dynamically adjusted, and the Pareto optimal solution set is output, where each solution corresponds to a set of values ​​of the decision variables. S7. Select the optimal solution that meets the preset constraints and decision preferences from the Pareto optimal solution set, and output the optimal results and construction schedule of the power distribution network project.

2. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The static benchmark weights mentioned in step S2 are determined by a combination of the analytic hierarchy process (AHP) and the entropy weight method. The AHP is used to calculate the subjective weights of each data dimension, while the entropy weight method is used to calculate the objective weights based on the numerical distribution of each item in the data dimension. The subjective weights and objective weights are then weighted and summed to obtain the static benchmark weights.

3. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The method for calculating the dynamic comprehensive score in step S2 is as follows: the standardized values ​​of each project in each data dimension are weighted and summed with the dynamic weight of the corresponding planning year to obtain the dynamic comprehensive score of the project in the planning year; wherein, the dynamic weight of each planning year is obtained by normalizing the weight of the previous year after adding the weight increment, and the weight increment is determined according to the policy orientation or load demand of the planning year.

4. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The degree of overlap mentioned in step S3 is measured by Jaccard similarity, which is the number of intersection elements of the two items' influence dimension subsets divided by the number of union elements; the consistency of change direction is measured by consistency coefficient, which is the number of dimensions in which the two items have the same change direction in the common influence dimension divided by the total number of common influence dimensions; the coupling relationship types include mutual assistance, constraint, dependence, conflict, and coexistence, each type corresponding to a preset correction coefficient; the coupling strength coefficient is obtained by multiplying the Jaccard similarity, consistency coefficient, and correction coefficient.

5. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 4, characterized in that, The correction coefficient is determined according to the type of coupling relationship: positive for mutual assistance, negative for constraint, positive for dependency (between 0 and 1), negative for conflict, and positive for coexistence.

6. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The risk types mentioned in step S4 include safety-related, benefit-related, and policy-related. The revenue loss function for safety-related projects includes equipment failure rate, probability of natural disasters, and operation and maintenance cost fluctuation factors. The revenue loss function for benefit-related projects includes electricity sales price volatility, benefit achievement rate deviation, and environmental protection cost growth rate factors. The revenue loss function for policy-related projects includes subsidy standard adjustment factors and development planning matching degree deviation factors.

7. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The risk scenarios described in step S4 are generated through Monte Carlo simulation. The probability distribution of each risk factor is fitted based on historical data, and multiple sets of scenario samples are randomly selected. The tail expectation of the loss value is calculated using Conditional Value at Risk (CVaR). Under a preset confidence level, the conditional expectation of the loss value exceeding the Value at Risk (VaR) is calculated and used as the investment risk value of the project.

8. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The preset constraints mentioned in step S5 include: investment limit constraints, i.e., the total investment in each planning year and the entire planning period shall not exceed the preset limit; resource supply constraints, i.e., the number of projects with different resource demand levels in the same planning year shall not exceed the corresponding preset upper limit; coupling relationship constraints, i.e., logical restrictions imposed on decision variables according to the type of coupling relationship, including prohibiting the simultaneous selection of restrictive project pairs, the simultaneous or non-selection of mandatory coexistence project pairs, and requiring that subsequent projects in dependent project pairs can only be selected after the completion of the preceding project; and time sequence constraints, i.e., mandatory projects shall be selected at least once in the planning period, and a single project shall be selected at most once in multiple planning years.

9. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, The multi-objective evolutionary algorithm mentioned in step S6 is an improved NSGA-II algorithm. The dynamic adjustment strategy for maintaining population diversity includes: setting a dynamic crowding threshold that decays exponentially with the number of iterations; using a larger threshold in the early stage of iteration to maintain population diversity; and using a smaller threshold in the later stage of iteration to focus on the local optimal region. The dynamic adjustment of crossover and mutation probabilities includes: adaptively adjusting the crossover and mutation probabilities based on the comparison between individual fitness and the population average fitness, wherein individuals with fitness better than the average fitness are given lower crossover and mutation probabilities, and individuals with fitness worse than the average fitness are given higher crossover and mutation probabilities.

10. The multi-objective equilibrium investment decision-making method for distribution networks based on time-series coupling according to claim 1, characterized in that, Step S7 specifically includes: The planning period is divided into several decision-making stages by year, and the set of completed projects, remaining investment amount, remaining resource capacity and coupling relationship status of each stage are defined. The stage state transition verification is performed on each candidate solution in the Pareto optimal solution set in turn, and candidate solutions with investment exceeding the limit, resource exceeding the capacity, dependency timing misalignment, conflicting construction at the same time or coexisting but not constructed synchronously are eliminated. For the candidate solutions that pass the verification, they are sorted according to the normalized closeness of comprehensive benefits, investment risk and whole life cycle cost, and the optimal solution is selected to determine the construction year of each project and output it.

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