Power distribution network project construction period evaluation method based on chance-constrained programming

Abstract

The invention relates to the technical field of power system engineering project management, in particular to a power distribution network project construction period evaluation method based on chance-constrained programming, which comprises the following steps: firstly, collecting historical data of a power distribution network engineering project, and preprocessing the collected historical data to obtain a standardized data sequence; establishing an opportunity constraint construction period evaluation model, describing a task dependency relationship through a directed acyclic graph, and introducing opportunity constraint; then, mixed solution is carried out, the influence of each uncertainty factor on the total construction period is calculated, a sensitivity index is obtained, which factors have the largest influence on the total construction period is recognized, the resource utilization rate is monitored in real time, potential bottlenecks are early warned in advance, the calculation efficiency is high, risk control is accurate, and robustness is high; high-sensitivity uncertainty factors are simulated through a scene method, the response ability of the model to extreme conditions is enhanced, the excessive conservative or underestimated risk is avoided, and the method is suitable for construction period evaluation and resource allocation of a power distribution network project containing multiple construction links.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system engineering project management, in particular to a distribution network engineering duration assessment method based on Chance-Constrained Programming (CCP), and a hybrid solution strategy combining analytical method, discretization processing and scenario method, for realizing accurate prediction and risk control of duration under multiple uncertainty environment. BACKGROUND

[0002] With the development of new energy technology and the promotion of the "double carbon" goal, as the key link connecting the power generation side and user demand, the construction quality and progress of the distribution network directly affect the efficiency of new energy access and the stability of the system. However, traditional deterministic duration assessment methods such as Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) are difficult to cope with multiple uncertainty problems such as weather changes, equipment supply delays, approval efficiency fluctuations, and human resource shortages in distribution network projects, leading to frequent project schedule delays. Although existing research attempts to introduce Monte Carlo simulation, fuzzy logic and other methods to improve uncertainty modeling capabilities, there are still limitations: high computational complexity, traditional CCP methods have high computational complexity when dealing with high-dimensional complex systems, making it difficult to meet the demand for rapid response of engineering projects; conservative solution space, single solution method has limitations in expression ability and risk control, which can easily lead to overoptimism or underestimate risks; lack of flexibility, unable to effectively handle non-normal distribution uncertainty factors such as extreme weather and supply chain disruptions, resulting in insufficient model robustness. Therefore, there is an urgent need for a new duration assessment method that can efficiently solve and flexibly respond to multiple uncertainties. SUMMARY

[0003] The present application aims to overcome the shortcomings of the prior art and address the deficiencies of existing distribution network engineering duration assessment methods in terms of computational complexity, solution space conservatism, and robustness. It provides a distribution network engineering duration assessment method based on Chance-Constrained Programming, which accurately handles multiple sources of uncertainty while ensuring computational efficiency. Through a hybrid solution strategy, it balances computational complexity and risk control accuracy, enhances the ability to respond to extreme situations, and ensures that the project is completed on schedule. Sensitivity analysis identifies key influencing factors, providing a scientific basis for project management.

[0004] To achieve the above-mentioned purpose, the present application adopts the following technical solutions: A distribution network engineering duration assessment method based on Chance-Constrained Programming, specifically comprising the following steps: S1. Data Acquisition and Preprocessing: Collect historical data of power distribution network engineering projects. The historical data includes construction resource pool, personnel and equipment availability, and environmental disturbance information. Perform sparse data removal, missing value repair and normalization on the collected historical data to obtain a standardized data sequence. S2. Construction of Opportunity-Constrained Schedule Assessment Model: Establish an opportunity-constrained schedule assessment model, describe task dependencies using a directed acyclic graph (DAG), and introduce opportunity constraints to ensure that the project is completed on time under a given confidence level; S3. Hybrid Solution: Determine whether to use the analytical method or the discretization method based on the distribution of tasks. If the task duration distribution is clear and simple, use both analytical and discretization methods. For task durations that cannot be discretized and have no clear distribution, use the scenario method to solve the problem. S4. Sensitivity Analysis and Bottleneck Early Warning: By calculating the impact of each uncertainty factor on the total project duration, a sensitivity index is obtained. By calculating the sensitivity index, the factors with the greatest impact on the total project duration are identified, and resource utilization is monitored in real time. When the average daily resource utilization rate is consistently higher than the set value, a bottleneck early warning is triggered to provide early warning of potential bottlenecks.

[0005] As a further technical solution of the present invention, the specific process of step S2 is as follows: the duration of the task... Represented as: ,in E represents a function based on factors such as resource R, power outage plan W, design change D, and live-line working capacity C. k To account for the impact of environmental disturbances and other uncertainties, a planned construction period should be set for the project. and confidence level Then, the total project duration T is required to not exceed the planned duration T at this confidence level. P ,Right now: .

[0006] As a further technical solution of the present invention, the analytical method described in step S3 quickly estimates uncertainties with well-defined distributions and derives key indicators such as expected construction period and probability of on-time completion: ,in, For the expected construction period, Let n be the expected duration of task k and n be the number of tasks. The expected duration is obtained through analytical methods, and the probability of timely completion is initially estimated. Analytical methods can also be embedded in ε-constraint methods, especially in multi-objective optimization problems. ε-constraint methods transform a multi-objective problem into a single-objective problem. First, the upper and lower limits of the risk objective are determined based on the objective function and reliability risk. After determining the threshold range, the risk space is discretized, which facilitates the solution. The discretization processing converts continuous probability distribution into a limited number of scenes, facilitating simulation and calculation, and effectively processing complex random variables using the discretization method: Wherein is the probability of scene , is the indicator function of the opportunity constraint of the duration under scene , and m is the number of discrete scenes. The scene method generates different duration scenes through simulation, and estimates the risk of the total duration according to the probability distribution of these scenes. The scene method does not depend on the distribution form of the task duration, and can flexibly handle different situations.

[0007] As a further technical solution of the present application, the sensitivity index in step S4 is: Wherein is the sensitivity index of the kth factor, is the kth uncertainty factor.

[0008] Compared with the prior art, the present application has the following remarkable effects: high calculation efficiency, compared with the traditional CCP method, the present strategy significantly reduces the calculation complexity through a hybrid solving method, and is suitable for the rapid decision-making requirements of large-scale complex systems; precise risk control, the completion probability is controlled through explicit opportunity constraints to ensure that the project is completed on schedule under the preset confidence level, and the risk of progress delay is effectively reduced; strong robustness, high sensitivity uncertainty factors are simulated through the scene method to enhance the response ability of the model to extreme situations and avoid over-conservatism or underestimation of risks; timely bottleneck warning, potential construction bottlenecks can be identified in advance through resource utilization rate analysis to provide decision-making basis for resource allocation and progress adjustment, forming a power distribution network duration evaluation solving paradigm that takes into account multiple uncertainties, which can adapt to power distribution network engineering under different regional and environmental conditions, and provides a reliable solution for power distribution network engineering planning and construction scheme designation, has significant technical comprehensive benefits and application value, and is suitable for power distribution network engineering duration evaluation and resource allocation of multiple construction links. BRIEF DESCRIPTION OF DRAWINGS

[0009] Figure 1 The workflow diagram of the present application.

[0010] Figure 2 The directed acyclic task network diagram used in the present application.

[0011] Figure 3 The project total duration evaluation result comparison diagram of embodiment 2 of the present application.

[0012] Figure 4 The mixed solving strategy duration distribution histogram of embodiment 2 of the present application.

[0013] Figure 5 This is a risk analysis diagram of project delay in Embodiment 2 of the present invention.

[0014] Figure 6 Sensitivity analysis of key processes in Embodiment 2 of the present invention Detailed Implementation

[0015] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0016] Example 1: like Figure 1 and Figure 2 As shown in the figure, this embodiment provides a method for evaluating the construction period of a power distribution network project based on chance-constrained programming, which specifically includes the following steps: S1. Data Acquisition and Preprocessing: Collect historical data of power distribution network projects. The historical data includes construction resource pool, personnel and equipment availability, and environmental disturbance information. Perform sparse data removal, missing value repair and normalization on the collected historical data to obtain a standardized data sequence.

[0017] S2. Opportunity-Constrained Schedule Assessment Model Construction: An opportunity-constrained schedule assessment model is established, using a directed acyclic graph (DAG) to describe task dependencies and introducing opportunity constraints to ensure the project is completed on time under a given confidence level; the duration of tasks is... Represented as: ,in E represents a function based on factors such as resource R, power outage plan W, design change D, and live-line working capacity C. k To account for the impact of environmental disturbances and other uncertainties, a planned construction period should be set for the project. and confidence level Then, the total project duration T is required to not exceed the planned duration T at this confidence level. P ,Right now: This constraint allows the project to be completed on time with a certain probability, thereby effectively controlling the risk of project delays.

[0018] S3. Hybrid Solution: The choice between analytical and discretization methods is determined based on the task distribution. If the task duration distribution is clear and simple, both analytical and discretization methods are used. For tasks whose durations cannot be discretized and have no clear distribution, a scenario-based approach is employed. The analytical method rapidly estimates uncertainties with clear distributions, deriving key indicators such as expected duration and on-time completion probability. ,in, For the expected construction period, Let n be the expected duration of task k and n be the number of tasks. The expected duration is obtained through analytical methods, and the probability of timely completion is initially estimated. Analytical methods can also be embedded in ε-constraint methods, especially in multi-objective optimization problems. ε-constraint methods transform a multi-objective problem into a single-objective problem. First, the upper and lower limits of the risk objective are determined based on the objective function and reliability risk. After determining the threshold range, the risk space is discretized, which facilitates the solution. The discretization process transforms a continuous probability distribution into a finite number of scenarios, facilitating simulation and computation. For random variables with unclear distributions or complexities, the discretization method is used for effective processing. ,in For the scene The probability, For the scene The indicator function for satisfying the opportunity constraint in the next construction period, where m is the number of discrete scenarios; The scenario method simulates different project duration scenarios and estimates the risk of the total project duration based on the probability distribution of these scenarios. The scenario method does not depend on the distribution of task durations and can flexibly handle different situations.

[0019] S4. Sensitivity Analysis and Bottleneck Early Warning: By calculating the impact of each uncertainty factor on the total project duration, a sensitivity index is obtained. ,in Let be the sensitivity index of the k-th factor. For the k-th uncertainty factor, the sensitivity index is calculated to identify which factors have the greatest impact on the total project duration. Resource utilization is monitored in real time, and a bottleneck warning is triggered when the average daily resource utilization rate is consistently higher than the set value, thus providing early warning of potential bottlenecks.

[0020] Example 2: This embodiment adopts the technical solution of Embodiment 1. First, considering the uncertainty of task duration in distribution network engineering, a probabilistic control mechanism is introduced. The deterministic duration of each task in the traditional critical path method is extended to a random variable. With the critical path completion time T as the core decision object, a chance constraint condition satisfying the confidence level β is constructed. This approach enables quantitative control of overall project delay risks, flexibly setting the timeframe to minimize the expected total duration or maximize the probability of on-time completion, adapting to different risk appetites and project management needs. An opportunity-constrained duration assessment model is established, incorporating factors such as human resources, equipment resources, environmental disturbances, and design changes. A Directed Acyclic Graph (DAG) describes the dependencies between various processes. Addressing the computational complexity and solution space conservatism issues in solving the opportunity-constrained model, a three-stage hybrid strategy is proposed. An analytical method is used to derive confidence intervals and risk thresholds based on probability distribution functions, achieving rapid calculations under specific distribution assumptions. Uncertain variables are discretized, and finite scenarios are constructed and assigned probability weights to simplify the model structure. The planned duration and confidence level are set, and the risk threshold is quickly estimated using an analytical method. Through discretization, continuous variables are transformed into finite scenarios, and the impact of extreme weather and supply chain disruptions is simulated using a scenario-based approach. The expected duration is determined to be 58.3 days, with an on-time completion probability of 95.2%, satisfying the constraint sensitivity analysis and bottleneck early warning. Oversensitivity analysis reveals that civil construction has the greatest impact on the total duration; a 10% increase in its duration will lead to an approximately 15.2% increase in the total duration. Simultaneously, resource utilization curves for each stage were output. It was found that during the equipment installation phase (days 35-40), the average daily utilization rate of hoisting equipment reached 92%, triggering a "bottleneck warning." It was recommended to coordinate equipment leasing or adjust the construction sequence in advance. The evaluation results of this strategy were compared with actual project data and with the traditional CPM method. The results showed that the average error in the project duration prediction using this strategy was 4.1 days, significantly lower than the 6.7 days of the CPM method, and the resource warning accuracy rate reached 85%.

[0021] This invention proposes a three-stage hybrid solution strategy that combines analytical methods, discretization, and scenario-based approaches, balancing computational efficiency with risk control accuracy. It focuses on constructing an opportunity-constrained model, using a directed acyclic graph (DAG) to describe task dependencies and introducing opportunity constraints to ensure timely project completion at a given confidence level. This achieves a flexible balance between project schedule and risk tolerance, forming a multi-source uncertainty handling framework that distinguishes between exogenous and endogenous uncertainties. The duration of key processes is modeled as a random variable, and historical data is used for distribution fitting and correlation analysis to improve the accuracy of uncertainty characterization. This enables sensitivity analysis and bottleneck early warning for power distribution networks, identifying key influencing factors through sensitivity analysis, monitoring resource utilization in real time, and providing early warning of potential bottlenecks, thus providing a scientific basis for project management.

[0022] The structures, networks, and algorithms not described in detail in this article are all general techniques in this field.

[0023] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0024] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for evaluating the construction period of a power distribution network project based on chance-constrained programming, characterized in that, Specifically, the following steps are included: S1. Data Acquisition and Preprocessing: Collect historical data of power distribution network engineering projects. The historical data includes construction resource pool, personnel and equipment availability, and environmental disturbance information. Perform sparse data removal, missing value repair and normalization on the collected historical data to obtain a standardized data sequence. S2. Construction of Opportunity-Constrained Schedule Assessment Model: Establish an opportunity-constrained schedule assessment model, describe task dependencies through a directed acyclic graph, and introduce opportunity constraints to ensure that the project is completed on time under a given confidence level; S3. Hybrid Solution: Determine whether to use the analytical method or the discretization method based on the distribution of tasks. If the task duration distribution is clear and simple, use both analytical and discretization methods. For task durations that cannot be discretized and have no clear distribution, use the scenario method to solve the problem. S4. Sensitivity Analysis and Bottleneck Early Warning: By calculating the impact of each uncertainty factor on the total project duration, a sensitivity index is obtained. By calculating the sensitivity index, the factors with the greatest impact on the total project duration are identified, and resource utilization is monitored in real time. When the average daily resource utilization rate is consistently higher than the set value, a bottleneck early warning is triggered to provide early warning of potential bottlenecks.

2. The method for evaluating the construction period of a power distribution network project based on chance-constrained programming as described in claim 1, characterized in that, The specific process of step S2 is as follows: Set the duration of the task. Represented as: ,in E represents a function based on factors such as resource R, power outage plan W, design change D, and live-line working capacity C. k To account for the impact of environmental disturbances and other uncertainties, a planned construction period should be set for the project. and confidence level Then, the total project duration T is required to not exceed the planned duration T at this confidence level. P ,Right now: .

3. The method for evaluating the construction period of a power distribution network project based on chance-constrained programming as described in claim 2, characterized in that, The analytical method described in step S3 quickly estimates uncertainties with well-defined distributions, deriving key indicators such as expected construction period and probability of on-time completion. ,in, For the expected construction period, Let n be the expected duration of task k and n be the number of tasks. The expected duration is obtained through analytical methods, and the probability of timely completion is initially estimated. Analytical methods can also be embedded in ε-constraint methods, especially in multi-objective optimization problems. ε-constraint methods transform a multi-objective problem into a single-objective problem. First, the upper and lower limits of the risk objective are determined based on the objective function and reliability risk. After determining the threshold range, the risk space is discretized, which facilitates the solution. The discretization process transforms a continuous probability distribution into a finite number of scenarios, facilitating simulation and computation. For random variables with unclear distributions or complexities, the discretization method is used for effective processing. ,in For the scene The probability, For the scene The indicator function for satisfying the opportunity constraint in the next construction period, where m is the number of discrete scenarios; The scenario method simulates different project duration scenarios and estimates the risk of the total project duration based on the probability distribution of these scenarios. The scenario method does not depend on the distribution of task durations and can flexibly handle different situations.

4. The method for evaluating the construction period of a power distribution network project based on chance-constrained programming according to claim 3, characterized in that, The sensitivity index mentioned in step S4 is: ,in Let be the sensitivity index of the k-th factor. This is the kth uncertainty factor.

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