Multi-region collaborative power grid planning system and method based on improved multi-target particle swarm optimization

Abstract

The invention discloses a multi-region collaborative power grid planning system and method based on an improved multi-target particle swarm optimization algorithm, relates to the technical field of power system planning, and solves the problems of multi-target coupling and cross-region coordination in traditional power grid planning by constructing an economical, environment-friendly and reliable multi-dimensional target function and introducing a game theory method to quantify a multi-target constraint relation. The system comprises a data acquisition module, a multi-objective optimization model construction module, an improved particle swarm algorithm execution module, a collaborative decision module and a result output module, the improved particle swarm algorithm adopts dynamic adaptive inertia weight, time-varying acceleration coefficient and differential mutation operation, and the convergence speed and Pareto frontier distribution quality are remarkably improved; and the collaborative decision-making module realizes cross-regional parameter interaction and scheme optimization through a hierarchical collaborative mechanism and a fuzzy entropy theory. According to the method, collaborative optimization of calculation efficiency and scheme balance is realized in multi-regional power grid collaborative planning, and technical support is provided for scientific planning of a complex power grid system.

Description

Technical Field

[0001] This invention belongs to the field of power system planning technology, specifically relating to a multi-regional collaborative power grid planning system and method based on an improved multi-objective particle swarm optimization algorithm. Background Technology

[0002] The current field of power grid planning suffers from the following main technical shortcomings: First, traditional single-objective optimization methods cannot effectively coordinate multiple conflicting objectives in power grid planning, such as economy, environmental protection, and reliability. Second, the standard particle swarm optimization algorithm is prone to premature convergence when dealing with optimization problems with three or more objectives, making it difficult to obtain a uniformly distributed Pareto optimal solution set. Third, existing methods do not accurately model inter-regional power exchange constraints, potentially leading to feasibility issues in the final planning scheme during actual operation. Furthermore, conventional multi-objective optimization algorithms lack effective diversity preservation mechanisms during solution set selection, affecting decision quality.

[0003] These technical deficiencies severely restrict the scientific and economical nature of power grid planning under the new power system, and there is an urgent need for an innovative method that can balance multi-objective optimization performance with cross-regional coordination accuracy. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing technologies, this invention proposes a multi-regional collaborative power grid planning system and method based on an improved multi-objective particle swarm optimization algorithm.

[0005] This invention is achieved through the following technical solution:

[0006] This invention provides a multi-regional collaborative power grid planning system and method based on an improved multi-objective particle swarm optimization algorithm. The system includes a data acquisition module, a multi-objective optimization model construction module, an improved particle swarm optimization algorithm execution module, a collaborative decision-making module, and a result output module. The data acquisition module acquires real-time data on power grid load demand, renewable energy output forecasts, and cross-regional transmission channel status parameters for each region. The multi-objective optimization model construction module establishes a multi-dimensional objective function with economic efficiency, environmental friendliness, and reliability as optimization objectives, including investment cost, network loss, carbon emissions, and power supply reliability, and quantifies the constraints between multiple objectives using game theory. The improved particle swarm optimization algorithm execution module adopts a dynamic adaptive inertia weight strategy, adjusting weight coefficients according to particle swarm diversity indicators during iteration, and introducing mutation operations from differential evolution algorithms to enhance local search capabilities. The collaborative decision-making module achieves inter-regional optimization parameter interaction through a hierarchical collaborative mechanism, selecting non-dominated solution sets as candidate schemes in each iteration, and calculating the comprehensive satisfaction index of each scheme based on fuzzy entropy theory. The result output module generates multiple planning schemes based on Pareto front distribution characteristics and selects the optimal solution based on decision-maker preferences.

[0007] Furthermore, this invention also provides a multi-regional cooperative power grid planning method based on an improved multi-objective particle swarm optimization algorithm, comprising the following steps:

[0008] S1. Real-time acquisition of power grid load demand, renewable energy output forecast data, and cross-regional power transmission channel status parameters in various regions;

[0009] S2. With economy, environmental protection and reliability as optimization objectives, a multi-dimensional objective function is established that includes investment cost, network loss, carbon emissions and power supply reliability. The constraint relationship between the multiple objectives is quantified by game theory.

[0010] S3. A dynamic adaptive inertia weight strategy is adopted, which adjusts the weight coefficients according to the particle swarm diversity index during the iteration process, and introduces the mutation operation of the differential evolution algorithm to enhance the local search capability.

[0011] S4. The interaction of optimization parameters between regions is realized through a hierarchical collaboration mechanism. In each iteration, the non-dominated solution set is selected as the candidate scheme, and the comprehensive satisfaction index of each scheme is calculated based on the fuzzy entropy theory.

[0012] S5. Generate multiple planning schemes based on the characteristics of the Pareto frontier distribution, and select the optimal solution by combining the decision-maker's preferences.

[0013] As a further aspect of the present invention, step S1 includes the following steps:

[0014] First, load demand data of the power grid in each region is collected. The data includes historical electricity load curves, typical daily load forecasts, and seasonal fluctuation coefficients. The data is periodically acquired and stored in the database.

[0015] Secondly, renewable energy output forecast data is obtained. The data is based on historical power generation records of wind farms and photovoltaic power plants, as well as wind speed and solar intensity forecast information provided by meteorological departments. The power output curve for future periods is generated through a preset forecast model.

[0016] Then, the status parameters of the cross-regional power transmission channel are collected, including line power flow distribution, node voltage amplitude, transmission capacity and safety margin under the N-1 fault scenario. The data integrity is updated in real time and verified through the online monitoring system.

[0017] Next, outlier detection and correction were performed on the original data. The sliding window statistical method was used to identify abnormal fluctuations, and the missing data was filled in by linear interpolation. The numerical range of data with different dimensions was unified by normalization.

[0018] Finally, a standardized dataset is constructed by matching load demand, renewable energy output, and transmission parameters with regional identifiers according to timestamps to form a structured data package, which serves as input data for the multi-objective optimization model construction module.

[0019] As a further aspect of the present invention, the method for establishing a multi-dimensional objective function that includes investment cost, network loss, carbon emissions, and power supply reliability in step S2, with economic efficiency, environmental friendliness, and reliability as optimization objectives, includes the following steps:

[0020] First, an economic function is constructed with the objective of minimizing the regional power grid construction investment cost and operation loss cost. The investment cost calculation formula is as follows: In the formula N area α represents the number of regions. i β i C represents the unit cost correction factor for the transmission line and transformer in region i, respectively. line,i C trans,i L represents the unit price of the corresponding equipment. i T i The line length and number of transformers are used as factors; network loss costs are determined by power flow calculations under typical load scenarios, using the following formula: Where γ t As scene weights, R j For the line resistance, I j ,t is the line current value under scenario t, and Δt is the duration of the scenario;

[0021] Based on this, an environmental friendliness function is constructed with the goal of minimizing carbon emission costs, and its expression is: In the formula η i ζ i For carbon emission factors of thermal power and gas-fired power, θ i P is the renewable energy substitution factor. coal i、P gas i、P RES ,i represent the output of thermal power, gas power, and renewable energy units in region i, respectively. Meanwhile, the reliability objective function uses the power supply reliability index R. reliab The quantification and calculation formula is as follows: U load Let i be the average annual load shedding in region i, and P be the load shedding amount. demand , i represents the total load demand of the region.

[0022] As a further aspect of the present invention, the step of quantifying the constraint relationships between multiple objectives using game theory in step S2 is as follows:

[0023] Using game theory, economic efficiency, environmental friendliness, and reliability are treated as three parties in a non-cooperative game. A Nash equilibrium model is constructed to coordinate the competitive relationship between these objectives. The model includes constraints such as power balance, transmission capacity, and renewable energy penetration. Its mathematical form is as follows:

[0024]

[0025] Among them G i Let K be the set of generating units within region i. i Let S be the set of inter-regional power transmission channels in region i. j λ represents the apparent power of the line, and λ is the minimum requirement for the proportion of renewable energy in the entire network.

[0026] Finally, the weighted summation method is used to transform the multi-objective function into a comprehensive objective function:

[0027]

[0028] In the formula, w1, w2, and w3 are weighting coefficients, satisfying w1 + w2 + w3 = 1, C base C emis,base Using baseline costs and emissions values, the weight allocation is dynamically optimized through an interactive adjustment module to ensure a uniform distribution of the Pareto front.

[0029] As a further aspect of the present invention, step S3 includes the following steps:

[0030] First, an initial particle swarm is generated using the Latin hypercube sampling method. Then, an initial solution set is uniformly distributed within the decision variable space using a stratified sampling strategy. Let the particle position vector X... p =(x p1 ,x p2 ,...,x pn Let V represent the planning scheme of the p-th particle in the n-dimensional decision space, and let V be the particle velocity vector. p =(v p1 ,v p2 ,...,v pn The search direction and step size are represented by ). After initialization, the objective function value F of each particle is evaluated through power flow calculation and constraint verification. p =(f p1 ,f p2 ,f p3 ), where f p1 f p2 f p3 These correspond to economic efficiency, environmental friendliness, and reliability indicators, respectively.

[0031] During the iteration process, a dynamic adaptive inertia weight strategy is adopted to balance global exploration and local development capabilities. The update formula for the inertia weight ω is: In the formula ω (k) ω represents the inertia weight at the k-th iteration. max ω min Its range of values, div(k) is the current population diversity index, defined as the standard deviation of particle positions, div maxAs the maximum diversity threshold, when population diversity decreases to the set threshold, ω adaptively decreases to enhance local search accuracy, and vice versa to maintain global exploration capability; simultaneously, a time-varying acceleration coefficient is designed to adjust the individual extreme value pbest. p The update formulas for the influence weights of the global extremum gbest and the acceleration coefficients c1 and c2 are as follows:

[0032]

[0033] Where K max To maximize the number of iterations, c1 decreases linearly from a high value as the number of iterations increases, gradually reducing the particles' dependence on individual experience, while c2 increases from a low value to enhance the group's collaborative ability, thereby achieving a dynamic balance between rapid exploration in the early stage and fine convergence in the later stage.

[0034] When no significant improvement in the Pareto front is detected in successive iterations, Cauchy mutation is performed on the stagnant particles:

[0035] x′ pd =x pd +σ·Cauchy(0,1);

[0036] In the formula, σ is the variable asynchronous length factor, Cauchy(0,1) is a standard Cauchy distribution random number, and the particle after mutation needs to re-verify the feasibility constraints and update the objective function value;

[0037] In terms of maintaining the non-dominated solution set, an external archive A is constructed to store all non-dominated solutions generated during the iteration process. The diversity of the solution set is maintained by using a crowding comparison operator. After each iteration, fast non-dominated sorting is used to stratify the solutions in the archive, calculate the crowding distance of each solution, and delete the solution with the smallest crowding until the archive capacity does not exceed the preset value N. arch ;

[0038] Finally, when the maximum number of iterations is reached or the Pareto front converges, the archive is output. The non-dominated solution set is passed to the collaborative decision-making module as a set of candidate solutions for multi-attribute evaluation.

[0039] As a further aspect of the present invention, step S4 includes the following steps:

[0040] First, a hierarchical collaborative architecture is established, dividing the multi-regional power grid into regional decision-making units and a global coordination center. Regional units are responsible for generating local optimization parameters, while the global coordination center coordinates the configuration and resource allocation of inter-regional transmission channels. In each iteration, the regional decision-making unit will generate the non-dominated solution set P of the current particle swarm. i (i = 1, 2, ..., N) area Uploaded to the global coordination center, and received optimization parameters from other regions as external constraints;

[0041] Based on this, the global coordination center updates the candidate solution set through cross-regional parameter interaction: adopting a consistency constraint update strategy, the transmission capacity demand C of region i is... tie,i Power transmission capacity P of adjacent region j export Matching is performed on j to construct the cross-regional power flow balance equation:

[0042]

[0043] Where K i L j Let μ be the set of power receiving channels for region i and the set of power transmitting channels for region j, respectively. When an inter-regional power flow conflict is detected, the load allocation coefficient μ between regions is adjusted. ij The weights w1, w2, and w3 of the objective function for each region are dynamically adjusted to ensure the feasibility of the global solution.

[0044] As a further aspect of this invention, for the Pareto front non-dominated solution set A output by the improved particle swarm optimization algorithm, fuzzy entropy theory is used to calculate the comprehensive satisfaction index of each scheme, and a fuzzy membership function μ is defined. m (f m ) represents the m-th objective function value f m The contribution to the optimal solution is expressed as:

[0045]

[0046] In the formula These are the minimum and maximum thresholds of the m-th objective function, respectively;

[0047] Based on this, the fuzzy entropy E of each solution s∈A is calculated. s : Where M=3 is the number of optimization objectives, f sm To find the function value of s under the m-th objective, a solution with a smaller fuzzy entropy indicates better balance among multiple objectives. Therefore, according to E... s Select the top N from smallest to largest opt Each solution is considered a high-priority candidate solution;

[0048] Subsequently, a dynamic feedback mechanism is introduced to achieve iterative convergence control, if continuous T converge If the Pareto front distribution deviation rate δ of the candidate solution set in the next iteration is less than the preset threshold ∈, then the algorithm is considered to have converged, and the final decision set is output; otherwise, the algorithm returns to the improved particle swarm optimization module for a new round of solving, where the calculation formula is: In the formula This represents the symmetric difference operation of sets, and ||·| is the set potential energy function.

[0049] As a further aspect of the present invention, step S5 includes the following steps:

[0050] First, Pareto front hierarchical analysis is performed on the non-dominated solution set A provided by the collaborative decision-making module. The solution set is then divided into multiple levels, denoted as F1, F2, ..., F, using a fast non-dominated sorting algorithm. L F1 is the optimal frontier layer. The convergence and uniformity of the solution set at each level are quantified by calculating the hypervolume index (HV) and spacing index (SP). The formula is as follows:

[0051]

[0052]

[0053] Where d s To find the Euclidean distance from solution s to its nearest neighbor solution, The average distance, The upper limit of the reference point for the objective function m is used to dynamically adjust the weights of the frontier level based on the HV and SP indices, prioritizing the retention of solution sets with high convergence and wide distribution range.

[0054] Based on this, a set of multiple candidate planning schemes S = {S1, S2, ..., S...} is generated. K}, where each scheme S k It includes the scale of transmission line expansion, the number of transformers, the cross-regional power flow matrix, and the corresponding economic, environmental, and reliability targets. The key parameters of the scheme are presented in the form of radar charts and parallel coordinate graphs through a visual interactive interface, allowing decision-makers to conduct multi-attribute comparative analysis.

[0055] A decision-maker preference feedback mechanism is constructed. The Analytic Hierarchy Process (AHP) is used to determine the weight coefficients w1, w2, and w3 for each objective. After the decision-maker inputs the preference weights via a slider, the system calculates the weighted comprehensive index in real time.

[0056]

[0057] Where f m,k For scheme S k The normalized value under the objective m The extreme value thresholds for each objective are used to calculate the overall score F. score,k Smaller solutions indicate better alignment with decision-making preferences. The system ranks candidate solutions based on their scores and outputs the top N. final Names are used as a set of recommended solutions;

[0058] Simultaneously, a historical planning scheme comparison module is introduced to calculate the new scheme and the historical best scheme S. hist Similarity metrics: In the formula X kX hist For scheme S k If Sim > τ, the decision variable vector of historical schemes is used to mark the scheme as a low-risk scheme and prioritize its display in the recommendation list. The threshold τ can be configured by the user.

[0059] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention, based on an improved multi-objective particle swarm optimization algorithm, provides a multi-regional collaborative power grid planning system and method. By constructing multi-dimensional objective functions of economy, environmental protection, and reliability, and introducing game theory methods to quantify the coupling constraints between objectives, it effectively solves the problem of difficult balanced optimization of multiple objectives in traditional power grid planning. The improved particle swarm optimization algorithm adopts a dynamic adaptive inertia weight strategy and differential mutation operation, balancing global exploration and local development capabilities during the iteration process, significantly improving the algorithm's convergence speed and stability. Simultaneously, a congestion degree archiving and maintenance mechanism ensures the uniform distribution of the Pareto front. The hierarchical collaborative decision-making mechanism, through cross-regional parameter interaction and fuzzy entropy satisfaction evaluation, achieves dynamic coordination of inter-regional power flow and resource allocation, avoiding the surge in computational complexity caused by large-scale variable associations. Finally, the interactive screening module, combining decision-maker preference weights with historical scheme comparison, not only enhances the interpretability and flexibility of the planning scheme but also ensures the feasibility of project implementation through scheme similarity analysis. The overall technical solution achieves balanced optimization of multi-dimensional performance indicators in multi-regional power grid collaborative planning, significantly improving planning efficiency and scheme quality. Attached Figure Description

[0060] Figure 1 This is a flowchart of the present invention; Detailed Implementation

[0061] like Figure 1 As shown, the method in this embodiment specifically includes:

[0062] Step 1) The data acquisition module acquires real-time data on power grid load demand, renewable energy output forecasts, and cross-regional transmission channel status parameters for each region. The raw data is then cleaned and standardized to provide an input basis for subsequent modeling.

[0063] Step 2) A mathematical model is built using the multi-objective optimization model construction module. The optimization objectives are economy, environmental protection and reliability. The coupling constraint relationship between multiple objectives is quantified by game theory to form a multi-dimensional objective function and constraint set.

[0064] Step 3) Improve the particle swarm algorithm execution module by adopting a dynamic adaptive inertia weight strategy, combining Latin hypercube sampling to initialize a uniformly distributed particle swarm, balancing global exploration and local exploitation capabilities through time-varying acceleration coefficients, and introducing differential mutation operations during the iteration process to enhance the algorithm's ability to escape local optima, while maintaining the non-dominated solution set of the external archive.

[0065] Step 4) The collaborative decision-making module is based on a hierarchical collaborative mechanism. It updates the candidate solution set through cross-regional parameter interaction and uses fuzzy entropy theory to calculate the comprehensive satisfaction index of each non-dominated solution, thereby realizing the collaborative optimization and iterative convergence of multi-regional planning schemes.

[0066] Step 5) The result output module generates multiple candidate schemes based on the Pareto front distribution characteristics output by the algorithm, sorts the schemes by combining the decision-maker's preference weights, and finally outputs the optimal solution for multi-regional collaborative power grid planning that takes into account economy, environmental protection and reliability.

[0067] In step 1), it is first necessary to collect load demand data of the power grid in each region. The data includes historical electricity load curves, typical daily load forecasts and seasonal fluctuation coefficients, which are periodically acquired and stored in the database.

[0068] Secondly, renewable energy output forecast data is obtained. The data is based on historical power generation records of wind farms and photovoltaic power plants, as well as wind speed and solar intensity forecast information provided by meteorological departments. The power output curve for future periods is generated through a preset forecast model.

[0069] Then, the status parameters of the cross-regional power transmission channel are collected, including line power flow distribution, node voltage amplitude, transmission capacity and safety margin under the N-1 fault scenario. The data integrity is updated in real time and verified through the online monitoring system.

[0070] Next, outlier detection and correction were performed on the original data. The sliding window statistical method was used to identify abnormal fluctuations, and the missing data was filled in by linear interpolation. The numerical range of data with different dimensions was unified by normalization.

[0071] Finally, a standardized dataset is constructed by matching load demand, renewable energy output, and transmission parameters with regional identifiers according to timestamps to form a structured data package, which serves as input data for the multi-objective optimization model construction module.

[0072] In step 2), a mathematical model for multi-regional power grid planning is established through a multi-objective optimization model construction module. Its core lies in the comprehensive optimization of three categories: economy, environmental protection and reliability, and the quantification of the coupling constraint relationship between objectives through game theory.

[0073] First, an economic function is constructed with the objective of minimizing the regional power grid construction investment cost and operation loss cost. The investment cost calculation formula is as follows: In the formula N area α represents the number of regions. i β i C represents the unit cost correction factor for the transmission line and transformer in region i, respectively. line,i Ctrans,i L represents the unit price of the corresponding equipment. i T i The line length and number of transformers are used as factors; network loss costs are determined by power flow calculations under typical load scenarios, using the following formula: Where γ t As scene weights, R j For the line resistance, I j ,t is the line current value under scenario t, and Δt is the duration of the scenario.

[0074] Based on this, an environmental friendliness function is constructed with the goal of minimizing carbon emission costs, and its expression is: In the formula η i ζ i For carbon emission factors of thermal power and gas-fired power, θ i P is the renewable energy substitution factor. coal i、P gas i、P RES Let ,i represent the power output of thermal power, gas-fired power, and renewable energy units within region i, respectively. Meanwhile, the reliability objective function uses the power supply reliability index R. reliab The quantification and calculation formula is as follows: U load Let i be the average annual load shedding in region i, and P be the load shedding amount. demand , i represents the total load demand of the region.

[0075] Furthermore, using game theory, the objectives of economic efficiency, environmental friendliness, and reliability are treated as three parties in a non-cooperative game, and a Nash equilibrium model is constructed to coordinate the competitive relationship among these objectives. This model includes constraints such as power balance, transmission capacity, and renewable energy penetration rate, and its mathematical form is: Among them G i Let K be the set of generating units within region i. i Let S be the set of inter-regional power transmission channels in region i. j λ represents the apparent power of the line, and λ represents the minimum requirement for the proportion of renewable energy in the entire network.

[0076] Finally, the weighted summation method is used to transform the multi-objective function into a comprehensive objective function: In the formula, w1, w2, and w3 are weighting coefficients, satisfying w1 + w2 + w3 = 1, C base C emis,base Using baseline costs and emissions values, the weight allocation is dynamically optimized through an interactive adjustment module to ensure a uniform distribution of the Pareto front.

[0077] By constructing multi-dimensional objective functions and constraints, the problem of the coupling of economic, environmental, and reliability objectives in multi-regional power grid planning is solved. The Nash equilibrium model based on game theory effectively coordinates the competitive relationship among multiple objectives, while the normalized weighted summation method provides a unified optimization framework for improving the particle swarm optimization algorithm, ensuring the balance of planning schemes among multi-dimensional performance indicators.

[0078] In step 3), the multi-objective optimization model is solved efficiently by improving the particle swarm optimization algorithm execution module. The core of this method lies in introducing a dynamic adaptive inertia weight strategy, differential mutation operation, and non-dominated solution set maintenance mechanism. The specific implementation process is as follows:

[0079] First, an initial particle swarm is generated using the Latin hypercube sampling method, and the initial solution set is uniformly distributed in the decision variable space through a hierarchical sampling strategy. Let the particle position vector X... p =(x p1 ,x p2 ,...,x pn Let V represent the planning scheme of the p-th particle in the n-dimensional decision space, and let V be the particle velocity vector. p =(v p1 ,v p2 ,...,v pn The search direction and step size are represented by ). After initialization, the objective function value F of each particle is evaluated through power flow calculation and constraint verification. p =(f p1 ,f p2 ,f p3 ), where f p1 f p2 f p3 These correspond to economic efficiency, environmental friendliness, and reliability indicators, respectively.

[0080] During the iteration process, a dynamic adaptive inertia weight strategy is adopted to balance global exploration and local development capabilities. The update formula for the inertia weight ω is: In the formula ω (k) ω represents the inertia weight at the k-th iteration. max ω min Its range of values, div(k) is the current population diversity index, defined as the standard deviation of particle positions, div max The threshold for maximum diversity is defined. When population diversity decreases to the set threshold, ω adaptively decreases to enhance local search accuracy, and vice versa to maintain global exploration capability. Simultaneously, a time-varying acceleration coefficient is designed to adjust the individual extreme value pbest. p The influence weights of the global extremum gbest. The update formulas for the speedup coefficients c1 and c2 are: Where K maxTo maximize the number of iterations, c1 decreases linearly from a high value as the number of iterations increases, gradually reducing the particles' dependence on individual experience. Meanwhile, c2 increases from a low value to enhance the group's collaborative ability, thereby achieving a dynamic balance between rapid exploration in the early stage and fine convergence in the later stage.

[0081] To avoid the algorithm getting trapped in local optima, a mutation operation from the differential evolution algorithm is introduced. When no significant improvement is detected in the Pareto front across consecutive iterations, Cauchy mutation is performed on the stagnant particle: x′ pd =x pd +σ·Cauchy(0,1), where σ is the variable asynchronous length factor and Cauchy(0,1) is a standard Cauchy distribution random number. After mutation, the particle needs to re-verify the feasibility constraints and update the objective function value.

[0082] For maintaining the non-dominated solution set, an external archive A is constructed to store all non-dominated solutions generated during the iteration process, and the diversity of the solution set is maintained through a crowding comparison operator. After each iteration, fast non-dominated sorting is used to stratify the solutions in the archive, calculate the crowding distance of each solution, and delete the solution with the smallest crowding until the archive capacity does not exceed a preset value N. arch .

[0083] Finally, when the maximum number of iterations is reached or the Pareto front converges, the archived non-dominated solution set is output as a candidate solution set and passed to the collaborative decision-making module for multi-attribute evaluation.

[0084] In step 4), the cross-regional coordination and iterative optimization of multi-regional power grid planning schemes are achieved through a collaborative decision-making module. The core of this approach lies in dynamically updating the candidate scheme set based on a hierarchical collaborative mechanism and quantifying the comprehensive satisfaction index of each non-dominated solution using fuzzy entropy theory. First, a hierarchical collaborative architecture is established, dividing the multi-regional power grid into regional decision-making units and a global coordination center. Regional units are responsible for generating local optimization parameters, while the global coordination center coordinates the configuration of cross-regional transmission channels and resource allocation. In each iteration, the regional decision-making unit updates the non-dominated solution set P of the current particle swarm. i (i = 1, 2, ..., N) area The data is uploaded to the global coordination center and receives optimization parameters from other regions as external constraints.

[0085] Based on this, the global coordination center updates the candidate solution set through cross-regional parameter interaction. Specifically, a consistency constraint update strategy is adopted to update the transmission capacity demand C of region i. tie,i Power transmission capacity P of adjacent region j export Matching is performed on j to construct the cross-regional power flow balance equation: Where K i L jThese represent the set of power receiving channels for region i and the set of power transmitting channels for region j, respectively. When an inter-regional power flow conflict is detected, the inter-regional load allocation coefficient μ is adjusted. ij The weights w1, w2, and w3 of the objective function for each region are dynamically adjusted to ensure the feasibility of the global solution.

[0086] Furthermore, for the Pareto front non-dominated solution set A output by the improved particle swarm optimization algorithm, fuzzy entropy theory is used to calculate the comprehensive satisfaction index of each scheme. The fuzzy membership function μ is defined. m (f m ) represents the m-th objective function value f m The contribution to the optimal solution is expressed as: In the formula These are the minimum and maximum thresholds for the m-th objective function, respectively.

[0087] Based on this, the fuzzy entropy E of each solution s∈A is calculated. s : Where M=3 is the number of optimization objectives, f sm Let be the function value of s under the m-th objective. A solution with a smaller fuzzy entropy indicates better balance among multiple objectives; therefore, according to E... s Select the top N from smallest to largest opt Each solution is selected as a high-priority candidate.

[0088] Subsequently, a dynamic feedback mechanism is introduced to achieve iterative convergence control. If T is continuous... converge If the Pareto front distribution deviation rate δ of the candidate solution set in the next iteration is less than the preset threshold ∈, then the algorithm is considered to have converged, and the final decision set is output; otherwise, the algorithm returns to the improved particle swarm optimization module for a new round of solving, where the calculation formula is: In the formula This represents the symmetric difference operation of sets, and ||·| is the set potential energy function.

[0089] This step, through a hierarchical collaborative mechanism and a fuzzy entropy evaluation system, achieves deep integration of cross-regional parameter interaction, dynamic optimization of candidate schemes, and multi-attribute decision support in multi-regional power grid planning. This method significantly reduces the computational complexity caused by large-scale variable correlations, improves collaborative decision-making efficiency while ensuring the feasibility of schemes, and provides a solution for multi-regional power grid planning that balances technical and economic efficiency with cross-regional coordination.

[0090] In step 5), the candidate solutions output by the collaborative decision-making module are comprehensively evaluated and optimized through the result output module. The core of this process is to generate multiple planning schemes based on the Pareto front distribution characteristics and to select the optimal solution by combining the decision-maker's preference weights. First, a Pareto front hierarchical analysis is performed on the non-dominated solution set A provided by the collaborative decision-making module. A fast non-dominated sorting algorithm is used to divide the solution set into multiple levels, denoted as F1, F2, ..., F... L F1 is the optimal frontier layer. The convergence and uniformity of the solution set at each level are quantified by calculating the hypervolume index (HV) and spacing index (SP), as shown in the following formula: Where d s To find the Euclidean distance from solution s to its nearest neighbor solution, The average distance, This represents the upper limit of the reference point for the objective function m. The weights of the frontier layers are dynamically adjusted based on the HV and SP indices, prioritizing the retention of solution sets with high convergence and wide distribution range.

[0091] Based on this, a set of multiple candidate planning schemes S = {S1, S2, ..., S...} is generated. K}, where each scheme S k It includes the scale of transmission line expansion, the number of transformers, the inter-regional power flow matrix, and the corresponding economic, environmental, and reliability targets. Key parameters of the plan are presented in radar charts and parallel coordinate graphs through a visual interactive interface, allowing decision-makers to conduct multi-attribute comparative analysis.

[0092] Furthermore, a decision-maker preference feedback mechanism is constructed, and the Analytic Hierarchy Process (AHP) is used to determine the weight coefficients w1, w2, and w3 for each objective. After the decision-maker inputs the preference weights via a slider, the system calculates the weighted composite index in real time.

[0093] Where f m,k For scheme S k The normalized value under the objective m The extreme value thresholds for each objective are used to calculate the overall score F. score,k Smaller solutions indicate a better fit for decision-making preferences. The system ranks candidate solutions based on their scores and outputs the top N. final Names are used as the recommended solution set.

[0094] Meanwhile, to ensure the engineering feasibility of the plan, a historical planning scheme comparison module is introduced. This involves calculating the new scheme and the historical best scheme S. hist Similarity metrics: In the formula X k X hist For scheme S kIf the decision variable vector of historical solutions is Sim>τ (the threshold τ is configurable), then the solution is marked as a low-risk solution and given priority in the recommendation list.

[0095] Ultimately, the system generates a complete planning report including technical parameters, economic analysis, environmental benefits, and reliability assessment. This step achieves efficient transformation from a vast pool of candidate solutions to an executable plan through a Pareto frontier hierarchical assessment and a decision-maker preference fusion mechanism. Similarity analysis based on historical data comparison enhances the feasibility of the solution, while interactive weight adjustment enhances the flexibility and transparency of decision-making. The final output planning scheme achieves a multi-dimensional balance and optimization among economic efficiency, environmental friendliness, and reliability.

[0096] As a preferred embodiment of the present invention, the present invention also provides a multi-regional collaborative power grid planning system based on an improved multi-objective particle swarm algorithm, including a data acquisition module, a multi-objective optimization model construction module, an improved particle swarm algorithm execution module, a collaborative decision-making module, and a result output module;

[0097] The data acquisition module is used to acquire real-time data on power grid load demand, renewable energy output forecasts, and cross-regional power transmission channel status parameters in various regions.

[0098] The multi-objective optimization model construction module takes economy, environmental protection and reliability as optimization objectives, establishes a multi-dimensional objective function including investment cost, network loss, carbon emissions and power supply reliability, and quantifies the constraint relationship between multiple objectives through game theory.

[0099] The improved particle swarm algorithm execution module adopts a dynamic adaptive inertia weight strategy, which adjusts the weight coefficients according to the particle swarm diversity index during the iteration process, and introduces the mutation operation of the differential evolution algorithm to enhance the local search capability.

[0100] The collaborative decision-making module realizes the interaction of optimization parameters between regions through a hierarchical collaborative mechanism. In each iteration, it selects the non-dominated solution set as a candidate scheme and calculates the comprehensive satisfaction index of each scheme based on fuzzy entropy theory.

[0101] The output module generates multiple planning schemes based on the Pareto front distribution characteristics and selects the optimal solution based on the decision-maker's preferences.

[0102] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A multi-regional cooperative power grid planning system based on an improved multi-objective particle swarm optimization algorithm, characterized in that: It includes a data acquisition module, a multi-objective optimization model construction module, an improved particle swarm optimization algorithm execution module, a collaborative decision-making module, and a result output module; The data acquisition module is used to acquire real-time data on power grid load demand, renewable energy output forecasts, and cross-regional power transmission channel status parameters in various regions. The multi-objective optimization model construction module takes economy, environmental protection and reliability as optimization objectives, establishes a multi-dimensional objective function including investment cost, network loss, carbon emissions and power supply reliability, and quantifies the constraint relationship between multiple objectives through game theory. The improved particle swarm algorithm execution module adopts a dynamic adaptive inertia weight strategy, which adjusts the weight coefficients according to the particle swarm diversity index during the iteration process, and introduces the mutation operation of the differential evolution algorithm to enhance the local search capability. The collaborative decision-making module realizes the interaction of optimization parameters between regions through a hierarchical collaborative mechanism. In each iteration, it selects the non-dominated solution set as a candidate scheme and calculates the comprehensive satisfaction index of each scheme based on fuzzy entropy theory. The output module generates multiple planning schemes based on the Pareto front distribution characteristics and selects the optimal solution based on the decision-maker's preferences.

2. A multi-regional cooperative power grid planning method based on an improved multi-objective particle swarm optimization algorithm, characterized in that: The steps include: S1. Real-time acquisition of power grid load demand, renewable energy output forecast data, and cross-regional power transmission channel status parameters in various regions; S2. With economy, environmental protection and reliability as optimization objectives, a multi-dimensional objective function is established that includes investment cost, network loss, carbon emissions and power supply reliability. The constraint relationship between the multiple objectives is quantified by game theory. S3. A dynamic adaptive inertia weight strategy is adopted, which adjusts the weight coefficients according to the particle swarm diversity index during the iteration process, and introduces the mutation operation of the differential evolution algorithm to enhance the local search capability. S4. The interaction of optimization parameters between regions is realized through a hierarchical collaboration mechanism. In each iteration, the non-dominated solution set is selected as the candidate scheme, and the comprehensive satisfaction index of each scheme is calculated based on the fuzzy entropy theory. S5. Generate multiple planning schemes based on the characteristics of the Pareto frontier distribution, and select the optimal solution by combining the decision-maker's preferences.

3. The multi-regional cooperative power grid planning method based on the improved multi-objective particle swarm optimization algorithm according to claim 2, characterized in that, Step S1 includes the following steps: First, load demand data of the power grid in each region is collected. The data includes historical electricity load curves, typical daily load forecasts, and seasonal fluctuation coefficients. The data is periodically acquired and stored in the database. Secondly, renewable energy output forecast data is obtained. The data is based on historical power generation records of wind farms and photovoltaic power plants, as well as wind speed and solar intensity forecast information provided by meteorological departments. The power output curve for future periods is generated through a preset forecast model. Then, the status parameters of the cross-regional power transmission channel are collected, including line power flow distribution, node voltage amplitude, transmission capacity and safety margin under the N-1 fault scenario. The data integrity is updated in real time and verified through the online monitoring system. Next, outlier detection and correction were performed on the original data. The sliding window statistical method was used to identify abnormal fluctuations, and the missing data was filled in by linear interpolation. The numerical range of data with different dimensions was unified by normalization. Finally, a standardized dataset is constructed by matching load demand, renewable energy output, and transmission parameters with regional identifiers according to timestamps to form a structured data package, which serves as input data for the multi-objective optimization model construction module.

4. The multi-regional cooperative power grid planning method based on the improved multi-objective particle swarm optimization algorithm according to claim 3, characterized in that, The method for establishing a multi-dimensional objective function that includes investment cost, network loss, carbon emissions, and power supply reliability in step S2, with economic efficiency, environmental protection, and reliability as optimization objectives, includes the following steps: First, an economic function is constructed with the objective of minimizing the regional power grid construction investment cost and operation loss cost. The investment cost calculation formula is as follows: In the formula N area α represents the number of regions. i β i C represents the unit cost correction factor for the transmission line and transformer in region i, respectively. line,i C trans,i L represents the unit price of the corresponding equipment. i T i The line length and number of transformers are used as factors; network loss costs are determined by power flow calculations under typical load scenarios, using the following formula: Where γ t As scene weights, R j For the line resistance, I j ,t is the line current value under scenario t, and Δt is the duration of the scenario; Based on this, an environmental friendliness function is constructed with the goal of minimizing carbon emission costs, and its expression is: In the formula η i ζ i For carbon emission factors of thermal power and gas-fired power, θ i P is the renewable energy substitution factor. coal i、P gas i、P RES ,i represent the output of thermal power, gas power, and renewable energy units in region i, respectively. Meanwhile, the reliability objective function uses the power supply reliability index R. reliab The quantification and calculation formula is as follows: U load Let i be the average annual load shedding in region i, and P be the load shedding amount. demand , i represents the total load demand of the region.

5. The multi-regional cooperative power grid planning method based on the improved multi-objective particle swarm optimization algorithm according to claim 4, characterized in that, The steps in step S2 that quantify the constraint relationships among multiple objectives using game theory are as follows: Using game theory, economic efficiency, environmental friendliness, and reliability are treated as three parties in a non-cooperative game. A Nash equilibrium model is constructed to coordinate the competitive relationship between these objectives. The model includes constraints such as power balance, transmission capacity, and renewable energy penetration. Its mathematical form is as follows: Among them G i Let K be the set of generating units within region i. i Let S be the set of inter-regional power transmission channels in region i. j λ represents the apparent power of the line, and λ is the minimum requirement for the proportion of renewable energy in the entire network. Finally, the weighted summation method is used to transform the multi-objective function into a comprehensive objective function: In the formula, w1, w2, and w3 are weighting coefficients, satisfying w1 + w2 + w3 = 1, C base C emis,base Using baseline costs and emissions values, the weight allocation is dynamically optimized through an interactive adjustment module to ensure a uniform distribution of the Pareto front.

6. The multi-regional cooperative power grid planning system and method based on the improved multi-objective particle swarm optimization algorithm according to claim 5, characterized in that, Step S3 includes the following steps: First, an initial particle swarm is generated using the Latin hypercube sampling method. Then, an initial solution set is uniformly distributed within the decision variable space using a stratified sampling strategy. Let the particle position vector X... p =(x p1 ,x p2 ,...,x pn Let V represent the planning scheme of the p-th particle in the n-dimensional decision space, and let V be the particle velocity vector. p =(v p1 ,v p2 ,...,v pn The search direction and step size are represented by ). After initialization, the objective function value F of each particle is evaluated through power flow calculation and constraint verification. p =(f p1 ,f p2 ,f p3 ), where f p1 f p2 f p3 These correspond to economic efficiency, environmental friendliness, and reliability indicators, respectively. During the iteration process, a dynamic adaptive inertia weight strategy is adopted to balance global exploration and local development capabilities. The update formula for the inertia weight ω is: In the formula ω (k) ω represents the inertia weight at the k-th iteration. max ω min Its range of values, div(k) is the current population diversity index, defined as the standard deviation of particle positions, div max As the maximum diversity threshold, when population diversity decreases to the set threshold, ω adaptively decreases to enhance local search accuracy, and vice versa to maintain global exploration capability; simultaneously, a time-varying acceleration coefficient is designed to adjust the individual extreme value pbest. p The update formulas for the influence weights of the global extremum gbest and the acceleration coefficients c1 and c2 are as follows: Where K max To maximize the number of iterations, c1 decreases linearly from a high value as the number of iterations increases, gradually reducing the particles' dependence on individual experience, while c2 increases from a low value to enhance the group's collaborative ability, thereby achieving a dynamic balance between rapid exploration in the early stage and fine convergence in the later stage. When no significant improvement in the Pareto front is detected in successive iterations, Cauchy mutation is performed on the stagnant particles: x′ pd =x pd +σ·Cauchy(0,1); In the formula, σ is the variable asynchronous length factor, Cauchy(0,1) is a standard Cauchy distribution random number, and the particle after mutation needs to re-verify the feasibility constraints and update the objective function value; In terms of maintaining the non-dominated solution set, an external archive A is constructed to store all non-dominated solutions generated during the iteration process. The diversity of the solution set is maintained by using a crowding comparison operator. After each iteration, fast non-dominated sorting is used to stratify the solutions in the archive, calculate the crowding distance of each solution, and delete the solution with the smallest crowding until the archive capacity does not exceed the preset value N. arch ; Finally, when the maximum number of iterations is reached or the Pareto front converges, the archived non-dominated solution set is output as a candidate solution set and passed to the collaborative decision-making module for multi-attribute evaluation.

7. The multi-regional cooperative power grid planning system and method based on the improved multi-objective particle swarm optimization algorithm according to claim 6, characterized in that, Step S4 includes the following steps: First, a hierarchical collaborative architecture is established, dividing the multi-regional power grid into regional decision-making units and a global coordination center. Regional units are responsible for generating local optimization parameters, while the global coordination center coordinates the configuration and resource allocation of inter-regional transmission channels. In each iteration, the regional decision-making unit will generate the non-dominated solution set P of the current particle swarm. i (i = 1, 2, ..., N) area Uploaded to the global coordination center, and received optimization parameters from other regions as external constraints; Based on this, the global coordination center updates the candidate solution set through cross-regional parameter interaction: adopting a consistency constraint update strategy, the transmission capacity demand C of region i is... tie,i Power transmission capacity P of adjacent region j export Matching is performed on j to construct the cross-regional power flow balance equation: Where K i , L j Let μ be the set of power receiving channels for region i and the set of power transmitting channels for region j, respectively. When an inter-regional power flow conflict is detected, the load allocation coefficient μ between regions is adjusted. ij The weights w1, w2, and w3 of the objective function for each region are dynamically adjusted to ensure the feasibility of the global solution.

8. The multi-regional cooperative power grid planning system and method based on the improved multi-objective particle swarm optimization algorithm according to claim 7, characterized in that, For the Pareto front non-dominated solution set A output by the improved particle swarm optimization algorithm, fuzzy entropy theory is used to calculate the comprehensive satisfaction index of each scheme, and the fuzzy membership function μ is defined. m (f m ) represents the m-th objective function value f m The contribution to the optimal solution is expressed as: In the formula These are the minimum and maximum thresholds of the m-th objective function, respectively; Based on this, the fuzzy entropy E for each solution s∈A is calculated. s : Where M=3 is the number of optimization objectives, f sm To find the function value of s under the m-th objective, a solution with a smaller fuzzy entropy indicates better balance among multiple objectives. Therefore, according to E... s Select the top N from smallest to largest opt Each solution is considered a high-priority candidate solution; Subsequently, a dynamic feedback mechanism is introduced to achieve iterative convergence control, if continuous T converge If the Pareto front distribution deviation rate δ of the candidate solution set is less than the preset threshold ∈ in the next iteration, then the algorithm is considered to have converged and the final decision set is output. Otherwise, return to the improved particle swarm optimization algorithm execution module for a new round of solving, where the calculation formula is: In the formula This represents the symmetric difference operation of sets, and ||·| is the set potential energy function.

9. The multi-regional cooperative power grid planning system and method based on the improved multi-objective particle swarm optimization algorithm according to claim 8, characterized in that, Step S5 includes the following steps: First, Pareto front hierarchical analysis is performed on the non-dominated solution set A provided by the collaborative decision-making module. The solution set is then divided into multiple levels, denoted as F1, F2, ..., F, using a fast non-dominated sorting algorithm. L F1 is the optimal frontier layer. The convergence and uniformity of the solution set at each level are quantified by calculating the hypervolume index (HV) and spacing index (SP). The formula is as follows: where d s To find the Euclidean distance from solution s to its nearest neighbor solution, The average distance, The upper limit of the reference point for the objective function m is used to dynamically adjust the weights of the frontier level based on the HV and SP indices, prioritizing the retention of solution sets with high convergence and wide distribution range. Based on this, a set of multiple candidate planning schemes S = {S1, S2, ..., S...} is generated. K }, where each scheme S k It includes the scale of transmission line expansion, the number of transformers, the cross-regional power flow matrix, and the corresponding economic, environmental, and reliability targets. The key parameters of the scheme are presented in the form of radar charts and parallel coordinate graphs through a visual interactive interface, allowing decision-makers to conduct multi-attribute comparative analysis. A decision-maker preference feedback mechanism is constructed. The Analytic Hierarchy Process (AHP) is used to determine the weight coefficients w1, w2, and w3 for each objective. After the decision-maker inputs the preference weights via a slider, the system calculates the weighted comprehensive index in real time. Where f m,k For scheme S k The normalized value under the objective m The extreme value thresholds for each objective are used to calculate the overall score F. score,k Smaller solutions indicate better alignment with decision-making preferences. The system ranks candidate solutions based on their scores and outputs the top N. final Names are used as a set of recommended solutions; Simultaneously, a historical planning scheme comparison module is introduced to calculate the new scheme and the historical best scheme S. hist Similarity metrics: In the formula X k 、X hist For scheme S k If Sim > τ, where τ is a threshold, the decision variable vector of historical solutions is compared with that of historical solutions. If the vector is low-risk, the solution is marked as low-risk and will be given priority in the recommendation list.

10. The multi-regional cooperative power grid planning system and method based on the improved multi-objective particle swarm optimization algorithm according to claim 9, characterized in that, The threshold τ can be configured automatically.

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