Power distribution network resource configuration and planning method based on variable step size NSGA-II and entropy weight evaluation

Abstract

The application discloses a power distribution network resource configuration and planning method based on a variable step size NSGA-II and an entropy weight evaluation, and comprises the following steps: S1, acquiring power distribution network static model data and all-quantity user voltage data, constructing a typical operation scenario set and determining the occurrence probability of each scenario; S2, performing power flow calculation to obtain network nodes and all-quantity user voltages; S3, calculating voltage-reactive power sensitivity to form a candidate installation location set and capacity / gear upper limit; S4, establishing a multi-objective planning model and setting constraint conditions; S5, using a variable step size mutation operator NSGA-II algorithm to solve the model to obtain a scheme set; and S6, using an entropy weight method for comprehensive evaluation and sorting; the method can accurately identify the key nodes and resource types that have the greatest influence on voltage overrun, uses a multi-objective planning model and a variable step size algorithm to solve and give consideration to voltage quality improvement and investment economy, and finally eliminates subjective bias through the entropy weight method, so that scientific and traceable decision-making basis is provided for power distribution network reconstruction.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning and voltage management technology, and in particular to a distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation. Background Technology

[0002] With the continuous increase in the scale of distributed generation in medium-voltage distribution networks, the operating status of distribution networks exhibits significant time-varying and uncertainties. Especially under typical operating conditions such as heavy loads, low output from distributed generation, or limited reactive power support on the user side, insufficient multi-level reactive power resource supply capacity or limited availability margin can easily lead to reactive power deficits in the system, resulting in increased line voltage drops and decreased voltage support capacity, causing the voltage at the user access point to exceed the lower limit. This type of undervoltage exhibits obvious spatial distribution and hierarchical transmission characteristics, often spreading step-by-step from substation outgoing lines, key feeder sections, distribution transformer areas, down to the user access point, and concentrating at the end and user side. Due to the large number and wide distribution of user access points, using only a few busbar or end-node voltages to represent the overall network voltage level can easily lead to situations where some nodes meet the standard but users still experience undervoltage. Furthermore, under typical operating conditions such as light loads, high output from distributed generation, or insufficient reactive power absorption capacity, reverse power flow and voltage rise can easily cause the voltage at the user access point to exceed the upper limit, making it difficult to meet the governance requirements for voltage compliance for all users. Existing upgrade configuration and planning methods still have the following shortcomings:

[0003] (1) Insufficient scenario coverage: Many methods are designed for configuration under single or few working conditions, without fully considering the differences in the over-limit of multiple scenarios caused by changes in load and distributed power output, which makes the improvement effect of the planning scheme unstable in other typical scenarios.

[0004] (2) Insufficient evaluation objects: Some methods use node voltage or a small number of measurement point voltages as evaluation indicators, without including the voltage over-limit of all users in a unified objective function, making it difficult to ensure that the risk of voltage over-limit of all users is systematically improved at the planning level.

[0005] (3) Insufficient multi-level resource coordination: There are differences in the scope of action, adjustment granularity and constraint form between the station end, feeder layer, distribution transformer area layer and user side. If there is a lack of unified quantitative basis for hierarchical aggregation and coordinated configuration, problems such as blind selection of candidate locations, redundant resource allocation or insufficient local governance may occur.

[0006] (4) Excessive candidate space and low solution efficiency: When facing large-scale users and multiple candidate installation points, the planning variables exhibit a mixture of discrete (installation 0-1, gear) and continuous (capacity) characteristics. If effective screening is not carried out, the optimization problem has high dimensionality and low solution efficiency, making it difficult to quickly form a set of usable transformation schemes in engineering planning.

[0007] (5) Lack of objective evaluation in scheme selection: Multi-objective programming usually outputs a set of Pareto schemes. In current practice, the selection often relies on experience or subjective weights, resulting in insufficient interpretability and consistency of the selection results, which is not conducive to the formation of reusable recommended schemes and strategy libraries. Summary of the Invention

[0008] To overcome the above problems, the purpose of this invention is to provide a distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation. This planning method establishes a multi-objective optimization model, aggregates and sorts voltage-reactive power sensitivity at the online, variable, and user levels to screen and determine candidate installation locations and capacity / taper upper limits, and uses the NSGA-II algorithm with embedded variable step size mutation operators to solve the multi-objective planning model to obtain a Pareto upgrade configuration scheme set. Finally, an evaluation index system is constructed and the entropy weight method is used to comprehensively evaluate and rank the Pareto schemes, output recommended schemes and form a strategy library, and finally obtain a governance demand scheme for voltage compliance for all users.

[0009] The technical solution adopted in this invention is:

[0010] The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation includes the following steps:

[0011] S1: Obtain static model data of the distribution network and voltage data of all users, construct a set of typical operating scenarios and determine the probability of occurrence of each scenario.

[0012] S2: Perform power flow calculations for each typical operating scenario to obtain the voltage of network nodes and the voltage of all users.

[0013] S3: Calculate voltage-reactive power sensitivity based on power flow calculation results (by linearizing the power flow equation at the current operating point and inverting the Jacobian matrix, the sensitivity matrix of each node voltage to node reactive power injection is obtained (i.e., voltage-reactive power sensitivity), and then convert it into the sensitivity of the total user voltage to the resource capacity / level of each candidate installation location), and aggregate and sort it at the station, line, transformer, and user levels to form a set of candidate installation locations and capacity / level upper limits.

[0014] S4: Establish a multi-objective programming model with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total life cycle cost, and set constraints.

[0015] S5: The NSGA-II algorithm with embedded variable step size mutation operator is used to solve the multi-objective programming model to obtain the Pareto modification configuration scheme set.

[0016] S6: Construct an evaluation index system and use the entropy weight method to comprehensively evaluate and rank the Pareto modification configuration schemes, output recommended schemes and form a strategy library.

[0017] As a further description of the present invention, the static model data in S1 includes station-line-transformer-household topology mapping, line and transformer parameters, and load and distributed power source statistics.

[0018] As a further description of the present invention, the typical operating scenario set in S1 is obtained by clustering or segmenting the historical load curves, distributed power output curves and voltage over-limit records, and a probability is assigned to each scenario, and the sum of the probabilities is 1.

[0019] As a further description of the present invention, the sensitivity in S3 is obtained by inverting the Jacobian matrix obtained by linearizing the power flow equation to obtain the voltage sensitivity matrix to reactive power, and the sensitivity is converted into the user voltage sensitivity to resource capacity / level for candidate screening.

[0020] As a further description of the present invention, in S4, the voltage over-limit of all users is represented by bidirectional over-limit relaxation variables, and the over-limit expected target is constituted by the sum of relaxation variables weighted by scenario probability, thereby maintaining the feasibility of the model under the conditions of all users and multiple scenarios, and the over-limit expected target Defined as:

[0021] .

[0022] in, To exceed the expected target; For scene probabilities; For user u in scenario s, the voltage is lower than the limit, i.e., the undervoltage limit is lower; For user u in scenario s, the voltage exceeds the upper limit, i.e., the overvoltage exceeds the limit; For any scenario and ; For any user and .

[0023] The total life cycle cost in S4 consists of fixed resource installation costs and unit capacity / tier costs, and the total life cycle cost is expressed as follows:

[0024] .

[0025] in, Cost over the entire life cycle; Indicates the candidate position Is the installation type set to... Resources; This refers to a resource capacity / tier variable. To fix installation costs, Cost per unit capacity / tier The coefficient for operation and maintenance costs per unit time, where T is the planning period; This is the life-value adjustment factor. For equipment lifespan.

[0026] As a further description of the present invention, a multi-objective programming model is established in S4 with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total life cycle cost. The specific expression is as follows:

[0027] .

[0028] in, The expected target for voltage over-limit for all users. To achieve the investment and renovation cost target, For a multi-objective programming model (F is the result of...) The multi-objective programming model, which together constitutes the distribution network resource allocation planning problem, simultaneously aims to minimize the expected voltage exceedance of all users and the total lifecycle cost.

[0029] As a further description of the present invention, the decision variables of the multi-objective programming model in S4 include the installation 0-1 variables and capacity / gear variables of each resource type at the candidate location, and the capacity / gear variables satisfy the upper and lower bound constraints; the same candidate location satisfies resource mutual exclusion or combined installation constraints.

[0030] As a further description of the present invention, the constraints of the multi-objective programming model in S4 include power flow balance constraints, equipment capacity / gear constraints, and installation constraints.

[0031] The power flow balance constraint applies in any scenario The following is represented as:

[0032] .

[0033] .

[0034] in, For nodes Voltage amplitude; For nodes Voltage amplitude; The phase angle difference between nodes; Let the real and imaginary parts of the nodal admittance matrix be given. Inject power into the node.

[0035] The equipment capacity / level constraint is expressed as follows:

[0036] .

[0037] in, Set the location index for the candidate device. Index for resource types; To install decision variables, Indicates the candidate position Installation type is Resources Indicates that it will not be installed; For the corresponding resource capacity / level decision variables, when the resource is a continuously adjustable device... This indicates its configured capacity or upper limit for reactive power regulation, when the resource is a discrete-level device. Indicates its gear position; and They are resource types In position Minimum and maximum capacity / tier boundaries that can be configured.

[0038] The installation mutual exclusion / combination constraints satisfy:

[0039] The same candidate position pairs mutually exclusive resource type sets have:

[0040] .

[0041] Among them, the set of mutually exclusive resource types Given a set of mutually exclusive sets Mutual exclusion constraints only apply to resource types included in the mutual exclusion set; resource types not included in the mutual exclusion set are allowed to be combined and installed at the same candidate location.

[0042] As a further description of the present invention, the mutation operator of the NSGA-II algorithm with the variable step size mutation operator in S5 is set to a variable step size that decreases with the number of iterations, and the variable step size mutation operator is embedded in the mutation link of the NSGA-II algorithm and executed in an integrated manner with the overall NSGA-II process.

[0043] As a further description of the present invention, the evaluation indicators in S6 include the expectation exceeding the limit indicator and the investment cost indicator. After determining the indicator weights by the entropy weight method, the Pareto modification configuration schemes are comprehensively scored and ranked. Finally, the modification configuration scheme with the highest score is output as the recommended scheme.

[0044] The beneficial effects of this invention are:

[0045] This invention presents a distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation. By constructing a set of typical operating scenarios and combining voltage-reactive power sensitivity at multiple levels ("station-line-transformer-customer"), this invention can accurately identify the key nodes and resource types that have the greatest impact on voltage exceedances. Compared to traditional methods that rely on manual experience or single-section analysis, this strategy effectively avoids blind investment and ensures that limited upgrade resources are prioritized for allocation to locations with the most significant governance benefits.

[0046] This invention presents a distribution network resource allocation and planning method based on variable-step NSGA-II and entropy weight evaluation. It establishes a multi-objective programming model with the goals of minimizing the expected voltage exceedance for all users and minimizing the total lifecycle cost. This model comprehensively covers the entire lifecycle cost of reactive power compensation equipment, including fixed installation, capacity configuration, operation and maintenance, and lifecycle calculation. The Pareto retrofit configuration scheme set obtained through the NSGA-II algorithm clearly demonstrates the trade-off between voltage improvement and investment costs, providing decision-makers with diversified non-dominated scheme options and avoiding the problems of neglecting one aspect for another caused by single-objective optimization.

[0047] This invention presents a distribution network resource allocation and planning method based on variable-step-size NSGA-II and entropy-weighted evaluation. The embedded variable-step-size mutation operator enables the NSGA-II algorithm to have a large variable step size in the early stages of iteration, effectively enhancing its global exploration capability and preventing it from getting trapped in local optima prematurely. In the later stages of iteration, the step size gradually decreases, facilitating refined local searches near the Pareto front and improving the convergence accuracy and stability of the final solution set. This mechanism effectively balances the algorithm's exploration and development capabilities, making it suitable for complex, high-dimensional, nonlinear optimization problems such as distribution network planning.

[0048] This invention presents a distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation. After obtaining the Pareto solution set, it introduces the entropy weight method to construct an evaluation index system. The weights of each index (such as expected exceedance and investment cost) are objectively determined based on their data dispersion, avoiding biases caused by subjective weighting. By calculating and ranking the comprehensive scores of each solution, the optimal recommended solution can be selected from multiple non-dominated solutions, forming a strategy library that provides planners with clear and traceable decision-making basis.

[0049] This invention presents a distribution network resource allocation and planning method based on variable-step NSGA-II and entropy weight evaluation. This method includes all users in the voltage exceedance assessment scope and uses a scenario probability weighting approach to uniformly model multiple typical operating scenarios, ensuring that the planning scheme can effectively suppress voltage exceedance problems under different operating conditions such as heavy load and high photovoltaic output. This multi-scenario, full-user coverage modeling approach significantly improves the adaptability of distribution network transformation schemes to load and distributed power source fluctuations in actual operation. Simultaneously, the candidate location screening mechanism in this method fully considers the multi-level structure of "station, line, transformer, and user" in actual engineering projects. The capacity / taper upper limit setting is aligned with existing equipment selection specifications, and mutual exclusion / combination constraints can avoid redundant functional construction. The overall process is clear, highly modular, and easily integrated into existing distribution network planning software platforms, possessing strong engineering application and promotion value. Attached Figure Description

[0050] Figure 1 This is a flowchart of the distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation proposed in this invention. Detailed Implementation

[0051] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0052] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0053] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0054] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0055] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0056] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0057] like Figure 1 As shown, it illustrates a specific embodiment of the present invention:

[0058] Example 1:

[0059] The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation includes the following steps:

[0060] S1: Obtain static model data of the distribution network and voltage data of all users, construct a set of typical operating scenarios and determine the probability of occurrence of each scenario.

[0061] S2: Perform power flow calculations for each typical operating scenario to obtain the voltage of network nodes and the voltage of all users.

[0062] S3: Calculate voltage-reactive power sensitivity based on power flow calculation results (by linearizing the power flow equation at the current operating point and inverting the Jacobian matrix, the sensitivity matrix of each node voltage to node reactive power injection is obtained (i.e., voltage-reactive power sensitivity), and then convert it into the sensitivity of the total user voltage to the resource capacity / level of each candidate installation location), and aggregate and sort it at the station, line, transformer, and user levels to form a set of candidate installation locations and capacity / level upper limits.

[0063] S4: Establish a multi-objective programming model with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total life cycle cost, and set constraints.

[0064] S5: The NSGA-II algorithm with embedded variable step size mutation operator is used to solve the multi-objective programming model to obtain the Pareto modification configuration scheme set.

[0065] S6: Construct an evaluation index system and use the entropy weight method to comprehensively evaluate and rank the Pareto modification configuration schemes, output recommended schemes and form a strategy library.

[0066] In this embodiment, as Figure 1 As shown, this distribution network resource allocation and planning method establishes a multi-objective optimization model. Based on the aggregation and ranking of voltage-reactive power sensitivity at the online, transformer, and user levels, it achieves the screening and determination of candidate installation locations and capacity / taper upper limits. The NSGA-II algorithm with embedded variable step size mutation operators is used to solve the multi-objective programming model to obtain a Pareto upgrade configuration scheme set. Finally, an evaluation index system is constructed, and the entropy weight method is used to comprehensively evaluate and rank the Pareto schemes, output recommended schemes, and form a strategy library. Ultimately, a governance requirement scheme for voltage compliance for all users is obtained.

[0067] Example 2:

[0068] Specifically, the static model data in S1 includes station-line-transformer-household topology mapping, line and transformer parameters, and load and distributed power generation statistics.

[0069] Specifically, the typical operating scenario set in S1 is obtained by clustering or segmenting the historical load curves, distributed power output curves and voltage over-limit records, and a probability is assigned to each scenario, and the sum of the probabilities is 1.

[0070] In this embodiment, the typical operating scenarios mainly include four scenarios: substations, medium-voltage lines, distribution transformers, and voltage exceeding limits at the user end due to insufficient reactive power compensation. A probability of occurrence is assigned to each scenario. ,in .

[0071] in, The probability of occurrence in each scenario, Number the scene.

[0072] Specifically, the sensitivity in S3 is obtained by inverting the Jacobian matrix obtained by linearizing the power flow equation to obtain the voltage sensitivity matrix to reactive power, and this sensitivity is converted into the user voltage sensitivity to resource capacity / level for candidate screening.

[0073] In this embodiment, the specific process of S3 is as follows:

[0074] In the scene Linearizing the power flow equations at the operating point, we have:

[0075] .

[0076] in, This is the active power deviation vector at the nodes. This represents the reactive power deviation vector at the nodes. This is the submatrix of partial derivatives of active power with respect to node phase angle. This is a submatrix of partial derivatives of active power with respect to node voltage magnitude. This is the submatrix of the partial derivatives of reactive power with respect to the node phase angle. This is the partial derivative submatrix of reactive power with respect to node voltage magnitude. This is the node voltage phase angle deviation vector. This is the node voltage amplitude deviation vector.

[0077] make The sensitivity matrix of node voltage to node reactive power injection can be obtained:

[0078] .

[0079] Furthermore, regarding candidate positions Resource control quantity (Capacity or level), construct user sensitivity:

[0080] .

[0081] in, Let be the sensitivity coefficient of the voltage amplitude of user u in scenario s to the control quantity (capacity or level) of resource r at candidate location i. The node voltage amplitude for user u in scenario s. Candidate positions Resource The control quantity.

[0082] In this embodiment, the candidate screening in S3 involves aggregating and sorting sensitivity at the station, line, transformer, and user levels, and using a consistent out-of-limit contribution score; specifically, for any candidate location... With resources Constructing a limit-crossing sensitivity coupling score:

[0083] .

[0084] .

[0085] in, This is the over-limit slack under the baseline operating condition (unmodified or existing configuration), used to characterize the severity of over-limit.

[0086] This is used to ensure that only resources and locations that can improve voltage over-limit situations are selected;

[0087] This represents the over-limit relaxation amount of user u in scenario s under the baseline operating condition (unmodified configuration), reflecting the severity of the current undervoltage over-limit.

[0088] This represents the over-limit relaxation amount of user u in scenario s under the baseline operating condition (unmodified configuration), reflecting the severity of the current overvoltage over-limit.

[0089] The limit-sensitivity coupling score for resource type r at candidate location i comprehensively reflects the contribution of the candidate configuration to the improvement of voltage limit for all users.

[0090] To each level Sort in descending order and select the top-ranked items. Each candidate position is used as a level. Download resources Candidate installation point set ,in It is an integer that is preset or determined according to the scale of the project.

[0091] Will The results are summed and sorted according to the station, line, transformer, and user levels to obtain the candidate set for each level and its capacity / level limit.

[0092] Specifically, in S4, the voltage over-limit of all users is represented by a two-way over-limit slack variable, and the sum of the slack variables weighted by the scenario probability constitutes the expected over-limit target, thereby maintaining the feasibility of the model under the conditions of all users and multiple scenarios.

[0093] Specifically, for any scenario With any user Define an over-limit slack variable:

[0094] ;

[0095] ;

[0096] ;

[0097] in, For users In the scene Voltage amplitude under, This is the lower limit of voltage. This is the upper limit of voltage; This refers to the voltage relaxation amount for user u in scenario s, where the actual voltage is below the lower limit. The deviation value is taken as a non-negative value. This refers to the voltage relaxation amount for user u in scenario s when the voltage exceeds the upper limit, i.e., the actual voltage is higher than the upper limit. The deviation value is taken as a non-negative value.

[0098] The definition of an out-of-limit expected target is:

[0099] .

[0100] in, Let be the probability of scenario s occurring, such that the sum of the probabilities of all scenarios is 1. This is an expected goal that exceeds the limit.

[0101] Specifically, the total life cycle cost in S4 consists of fixed resource installation costs and unit capacity / tier costs.

[0102] In this embodiment, the total life cycle cost can also be referred to as the investment and modification cost, and is expressed as:

[0103] .

[0104] in, Cost over the entire life cycle; Indicates the candidate position Is the installation type set to... Resources; This refers to a resource capacity / tier variable. To fix installation costs, Cost per unit capacity / tier The coefficient for operation and maintenance costs per unit time, where T is the planning period; This is the life-value adjustment factor. For equipment lifespan.

[0105] In this embodiment, the multi-objective programming model established in S4 with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total lifecycle cost is specifically expressed as follows:

[0106] .

[0107] in, The expected target for voltage over-limit for all users. To achieve the investment and renovation cost target, For a multi-objective programming model (F is the result of...) The multi-objective programming model, which together constitutes the distribution network resource allocation planning problem, simultaneously aims to minimize the expected voltage exceedance of all users and the total lifecycle cost.

[0108] Specifically, the decision variables in S4 include the 0-1 variables of each resource type at the candidate location and the capacity / level variables, and the capacity / level variables satisfy the upper and lower bound constraints; the same candidate location satisfies the resource mutual exclusion or combined installation constraints.

[0109] The constraints described in S4 include power flow balance constraints, equipment capacity / gear constraints, installation mutual exclusion / combination constraints, and voltage constraints.

[0110] In this embodiment, the power flow balance constraint applies to any scenario. The following is represented as:

[0111] ;

[0112] .

[0113] in, For nodes Voltage amplitude, For nodes Voltage amplitude; The phase angle difference between nodes; Let the real and imaginary parts of the nodal admittance matrix be given. Inject power into the node.

[0114] In this embodiment, the equipment capacity / level constraint is expressed as follows:

[0115] .

[0116] in, Set the location index for the candidate device. Index for resource types; To install decision variables, Indicates the candidate position Installation type is Resources Indicates that it will not be installed; For the corresponding resource capacity / level decision variables, when the resource is a continuously adjustable device... This indicates its configured capacity or upper limit for reactive power regulation, when the resource is a discrete-level device. Indicates its gear position; and They are resource types In position Minimum and maximum capacity / tier boundaries that can be configured.

[0117] In this embodiment, the installation of mutual exclusion / combination constraints satisfies:

[0118] The same candidate position pairs mutually exclusive resource type sets have:

[0119] .

[0120] Among them, the set of mutually exclusive resource types Given a set of mutually exclusive sets Mutual exclusion constraints only apply to resource types included in the mutual exclusion set; resource types not included in the mutual exclusion set are allowed to be combined and installed at the same candidate location. For example, the mutual exclusion set could be:

[0121] .

[0122] This is used to indicate that the same candidate location adopts a mutually exclusive configuration for dynamic reactive power compensation resource types to avoid redundant construction caused by functional overlap; when there are multiple specifications of parallel capacitors or parallel reactors, they can be constructed separately:

[0123] .

[0124] Used to indicate mutually exclusive selection of similar fixed compensation schemes for the same candidate location.

[0125] Specifically, in S5, the mutation operator of the NSGA-II algorithm with the variable step size mutation operator is set to a variable step size that decreases with the iteration number, so that there is a larger step size in the early stage of the iteration to enhance the global search capability, and a smaller step size in the later stage of the iteration to enhance the local convergence capability. Furthermore, the variable step size mutation operator is embedded in the mutation link of the NSGA-II algorithm and is executed in an integrated manner with the overall NSGA-II process.

[0126] In this embodiment, the variable step size decreases with the number of iterations. The step size is larger in the early stages of iteration to enhance global search capability, and smaller in the later stages to enhance local convergence capability. For example, the variation of continuous capacity variables can be achieved using:

[0127] ;

[0128] .

[0129] Where g is the current algebra and G is the maximum algebra. These are the initial and later step size coefficients, respectively. The larger the value, the greater the variable length in the early stage of iteration, which is beneficial for enhancing global exploration and escaping local optima, but may reduce the proportion of feasible solutions in the early stage; The smaller the value, the smaller the asynchronous length in the later stage of the iteration and the smaller the perturbation range converges, which is beneficial to refine the local search and improve the stability and convergence of the Pareto front. However, if the value is too small, it may lead to a slower convergence speed.

[0130] Specifically, the evaluation indicators in S6 include at least the expectation exceeding the limit indicator and the investment cost indicator. After determining the indicator weights using the entropy weight method, the Pareto schemes are comprehensively scored and ranked.

[0131] In this embodiment, the specific process of S6 is as follows: the k-th index value of the m-th Pareto scheme is denoted as... After normalization and homogenization, we obtain Define the proportion:

[0132] ;

[0133] Calculate information entropy:

[0134] ;

[0135] Obtain the entropy weight:

[0136] ;

[0137] Overall Score:

[0138] .

[0139] according to The Pareto schemes are ranked, recommended schemes are output, and a strategy library is formed.

[0140] Example 3:

[0141] Building upon Embodiments 1 and 2 described above, this embodiment provides a more specific application example. This embodiment uses a suburban power distribution network comprising 10kV feeders, distribution transformers, and low-voltage users as an example. Historical data for this area shows that during peak load periods, some line ends and low-voltage users in the distribution area experience voltage underestimation (below 0.93 pu), while during peak distributed photovoltaic power generation periods, some nodes experience voltage overestimation (above 1.07 pu). The planning objective is to add reactive power compensation resources (including parallel capacitor banks and static var generators, SVG) to address the voltage over-limit problem while controlling investment costs.

[0142] The specific implementation steps are as follows:

[0143] S1: Construct a set of typical operating scenarios.

[0144] Obtain the static model data of the distribution network, including the topological connection relationship of "station-line-transformer-household", line impedance, transformer parameters, historical load data of each node, and historical output data of distributed photovoltaic power generation.

[0145] By performing K-means cluster analysis on historical load curves and photovoltaic output curves, and statistically analyzing voltage over-limit records, three typical operating scenarios were constructed:

[0146] Scenario 1 (Heavy Load Scenario): During the evening rush hour in winter, the load level is high, and the photovoltaic output is close to zero. What is the probability of this scenario occurring? .

[0147] Scenario 2 (High PV Scenario): At midday in spring, the load level is moderate, and PV output reaches its peak. What is the probability of this scenario occurring? .

[0148] Scenario 3 (Light Load Scenario): In the early morning of summer, the load level is low, and photovoltaic output is zero. What is the probability of this scenario occurring? .

[0149] S2: Power flow calculation.

[0150] Power flow calculations were performed for the three typical operating scenarios described above. The voltage amplitude of each node in each scenario was calculated. Especially the voltage value of the end user node.

[0151] S3: Filtering candidate installation locations.

[0152] Based on the power flow calculation results of Scenario 1, the Jacobian matrix is ​​obtained using the Newton-Raphson method, and the sensitivity matrix of node voltage to node reactive power injection is calculated. .

[0153] Subsequently, for all user nodes and candidate reactive power compensation locations (such as critical line nodes and the low-voltage side of distribution transformers), the sensitivity of user voltage to reactive power capacity at candidate locations was calculated. By combining the scenario probability and the voltage over-limit relaxation amount under the baseline operating condition, the over-limit-sensitivity coupling score is calculated. .

[0154] In this embodiment, the calculation results show that the low-voltage side busbar of distribution transformer T2 (location) Install SVG (resources) )of The highest-rated line is the end of Line L5 (location). Install parallel capacitor banks (resources) The score for ) was second. Based on the preset project scale (selecting the first two candidate locations at each voltage level), the final set of candidate installation locations was determined as follows:

[0155] {Transformer T2 low-voltage side (equipped with SVG, maximum capacity 1.2Mvar), line L5 end (equipped with capacitor bank, maximum capacity 0.6Mvar), transformer T5 low-voltage side (equipped with SVG, maximum capacity 0.8Mvar)}.

[0156] S4: Establish a multi-objective programming model.

[0157] Establish a multi-objective programming model with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total life cycle cost.

[0158] The objective function for exceeding the limit is:

[0159] .

[0160] in, and Representing scenes respectively Next user Low-pressure over-limit relaxation and high-pressure over-limit relaxation.

[0161] The life-cycle cost function is:

[0162] .

[0163] For SVG, the fixed installation cost is 50,000 yuan per unit, and the unit capacity cost is 2,000 yuan per kvar.

[0164] Decision variables:

[0165] .

[0166] : 0-1 variable, representing the candidate position Whether to install resource type r, for example, .

[0167] : Continuous or discrete variables, representing resource capacity or tier. For example, The range of values ​​is Mvar.

[0168] Constraints:

[0169] Power flow balance constraint: Ensure power balance in each scenario.

[0170] Equipment capacity / level constraints: For example, And only if hour, Only then can it be greater than 0.

[0171] Install mutual exclusion / combination constraints: For example, stipulate that SVC and SVG cannot be installed at the same location at the same time. Therefore, if there are candidate locations that consider both types of resources, mutual exclusion constraints need to be added. In this embodiment, all candidate locations are of a single resource type, therefore this constraint does not apply.

[0172] S5: Solve the multi-objective programming model.

[0173] The NSGA-II algorithm with an embedded variable-step mutation operator is used to solve the above model. The population size is set to 100, and the maximum number of iterations G=200. The mutation operator adopts a variable-step strategy:

[0174] .

[0175] Set the initial step size coefficient Later step size coefficient In the early stages of iteration, the variable asynchronous length is relatively large (close to 0.5), allowing the population to extensively explore the solution space and find voltage improvement schemes under different investment costs. In the later stages of iteration, the variable asynchronous length gradually decreases to 0.05, which helps to perform fine-grained searches near the Pareto front and improve the accuracy of the solution.

[0176] After 200 iterations of optimization, the algorithm converged, yielding a set of Pareto reconfiguration schemes containing 30 non-dominated solutions. Each scheme corresponds to a set of reactive resource configuration capacity combinations for candidate locations, and their corresponding... (Exceeding expectations) and (Life cycle cost).

[0177] S6: Comprehensive evaluation and ranking of the proposed solutions.

[0178] Construct an evaluation index system and select "expected voltage exceedance for all users". "and total life cycle cost" "These are two evaluation indicators. Since both indicators are better the smaller they are, they are directly homogenized (no conversion is needed)."

[0179] For the 30 solutions in the Pareto solution set, the entropy weight method is applied to determine the weights:

[0180] 1. Construct a 30×2 decision matrix and calculate the weight of each indicator. .

[0181] 2. Calculate the information entropy of each indicator. .For example, The indicators are scattered and have low information entropy; The distribution of indicators is relatively concentrated, and the information entropy is relatively high.

[0182] 3. Calculate the entropy weight The results showed that The weight is 0.65. The weight is 0.35, indicating that in this application example, improving voltage quality (reducing overruns) is more important than simply reducing costs.

[0183] 4. Calculate the overall score for each Pareto scheme based on its weight. And sort them by score from highest to lowest.

[0184] Ultimately, the top-ranked solution was output as the recommended solution. This solution suggests installing a 0.9 Mvar SVG on the low-voltage side of distribution transformer T2 and a 0.4 Mvar parallel capacitor bank at the end of line L5. Verification showed that this solution can control the voltage of all users within the range of [0.95, 1.05] pu in three typical scenarios, while maintaining a low life-cycle cost, achieving an optimal balance between voltage quality improvement and investment economics. This recommended solution, along with other non-dominated solutions in the Pareto frontier, will be stored in the strategy library for decision-makers' reference.

[0185] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0186] Many other changes and modifications can be made without departing from the concept and scope of this invention. It should be understood that this invention is not limited to the specific embodiments, and the scope of this invention is defined by the appended claims.

Claims

1. A distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation, characterized in that, Includes the following steps: S1: Obtain static model data of the distribution network and full user voltage data, construct a set of typical operating scenarios and determine the probability of occurrence of each scenario; S2: Perform power flow calculations for each typical operating scenario to obtain the voltage of network nodes and the voltage of all users; S3: Calculate voltage-reactive power sensitivity based on voltage results from power flow calculation, and aggregate and sort them at the station, line, transformer, and customer levels to form a set of candidate installation locations and capacity or tap limit. S4: Establish a multi-objective programming model with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total life cycle cost, and set constraints. S5: The NSGA-II algorithm with embedded variable step size mutation operator is used to solve the multi-objective programming model to obtain the Pareto modification configuration scheme set; S6: Construct an evaluation index system and use the entropy weight method to comprehensively evaluate and rank the Pareto modification configuration schemes, output recommended schemes and form a strategy library.

2. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The static model data in S1 includes the station-line-transformer-household topology mapping, line and transformer parameters, and load and distributed power generation statistics.

3. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The typical operating scenario set in S1 is obtained by clustering or segmenting historical load curves, distributed power output curves and voltage over-limit records, and a probability is assigned to each scenario, with the sum of the probabilities being 1.

4. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The sensitivity in S3 is obtained by inverting the Jacobian matrix obtained by linearizing the power flow equation to obtain the voltage sensitivity matrix to reactive power, and then converting the sensitivity to user voltage to resource capacity or level for candidate screening.

5. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, In S4, the voltage over-limit for all users is represented by bidirectional over-limit relaxation variables, and the expected over-limit target is constructed by the sum of relaxation variables weighted by scenario probability. This ensures model feasibility under both full-user and multi-scenario conditions, and the expected over-limit target... Defined as: ； in, The expected target for voltage over-limit for all users; For scene probabilities; This is a relaxation variable for user u when the voltage is below the lower limit in scenario s, i.e., the undervoltage limit. This is a relaxation variable for user u when the voltage exceeds the upper limit in scenario s, i.e., overvoltage exceeding the limit; For any scenario and ; For any user and ; The total life-cycle cost in S4 consists of fixed resource installation costs and unit capacity or tier costs, and the total life-cycle cost is expressed as follows: ； in, Cost over the entire life cycle; Indicates the candidate position Is the installation type set to... Resources; This refers to resource capacity or tier variables. To fix installation costs, Cost per unit capacity or grade The coefficient for operation and maintenance costs per unit time, where T is the planning period; This is the life-value adjustment factor. For equipment lifespan.

6. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, In S4, a multi-objective programming model is established with the objectives of minimizing the expected voltage exceedance of all users and minimizing the total lifecycle cost. The specific expression is as follows: ； in, The expected target for voltage over-limit for all users. For total life cycle cost, This is a multi-objective programming model.

7. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The decision variables of the multi-objective programming model in S4 include the installation 0-1 variables and capacity or gear variables of each resource type at the candidate location, and the capacity or gear variables satisfy the upper and lower bound constraints; the same candidate location satisfies the resource mutual exclusion or combined installation constraints.

8. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The constraints of the multi-objective programming model in S4 include power flow balance constraints, equipment capacity or gear constraints, and installation constraints. The power flow balance constraint applies in any scenario The following is represented as: ； ； in, For nodes Voltage amplitude, For nodes Voltage amplitude, The phase angle difference between nodes; Let the real and imaginary parts of the nodal admittance matrix be given. Inject power into the node; The equipment capacity or gear constraint is expressed as follows: ； in, Set the location index for the candidate device. Index for resource types; To install decision variables, Indicates the candidate position Installation type is Resources Indicates that it will not be installed; For the corresponding resource capacity or level decision variables, when the resource is a continuously adjustable device This indicates its configured capacity or upper limit for reactive power regulation, when the resource is a discrete-level device. Indicates its gear position; and Respectively, resource types In position Allowed minimum and maximum capacity or gear boundaries; The mutual exclusion or combination constraints for installation satisfy: The same candidate position pairs mutually exclusive resource type sets have: ； Among them, the set of mutually exclusive resource types Given a set of mutually exclusive sets Mutual exclusion constraints only apply to resource types included in the mutual exclusion set; resource types not included in the mutual exclusion set are allowed to be combined and installed at the same candidate location.

9. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The mutation operator of the NSGA-II algorithm with the variable step size mutation operator in S5 is set to a variable step size that decreases with the number of iterations, and the variable step size mutation operator is embedded in the mutation stage of the NSGA-II algorithm and executed in an integrated manner with the overall NSGA-II process.

10. The distribution network resource allocation and planning method based on variable step size NSGA-II and entropy weight evaluation according to claim 1, characterized in that, The evaluation indicators in S6 include the expectation exceeding the limit indicator and the investment cost indicator. After determining the indicator weights using the entropy weight method, the Pareto modification configuration schemes are comprehensively scored and ranked. The modification configuration scheme with the highest score is then output as the recommended scheme.

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