A method for optimizing configuration of distributed power supply and capacitor in power distribution network

Abstract

This invention proposes an optimal configuration method for distributed generation (DG) and capacitors in distribution networks, relating to the technical field of DG and capacitor configuration in distribution networks. The method first utilizes normal distribution and Monte Carlo sampling to construct diverse operating scenarios with stochastic load and DG output, selecting typical scenarios through probability density. Then, it constructs a multi-objective optimization model centered on minimizing network losses, improving voltage stability, and balancing branch currents. By introducing a multi-objective particle swarm optimization algorithm and using an improved forward-backward substitution method to calculate various indicators, it selects non-dominated solution sets. An external archive mechanism is used to approximate the complete Pareto front. Finally, considering engineering requirements, the optimal scheme with the best overall benefits is selected from the Pareto front, achieving optimal configuration of DG and capacitors and improving the stability and economy of distribution network operation.

Description

Technical Field

[0001] This invention relates to the field of distributed generation and capacitor configuration technology in distribution networks, specifically to a method for optimizing the configuration of distributed generation and capacitors in distribution networks using uncertainty modeling, multi-objective particle swarm optimization, and Pareto front. Background Technology

[0002] Driven by both the "dual carbon" goals and the construction of a new power system, my country's new energy industry has achieved rapid development, with distributed generation (DG), represented by wind and solar power, being massively integrated into the distribution network. This transformation has gradually shifted the traditionally passive power supply-driven distribution network towards a more complex operating mode of "active management and bidirectional power flow." However, due to the significant randomness and volatility of DG output from solar and wind power, the distribution network is prone to mismatches between DG output and load demand in actual operation, leading to problems such as backflow and voltage exceeding limits, resulting in decreased voltage stability. Simultaneously, changes in power flow distribution caused by DG integration may increase network active power losses and reduce the operational economy of the distribution network. These problems not only affect the stability and economy of the distribution network under the current operating mode but also restrict the further large-scale integration of DG, hindering the healthy development of new energy sources.

[0003] To address the aforementioned issues, existing research has proposed various distributed generation (DG) configuration planning methods. However, most traditional methods are based on deterministic models and power flow analysis under single scenarios, failing to fully consider the stochasticity of photovoltaic output and load fluctuations. This results in poor adaptability of the planning schemes to different operating scenarios and a lack of sufficient robustness. Furthermore, existing methods typically treat the configuration of DG and capacitors as two independent problems for separate optimization, ignoring their synergistic potential in reactive power compensation and voltage support, making it difficult to achieve optimal overall system performance.

[0004] In summary, in order to overcome the limitations of traditional distribution network DG planning methods and improve the robustness and economy of planning schemes under uncertain conditions, it is urgent to develop a distribution network planning method that can comprehensively consider the coordinated configuration of DG and capacitors, adapt to multiple operating conditions, and take into account the optimization of multiple objectives. Summary of the Invention

[0005] This invention provides a distribution network optimization configuration method that can cope with source load uncertainty, achieve coordinated configuration of DG and capacitors, perform multi-objective comprehensive optimization, and has engineering applicability, so as to improve the economy, stability and robustness of distribution network operation.

[0006] This invention provides a method for optimizing the configuration of distributed generation sources and capacitors in a power distribution network, comprising: Uncertainty modeling of distributed generation output and load demand is performed using normal distribution and Monte Carlo sampling. The most likely typical scenarios are selected by probability density, and the output parameters and load parameters of distributed generation under each scenario are obtained. Using the selected typical scenarios as the operating environment, the objective functions are to minimize the network loss of the distribution network, improve the voltage stability and balance the branch current. A multi-objective optimization model is constructed by comprehensively considering power balance constraints, voltage constraints, distributed power generation capacity and operation constraints, capacitor capacity constraints, reactive power constraints and thermal stability constraints. Using the objective function in the multi-objective optimization model as the fitness evaluation basis and the constraints therein as the feasible region boundary, a multi-objective particle swarm optimization algorithm is introduced to simultaneously optimize the configuration location and capacity of distributed power sources and capacitors. In each iteration, the improved forward-backward substitution method is used to calculate the distribution network operation indicators corresponding to each candidate scheme under the current iteration, and the non-dominated solution set of the current iteration is selected by comparison based on the Pareto dominance criterion. The non-dominated solution set generated in each iteration is cumulatively updated and its diversity is maintained using an external archive mechanism. Dominated inferior solutions are eliminated and high-quality solutions are retained, so that the solution set in the archive gradually approaches the complete and evenly distributed Pareto front. Using the approximate Pareto front as a pool of candidate solutions, and combining the actual engineering needs of the distribution network, the solution with the best overall benefits is selected from the front, and the optimized configuration results of distributed power sources and capacitors are output.

[0007] In some instances, the uncertainty modeling of distributed generation output and load demand is performed using normal distribution and Monte Carlo sampling, and the most likely typical scenarios are selected through probability density filtering to obtain the distributed generation output parameters and load parameters under each scenario, including: The normal distribution model is used to describe the output fluctuation of distributed photovoltaic power generation and the load prediction error, respectively, and the load and photovoltaic models and probability density functions are obtained. The total sample set is generated by Monte Carlo simulation. The product of the load fluctuation probability density and the distributed power output fluctuation probability density in each scenario is taken as the joint probability density of that scenario. After sorting all scenarios from largest to smallest joint probability density, a preset number of scenarios with the highest probability are selected as typical scenarios.

[0008] In some instances, the objective function for minimizing network losses is: the sum of the products of the squares of the currents in all branches of the network and the corresponding branch resistances, with the goal of minimizing this sum. The voltage stability objective function is: the reciprocal of the minimum value of the voltage stability index of all nodes in the network, wherein the voltage stability index of a single node is determined by subtracting four correction terms related to active power, reactive power, line resistance, and line reactance from the fourth power of the voltage of the upstream node of that node. The objective function for balancing branch currents is to minimize the system current index, which is obtained by normalizing and summing the deviations of each branch current from the maximum branch current and then dividing by the total number of branches.

[0009] In some instances, the multi-objective particle swarm optimization algorithm is introduced to simultaneously optimize the location and capacity of distributed power sources and capacitors. In each iteration, an improved forward-backward substitution method is used to calculate the distribution network operation indicators corresponding to each candidate scheme in the current iteration. The non-dominated solution set for the current iteration is then selected based on the Pareto dominance criterion, including: Initialize a group of randomly generated particles. The coordinate vector of each particle contains the installation location of the distributed power source, the installation capacity of the distributed power source, the installation location of the capacitor, and the installation capacity of the capacitor. At the same time, the velocity of each particle is randomly initialized. For each configuration scheme represented by a particle, an improved forward-backward substitution method is used to calculate the power flow. Based on the power flow calculation results, the objective value of each particle is calculated according to the objective function. If all objective values ​​of a solution are not inferior to another solution, and at least one objective value is superior to the other solution, then the former is determined to dominate the latter. Based on the Pareto dominance criterion, solutions that are not dominated by any other particle in the current iteration are selected to form the non-dominated solution set of the current iteration; Combining the contraction factor, dynamic inertia weight, two acceleration constants, and two random numbers, the velocity and position of each particle are updated sequentially based on the individual historical best position and the global best position of the group. The dynamic inertia weight decreases linearly from the maximum weight to the minimum weight with the number of iterations. Repeat the steps of power flow calculation, fitness evaluation, non-dominated solution set screening and particle update until the preset maximum number of iterations is reached or the particle fitness does not change significantly in multiple consecutive iterations.

[0010] In some instances, the particle velocity is updated as follows: the product of the contraction factor, the dynamic inertia weight, and the old velocity, plus the sum of the products of the two acceleration constants multiplied by their corresponding random numbers and the individual optimal deviation and the global optimal deviation. The particle's position is updated by adding the updated velocity to the original position; the dynamic inertia weight decreases linearly from the maximum weight to the minimum weight according to the proportion of the current iteration number to the maximum iteration number.

[0011] In the process of updating particle velocity and position, an adaptive search adjustment mechanism is set up to dynamically adjust the search step size and search direction of the particles based on the current iteration number, the distribution state of the non-dominated solutions of the particle swarm, and the crowding distance of the solutions in the external archive.

[0012] In some instances, the power flow calculation for each configuration represented by a particle employs an improved forward-backward substitution method, including: First, calculate the load current of each node. Then, calculate the voltage of each node from the end to the beginning through a forward push process. Next, calculate the current of each branch from the beginning to the end through a backward push process. Set the maximum value of the node voltage change as a convergence criterion.

[0013] In some instances, the method of using an external archive mechanism to cumulatively update and maintain the diversity of the non-dominated solution set generated in each iteration includes: The dominance relationship between the non-dominated solution generated in the current iteration and the existing solutions in the external archive is compared. If the new solution is better than or independent of the existing solutions in the archive, it is included in the archive. At the same time, all inferior solutions dominated by the new solution are removed from the archive to ensure that the archive always stores the current set of non-dominated solutions of the highest quality.

[0014] In some instances, the method further includes: when the number of solutions in the external archive exceeds a preset capacity limit, by calculating the crowding distance of each solution in the target space, prioritizing the retention of solutions with larger crowding distances in order to maintain the distribution balance of the Pareto front in the target space.

[0015] In some instances, the method of using the approximate Pareto front as a pool of candidate solutions, and selecting the solution with the best overall benefits from the front based on the actual engineering needs of the distribution network, includes: Based on the project requirements, the weights of each objective function and economic indicator are set. After normalizing each objective function indicator and economic indicator, a weighted comprehensive score is calculated. The scheme with the highest score is selected as the final configuration scheme. The economic indicator includes the sum of the investment cost and operation and maintenance cost of distributed power sources and capacitors.

[0016] In some instances, the distributed power source includes photovoltaic power generation equipment, and the capacitors are parallel capacitor banks with a configured capacity that is an integer multiple of the standard specification capacity.

[0017] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: This invention addresses the voltage stability, network loss, and branch current balance issues arising from the increased penetration of distributed generation in modern power distribution networks. It proposes a collaborative configuration method for distributed generation and capacitors based on a multi-objective particle swarm optimization algorithm, which can simultaneously improve voltage quality, reduce network losses, and cope with load and DG output fluctuations. The method simulates the fluctuations in distributed generation (DG) output and load demand using a normal distribution model during scenario construction. Monte Carlo simulation and probability density methods are used to screen different output scenarios, validating the adaptability of the planning scheme across multiple scenarios. Then, a multi-objective optimization model is established, encompassing network active power loss, voltage stability, and branch current balance. Compared to single-objective optimization planning, this model achieves synergistic complementarity between DG and capacitors, realizing a globally balanced power flow distribution. This more thoroughly eliminates local hotspots and voltage bottlenecks that are difficult to eradicate under single-point governance models. By introducing an improved multi-objective particle swarm optimization algorithm, the method effectively overcomes the shortcomings of traditional algorithms, such as being prone to getting trapped in local optima and slow convergence speed in later stages. Through adaptive adjustment of the search step size and direction, it significantly improves global optimization efficiency while ensuring the diversity of non-dominated solution sets. Based on this, a dynamic maintenance mechanism for external archives based on the Pareto dominance criterion is constructed to maximize the diversity and distribution breadth of the final solution set, accurately approximating a complete and representative Pareto front. Finally, combined with engineering requirements, the final scheme is selected through linear weighting. This method can effectively overcome the limitations of traditional deterministic models in dealing with random fluctuations in source loads. By globally coordinating distributed power sources and reactive power compensation resources, it achieves a deep balance between technical indicators and economic costs while ensuring grid security constraints, thereby enhancing the system's ability to accommodate distributed power sources and providing practical technical support for building a safe, efficient, and green modern power distribution system. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram illustrating the implementation process of the method for optimizing the configuration of distributed power sources and capacitors in a power distribution network provided in an embodiment of the present invention. Figure 2 This is a flowchart illustrating the multi-objective particle swarm optimization algorithm provided in an embodiment of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] In the following description, specific embodiments of the invention will be illustrated with reference to steps and symbols performed by one or more computers, unless otherwise stated. Therefore, these steps and operations will be referred to several times as being performed by a computer, and computer execution as referred to herein includes operations by a computer processing unit representing electronic signals of data in a structured format. This operation transforms the data or maintains it at a location in the computer's memory system, which can be reconfigured or otherwise alter the operation of the computer in a manner well known to those skilled in the art. The data structure maintained by the data is the physical location of the memory, which has specific characteristics defined by the data format. However, the principles of the invention described above are not intended to be limiting, and those skilled in the art will understand that many of the following steps and operations can also be implemented in hardware.

[0022] The terms "module" or "unit" as used herein can be considered as software objects executing on the computing system. Different components, modules, engines, and services described herein can be considered as implementations on the computing system. The apparatus and methods described herein are preferably implemented in software, but can also be implemented in hardware, both of which are within the scope of this invention.

[0023] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0024] To overcome the limitations of traditional planning methods and improve the robustness and sustainability of distribution networks in DG and capacitor planning schemes, this invention proposes an uncertainty modeling, multi-objective particle swarm optimization, and Pareto front optimization method for the optimal configuration of distributed generation and capacitors in distribution networks. This method first models the uncertainty of distributed generation (DG) and load using normal distribution and Monte Carlo sampling, and then filters the most likely scenarios through probability density to improve the adaptability of the planning scheme to scenario fluctuations. Next, it selects minimizing network losses, improving voltage stability, and balancing branch currents as objective functions to construct a multi-objective optimization model, and collaborative optimization ensures the comprehensive governance capability of the scheme. A multi-objective particle swarm optimization algorithm is introduced to simultaneously optimize the configuration location and capacity of DG and capacitors, taking into account system loss reduction benefits, voltage quality improvement, and the robustness of the planning scheme under random fluctuations. An improved forward-backward substitution method is used to calculate various indicators of the distribution network under the current iteration, and non-dominated solutions are selected through comparison. An external archive mechanism is used to maintain the diversity and distribution balance of the non-dominated solutions, gradually approaching the complete Pareto front. Finally, combined with engineering requirements, a weighted scoring method is used to select the scheme with the best comprehensive benefits from the Pareto front, ensuring that the scheme specifically addresses the problems existing in the distribution network, achieves optimized configuration of distributed generation and capacitors, and improves the stability and economy of distribution network operation. This method takes into account the uncertainties of distributed generation (DG) and load, and coordinates the optimization of DG and capacitors. It uses a multi-objective optimization model to consider multiple operating indicators simultaneously, which effectively improves the robustness and sustainability of the configuration scheme and provides a scientific basis for optimizing the configuration of DG and capacitors in distribution networks to improve the stability and economy of operation.

[0025] Combination Figure 1 The present invention specifically describes a method for optimizing the configuration of distributed power sources and capacitors in a power distribution network, as detailed below: Step 1: Model the uncertainty of DG and load through normal distribution and Monte Carlo sampling, and select the most likely typical scenario through probability density to obtain the DG output and load parameters of the scenario; First, data from typical photovoltaic (PV) output and load scenarios in the distribution network are selected. Then, a normal distribution is used to model the uncertainties of PV output (in this case, distributed generation (DG) represented by PV) and user load, simulating PV output and load fluctuations under different scenarios to avoid the impact of scenario simplification on the robustness of the planning scheme. Assuming that load forecasting errors and PV output fluctuations follow a normal distribution, the load and PV models and probability density functions are obtained, as expressed below:

[0026]

[0027] In the formula Let i be the load of node i in scenario k. Let i be the load baseline value for node i in a deterministic scenario. It is the load forecasting error extracted from the normal distribution. To provide photovoltaic power in scenario k, This is the baseline value of photovoltaic output at node i under a deterministic scenario. It is the photovoltaic power output fluctuation extracted from the normal distribution. It is the probability density function under a normal distribution. To achieve the desired value of 0, The standard deviation is taken as 10%.

[0028] After obtaining the load and photovoltaic models, a total sample set is generated through Monte Carlo simulation. Assuming that load and photovoltaic fluctuations are independent of each other, the joint probability density of scenario k is the product of the probability densities of the two. All scenarios are sorted in descending order of probability density, and the top K most likely scenarios are selected.

[0029]

[0030]

[0031] In the formula Let k be the probability of the k-th scenario occurring. It is the set of the K scenarios with the highest probability of occurrence.

[0032] The total sample set size can be set to 1000, and the number of scenarios ultimately selected through probability density sorting should be around 10-20. Selecting more scenarios can improve the robustness of the solution, reduce discretization error, and avoid overfitting, but it will lead to increased computation time and increased convergence difficulty.

[0033] Step 2: Subsequently, minimizing network losses, improving voltage stability, and balancing branch currents are selected as objective functions to construct a multi-objective optimization model; First, the sum of the losses of each branch is calculated to obtain the sum of the active power losses of the network. Then, the objective function f1 for minimizing network losses is obtained, and its specific expression is as follows:

[0034] In the formula This is the sum of the network's active power losses. For the number of branches, , Let be the current in branch m and the line resistance of branch m, respectively.

[0035] To obtain the voltage stability objective function f2, we first calculate the voltage stability index of each node, and select the weakest point in the network as the index to measure the voltage stability of the entire network. The larger the index, the more stable the network voltage. Since optimization is to find the minimum value of the objective function, f2 is taken as the reciprocal of the stability index. The calculation method and expression are as follows:

[0036]

[0037] In the formula Let be the voltage stability index of node i. Let i be the voltage of the upstream node j. , Let be the active power and reactive power of node i, respectively. , Let be the impedance of the branch between node j and node i. Indicates the number of nodes.

[0038] The objective function f3 for branch current balance uses the system current index (SCI) to measure the uniformity of current distribution in the network. Minimizing f3 aims to obtain a more balanced current distribution and avoid situations where some lines are overloaded while others are idle. The expression is as follows:

[0039]

[0040] In the formula For the number of branches, Let the current in branch b be... This is the maximum value among all branch currents.

[0041] When optimizing the objective function, the following constraints must be met: power balance constraint, voltage constraint, DG capacity and operation constraint, capacitor capacity constraint, reactive power constraint, and thermal stability constraint.

[0042] (1) Power balance constraint During the optimization process, power balance must be ensured, and the injected power must be equal to the sum of the outflow power and the losses.

[0043]

[0044] In the formula The active power emitted by node i (from DG or power source). Let i be the active power demand of node i. Let be the mutual admittance between node i and node j. Let be the admittance angle of the line between node i and node j. Let i be the reactive power emitted by node i. Let i be the reactive power requirement of node i.

[0045] (2) Voltage constraint After calculating the voltage of each node, it is essential to ensure that the node voltages remain within the standard range to prevent overvoltage or undervoltage; otherwise, the scheme will be invalid.

[0046]

[0047]

[0048] In the formula It is the voltage of the downstream node i+1 connected to node i. The resistance of the line between the two nodes. The reactance of the line between the two nodes. The minimum allowable value for the specified node voltage. This refers to the maximum allowable value of the specified node voltage.

[0049] (3) DG capacity and operational constraints The installed capacity of the DG must not exceed the allowable range (affected by factors such as site, policy and equipment specifications), and the power factor during operation must be within the normal operating range of the equipment.

[0050]

[0051]

[0052] In the formula, This is the minimum capacity requirement for DG installation. This is the maximum capacity limit for DG installation. The capacity of the DG installed for node i. , The minimum and maximum power factors allowed for DG operation. The power factor of the DG installed on node i during runtime.

[0053] (4) Capacitor capacitance constraint In actual installation, due to limitations in device specifications, the capacity of capacitors can only be set to an integer multiple of the standard specifications, and the total capacity of installed capacitors is limited by budget and installation space constraints.

[0054]

[0055]

[0056] In the formula, Let be the compensation capacity of the capacitor installed at node i. This represents the standard capacitor compensation capacity, where n is an integer representing the multiple of the set capacitor capacity to the standard capacity.

[0057] (5) Reactive power constraint To simulate voltage problems caused by overcompensation leading to reactive power backflow from the distribution network to the main grid, the total compensation capacity must be less than or equal to the total reactive power demand of the distribution network.

[0058]

[0059] In the formula, The reactive power generated by the DG installed on node i. This represents the total reactive power demand of the network.

[0060] (6) Thermal stability constraint The apparent power flowing through each line must not exceed the line's rated capacity to prevent excessive current from causing the conductors to overheat, the insulation to age, or even malfunction.

[0061]

[0062] In the formula, The apparent power flowing through line b. This represents the maximum apparent power allowed to flow through line b.

[0063] Step 3: Introduce a multi-objective particle swarm optimization algorithm to simultaneously optimize the configuration location and capacity of the distribution network and capacitors. Use an improved forward-backward substitution method to calculate various indicators of the distribution network under the current iteration, and compare and select the non-dominated solution set. First, a group of randomly generated particles is initialized. The coordinate vector of each particle contains: DG installation location, DG capacity, capacitor location, and capacitor capacity. The particle velocities are also randomized. An improved forward-backward power flow calculation is run on the solution represented by each particle. The results are used to calculate the objective functions f1, f2, and f3, as well as constraint violations. By performing non-dominated sorting on the solutions represented by each particle, the initial non-dominated solution set, individual optima, and global optima are obtained.

[0064] Calculate the node load current:

[0065] The forward calculation process calculates the node voltage:

[0066] Calculate branch current using the back-substitution process:

[0067] Convergence Criterion:

[0068] Pareto dominance criteria, definition solution Dominant Solution The formula is as follows:

[0069] In the formula, , Let i be the load current and node voltage. , , , These represent the total power of residential load, commercial load, public facility load, and industrial load, respectively. , , , For four simultaneous load rates, Let i be the voltage at the terminal node i of branch b. Let i+1 be the voltage at the starting node of the branch. Let the line impedance of branch b be . Let D be the current in branch b, and D be the set of downstream nodes. Let be the voltage at node i in the d-th iteration. The convergence criterion is denoted by m, where m is the number of objective functions. Let be the i-th objective function.

[0070] By combining individual and global optima with a contraction factor and dynamic inertia weights, the search step size and direction of particles are adaptively adjusted, and particle positions and velocities are updated. The particle velocity reflects the search step size in the current iteration, while the sign and direction of the velocity reflect the search direction. The dynamic inertia weights change with the number of iterations to adjust the degree to which particles inherit the search velocity from the previous generation. This allows particles to maintain a larger search step size in the early stages of iteration to enhance global search capabilities, and gradually decrease the search step size in the later stages to improve local optimization accuracy. Individual and global optima together determine the particle's search direction, enabling particles to dynamically adjust their search paths based on their historical best position and the group's best position. Power flow calculations are performed on the solutions represented by new particles, indices are compared, and non-dominated sorting is performed to obtain a new non-dominated solution set. The particles are then updated, and this process is repeated until the maximum number of iterations is reached or the particle fitness no longer changes significantly after several iterations. Once these conditions are met, the solution set is output.

[0071] Speed ​​update, i.e., update of search step size and search direction:

[0072] Location update:

[0073] The contraction factor and dynamic inertia weight, i.e., the search step size adjustment parameters:

[0074]

[0075]

[0076] Speed ​​limit, i.e., search step size boundary constraint:

[0077] In the formula, Let be the velocity of the particle in the d-th iteration. Let be the position of the particle in the d-th iteration. It is a contractile factor. For dynamic inertia weights, , For the maximum and minimum weights, , The acceleration constant is denoted by rand, which is a random number between [0,1]. For the individual's historical best, For the global optimum of the group, This represents the current iteration number. The maximum number of iterations, This is the maximum speed limit. Among them, particle velocity... The amplitude determines the particle search step size. and Together they determine the particle search direction; dynamic inertia weights The shrinkage factor adapts to the number of iterations. and speed limit The search range of particles is constrained by a common constraint, thereby enabling dynamic adaptive adjustment of the particle search step size and search direction.

[0078] Step 4: Use external archive mechanisms to maintain the diversity and distribution equilibrium of non-dominated solution sets, gradually approaching the complete Pareto front; External archive updates use the Pareto dominance criterion to identify non-dominated solutions generated during the iteration process in real time. New solutions superior to historical records are included in the archive, while dominated inferior solutions are removed, ensuring that the archive always stores the highest quality planning solutions. This mechanism ensures that the final Pareto front exhibits good continuity, diversity, and broad coverage within the target space.

[0079] External archives updated, new solutions added and inferior solutions removed:

[0080] In the formula, For the tth generation external archive, This is a new interpretation.

[0081] Step 5: Based on engineering requirements, select the scheme with the best overall benefits from the Pareto front to achieve the optimal configuration of distributed power sources and capacitors.

[0082] The final solution is selected using a weighted summation method.

[0083] In the formula, For the final score of scheme k, , , , Weights for each objective, , , The objective function index is the normalized objective function index. These are normalized economic indicators.

[0084] The weights of the indicators are set according to the project requirements, and the highest score is selected as the final configuration scheme.

[0085] Since the Pareto front is ultimately a mathematically equivalent set of non-dominated solutions, where each solution represents a trade-off between different objective functions (e.g., low losses may be accompanied by high costs, or high voltage stability may be accompanied by high investment), a single mathematically optimal solution does not exist physically. Therefore, it is necessary to combine practical engineering needs and adopt a weighted evaluation method to select the scheme with the best overall benefits from the Pareto front. This not only solves the problem of the difficulty in directly comparing indicators with different dimensions, but also organically combines the planners' subjective preferences with the objective constraints of power grid operation.

[0086] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be performed by instructions, or by instructions controlling related hardware. These instructions can be stored in a computer-readable storage medium and loaded and executed by a processor.

[0087] Therefore, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, the computer program being loaded by a processor to execute the steps of any method provided in the embodiments of the present invention.

[0088] For details on the implementation of each of the above operations, please refer to the previous examples, which will not be repeated here.

[0089] The computer-readable storage medium may include: read-only memory (ROM), random access memory (RAM), disk or optical disk, etc.

[0090] Since the computer program stored in the computer-readable storage medium can execute the steps of any of the methods provided in the embodiments of the present invention, the beneficial effects that any of the methods provided in the embodiments of the present invention can achieve can be realized, as detailed in the preceding embodiments, and will not be repeated here.

[0091] The above provides a detailed description of a method for optimizing the configuration of distributed power sources and capacitors in a power distribution network, as provided by embodiments of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, those skilled in the art will recognize that there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for optimizing the configuration of distributed generation sources and capacitors in a power distribution network, characterized in that, include: Uncertainty modeling of distributed generation output and load demand is performed using normal distribution and Monte Carlo sampling. The most likely typical scenarios are selected by probability density, and the output parameters and load parameters of distributed generation under each scenario are obtained. Using the selected typical scenarios as the operating environment, the objective functions are to minimize the network loss of the distribution network, improve the voltage stability and balance the branch current. A multi-objective optimization model is constructed by comprehensively considering power balance constraints, voltage constraints, distributed power generation capacity and operation constraints, capacitor capacity constraints, reactive power constraints and thermal stability constraints. Using the objective function in the multi-objective optimization model as the fitness evaluation basis and the constraints therein as the feasible region boundary, a multi-objective particle swarm optimization algorithm is introduced to simultaneously optimize the configuration location and capacity of distributed power sources and capacitors. In each iteration, the improved forward-backward substitution method is used to calculate the distribution network operation indicators corresponding to each candidate scheme under the current iteration, and the non-dominated solution set of the current iteration is selected by comparison based on the Pareto dominance criterion. The non-dominated solution set generated in each iteration is cumulatively updated and its diversity is maintained using an external archive mechanism. Dominated inferior solutions are eliminated and high-quality solutions are retained, so that the solution set in the archive gradually approaches the complete and evenly distributed Pareto front. Using the approximate Pareto front as a pool of candidate solutions, and combining the actual engineering needs of the distribution network, the solution with the best overall benefits is selected from the front, and the optimized configuration results of distributed power sources and capacitors are output.

2. The method according to claim 1, characterized in that, The uncertainty modeling of distributed generation output and load demand is performed using normal distribution and Monte Carlo sampling. The most likely typical scenarios are then selected through probability density analysis to obtain the distributed generation output parameters and load parameters for each scenario, including: The normal distribution model is used to describe the output fluctuation of distributed photovoltaic power generation and the load prediction error, respectively, and the load and photovoltaic models and probability density functions are obtained. The total sample set is generated by Monte Carlo simulation. The product of the load fluctuation probability density and the distributed power output fluctuation probability density in each scenario is taken as the joint probability density of that scenario. After sorting all scenarios from largest to smallest joint probability density, a preset number of scenarios with the highest probability are selected as typical scenarios.

3. The method according to claim 1, characterized in that, The objective function for minimizing network losses is: the sum of the products of the squares of the currents of all branches in the network and the corresponding branch resistances, with the goal of minimizing this sum. The voltage stability objective function is: the reciprocal of the minimum value of the voltage stability index of all nodes in the network, wherein the voltage stability index of a single node is determined by subtracting four correction terms related to active power, reactive power, line resistance, and line reactance from the fourth power of the voltage of the upstream node of that node. The objective function for balancing branch currents is to minimize the system current index, which is obtained by normalizing and summing the deviations of each branch current from the maximum branch current and then dividing by the total number of branches.

4. The method according to any one of claims 1 to 3, characterized in that, The introduced multi-objective particle swarm optimization algorithm simultaneously optimizes the configuration location and capacity of distributed power sources and capacitors. In each iteration, an improved forward-backward substitution method is used to calculate the distribution network operation indicators corresponding to each candidate scheme under the current iteration. The non-dominated solution set for the current iteration is then compared and selected based on the Pareto dominance criterion, including: Initialize a group of randomly generated particles. The coordinate vector of each particle contains the installation location of the distributed power source, the installation capacity of the distributed power source, the installation location of the capacitor, and the installation capacity of the capacitor. At the same time, the velocity of each particle is randomly initialized. For each configuration scheme represented by a particle, an improved forward-backward substitution method is used to calculate the power flow. Based on the power flow calculation results, the objective value of each particle is calculated according to the objective function. If all objective values ​​of a solution are not inferior to another solution, and at least one objective value is superior to the other solution, then the former is determined to dominate the latter. Based on the Pareto dominance criterion, solutions that are not dominated by any other particle in the current iteration are selected to form the non-dominated solution set of the current iteration; Combining the contraction factor, dynamic inertia weight, two acceleration constants, and two random numbers, the velocity and position of each particle are updated sequentially based on the individual historical best position and the global best position of the group. The dynamic inertia weight decreases linearly from the maximum weight to the minimum weight with the number of iterations. Repeat the steps of power flow calculation, fitness evaluation, non-dominated solution set screening and particle update until the preset maximum number of iterations is reached or the particle fitness does not change significantly in multiple consecutive iterations.

5. The method according to claim 4, characterized in that, The particle velocity update method is: the sum of the product of the contraction factor, the dynamic inertia weight, and the old velocity, plus the product of the two acceleration constants multiplied by their corresponding random numbers, and the product of the individual optimal deviation and the global optimal deviation; The particle's position is updated by adding the updated velocity to the original position; the dynamic inertia weight decreases linearly from the maximum weight to the minimum weight according to the proportion of the current iteration number to the maximum iteration number. In the process of updating particle velocity and position, the search step size and search direction of the particles are dynamically adjusted according to the current iteration number, the distribution state of the non-dominated solutions of the particle swarm, and the crowding distance of the solutions in the external archive.

6. The method according to claim 5, characterized in that, For each configuration scheme represented by a particle, a modified forward-backward substitution method is used for power flow calculation, including: First, calculate the load current of each node. Then, calculate the voltage of each node from the end to the beginning through a forward push process. Next, calculate the current of each branch from the beginning to the end through a backward push process. Set the maximum value of the node voltage change as a convergence criterion.

7. The method according to claim 6, characterized in that, The step of using an external archive mechanism to cumulatively update and maintain the diversity of the non-dominated solution set generated in each iteration includes: The dominance relationship between the non-dominated solution generated in the current iteration and the existing solutions in the external archive is compared. If the new solution is better than or independent of the existing solutions in the archive, it is included in the archive. At the same time, all inferior solutions dominated by the new solution are removed from the archive to ensure that the archive always stores the current set of non-dominated solutions of the highest quality.

8. The method according to claim 7, characterized in that, The method further includes: when the number of solutions in the external archive exceeds the preset capacity limit, by calculating the crowding distance of each solution in the target space, prioritizing the retention of solutions with larger crowding distances in order to maintain the distribution balance of the Pareto front in the target space.

9. The method according to claim 8, characterized in that, The process of using the approximate Pareto front as a pool of candidate solutions, and selecting the solution with the best overall benefits from the front based on the actual engineering needs of the distribution network, includes: Based on the project requirements, the weights of each objective function and economic indicator are set. After normalizing each objective function indicator and economic indicator, a weighted comprehensive score is calculated. The scheme with the highest score is selected as the final configuration scheme. The economic indicator includes the sum of the investment cost and operation and maintenance cost of distributed power sources and capacitors.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method according to any one of claims 1 to 9.

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