A method for assessing the carrying capacity of distribution networks considering photovoltaic distribution characteristics

Abstract

A method for assessing the carrying capacity of a distribution network considering the distribution characteristics of photovoltaics includes the following steps: Step 1: Modeling source-load uncertainty and generating typical scenarios; Step 2: Constructing distribution characteristic indicators of photovoltaic access status; Step 3: Considering the temporal characteristics of source-load, performing time-series power flow analysis; Step 4: Solving the model using an improved particle swarm optimization algorithm. The purpose of this invention is to address the technical problems in existing photovoltaic access capacity assessment methods, such as the typically fixed photovoltaic access location and capacity settings, the limited assessment scenarios, and the difficulty in accurately reflecting the spatiotemporal dynamic characteristics of photovoltaic access status in actual engineering projects. This leads to insufficient accuracy in the power flow distribution and carrying capacity assessment results of the distribution network, and the existing methods do not fully consider the correlation between photovoltaic output and load in the time series, failing to accurately reflect its regulatory role during critical periods. Therefore, this invention provides a solution.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of clean energy, new energy and power distribution, and particularly relates to a power distribution network carrying capacity evaluation method considering photovoltaic distribution characteristics. BACKGROUND

[0002] With the continuous promotion of the "double carbon" goal, the power system is accelerating the transformation towards clean and low-carbon, and the penetration rate of distributed photovoltaic (PV) in the distribution network is continuously increasing. However, due to the limitations of the structure and operation mode of the existing distribution network, high proportion of distributed power access has caused a series of operation problems such as voltage out-of-limit, line overload and power flow reverse, which has significantly increased the operation pressure of the distribution network. The above phenomenon not only restricts the large-scale access of distributed power, but also becomes one of the key bottlenecks affecting its efficient consumption. Therefore, it is urgent to build a scientific and reasonable, highly operable distribution network carrying capacity evaluation method.

[0003] The existing evaluation methods for the access capacity of distributed photovoltaic in the distribution network, such as "Distribution Network Distributed Power Carrying Capacity Evaluation Based on APDE Algorithm", integrate source and load uncertainty and opportunity constraints, and quantitatively analyze the maximum carrying capacity of the distribution network for distributed power under different confidence levels. "Interval Affine Analysis of Distributed Photovoltaic Acceptance Capacity Based on Interval Overvoltage Risk", combines static voltage stability indicators with random scenario simulation method, and comprehensively improves the evaluation accuracy and solving efficiency of the carrying capacity. "Data-driven Evaluation Technology of Distributed Photovoltaic Carrying Capacity in Distribution Network", proposes a data-driven evaluation method of distributed photovoltaic carrying capacity in distribution network, which unifies the fusion of multi-dimensional constraint conditions, has low modeling dependence and strong adaptability, and realizes efficient evaluation and visual expression of PV carrying capacity. Although the above evaluation methods use various analysis methods to improve the evaluation accuracy, they generally do not include the access location in the modeling process, which has certain limitations. Specifically, they do not consider the location characteristics of the access node, and it is difficult to accurately reflect the differences in electrical parameters, operating state and topological position of different access nodes. In actual application, the access capacity and the access location are highly coupled, and both of them jointly affect the carrying capacity level of the distribution network. Therefore, it is of great significance to introduce the spatial factor of access location characteristics in the carrying capacity evaluation.

[0004] In view of the above problems, some researches introduce the influence of access location in the evaluation of distribution network carrying capacity, such as Renewable energy hosting capacity assessment in distribution networks based on multi‐strategy improved whale optimization algorithm "Research on the Influence of Photovoltaic Access on Small Signal Stability of System", reveals the key restriction factors of carrying capacity improvement from the perspective of distribution network topology. "Research on the Influence of Photovoltaic Access on Small Signal Stability of System", quantitatively analyzes the economic and environmental benefits of photovoltaic grid-connected power station and distribution network, and obtains the photovoltaic carrying capacity with the highest economic benefit by taking the joint economic benefit of photovoltaic power station and distribution network as the optimization target.Position-Capacity Optimization Method for Distributed Photovoltaic Accessing to Distribution Network Based on PV Load Uncertainty Quantification. "Further consider the uncertainty of photovoltaic and load, build the uncertainty quantitative evaluation based on the distribution network photovoltaic access location-capacity evaluation model, to the minimum line loss as the goal, the access capacity of each node is optimized configuration." Robust Assessment of Hosting Capacity of Renewable Generation in Distribution Systems Considering the Active Network Management ."Further put forward a kind of renewable energy carrying capacity evaluation method considering wind and light uncertainty, ensure the safe operation of distribution network under all disturbance scenarios through constraint adjustment mechanism.Although the above method uses a variety of intelligent optimization algorithm, can represent the optimal configuration of photovoltaic access, and to a certain extent, consider the influence of access location and capacity, but still have the following shortcomings: the location and capacity of photovoltaic access are relatively fixed, the access scene is single, it is difficult to truly reflect the PV carrying capacity under actual working conditions.In actual engineering, the access state of photovoltaic has significant space-time dynamic characteristics, and its change will directly affect the power flow distribution of distribution network and the accuracy of evaluation results;The correlation of source and load output in time series is not considered.PV usually reaches the peak output in the afternoon, and has no output at night.If the peak load of a certain area occurs at night, the maximum load is still used as the basis for evaluation, which may lead to overestimation of the carrying capacity of photovoltaic distribution network.Because in the actual highest load period, the regulation effect of PV is weak or even invalid, which cannot reflect its real carrying capacity level.

[0005] In summary, although the existing evaluation methods have partially introduced the access location and uncertainty factors, they still have deficiencies in dynamic modeling of access state and correlation of source and load in time series. SUMMARY

[0006] The purpose of the present application is to solve the technical problems in the existing photovoltaic access capacity evaluation method, such as the fixed photovoltaic access location and capacity, the single evaluation scene, the difficulty in truly reflecting the space-time dynamic characteristics of photovoltaic access state in actual engineering, the insufficient accuracy of distribution network power flow distribution and carrying capacity evaluation results, and the inability of existing methods to fully consider the correlation of photovoltaic output and load in time series and accurately reflect the regulation effect in key period, and to provide a method.

[0007] To solve the above technical problems, the technical scheme adopted by the present application is as follows:

[0008] A distribution network carrying capacity evaluation method considering photovoltaic distribution characteristics, comprising the following steps:

[0009] Step 1: source and load uncertainty modeling and typical scene generation;

[0010] Step 2: construction of photovoltaic access state distribution characteristic index;

[0011] Step 3: Consider the time-series characteristics of the source loads and perform time-series power flow analysis;

[0012] Step 4: Improve the particle swarm optimization algorithm to solve the model.

[0013] Step one includes the following sub-steps:

[0014] Step 1.1: Generate a photovoltaic power output scenario;

[0015] Step 1.2: Reduce scenes with similar characteristics;

[0016] Step 1.1 includes the following sub-steps:

[0017] Step 1.1.1) Construct a probability distribution model of photovoltaic power output based on historical data using the kernel density estimation method;

[0018] The probability density function of the probability distribution model for photovoltaic power output is:

[0019] (1);

[0020] In the formula: n It is the sample size. h It's the width of the window. K It's a kernel function. For point x The probability density function estimate at point , i It is the sample number. These are sample data points;

[0021] Step 1.1.2) After obtaining the kernel density function, further obtain the distribution function. The total number of samples is set to be R Monte Carlo simulation was performed using the inverse transform sampling method;

[0022] make Substituting this into the distribution function, we obtain the photovoltaic output as:

[0023] (2);

[0024] Step 1.1.3) Repeat step 1.1.2). R Next, generate R A photovoltaic power generation scenario.

[0025] In step 1.2, the K-means method is used to reduce scenes with similar features. The specific operation is as follows:

[0026] Let the initial set be ,in The initial reduction set is The specific reduction steps are as follows:

[0027] Step 1.2.1) From the scene set T Random selection K Each scenario is used as a cluster center, denoted as _____. ;in, This refers to the Kth cluster center;

[0028] Step 1.2.2) Set the scene Assigned to the cluster containing the nearest cluster center , To each of its cluster centers The Euclidean distance is:

[0029] (3);

[0030] Where N refers to the data dimension. It refers to belonging to The coordinate of the i-th data point of the j-th data point This refers to the center coordinates of the i-th data point in the k-th cluster;

[0031] Step 1.2.3) Recalculate the cluster center as the mean of all scenes within the cluster:

[0032] (4);

[0033] In the formula: Cluster The number of scenes;

[0034] Step 1.2.4) Repeat steps 1.2.2 and 1.2.3 until the cluster centers no longer change significantly or the maximum number of iterations is reached;

[0035] Step 1.2.5) Select a representative scene from each cluster to generate a cut-off set. S ;

[0036] The above steps can be used to obtain typical photovoltaic power output scenarios, and the same steps can be used to obtain typical load scenarios.

[0037] In step two, the constructed distribution characteristic indicators of photovoltaic grid connection status include:

[0038] 2.1: Node distribution density; its expression is:

[0039] (5);

[0040] In the formula: The number of nodes connected to distributed photovoltaic systems. This represents the total number of nodes in the distribution network.

[0041] 2.2: Access capacity dispersion; its expression is:

[0042] (6);

[0043] In the formula: It is a set of distributed photovoltaic access nodes. For nodes l The capacity of distributed photovoltaic power generation connected to the grid;

[0044] 2.3: Location dispersion; its expression is:

[0045] (7);

[0046] In the formula: , They are nodes l , m The voltage amplitude;

[0047] 2.4: Comprehensive distribution characteristic index; its expression is:

[0048] (8);

[0049] (9);

[0050] (10);

[0051] (11);

[0052] In the formula: For nodes l Normalized voltage sensitivity factor; The standard deviation of the sensitivity factor is normalized for all access nodes; For the node l After injecting unit power, the first m The voltage of each node, For the original power flow, the first m The voltage of each node; It is a node m The normalized voltage sensitivity factor, It is the sum of the sensitivity factors of all candidate access nodes. This is the comprehensive distribution characteristic index of the current scheme. For empirical reference value, The deviation is a comprehensive distribution characteristic index.

[0053] In step three, the objective function used is:

[0054] The objective functions are to maximize the total grid-connected capacity of distributed photovoltaic power and minimize the deviation of the comprehensive distribution characteristic index, respectively:

[0055] (12);

[0056] In the formula: This is a set of distributed photovoltaic (PV) grid connection schemes, among which .

[0057] In step three, the constraints used are as follows:

[0058] 3.1 Constraints on Distributed Photovoltaic Output:

[0059] (13);

[0060] In the formula: The maximum photovoltaic capacity allowed to be connected to a single node. Refers to any node ;

[0061] 3.2 Current Constraints:

[0062] (14)

[0063] In the formula: , The first l Distributed photovoltaic systems at individual nodes t Active power and reactive power at all times; , The first l Each node t Active and reactive power of the load at any given time; , They are nodes l , m The electrical conductance and susceptance between them; The phase angle between nodes l and m; for l Node at t Voltage amplitude at any given moment; express m Node in time t The voltage amplitude, where N is the total number of nodes in the network. B Let M be the set of all nodes in the network; M is the set of all branches in the network.

[0064] 3.3 Node voltage constraints:

[0065] The node voltage constraints are described in the form of chance constraints as follows:

[0066] (15);

[0067] In the formula: This represents the probability that the constraint is satisfied. , These are the upper and lower limits of the voltage amplitude, respectively. This represents the confidence level value for the node voltage constraint.

[0068] 3.4 Line current carrying capacity constraints:

[0069] The line current carrying capacity constraint is described in the form of opportunity constraint as follows:

[0070] (16);

[0071] In the formula: For the line lm exist t The current carrying capacity at any given moment; This represents the maximum carrying capacity of the line. This represents the confidence level value for the line current carrying capacity constraint.

[0072] 3.5 Reverse load factor constraint:

[0073] When the distributed photovoltaic capacity connected to the distribution network is large, power may be fed back to the upstream grid. To limit the degree of reverse power flow, the reverse load rate constraint is described in the form of an opportunity constraint:

[0074] (17);

[0075] (18);

[0076] In the formula: For distribution network t Reverse load rate at any given time; for t Network losses in the distribution network at all times; This is the upper limit of the reverse load rate; This represents the confidence level value for the reverse load factor constraint. For a moment t All load nodes m (belongs to a set) B Total load power; For a moment t All load nodes l (belongs to a set) Ω Total load power, This refers to the rated capacity of the distribution transformer.

[0077] To simplify constraint handling and improve solution efficiency, the penalty function method is used to embed the constraint conditions, namely equations (15), (16) and (17), into the objective function, namely equation (12);

[0078] The penalty term is expressed as follows:

[0079] (19);

[0080] The objective function with added penalty function can be expressed as:

[0081] (20);

[0082] Is with penalty items pen Related weights, It is the deviation term Relevant weights.

[0083] In step four, the improved particle swarm optimization algorithm is used to solve the objective function, i.e., equation (20); specifically, the following steps are included:

[0084] Step 4.1: Initialize the particles;

[0085] Step 4.2: Generate the initial particle access capacity;

[0086] Step 4.3: Perform the solution operation.

[0087] Step 4.1 includes the following steps:

[0088] Step 4.1.1) Obtain the node number vector:

[0089] (twenty one);

[0090] This is the number of the last photovoltaic node. This is the maximum number of photovoltaic nodes. For the first l The node number of each photovoltaic node;

[0091] Step 4.1.2) Obtain the access capacity vector:

[0092] (twenty two);

[0093] In the formula: For access nodes Distributed photovoltaic capacity; For access nodes The distributed photovoltaic capacity, if there is no distributed photovoltaic grid connection at this location, then ;

[0094] Step 4.1.3) Obtain the mask vector:

[0095] (twenty three);

[0096] In the formula: For the first l The mask value at each position, if This indicates that there is effective distributed photovoltaic power at that location;

[0097] Step 4.1.4) Define the particle triplet structure:

[0098] (twenty four);

[0099] In step 4.2, the initial particle access capacity is generated, specifically as follows:

[0100] (25);

[0101] In the formula: To accommodate a uniformly distributed perturbation factor, random sampling is used within a preset capacity range to achieve flexibility and dispersion in capacity configuration. Figure 1 Indicates uniform distribution. This indicates the maximum allowable grid connection capacity for a single photovoltaic node. This represents the minimum value of the disturbance factor. This represents the maximum value of the disturbance factor.

[0102] In step 4.3, the solution operation includes:

[0103] 4.3.1) Input the distribution network structure parameters, load and typical photovoltaic scenario data, and algorithm parameters;

[0104] 4.3.2) Perform power flow disturbance analysis on the basic network model, numerically calculate the sensitivity of active power injection at each node to the system voltage, and construct the voltage sensitivity matrix;

[0105] 4.3.3) Generate the initial population according to formula (24) in a joint coding structure, including node number, capacity vector and mask vector;

[0106] 4.3.4) Calculate the objective function for each particle according to formula (12);

[0107] 4.3.5) Perform probabilistic time-series power flow calculations on the distribution network, check whether individuals in the population meet the constraints, judge whether individuals meet the chance constraint confidence requirements according to the law of large numbers, extract the maximum voltage limit, current carrying capacity and reverse load rate, and construct the penalty term according to formula (19);

[0108] 4.3.6) According to formula (20), the non-dominated solutions that satisfy the constraints in the initial population are added to the external elite solution set as the initial value of the Pareto solution set;

[0109] 4.3.7) Determine if the number of iterations has been reached; if it is less than the number of iterations, update the particle velocity and position and return to step 3; if the iteration requirements have been met, output the final optimal photovoltaic access scheme set.

[0110] Compared with the prior art, the present invention has the following technical effects:

[0111] This invention proposes a method for assessing the carrying capacity of a distribution network that considers the distribution characteristics of photovoltaics. The method introduces a comprehensive distribution characteristic index during the assessment process, systematically considering the rationality of photovoltaic access locations and capacity configurations. Under the premise of meeting various operational constraints, compared to traditional methods that only aim to maximize total access capacity, the proposed method generates access schemes with superior distribution characteristics, thus significantly improving the overall carrying capacity of the distribution network. Compared to methods based on a single static moment, this invention effectively avoids the risk overestimation problem caused by static power flow calculations by introducing a time-series power flow calculation mechanism, significantly improving the safety and reliability of the assessment results. Sensitivity analysis results with different confidence levels show that, under the same change range, the carrying capacity improvement brought about by relaxing voltage constraints is far greater than that of current carrying capacity and reverse load rate constraints, indicating that voltage constraints are currently the main bottleneck for the distribution network to accommodate distributed photovoltaics. Attached Figure Description

[0112] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0113] Figure 2 This is a flowchart of the model solution based on the improved particle swarm optimization algorithm of this invention patent;

[0114] Figure 3 This is a schematic diagram of the IEEE 33-node distribution network system topology;

[0115] Figure 4 It shows the load curves for each typical day;

[0116] Figure 5 This is a graph showing the photovoltaic power output on typical days;

[0117] Figure 6 It is a multi-objective convergence curve;

[0118] Figure 7 This is a schematic diagram of the Pareto non-dominated solution set;

[0119] Figure 8 This is a schematic diagram of the voltage results for Method 2 in the comparison of methods for assessing the carrying capacity of distribution networks;

[0120] K(x) This is a schematic diagram of the voltage results for Method 3 in the comparison of methods for assessing the carrying capacity of distribution networks. Detailed Implementation

[0121] A method for assessing the carrying capacity of a distribution network that considers the characteristics of photovoltaic distribution includes the following steps:

[0122] Step 1: Modeling source load uncertainty and generating typical scenarios

[0123] 1. Generate photovoltaic power output scenarios

[0124] 1.1 A probability distribution model of photovoltaic power output is constructed based on historical data using the kernel density estimation method. The probability density function of the photovoltaic power output probability distribution model is: (1), where: n It is the sample size. h It's the width of the window. Ω It's a kernel function. For point x The probability density function estimate at point , i It is the sample number. These are sample data points.

[0125] 1.2 After obtaining the kernel density function, the distribution function can be further obtained. The total number of samples is set to be R Monte Carlo simulation is performed using the inverse transform sampling method. Let... Substituting this into the distribution function, we obtain the photovoltaic output as: (2)

[0126] 1.3 Repeat the above steps R Next, generate R A photovoltaic power generation scenario.

[0127] 2. Use the K-means method to reduce scenes with similar features.

[0128] Let the initial set be ,in The initial reduction set is The specific reduction steps are as follows:

[0129] 2.1 From the scene set T Random selection K Each scenario is used as a cluster center, denoted as _____. ,in, This refers to the Kth cluster center.

[0130] 2.2 Scene Assigned to the cluster containing the nearest cluster center , To each of its cluster centers The Euclidean distance is: (3) Where N refers to the data dimension, It refers to belonging to The coordinate of the i-th data point of the j-th data point This refers to the center coordinates of the i-th data point in the k-th cluster;

[0131] 2.3 Recalculate the cluster center as the mean of all scenes within the cluster: (4), where: Cluster The number of scenarios.

[0132] 2.4 Repeat steps 2.2 and 2.3 until the cluster centers no longer change significantly or the maximum number of iterations is reached.

[0133] 2.5 Select a representative scene from each cluster to generate a cut-off set. S .

[0134] The above steps can be used to obtain typical photovoltaic power output scenarios, and the same steps can be used to obtain typical load scenarios.

[0135] Step 2: Construction of Distribution Characteristic Indicators for Photovoltaic Grid Connection Status

[0136] The impact of system-quantified photovoltaic distribution methods on the carrying capacity of the distribution network

[0137] 1.1 Node Distribution Density

[0138] The node distribution density index characterizes the degree of integration of distributed photovoltaic (PV) systems into the distribution network, reflecting their widespread distribution. The higher the value, the more nodes are connected to the distributed PV system, and the wider its distribution within the distribution network. Its expression is... (5), where: The number of nodes connected to distributed photovoltaic systems. This represents the total number of nodes in the distribution network.

[0139] 1.2 Access capacity dispersion

[0140] If distributed photovoltaic (PV) capacity is highly concentrated in a few nodes, it will significantly increase the risk of voltage spikes or even exceeding limits at local nodes, thereby weakening the overall carrying capacity of the distribution network. Therefore, a capacity concentration index is introduced to measure the uniformity of the connected capacity. A larger index value indicates a more uneven capacity distribution, implying a risk of highly concentrated PV access; conversely, a smaller value indicates a more uniform capacity distribution. Its expression is: (6), where: It is a set of distributed photovoltaic access nodes. For nodes l The capacity of distributed photovoltaic power generation connected to the grid.

[0141] 1.3 Access Location Dispersion

[0142] To characterize the spatial dispersion of distributed photovoltaic (PV) grid connections within a distribution network, this invention introduces a grid connection dispersion index. Considering that in a typical radial distribution network, node voltage generally decreases gradually with increasing electrical distance from the main substation; however, when distributed PV injects active power at the end nodes, its voltage rises more easily due to line impedance. Therefore, under the same PV output conditions, the degree of change in node voltage can reflect the node's topological location within the network. If the voltage values ​​of the connected nodes differ significantly, the PV grid connection locations can be considered relatively dispersed; conversely, similar voltages indicate concentrated grid connections. Based on this, the grid connection dispersion index is defined as follows: (7), where: , They are nodes l , m The voltage amplitude;

[0143] 1.4 Comprehensive Distribution Characteristic Indicators

[0144] Since the node distribution density index only considers the number of distributed photovoltaic (PV) access nodes, if some nodes have extremely small access capacity, it can significantly interfere with the evaluation results. The capacity dispersion index only reflects the uniformity of capacity configuration and cannot distinguish access schemes with the same capacity distribution but significant location differences. The access location dispersion index focuses on spatial distribution; if some locations are dispersed but have a small capacity share, it may also lead to biased evaluation results. Therefore, this invention proposes a comprehensive distribution characteristic index based on the above indices. Using a voltage sensitivity matrix as a basis, it weights the normalized node voltage sensitivity with the access capacity to reflect the degree of dispersion of access capacity. Simultaneously, it introduces the sensitivity standard deviation to characterize the dispersion of access locations, thereby achieving a unified quantification of the characteristics of distributed PV access. The calculation formula is as follows: (8), (9), (10) (11), where: For nodes l Normalized voltage sensitivity factor; The standard deviation of the sensitivity factor is normalized for all access nodes; For the node l After injecting unit power, the first m The voltage of each node, For the original power flow, the first m The voltage of each node; It is a nodem The normalized voltage sensitivity factor, It is the sum of the sensitivity factors of all candidate access nodes; This is the comprehensive distribution characteristic index of the current scheme. For empirical reference value, The deviation is a comprehensive distribution characteristic index.

[0145] Step 3: Consider the temporal characteristics of the source loads and perform time-series power flow analysis.

[0146] 1. Calculate the objective function

[0147] The objective functions are to maximize the total grid-connected capacity of distributed photovoltaic power and minimize the deviation of the comprehensive distribution characteristic index, respectively: (12), where: This is a set of distributed photovoltaic (PV) grid connection schemes, among which .

[0148] 2. Constraints

[0149] 2.1 Output Constraints of Distributed Photovoltaic Power Generation (13), where: This represents the maximum photovoltaic capacity that a single node is allowed to connect to.

[0150] 2.2 Current Constraints

[0151] (14);

[0152] In the formula: , The first l Distributed photovoltaic systems at individual nodes t Active power and reactive power at all times; , The first l Each node t Active and reactive power of the load at any given time; , They are nodes l , m The electrical conductance and susceptance between them; The phase angle between nodes l and m; for l Node at t Voltage amplitude at any given moment; express m Node in time t The voltage amplitude; N is the total number of nodes in the network; B is the set of all nodes in the network; M is the set of all branches in the network.

[0153] 2.3 Node Voltage Constraints

[0154] The node voltage constraints are described in the form of chance constraints as follows: (15), where: This represents the probability that the constraint is satisfied. This represents the confidence level value for the node voltage constraint.

[0155] 2.4 Line current carrying capacity constraints

[0156] The line current carrying capacity constraint is described in the form of opportunity constraint as follows: (16), where: For the line lm exist t The current carrying capacity at any given moment; This represents the maximum carrying capacity of the line. This represents the confidence level value for the line current carrying capacity constraint.

[0157] 2.5 Reverse Load Rate Constraint

[0158] When the distributed photovoltaic capacity connected to the distribution network is large, power may be fed back to the upstream grid. To limit the degree of reverse power flow, the reverse load rate constraint is described in the form of an opportunity constraint: (17) (18), where: For distribution network t Reverse load rate at any given time; for t Network losses in the distribution network at all times; This is the upper limit of the reverse load rate; For a moment t All load nodes m (belongs to a set) B Total load power; For a moment t All load nodes l (belongs to a set) pen Total load power; This refers to the rated capacity of the distribution transformer. This represents the confidence level value for the reverse load rate constraint.

[0159] 3. Inequality handling

[0160] To simplify constraint handling and improve solution efficiency, this invention employs a penalty function method to embed constraints (15), (16), and (17) into the objective function. The penalty term is expressed as: (19) The objective function with added penalty function can be expressed as: (20), where: Is with penalty items Figure 1 Related weights, It is the deviation term Relevant weights.

[0161] Step 4: Improve the particle swarm algorithm to solve the objective function, i.e., equation (20).

[0162] 1. Initialize particles

[0163] 1.1 Node Numbering Vector

[0164] (twenty one);

[0165] In the formula: This is the number of the last photovoltaic node. This is the maximum number of photovoltaic nodes. For the first l The node number of each photovoltaic node;

[0166] 1.2 Access Capacity Vector

[0167] (twenty two);

[0168] In the formula: For access nodes Distributed photovoltaic capacity; For access nodes The distributed photovoltaic capacity, if there is no distributed photovoltaic grid connection at this location, then .

[0169] 1.3 Mask Vector

[0170] (twenty three);

[0171] In the formula: For the first l The mask value at each position, if This indicates that there is effective distributed photovoltaic power at that location.

[0172] 1.4 Define the particle triplet structure:

[0173] (twenty four);

[0174] 2. Initial particle access capacity:

[0175] (25);

[0176] In the formula: The disturbance factor is a uniformly distributed disturbance factor used for random sampling within a preset capacity range to achieve flexibility and dispersion in capacity configuration. μ(⋅) represents uniform distribution, represents the maximum allowable access capacity of a single photovoltaic node, represents the minimum value of the disturbance factor, and represents the maximum value of the disturbance factor.

[0177] 3. Specific solution steps:

[0178] 3.1 Input the distribution network parameters, load and typical photovoltaic scenario data and algorithm parameters.

[0179] 3.2 Perform power flow disturbance analysis on the basic network model, numerically calculate the sensitivity of active power injection at each node to the system voltage, and construct the voltage sensitivity matrix.

[0180] 3.3 Generate the initial population according to formula (24) in the joint coding structure, including node number, capacity vector and mask vector.

[0181] 3.4 Calculate the objective function for each particle according to formula (12).

[0182] 3.5 Perform probabilistic time-series power flow calculations on the distribution network, check whether individuals in the population meet the constraints, determine whether individuals meet the chance constraint confidence requirements based on the law of large numbers, extract the maximum voltage limit, current carrying capacity and reverse load rate, and construct a penalty term according to formula (19).

[0183] 3.6 According to formula (20), the non-dominated solutions that satisfy the constraints in the initial population are added to the external elite solution set as the initial value of the Pareto solution set.

[0184] 3.7 Determine if the iteration count has been reached. If it is less than the iteration count, update the particle velocity and position, and return to step 3; if the iteration requirements have been met, output the final optimal photovoltaic grid connection scheme set.

[0185] The specific solution process is as follows: Figure 2 As shown.

[0186] Step 5: Conduct simulation experiments on the IEEE 33-bus system.

[0187] 5.1 Example Description

[0188] This invention conducts a distributed photovoltaic carrying capacity assessment and analysis based on the IEEE 33-node distribution network system, whose topology is as follows: Figure 3As shown in the figure. To fully reflect the spatial distribution characteristics of photovoltaic (PV) grid connection, except for the first-end node, the remaining 32 nodes are all considered as candidate grid connection points for distributed PV, and all PV units operate at unity power factor. Based on historical load and solar irradiance data for Hubei Province, 10 typical load day scenarios and 10 typical PV output day scenarios were generated, combined into a load-PV joint scenario. The load and PV output curves for each typical day are shown in the figure. Figure 4 , Figure 5 As shown, the corresponding probabilities of occurrence are listed in Table 1:

[0189] Table 1. Probabilities for each scenario

[0190]

[0191] The simulation parameters are shown in Table 2:

[0192] Table 2 Simulation Parameters

[0193]

[0194] All simulation calculations were performed in the Matlab 2022b environment using an i7-9700 3.00GHz, 64-bit Windows system platform.

[0195] 5.2 Process Simulation

[0196] The multi-objective convergence curve and Pareto non-dominated solution set obtained by this invention are as follows: Figure 6 , Figure 7 As shown.

[0197] The multi-objective convergence curves show that as the comprehensive distribution characteristic deviation of distributed photovoltaic (PV) grid connection schemes gradually decreases, the total grid-connected capacity of PV gradually converges to a larger value. The Pareto non-dominated solution set indicates that the total grid-connected capacity of PV is mainly distributed in the range of 7.2–7.6 MW. This result demonstrates that comprehensively considering the distribution characteristics of distributed PV grid connection schemes during the optimization process helps the distribution network assess its maximum carrying capacity. Subsequent analysis will focus on the scheme with the largest grid-connected capacity in the Pareto non-dominated solution set.

[0198] 5.3 Comparative Simulation

[0199] To verify the effectiveness of the proposed method for assessing the carrying capacity of power distribution networks, the following three methods were designed for comparative analysis.

[0200] Method 1: A method for assessing the carrying capacity of distribution networks without considering the distribution characteristics of distributed photovoltaic power;

[0201] Method 2: A distribution network carrying capacity assessment method based on static power flow calculation, considering the distribution characteristics of distributed photovoltaic power;

[0202] Method 3: A distribution network carrying capacity assessment method that considers the distribution characteristics of distributed photovoltaic power and uses time-series power flow calculation, which is the method of this invention.

[0203] The simulation results obtained by the above three methods are shown in Table 3:

[0204] Table 3 Comparison of simulation results for each method

[0205]

[0206] 5.3.1 Effectiveness Analysis Considering Photovoltaic Distribution Characteristics

[0207] To verify the effectiveness of considering photovoltaic distribution characteristics in the distribution network carrying capacity assessment process, the simulation results of Method 1 and Method 2 in Table 3 are compared.

[0208] As shown in Table 3, the total distributed photovoltaic (PV) capacity connected to the distribution network in Method 2 increased by 29.40% compared to Method 1, and the comprehensive distribution characteristic index deviation of the distributed PV access scheme was smaller. From the perspective of the capacity configuration of each distributed PV access node, compared to Method 1, the PV access capacity distribution in Method 2 is more uniform, without excessive concentration of node capacity, avoiding extreme capacity allocation situations such as the 1.552 MW third node in Method 1, effectively mitigating the risk of local voltage exceedance. Furthermore, Method 1 did not consider the distribution of distributed PV access locations, while Method 2, by introducing a distribution index based on voltage sensitivity, incorporates the spatial layout characteristics of PV access into the optimization process. Through sensitivity analysis, nodes with less impact on voltage are prioritized for access, thereby improving the feasible solution space under voltage constraints.

[0209] The main reason for this result is that Method 1 only aims to maximize the total capacity of distributed photovoltaic access without considering the rationality of its access distribution in the distribution network. Method 2 introduces a comprehensive distribution characteristic index of distributed photovoltaic access scheme, which forces the photovoltaic access to be distributed reasonably in terms of node location and capacity, thereby improving the overall carrying capacity of the system.

[0210] In summary, by introducing photovoltaic distribution characteristic indicators and comprehensively considering the multi-factor influence of node location and capacity configuration, photovoltaic access is made more scientific and reasonable, and the carrying capacity of the distribution network is significantly improved while meeting various operational constraints.

[0211] 5.3.2 Necessity Analysis of Considering Time-Sequence Power Flow Calculation for Carrying Capacity Assessment

[0212] To verify the necessity of using time-series power flow calculation in the distribution network carrying capacity assessment process, the simulation results of Method 2 and Method 3 in Table 3 are compared. Figure 8 ,Figure 7 The voltage status of each node in the distribution network over 24 hours is shown under the optimal distributed photovoltaic access scheme obtained by Method 2 and Method 3.

[0213] As shown in Table 3, the total distributed photovoltaic (PV) capacity in the distribution network accessed by Method 3 is reduced by 12.06% compared to Method 2, while the deviation of the comprehensive distribution characteristic index of the distributed PV access schemes is almost the same. Superficially, the distribution network evaluated by Method 2 has a higher carrying capacity. However, further verification of its operational safety reveals some problems. Method 2 only conducts carrying capacity assessment based on static power flow calculations, specifically selecting and determining the capacity of distributed PV under the conditions of maximum load and maximum PV output. This approach does not consider the coupling relationship between PV and load over a 24-hour time series, which may lead to undetected violations of operational constraints during certain periods. Taking voltage constraints as a safety constraint verification example, a full-time power flow verification was performed on the access scheme based on Method 2. ​ It can be seen that nodes 9, 10, 11, 12, and 13 experienced voltage over-limit phenomena during the period from 13:00 to 14:00.

[0214] The main reason for this problem is that the static calculation conditions relied upon by Method 2 cannot cover the most unfavorable operating conditions throughout the entire day. Especially during the midday period when photovoltaic output is high and load is low, the concentrated access of distributed photovoltaic power may cause voltage rise at some nodes, thus triggering voltage limit exceedance issues. In contrast, Method 3 uses time-series power flow calculations to assess the dynamic changes in photovoltaic output and load demand. It determines the photovoltaic access capacity while ensuring that voltage constraints are met throughout the day. Therefore, although its assessment result is slightly lower, it has higher safety and practical feasibility.

[0215] In summary, by introducing a time-series power flow assessment mechanism, the reliability and security of the carrying capacity assessment results are significantly enhanced, effectively avoiding the overestimation of risks caused by the limitations of static power flow calculation.

[0216] 5.4 Analysis of the impact on the carrying capacity of the distribution network under different confidence levels

[0217] To analyze the impact of voltage constraints, current carrying capacity constraints, and reverse load rate constraints on the distribution network carrying capacity assessment results, the impact of three types of operating constraints on the assessment results under different confidence levels (i.e., the probability of the constraints being met) was set. Specifically, when analyzing the impact of one type of constraint, the confidence level of the other two types of constraints was fixed at 0.95, and only the confidence level of the target constraint was varied, with its value range set between [0.8, 1.0]. The distribution network carrying capacity under the above constraints at different confidence levels is shown in Table 4 below:

[0218] Table 4 Distribution network carrying capacity at different confidence levels

[0219]

[0220] As shown in Table 4, the distribution network's capacity to support distributed photovoltaic (PV) power generation increases as the confidence levels of voltage, current carrying capacity, and reverse load factor constraints gradually decrease. Specifically, when the confidence levels of current carrying capacity and reverse load factor constraints remain constant, and only the confidence level of voltage constraint is relaxed from 1 to 0.80, the PV carrying capacity significantly increases from 7.417 MW to 9.725 MW, a growth rate of 31.12%. In contrast, when the current carrying capacity and reverse load factor constraints are relaxed respectively, the increase in carrying capacity is only 4.76% and 6.11%. Therefore, voltage constraint is the dominant factor affecting the distribution network's carrying capacity, and it has the most significant impact on the capacity of distributed PV power generation.

[0221] In summary, the purpose of this invention is to propose a method for assessing the carrying capacity of a distribution network that considers the characteristics of photovoltaic (PV) distribution. This method simultaneously considers the carrying capacity of PV access locations, capacity distribution, and time-series characteristics. This invention: ① Employs Monte Carlo simulation and K-means clustering to generate typical source-load joint scenarios, achieving effective modeling and simplification of source-load uncertainties; ② Systematically quantifies the impact of PV distribution patterns on the carrying capacity of the distribution network, defines PV distribution characteristic indicators, and comprehensively reflects the PV access status; ③ Introduces a joint-encoding particle structure and designs an improved particle swarm optimization algorithm to solve the above model, balancing the consistency of encoding dimensions with the variability of the number of access nodes, improving global search capabilities and solution feasibility; ④ Introduces time-series power flow calculation and penalty mechanisms to comprehensively evaluate the operational safety and feasibility of the scheme throughout all time periods.

Claims

1. A method for power distribution network carrying capacity assessment considering photovoltaic distribution characteristics, characterized in that, The method comprises the following steps: Step one: source load uncertainty modeling and typical scenario generation; Step two: construction of distribution characteristic index of photovoltaic access state; Step three: establishment of objective function by maximizing total access capacity of distributed photovoltaic and minimizing deviation of comprehensive distribution characteristic index, and time sequence characteristics are considered for time sequence power flow analysis; Step four: improved particle swarm algorithm is used to solve the model; In step two, the distribution characteristic index of photovoltaic access state comprises: Step 2.1: obtain node distribution density; its expression is: （5）； In the formula: is the number of nodes connected to the distributed photovoltaic, is the total number of nodes in the distribution network; Step 2.2: obtain access capacity dispersion degree; its expression is: （6）； wherein: is a set of distributed photovoltaic access nodes, is a node l accessed distributed photovoltaic capacity; Step 2.3: obtain access location dispersion degree; its expression is: （7）； In the formula: , are the voltage amplitudes of the node l , the node m , respectively. Step 2.4: obtain comprehensive distribution characteristic index; its expression is: （8）； （9）； （10）； （11）； In the formula: is the node l is the normalized voltage sensitivity factor; is the normalized sensitivity factor standard deviation of all access nodes; is the voltage of the node l after injecting a unit power, m is the voltage of the node under the original power flow; m is the voltage of the node under the original power flow; m is the normalized voltage sensitivity factor of the node is the sum of the sensitivity factors of all candidate access nodes, is the comprehensive distribution characteristic index of the current scheme, is the empirical reference value, is the deviation of the comprehensive distribution characteristic index. In step three, the objective function is: The objective function is to maximize the total access capacity of distributed photovoltaic and minimize the deviation of comprehensive distribution characteristic index, and the specific operation is: （12）； wherein: is a set of distributed photovoltaic access schemes, wherein , is a node l accessed distributed photovoltaic capacity, is a set of distributed photovoltaic access nodes, is a comprehensive distribution characteristic index deviation.

2. The method of claim 1, wherein, In step one, the following sub-steps are included: Step 1.1: generate photovoltaic output scenario; Step 1.2: reduce scenarios with similar characteristics; In step 1.1, the following sub-steps are included: Step 1.1.1) based on historical data, the kernel density estimation method is used to construct the probability distribution model of photovoltaic output; The probability density function of the probability distribution model of photovoltaic output is: （1）； In the formula: n It is the sample size. h It's the width of the window. K It's a kernel function. For point x The probability density function estimate at point , i It is the sample number. These are sample data points; Step 1.1.2) After obtaining the kernel density function, further obtain the distribution function , set the total number of samples as R , perform Monte Carlo simulation by inverse transform sampling method; Let Substituting into the distribution function, the photovoltaic output is: （2）； Step 1.1.3) Repeat step 1.1.2 R a plurality of photovoltaic power scenarios is generated. R a plurality of photovoltaic power scenarios is generated.

3. The method of claim 2, wherein, In step 1.2, the K-means method is used to reduce scenarios with similar characteristics, and the specific operation is as follows: Let the initial reserved set be where ; the initial reduction set is ; the specific reduction steps are as follows: Step 1.2.1) Randomly select K scenes from the set of scenes as cluster centers, denoted as T K ; where, denotes the Kth cluster center.​​ Step 1.2.2) Assign the scene to the cluster whose cluster center is closest to the scene , to its each cluster center is: （3）； where N refers to the dimension of the data, refers to the i-th coordinate of the j-th data point belonging to the k-th cluster, refers to the i-th coordinate of the j-th data point belonging to the k-th cluster, refers to the i-th coordinate of the j-th data point belonging to the k-th cluster, Step 1.2.3) recalculate the cluster center as the mean value of all scenarios in the cluster: （4）； In the formulae: represents the number of scenes of the cluster ​ Step 1.2.4) repeat step 1.2.2 and step 1.2.3 until the cluster center no longer changes obviously or the maximum iteration number is reached; Step 1.2.5) Select one representative scene from each cluster to generate the reduced set S .

4. The method of claim 1, wherein, In step three, the constraint condition is: Step 3.1: obtain distributed photovoltaic output constraint: （13）； In the formula: is the maximum photovoltaic capacity allowed to access for a single node, refers to any one node ; Step 3.2: obtain power flow constraint: （14）； In the formula: , The first l Distributed photovoltaic systems at individual nodes t Active power and reactive power at all times; , The first l Each node t Active and reactive power of the load at any given time; , They are nodes l , m The electrical conductance and susceptance between them; The phase angle between nodes l and m; for l Node at t Voltage amplitude at any given moment; express m Node in time t The voltage amplitude, where N is the total number of nodes in the network. B Let M be the set of all nodes in the network; M is the set of all branches in the network. Step 3.3: obtain node voltage constraint: The node voltage constraint is described in the form of chance constraint as: （15）； In the formula: represents the probability that the constraint is satisfied; , are the upper and lower limits of the voltage amplitude, respectively; is the confidence level value of the node voltage constraint; Step 3.4: obtain line current carrying capacity constraint: The line current carrying capacity constraint is described in the form of chance constraint as: （16）； wherein: is the line lm at time t; t is the traffic volume at time t; is the maximum traffic volume of the line; is the confidence level value of the line traffic volume constraint; Step 3.5: obtain reverse load rate constraint: When the capacity of distributed photovoltaic accessed in the distribution network is large, the power is sent to the upper grid in the opposite direction; in order to limit the degree of reverse power flow, the reverse load rate constraint is described in the form of chance constraint as: （17）； （18）； wherein: is the reverse load ratio at the time instant t; t is the network loss in the distribution network at the time instant t; is the upper limit of the reverse load ratio; t is the network loss in the distribution network at the time instant t; is the upper limit of the reverse load ratio; is the confidence level value of the reverse load ratio constraint; is the total load power of all load nodes at the time instant t; t is the total load power of all load nodes at the time instant t; m is the total load power of all load nodes at the time instant t; is the total load power of all load nodes at the time instant t; t is the total load power of all load nodes at the time instant t; l is the total load power of all load nodes at the time instant t; is the rated capacity of the distribution transformer.

5. The method of claim 4, wherein, The penalty function method is used to embed constraint conditions formula (15), formula (16) and formula (17) into objective function formula (12); Wherein, the penalty term is expressed as: （19）； The objective function with the penalty function is expressed as: （20）； is a weight associated with the penalty term pen is a weight associated with the bias term is a weight associated with the bias term is a weight associated with the bias term 6. The method of claim 5, wherein, In step four, the improved particle swarm algorithm is used to solve the objective function formula (20); specifically, the following steps are included: Step 4.1: initialize particles; Step 4.2: generate initial particle access capacity; Step 4.3: execute solving operation.

7. The method of claim 6, wherein, In step 4.1, the following steps are included: Step 4.1.1) obtain node number vector: （21）； is the number of the last photovoltaic node, is the maximum number of photovoltaic nodes, is the node number of the l th photovoltaic node; Step 4.1.2) obtain access capacity vector: （22）； In the formula: is the distributed PV capacity of the access node if there is no distributed PV access at the location, then ; Step 4.1.3) obtain mask vector: （23）； In the formula: is the mask value of the l th position, and if it indicates that the position has distributed photovoltaic effective access; Step 4.1.4) define particle triple structure: （24）； In step 4.2, the access capacity of the initial particle is generated, specifically: （25）； In the formula: is a perturbation factor obeying uniform distribution, used for random sampling within a preset capacity range, realizing flexibility and dispersion of capacity configuration, μ( ) represents uniform distribution, represents the maximum allowed access capacity of a single photovoltaic node, represents the minimum value of the perturbation factor, represents the maximum value of the perturbation factor.

8. The method of claim 7, wherein, In step 4.3, the solving operation is performed, including: Step 4.3.1) input the power grid framework parameters, load and photovoltaic typical scene data and algorithm parameters; Step 4.3.2) perform power flow disturbance analysis on the basic network model, numerically calculate the sensitivity of active power injection at each node to the system voltage, and construct a voltage sensitivity matrix; Step 4.3.3) generate the initial population according to formula (24) according to the joint coding structure, including node number, capacity vector and mask vector; Step 4.3.4) calculate the objective function of each particle according to formula (12); Step 4.3.5) perform probabilistic time sequence power flow calculation on the distribution network, check whether the individuals in the population meet the constraints, judge whether the individuals meet the confidence requirement of opportunity constraints according to the law of large numbers, extract the maximum voltage overrun value, load flow and reverse load rate, and construct the penalty term according to formula (19); Step 4.3.6) add the non-dominated solution in the initial population that meets the constraint condition to the external elite solution set according to formula (20) as the initial value of the Pareto solution set; Step 4.3.7) judge whether the iteration number is reached; if less than the iteration number, update the particle speed and position, and return to step 3; if the iteration requirement is met, output the final optimal photovoltaic access scheme set.

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