Distribution Network Cluster Division Method and System Considering Uncertainty and Comprehensive Performance

Abstract

A method and system for clustering distribution networks that considers uncertainty and comprehensive performance, belonging to the technical field of power system planning and optimization, includes: using probability distribution to characterize the random characteristics of distributed energy resources, load demand, and distribution-microgrid interaction power contained in the distribution network, generating multiple scenarios; selecting at least one structural indicator and one functional indicator that characterize cluster performance indicators, and fusing the multiple cluster performance indicators to form a cluster comprehensive performance indicator as a distribution network cluster partitioning model that considers cluster comprehensive performance; performing power flow calculations on the distribution network for the multiple scenarios that characterize uncertainty, substituting the power flow calculation results into the distribution network cluster partitioning model that considers cluster comprehensive performance; and solving the distribution network cluster partitioning model to obtain distribution network cluster partitioning results. The present invention helps improve the autonomy of the cluster from within, reducing problems such as severe network losses and voltage over-limit caused by large-scale transmission of electric energy.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system planning and optimization, and relates to a method for clustering an active distribution network containing multiple microgrids suitable for distribution network planning, operation and analysis. More specifically, it relates to a method and system for clustering an active distribution network containing multiple microgrids that takes into account uncertainty and comprehensive cluster performance. Background Art

[0002] With the continuous advancement of new power system construction, the characteristics of distribution networks are gradually changing from passive to active, unidirectional to bidirectional, and deterministic to random. Their planning and operational objectives are also evolving from improving power supply security to promoting multi-energy integration, complementarity, and multi-faceted interaction. At the same time, the integration of a high proportion of renewable energy and multiple microgrids into active distribution networks has further exacerbated system complexity and uncertainty, posing numerous challenges to the safe and economic operation of distribution networks, such as changes in power flow distribution, power backflow, increased system losses, and excessive node voltages.

[0003] In a distribution network system containing multiple microgrids, dividing and integrating access units such as distributed power sources, loads, and microgrids into clusters with dispatching, control, and autonomy is a solution for achieving and ensuring the orderly, reliable, and efficient integration of large-scale distributed power sources and microgrids into the distribution network. Therefore, clustering an active distribution network containing multiple microgrids can rationally reorganize distributed resources, microgrids, loads, and other resources within the cluster, creating strong coupling within the cluster and weak coupling between clusters, enabling clusters to operate independently and coordinate with each other. Furthermore, the clustering results can provide an important reference for addressing the problems of accommodating high proportions of renewable energy, reactive power shortages and voltage violations caused by grid connection, as well as the site selection and capacity planning of energy storage systems and reactive power compensation equipment. These results also provide guidance for active and reactive power planning in active distribution networks containing multiple microgrids.

[0004] When clustering active distribution networks containing multiple microgrids, clustering metrics are crucial, directly determining the effectiveness of cluster optimization, which in turn impacts the network's operational efficiency, stability, and the effectiveness of active-reactive power coordination planning. Clustering metrics are generally divided into two categories: structural and functional. Structural metrics focus on coupling relationships based on geographic space or electrical distance, meaning that nodes within a cluster are closely connected while inter-cluster relationships are sparse. Functional metrics, on the other hand, focus on the collaborative capabilities of nodes within a cluster, reflecting the cluster's regulatory objectives.

[0005] Generally speaking, each cluster after cluster division needs to meet the following principles:

[0006] (1) Logical principle: there should be no overlapping nodes between clusters, and each node within a cluster must meet physical connectivity requirements;

[0007] (2) Under the functional indicator division, each cluster must have a certain degree of self-coordination ability. The existing cluster indicators take into account the combination of structural indicators and functional indicators including active / reactive power balance, but fail to take into account the level of flexibility supply and demand within the cluster, that is, the flexibility supply and demand matching indicator is not taken into account. In addition, the impact of multiple microgrids on the active distribution network is not fully considered when dividing the cluster.

[0008] Furthermore, when clustering, the typical daily wind and photovoltaic output values, load values, and interaction power values between distribution and microgrids are often selected, ignoring the inherent uncertainty of these factors. However, compared to conventional energy sources, the output and load values of renewable energy sources such as wind and photovoltaic power exhibit significant randomness and volatility. For distribution networks connected to multiple microgrids, the interaction power between distribution networks and microgrids is also uncertain. Therefore, when clustering, it is particularly important to analyze and address the uncertainty of wind power, photovoltaic power, and the interaction power between microgrids and distribution networks.

[0009] In summary, there is an urgent need to provide a cluster partitioning method and system for active distribution networks containing multiple microgrids that takes into account uncertainty and comprehensive cluster performance. Summary of the Invention

[0010] In order to solve the deficiencies in the prior art, the present invention provides a method and system for partitioning a multi-microgrid active distribution network cluster taking into account uncertainty and comprehensive cluster performance.

[0011] The present invention adopts the following technical solutions.

[0012] A first aspect of the present invention provides a method for dividing distribution network clusters taking into account uncertainty and comprehensive performance, wherein the distribution network is an active distribution network set including multiple microgrids, and the method for dividing distribution network clusters comprises the following steps:

[0013] The probability distribution is used to characterize the random characteristics of distributed energy, load demand and interactive power of distribution microgrids contained in the distribution network, and multiple scenarios are generated to characterize the uncertainty of active distribution network containing multiple microgrids.

[0014] At least one structural indicator and one functional indicator are selected to characterize cluster performance indicators, and multiple cluster performance indicators are integrated to form a cluster comprehensive performance indicator as a distribution network cluster partitioning model taking into account the comprehensive performance of the cluster;

[0015] For various scenarios that represent uncertainty, power flow calculations are performed on the distribution network, and the results are substituted into the distribution network cluster partitioning model that takes into account the comprehensive performance of the cluster;

[0016] The distribution network cluster division model is solved to obtain the distribution network cluster division result.

[0017] Preferably, the characterization of uncertainty of an active distribution network containing multiple microgrids specifically includes:

[0018] Determine the probability distribution model of distributed energy, load demand and distribution microgrid interaction power;

[0019] Randomly sample the probability distribution model of distributed energy, load demand, and distribution and microgrid interaction power to generate a set number of scenarios representing different operating states;

[0020] Scenarios representing different operating states are clustered and reduced from the set number to multiple typical representative scenarios.

[0021] Preferably, the characterization of uncertainty of an active distribution network containing multiple microgrids specifically includes:

[0022] Determine the probability distribution model of wind power, photovoltaic power, load demand and distribution network interaction power by analyzing historical data or based on physical models;

[0023] The Monte Carlo method is used to randomly sample the probability distribution model to generate scenarios with different numbers of review groups;

[0024] Apply K-means clustering algorithm to cluster the generated Monte Carlo scenarios with a set number of groups;

[0025] According to the results of K-means clustering, representative cluster centers are selected as the final scene set.

[0026] Preferably, the selecting of at least one structural indicator and one functional indicator representing the cluster performance indicator includes:

[0027] The modularity index is selected as the structural index, and at least one of the active power balance, reactive power balance, and flexibility supply and demand matching index is selected as the functional index.

[0028] Preferably, based on the constructed modularity index of electrical distance of active and reactive sensitivity, active and reactive balance index and flexibility supply and demand matching index, the objective function of the distribution network cluster partitioning model taking into account the comprehensive performance of the cluster is established according to weight fusion.

[0029] Preferably, constructing a modularity index of the electrical distance of active and reactive sensitivity includes: calculating an active voltage sensitivity matrix and a reactive voltage sensitivity matrix, using sensitivity matrix elements to calculate the electrical distance between nodes in the distribution network, constructing an electrical distance matrix, obtaining the maximum value thereof as an edge weight connecting two nodes, and calculating a modularity ρ based on the edge weight as a modularity index;

[0030] Establishing active and reactive power balance indicators includes: establishing an active power balance indicator based on the sum of the net loads of each cluster, and establishing a reactive power balance indicator based on the ratio of the maximum reactive power supply to the demand value within the cluster;

[0031] Constructing a flexibility supply and demand matching index includes: calculating the cluster flexibility demand value based on the upward and downward adjustment of the cluster flexibility demand value, and establishing a flexibility supply and demand matching index.

[0032] Preferably, the integration of multiple cluster performance indicators to form a cluster comprehensive performance indicator as a distribution network cluster partitioning model taking into account the cluster comprehensive performance includes:

[0033] The modularity index, active power balance index, reactive power balance index and flexibility supply and demand matching index are multiplied by their weights respectively and then added together, with the maximum sum as the objective function; among them, the sum of the weights of the modularity index, active power balance index, reactive power balance index and flexibility supply and demand matching index is 1.

[0034] Preferably, solving the distribution network cluster division model to obtain the distribution network cluster division result includes:

[0035] The power type, output and load conditions of each node, as well as the flexibility demand response conditions, are input into the model. Various cluster division methods are encapsulated as populations and solved using a genetic algorithm to obtain the distribution network cluster division results.

[0036] Preferably, the distribution network cluster division method further includes:

[0037] Analyze the clustering results to verify the effectiveness of the proposed clustering method, and use the verified scheme as the clustering scheme;

[0038] The analysis of the cluster division results includes: partially setting the weight coefficients of various indicators to zero or setting them all to non-zero, combining the new energy penetration rate, and judging the operating status of the distribution network system according to the values of the comprehensive performance indicators.

[0039] A second aspect of the present invention provides a distribution network cluster division system taking uncertainty and comprehensive performance into account, which runs a distribution network cluster division method taking uncertainty and comprehensive performance into account according to the first aspect, including:

[0040] An uncertainty processing module is used to characterize the random characteristics of distributed energy resources, load demand, and distribution-microgrid interaction power contained in the distribution network using probability distribution, and generate multiple scenarios that characterize the uncertainty of the active distribution network containing multiple microgrids;

[0041] The power flow calculation module is used to characterize various scenarios of uncertainty and perform power flow calculations on the distribution network;

[0042] A cluster comprehensive performance evaluation module is used to select at least one structural indicator and one functional indicator that characterize cluster performance indicators, and fuse multiple cluster performance indicators to form a cluster comprehensive performance indicator to form a distribution network cluster division model;

[0043] The solver is used to solve the distribution network cluster partitioning model and obtain the distribution network cluster partitioning result.

[0044] Compared to the prior art, the present invention has at least the following beneficial effects: Compared to conventional cluster division approaches, the present invention's cluster division method and system for active distribution networks containing multiple microgrids fully considers the dominant uncertainty factors within active distribution networks containing multiple microgrids and proposes a method for addressing these uncertainties. Furthermore, the present invention proposes comprehensive indicators that consider the degree of flexible supply and demand matching, fully leveraging the cluster's internal structural, active and reactive power coordination capabilities, and flexible response capabilities. This helps improve the cluster's internal autonomy, mitigates severe network losses and voltage over-limit issues caused by large-scale power transmission, and provides a theoretical basis and technical support for active and reactive power planning in active distribution networks containing multiple microgrids. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of a cluster partitioning method for active distribution networks containing multiple microgrids that takes into account uncertainty and comprehensive cluster performance, as proposed by the present invention;

[0046] Figure 2 This is a typical structure of the radial distribution network adopted by the present invention;

[0047] Figure 3 To improve the IEEE33 node system;

[0048] Figure 4 Typical daily scenario data for wind power, photovoltaic power, load, and distribution microgrid interaction power;

[0049] Figure 5 This is the voltage fluctuation data for the 24 hours before photovoltaic and wind power are connected in a typical day scenario;

[0050] Figure 6 This is the 24-hour voltage fluctuation data after photovoltaic and wind power are connected in a typical daily scenario;

[0051] Figure 7 This is the cluster division situation of mode 1;

[0052] Figure 8 This is the cluster division situation of mode 2;

[0053] Figure 9 This is the cluster division situation of mode 3;

[0054] Figure 10 This is the cluster division situation of mode 4;

[0055] Figure 11 Mode 4: The number of clusters is 4;

[0056] Figure 12 Cluster division when the new energy penetration rate is 20%;

[0057] Figure 13 Cluster division when the new energy penetration rate is 60%. DETAILED DESCRIPTION

[0058] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention, not all of them. Based on the spirit of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0059] like Figure 1 As shown, embodiment 1 of the present invention provides a method for clustering active distribution networks containing multiple microgrids taking into account uncertainty and comprehensive cluster performance, comprising the following steps:

[0060] Step 1: Perform uncertainty processing on the interactive power of photovoltaic, wind power, load and distribution microgrid to obtain the final scenario power data.

[0061] Preferably but not limitedly, step 1 specifically includes:

[0062] Step 1.1: Use probability distribution to characterize the random characteristics of distributed energy, load demand, and distribution microgrid interaction power, so as to characterize the uncertainty of the active distribution network containing multiple microgrids. Preferably, but not limited to, the probability distribution model of wind power, photovoltaic power, load demand, and distribution microgrid interaction power is determined by analyzing historical data or based on physical models.

[0063] To characterize the randomness of wind power, Weibull distribution is often used to simulate the randomness of wind speed, which is expressed as follows:

[0064]

[0065] Where:

[0066] v is the wind speed;

[0067] λ is the scale parameter, which controls the extension range of the distribution;

[0068] k is the shape parameter that determines the shape of the distribution.

[0069] The characteristics of the Weibull distribution can well describe the asymmetry of wind speed. The wind speed range is 0-35 (m / s), the scale parameter is 15, and the shape parameter is 2.3.

[0070] The Beta distribution is generally used to model the randomness of photovoltaics. Photovoltaic irradiance (i.e., solar intensity) is generally considered a proportional or probability value between 0 and 1. The Beta distribution can be used to estimate the probability density function at different irradiance levels, thereby understanding the distribution patterns and characteristics of photovoltaic irradiance and providing support for the design and operation of photovoltaic power generation systems. Specifically, the probability density function of the Beta distribution is expressed as follows:

[0071]

[0072] Where:

[0073] B(α,β) is the Beta function, which is a normalizing constant that ensures the total probability of the distribution is 1.

[0074] The normal distribution is generally used to characterize the randomness of load demand and the interactive power between distribution and microgrids. This is based on multiple practical and theoretical reasons. The variations in load and interactive power between distribution and microgrids are the result of multiple factors, which are inherently independent and additive. This allows load data to be approximated using a normal distribution.

[0075] It is understandable that the normal distribution (Normal), also known as the Gaussian distribution, is one of the most important distributions in statistics. It has the characteristics of a bell-shaped curve. The probability density function of the normal distribution is expressed as follows:

[0076]

[0077] Where:

[0078] x is a random variable;

[0079] μ is the mean;

[0080] σ is the standard deviation.

[0081] In step 1.2, a large number of random samples are randomly sampled from the above probability distribution using the Monte Carlo method to generate 500 different scenarios. Each sampled scenario represents a possible system operating state, including PV and wind power output, load demand, and interactive power scenario data between the microgrid and the distribution network.

[0082] In step 1.3, the K-means clustering algorithm is used to cluster the 500 generated Monte Carlo scenarios. The goal is to aggregate a large number of random scenarios into a number of representative scenarios. Each cluster represents a class of similar scenarios, such as similar wind speed, light intensity, load demand, and interaction power.

[0083] In step 1.4, based on the K-means clustering results, select representative cluster centers as the final scenario set. Calculate the probability of each scenario cluster and, based on the scenario data and scenario probabilities, obtain the final PV, wind power, load, and distribution network interaction power data.

[0084] As one of the outstanding substantive features of the present invention, scenario generation and reduction through the probability distribution model of wind power, photovoltaic power, load demand and distribution microgrid interactive power combined with the Monte Carlo method and the K-means clustering algorithm is an effective method for dealing with the dominant factors of uncertainty.

[0085] Specifically, probabilistic models effectively describe the stochastic characteristics of distributed energy resources, loads, and interactive power. Monte Carlo methods generate diverse scenarios through a large number of random samples to simulate the various possible variations of uncertain factors. The K-means clustering algorithm is used to extract representative scenarios from the massive amount of generated scenarios, thereby reducing computational complexity and improving optimization efficiency.

[0086] Therefore, one of the significant advances of this invention over the prior art lies in its approach to uncertainty management, which effectively reduces computing resource consumption while ensuring that uncertainty is fully accounted for. This approach is particularly applicable to the scheduling and planning of complex systems. In particular, it can better address system uncertainty and volatility in scenarios with multiple microgrids and a high proportion of renewable energy access.

[0087] Step 2: Based on the obtained data and system parameters, the power flow calculation of the active distribution network containing multiple microgrids is performed to obtain the basic data required for cluster division.

[0088] Step 3: Select at least one indicator from each of the structural indicators and functional indicators to characterize cluster performance, and integrate multiple cluster performance indicators to form a cluster comprehensive performance indicator. Establish a distribution network cluster division model based on the cluster comprehensive performance indicator. Preferably, but not limited to, establish a distribution network cluster division model with modularity, active / reactive power balance, and flexibility supply and demand matching as cluster comprehensive performance indicators.

[0089] Preferably but not limiting, step 3 specifically includes:

[0090] Step 3.1: Construct the modularity index, active power and reactive power balance index, and flexibility supply and demand matching index respectively.

[0091] Further preferably but not limiting, step 3.1 specifically includes:

[0092] A. Construct a modularity index for electrical distance based on active and reactive sensitivity.

[0093] The modularity index based on electrical distance is used as a structural index. The larger the modularity value, the closer the internal connection of the cluster. Unlike traditional community partitioning techniques, this approach can quantify the strength of the community structure in the network without having to determine the number of communities in advance, solving the problem of complex networks in community partitioning. An improved modularity function with electrical distance as the weight is used to characterize the degree of electrical coupling between nodes in the distribution network, expressed as follows:

[0094]

[0095] Where:

[0096] e ij is the weight of the edge connecting node i and node j, referred to as edge weight, which refers to the electrical distance in this invention;

[0097] , is the sum of all edge weights in the network;

[0098] represents the sum of all edge weights connected to node i;

[0099] When nodes i and j are in the same cluster ,otherwise .

[0100] Electrical distance is used to measure the tightness of electrical coupling between two nodes in the network. It is generally obtained by the sensitivity relationship between voltage and active and reactive power. Specifically, the power flow calculation correction equation in the polar coordinates of the distribution network is expressed as follows:

[0101]

[0102] Where:

[0103] ΔP and ΔQ are the changes in active power and reactive power of the node respectively;

[0104] Δθ and ΔU are the changes in the node voltage phase angle and amplitude, respectively;

[0105] J is the Jacobian matrix for power flow calculation;

[0106] H, N, M, and L are the corresponding Jacobian sub-matrices. Expand the above formula to express it as follows:

[0107]

[0108] After eliminating Δθ, it can be expressed as follows:

[0109]

[0110] Where:

[0111] S P 、S Q They are active voltage sensitivity matrix and reactive voltage sensitivity matrix respectively, and the element S in row i and column j is Pij 、S Qij are the changes in the voltage at node i when the active and reactive powers at node j change by unit value.

[0112] Considering the mutual influence between nodes, the electrical distance between nodes in the distribution network can be represented by the following formula:

[0113]

[0114] Where:

[0115] D ij 、D ji are the electrical distances between nodes i and j;

[0116] d ij It represents the degree of influence of the power change injected into node j on the voltage of node i, where power includes active power and reactive power.

[0117] Therefore, the modularity index It is expressed as the following formula:

[0118]

[0119] Where:

[0120] max(D ij ) is the maximum value in the electrical distance matrix.

[0121] B. Construct active power balance index.

[0122] In order to give priority to the autonomous capabilities within the cluster and avoid serious network losses caused by large-scale transmission of electric energy, the active power balance index is used to divide the nodes in the distribution network.

[0123] For the divided clusters, in the entire planning or scheduling period T, cluster c in each scheduling time period t is divided into i The net load of each node is summed up to get P net,ci (t), and find the maximum cluster net load max(P net,ci(t)). Then the active power balance index is expressed as follows:

[0124]

[0125]

[0126] Where:

[0127] P net,ci For cluster c i Active power balance value;

[0128] γ P is the active power balance index,

[0129] C is the number of clusters divided.

[0130] C. Construct reactive power balance index.

[0131] To address voltage over-limit control issues, the cluster should also have a certain voltage regulation capability. Therefore, it is necessary to set a reactive power balance index.

[0132] Consider the impact of distributed photovoltaic and wind power access to the distribution network nodes. Among them, wind power only considers its output active power, while photovoltaic can output active power and can also output or absorb reactive power. PV If the photovoltaic output active power P is PV,t When , the reactive power that photovoltaic can output or absorb is expressed as follows:

[0133]

[0134] Where:

[0135] Q PV,t The reactive power output of photovoltaic.

[0136] Taking the radial distribution network as an example, the impact of large-scale photovoltaic and wind power access to the distribution network on node voltage and line network loss is analyzed. Its typical structure is as follows Figure 2 As shown. Figure 2 In the example, there are N users distributed along the line, and the reactance between the i-th and j-th users is R j +jX j The voltage at the beginning of the line is U0, and the voltage at the i-th user is U i , load power is expressed as P j +jQ j , photovoltaic power generation is expressed as P PV +jQ PV , wind power generation power is expressed as P WG .

[0137] When photovoltaic and wind power are not connected, the voltage difference ΔU between line nodes i and j j It is expressed as the following formula:

[0138]

[0139] Where:

[0140] U i 、U j are the voltages of nodes i and j respectively;

[0141] Ω j is the set of all nodes from node j to the end of the line;

[0142] P k , Q k are the active power and reactive power of each node from node j to the end node of the line respectively.

[0143] It can be seen that when photovoltaic and wind power are not connected, the load of the node is usually positive, so ΔU j It is positive, indicating that the node voltage is gradually decreasing with the transmission of the line, that is, the node voltage gradually decreases along the line starting from the root node.

[0144] When photovoltaic and wind power are connected to each node, the voltage difference between nodes i and j is the voltage difference between nodes i and j, which is expressed as the following formula:

[0145]

[0146] Where:

[0147] Where:

[0148] P PV,k 、P WG,k are the active power of photovoltaic and wind power connected to node k respectively;

[0149] Q PV,k is the reactive power of the photovoltaic connected to node k.

[0150] From the above formula, we can see that when the total output of photovoltaic and wind power at node k exceeds the total load at that node, the voltage at node k along the k line will increase; conversely, if the total output is insufficient to meet the load demand, the voltage will show a downward trend along the line, and undervoltage will occur when the load is too large; if the total output is exactly balanced with the load, no voltage drop will occur on this branch.

[0151] When photovoltaic and wind power are not connected, the system line loss ΔP loss It is expressed as the following formula:

[0152]

[0153] Where:

[0154] Ω N is the number of nodes in the distribution network.

[0155] When photovoltaic and wind power are connected to each node, the system line loss ΔP loss It is expressed as the following formula:

[0156]

[0157] Where:

[0158] Ω N is the number of nodes in the distribution network.

[0159] As can be seen from the above formula, when the total output of photovoltaic and wind power at node k does not exceed the total load at that node, the active power demand at the node is reduced, which can reduce the network loss of the distribution network. Conversely, if the total output exceeds the total load at that node, the excess power will be transmitted upward, increasing the power flow in the line, resulting in increased system network loss and even possible line overload problems.

[0160] Therefore, considering the aforementioned impacts of large-scale photovoltaic and wind power integration at distribution network nodes, the primary consideration is the impact on voltage overshoot. When node voltage is excessively high, the node must increase reactive power demand to reduce the node voltage. Therefore, within the dispatch period T, the moment of most severe voltage overshoot at each distribution network node is determined, i.e., the moment when photovoltaic and wind power output is at its highest. At this moment, the reactive power supply within the cluster should meet the local reactive power demand as much as possible, while also reducing reactive power transfer across clusters.

[0161] The reactive balance index setting is expressed as follows:

[0162]

[0163]

[0164] Where:

[0165] Q ci For cluster c i Reactive power balance;

[0166] γ Q It is the reactive balance index;

[0167] Q ci,sup The maximum reactive power supply within the cluster, including the reactive power provided by the node reactive power compensation device and the reactive power that can be provided by the photovoltaic inverter;

[0168] Q ci,needis the reactive power demand value within the cluster.

[0169] It should be noted that Q ci,need It not only refers to the normal reactive power demand of the node, but also includes the minimum reactive power demand required when the voltage of each node exceeds the limit most seriously within the scheduling period T, that is, when the output of photovoltaic and wind power is the largest. It is expressed as follows:

[0170]

[0171] Where:

[0172] Q ci,V To adjust cluster c i Minimum reactive power required at the overvoltage node;

[0173] ΔU j is the difference between the voltage value of node i at the most serious voltage exceeding limit moment t and the voltage value when no photovoltaic or wind power is connected;

[0174] S Q,ii is the reactive voltage sensitivity of node i with respect to itself.

[0175] D. Construct a flexibility supply and demand matching indicator.

[0176] Power system flexibility, as a supplement to active power balance, focuses on addressing fluctuations in system power over a specific timescale. Fluctuations in both source and load require the use of flexible resources. Insufficient system flexibility creates the risk of wind curtailment and load shedding. Quantifying power system flexibility requires determining flexibility requirements.

[0177] The volatility and uncertainty of renewable energy and load are the main sources of node flexibility demand. Therefore, the node flexibility demand is expressed as the sum of the fluctuation of the node net load and the difference between the load and renewable energy forecast errors on a quantitative time scale, expressed as follows:

[0178]

[0179] Where:

[0180] F i,t is the flexibility requirement of node i at time t;

[0181] P net,i,t is the net load of node i at time t;

[0182] e res,i,t 、e l,i,t is the prediction error of the renewable energy output and load of node i at time t.

[0183] Further, based on the direction of net load fluctuation, flexibility demand can be divided into upward flexibility demand and downward flexibility demand. Specifically, it can be expressed as follows:

[0184]

[0185] Where:

[0186] F up,i,t To adjust flexibility requirements upwards;

[0187] F down,i,t To lower the flexibility requirements.

[0188] It can be seen from the above formula that the system's upward and downward flexibility requirements at any time must not be less than 0.

[0189] The flexibility of a cluster is defined as follows: in the power balance at the time scale of interest, the cluster optimizes and deploys various flexibility resources within the cluster to adapt to the flexibility requirements of power increase or decrease.

[0190] Therefore, the cluster's flexibility supply and demand matching index is expressed as follows:

[0191]

[0192]

[0193]

[0194] Where:

[0195] F up,ci 、F down,ci Cluster c i The upward and downward flexibility requirements;

[0196] F ci For cluster c i Flexibility requirement value;

[0197] γ F For flexible supply and demand matching.

[0198] Step 3.2: Based on the modularity index of the electrical distance of active and reactive sensitivity, the active and reactive balance index, and the flexibility supply and demand matching index constructed in step 3.1, the objective function is established by integration.

[0199] Based on the above analysis of the cluster division indicators, in order to give full play to the cluster's active and reactive autonomy and flexible response capabilities, the objective function ψ is established by comprehensively considering the modularity, active power balance, reactive power balance, and flexible supply and demand matching indicators. It is expressed as the following formula:

[0200]

[0201] Where:

[0202] λ1, λ2, λ3, and λ4 are the weight coefficients of each indicator, and they satisfy λ1+λ2+λ3+λ4=1.

[0203] Among the various indicators, modularity, based on electrical distance and active and reactive power sensitivity, ensures system structure and is the most fundamental metric, generally carrying a significant weight. Active and reactive power balance are fundamental to achieving a certain level of coordination within the cluster and hold a relatively important position among the various functional indicators. On top of achieving power balance within the cluster, the weighting of the flexible supply-demand matching indicator can be fully considered.

[0204] Step 3.3: Solve the objective function established in step 3.2.

[0205] Clustering algorithms can generally be categorized into clustering algorithms, optimization algorithms, and community discovery in complex networks. Genetic algorithms are one of the most commonly used optimization algorithms for solving clustering problems. Traditional genetic algorithms use fixed crossover and mutation probabilities. High-quality and low-quality individuals undergo crossover and mutation operations with the same probability. As the number of iterations increases, the resulting clusters become increasingly close, and the fixed crossover probability loses its meaning, thus reducing the algorithm's global search capability and convergence speed. Therefore, adaptive operations are employed, with dynamically changing mutation and crossover probabilities. As the number of iterations increases, the mutation probability should be gradually increased to improve the algorithm's global search capability, while the crossover probability should be gradually decreased to enhance convergence.

[0206] The specific cross-mutation adaptive adjustment is expressed as follows:

[0207]

[0208] Where:

[0209] p c and p m are the crossover and mutation probabilities, respectively;

[0210] p c,max 、p c,min are the maximum and minimum values of the crossover probability respectively;

[0211] p m,max 、p m,min The maximum and minimum values of the mutation probability respectively;

[0212] I is the number of iterations;

[0213] Imax is the maximum number of iterations;

[0214] f is the larger fitness value of the two individuals undergoing the crossover operation;

[0215] f m is the individual fitness value for the mutation operation;

[0216] f avg is the average fitness of the population.

[0217] The specific process of improving the adaptive genetic algorithm to solve the cluster partition problem is as follows: Figure 1 As shown in the figure, the basic input parameters include the power source type, output, and load of each node in the system, as well as the flexibility demand response. The final clustering objective function serves as the fitness function of the improved genetic algorithm to determine the quality of individuals in the group, thereby achieving the survival of the fittest. The algorithm terminates when the fitness of the optimal individual reaches a given threshold or the number of iterations reaches a preset value. The final clustering results serve as the basis for cluster division.

[0218] Step 4: Analyze the results of clustering to verify the effectiveness of the proposed clustering method.

[0219] In order to verify the influence of different indicators on the cluster division results, the following multiple weight setting modes are constructed, and the values of various indicators after cluster division are compared and analyzed to analyze the influence of different functional indicators on cluster division.

[0220] The specific weight setting mode is as follows:

[0221] Mode 1: λ1=1, λ2=λ3=λ4=0, i.e., only structural indicators;

[0222] Mode 2: λ1=0.5, λ2=0.5, λ3=λ4=0, that is, only the active power balance within the cluster is taken into account;

[0223] Mode 3: λ1=0.4, λ2=λ3=0.3, λ4=0, which comprehensively considers the active and reactive power balance within the cluster, but does not consider the flexibility of supply and demand matching;

[0224] Mode 4: λ1=0.4, λ2=0.3, λ3=λ4=0.15, which comprehensively considers all the proposed indicators.

[0225] Considering the impact of different proportions of renewable energy grid connection at each node on cluster division, we set cluster divisions based on all indicators with renewable energy penetration rates of 20%, 60%, and 100%. We also analyze the impact of different renewable energy penetration rates on cluster division.

[0226] The specific setting modes are as follows:

[0227] Model 5: New energy penetration rate is 20%;

[0228] Model 6: New energy penetration rate is 60%;

[0229] Model 7: New energy penetration rate is 100%.

[0230] Step 5: Adopt this cluster division scheme through verification.

[0231] It is worth noting that Example 1 provides a method for clustering active distribution networks containing multiple microgrids, taking into account uncertainty and the overall performance of the cluster. The steps are performed according to strict logic, and the steps cannot be simply split or omitted to perform cluster division. Based on the results of cluster division under all steps, the active power, reactive power, and flexibility supply and demand matching index values within the divided clusters can provide an important reference for the subsequent site selection and sizing of active and reactive power source planning for the distribution network, as well as the operation and scheduling of the distribution network.

[0232] Embodiment 2 of the present invention provides a system for clustering an active distribution network including multiple microgrids taking into account uncertainty and comprehensive cluster performance, and executes the method for clustering an active distribution network including multiple microgrids taking into account uncertainty and comprehensive cluster performance as described in embodiment 1, including:

[0233] Uncertainty processing module, used to process uncertainty of power data and obtain its final scene power data;

[0234] The power flow calculation module is used to perform power flow calculation on the scene power data and distribution network parameters to obtain cluster division data;

[0235] Cluster comprehensive performance evaluation module, used to establish a distribution network cluster division model based on cluster division basic data;

[0236] The solver is used to solve the distribution network cluster partitioning model and obtain the distribution network cluster partitioning result.

[0237] Embodiment 3 of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the method for cluster division of an active distribution network containing multiple microgrids taking into account uncertainty and comprehensive cluster performance according to embodiment 1 is implemented.

[0238] Embodiment 4 of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the method for partitioning a cluster of an active distribution network containing multiple microgrids taking into account uncertainty and comprehensive cluster performance as described in embodiment 1 is implemented.

[0239] In order to verify the effectiveness of the clustering method proposed in this invention, we use Figure 3The improved IEEE33-node system shown in the figure is used for example analysis.

[0240] The system consists of 8 photovoltaic nodes, 7 wind power nodes, 5 reactive compensation device nodes, and 3 nodes connected to the microgrid. The photovoltaic installed capacity in the system is 400kW, the wind power installed capacity is 200kW, and the maximum exchange power between the microgrid and the distribution network is 150kW. Through the proposed uncertainty processing method, the typical daily scenario data of wind power, photovoltaic power, load and distribution network interaction power are obtained as follows Figure 4 shown.

[0241] After the flow calculation and analysis, the 24h voltage fluctuation data before and after photovoltaic and wind power are connected are obtained. Figure 5 and Figure 6 shown.

[0242] In this scenario, it can be seen that nodes experience significant active power reverse flow during the peak sunlight hours of midday, leading to severe voltage overshoots. Calculations show that 2:00 PM is when photovoltaic and wind power penetration rates are highest, and voltage overshoots are most severe. Therefore, this time is selected to calculate the reactive power balance indicator for cluster partitioning.

[0243] Adaptive genetic algorithm was used with the population size N = 60, the maximum number of iterations Imax = 500, the crossover probability pc = (0.6, 0.8), and the mutation probability pm = (0.01, 0.1) to obtain clustering results under different indicator weights.

[0244] In order to verify the influence of different indicators on the cluster division results, the following multiple weight setting modes are constructed, and the values of various indicators after cluster division are compared and analyzed to analyze the influence of different functional indicators on cluster division.

[0245] The specific weight setting mode is as follows:

[0246] Mode 1: λ1=1, λ2=λ3=λ4=0, i.e., only structural indicators;

[0247] Mode 2: λ1=0.5, λ2=0.5, λ3=λ4=0, that is, only the active power balance within the cluster is taken into account;

[0248] Mode 3: λ1=0.4, λ2=λ3=0.3, λ4=0, which comprehensively considers the active and reactive power balance within the cluster, but does not consider the flexibility of supply and demand matching;

[0249] Mode 4: λ1=0.4, λ2=0.3, λ3=λ4=0.15, which comprehensively considers all the proposed indicators.

[0250] The calculation results of cluster division indicators under different modes are shown in the following table:

[0251] Table 1 Calculation results of various indicators of cluster division under different modes

[0252]

[0253] The corresponding nodes of cluster division in different modes are as follows Figures 7 to 10 As shown:

[0254] As shown in the table, Mode 1, which only considers the modularity structural index, has the best modularity index after cluster division, indicating that the nodes within each cluster are closely connected electrically. However, the active and reactive power balance index after division is low, indicating that the active and reactive power output cannot be effectively coordinated within the cluster, and large-scale power transmission occurs in actual operation.

[0255] Mode 2 takes both modularity and active power balance into consideration, and its active power balance index is improved compared with Mode 1, but the modularity index is relatively sacrificed.

[0256] Mode 3 further considers reactive power balance based on Mode 2. It can be found that compared with the previous two modes, its reactive power matching is effectively improved, while the active power matching effect is still good, but the structural performance is reduced.

[0257] After comprehensively considering all indicators, although the various indicators after cluster division of mode 4 are not the highest compared with the first three modes, its comprehensive indicators are the best among all modes, indicating that after fully considering various indicators, cluster division can achieve the best overall result.

[0258] At the same time, it can be noticed that under the effect of the comprehensive index of mode 4, the distribution network is divided into 3 clusters, while the first 3 modes all generate 4 clusters. In order to eliminate the inconsistency problem caused by the different number of clusters in the comparison of the index values of the above modes, mode 4 is pre-specified to output four clusters and solve the optimal cluster division result. The obtained index values and cluster division nodes are shown in the following table and Figure 11 shown.

[0259] It can be seen that the values of various indicators when the number of clusters is 4 are not as good as when the number is 3. However, compared with modes 1, 2, and 3, the overall performance of the division results under the comprehensive indicators is still better than the division results under a single indicator or fewer indicators.

[0260] Table 2 Calculation results of various indicators under different numbers of clusters in mode 4

[0261]

[0262] The above model describes cluster division when all renewable energy is connected to the grid at each node. Next, we consider the impact of varying renewable energy penetration rates on cluster division, setting cluster divisions based on all indicators, with renewable energy penetration rates of 20%, 60%, and 100%. The results for 100% renewable energy penetration represent those for Model 4.

[0263] The cluster division index results under different new energy penetration rates are as follows:

[0264] Table 3 Calculation results of various indicators under different new energy penetration rates

[0265]

[0266] The corresponding nodes of cluster division under different new energy penetration are as follows Figure 12 、 Figure 13 As shown, Figure 12 This is the cluster division when the new energy penetration rate is 20%. Figure 13 This is the cluster division when the new energy penetration rate is 60%.

[0267] The above results show that the best indicator value is achieved when the renewable energy penetration rate is 60%. Therefore, we can conclude that the system operates best at this point. When the renewable energy penetration rate is too low or too high, the impact on system operation is more severe. This also shows that the clustering indicators can, to a certain extent, reflect the overall system operation status.

[0268] Compared with existing technologies, the present invention offers at least the following benefits: fully considering the dominant factors of uncertainty within active distribution networks containing multiple microgrids and proposing methods for addressing these uncertainties. Furthermore, the present invention proposes comprehensive indicators that consider flexibility, including supply-demand matching, fully leveraging the cluster's internal structural, active and reactive power coordination, and flexible response capabilities. This helps improve the cluster's internal autonomy, mitigates the severe network losses and voltage over-limit issues associated with large-scale power transmission, and provides a theoretical basis and technical support for active and reactive power planning in active distribution networks containing multiple microgrids.

[0269] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A method for dividing distribution network clusters into considerations of uncertainty and comprehensive performance, wherein the distribution network is an active distribution network including multiple microgrids, and the method for dividing distribution network clusters into considerations of uncertainty and comprehensive performance, wherein the method comprises the following steps: The probability distribution is used to characterize the random characteristics of distributed energy, load demand and interactive power of distribution microgrids contained in the distribution network, and multiple scenarios are generated to characterize the uncertainty of active distribution network containing multiple microgrids. At least one structural indicator and one functional indicator are selected to characterize cluster performance indicators, and multiple cluster performance indicators are integrated to form a cluster comprehensive performance indicator as a distribution network cluster partitioning model taking into account the comprehensive performance of the cluster; among them, the modularity indicator is selected as the structural indicator, and at least one of the active power balance, reactive power balance, and flexibility supply and demand matching indicators is selected as the functional indicator; For various scenarios that represent uncertainty, power flow calculations are performed on the distribution network, and the results are substituted into the distribution network cluster partitioning model that takes into account the comprehensive performance of the cluster; The distribution network cluster division model is solved to obtain the distribution network cluster division result.

2. A distribution network cluster division method considering uncertainty and comprehensive performance according to claim 1, characterized in that: The uncertainty characterization of the active distribution network containing multiple microgrids specifically includes: Determine the probability distribution model of distributed energy, load demand and distribution microgrid interaction power; Randomly sample the probability distribution model of distributed energy, load demand, and distribution and microgrid interaction power to generate a set number of scenarios representing different operating states; Scenarios representing different operating states are clustered and reduced from the set number to multiple typical representative scenarios.

3. A distribution network cluster division method taking uncertainty and comprehensive performance into account according to claim 1 or 2, characterized in that: The uncertainty characterization of the active distribution network containing multiple microgrids specifically includes: Determine the probability distribution model of wind power, photovoltaic power, load demand and distribution network interaction power by analyzing historical data or based on physical models; The Monte Carlo method is used to randomly sample the probability distribution model to generate scenarios with different set numbers; Apply K-means clustering algorithm to cluster the generated Monte Carlo scenarios with a set number of groups; According to the results of K-means clustering, representative cluster centers are selected as the final scene set.

4. The method for dividing distribution network clusters taking into account uncertainty and comprehensive performance according to claim 1, characterized in that: Based on the constructed modularity index of electrical distance of active and reactive sensitivity, active and reactive balance index and flexibility supply and demand matching index, the objective function of the distribution network cluster division model taking into account the comprehensive performance of the cluster is established according to weight fusion.

5. The method for dividing distribution network clusters taking into account uncertainty and comprehensive performance according to claim 4, characterized in that: Constructing a modularity index for electrical distance of active and reactive sensitivity includes: calculating an active voltage sensitivity matrix and a reactive voltage sensitivity matrix, using the sensitivity matrix elements to calculate the electrical distance between nodes in the distribution network, constructing an electrical distance matrix, obtaining the maximum value as the edge weight connecting two nodes, and calculating the modularity ρ based on the edge weight as the modularity index; Establishing active and reactive power balance indicators includes: establishing an active power balance indicator based on the sum of the net loads of each cluster, and establishing a reactive power balance indicator based on the ratio of the maximum reactive power supply to the demand value within the cluster; Constructing a flexibility supply and demand matching index includes: calculating the cluster flexibility demand value based on the upward and downward adjustment of the cluster flexibility demand value, and establishing a flexibility supply and demand matching index.

6. The method for dividing distribution network clusters taking into account uncertainty and comprehensive performance according to claim 5, characterized in that: The cluster comprehensive performance index formed by integrating multiple cluster performance indicators as a distribution network cluster division model taking into account the comprehensive performance of the cluster includes: The modularity index, active power balance index, reactive power balance index and flexibility supply and demand matching index are multiplied by their weights respectively and then added together, with the maximum sum as the objective function; among them, the sum of the weights of the modularity index, active power balance index, reactive power balance index and flexibility supply and demand matching index is 1.

7. The method for dividing distribution network clusters taking into account uncertainty and comprehensive performance according to claim 6, characterized in that: Solving the distribution network cluster division model to obtain the distribution network cluster division result includes: The power type, output and load conditions of each node, as well as the flexibility demand response conditions, are input into the model. Various cluster division methods are encapsulated as populations and solved using a genetic algorithm to obtain the distribution network cluster division results.

8. The method for dividing distribution network clusters taking into account uncertainty and comprehensive performance according to claim 7, characterized in that: The distribution network cluster division method further includes: Analyze the clustering results to verify the effectiveness of the proposed clustering method, and use the verified scheme as the clustering scheme; The analysis of the cluster division results includes: partially setting the weight coefficients of various indicators to zero or setting them all to non-zero, combining the new energy penetration rate, and judging the operating status of the distribution network system according to the values of the comprehensive performance indicators.

9. A distribution network cluster division system taking uncertainty and comprehensive performance into account, running a distribution network cluster division method taking uncertainty and comprehensive performance into account according to any one of claims 1 to 8, characterized in that: include: An uncertainty processing module is used to characterize the random characteristics of distributed energy resources, load demand, and distribution-microgrid interaction power contained in the distribution network using probability distribution, and generate multiple scenarios that characterize the uncertainty of the active distribution network containing multiple microgrids; The power flow calculation module is used to characterize various scenarios of uncertainty and perform power flow calculations on the distribution network; A cluster comprehensive performance evaluation module is used to select at least one structural indicator and one functional indicator that characterize cluster performance indicators, and fuse multiple cluster performance indicators to form a cluster comprehensive performance indicator to form a distribution network cluster division model; The solver is used to solve the distribution network cluster partitioning model and obtain the distribution network cluster partitioning result.

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