Low-voltage area topology-based power distribution line voltage quality real-time monitoring method

Abstract

The application relates to the technical field of voltage quality monitoring, in particular to a power distribution line voltage quality real-time monitoring method based on a low-voltage transformer area topology, which comprises the following steps: based on the historical output power of each distributed photovoltaic in the power grid topology structure of the low-voltage transformer area, a probability density distribution model is established, the distributed photovoltaic is classified, and the weight coefficients of each distributed photovoltaic are quantified, and the typical probability distribution model corresponding to each category is extracted; the fluctuation range of the output power is divided into multiple focal element intervals, and a basic trust degree is allocated to the focal element intervals to establish a focal element model of photovoltaic output; a probability interval power flow model is constructed; the probability interval power flow model is solved to obtain an interval solution of the node voltage amplitude, an accumulated trust function curve is constructed through evidence theory, and the quality confidence of the node voltage is obtained, so that the voltage quality of the power distribution line is evaluated. The application effectively improves the identification accuracy and early warning response capability of the voltage out-of-limit risk of the power distribution line.

Description

Technical Field

[0001] This application relates to the field of voltage quality monitoring technology, specifically to a method for real-time monitoring of voltage quality of distribution lines based on low-voltage distribution area topology. Background Technology

[0002] With the construction of new power systems, renewable energy sources, represented by distributed photovoltaic power, are being integrated into low-voltage distribution transformer areas on a large scale. The strong randomness of their output, coupled with the uncertainty of load consumption, leads to a complex bidirectional flow characteristic in the power flow distribution of the transformer areas, making the problem of voltage exceeding limits in the transformer areas increasingly serious.

[0003] Traditional power flow calculation methods for distribution networks, such as probabilistic power flow calculation, are prone to inaccurate results when load statistics are scarce, while interval power flow calculation completely discards the high-value probabilistic data accumulated by photovoltaics, resulting in overly conservative assessment results. Existing probabilistic interval power flow methods, by dividing photovoltaic output with rich probabilistic information into covariate intervals with basic confidence levels, and combining them with load intervals that only have upper and lower limits, can solve the problem of fusion calculation of multi-source heterogeneous uncertain variables to a certain extent. However, the covariate interval division generally adopts a simple equal-width division strategy. In reality, the output of distributed photovoltaics is affected by seasonal changes, sudden weather changes, etc., and has significant non-uniform probability distribution characteristics. The equal-width covariate division scheme cannot dynamically respond to changes in the distribution pattern of photovoltaic output, resulting in insufficient accuracy in the characterization of areas with high probability density and waste of computational resources in areas with low probability density. The accuracy of the assessment results fluctuates drastically under different operating scenarios, making it difficult to accurately identify extreme voltage over-limit risks. Summary of the Invention

[0004] To address the aforementioned technical issues, a method for real-time monitoring of power distribution line voltage quality based on low-voltage distribution area topology is provided.

[0005] The solution to the technical problem presented in this application is to provide a method for real-time monitoring of power line voltage quality based on low-voltage distribution area topology, comprising the following steps:

[0006] Based on the historical output power of each distributed photovoltaic (PV) in the power grid topology of the low-voltage distribution area, a probability density distribution model is established. The morphological distribution characteristics of the probability density distribution models of different distributed PVs are judged to classify distributed PVs. Based on the classification results, the distribution differences of the probability density distribution models of different distributed PVs and the reliability of historical data are analyzed to quantify the weight coefficients of each distributed PV. Thus, the probability density distribution models of all distributed PVs under the same category are weighted and fused to extract the typical probability distribution models corresponding to each category.

[0007] Based on the cross-boundary characteristics of different typical probability distribution models and the equal division characteristics of their own probabilities, the fluctuation range of output power is divided into multiple coke element intervals, and basic confidence is assigned to them to establish a coke element model of photovoltaic power output.

[0008] A load interval model is established based on the historical load data of each node in the power grid topology. This model, along with the coke element model of photovoltaic power output, is then substituted into the power flow equation of the distribution network in rectangular coordinates to construct a probabilistic interval power flow model.

[0009] Based on the real-time output power of different distributed photovoltaic systems and the real-time load power at the nodes, the probabilistic interval power flow model is solved to obtain the interval solution of the node voltage amplitude. Combined with the basic confidence level, the cumulative confidence function curve is constructed through evidence theory. Based on this curve, the minimum credible probability of the voltage distribution within the qualified range is evaluated to obtain the quality confidence level of the node voltage, and the voltage quality of the distribution line is evaluated.

[0010] Preferably, the step of judging the morphological distribution characteristics of the probability density distribution models of different distributed photovoltaics to classify distributed photovoltaics includes: for each distributed photovoltaic, calculating the skewness coefficient and kurtosis coefficient of the probability density distribution model within a preset power range; combining the skewness coefficient and kurtosis coefficient of each distributed photovoltaic to form a feature vector; and clustering the feature vectors of all distributed photovoltaics in the power grid topology to obtain multiple categories.

[0011] Preferably, the calculation process for the weighting coefficient of each distributed photovoltaic power station is as follows:

[0012] Calculate the KL divergence of the probability density distribution models of any two distributed photovoltaics within the same category, and use it as the amount of information loss;

[0013] The sum of the information loss between each distributed photovoltaic (PV) photovoltaic unit and all other distributed PV photovoltaic units within its category is taken as the cumulative loss degree.

[0014] The sample size of the historical output power of each distributed photovoltaic power generation unit is statistically analyzed; the average sample size of all distributed photovoltaic power generation units within the same category is calculated, and the ratio of the sample size of each distributed photovoltaic power generation unit within each category to this average value is used as the data reliability.

[0015] The weighting coefficients are positively correlated with data reliability, but negatively correlated with cumulative loss.

[0016] Preferably, the division of multiple focal element intervals includes:

[0017] Based on the typical probability distribution model corresponding to each category, calculate its cumulative distribution function, and divide the entire cumulative probability interval [0,1] into multiple sub-intervals according to the principle of equal probability, so that each sub-interval has an equal probability value; extract the output power corresponding to the cumulative probability value of the right boundary of each sub-interval when the cumulative distribution function is equal to the cumulative probability value of each sub-interval, and use it as the equal probability quantile of the typical probability distribution model; gather the equal probability quantiles extracted from all categories into a first set, and count the total number of all equal probability quantiles in the first set as the first quantity;

[0018] Calculate all intersection points of the typical probability distribution models corresponding to any two categories, extract the output power at the intersection points, and define them as isodense quantiles. Form a second set from all isodense quantiles extracted from any two categories, and count the total number of isodense quantiles in the second set as the second quantity.

[0019] If the second quantity is less than or equal to the first quantity, then all isodense quantiles in the second set are retained to form the third set; otherwise, all isodense quantiles in the second set are filtered, and the filtered isodense quantiles are formed into the third set; the union of the first set and the third set is calculated, and all elements in the union and the two endpoints of the preset power interval are arranged in ascending order to form an ordered sequence. The ordered sequence is divided into multiple ordered subsequences, and the preset power interval is divided into multiple focal element intervals according to the boundaries of the ordered subsequences.

[0020] Preferably, the filtering process for all isodense quantiles in the second set includes: arranging all isodense quantiles in the second set in ascending order to form a sequence; using the Jenks optimization algorithm to divide the sequence into multiple subsequences, wherein the number of subsequences is equal to the first number; if each subsequence contains an isodense quantile, then the isodense quantile is directly retained as the representative value of the subsequence; otherwise, the median of all isodense quantiles in the subsequence is taken as the representative value of the subsequence, and the representative values ​​of all subsequences are combined to form a third set.

[0021] Preferably, the allocation of basic trust levels to establish a coke element model for photovoltaic power output includes:

[0022] The number of all distributed photovoltaic (PV) systems in each category is counted, and their proportion in the total number of distributed PV systems in the power grid topology is calculated as the model weight for each category. Based on the model weight, the typical probability distribution models corresponding to all categories are weighted and averaged to form the integrated power output distribution model. The integral value of this integrated power output distribution model in each coke cell interval is calculated as the basic confidence level for each coke cell interval.

[0023] The output coke element model of distributed photovoltaic power generation is formed by each coke element interval and its corresponding basic confidence level.

[0024] Preferably, the establishment of the load interval model includes: setting interval variables with upper and lower limits for the load power of each node in the power grid topology, as the load interval model.

[0025] Preferably, the construction of the cumulative trust function curve includes:

[0026] Based on the real-time power injected by each distributed photovoltaic (PV) system, and using a preset fluctuation error, the fluctuation range of each PV system is determined. Based on the fluctuation range of each PV system, the focal element model is searched to determine all focal element intervals it traverses, which are defined as effective focal elements. The Cartesian product method is used to combine the effective focal elements of all distributed PV systems to form multiple effective focal element combinations, and the joint confidence degree of each effective focal element combination is calculated.

[0027] Based on the real-time load power of each node, and using the preset fluctuation error, a real-time load interval model is established. The real-time load interval model and each effective focal element combination are substituted into the probabilistic interval power flow model to solve the interval solution of the node voltage under the effective focal element combination.

[0028] Based on the interval solutions of the node voltages under all effective focal element combinations and their corresponding joint confidence degrees, the cumulative confidence function curves of the node voltages are constructed using evidence theory.

[0029] Preferably, the process of obtaining the quality confidence of the node voltage is as follows: for the cumulative confidence function curve, extract the cumulative confidence value at the preset lower voltage threshold and the preset upper voltage threshold respectively, and take the difference between the cumulative confidence value at the preset upper voltage threshold and the cumulative confidence value at the preset lower voltage threshold as the quality confidence of the node voltage.

[0030] Preferably, the assessment of the voltage quality of the distribution line includes: if the confidence level of the node voltage quality is less than a preset threshold, then there is a risk of the voltage exceeding the limit; otherwise, there is no risk of the voltage exceeding the limit.

[0031] This application has at least the following beneficial effects:

[0032] This application establishes a probability density distribution model and clusters it using historical output power and nonparametric kernel density estimation. Its advantages lie in its ability to accurately capture the extremely irregular, long-tailed, or skewed characteristics of photovoltaic power output due to factors such as weather shading. Simultaneously, by classifying and clustering its morphological characteristics, it achieves efficient dimensionality reduction from massive historical operating scenarios to typical meteorological models, laying a high-precision data model foundation for subsequent adaptive dynamic evaluation. The weighting coefficients for each distributed photovoltaic unit have the advantage of integrating the common output characteristics of photovoltaic units within the same category with the reliability criteria of probability density estimation, thereby assigning high reliability and... Photovoltaics with smaller distributional differences are given higher weights, allowing the most representative and reliable photovoltaic data to dominate the typical distribution fusion process. This effectively filters out individual noise and statistical bias, improving the accuracy and robustness of subsequent typical distribution models. Extracting typical probability distribution models for each category has the beneficial effect of eliminating individual noise introduced by local micro-meteorological differences, equipment characteristic differences, or random data fluctuations in individual photovoltaic systems. It extracts the pure common distribution structure represented by the output mode of that category, improving the representativeness of the typical distribution models. Based on the cross-boundary characteristics of different typical probability distribution models and their own probability equal division characteristics, [the following steps are taken]. The output power fluctuation range is divided into multiple coulomb intervals. This approach overcomes the shortcomings of traditional equal-width division strategies. The inherent probability-based division allows for finer segmentation in dense probability regions and wider segmentation in flat regions, fully accommodating the non-uniform distribution of photovoltaic power. Furthermore, the cross-boundary features accurately pinpoint the critical watershed where the dominant risk of exceeding limits shifts under different weather conditions. Combining these two approaches and optimizing them with Jenks' algorithm, not only does it adaptively find the physically optimal cutting boundary, but it also gives the resulting coulomb model a highly sensitive ability to identify extreme high-risk scenarios, effectively improving the probability interval power flow calculation for voltage exceeding limits. The advantages of establishing a coulomb model for photovoltaic power output, which improves event capture accuracy and response speed, are that it fully preserves the probabilistic quality information of photovoltaic power output, providing accurate input for subsequent evidence theory synthesis and realizing precise information conversion from probability distribution to coulomb model. Constructing a probabilistic interval power flow model has the advantage that it uses the coulomb model for photovoltaic power to preserve probabilistic information and the interval model for load power with only upper and lower bounds, realizing differentiated modeling of nodes with different levels of information mastery under the same power flow calculation framework. This avoids the dual defects of probabilistic power flow being distorted due to insufficient load information and interval power flow being overly conservative due to wasted photovoltaic information.Solving the probabilistic interval power flow model to construct the cumulative confidence function curve yields the quality confidence of node voltages for evaluating distribution line voltage quality. Its beneficial effect lies in employing evidence theory, considering load interval uncertainties, to obtain the cumulative confidence function curve of node voltages. Using the confidence function as the basis for quality confidence extraction reflects a conservative evaluation principle, effectively improving the accuracy of identifying and responding to voltage exceedance risks in distribution lines. Attached Figure Description

[0033] The following section provides a more detailed description of the real-time voltage quality monitoring method for distribution lines based on low-voltage distribution area topology, in conjunction with the accompanying drawings.

[0034] Figure 1 A flowchart illustrating the steps of a real-time voltage quality monitoring method for distribution lines based on low-voltage distribution area topology provided in this application embodiment;

[0035] Figure 2 A flowchart illustrating the steps of a method for extracting a typical probability distribution model provided in an embodiment of this application. Detailed Implementation

[0036] The following description, in conjunction with the accompanying drawings and embodiments, provides a more detailed explanation of the real-time voltage quality monitoring method for distribution lines based on low-voltage distribution area topology proposed in this application.

[0037] Please see Figure 1 The diagram illustrates a flowchart of a real-time voltage quality monitoring method for distribution lines based on low-voltage distribution area topology, according to an embodiment of this application. The method includes the following steps:

[0038] Step 1: Based on the historical output power of each distributed photovoltaic (PV) in the power grid topology of the low-voltage distribution area, establish a probability density distribution model, determine the morphological distribution characteristics of the probability density distribution models of different distributed PVs to classify distributed PVs, analyze the distribution differences of the probability density distribution models of different distributed PVs and the reliability of historical data based on the classification results, quantify the weight coefficient of each distributed PV, and then perform weighted fusion of the probability density distribution models of all distributed PVs under the same category to extract the typical probability distribution model corresponding to each category;

[0039] Step 2: Based on the cross-boundary characteristics of different typical probability distribution models and the equal division characteristics of their own probabilities, the fluctuation range of output power is divided into multiple coke element intervals, and basic confidence is assigned to them to establish a coke element model of photovoltaic output.

[0040] Step 3: Establish a load interval model based on the historical load data of each node in the power grid topology. Substitute this model and the photovoltaic output coulomb model into the power flow equation of the distribution network in rectangular coordinates to construct a probabilistic interval power flow model. Based on the real-time output power of different distributed photovoltaics and the real-time load power at the nodes, solve the probabilistic interval power flow model to obtain the interval solution of the node voltage amplitude. Combined with the basic confidence level, construct the cumulative confidence function curve through evidence theory. Based on this curve, evaluate the minimum credible probability that the voltage distribution is within the qualified range to obtain the quality confidence level of the node voltage and evaluate the voltage quality of the distribution line.

[0041] Furthermore, in step 1, the specific steps are as follows:

[0042] Based on the parameter information and electrical connection relationships of different electrical equipment in the low-voltage distribution area, the power grid topology of the low-voltage distribution area is constructed.

[0043] In this embodiment, key parameters such as the rated capacity and short-circuit impedance of the distribution transformer are extracted. The conductor type, line length, unit impedance parameter, and phase of each feeder branch in the distribution area are then analyzed. Subsequently, the connection location, connection phase, and rated capacity of each distributed photovoltaic grid connection point and grid node are recorded. Finally, with the low-voltage side busbar of the distribution transformer as the unified topology root node, a grid topology structure for the low-voltage distribution area is established that can completely represent the three-phase four-wire electrical connection relationship, branch impedance parameters, and equipment access information of the distribution area. This provides an accurate physical network skeleton for the subsequent accurate construction of the node admittance matrix and probabilistic interval power flow calculation.

[0044] Collect the output power of each distributed photovoltaic system in the power grid topology during historical periods, including active power output and reactive power output;

[0045] For each distributed photovoltaic system, a probability density distribution model is established based on its output power in historical periods, including a probability density distribution model for active power output and a probability density distribution model for reactive power output.

[0046] Specifically, a probability density distribution model of active power output is established using a non-parametric kernel density estimation method based on the active power output power in historical periods, and a probability density distribution model of reactive power output is established using a non-parametric kernel density estimation method based on the reactive power output power in historical periods.

[0047] In this embodiment, the active and reactive power output of each distributed photovoltaic system over the past year are collected, and the total number of recorded data points is used as the sample size. As for other implementation methods, the implementer can set the sample size according to the actual situation. Since photovoltaic power output is affected by weather, cloud cover, etc., its actual probability distribution shape is very complex and irregular. A non-parametric kernel density estimation method is used to establish a probability density distribution model.

[0048] Due to differences in photovoltaic capacity, before extracting kernel parameters, it is necessary to first obtain the inherent rated installed capacity of each distributed photovoltaic system. Secondly, the active and reactive power outputs extracted within the corresponding historical output cycle are divided by their respective rated installed capacities to obtain per-unit values ​​compressed within a uniform percentage range. These per-unit values ​​are then input into the nonparametric kernel parameter equation to establish a probability density distribution model. The formula for the probability density distribution model of active power output is as follows:

[0049] in, For distributed photovoltaic power with active power output of The probability density estimate at time , In this embodiment, a Gaussian function is selected as the kernel function. For distributed photovoltaics, the first in history The per-unit value of the active power output at each sampling point. The bandwidth is responsible for controlling the smoothness of the density estimation; The total number of all samples within the historical period;

[0050] It should be noted that the nonparametric kernel density estimation method is a well-known technique and will not be elaborated upon here.

[0051] Furthermore, power flow calculation is a fundamental tool for steady-state analysis of power systems. Probabilistic power flow calculation and interval power flow calculation are applicable to two extreme cases: one with sufficient historical statistical information and the other with insufficient historical statistical information in the distribution network. In actual low-voltage distribution area operation, the degree of uncertainty information that operators have access to for different grid nodes often varies. For example, for distributed photovoltaic (PV) systems, a certain amount of historical statistical data is usually accumulated, and the probabilistic information of PV output is relatively rich. However, for the load at the node, only the fluctuation range is known, and detailed probabilistic information is lacking. If the probabilistic power flow method is used for calculation, it is easy to result in inaccurate results due to insufficient statistical information on the node load. If the interval power flow method is used for calculation, it is easy to waste the probabilistic information of PV systems.

[0052] To address the shortcomings of the two aforementioned power flow calculation methods, the probabilistic interval power flow method introduces the mathematical framework of Evidence Theory. Specifically, it discretizes the continuous range of uncertain variables such as photovoltaic active power output into several intervals with basic confidence levels, i.e., coke-element intervals. This achieves the fusion of probabilistic and interval information, ultimately combining Evidence Theory to output the probability-interval distribution of node voltage and branch power flow in the form of probability boxes, providing data support for real-time monitoring of the transformer substation's operating status. However, existing technologies often employ an equal-width partitioning strategy when dividing coke-element intervals, failing to consider the non-uniform probability distribution characteristics of actual photovoltaic output due to factors such as weather. This leads to large fluctuations in calculation accuracy and insufficient ability to distinguish extreme events. To overcome this deficiency and achieve adaptive dynamic partitioning of coke-element intervals, it is necessary to first extract the morphological features of the output probability distribution of distributed photovoltaics and perform similar pattern clustering, specifically:

[0053] For each distributed photovoltaic system, calculate the skewness coefficient and kurtosis coefficient of its active power output probability density distribution model within the preset active power range.

[0054] For each distributed photovoltaic system, calculate the skewness coefficient and kurtosis coefficient of its reactive power output probability density distribution model within the preset reactive power range.

[0055] In this embodiment, the preset active power range is: ,in, , These are the per-unit values ​​corresponding to the minimum and maximum active power output of all distributed photovoltaic systems during a historical period; the preset reactive power range is... ,in, , These are the per-unit values ​​corresponding to the minimum and maximum reactive power output of all distributed photovoltaic systems during historical periods.

[0056] It should be noted that skewness coefficient and kurtosis coefficient are well-known technologies and will not be elaborated upon here. Secondly, regarding active power output, the probability distribution of active power output in distributed photovoltaic (PV) systems typically exhibits asymmetry. Under sunny weather conditions, PV active power output is concentrated in the high-power region, showing a left-skewed distribution. However, under cloudy or rainy weather conditions, PV active power output is concentrated in the low-power region, showing a right-skewed distribution. Therefore, the skewness coefficient is used to reflect the direction and intensity of this asymmetry. A skewness coefficient less than 0 indicates that the active power output of distributed PV is concentrated in the high-power region, requiring vigilance regarding the risk of voltage rise in the distribution area. A skewness coefficient greater than 0 indicates that the active power output of distributed PV is concentrated in the low-power region, which may cause voltage drop in the distribution area. A skewness coefficient equal to 0 indicates that the probability distribution of PV output is... The distribution is perfectly symmetrical, with no obvious bias towards high or low power regions. The kurtosis coefficient reflects the thickness of the probability distribution in the tail region, indicating the probability of extreme events occurring in distributed photovoltaic (PV) systems. For example, continuous cloudy days may lead to persistently low active power output from PV systems, or continuous sunny days may lead to persistently high active power output. If the value is greater than 0, it indicates that the probability of extreme events in PV output is higher than the normal distribution assumption, and PV systems may cause more frequent voltage overruns. If the value is less than 0, it indicates that the probability of extreme events in PV output is lower than the normal distribution assumption, and PV output is relatively concentrated near the mean. If the kurtosis coefficient is equal to 0, it means that the probability of extreme events is completely consistent with the expected standard normal distribution.

[0057] For active power output, the skewness coefficient and kurtosis coefficient of each distributed photovoltaic power generation unit are combined to form a feature vector; the feature vectors of all distributed photovoltaic power generation units in the power grid topology are clustered to obtain multiple categories;

[0058] In this embodiment, for active power output, the Z-score normalization method is used to normalize the skewness coefficient and kurtosis coefficient of all distributed photovoltaic systems. The normalized skewness coefficient and normalized kurtosis coefficient constitute a feature vector. The Z-score normalization method is a well-known technique and will not be described in detail here. Next, the K-means clustering algorithm is used for clustering. The number of clusters is determined by the elbow rule. Both the K-means clustering algorithm and the elbow rule are well-known techniques and will not be described in detail here. Correspondingly, for reactive power output, the same method as for active power output is used for clustering.

[0059] It should be noted that each category corresponds to a photovoltaic active power output mode, and distributed photovoltaics within the same category have similar probability distribution characteristics of active power output.

[0060] Secondly, after determining the active or reactive power output modes of each distributed photovoltaic (PV) system, it is necessary to extract a power output distribution model that represents the common characteristics of the mode from the power output modes characterized by the same category. To avoid distribution estimation bias caused by random data fluctuations or local micro-meteorological differences in a single distributed PV system, it is necessary to perform weighted fusion of the probability density distribution models corresponding to all distributed PV systems within the same category. This eliminates individual-specific noise and extracts the common distribution structure of the mode. Furthermore, the flowchart of the extraction method of the typical probability distribution model provided in this application embodiment is as follows: Figure 2 As shown.

[0061] Calculate the KL divergence of the probability density distribution model of the active power output of any two distributed photovoltaics within the same category, and use it as the amount of information loss;

[0062] It should be noted that KL divergence is a well-known technique and will not be elaborated upon here.

[0063] The sum of the information loss between each distributed photovoltaic (PV) photovoltaic unit and all other distributed PV photovoltaic units within its category is taken as the cumulative loss degree.

[0064] The sample size of active power output of each distributed photovoltaic system during historical periods was statistically analyzed.

[0065] Calculate the average sample size of all distributed photovoltaics within the same category, and use the ratio of the sample size of each distributed photovoltaic in each category to this average value as the data reliability.

[0066] The weighting coefficients of each distributed photovoltaic system are positively correlated with data reliability, but negatively correlated with cumulative loss.

[0067] In this embodiment, the normalized result of the ratio of data reliability to cumulative loss is used as a weighting coefficient. The normalization process is as follows: the sum of the ratios of all distributed photovoltaics within the same category is calculated, and the ratio of the ratio of each distributed photovoltaic within the category to the sum is used as a weighting coefficient. It should be noted that, in order to avoid the denominator being 0 when calculating the ratio, a parameter adjustment factor is added to the denominator. This parameter adjustment factor is set to 1e-6. As another implementation method, the implementer can set it according to the actual situation.

[0068] It should be noted that the smaller the information loss, the more similar the output characteristics of the two photovoltaics are; the smaller the cumulative loss, the more consistent the output distribution of the photovoltaic with most photovoltaics in the cluster, reflecting the degree of commonality of the photovoltaic's output within the cluster. The greater the data reliability, the more historical data the photovoltaic has accumulated, measuring the reliability of the data foundation for probability density estimation. The design of the obtained weighting coefficient follows the dual weighting criterion of information loss and sample size, comprehensively considering the quality and representativeness of the photovoltaic active power output distribution. The sample size of the historical active power output data carried by the photovoltaic reflects the reliability of the active power output probability distribution estimation. Information loss determines whether the photovoltaic can represent the common characteristics of the active power output pattern characterized by this category. The larger this value, the more the photovoltaic has both massive data support and typical characteristics that can represent the common output characteristics of this category, and should occupy a dominant position when weighting and fusing the probability density distribution model.

[0069] Based on the weighting coefficients, the probability density distribution models of active power output of all distributed photovoltaics within the same category are weighted and summed to form the typical probability distribution models corresponding to each category.

[0070] It should be noted that the typical probability distribution model effectively filters out individual-specific noise caused by local micro-meteorological conditions or measurement errors in a single distributed photovoltaic system, and truly reflects the standard statistical law and common probabilistic characteristics of the output of the distributed photovoltaic group under the active power output mode represented by this category.

[0071] Because the fixed-width, equally divided coaxial cell interval strategy struggles to accurately characterize the probability density differences within different output intervals, it suffers from reduced accuracy in high-probability-density regions due to coarse division, and wastes computational resources in low-probability-density regions due to overly fine division. Furthermore, it fails to effectively capture the scene boundary characteristics between different output modes, impacting both the accuracy and efficiency of subsequent probability interval power flow calculations. Therefore, it is necessary to adaptively determine the boundary positions of the coaxial cell intervals based on the probability distribution of photovoltaic active power output. This allows the intervals to automatically densify in high-probability-density regions and sparse in low-probability-density regions, with interval boundaries set at the natural boundaries between different output modes.

[0072] Furthermore, in step 2, the specific steps are as follows:

[0073] Based on the typical probability distribution models corresponding to each category, calculate their cumulative distribution functions, and divide the entire cumulative probability interval according to the principle of equal probability. Divide the data into multiple sub-intervals, such that each sub-interval has an equal probability value;

[0074] In this embodiment, calculating the cumulative distribution function using a probability distribution model is a well-known technique and will not be elaborated further. Secondly, the number of sub-intervals is set to 8; however, in other implementation methods, the implementer can set this number according to actual circumstances. Therefore, the probability value of each sub-interval is... .

[0075] Extract the active power output corresponding to the cumulative probability value of the right boundary of each sub-interval when the cumulative distribution function is equal to the cumulative probability value of each sub-interval, and use it as the equiprobability quantile of this typical probability distribution model;

[0076] It should be noted that if the number of sub-intervals is set to 8, the corresponding cumulative probability values ​​of the right boundary are 1 / 8, 2 / 8, ..., 7 / 8 respectively. For the last sub-interval, the right boundary is 1, which corresponds to the maximum active power output of distributed photovoltaic power, and there is no need to extract the quantiles separately.

[0077] Collect the equal probability quantiles extracted from all categories into a first set, and count the total number of all equal probability quantiles in the first set as the first quantity;

[0078] It should be noted that by using equiprobable quantiles, the interval division is automatically refined in regions with high probability density and automatically coarsened in regions with low probability density, thus achieving adaptive tracking of the photovoltaic power output distribution pattern by the coke element boundary.

[0079] Calculate all intersection points of the typical probability distribution models corresponding to any two categories, extract the active power output at the intersection points, and define them as equal density quantiles. Form a second set from all the equal density quantiles extracted from any two categories, and count the total number of all equal density quantiles in the second set as the second quantity.

[0080] It should be noted that when calculating the intersection point, a simultaneous equation can be established: ,in, For the first Typical probability distribution models for each category For the first Typical probability distribution models corresponding to each category, through... Solving this equation within the range yields the active power output at all intersection points of the two typical probability distribution models. If the active power output at the intersection points... It is a solution to a simultaneous equation. At this point, the two output modes corresponding to the two categories have the same probability density, meaning that the two modes have an equal probability of producing output at that instant. Therefore... It can serve as a natural dividing point between different power output modes; in probabilistic power flow calculations, It can be used as a boundary to divide the running scenarios, in In certain regions, the output mode corresponding to one category contributes more to the risk of voltage exceeding limits in the distribution area. In the region, the output mode corresponding to the other category contributes more to the risk of voltage exceeding limits. Therefore, extracting this intersection point helps to accurately capture extreme risk scenarios in subsequent interval division.

[0081] If the second quantity is less than or equal to the first quantity, then all isodense quantiles in the second set are retained to form the third set; otherwise, all isodense quantiles in the second set are filtered, and the filtered isodense quantiles are used to form the third set.

[0082] The specific selection process is as follows: All isodense quantiles in the second set are sorted in ascending order to form a sequence. The Jenks optimization algorithm is used to divide the sequence into multiple subsequences, where the number of subsequences is equal to the number of subsequences in the first set. If each subsequence contains an isodense quantile, the isodense quantile is directly retained as the representative value of the subsequence. Otherwise, the median of all isodense quantiles in the subsequence is taken as the representative value of the subsequence. The representative values ​​of all subsequences are combined to form the third set.

[0083] It should be noted that the Jenks optimization algorithm is a well-known technique and will not be elaborated here. Secondly, by screening all equal-density quantiles in the second set, redundant points caused by local fluctuations in distribution and discrete sampling are eliminated, ensuring that the final retained third set has a similar order of magnitude to the first set.

[0084] It should be noted that by using the intersection of typical distributions as natural scene boundaries, the focal element boundary can effectively distinguish the differentiated impact of different output modes on voltage over-limit risk.

[0085] Find the union of the first set and the third set, sort all elements in the union and the two endpoints of the preset active power range in ascending order to form an ordered sequence, divide the ordered sequence into multiple ordered subsequences, and divide the preset active power range into multiple focal element intervals according to the boundaries of the ordered subsequences.

[0086] In this embodiment, the Jenks optimization algorithm is used to divide the ordered sequence into 8 ordered subsequences. The left boundary of the first focal element interval is the left endpoint of the preset active power interval. The right boundary of the last focal element interval is the right endpoint of the preset active power interval. For the remaining focal intervals, for example, the right boundary of the nth focal interval is equal to the average of the right boundary of the nth ordered subsequence and the left boundary of the (n+1)th ordered subsequence; the left boundary of the (n+1)th focal interval is equal to the right boundary of the nth focal interval. Therefore, 8 focal intervals are obtained. As other implementation methods, implementers can set them according to the actual situation.

[0087] The number of all distributed photovoltaic (PV) systems in each category is counted, and their proportion in the total number of distributed PV systems in the power grid topology is calculated as the model weight for each category.

[0088] Based on the model weights, the typical probability distribution models corresponding to all categories are weighted and averaged to form the comprehensive power output distribution model. The integral value of this comprehensive power output distribution model in each coke element interval is calculated as the basic confidence level of each coke element interval. Thus, each coke element interval and its corresponding basic confidence level together constitute the active power output coke element model of distributed photovoltaic.

[0089] It should be noted that the sum of the basic confidence levels of all coke element intervals is 1. It should also be noted that after the coke element intervals are discretized to establish a coke element model with probabilistic characteristics, this coke element model is multiplied back by the inherent rated installed capacity of the corresponding distributed photovoltaic at the time of extraction, and restored to a coke element model with physical power having actual absolute operating boundaries.

[0090] Accordingly, based on the probability density distribution model of reactive power output of each distributed photovoltaic power generation unit, and following the construction process of the above-mentioned active power output coke element model, a reactive power output coke element model of distributed photovoltaic power generation unit is established.

[0091] The active power output coke element model and the reactive power output coke element model of distributed photovoltaic power generation are used as the coke element model of photovoltaic power output.

[0092] For the active and reactive loads of each node in the low-voltage distribution area, since we usually only know their fluctuation range and lack detailed probability distribution information, they are treated as simple interval variables.

[0093] Furthermore, in step 3, the specific steps are as follows:

[0094] For each node in the power grid topology, an interval variable with upper and lower bounds is set for its load power, which serves as a load interval model;

[0095] In this embodiment, the load power includes the load active power and the load reactive power, and interval variables with upper and lower limits are set for each, serving as the load interval model. The load interval model is: the load active power at node i... The reactive power of the load at node i ,in, Let i be the lower bound of the active load. Let i be the upper bound of the active load. Let i be the lower bound of the reactive load. This is the upper limit of the reactive load of node i.

[0096] It should be noted that the modeling method of this load interval model only provides the range of values ​​for the variables and does not involve any probability information. It is suitable for situations where there is limited information about the distribution of the variables.

[0097] Based on the conductor type, line length and unit impedance parameters of each branch recorded in the power grid topology of the low-voltage distribution area, a node admittance matrix is ​​constructed.

[0098] It should be noted that the nodal admittance matrix is ​​a well-known technique and will not be elaborated upon here.

[0099] By substituting the distributed photovoltaic power generation model (FCP) and the load interval model of each node into the power flow equations of the distribution network in a rectangular coordinate system, a probabilistic interval power flow model is constructed, specifically as follows: ; ;

[0100] In the formula, , For nodes The active and reactive power injected by distributed photovoltaic systems. , For nodes The active power and reactive power of the load at the location, , They are nodes The real and imaginary parts of voltage, For nodes Voltage amplitude at the location, , The first node in the admittance matrix is ​​the... Line 1 The real and imaginary parts of a column element. For the set of PQ and PV nodes, For the PQ node set, It is a set of PV nodes.

[0101] It should be noted that the PQ node set and PV node set represent classifications of computational nodes in the power grid topology with different known variable attributes, respectively. Specifically, the PQ node set represents the set of power grid nodes where active and reactive power are known, but voltage magnitude and phase angle are yet to be determined; the PV node set represents the set of power grid nodes where active power and voltage magnitude are known, but reactive power and phase angle are yet to be determined. The purpose of classifying these node sets is to provide clear mathematical constraints for the joint solution of the distribution network power flow equations.

[0102] Based on the real-time power injected by each distributed photovoltaic (PV) system, and using a preset fluctuation error, the fluctuation range of each PV system is determined. Based on the fluctuation range of each PV system, a cog element model is found, and all cog element intervals it crosses are determined and defined as effective cog elements. The Cartesian product method is used to combine the effective cog elements of all distributed PV systems to form multiple effective cog element combinations, and the joint confidence degree of each effective cog element combination is calculated.

[0103] Based on the real-time load power of each node, and using the preset fluctuation error, a real-time load interval model is established. The real-time load interval model and each effective focal element combination are substituted into the probabilistic interval power flow model to solve the interval solution of the node voltage under the effective focal element combination.

[0104] In this embodiment, the real-time power injected by distributed photovoltaic power includes real-time active power and real-time reactive power. Using a preset fluctuation error, active power fluctuation range and reactive power fluctuation range are established respectively. The preset fluctuation error is set to 10%. Therefore, the active power fluctuation range is... The reactive power fluctuation range is ,in, For real-time active power, As a real-time reactive power, and as another implementation method, the implementer can set it according to the actual situation;

[0105] By searching the active power output coke element model based on the active power fluctuation range, the entire coke element interval it crosses is determined and defined as an effective active power coke element. Correspondingly, based on the reactive power fluctuation range, the entire coke element interval it crosses is determined and defined as an effective reactive power coke element. Using the Cartesian product method, all effective active power coke elements and effective reactive power coke elements of distributed photovoltaics are combined to form multiple effective coke element combinations, and the joint confidence degree of each effective coke element combination is calculated.

[0106] The process of obtaining the joint trust is as follows: the basic trust of each focal element in the effective focal element combination is extracted and multiplied to obtain the initial joint trust. The initial joint trust of all effective focal element combinations is then normalized, and the normalized value is used as the joint trust of each effective focal element combination. The normalization process is as follows: the ratio between the initial joint trust of each effective focal element combination and the sum of the initial joint trust of all effective focal element combinations is used as the result of normalization.

[0107] Real-time load power includes real-time load active power and real-time load reactive power. A real-time load interval model is established using a preset fluctuation error, set at 10%. Therefore, the real-time load interval model is: Active power of node i... The reactive power of the load at node i ,in, This is the lower bound of the active load at node i, and its value is 90% of the real-time load active power. This is the upper limit of the active load at node i, and its value is 110% of the real-time load active power. This is the lower limit of the reactive load at node i, and its value is 90% of the real-time reactive power. This is the upper limit of the reactive load of node i. This value is 110% of the real-time load reactive power. As for other implementation methods, the implementer can set it according to the actual situation.

[0108] Substitute the real-time load interval model and each effective coke element combination into the probabilistic interval power flow model to solve the interval solution of the node voltage under the effective coke element combination.

[0109] It should be noted that the real-time load interval model and each effective focal element combination are input into the probabilistic interval power flow model. With the probabilistic interval power flow equation and power fluctuation boundary as constraints, and the node voltage as the objective function, the voltage amplitude is optimized by minimizing and maximizing the solution to obtain the worst-case lower bound and the best-case upper bound of the node voltage amplitude, which are used as the interval solution of the node voltage under the effective focal element combination. The process of introducing evidence theory to solve the interval solution in the probabilistic interval power flow method is a well-known technique and will not be elaborated here.

[0110] Based on the interval solutions of node voltages under all effective focal element combinations and their corresponding joint confidence degrees, the cumulative confidence function curves of node voltages are constructed using DS evidence theory.

[0111] The specific process is as follows: For node i, extract the upper limit of its solutions in each interval; for any given voltage threshold, select all valid focal element combinations whose upper limit of the interval solutions is less than or equal to the voltage threshold, and accumulate the joint confidence scores corresponding to the selected valid focal element combinations as the cumulative confidence score corresponding to the voltage threshold; by continuously increasing the voltage threshold and repeating the above selection and accumulation process, obtain a series of cumulative confidence scores, plot discrete probability distribution scatter points with the voltage threshold as the horizontal axis and the corresponding cumulative confidence scores as the vertical axis, and use the least squares method to smooth the discrete probability distribution scatter points to obtain the continuous cumulative confidence function curve of node i; among them, the least squares method and DS evidence theory are well-known techniques and will not be elaborated here.

[0112] For the cumulative confidence function curve of the node voltage, the cumulative confidence value at the preset lower voltage threshold and the preset upper voltage threshold is extracted respectively. The difference between the cumulative confidence value at the preset upper voltage threshold and the cumulative confidence value at the preset lower voltage threshold is used as the quality confidence of the node voltage.

[0113] In this embodiment, the voltage is converted to per-unit value. Therefore, the preset lower voltage threshold is set to 0.93pu and the preset upper voltage threshold is set to 1.07pu, where pu is a per-unit value. In other implementation methods, the implementer can set it according to the actual situation. By converting to per-unit value, the difference in physical dimensions of the actual reference voltage can be eliminated, and the degree to which the actual voltage of the node deviates from the rated voltage can be reflected intuitively, so that the over-limit assessment method is not limited by the voltage level of the specific transformer area.

[0114] It should be noted that when the preset lower voltage threshold and the preset upper voltage threshold reflect the acceptable range of voltage, the higher the quality confidence level, the higher the reliability that the node voltage is within the acceptable range and the more stable the operation of the transformer area; conversely, the lower the quality confidence level, the higher the probability that the node voltage is out of bounds.

[0115] Furthermore, based on voltage quality confidence, the node voltage quality is evaluated, specifically as follows:

[0116] If the quality confidence level of the node voltage is less than the preset threshold, the node voltage is at risk of exceeding the limit; otherwise, the node voltage is not at risk of exceeding the limit.

[0117] In this embodiment, the preset threshold is set to 0.9. As for other implementation methods, the implementer can set it according to the actual situation.

[0118] For nodes at risk of exceeding limits, it means that the voltage at that node is very likely to exceed the safety boundary specified by the power grid, resulting in substandard voltage quality.

Claims

1. A method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology, characterized in that, The method includes the following steps: Based on the historical output power of each distributed photovoltaic (PV) in the power grid topology of the low-voltage distribution area, a probability density distribution model is established. The morphological distribution characteristics of the probability density distribution models of different distributed PVs are judged to classify distributed PVs. Based on the classification results, the distribution differences of the probability density distribution models of different distributed PVs and the reliability of historical data are analyzed to quantify the weight coefficients of each distributed PV. Thus, the probability density distribution models of all distributed PVs under the same category are weighted and fused to extract the typical probability distribution models corresponding to each category. Based on the cross-boundary characteristics of different typical probability distribution models and the equal division characteristics of their own probabilities, the fluctuation range of output power is divided into multiple coke element intervals, and basic confidence is assigned to them to establish a coke element model of photovoltaic power output. A load interval model is established based on the historical load data of each node in the power grid topology. This model, along with the coke element model of photovoltaic power output, is then substituted into the power flow equation of the distribution network in rectangular coordinates to construct a probabilistic interval power flow model. Based on the real-time output power of different distributed photovoltaic systems and the real-time load power at the nodes, the probabilistic interval power flow model is solved to obtain the interval solution of the node voltage amplitude. Combined with the basic confidence level, the cumulative confidence function curve is constructed through evidence theory. Based on this curve, the minimum credible probability of the voltage distribution within the qualified range is evaluated to obtain the quality confidence level of the node voltage, and the voltage quality of the distribution line is evaluated.

2. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The method of classifying distributed photovoltaics by judging the morphological distribution characteristics of the probability density distribution models of different distributed photovoltaics includes: calculating the skewness coefficient and kurtosis coefficient of the probability density distribution model within a preset power range for each distributed photovoltaic; combining the skewness coefficient and kurtosis coefficient of each distributed photovoltaic to form a feature vector; and clustering the feature vectors of all distributed photovoltaics in the power grid topology to obtain multiple categories.

3. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The calculation process for the weighting coefficients of each distributed photovoltaic system is as follows: Calculate the KL divergence of the probability density distribution models of any two distributed photovoltaics within the same category, and use it as the amount of information loss; The sum of the information loss between each distributed photovoltaic (PV) photovoltaic unit and all other distributed PV photovoltaic units within its category is taken as the cumulative loss degree. The sample size of the historical output power of each distributed photovoltaic power generation unit is statistically analyzed; the average sample size of all distributed photovoltaic power generation units within the same category is calculated, and the ratio of the sample size of each distributed photovoltaic power generation unit within each category to this average value is used as the data reliability. The weighting coefficients are positively correlated with data reliability, but negatively correlated with cumulative loss.

4. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The division of multiple focal element intervals includes: Based on the typical probability distribution model corresponding to each category, calculate its cumulative distribution function, and divide the entire cumulative probability interval [0,1] into multiple sub-intervals according to the principle of equal probability, so that each sub-interval has an equal probability value; extract the output power corresponding to the cumulative probability value of the right boundary of each sub-interval when the cumulative distribution function is equal to the cumulative probability value of each sub-interval, and use it as the equal probability quantile of the typical probability distribution model; gather the equal probability quantiles extracted from all categories into a first set, and count the total number of all equal probability quantiles in the first set as the first quantity; Calculate all intersection points of the typical probability distribution models corresponding to any two categories, extract the output power at the intersection points, and define them as isodense quantiles. Form a second set from all isodense quantiles extracted from any two categories, and count the total number of isodense quantiles in the second set as the second quantity. If the second quantity is less than or equal to the first quantity, then all isodense quantiles in the second set are retained to form the third set; otherwise, all isodense quantiles in the second set are filtered, and the filtered isodense quantiles are formed into the third set; the union of the first set and the third set is calculated, and all elements in the union and the two endpoints of the preset power interval are arranged in ascending order to form an ordered sequence. The ordered sequence is divided into multiple ordered subsequences, and the preset power interval is divided into multiple focal element intervals according to the boundaries of the ordered subsequences.

5. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 4, characterized in that, The filtering process for all isodense quantiles in the second set includes: arranging all isodense quantiles in the second set in ascending order to form a sequence; using the Jenks optimization algorithm to divide the sequence into multiple subsequences, wherein the number of subsequences is equal to the first set; if each subsequence contains an isodense quantile, then the isodense quantile is directly retained as the representative value of the subsequence; otherwise, the median of all isodense quantiles in the subsequence is taken as the representative value of the subsequence; and the representative values ​​of all subsequences are combined to form a third set.

6. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The allocation of basic trust levels to establish the coke element model for photovoltaic power output includes: The number of all distributed photovoltaic (PV) systems in each category is counted, and their proportion in the total number of distributed PV systems in the power grid topology is calculated as the model weight for each category. Based on the model weight, the typical probability distribution models corresponding to all categories are weighted and averaged to form the integrated power output distribution model. The integral value of this integrated power output distribution model in each coke cell interval is calculated as the basic confidence level for each coke cell interval. The output coke element model of distributed photovoltaic power generation is formed by each coke element interval and its corresponding basic confidence level.

7. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The establishment of the load interval model includes: setting interval variables with upper and lower limits for the load power of each node in the power grid topology, as the load interval model.

8. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 6, characterized in that, The construction of the cumulative trust function curve includes: Based on the real-time power injected by each distributed photovoltaic (PV) system, and using a preset fluctuation error, the fluctuation range of each PV system is determined. Based on the fluctuation range of each PV system, the focal element model is searched to determine all focal element intervals it traverses, which are defined as effective focal elements. The Cartesian product method is used to combine the effective focal elements of all distributed PV systems to form multiple effective focal element combinations, and the joint confidence degree of each effective focal element combination is calculated. Based on the real-time load power of each node, and using the preset fluctuation error, a real-time load interval model is established. The real-time load interval model and each effective focal element combination are substituted into the probabilistic interval power flow model to solve the interval solution of the node voltage under the effective focal element combination. Based on the interval solutions of the node voltages under all effective focal element combinations and their corresponding joint confidence degrees, the cumulative confidence function curves of the node voltages are constructed using evidence theory.

9. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The process of obtaining the quality confidence of the node voltage is as follows: For the cumulative confidence function curve, extract the cumulative confidence value at the preset lower voltage threshold and the preset upper voltage threshold respectively, and take the difference between the cumulative confidence value at the preset upper voltage threshold and the cumulative confidence value at the preset lower voltage threshold as the quality confidence of the node voltage.

10. The method for real-time monitoring of distribution line voltage quality based on low-voltage distribution area topology as described in claim 1, characterized in that, The assessment of the voltage quality of the power distribution line includes: if the confidence level of the node voltage quality is less than a preset threshold, then there is a risk of the voltage exceeding the limit; otherwise, there is no risk of the voltage exceeding the limit.

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