Improved semi-invariant photovoltaic power distribution network load flow calculation method, system and equipment and medium

Abstract

The invention relates to the technical field of power system operation and dispatching, in particular to an improved semi-invariant photovoltaic power distribution network load flow calculation method, system and device and a medium. An improved modeling and estimation method is adopted to calculate photovoltaic output, and probability density and a cumulative distribution function are obtained; calculating and converting characteristic parameters based on the obtained probability information; analyzing and solving the uncertainty component in combination with a linearization equation to obtain a probability distribution result of the power grid operation characteristics; fitting and correcting a probability distribution result by adopting a series expansion method to form an operation state probability distribution curve; by introducing an improved semi-invariant method and combining daily variation curve data of photovoltaic and load, probability modeling of random output and load fluctuation is realized, load flow calculation is performed by using an analysis form, and the method is suitable for real-time scheduling and operation analysis under large-scale new energy access.

Description

Technical Field

[0001] This invention relates to the field of power system operation and dispatching technology, and in particular to an improved semi-invariant method, system, equipment and medium for calculating power flow in photovoltaic distribution networks. Background Technology

[0002] With the rapid development of distributed generation technologies, represented by photovoltaics, the installed capacity of photovoltaic power generation equipment in distribution networks is continuously increasing, and the penetration rate of new energy in the power system is rising significantly. Due to the influence of random factors such as weather, temperature, and irradiance, the output power of photovoltaic units exhibits significant fluctuations and uncertainties, making the operation of distribution networks more complex and placing higher demands on the accuracy of power flow calculations and scheduling analysis. To more realistically reflect the operating characteristics of distributed power sources such as photovoltaics in distribution networks, modeling and calculating the uncertainty of power output based on probability theory has become a key research direction.

[0003] However, existing probabilistic power flow calculation methods largely rely on assumptions about the distribution of photovoltaic (PV) output or load power, resulting in limited model accuracy and difficulty in adapting to the non-parametric characteristics of actual output. Furthermore, traditional methods require extensive convolution operations when solving for high-dimensional random variables, leading to high computational cost and low efficiency, which hinders their widespread application in large-scale distribution networks. To address these issues, this invention proposes an improved probabilistic power flow analysis method based on semi-invariant calculations. By introducing adaptive kernel density estimation and a semi-invariant aggregation strategy, it accurately obtains the probability distribution information of PV and load power, and combines this with series expansion for fitting calculations. This improves the accuracy and efficiency of probabilistic power flow calculations in distribution networks containing PV without relying on distribution assumptions. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides an improved semi-invariant method and system for calculating power flow in photovoltaic (PV) distribution networks, solving the problems of strong randomness in PV output, inaccurate distribution assumptions, and low computational efficiency in existing probabilistic power flow calculations. By improving kernel density estimation to determine the probabilistic characteristics of PV and loads, and combining AC power flow linearization and series expansion, high-precision fitting of node voltages and branch power is achieved, improving the accuracy and applicability of probabilistic power flow calculations for PV-containing distribution networks.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides an improved method for calculating power flow in a photovoltaic distribution network with semi-invariants, comprising: Acquire power and grid operation data, including those from distributed power sources; Based on the power output of distributed generation sources and grid operation data, an improved modeling and estimation method is used to calculate photovoltaic output and obtain probability density and cumulative distribution function; Based on the probability information output by the probability density and cumulative distribution function, feature parameters are calculated and transformed to construct a unified feature parameter system. Based on a unified system of characteristic parameters and combined with linearized equations, the uncertainty components are analyzed and solved to obtain the probability distribution results of the power grid operation characteristics. The probability distribution results of the power grid operation characteristics are fitted and corrected by the series expansion method to form the probability distribution curve of the operation state.

[0007] As a preferred embodiment of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described in this invention, the step of obtaining power and grid operation data including distributed generation includes: Obtain power information of distributed power sources and loads in the distribution network, and collect power output under different time periods and operating conditions; Collect topology and line parameter information of the power grid, and extract operational data of node and branch parameters; The collected data is preprocessed and organized to eliminate outliers and maintain time-series consistency.

[0008] As a preferred embodiment of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described in this invention, the step of calculating photovoltaic output and obtaining probability density and cumulative distribution function based on the power of distributed generation sources and grid operation data using an improved modeling and estimation method includes: Based on the collected power of distributed power sources and the extracted grid operation data, a probabilistic modeling framework for photovoltaic power output and load power is established to describe the data distribution relationship. An adaptive bandwidth kernel density estimation method is used to perform distribution calculations on load power data in the probabilistic modeling framework of photovoltaic power output and load power, and to obtain the probability distribution information of load power output in different intervals. After obtaining the probability distribution information, the estimated probability density function and cumulative distribution function are solved and calibrated to form a quantitative expression of the power output probability model.

[0009] As a preferred embodiment of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described in this invention, the step of calculating and transforming characteristic parameters based on the probability information output by the probability density and cumulative distribution function to construct a unified characteristic parameter system includes: Based on the probability information output by the probability density and cumulative distribution function, statistical analysis is performed on the power output and load characteristics, key statistical features are extracted and moment parameters are calculated. The obtained moment information is transformed to obtain different moment information and related features; The transformed moment information is summarized and correlated to construct a unified feature parameter system.

[0010] As a preferred embodiment of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described in this invention, the establishment of the probabilistic modeling framework for photovoltaic output and load power includes constructing a non-parametric probabilistic modeling framework for photovoltaic and load power based on the characteristics of photovoltaic power output being affected by random factors such as weather and temperature, and using an improved model of kernel density estimation and bandwidth calculation method to characterize the actual distribution characteristics of photovoltaic power and load power.

[0011] As a preferred embodiment of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described in this invention, the step of analyzing and solving the uncertainty components based on a unified characteristic parameter system and linearized equations to obtain the probability distribution results of the power grid operating characteristics includes: solving the probabilistic power flow part of the distribution network based on semi-invariant information according to the unified characteristic parameter system and the linearized AC power flow equations at the reference point; accumulating the uncertainty and deterministic power flow information; and calculating the power injected at the end of the branch as the calculation power, including the active and reactive power of the node itself. , and the sum of active and reactive power of all subordinate branches , , is represented as: in, , Represents the active and reactive power of the end nodes. Represents a node Down to the next level node The active power transmitted on the branch line, Represents a node Down to the next level node Reactive power transmitted on the branch line, Represents a node The number of subordinate branches.

[0012] The beneficial effects of this preferred technical solution are as follows: By introducing linearized AC power flow equations at the benchmark point, the random uncertainties in the operation of the distribution network are decomposed and solved, allowing the statistical characteristics of semi-invariants to be combined with the deterministic power flow component, thereby achieving an accurate characterization of power flow changes caused by fluctuations in photovoltaic output. This solution incorporates the injected power at the end of the branch as the calculated power, uniformly accumulating the active and reactive power of the node itself and its subordinate branches. This reflects the power transmission relationship and hierarchical influence between nodes, avoiding the accumulation of biases caused by the simplification of node power in traditional power flow algorithms.

[0013] As a preferred embodiment of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described in this invention, the step of fitting and correcting the probability distribution results of the power grid operating characteristics using a series expansion method to form the operating state probability distribution curve includes: using Cornish-Fisher series expansion to fit the probability information of the node voltage and branch power to be solved, i.e., the probability density function pdf and the cumulative distribution function cdf, to complete the probabilistic power flow calculation; and calculating the distribution network node voltage amplitude and branch power as random variables. Calculate the relevant information of the moments at the origin and the central moments, and obtain the mean value. and standard deviation Standardize the variables; based on the standardized vectors, calculate and expand the Cornish-Fisher formula to obtain the probability density function pdf of the power of a node and branch in the distribution network containing photovoltaic and load uncertainties.

[0014] The beneficial effects of this preferred technical solution are as follows: by adopting the Cornish-Fisher series expansion method, the probability distribution results of node voltage and branch power are fitted and corrected. This method treats the node voltage amplitude and branch power as random variables, describes their probability characteristics by obtaining the origin moment and central moment, and expands the PDF and CDF functions based on the standardized variables, thereby obtaining the power flow distribution under the uncertainty of photovoltaic output and load.

[0015] Secondly, the present invention provides an improved power flow calculation system for a photovoltaic distribution network with semi-invariant components, comprising: The data acquisition module acquires power data, including data from distributed power sources, and data on grid operation. The modeling and estimation module calculates photovoltaic output and obtains probability density and cumulative distribution function based on the power of distributed generation and grid operation data using improved modeling and estimation methods. The feature calculation module calculates and transforms feature parameters based on the probability information output by the probability density and cumulative distribution function, and constructs a unified feature parameter system. The linear analysis module analyzes and solves the uncertainty components based on a unified system of characteristic parameters and linearized equations, and obtains the probability distribution results of the power grid operation characteristics. The distribution fitting module uses a series expansion method to fit and correct the probability distribution results of the power grid operation characteristics, forming the probability distribution curve of the operation state.

[0016] Thirdly, the present invention provides an electronic device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions, which, when executed by the processor, implement the steps of an improved semi-invariant power flow calculation method for photovoltaic power distribution networks.

[0017] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the improved semi-invariant photovoltaic power flow calculation method.

[0018] Compared with existing technologies, the advantages of this invention are as follows: In power flow calculations for distribution networks containing photovoltaic (PV) power, this invention introduces an improved semi-invariant method and combines it with the daily variation curves of PV power and load to achieve accurate probabilistic modeling of random power output and load fluctuations. This improvement avoids the drawbacks of traditional methods that require assumptions about power distribution patterns or rely on a large amount of random sampling, making the calculation results more consistent with actual operating characteristics. This method uses analytical calculations to solve power flow problems, making it suitable for real-time scheduling and operation analysis scenarios. Furthermore, by modeling and correcting the uncertainties in the output characteristics of distributed power sources such as PV and wind power, it can reflect the fluctuation patterns of node voltage and branch power flow under conditions of large-scale renewable energy integration. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating an improved semi-invariant power flow calculation method for photovoltaic distribution networks according to an embodiment of the present invention.

[0021] Figure 2 This is an IEEE 33-node topology diagram of a distribution network for an improved semi-invariant power flow calculation method for photovoltaic distribution networks, as described in one embodiment of the present invention.

[0022] Figure 3 The graph shows the active power probability density function and cumulative distribution function of node 10 calculated by an improved semi-invariant power flow calculation method for photovoltaic distribution networks according to an embodiment of the present invention. Detailed Implementation

[0023] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0024] Example 1, referring to Figure 1 As an embodiment of the present invention, an improved method for calculating power flow in a photovoltaic distribution network with semi-invariants is provided, comprising: S1: Obtain power and grid operation data including distributed power sources; S2: Based on the power output of distributed generation sources and grid operation data, an improved modeling and estimation method is used to calculate photovoltaic output and obtain probability density and cumulative distribution function; S3: Based on the probability information output by the probability density and cumulative distribution function, perform feature parameter calculation and transformation to construct a unified feature parameter system; S4: Based on a unified system of characteristic parameters and combined with linearized equations, the uncertainty components are analyzed and solved to obtain the probability distribution results of the power grid operation characteristics; S5: The probability distribution results of the power grid operation characteristics are fitted and corrected by the series expansion method to form the probability distribution curve of the operation state.

[0025] It should be noted that existing power flow calculations for distribution networks including photovoltaics are mostly based on assumptions about power output distribution. However, when photovoltaic output and load power change with environmental factors such as weather and temperature, the accuracy of the models is often difficult to guarantee. At the same time, the traditional convolutional moment calculation process is complex and computationally intensive, making it difficult to apply to the probabilistic analysis of large-scale distribution networks.

[0026] Therefore, addressing the aforementioned issues of strong power output randomness, large deviations in distribution assumptions, and heavy computational burden, this paper, through steps S1-S5, sequentially completes the entire process from distributed power source data acquisition and preprocessing, photovoltaic power output probabilistic modeling and estimation, characteristic parameter extraction and moment transformation, to solving the uncertain power flow based on linearized equations and fitting the probability distribution using series expansion. An improved semi-invariant power flow calculation method that accurately characterizes the random characteristics of photovoltaic power is established, achieving efficient solutions for probabilistic power flow and providing an implementable technical path for the operational status analysis of distribution networks containing distributed photovoltaic power.

[0027] Example 2, refer to Figures 1-3 As an embodiment of the present invention, based on the above embodiment, an improved method for calculating power flow in a photovoltaic distribution network with semi-invariants is provided.

[0028] In this embodiment of the application, step S1, acquiring power and grid operation data including distributed power sources, includes: A1: Obtain power information of distributed power sources and loads in the distribution network, and collect power output under different time periods and operating conditions; A2: Collect topology and line parameter information of the power grid, and extract the operating data of node and branch parameters; A3: Based on the collection results, the collected data is preprocessed and organized to eliminate abnormal data and maintain time sequence consistency.

[0029] Specifically, A1~A3 includes acquiring information such as power output and load power under distributed photovoltaic power, as well as basic data of the power grid system; dividing each node of the distribution network into layers, determining the type of each node, acquiring active power, reactive power, voltage amplitude and other data of each node from the power grid system, considering whether reactive power compensation components are included, and collecting load power curve data of the node over a period of time.

[0030] For example, the active and reactive power output data of photovoltaic units collected every 15 minutes at a new energy power station containing distributed photovoltaic power, as well as the active and reactive power data of the distribution network load at the same time, are obtained and normalized.

[0031] In this embodiment of the application, step S2 calculates the photovoltaic output and obtains the probability density and cumulative distribution function based on the power of the distributed generation and grid operation data using an improved modeling and estimation method, including: B1: Based on the collected power of distributed power sources and the extracted grid operation data, establish a probabilistic modeling framework for photovoltaic power output and load power to describe the data distribution relationship; B2: The kernel density estimation method with adaptive bandwidth is used to perform distribution calculation on the load power data in the probabilistic modeling framework of photovoltaic power output and load power, and obtain the probability distribution information of load power output in different intervals; B3: After obtaining the probability distribution information, the estimated probability density function and cumulative distribution function are solved and calibrated to form a quantitative expression of the power output probability model.

[0032] Specifically, B1~B3 also include calculating the kernel density estimation bandwidth of the Gaussian kernel function using the maximum likelihood method based on the k-fold cross-validation approach; and constructing a model for solving the kernel density estimation bandwidth using the maximum likelihood method, expressed as: in, , The number of each random variable; To set the number of test sets used for the k-fold cross-validation method; To set the size of the training set used for the k-fold cross-validation method; Represented as the test set; This represents the numerical values ​​of the sample set, which is the sample data of the random variable; This represents the set of observation data used for observation. This represents the bandwidth value in the maximum likelihood estimation model. Represented as the kernel density function, it is a Gaussian kernel function, i.e. .

[0033] Calculate the set first Each fold corresponds to The value is calculated by averaging the scores of each section as follows, to obtain each... The value of the maximum likelihood cross-validation constructor corresponding to the value is represented as: in, This represents the total number of folds in the constructed k-fold cross-validation method, from which we obtain... The value corresponding to the maximum Value, denoted as fixed bandwidth .

[0034] Further overall corrections were made, using the integral mean square error (IMF) index to determine the difference between the fitted kernel density estimation function and the calculated empirical function as the optimization objective, and employing a particle swarm optimization algorithm for optimization; where the IMF index is expressed as: in, It is represented as the probability density function of the real sample, i.e., the empirical function; Let be the calculated kernel density estimation function; where This indicates the magnitude of its mathematical expectation.

[0035] The particle swarm optimization algorithm is incorporated for optimization, and calculations are performed. This makes different Under these conditions, the aforementioned integral mean square error index can be minimized. During the iteration process, each particle in the particle swarm optimization algorithm possesses a velocity... and location Two properties, and the particle can be located at its own historical best position. and the optimal position of the population To perform an update and iteration, it is represented as: in, Indicates the number of iterations; Indicates the set number One particle; Indicates inertia weight; Indicates the learning factor; Represented as a range The random number, where , , , With the particle count set to 20, the calculations yielded... This is the most suitable segmented bandwidth sequence.

[0036] Calculation based on The daily variation probability density function (pdf) and cumulative distribution function (cdf) of photovoltaic and load output for each segment of the bandwidth sequence.

[0037] In this embodiment of the application, the specific steps for calculating photovoltaic output using the improved modeling and estimation method in step S2 are as follows: Kernel density estimation is performed using k-fold cross-validation, and the basic bandwidth is calculated using a Gaussian kernel function. The estimated density function is calculated, and the actual photovoltaic and load power sequences are divided into multiple intervals. The bandwidth adjustment factor is calculated using the ratio of the geometric mean of the power data in each interval. This leads to the corrected kernel density estimation bandwidth sequence. Using the integral mean square error (MISE) index as the optimization objective, the fit difference between the kernel density estimation function and the empirical distribution function is measured, and the adaptive gain coefficient is solved using the particle swarm optimization algorithm. The optimal bandwidth for each interval is obtained by combining the bandwidth sequence. Based on the optimal bandwidth of each interval Kernel density estimation is performed to obtain the probability density function and cumulative distribution function of photovoltaic output and load power.

[0038] For example, using IEEE 33-node line information data as the main research subject, the photovoltaic uncertainty model is constructed using a beta model with shape parameters. , The active power output is 300kW, with a constant power factor of 0.98. The nodes connected to the IEEE 33 model are nodes 12, 21, 23, and 29. The load uncertainty is modeled using a standard normal distribution with shape parameters... , The basic load data is consistent with the load data of the IEEE 33-node system; the two models each generate 96 random points to obtain values ​​taken every 15 minutes on a certain day, denoted as [missing data]. , , , and .

[0039] In an optional implementation, the improved modeling and estimation method in step S2 can also be achieved by setting a time-segmented dynamic bandwidth adjustment mechanism. Specifically, the kernel density estimation bandwidth can be dynamically adjusted according to the changing patterns of light intensity, temperature, and load levels in different time periods; the bandwidth sequence can be reconstructed within each time window to more accurately reflect the difference in photovoltaic power output between the low irradiance periods in the morning and evening and the peak period at noon, making the probabilistic modeling results more consistent with the time-varying characteristics of the distribution network operation and improving the temporal accuracy and continuity of photovoltaic power output distribution estimation.

[0040] In another optional implementation, the improved modeling and estimation method in step S2 can also be achieved through regionalized power modeling that introduces spatial correlation constraints. Considering the geographical distribution characteristics of multiple photovoltaic access nodes, a spatial correlation coefficient matrix between nodes is introduced into the modeling to constrain the covariance relationship of power fluctuations between adjacent nodes, thus reflecting the output correlation within areas with similar local meteorological conditions. In multi-node photovoltaic centralized access scenarios, this method can improve the coordination and consistency of overall power distribution estimation, providing probabilistic input parameters that are closer to actual operating characteristics for subsequent power flow solutions.

[0041] In a preferred embodiment of the present invention, step S2 employs an improved modeling and estimation method to characterize the probability distribution of photovoltaic power output and load power. Specifically, an adaptive bandwidth kernel density estimation method is used, combined with k-fold cross-validation maximum likelihood optimization and particle swarm optimization, to adaptively determine the optimal bandwidth under different data distribution conditions, thereby avoiding the distribution bias caused by traditional fixed bandwidth estimation. By setting up a multi-interval division and bandwidth correction mechanism, the random variation law of photovoltaic power output under different operating conditions can be reflected. At the same time, a time-segmented bandwidth adjustment method can be selected according to actual needs to track the time-domain variation of photovoltaic power output at different times throughout the day.

[0042] In this embodiment of the application, the specific steps of using the adaptive bandwidth kernel density estimation method to perform distribution calculations on the load power data in the probabilistic modeling framework of photovoltaic power output and load power in step B2 are as follows: The segmented bandwidths of photovoltaic and load outputs under the kernel density estimation correction method are calculated, including the calculation of the precursor estimation function, which is expressed as follows: in, Represented as historical sample values ​​of photovoltaic power output; This represents actual sample data of photovoltaic power output; it is the distribution value under the standard beta distribution under the same parameter conditions. A total of four photovoltaic units are connected to the IEEE 33-bus system. , .

[0043] The local adjustment factor is calculated and expressed as: in, This is expressed as a sensitivity parameter, typically with a value of 0.5; The leading estimate function is expressed as calculated from the density estimates of all random variables. The geometric mean is expressed as: The local adjustment factor for each segment under the set power output sequence is calculated, and based on... The corrected kernel density estimation bandwidth is obtained.

[0044] In an optional implementation, the kernel density estimation method with adaptive bandwidth in step B2 can also be implemented by introducing a dynamic partitioning strategy for the sample density distribution. Specifically, the power range can be dynamically divided according to the power fluctuation characteristics of photovoltaic output at different times: for periods with more drastic power changes, a smaller bandwidth is used to improve the accuracy of local estimation; for periods with relatively stable power changes, a larger bandwidth is used to reduce the impact of noise, thus maintaining the stability of the kernel density estimation results under non-stationary operating conditions such as photovoltaic sunrise and sunset.

[0045] In another optional implementation, the kernel density estimation method for adaptive bandwidth in step B2 can also be combined with a time-series correlation weight correction strategy. When calculating the local adjustment factor, a time correlation parameter between photovoltaic power and historical load output is introduced, and the power change trend of adjacent time periods is used as a correction weight to dynamically adjust the smoothness of the bandwidth. This strategy can fully reflect the correlation in the time dimension when photovoltaic power has obvious periodic or trend characteristics, making the bandwidth change more consistent with the actual operating law of photovoltaic power output.

[0046] In a preferred embodiment of the present invention, this is achieved by combining a time-series correlation weight correction strategy. When calculating the local adjustment factor, a time correlation parameter between the photovoltaic and the historical output of the load is introduced, and the power change trend of adjacent time periods is used as a correction weight to dynamically adjust the smoothness of the bandwidth. This strategy can reflect the correlation in the time dimension in scenarios where the photovoltaic output has obvious periodic or trend characteristics, so that the bandwidth change conforms to the operating law of the photovoltaic output.

[0047] In this embodiment of the application, step S3, based on the probability information output by the probability density and cumulative distribution function, performs feature parameter calculation and transformation processing to construct a unified feature parameter system, including: C1: Based on the probability information output by the probability density and cumulative distribution function, perform statistical analysis on power output and load characteristics, extract key statistical features and calculate moment parameters; C2: Perform formal transformation on the obtained moment information to obtain different moment information and related features; C3: Summarize and correlate the transformed moment information to construct a unified feature parameter system.

[0048] In this embodiment of the application, the specific steps for calculating and converting the feature parameters in step S3 are as follows: The semi-invariants of the PDF data for each random variable can be obtained from the raw moments of the PDF of each order, and the relationship is expressed as: in, express Semi-invariant of order.

[0049] By utilizing the additivity and homogeneity of semi-invariants, the linear addition and convolution operations between semi-invariants are equivalent to the results of obtaining moments of each order. By accumulating the semi-invariant information of each random variable, the overall semi-invariant information can be obtained.

[0050] In an optional implementation, the calculation and conversion of characteristic parameters in step S3 can also be achieved by introducing a weighted characteristic statistical mechanism. When extracting the characteristic parameters of photovoltaic output and load, weighting factors can be set for different time periods or operating states to highlight the statistical characteristics of high fluctuation ranges or key operating stages. This method enables the calculation results of semi-invariants to closely match the dynamic changes in grid operation.

[0051] In another optional implementation, the calculation and transformation of feature parameters in step S3 can also be completed using a partitioned aggregation model. After transforming the moment information of each random variable, this model can perform partitioned aggregation processing on nodes with similar load patterns or photovoltaic access characteristics based on the power grid topology and the geographical distribution characteristics of the nodes. Subsequently, the semi-invariant information within each partition is accumulated and transformed regionally to construct a regional-level feature parameter system.

[0052] In a preferred embodiment of the present invention, by calculating and transforming the characteristic parameters of the probability distribution information of photovoltaic power output and load power, the structured and hierarchical expression of moment information can be achieved while retaining the random fluctuation characteristics of power. Furthermore, by introducing a weighted feature statistics mechanism, the feature contribution of high fluctuation ranges can be strengthened. At the same time, by constructing a partitioned aggregation model, the moment information can be partitioned and aggregated in combination with the topological characteristics of the distribution network to form a hierarchical feature parameter system.

[0053] In this embodiment of the application, the specific steps for calculating the moment parameters in step C1 are as follows: Based on the probability density function (pdf) values ​​of the photovoltaic unit and the load, and according to the definitions of raw moment and central moment, the raw moment and central moment information of different random variables are calculated. The definition of raw moment is as follows: in, Represents the sample values ​​of a random variable. It represents the probability density function of its random variable sample values.

[0054] The central moment is expressed as: in, It is expressed as the mathematical expectation of the sample values ​​of the random variable.

[0055] In an optional implementation, the moment parameter calculation in step C1 can also be achieved through a statistical solution method based on adaptive segmentation of the sample distribution; according to the fluctuation pattern of photovoltaic output and load power in different time periods or operating states, the sample interval is dynamically divided according to the power density change rate; on this basis, the origin moment and central moment of the probability density function in each segment are calculated and weighted and summarized.

[0056] In another optional implementation, the moment parameter calculation in step C1 can also be achieved by combining time series smoothing and sliding window statistical methods. By introducing a sliding window mechanism into the moment calculation, local smoothing and dynamic statistics are performed on the time series data of photovoltaic power and load power, and the changing trend of moment parameters within continuous time periods is extracted. This can effectively suppress the interference of abrupt changes or short-term outliers on the overall statistical results, making the obtained moment characteristics more consistent with the continuity of photovoltaic and load changes over time in the distribution network, and providing support for the subsequent stable solution of probabilistic power flow.

[0057] In a preferred embodiment of the present invention, by introducing an adaptive piecewise statistics and sliding window calculation mechanism, the statistical variation law of random variables can be characterized when the photovoltaic output and load power fluctuate significantly, so that the obtained moment parameters can better reflect the operating characteristics of photovoltaic and load power.

[0058] In this embodiment, step S4 analyzes and solves the uncertainty components based on a unified characteristic parameter system and linearized equations to obtain the probability distribution results of the power grid operating characteristics. This includes solving the distribution network probabilistic power flow part based on the above-mentioned semi-invariant information at each order, combined with the linearized AC power flow equations at the reference point. The results are then accumulated as uncertainty and deterministic power flow information. The power flow linearization method is based on the power forwarding process of the backward substitution method, that is, first calculating the power forwarding process of the branch end. Injected power, as operational power, includes the node's own active and reactive power. , and the sum of active and reactive power of all subordinate branches , , is represented as: in, , Represents the active and reactive power of the end nodes. Represents a node Down to the next level node The active power transmitted on the branch line, Represents a node Down to the next level node Reactive power transmitted on the branch line, Represents a node The number of subordinate branches.

[0059] The active and reactive power of the end nodes were obtained. , The power flowing in a branch depends on the branch resistance. and branch resistance The calculation shows that: The solution for the above branch power is linearized based on Taylor expansion, according to... Node reference power , The square of the node voltage , and the change in power at that node , get: The voltage back-substitution equation in the forward-backward substitution method is obtained by gradually substituting back the branch power value after knowing it in advance. Therefore, the Newton-Raphson equation is chosen to be used for solving. The semi-invariant information of the calculation is added to obtain the information such as the voltage of each node and the power of each branch under the distribution network topology. The matrix information such as the origin moment and central moment of the distribution network node and branch under the inverse comprehensive random variable is obtained.

[0060] In this embodiment, step S5 uses a series expansion method to fit and correct the probability distribution results of the power grid operating characteristics, forming an operating state probability distribution curve. This includes using a Cornish-Fisher series expansion to fit and correct the probability distribution results, obtaining the probability information of the node voltage and branch power to be solved, i.e., the probability density function pdf and the cumulative distribution function cdf, thus completing the probabilistic power flow calculation. The distribution network node voltage amplitude and branch power are calculated as random variables. Calculate the relevant information of the moments at the origin and the central moments, and obtain the mean value. and standard deviation Standardize the variables; based on the standardized vectors, calculate and expand the Cornish-Fisher formula to obtain the probability density function pdf of the power of a node and branch in the distribution network containing photovoltaic and load uncertainties.

[0061] Specifically, Cornish-Fisher series expansion is used to fit the probability information of the node voltage and branch power that need to be solved, namely the probability density function pdf and the cumulative distribution function cdf, to complete the probabilistic power flow calculation.

[0062] In step S4, the voltage amplitude at a certain node or the power of a branch in the distribution network is calculated as a random variable. Since the relevant information such as the moment at the origin and the central moment are obtained through calculation, their mean value can be obtained. and standard deviation Standardize the variables and represent them as follows: Based on the standardized vectors, the expanded Cornish-Fisher formula is calculated and expressed as: in, It is a standard normal distribution at probability level The quantile below, i.e. ; This is expressed as skewness; Represented as excess kurtosis, obtained The relationship between the quantiles of the standard normal distribution and the quantiles of the above quantile function is numerically calculated, and the derivative is expressed as: Therefore, the probability density function pdf can be fitted using the following formula, expressed as: in, This represents the probability density function.

[0063] The probability density function pdf of the power at a node or branch in a distribution network with photovoltaic and load uncertainties is obtained.

[0064] In summary, this invention establishes a probabilistic analysis system that reflects the stochastic characteristics of photovoltaic (PV) output and load power by introducing adaptive kernel density estimation, linearized power flow solution, and Cornish-Fisher series expansion. This method obtains the probabilistic distribution results of node voltage and branch power without pre-setting the power distribution type. Through adaptive bandwidth optimization and segmented estimation, it overcomes the problems of insufficient description of PV output fluctuations and high computational complexity in traditional methods. Furthermore, by combining extended modeling with time-segmented bandwidth and spatial correlation constraints, the obtained results conform to the time-varying laws and spatial correlation characteristics of distribution network operation.

[0065] Example 3, referring to Figures 2-3 As an embodiment of the present invention, a method is provided. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments.

[0066] like Figure 2 The IEEE 33-node topology with photovoltaics shown is used to build a corresponding simulation model on the Matlab simulation platform. Specific parameter settings include photovoltaic and load settings, particle swarm optimization parameter settings, and IEEE 33-node line information data as the main research subject. For ease of explanation, the photovoltaic uncertainty model is constructed using a beta model, with shape parameters... , The active power output is 300kW, with a constant power factor of 0.98. The nodes connected to the IEEE 33 model are nodes 12, 21, 23, and 29. The load uncertainty is modeled using a standard normal distribution with shape parameters... , The basic load data is consistent with the load data of the IEEE 33-node system; both models generate 96 random points to simulate values ​​taken every 15 minutes on a given day. , , , The number of particles is set to 20.

[0067] The probabilistic power flow fitting calculation method for distributed photovoltaic (PV) distribution networks using an improved semi-invariant calculation method is employed. Using the active and reactive power outputs of the PV power grid at 10:00 AM (beta model) as a sample set, improved kernel density estimation is performed. An adaptive bandwidth is obtained by incorporating particle swarm optimization (PSO) to calculate the probability density function (pdf) of active and reactive power outputs. Then, based on the semi-invariant method, probabilistic power flow calculations with AC linearization are performed. The resulting active power probability density function and cumulative distribution function for node 10 are shown below. Figure 3 As shown, with the Monte Carlo simulation method as a reference, the active power probability distribution obtained by this method is basically consistent with the theoretical value.

[0068] Example 4 illustrates an improved semi-invariant power flow calculation method for photovoltaic distribution networks. It should be noted that the technical solution of this improved semi-invariant power flow calculation system for photovoltaic distribution networks belongs to the same concept as the improved semi-invariant power flow calculation method for photovoltaic distribution networks described above. Details not described in detail in this example can be found in the description of the improved semi-invariant power flow calculation method for photovoltaic distribution networks described above.

[0069] This embodiment also provides an improved power flow calculation system for photovoltaic distribution networks with semi-invariants, including: The data acquisition module acquires power data, including data from distributed power sources, and data on grid operation. The modeling and estimation module calculates photovoltaic output and obtains probability density and cumulative distribution function based on the power of distributed generation and grid operation data using improved modeling and estimation methods. The feature calculation module calculates and transforms feature parameters based on the probability information output by the probability density and cumulative distribution function, and constructs a unified feature parameter system. The linear analysis module analyzes and solves the uncertainty components based on a unified system of characteristic parameters and linearized equations, and obtains the probability distribution results of the power grid operation characteristics. The distribution fitting module uses a series expansion method to fit and correct the probability distribution results of the power grid operation characteristics, forming the probability distribution curve of the operation state.

[0070] This embodiment also provides an electronic device applicable to an improved semi-invariant power flow calculation method for a photovoltaic power distribution network, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the improved semi-invariant power flow calculation method for a photovoltaic power distribution network as proposed in the above embodiment.

[0071] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements an improved semi-invariant power flow calculation method for photovoltaic distribution networks as proposed in the above embodiments.

[0072] The storage medium proposed in this embodiment and the method for calculating power flow in a photovoltaic distribution network with improved semi-invariants proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0073] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0074] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for power flow calculation of photovoltaic distribution network with improved semi-invariant, characterized in that, The method comprises the following steps: acquiring power and grid operation data containing distributed power supply; calculating photovoltaic output and obtaining probability density and cumulative distribution function by using improved modeling and estimation method according to the power and grid operation data of the distributed power supply; calculating and converting the characteristic parameters based on the probability information output by the probability density and cumulative distribution function, and constructing a unified characteristic parameter system; analyzing and solving the uncertainty components according to the unified characteristic parameter system and combining linear equations to obtain the probability distribution results of the grid operation characteristics; fitting and correcting the probability distribution results of the grid operation characteristics by using the series expansion method to form the operation state probability distribution curve.

2. The method for power flow calculation of photovoltaic distribution network with improved semi-invariant, as claimed in claim 1 wherein, The step of acquiring power and grid operation data containing distributed power supply comprises the following steps: acquiring power information of the distributed power supply and the load in the distribution network, and collecting the power output under different time periods and operation states; collecting the topology and line parameter information of the grid, and extracting the operation data of the node and branch parameters; preprocessing and arranging the collected data according to the collection results, eliminating abnormal data and maintaining time sequence consistency.

3. The method for power flow calculation of a power distribution network with photovoltaic power according to claim 2, wherein, The step of calculating photovoltaic output and obtaining probability density and cumulative distribution function by using improved modeling and estimation method according to the power and grid operation data of the distributed power supply comprises the following steps: establishing a probability modeling framework of photovoltaic output and load power according to the collected power of the distributed power supply and the extracted grid operation data, and describing the data distribution relationship; calculating the distribution of the load power data in the probability modeling framework of photovoltaic output and load power by using the kernel density estimation method with adaptive bandwidth, and acquiring the probability distribution information of the load power output under different intervals; after obtaining the probability distribution information, solving and calibrating the parameters of the estimated probability density function and cumulative distribution function to form the quantitative expression of the probability model of the power output.

4. The method for power flow calculation of power distribution network with PV plant of claim 3, wherein, The step of calculating and converting the characteristic parameters based on the probability information output by the probability density and cumulative distribution function, and constructing a unified characteristic parameter system comprises the following steps: based on the probability information output by the probability density and cumulative distribution function, statistically analyzing the power output and load characteristics, extracting key statistical characteristic quantities and calculating moment parameters; performing form conversion on the obtained moment information to obtain different moment information and related characteristics; summarizing and associating the converted moment information to construct a unified characteristic parameter system.

5. The method for power flow calculation of photovoltaic power distribution network with improved semi-invariant as claimed in claim 4, wherein, The step of establishing a probability modeling framework of photovoltaic output and load power comprises the following steps:

6. The method for power flow calculation of photovoltaic power distribution network with improved semi-invariant as claimed in claim 5 wherein, based on the characteristics of photovoltaic power output being affected by random factors such as weather and temperature, constructing a non-parametric probability modeling framework of photovoltaic and load power, and using the improved model and bandwidth calculation method of kernel density estimation to describe the actual distribution characteristics of photovoltaic power and load power. The injection power at the end of the branch circuit is calculated as the operating power, including the active and reactive power of the node itself and the sum of the active and reactive power of all branches at the lower level , , , and is expressed as:​ wherein, , denotes the active, reactive power of the end node, denotes the node transmits to the lower-level nodes active power transmitted on the branch, denotes the node transmits to the lower-level nodes reactive power transmitted on the branch, denotes the node number of lower-level branches.

7. The method for power flow calculation of a power distribution network with photovoltaic power according to claim 6, wherein, The probability distribution results of the power grid operation characteristics are fitted and corrected by using the series expansion method to form an operation state probability distribution curve, which comprises: using Cornish-Fisher series expansion to fit the probability information of the node voltage and branch power, i.e. the probability density function pdf and the cumulative distribution function cdf, to complete the calculation of the probability power flow; taking the distribution network node voltage amplitude and branch power as random variables ; calculating the related information of the origin moment and the central moment to obtain the mean and the standard deviation , and performing standardization variable; according to the standardized vector, the expansion Cornish-Fisher formula is calculated to obtain the value of the probability density function pdf of the certain node and branch power of the distribution network containing the uncertainty of the photovoltaic and load.

8. An improved half invariant based power flow calculation system for photovoltaic integrated power distribution network, applying the improved half invariant based power flow calculation method for photovoltaic integrated power distribution network according to any one of claims 1-7, characterized in that, The step of analyzing and solving the uncertainty components according to the unified characteristic parameter system and combining linear equations to obtain the probability distribution results of the grid operation characteristics comprises the following steps: based on the unified characteristic parameter system, combining the linearized alternating current flow equation at the reference point, solving the distribution network probability power flow based on the semi-invariant information, and accumulating the uncertainty and deterministic power flow information; A data acquisition module acquires power and grid operation data containing distributed power sources; A modeling estimation module calculates photovoltaic output and obtains probability density and cumulative distribution function by using an improved modeling and estimation method according to the power and grid operation data of the distributed power sources; A feature calculation module performs calculation and conversion processing of feature parameters based on probability information output by the probability density and cumulative distribution function, and constructs a unified feature parameter system; A linear analysis module analyzes and solves the uncertainty components according to the unified feature parameter system and in combination with linearization equations, and obtains probability distribution results of grid operation characteristics; A distribution fitting module fits and corrects the probability distribution results of the grid operation characteristics by using a series expansion method, and forms an operation state probability distribution curve. 9.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-8 when the computer program is executed by the processor. The processor executes the computer program to implement the steps of the improved semi-invariant power flow calculation method for photovoltaic distribution networks in any one of claims 1 to 7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the improved semi-invariant power flow calculation method for photovoltaic distribution networks in any one of claims 1 to 7.

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