Photovoltaic system optimal configuration method and system considering random characteristics

Abstract

The invention relates to the technical field of data processing, and discloses a photovoltaic system optimal configuration method and system considering random features. The method comprises the following steps: acquiring historical irradiance data, and generating an irradiance scene sample based on beta distribution; acquiring historical load data, and performing time sequence pairing on a load scene and an irradiance scene sample to generate a combined scene set; calculating a shadow effect correction factor according to the surrounding shielding information, correcting an irradiance value in the combined scene set, and obtaining a corrected photovoltaic output value; carrying out load flow calculation based on the corrected photovoltaic output value, carrying out statistics on node voltage and branch current default probabilities, and constructing an optimization target containing a penalty term; and adopting a teaching and learning optimization algorithm to carry out iterative optimization on the photovoltaic installation position, and outputting an optimal photovoltaic configuration scheme. According to the method, the problems of inaccurate random modeling, conservative constraint processing and insufficient shadow effect consideration in photovoltaic system planning are solved, and the equipment capacity redundancy and the investment cost are reduced.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and system for optimizing the configuration of a photovoltaic system that takes into account random characteristics. Background Technology

[0002] Against the backdrop of global energy transition, large-scale photovoltaic (PV) grid integration has become an important trend. Existing PV system planning methods mainly employ deterministic optimization models or stochastic optimization models based on Monte Carlo simulations to determine the optimal installation location and capacity configuration of PV systems in the distribution network. Deterministic optimization models typically assume that solar irradiance and load demand are fixed values ​​and perform optimization solutions based on a single typical scenario. Stochastic optimization models generate multiple stochastic scenarios to simulate the uncertainty of irradiance and load, and use intelligent optimization algorithms such as genetic algorithms and particle swarm optimization to solve the objective function of minimizing system power loss or maximizing economic benefits. In terms of constraint handling, existing methods usually require that node voltages and branch currents strictly meet safe operation limits in all scenarios.

[0003] However, existing technologies have three main shortcomings: First, traditional methods are mostly based on deterministic scenario assumptions or use a normal distribution to simply describe the randomness of irradiance, making it difficult to accurately capture the true random fluctuation characteristics of solar irradiance. The beta distribution is more suitable than the normal distribution for describing irradiance variables with limited value ranges, but existing methods do not fully utilize the beta distribution for modeling, and their insufficient coverage of extreme weather or low-probability events leads to poor robustness of planning schemes when facing abnormal operating conditions. Second, traditional methods require all operating scenarios to strictly meet hard constraints such as voltage and current, often requiring a large safety margin, resulting in equipment capacity redundancy and increased investment costs. When dealing with large-scale distribution networks, the efficiency of optimization is significantly reduced due to the need for detailed constraint verification for each scenario. Third, most existing methods fail to fully consider the local shading effect caused by clouds, vegetation, or building obstruction, systematically overestimating the actual output of photovoltaic power in the model, thus causing deviations in grid loss prediction and underestimation of operational risks.

[0004] Because the random characteristics of irradiance are not accurately modeled using beta distribution, the generated scene samples cannot fully cover the actual possible range of irradiance distribution. Consequently, the constraint verification and optimization solutions based on these incomplete scene samples lack representativeness. While strict hard constraints superficially ensure system safety, they are actually an overcompensation for insufficient scene representativeness. When further considering the impact of shading effects on photovoltaic output, the traditional deterministic modeling and hard constraint processing methods will lead to even more serious deviations between the planning scheme and actual operating conditions. Therefore, a photovoltaic system optimization configuration method that can accurately characterize random characteristics, reasonably handle constraints, and fully consider shading effects is needed to overcome the systemic defects of existing technologies. Summary of the Invention

[0005] This application provides a photovoltaic system optimization configuration method and system that takes into account stochastic characteristics, which can solve the problems of inaccurate stochastic modeling, overly conservative constraint handling, and insufficient consideration of shadowing effect in photovoltaic system planning, thereby reducing equipment capacity redundancy and investment costs.

[0006] Firstly, this application provides a method for optimizing the configuration of a photovoltaic system that takes into account random characteristics, the method comprising:

[0007] Step S1: Obtain historical solar irradiance data and generate multiple sets of irradiance scene samples based on beta distribution;

[0008] Step S2: Obtain historical load data, perform time-series pairing of load scenarios with the irradiance scenario samples, and generate a joint scenario set;

[0009] Step S3: Calculate the shadow effect correction factor based on the surrounding shading information of the candidate nodes, and correct the irradiance value in the joint scene set based on the shadow effect correction factor to obtain the corrected photovoltaic output value;

[0010] Step S4: Perform power flow calculation based on the corrected photovoltaic output value, calculate the default probability of node voltage and branch current under each scenario, and construct an optimization objective with penalty terms;

[0011] Step S5: Use the teaching and learning optimization algorithm to iteratively optimize the photovoltaic installation location, evaluate each configuration scheme according to the optimization objective, and output the optimal photovoltaic configuration scheme.

[0012] Secondly, this application provides a photovoltaic system optimization configuration system that takes into account random characteristics, the photovoltaic system optimization configuration system that takes into account random characteristics includes:

[0013] The acquisition module is used to acquire historical solar irradiance data and generate multiple sets of irradiance scene samples based on beta distribution;

[0014] The pairing module is used to acquire historical load data, perform time-series pairing of load scenarios with the irradiance scenario samples, and generate a joint scenario set;

[0015] The calculation module is used to calculate the shadow effect correction factor based on the surrounding shading information of the candidate nodes, and correct the irradiance value in the joint scene set based on the shadow effect correction factor to obtain the corrected photovoltaic output value.

[0016] The statistics module is used to perform power flow calculations based on the corrected photovoltaic output value, calculate the default probability of node voltage and branch current under each scenario, and construct an optimization target with penalties.

[0017] The iterative module is used to iteratively optimize the photovoltaic installation location using a teaching and learning optimization algorithm, evaluate each configuration scheme according to the optimization objective, and output the optimal photovoltaic configuration scheme.

[0018] Thirdly, a photovoltaic system optimization configuration device considering random characteristics is provided, comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to cause the photovoltaic system optimization configuration device considering random characteristics to execute the above-described photovoltaic system optimization configuration method considering random characteristics.

[0019] Fourthly, a computer-readable storage medium is provided, wherein instructions are stored therein, which, when executed on a computer, cause the computer to perform the aforementioned photovoltaic system optimization configuration method taking into account random characteristics.

[0020] The technical solution provided in this application uses beta distribution to model the random characteristics of solar irradiance and combines it with Latin hypercube sampling to generate multiple sets of irradiance scene samples. This overcomes the shortcomings of traditional deterministic methods and simple random sampling methods in accurately capturing the true fluctuation characteristics of irradiance. The support domain of beta distribution is naturally limited to the zero-to-one interval, which conforms to the physical constraints of normalized irradiance. By flexibly adjusting the shape parameters, it can accurately describe the asymmetric distribution characteristics in actual irradiance data caused by cloud cover and changes in atmospheric transparency. Compared with simple random sampling, Latin hypercube sampling can more uniformly cover the entire probability space with the same sample size, significantly improving the representativeness of scene samples for extreme weather and low-probability events. By temporally synchronizing and pairing load scenes with irradiance scenes and introducing the temporal correlation between irradiance and load through the Cholesky decomposition method, the high irradiance on clear days is preserved. The system generates a more realistic set of joint scenarios by considering the actual operating patterns of high air conditioning load during certain time periods and low load during cloudy and rainy weather, compared to the random combination method after independent generation. A three-dimensional shading model is established based on the shading information around the candidate nodes, and a ray tracing algorithm is used to calculate the shadow effect correction factor. This correction factor is applied to the photovoltaic output calculation to overcome the defect of existing technology that systematically overestimates the actual photovoltaic output. Based on the corrected photovoltaic output value, power flow calculation is performed and the probability of default is statistically analyzed to construct an optimization objective with a penalty term. By introducing probabilistic constraints, constraint violations in low-probability scenarios are allowed, avoiding the equipment capacity redundancy and increased investment costs caused by traditional hard constraint methods to cope with extreme scenarios. The penalty function mechanism ensures that when the probability of default exceeds the confidence level, penalties are automatically applied to guide the optimization algorithm to search for feasible solutions that satisfy the probabilistic constraints. This significantly reduces the conservatism of the planning while ensuring the overall safety and reliability of the system.

[0021] This paper proposes a teaching-learning optimization algorithm for iteratively optimizing photovoltaic (PV) installation locations. Three improvements are made to address the discrete characteristics and probabilistic constraints of the PV configuration problem. First, an adaptive teaching factor based on the default severity gradient is introduced, allowing individuals with high constraint violation rates a larger learning step size to accelerate their movement towards the feasible region. Second, a competitive learning mechanism based on constraint satisfaction is introduced during the learning phase, prioritizing individuals with large differences in constraint satisfaction to ensure sufficient but not excessive disparity in learning objects. Third, a local search mechanism based on probabilistic constraint repair is introduced to perform repair operations on individuals with default probabilities exceeding a threshold, identifying key nodes leading to constraint violations and adjusting their PV installation decisions using a greedy strategy. This repair mechanism ensures that the population maintains a certain proportion of feasible solutions, preventing the algorithm from getting trapped in the infeasible region. Compared to traditional optimization algorithms, the improved teaching-learning optimization algorithm converges faster and provides higher-quality solutions when solving PV configuration problems with probabilistic constraints. The entire optimization framework, through precise stochastic modeling, reasonable probabilistic constraint handling, and output correction considering the shading effect, achieves a balance between the economy and robustness of PV system configuration schemes while ensuring the safe and stable operation of the distribution network. Attached Figure Description

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of an embodiment of the photovoltaic system optimization configuration method that takes into account random characteristics in this application.

[0024] Figure 2 This is a schematic diagram of an embodiment of a photovoltaic system optimization configuration system that takes into account random characteristics in the present application.

[0025] Figure 3 This is a schematic block diagram of the structure of a photovoltaic system optimization configuration device that takes into account random characteristics in an embodiment of the present invention. Detailed Implementation

[0026] This application provides a method and system for optimizing the configuration of a photovoltaic system that takes into account random characteristics. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data used can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0027] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the photovoltaic system optimization configuration method that takes into account random characteristics in this application includes:

[0028] Step S1: Obtain historical solar irradiance data and generate multiple sets of irradiance scene samples based on beta distribution;

[0029] Step S2: Obtain historical load data, perform time-series pairing of load scenarios and irradiance scenario samples, and generate a joint scenario set;

[0030] Step S3: Calculate the shadow effect correction factor based on the surrounding shading information of the candidate nodes, and correct the irradiance value in the joint scene set based on the shadow effect correction factor to obtain the corrected photovoltaic output value.

[0031] Step S4: Perform power flow calculation based on the corrected photovoltaic output value, calculate the default probability of node voltage and branch current under each scenario, and construct an optimization objective with penalty terms;

[0032] Step S5: Use the teaching and learning optimization algorithm to iteratively optimize the photovoltaic installation location, evaluate each configuration scheme according to the optimization objective, and output the optimal photovoltaic configuration scheme.

[0033] It is understood that the executing entity of this application can be a photovoltaic system optimization configuration system that takes into account random characteristics, or it can be a terminal or a server; the specific implementation is not limited here. This application's embodiments use a server as an example for illustration.

[0034] Specifically, by acquiring historical solar irradiance data of each node within the distribution network planning area, statistical analysis is performed to obtain the mean μ and standard deviation σ of the irradiance. Then, the intermediate parameter ξ is calculated, which is obtained by multiplying the mean by one minus the mean, dividing by the square of the standard deviation, and then subtracting one. Next, based on the intermediate parameter, two shape parameters of the beta distribution are calculated. The first shape parameter α is equal to the product of the mean and the intermediate parameter, and the second shape parameter β is equal to the product of one minus the mean and the intermediate parameter. The advantage of the beta distribution over the normal distribution is that its value range is naturally limited to between zero and one, which conforms to the physical characteristics of normalized irradiance. The Latin hypercube sampling method is used to extract one hundred irradiance scene samples from the constructed beta distribution. Each scene sample contains the irradiance values ​​of all candidate photovoltaic installation nodes in the distribution network. Latin hypercube sampling divides the probability space into equal probability intervals and randomly samples within each interval, which can more uniformly cover the entire distribution space compared to simple random sampling. Step S2 obtains historical load data for each node of the distribution network, statistically calculates the mean and standard deviation of the load for each node, constructs a normal distribution based on these statistical parameters, and generates initial load scenario values ​​for each node. Then, by analyzing the synchronous variation pattern of irradiance and load in historical data, the time-series correlation coefficient matrix is ​​calculated. Each element of this matrix represents the degree of correlation between different variables. The Cholesky decomposition method is used to decompose the time-series correlation coefficient matrix into a lower triangular matrix, generating independent standard normal distribution random vectors with the same number of load scenarios. The lower triangular matrix is ​​multiplied with these random vectors to obtain correlated random vectors. Based on these correlated random vectors, the initial load scenario values ​​are linearly transformed to obtain adjusted load scenario values. The adjusted load scenario values ​​are paired with the corresponding irradiance scenario samples according to their sequence numbers to form a joint scenario set. This pairing method preserves the time-series correlation characteristics between irradiance and load. Step S3: Obtain the geographical coordinates of candidate nodes, the height information of surrounding buildings, and the vegetation distribution information to establish a three-dimensional occlusion model. This model includes the spatial location and geometric dimensions of obstacles around the nodes. Calculate the solar altitude angle and solar azimuth angle based on the time information corresponding to each scene in the joint scene set. The solar altitude angle represents the angle between the sun's rays and the ground plane, and the solar azimuth angle represents the angle between the sun's azimuth and due south. Based on the three-dimensional occlusion model, the solar altitude angle, and the solar azimuth angle, use a ray tracing algorithm to calculate the effective light-receiving area ratio of the photovoltaic array surface. The ray tracing algorithm emits virtual rays from the photovoltaic panel surface and detects whether these rays are blocked by surrounding obstacles. The proportion of the unblocked area to the total area is used as a shadow effect correction factor. Multiply this correction factor by the irradiance value of the corresponding node in the joint scene set to obtain the corrected irradiance value. Then, multiply the corrected irradiance value by the photovoltaic panel conversion efficiency and the photovoltaic panel area to obtain the corrected photovoltaic output value.Step S4 establishes power balance equations for each scenario based on the corrected photovoltaic output and load scenario values ​​in the combined scenario set. This equation states that the photovoltaic output of each node minus the load demand equals the sum of the power flowing out through the branches. The power balance equations are solved iteratively using a forward-backward substitution method. In the forward-subtraction stage, power is accumulated layer by layer from the end node to the root node; in the back-subtraction stage, voltage is calculated layer by layer from the root node to the end node. After multiple iterations until convergence, the node voltage values, node phase angle values, and branch current values ​​for each scenario are obtained. The node voltage values ​​exceeding the preset voltage are then statistically analyzed. The number of times the voltage exceeds or falls below the preset lower voltage limit is calculated. The number of times the voltage exceeds the lower limit is divided by the total number of scenarios to obtain the voltage default probability. Similarly, the number of times the branch current exceeds the preset upper current limit is calculated and divided by the total number of scenarios to obtain the current default probability. The power loss under each scenario is calculated and the average value is taken to obtain the expected power loss value. The difference between the voltage default probability and the preset voltage confidence level parameter is multiplied by the voltage penalty factor, and the difference between the current default probability and the preset current confidence level parameter is multiplied by the current penalty factor. The sum of the two penalty terms is added to the expected power loss value to construct the optimization objective with penalty terms. Step S5 sets the population size to fifty and the maximum number of iterations to two hundred. An initial population is randomly generated, and each individual is represented by a binary vector representing a photovoltaic installation location configuration scheme. Each element in the vector corresponds to a candidate node; a value of one indicates that the photovoltaic system will be installed at that node, and a value of zero indicates that it will not be installed. The voltage and current default probabilities for each individual are calculated, and the maximum value is taken as the default severity index. An adaptive teaching factor is calculated based on the default severity index. This factor equals one plus the default severity index, allowing individuals with higher constraint violation rates to have larger learning steps. During the teaching phase, the current optimal individual, the population mean, and the adaptive teaching factor are substituted into the update formula. The update formula is: current individual plus a random number multiplied by the optimal individual minus the adaptive teaching factor multiplied by the population mean plus the feasible solution guidance coefficient multiplied by the most feasible individual minus the current individual. Each individual is updated using this formula. For the photovoltaic installation location of the system, during the learning phase, individuals in the population are sorted according to the default degree index. Individuals with a sorting distance between one-quarter and one-half of the population size are paired. For each pair of individuals, if the optimization objective value of one is less than that of the other, a learning update is performed. The update formula is the inferior individual plus a random number multiplied by the superior individual minus the inferior individual. For individuals in the updated population whose default probability exceeds 1.5 times the voltage confidence level parameter or the current confidence level parameter, a constraint repair operation is performed. The key nodes that cause the constraint to exceed the limit are identified, and the photovoltaic installation decision of these nodes is adjusted one by one using a greedy strategy. After each adjustment, the default probability is recalculated until the constraint is met or the maximum number of repairs is reached (five). When the maximum number of iterations is reached or the improvement of the optimal objective value after fifty consecutive iterations is less than one ten-thousandth, the iteration is terminated, and the current best individual is output as the optimal photovoltaic configuration scheme.

[0035] In one specific embodiment, step S1 includes:

[0036] Obtain historical solar irradiance data for each node within the distribution network planning area, and calculate the mean and standard deviation of the historical solar irradiance data;

[0037] The intermediate parameter is calculated based on the mean and standard deviation. The formula for calculating the intermediate parameter is: mean multiplied by one minus mean divided by the square of the standard deviation minus one.

[0038] The shape parameters of the beta distribution are calculated based on the intermediate parameters. The first shape parameter is the product of the mean and the intermediate parameter, and the second shape parameter is the product of the mean minus the intermediate parameter.

[0039] A preset number of irradiance scene samples are extracted from the beta distribution using the Latin hypercube sampling method. Each set of scene samples corresponds to the irradiance values ​​of all candidate photovoltaic installation nodes in the distribution network.

[0040] Specifically, obtaining historical solar irradiance data for each node within the distribution network planning area refers to extracting solar irradiance observations from meteorological monitoring stations or historical operation records of photovoltaic power plants over a past period. This data includes irradiance variations at different times and under different weather conditions. The mean of historical solar irradiance data is calculated by summing all observations and dividing by the number of observations. The standard deviation is obtained by taking the square root of the sum of the squares of the differences between each observation and the mean, divided by the number of observations. The mean reflects the average level of irradiance, while the standard deviation reflects the degree of fluctuation of irradiance around the mean. The process of calculating intermediate parameters based on the mean and standard deviation involves first subtracting the mean from the mean to obtain the complement of the mean, then multiplying the mean by the complement to obtain the numerator. Next, the square of the standard deviation is calculated as part of the denominator. The numerator is then divided by the square of the standard deviation, and then subtracted to obtain the intermediate parameter. This intermediate parameter serves as a bridge connecting statistical characteristic parameters and beta distribution shape parameters, and its physical meaning reflects the comprehensive characteristics of the dispersion and central tendency of irradiance data. Calculating the shape parameters of the beta distribution based on intermediate parameters involves two steps. The first shape parameter is obtained by directly multiplying the mean by the intermediate parameter. The second shape parameter is obtained by first subtracting the mean from the mean to obtain the complement of the mean, and then multiplying it by the intermediate parameter. The beta distribution is a continuous probability distribution defined on the interval between zero and one. The two shape parameters together determine the shape of the distribution curve. When the first shape parameter is greater than the second shape parameter, the distribution exhibits a right-skewed characteristic. When the second shape parameter is greater than the first shape parameter, the distribution exhibits a left-skewed characteristic. When the two are equal, the distribution exhibits a symmetrical characteristic. This flexibility allows the beta distribution to accurately describe the asymmetric fluctuations of actual solar irradiance. The specific process of extracting a preset number of irradiance scene samples from the beta distribution using the Latin hypercube sampling method is as follows: First, the cumulative probability interval from zero to one is divided into a preset number of sub-intervals. A probability value is randomly selected in each sub-interval. Then, these probability values ​​are converted into corresponding irradiance sample values ​​through the inverse cumulative distribution function of the beta distribution. The advantage of Latin hypercube sampling compared to simple random sampling lies in its hierarchical sampling characteristics in the probability space. Simple random sampling suffers from sample clustering, leading to oversampling in some probability areas and undersampling in others. Latin hypercube sampling ensures that the samples are evenly distributed throughout the entire distribution range by forcing sampling within each probability layer. The irradiance values ​​of all candidate photovoltaic installation nodes in the distribution network corresponding to each set of scene samples refer to generating a vector containing the irradiance values ​​of all nodes for each sampling, rather than just a single value. There is a spatial correlation between the irradiance values ​​of each node in this vector. Adjacent nodes have similar irradiance characteristics due to their geographical proximity. This spatial correlation is obtained by analyzing the covariance matrix of the irradiance of each node in historical data and is maintained during the sampling process using a multivariate beta distribution or a Gaussian Copula function.

[0041] In one specific embodiment, step S2 includes:

[0042] Obtain historical load data for each node in the distribution network, and calculate the mean and standard deviation of the historical load data;

[0043] A normal distribution is constructed based on the mean and standard deviation of historical load data, and load scenario values ​​for each node are generated based on the normal distribution.

[0044] Obtain the time-series correlation coefficient matrix between irradiance scene samples and load scene values. The time-series correlation coefficient matrix is ​​calculated based on the synchronous change characteristics of irradiance and load in historical data.

[0045] The Cholesky decomposition method is used to decompose the time-series correlation coefficient matrix. Based on the decomposition results, the correlation of the load scene values ​​is adjusted. The adjusted load scene values ​​are then paired with the corresponding irradiance scene samples to generate a joint scene set.

[0046] Specifically, obtaining historical load data for each node in the distribution network refers to extracting the electricity load records of each node over a past period from the distribution network monitoring system or smart meters. These data reflect the changes in electricity consumption of each node under different time periods, seasons, and weather conditions. The mean of historical load data is calculated by summing all load observations of a node and dividing by the total number of observations. This mean reflects the average electricity consumption level of the node. The standard deviation is obtained by taking the square root of the sum of the squares of the differences between each load observation and the mean, divided by the number of observations. The larger the standard deviation, the more severe the load fluctuation of the node. Constructing a normal distribution based on the mean and standard deviation of historical load data refers to using the mean as the location parameter of the normal distribution and the standard deviation as the scale parameter to determine the shape of the probability density function of the normal distribution. The probability density function of the normal distribution reaches its peak at the mean and decreases symmetrically to both sides. The load scenario values ​​of each node are generated according to the normal distribution. Random numbers that follow the standard normal distribution are generated by a random number generator, and then multiplied by the standard deviation and added to the mean to complete the transformation from the standard normal distribution to the target normal distribution. In the initial state of the generated load scenario values, the nodes are independent of each other and the correlation between nodes is not considered. Obtaining the time-series correlation coefficient matrix between irradiance scenario samples and load scenario values ​​refers to analyzing the coordinated changes in solar irradiance and load demand over time in historical data. Each element of the time-series correlation coefficient matrix represents the Pearson correlation coefficient between a certain irradiance variable and a certain load variable. This correlation coefficient is obtained by calculating the covariance of the two variables and dividing it by the product of the standard deviations of the two variables. The covariance reflects the trend of the common change of the two variables. When irradiance increases and load also increases, the covariance is positive, indicating a positive correlation. When irradiance increases and load decreases, the covariance is negative, indicating a negative correlation. The correlation coefficient ranges from -1 to 1, and the closer the absolute value is to 1, the stronger the correlation.The Cholesky decomposition method for decomposing the time-series correlation coefficient matrix is ​​a numerical method that decomposes a symmetric positive definite matrix into the product of a lower triangular matrix and its transpose. The decomposition process starts from the top-left element and calculates each element of the lower triangular matrix row by row and column by column. The element in the first row and first column equals the square root of the corresponding element in the original matrix. Other elements in the first column equal the original element divided by the element in the first row and first column. Subsequent elements are calculated using a recursive relationship, where each element is subtracted from the sum of the products of the previous elements in the row and the previous elements in the corresponding column. The process of adjusting the correlation of load scenario values ​​based on the decomposition results involves generating independent standard normal distributed random vectors with the same number of load scenarios. These random vectors are independent, with a mean of 0 and a standard deviation of 1. The lower triangular matrix obtained from the Cholesky decomposition is then multiplied by these independent random vectors. The rule for matrix multiplication is that the first element of the resulting vector is the square root of the first element. The i components are equal to the sum of the products of each element in the i-th row of the lower triangular matrix and the corresponding component of the random vector. Through this matrix multiplication operation, the originally independent random vectors are transformed into correlated random vectors. The covariance structure of the correlated random vectors is consistent with the time-series correlation coefficient matrix. Based on the correlated random vectors, the initially generated load scenario values ​​are linearly transformed. The linear transformation is completed by multiplying the correlated random vectors by the load standard deviation and adding the load mean. The resulting adjusted load scenario values ​​not only follow a normal distribution, but the correlation between the variables is consistent with the irradiance-load correlation observed in historical data. Pairing the adjusted load scenario values ​​with the corresponding irradiance scenario samples means combining the i-th group of load scenario values ​​with the i-th group of irradiance scenario samples to form the i-th joint scenario. The resulting set of joint scenarios contains 100 such joint scenarios. Each joint scenario contains both the irradiance value and the load value of each node.Taking a commercial area's power distribution network as an example, historical data shows that a certain node experiences higher daytime loads and lower nighttime loads on weekdays. The average load at this node is 500 kW with a standard deviation of 100 kW. Based on these statistical parameters, a normal distribution is constructed, generating 100 initial load scenario values. Analysis of historical data reveals that the total load in this commercial area increases during sunny, high-irradiance periods due to increased air conditioning load. The time-series correlation coefficient between irradiance and load is calculated to be 0.7, indicating a strong positive correlation. After constructing the time-series correlation coefficient matrix, Cholesky decomposition is performed to obtain a lower triangular matrix. This generates 100 independent standard normal distribution random vectors, which are then multiplied by the lower triangular matrix to obtain correlated random vectors. In these correlated random vectors, the load is higher when the irradiance component is larger. The corresponding components also tend to be larger. The initial load scenario values ​​are adjusted based on the relevant random vectors. In the adjustment process, each component of the relevant random vector is multiplied by the standard deviation of 100 kW and the mean of 500 kW. In the adjusted load scenario values, the load values ​​corresponding to high irradiance scenarios are generally higher than the mean, while the load values ​​corresponding to low irradiance scenarios are generally lower than the mean. The 100 sets of adjusted load scenario values ​​are paired with the 100 sets of previously generated irradiance scenario samples according to their serial numbers. The first joint scenario contains the numerical combination of all nodes under low irradiance and low load conditions, corresponding to cloudy and rainy weather. The 50th joint scenario contains the numerical combination of medium irradiance and medium load, corresponding to cloudy weather. The 100th joint scenario contains the numerical combination of high irradiance and high load, corresponding to sunny and high-temperature periods.

[0047] In one specific embodiment, the Cholesky decomposition method is used to decompose the time-series correlation coefficient matrix. Based on the decomposition results, the load scene values ​​are re-adjusted for correlation. The adjusted load scene values ​​are then paired with corresponding irradiance scene samples to generate a joint scene set, including:

[0048] The time-series correlation coefficient matrix is ​​decomposed using Cholesky decomposition to obtain a lower triangular matrix.

[0049] Generate independent, standard normally distributed random vectors that match the number of scenarios and nodes in the load scenario value;

[0050] Perform matrix multiplication on the lower triangular matrix and the independent standard normal distributed random vector to obtain a correlated random vector;

[0051] The load scene values ​​are linearly transformed based on the correlated random vectors to obtain the adjusted load scene values. The adjusted load scene values ​​are then paired one-to-one with the irradiance scene samples of the corresponding sequence number to generate a joint scene set.

[0052] Specifically, Cholesky decomposition of the time-series correlation coefficient matrix is ​​a mathematical transformation method that decomposes a symmetric positive definite matrix into the product of a lower triangular matrix and its transpose. The decomposition process calculates the value of each element of the lower triangular matrix element by element from top left to bottom right. The element in the first row and first column of the lower triangular matrix is ​​equal to the square root of the element in the first row and first column of the time-series correlation coefficient matrix. The remaining elements in the first column of the lower triangular matrix are equal to the corresponding element in the time-series correlation coefficient matrix divided by the element in the first row and first column of the lower triangular matrix. The element in the second row and second column of the lower triangular matrix is ​​equal to the element in the second row and second column of the time-series correlation coefficient matrix. The square root of the square of the element in the second row and first column of the lower triangular matrix is ​​taken by subtracting the square of the element in the first row and second column of the lower triangular matrix. The elements in the second row and second column of the lower triangular matrix are equal to the element in the corresponding position of the time series correlation coefficient matrix minus the product of the element in the first column of the row and the element in the first column of the second row, and then divided by the element in the second row and second column of the lower triangular matrix. Subsequent row and column elements are calculated in a similar recursive manner. The calculation of each element requires subtracting the sum of the products of the elements in the preceding columns of the row containing the element and the elements in the corresponding row of the column containing the element. After the decomposition, the resulting lower triangular matrix has the structural characteristics of containing non-zero elements below the main diagonal and all zero elements above the main diagonal. Generating independent standard normal distribution random vectors that match the number of scenarios and nodes in the load scenario values ​​means generating 100 random vectors, each with a dimension equal to the total number of nodes in the distribution network. The meaning of independent standard normal distribution is that each random vector is independent of the others, and each component within each random vector is also independent of the others. The characteristics of standard normal distribution are a mean of 0 and a standard deviation of 1. The generation process uses the Box-Muller transformation method or the inverse transformation method. The Box-Muller transformation method generates two random numbers that follow a uniform distribution from 0 to 1. Then, the square root of the negative 2 natural logarithm of the first random number is taken to obtain the radius. The second random number is multiplied by 2 times pi to obtain the angle. The radius is multiplied by the cosine and sine of the angle to obtain two independent standard normal distribution random numbers. This process is repeated until the required number of random vectors are generated. Matrix multiplication of a lower triangular matrix with independent standard normal distributed random vectors refers to the linear combination operation of the lower triangular matrix as the left multiplication matrix with the random vector. Specifically, the i-th component of the resulting vector is equal to the element in the i-th row and i-th column of the lower triangular matrix multiplied by the first component of the random vector, plus the element in the i-th row and i-th column of the lower triangular matrix multiplied by the second component of the random vector, and so on, up to the element in the i-th row and i-th column of the lower triangular matrix multiplied by the i-th component of the random vector. Since only the first i columns of the i-th row of the lower triangular matrix have non-zero elements, the calculation of each resulting component only involves the first i components of the random vector. After the matrix multiplication operation, a correlated random vector is obtained. The components of this random vector are no longer independent of each other but exhibit a correlation structure described by the time series correlation coefficient matrix. The covariance matrix of the correlated random vector is equal to the product of the lower triangular matrix and its transpose, which is equal to the original time series correlation coefficient matrix.Linear transformation of load scenario values ​​based on correlated random vectors is a process of adjusting load scenario values ​​previously generated independently based on normal distributions according to correlation requirements. The specific operation of linear transformation is to multiply each component of the correlated random vector by the standard deviation of the corresponding node load and then add the mean of the corresponding node load. This transformation is essentially a standardized inverse transformation process of converting a standard normal distribution variable into a normal distribution variable with a specified mean and standard deviation. The adjusted load scenario values ​​obtained after linear transformation not only follow a normal distribution, but their mean and standard deviation are also consistent with the statistical characteristics of historical load data. At the same time, the correlation structure between node loads and between load and irradiance is completely consistent with the correlation structure described by the time series correlation coefficient matrix. Pairing the adjusted load scenario values ​​with the corresponding irradiance scenario samples one-to-one means combining the first set of adjusted load scenario values ​​with the first set of irradiance scenario samples to form the first joint scenario, combining the second set of adjusted load scenario values ​​with the second set of irradiance scenario samples to form the second joint scenario, and so on until the 100th set of adjusted load scenario values ​​is combined with the 100th set of irradiance scenario samples to form the 100th joint scenario. Each joint scenario contains two types of data: irradiance values ​​and load values ​​for all nodes in the distribution network under that scenario. The resulting set of joint scenarios contains all 100 joint scenarios, forming a complete irradiance-load joint probability distribution. By deploying a sample space, this joint scenario set not only preserves the marginal probability distribution characteristics of irradiance and load respectively, but also accurately reflects the temporal and spatial correlation between the two. Compared with the method of independently generating irradiance scenarios and load scenarios and then randomly combining them, the method of introducing correlation through Cholesky decomposition overcomes the defect of existing technologies that ignore the temporal correlation between irradiance and load. When the irradiance is high, the paired load scenario value also tends to be high, reflecting the actual operating pattern of increased temperature control loads such as air conditioning during sunny and high irradiance periods. When the irradiance is low, the paired load scenario value also tends to be low, reflecting the objective situation of decreased temperature control load demand during cloudy and rainy weather.

[0053] In one specific embodiment, step S3 includes:

[0054] Obtain the geographical coordinates of candidate nodes, the height information of surrounding buildings, and the vegetation distribution information to establish a three-dimensional occlusion model;

[0055] Calculate the solar altitude angle and solar azimuth angle based on the time information corresponding to each scene in the joint scene set;

[0056] Based on the three-dimensional shading model, solar elevation angle and solar azimuth angle, the ray tracing algorithm is used to calculate the effective light-receiving area ratio of the photovoltaic array surface at each candidate node, and the effective light-receiving area ratio is used as the shadow effect correction factor.

[0057] The shading effect correction factor is multiplied by the irradiance value of the corresponding node in the joint scene set to obtain the corrected irradiance value. The corrected irradiance value is then multiplied by the photovoltaic panel conversion efficiency and the photovoltaic panel area to obtain the corrected photovoltaic output value.

[0058] Specifically, obtaining the geographical coordinates of candidate nodes refers to acquiring the longitude, latitude, and altitude values ​​of each candidate photovoltaic installation node in the power distribution network through GPS positioning or geographic information system. The height information of surrounding buildings includes the height data of all buildings within a certain radius around the node and their relative azimuth angle data. The vegetation distribution information includes the height, crown diameter, and distance and azimuth relationship between trees and nodes. Establishing a three-dimensional occlusion model involves inputting this geographical information and obstacle information into a three-dimensional spatial coordinate system to construct a solid geometric model containing candidate nodes, surrounding buildings, and vegetation. In the model, each obstacle is represented by a polygonal mesh or voxel to indicate its spatial occupancy. Calculating the solar altitude angle and solar azimuth angle based on the time information corresponding to each scene in the joint scene set refers to extracting the date and time information corresponding to each scene from the joint scene set. The solar altitude angle represents the angle between the direction of sunlight and the ground plane, ranging from 0 to 90 degrees. The solar azimuth angle represents the angle between the projection of sunlight on the horizontal plane and the due south direction, ranging from 0 to 360 degrees. Calculating the solar altitude angle requires first calculating the solar declination angle, which is calculated using a formula based on the date and represents the latitude difference between the subsolar point and the equator. Then, the solar altitude angle is calculated based on the solar declination angle, the latitude of the candidate node, and the hour angle. The hour angle is calculated based on the deviation between the local time and noon. Similarly, the solar azimuth angle is calculated based on the solar declination angle, node latitude, hour angle, and solar altitude angle using trigonometric function relationships. The effective light-receiving area ratio of the photovoltaic array surface at each candidate node is calculated using a ray tracing algorithm based on a 3D shading model, solar altitude angle, and solar azimuth angle. The data processing steps are as follows: The ray tracing algorithm emits several virtual rays from the photovoltaic array surface of the candidate node. The direction of each ray is determined by the solar altitude angle and solar azimuth angle, pointing towards the sun. During the propagation of the virtual rays in 3D space, it is detected whether they intersect with buildings or vegetation in the 3D shading model. Intersection detection is determined by calculating the intersection point between the ray and the geometric surface of the obstacle. If the ray intersects with the surface of an obstacle and the intersection point is located between the ray's origin and the direction of the sun, then the ray is shaded. The effective light-receiving area ratio is the proportion of the number of unshaded virtual rays out of the total number of rays. This ratio is between 0 and 1. When all rays are unshaded, the ratio is 1, indicating no shadow. When all rays are shaded, the ratio is 0, indicating complete shadow. The effective light-receiving area ratio is used as a shadow effect correction factor and directly applied to subsequent photovoltaic output calculations.Multiplying the irradiance value of the corresponding node in the joint scene set by the shading effect correction factor means taking the irradiance value of a node in a certain scene of the joint scene set and multiplying it by the shading effect correction factor corresponding to that node at that moment in that scene. The physical meaning of the multiplication operation is to reduce the irradiance value under ideal unshaded conditions according to the actual shading situation. The corrected irradiance value reflects the actual solar radiation intensity received by the node at that moment after considering the shading effect. The specific process of multiplying the corrected irradiance value by the photovoltaic panel conversion efficiency and the photovoltaic panel area is as follows: first, multiply the corrected irradiance value by the photovoltaic panel area to obtain the total radiation power received by the photovoltaic array, and then multiply it by the photovoltaic panel conversion efficiency to obtain the actual output power of the photovoltaic system. The photovoltaic panel conversion efficiency is the efficiency ratio of the photovoltaic cell to convert solar radiation energy into electrical energy, usually ranging from 0.15 to 0.22. The photovoltaic panel area is the total light-receiving area of ​​the photovoltaic array installed at that node. The corrected photovoltaic output value represents the actual power generation of the node under the shading effect in that scene. Taking a company's rooftop photovoltaic (PV) system as an example, the candidate node is located at the center of the factory roof. GPS coordinates and roof height are obtained for this node. On-site surveys reveal a high-rise office building to the east of the factory and a row of trees to the west. Measurements show the office building is taller than the factory roof, while the trees are slightly shorter. The location and height information of the office building and trees are input into 3D modeling software to create a 3D occlusion model including the factory, office building, and trees. A scene from the combined scene set corresponds to 9 AM in summer. The solar declination angle is calculated based on this date and time. Combined with the factory's latitude and hour angle, the solar altitude angle is calculated to be approximately 45 degrees, and the solar azimuth angle is approximately 30 degrees east of south. 1000 uniformly distributed virtual rays are emitted from the surface of the factory rooftop PV array towards the sun. A ray tracing algorithm detects whether each ray intersects with the office building to the east. It was found that 200 rays intersected with the east facade of the office building and were blocked, while the remaining 800 rays were unblocked and reached the sun directly. The effective light-receiving area ratio was calculated as 800 divided by 1000, which equals 0.8. This ratio was used as a shading effect correction factor. In this scenario, the original irradiance value of this node was 0.7 kW / m². Multiplying 0.7 by the shading effect correction factor of 0.8 yielded a corrected irradiance value of 0.56 kW / m². Assuming that the planned photovoltaic panel area for this node is 100 m² and the photovoltaic panel conversion efficiency is 0.18, multiplying the corrected irradiance value of 0.56 by the area of ​​100 gives a total received radiation power of 56 kW. Multiplying this by the conversion efficiency of 0.18 gives a corrected photovoltaic output value of 10.08 kW. This value is significantly lower than the photovoltaic output value without considering the shading effect, overcoming the defect of overestimating the actual photovoltaic output in the existing technology.

[0059] In one specific embodiment, step S4 includes:

[0060] Based on the corrected photovoltaic output value and the load scenario value in the joint scenario set, power balance equations are established for each scenario. The forward-backward substitution method is used to solve the power balance equations to obtain the node voltage value, node phase angle value and branch current value for each scenario.

[0061] The number of times the node voltage value exceeds the preset voltage upper limit or falls below the preset voltage lower limit in each scenario is counted, and the ratio of the number of violations to the total number of scenarios is used as the voltage default probability.

[0062] The number of times the branch current value exceeds the preset current limit in each scenario is counted, and the ratio of the number of limit exceedances to the total number of scenarios is used as the current violation probability.

[0063] Calculate the desired power loss value by multiplying the difference between the voltage default probability and the preset voltage confidence level parameter and the difference between the current default probability and the preset current confidence level parameter by the corresponding penalty factors, and summing the results. Add the summation result to the desired power loss value to construct an optimization objective with penalty terms.

[0064] Specifically, establishing power balance equations for each scenario based on the corrected photovoltaic output and load scenario values ​​in the joint scenario set refers to writing an equality constraint for each node in each scenario, where the node's injected power equals its outflow power. The node's injected power equals the corrected photovoltaic output minus the load scenario value, and the node's outflow power equals the sum of the power transmitted from that node to adjacent nodes through its branches. The power balance equation is expressed as node injected power minus outflow power equals zero. Solving the power balance equation using the forward-backward substitution method is an iterative calculation method suitable for radial distribution networks. The forward-pushing process starts from the end node of the distribution network and accumulates the power flow of each branch layer by layer towards the root node. First, it is assumed that the voltage of all nodes is equal to the rated voltage. Based on the injected power of the end node and the assumed voltage, the current of the end branch is calculated. The current is calculated by dividing the injected power of the node by the node voltage. Then, the current of the branch is passed to the next higher level node, and the current of all downstream branches of the node is accumulated to obtain the current flowing through the upstream branch of the node. This process is repeated upwards until the root node completes one forward push. The backward push process updates the voltage of each node layer by layer from the root node to the end node. The voltage of the root node is taken as the rated voltage value. The voltage of the next level node is equal to the voltage of the previous level node minus the voltage drop of the branch between the two nodes. The voltage drop of the branch is equal to the branch current multiplied by the branch impedance. The branch impedance includes both resistance and reactance. This process is repeated downwards until the end node completes one backward push. The forward push and backward push processes are repeated until the change in node voltage obtained from two adjacent iterations is less than the preset convergence threshold. After convergence, the voltage amplitude, phase angle value and current value of all branches of all nodes in each scenario are obtained. The count of times a node's voltage value exceeds the preset upper voltage limit or falls below the preset lower voltage limit in each scenario involves iterating through all node voltage values ​​in each of 100 scenarios and comparing each node's voltage value with its preset upper and lower voltage limits. The preset upper voltage limit is typically 1.05 times the rated voltage, and the preset lower voltage limit is typically 0.95 times the rated voltage. When the voltage value of a node in a certain scenario is greater than the upper voltage limit or less than the lower voltage limit, the node experiences a voltage over-limit in that scenario. The count of voltage over-limit occurrences for that node across all scenarios is accumulated, and the ratio of the over-limit count to the total number of scenarios is taken as the voltage over-limit probability. The voltage over-limit probability reflects the frequency of voltage over-limit occurrences for that node under random operating conditions. The method of counting the number of times the branch current value exceeds the preset current limit in each scenario refers to iterating through all the branch current values ​​in each of the 100 scenarios, comparing the current value of each branch with the preset current limit of that branch. The preset current limit is the rated current carrying capacity of the conductor in that branch. When the current value of a branch in a certain scenario is greater than the current limit, the branch has a current over-limit in that scenario. The number of times the current over-limit occurs in all scenarios is accumulated, and the ratio of the number of over-limit to the total number of scenarios is used as the current over-limit probability. The current over-limit probability reflects the frequency of overload of the branch under random operating conditions.Calculating the expected power loss value involves calculating the total power loss of the distribution network in each of 100 scenarios and then taking the arithmetic mean. The power loss in a single scenario equals the sum of the power losses of all branches. The power loss of a single branch equals the square of the branch current multiplied by the branch resistance. The expected power loss value is obtained by summing the power loss values ​​of the 100 scenarios and dividing by 100. This expected value reflects the average loss level of the distribution network after considering randomness. The specific calculation process involves multiplying the difference between the voltage default probability and the preset voltage confidence level parameter, and the difference between the current default probability and the preset current confidence level parameter, by the corresponding penalty factors and then summing them. First, the voltage default probability is calculated by subtracting the preset voltage confidence level parameter to obtain the voltage default excess. The preset voltage confidence level parameter is usually set to 0.05, indicating that 5% of scenarios are allowed to exceed the voltage limit. When the voltage default probability is less than the confidence level parameter, the default excess is negative. The value is set to zero. When the voltage default probability is greater than the confidence level parameter, the default excess is positive. The voltage default excess is multiplied by the voltage penalty factor to obtain the voltage penalty. The voltage penalty factor is set to a large value, such as 5000, to ensure that a significant penalty is imposed when a default occurs. Similarly, the current default probability is calculated and the current default excess is obtained by subtracting the preset current confidence level parameter. The current default excess is multiplied by the current penalty factor to obtain the current penalty. The voltage penalty and the current penalty are added to obtain the total penalty. The sum is added to the expected power loss value to construct the optimization objective containing the penalty. The optimization objective function value is equal to the expected power loss value plus the total penalty. This objective function only considers minimizing loss when the default probability meets the confidence level requirement. When the default probability exceeds the confidence level, a penalty is automatically applied to guide the optimization algorithm to search for a feasible solution that satisfies the probability constraints. This overcomes the defect in the existing technology that requires strict satisfaction of constraints in all scenarios, resulting in equipment capacity redundancy.Taking a power distribution network in an industrial park as an example, the combined scenario set contains 100 scenarios. Under a certain photovoltaic configuration scheme, a power balance equation is established for each scenario and solved using the forward and backward substitution method. In the forward substitution process, starting from the end load node, it is assumed that the voltage of this node is the rated value of 1 per unit. After correction, the photovoltaic output of this node is 80 kW, the load scenario value is 100 kW, and the node injection power is -20 kW, indicating that power needs to be absorbed from the upstream. Based on the injected power and the assumed voltage, the current flowing through the upstream branch of this node is calculated, and this current is passed upward and accumulated with the current of other downstream branches of the first-level node. In the backward substitution process, starting from the rated voltage of the root node, the voltage of each node is calculated downward. The current of a certain branch is 50 amps, the branch impedance is 0.01 ohms, and the voltage drop is the current multiplied by the impedance, which equals 0.5 volts. The voltage of the downstream node is equal to the voltage of the upstream node minus the voltage drop. After multiple iterations, the sum of the voltage values ​​of all nodes under this scenario is obtained. For branch current values, statistics from 100 scenarios revealed that a certain node's voltage exceeded the upper limit of 1.05 per unit in 8 scenarios, with a voltage default probability of 8 divided by 100 equaling 0.08. Statistics also showed that a certain branch's current exceeded the upper limit of 300 amperes in 3 scenarios, with a current default probability of 3 divided by 100 equaling 0.03. The power loss for each of the 100 scenarios was calculated, summed, and divided by 100 to obtain an expected power loss value of 150 kW. The preset voltage confidence level parameter was 0.05. The voltage default probability of 0.08 exceeded the confidence level, and the excess default amount was 0.08 minus 0.05 equaling 0.03. Multiplying this by the voltage penalty factor of 5000 yielded a voltage penalty of 150. The current default probability of 0.03 was less than the preset current confidence level parameter of 0.05, so no penalty was generated. The total penalty was 150. The optimized objective function value equals the expected power loss value of 150 kW plus the total penalty of 150, resulting in 300.

[0065] In one specific embodiment, step S5 includes:

[0066] Set the preset population size and maximum number of iterations, randomly generate the initial population, and each individual in the initial population corresponds to a photovoltaic installation location configuration scheme;

[0067] The maximum values ​​of voltage default probability and current default probability of each individual are calculated as default degree indicators. Based on the default degree indicators, adaptive teaching factors are calculated. The current best individual, population mean and adaptive teaching factors are substituted into the teaching stage update formula to update the photovoltaic installation position of each individual.

[0068] Individuals in the population are sorted according to the degree of default, and pairs of individuals whose sorting distance is within a preset range are selected for pairing. The learning phase update is performed based on the difference in optimization objectives between the paired individuals to obtain the updated population.

[0069] For individuals in the updated population whose default probability exceeds a preset threshold, a constraint repair operation is performed to adjust the photovoltaic installation decisions of key nodes that cause the default. When the termination condition is met, the current best individual is output as the optimal photovoltaic configuration scheme.

[0070] Specifically, setting the preset population size to 50 means that the optimization algorithm maintains 50 candidate solutions simultaneously, and the maximum number of iterations to 200 means that the algorithm performs a maximum of 200 rounds of evolution and updates. The process of randomly generating the initial population involves generating a binary vector for each individual. The length of the vector is equal to the total number of candidate nodes in the distribution network. Each element in the vector corresponds to a candidate node. An element value of 1 indicates that a photovoltaic system is installed on that node, and an element value of 0 indicates that it is not installed. The random generation process involves randomly selecting a preset number of nodes and setting the corresponding positions to 1, while setting the remaining positions to 0. Each individual in the initial population corresponds to a photovoltaic installation location configuration scheme. The binary vectors of different individuals have different distributions of 1 positions, representing different installation schemes. Calculating the maximum voltage and current default probabilities of each individual as a default severity index involves performing power flow calculations on a specific configuration scheme to obtain the voltage default probabilities of all nodes and the current default probabilities of all branches under that scheme. The maximum voltage default probability is taken from all node voltage default probabilities, and the maximum current default probability is taken from all branch current default probabilities. The maximum value of both maximum voltage and maximum current default probabilities is then used as the default severity index for that individual. A higher default severity index indicates a more severe constraint violation of the configuration scheme. The formula for calculating the adaptive teaching factor based on the default severity index is: the adaptive teaching factor equals 1 plus the default severity index. In traditional teaching and learning optimization algorithms, the teaching factor is a fixed value of 1 or 2. The improved adaptive teaching factor dynamically adjusts according to the individual's default severity; individuals with higher default severity have a larger teaching factor, thus achieving better results. Larger learning steps accelerate movement towards the feasible region. Substituting the current optimal individual, population mean, and adaptive teaching factor into the teaching stage update formula involves first calculating the average of all individual configuration schemes in the population to obtain the population mean vector. Each element of the population mean vector equals the number of individuals with a value of 1 at that position divided by the population size. Then, the individual with the smallest objective function value is selected from the population as the current optimal individual. The teaching stage update formula is: the new position of an individual equals the current position of the individual plus a random number multiplied by the current optimal individual minus the adaptive teaching factor multiplied by the population mean plus a guidance coefficient multiplied by the most feasible individual minus the current position of the individual. The random number follows a uniform distribution from 0 to 1 to introduce randomness. The most feasible individual is the individual with the smallest default rate index in the population. The guidance coefficient is set to 0.3 to ensure that the individual moves towards both the optimal and feasible solutions simultaneously. The photovoltaic installation positions of each individual are updated by executing the above update formula to obtain the new position vector of each individual.Sort the individuals in the population according to the default severity index. This involves arranging 50 individuals in ascending order of default severity index to obtain a sorted sequence. The specific operation of pairing individuals whose sorting distance is within a preset range is as follows: For the i-th individual in the sorted sequence, select individuals whose sorting position is within the range of i plus one-quarter of the population size to i plus one-half of the population size as their pairing object. The sorting distance refers to the difference in position between two individuals in the sorted sequence. The preset range ensures that the default severity of the paired individuals has a certain difference, but not too large. The learning phase update based on the difference in the optimization objective between the paired individuals involves comparing the optimization objective function values ​​of the two paired individuals. If the objective function value of individual j is less than that of individual i, then individual i learns from individual j. The learning update formula is: the new position of individual i equals the current position of individual i plus a random number multiplied by the position of individual j minus the position of individual i. If the objective function value of individual j is greater than that of individual i, then individual j learns from individual i. The update is performed in the opposite direction to obtain the updated population containing the new position vectors of all individuals after the teaching and learning phases. Performing constraint repair operations on individuals in the updated population whose default probability exceeds a preset threshold involves iterating through all individuals in the updated population, calculating the default severity index for each individual, and initiating a repair operation when an individual's default severity index exceeds a preset threshold. The preset threshold is 1.5 times the voltage confidence level parameter or the current confidence level parameter. Adjusting the photovoltaic installation decisions of critical nodes that cause the over-limit involves identifying which nodes in the individual's configuration scheme have photovoltaic installations that cause voltage or current over-limits. The identification method is to remove each node with installed photovoltaics in the scheme one by one, recalculate the power flow, and compare the change in default probability before and after removal. The node with the largest decrease in default probability after removal is the critical node. The photovoltaic installation decision of the critical node is changed from 1 to 0 to cancel the installation of photovoltaics at that node, and the default severity index of the scheme is recalculated after repair. If the threshold is still exceeded, the next key node is identified and adjusted. This process is repeated until the default rate index is below the threshold or the maximum number of repairs is reached (5). When the termination condition is met, the current best individual is output as the optimal photovoltaic configuration scheme. The termination conditions include reaching the maximum number of iterations (200), or the improvement of the objective function value of the best individual in 50 consecutive iterations being less than 0.0001, or the default rate index of the current best individual being less than the confidence level parameter indicating that the probability constraint is fully satisfied. When any condition is met, the iteration is terminated, and the individual with the smallest objective function value and the default rate index in the current population is output as the optimal photovoltaic configuration scheme. The binary vector of this scheme indicates which nodes in the distribution network to install the photovoltaic system, overcoming the shortcomings of low solution efficiency and easy getting trapped in infeasible regions in the existing optimization algorithms.Taking a photovoltaic (PV) plan for a power distribution network as an example, the population size is set to 50 and the maximum number of iterations to 200. An initial population is randomly generated. For each individual, the binary vector is such that 3 out of the first 10 positions are 1 and the rest are 0, indicating that PV installations are being performed at 3 nodes. The default rate index for this individual is calculated. Through power flow calculation, it is found that the voltage default probability of a certain node is 0.12 and the current default probability of a certain branch is 0.08. The maximum value of these two, 0.12, is taken as the default rate index. The adaptive teaching factor is equal to 1 plus 0.12, which equals 1.12. The population mean vector is calculated, and the current optimal and most feasible individuals are identified. In the update formula during the teaching phase, the random number is set to 0. After the update, a position in the individual's new position vector that was originally 1 becomes 0, indicating that PV installation at that node has been cancelled. After sorting the population by default rate index, this individual is ranked 30th. The selection process is then initiated. Individuals ranked between 43 and 55 are selected as pairing targets. The 48th ranked individual is paired with the paired individual. Comparing their objective function values ​​reveals that the paired individual has a smaller objective function value. A learning update is performed, where the paired individual learns from its counterpart. After the update, the default rate of this individual in the population decreases to 0.10, but still exceeds the preset threshold of 0.075. A constraint repair operation is initiated, removing the three nodes with installed photovoltaics in the scheme one by one and recalculating the default probability. It is found that removing the second node results in the largest decrease in default probability. The installation decision for this node is changed to 0. After the repair, the default rate decreases to 0.06, below the threshold. After 200 iterations, the algorithm converges, outputting the individual with the smallest objective function value as the optimal scheme. This scheme indicates that installing the photovoltaic system at five specific nodes minimizes expected power loss while meeting the confidence level requirements for default probability.

[0071] The above describes the photovoltaic system optimization configuration method considering random characteristics in the embodiments of this application. The following describes the photovoltaic system optimization configuration system considering random characteristics in the embodiments of this application. Please refer to [link / reference]. Figure 2 One embodiment of the photovoltaic system optimization configuration system that takes into account random characteristics in this application includes:

[0072] The acquisition module is used to acquire historical solar irradiance data and generate multiple sets of irradiance scene samples based on beta distribution;

[0073] The pairing module is used to acquire historical load data, perform time-series pairing of load scenarios with the irradiance scenario samples, and generate a joint scenario set;

[0074] The calculation module is used to calculate the shadow effect correction factor based on the surrounding shading information of the candidate nodes, and correct the irradiance value in the joint scene set based on the shadow effect correction factor to obtain the corrected photovoltaic output value.

[0075] The statistics module is used to perform power flow calculations based on the corrected photovoltaic output value, calculate the default probability of node voltage and branch current under each scenario, and construct an optimization target with penalties.

[0076] The iterative module is used to iteratively optimize the photovoltaic installation location using a teaching and learning optimization algorithm, evaluate each configuration scheme according to the optimization objective, and output the optimal photovoltaic configuration scheme.

[0077] above Figure 2 The photovoltaic system optimization configuration system taking into account random characteristics in the embodiments of the present invention will be described in detail from the perspective of modular functional entities. The photovoltaic system optimization configuration device taking into account random characteristics in the embodiments of the present invention will be described in detail from the perspective of hardware processing.

[0078] Reference Figure 3 This invention also provides a photovoltaic system optimization configuration device that takes into account random characteristics. This photovoltaic system optimization configuration device that takes into account random characteristics can be a server, and its internal structure can be as follows: Figure 3 As shown. The photovoltaic system optimization configuration device considering random characteristics includes a processor, memory, display screen, input device, network interface, and database connected via a system bus. The processor, designed as a computer, provides computing and control capabilities. The memory of the photovoltaic system optimization configuration device considering random characteristics includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system, computer programs, and database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the photovoltaic system optimization configuration device considering random characteristics stores the data corresponding to this embodiment. The network interface of the photovoltaic system optimization configuration device considering random characteristics is used for communication with external terminals via network connection. When the computer program is executed by the processor, it implements the above-described method.

[0079] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the photovoltaic system optimization configuration device considering random characteristics to which the present invention is applied.

[0080] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the photovoltaic system optimization configuration method taking into account random characteristics.

[0081] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0082] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a photovoltaic system optimization configuration device (which may be a personal computer, server, or network device, etc.) that takes into account random characteristics to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0083] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the configuration of a photovoltaic system taking into account stochastic characteristics, characterized in that, The method includes: Step S1: Obtain historical solar irradiance data and generate multiple sets of irradiance scene samples based on beta distribution; Step S2: Obtain historical load data, perform time-series pairing of load scenarios with the irradiance scenario samples, and generate a joint scenario set; Step S3: Calculate the shadow effect correction factor based on the surrounding shading information of the candidate nodes, and correct the irradiance value in the joint scene set based on the shadow effect correction factor to obtain the corrected photovoltaic output value; Step S4: Perform power flow calculation based on the corrected photovoltaic output value, calculate the default probability of node voltage and branch current under each scenario, and construct an optimization objective with penalty terms; Step S5: Use the teaching and learning optimization algorithm to iteratively optimize the photovoltaic installation location, evaluate each configuration scheme according to the optimization objective, and output the optimal photovoltaic configuration scheme.

2. The photovoltaic system optimization configuration method considering random characteristics according to claim 1, characterized in that, Step S1 includes: Obtain historical solar irradiance data for each node within the distribution network planning area, and calculate the mean and standard deviation of the historical solar irradiance data; The intermediate parameter is calculated based on the mean and standard deviation. The formula for calculating the intermediate parameter is: mean multiplied by one minus mean divided by the square of the standard deviation minus one. The shape parameters of the beta distribution are calculated based on the intermediate parameters. The first shape parameter is the product of the mean and the intermediate parameter, and the second shape parameter is the product of the mean minus the intermediate parameter. A preset number of irradiance scene samples are extracted from the beta distribution using the Latin hypercube sampling method. Each set of scene samples corresponds to the irradiance values ​​of all candidate photovoltaic installation nodes in the distribution network.

3. The photovoltaic system optimization configuration method considering random characteristics according to claim 1, characterized in that, Step S2 includes: Obtain historical load data for each node in the distribution network, and calculate the mean and standard deviation of the historical load data; A normal distribution is constructed based on the mean and standard deviation of the historical load data, and load scenario values ​​for each node are generated according to the normal distribution. Obtain the time-series correlation coefficient matrix between the irradiance scene sample and the load scene value. The time-series correlation coefficient matrix is ​​calculated based on the synchronous change characteristics of irradiance and load in historical data. The time-series correlation coefficient matrix is ​​decomposed using the Cholesky decomposition method. Based on the decomposition results, the correlation of the load scene values ​​is adjusted. The adjusted load scene values ​​are then paired with the corresponding irradiance scene samples to generate a joint scene set.

4. The photovoltaic system optimization configuration method considering random characteristics according to claim 3, characterized in that, The Cholesky decomposition method is used to decompose the time-series correlation coefficient matrix. Based on the decomposition results, the correlation of the load scene values ​​is adjusted. The adjusted load scene values ​​are then paired with corresponding irradiance scene samples to generate a joint scene set, including: The time-series correlation coefficient matrix is ​​subjected to Cholesky decomposition to obtain a lower triangular matrix; Generate independent, standard normally distributed random vectors that match the number of scenarios and nodes in the load scenario value; Perform matrix multiplication on the lower triangular matrix and the independent standard normal distribution random vector to obtain a correlated random vector; The load scene value is linearly transformed based on the correlated random vector to obtain the adjusted load scene value. The adjusted load scene value is then paired one-to-one with the irradiance scene sample with the corresponding index to generate a joint scene set.

5. The photovoltaic system optimization configuration method considering random characteristics according to claim 1, characterized in that, Step S3 includes: Obtain the geographical coordinates of candidate nodes, the height information of surrounding buildings, and the vegetation distribution information to establish a three-dimensional occlusion model; Calculate the solar altitude angle and solar azimuth angle based on the time information corresponding to each scene in the joint scene set; Based on the three-dimensional shading model, the solar altitude angle and the solar azimuth angle, the effective light-receiving area ratio of the photovoltaic array surface at each candidate node is calculated using a ray tracing algorithm, and the effective light-receiving area ratio is used as a shadow effect correction factor. The shadow effect correction factor is multiplied with the irradiance value of the corresponding node in the joint scene set to obtain the corrected irradiance value. The corrected irradiance value is then multiplied with the photovoltaic panel conversion efficiency and the photovoltaic panel area to obtain the corrected photovoltaic output value.

6. The photovoltaic system optimization configuration method considering random characteristics according to claim 1, characterized in that, Step S4 includes: Based on the corrected photovoltaic output value and the load scenario value in the joint scenario set, power balance equations are established for each scenario. The power balance equations are solved by the forward-backward substitution method to obtain the node voltage value, node phase angle value and branch current value for each scenario. The number of times the node voltage value exceeds the preset voltage upper limit or falls below the preset voltage lower limit in each scenario is counted, and the ratio of the number of violations to the total number of scenarios is used as the voltage default probability. The number of times the branch current value exceeds the preset current limit in each scenario is counted, and the ratio of the number of limit exceedances to the total number of scenarios is used as the current violation probability. Calculate the desired power loss value by multiplying the difference between the voltage default probability and the preset voltage confidence level parameter and the difference between the current default probability and the preset current confidence level parameter by the corresponding penalty factors, and summing the results. Add the summation result to the desired power loss value to construct an optimization objective with penalty terms.

7. The photovoltaic system optimization configuration method considering random characteristics according to claim 1, characterized in that, Step S5 includes: Set a preset population size and maximum number of iterations, and randomly generate an initial population. Each individual in the initial population corresponds to a photovoltaic installation location configuration scheme. The maximum values ​​of voltage default probability and current default probability of each individual are calculated as default degree indicators. An adaptive teaching factor is calculated based on the default degree indicators. The current best individual, the population mean, and the adaptive teaching factor are substituted into the teaching stage update formula to update the photovoltaic installation position of each individual. Individuals in the population are sorted according to the degree of default, and pairs of individuals whose sorting distance is within a preset range are selected for pairing. The learning phase update is performed based on the difference in optimization objectives between the paired individuals to obtain the updated population. For individuals in the updated population whose default probability exceeds a preset threshold, a constraint repair operation is performed to adjust the photovoltaic installation decisions of key nodes that cause the default. When the termination condition is met, the current optimal individual is output as the optimal photovoltaic configuration scheme.

8. A photovoltaic system optimization configuration system taking into account random characteristics, characterized in that, A photovoltaic system optimization configuration method considering random characteristics as described in any one of claims 1-7, wherein the photovoltaic system optimization configuration system considering random characteristics comprises: The acquisition module is used to acquire historical solar irradiance data and generate multiple sets of irradiance scene samples based on beta distribution; The pairing module is used to acquire historical load data, perform time-series pairing of load scenarios with the irradiance scenario samples, and generate a joint scenario set; The calculation module is used to calculate the shadow effect correction factor based on the surrounding shading information of the candidate nodes, and correct the irradiance value in the joint scene set based on the shadow effect correction factor to obtain the corrected photovoltaic output value. The statistics module is used to perform power flow calculations based on the corrected photovoltaic output value, calculate the default probability of node voltage and branch current under each scenario, and construct an optimization target with penalties. The iterative module is used to iteratively optimize the photovoltaic installation location using a teaching and learning optimization algorithm, evaluate each configuration scheme according to the optimization objective, and output the optimal photovoltaic configuration scheme.

9. A photovoltaic system optimization configuration device taking into account random characteristics, characterized in that, The system includes a memory and a processor, the memory storing a computer program that can run on the processor, and the processor executing the computer program to implement the photovoltaic system optimization configuration method taking into account random characteristics as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is run by the processor, it causes the processor to perform the photovoltaic system optimization configuration method taking into account random characteristics as described in any one of claims 1 to 7.

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