A power distribution network photovoltaic openable capacity dynamic evaluation method fusing voltage stability margin and neural network optimization

Abstract

The application discloses a kind of power distribution network photovoltaic openable capacity dynamic evaluation method of fusion voltage stability margin and neural network optimization, to solve the problem of low computational efficiency and dynamic stability not being fully considered by traditional method. Firstly, the prediction method combining kernel density estimation and quantile regression is used to accurately quantify the uncertainty of distributed photovoltaic output. The core innovation is to introduce static voltage stability margin (VDSM) as a key constraint condition on the basis of traditional security constraints, and to construct a double-layer interval analysis model that can guarantee the dynamic stability of the power grid. Secondly, for efficient solution, the application proposes a framework of "neural network pre-screening + parallel optimization": after decomposing the model into optimistic subproblem and pessimistic subproblem through interval decoupling technology, the neural network model is used to quickly screen the vast number of candidate solutions, significantly reducing the feasible solution space, and then combining the improved particle swarm optimization algorithm to solve the submodel in parallel.

Description

Technical Field

[0001] This invention relates to a dynamic assessment method for the openable capacity of photovoltaic (PV) power in distribution networks, integrating voltage stability margin and neural network optimization, belonging to the field of power system planning and analysis. This method combines uncertainty quantification, voltage stability constraints, and intelligent optimization algorithms to quantify the impact of distributed PV output uncertainty on the carrying capacity of distribution networks. It provides a scientific basis for grid safety planning and operation in scenarios with high PV integration, and is particularly suitable for complex distribution network systems with multiple nodes and constraints. Background Technology

[0002] With the rapid increase in the penetration rate of distributed photovoltaic (PV) power in distribution networks, its inherent randomness, volatility, and intermittency pose serious challenges to the safe and stable operation of the power grid. Therefore, accurate and efficient assessment of the available capacity (also known as carrying capacity) of distributed PV power in distribution networks is crucial for guiding the scientific planning, safe grid connection, and optimized operation of PV systems.

[0003] Existing methods for assessing the available capacity of photovoltaic systems differ in their emphasis on modeling approaches, constraint handling, and solution efficiency, but they also reveal their respective limitations.

[0004] One category is methods based on deterministic or simplified models. These methods typically analyze under pre-defined "worst-case" scenarios (such as peak load or light load), offering simple calculations and ease of engineering application. For example, patent CN119419768A discloses an engineering calculation method based on reverse load factor and lookup tables, which, while fast, is overly simplistic. Similarly, patent CN113723031B proposes an evaluation method that calculates the carrying capacity under three independent constraints—voltage, feed-back power, and short-circuit current—and takes the minimum value. These methods ignore the uncertainty of photovoltaic output and the complex coupling relationships between various constraints, often resulting in overly conservative or optimistic evaluations that are difficult to guide practical planning.

[0005] Another category involves methods that consider more complex constraints and optimization models. To improve the accuracy of the evaluation, some studies have introduced more comprehensive constraints. For example, patent CN116247744B proposes a sequential verification method that comprehensively considers safety reliability, voltage quality, and harmonic effects. Patent CN114243778B uses voltage sensitivity ranking to iteratively adjust the photovoltaic grid connection scheme to solve the voltage limit exceeding problem. While these methods improve the completeness of constraints, they typically employ a step-by-step verification or iterative optimization approach, lacking a unified framework that can collaboratively optimize all variables, and they do not adequately quantify the uncertainty of photovoltaic output.

[0006] With the development of data-driven technologies, probabilistic assessment methods that consider uncertainty have become a research hotspot. These methods simulate the uncertainty of new energy output by learning from historical data. For example, patent CN119994983A uses a Copula function to describe the correlation between photovoltaic power and load, and combines K-means clustering to generate typical scenarios, then obtains the carrying capacity through optimization. These probabilistic methods can more comprehensively reflect the impact of uncertainty and represent the forefront of current technological development. However, methods based on scenario generation and clustering typically involve complex calculations, and the accuracy of the assessment results highly depends on the quality and representativeness of the generated scenarios. Computational efficiency remains a bottleneck for their application in real-time assessment.

[0007] In summary, the existing technology has the following main shortcomings:

[0008] 1) Insufficient consideration of dynamic stability: Existing assessments mostly focus on static limits such as voltage and power flow, and rarely incorporate the voltage stability margin (VDSM), which directly reflects the critical point of system collapse, as a hard constraint into the capacity assessment model, which may lead to dynamic safety hazards in the assessment results.

[0009] 2) The contradiction between solution efficiency and model complexity: In order to accurately describe uncertainty, the model often becomes very complex (such as mixed integer non-convex programming). When dealing with high-dimensional solution spaces, traditional optimization algorithms lack effective solution space exploration and pruning mechanisms, resulting in excessive computation time and difficulty in meeting the needs of dynamic evaluation.

[0010] Therefore, there is an urgent need for a dynamic assessment method for photovoltaic open capacity that can effectively integrate uncertainty quantification, dynamic stability constraints, and intelligent optimization algorithms, so as to balance the accuracy of assessment, computational efficiency, and model completeness, and provide reliable technical support for distribution network planning and operation under high-proportion distributed photovoltaic access. Summary of the Invention

[0011] To address the limitations of existing technologies, this invention proposes a dynamic assessment method for the openable capacity of distributed photovoltaic (PV) power in distribution networks, integrating voltage stability margin and neural network optimization. This method aims to more accurately assess the maximum grid-connected capacity of distributed PV in distribution networks, addressing the challenges posed by large-scale PV grid integration. The method employs a prediction approach combining kernel density estimation and quantile regression. Based on historical and meteorological data, it quantifies the uncertainty of distributed PV output, generating output prediction results and confidence intervals. Secondly, it introduces static voltage stability margin constraints on top of traditional safety constraints, constructing a two-layer PV openable capacity interval analysis model incorporating voltage stability margin indices. Subsequently, through interval decoupling techniques, the model is decomposed into optimistic and pessimistic sub-problems. A neural network is used to quickly screen the feasible solution space, and an improved particle swarm optimization algorithm is combined to perform parallel optimization of the sub-models. Finally, the fused results generate the optimal interval for openable capacity. This invention effectively calculates the maximum openable capacity of distributed PV in distribution networks, fully considers the uncertainty of distributed PV output, quantifies the range of changes in openable capacity under PV power fluctuations, provides valuable reference information for the rational planning and utilization of distributed PV, and ensures the safety and stability of distribution network operation under massive distributed PV grid integration.

[0012] To achieve the above objectives, the present invention adopts the following technical solution:

[0013] A dynamic assessment method for the exploitable photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization includes the following steps:

[0014] (1) Collect historical photovoltaic power output data and meteorological data to generate the probability distribution and dynamic confidence interval of distributed photovoltaic power output;

[0015] (2) Construct a two-layer photovoltaic open capacity range analysis model. The upper layer model takes maximizing the open capacity of photovoltaic power distribution network as the objective function, and the lower layer model has constraints including static voltage stability margin constraints.

[0016] (3) The photovoltaic open capacity range analysis model is decomposed into optimistic sub-problems and pessimistic sub-problems, and the feasible solution space is quickly screened using deep neural networks;

[0017] (4) An improved particle swarm optimization algorithm is used to solve the optimistic and pessimistic subproblems in parallel, and the fusion results generate the optimal range of photovoltaic open capacity.

[0018] Furthermore, in step (1), the meteorological data includes irradiance, temperature, and cloud cover;

[0019] The method for generating the probability distribution of distributed photovoltaic power output is to fit the probability density function f(P) of the photovoltaic power output using a Gaussian kernel function.pv ):

[0020]

[0021] In the formula: The number of samples; Given a sample of historical photovoltaic power output, P i It is the actual historical photovoltaic power output value obtained from actual measurements, and belongs to discrete variables; P pv It is the independent variable, a continuous variable, using discrete samples. To estimate continuous variable P pv In the entire interval [0, max(P) i The probability density on [ )]; For the bandwidth parameter, the Silverman criterion is used for optimization:

[0022]

[0023] In the formula: The standard deviation is the sample value, and the interquartile range is the interquartile range.

[0024] The method for generating dynamic confidence intervals is as follows:

[0025] Using meteorological data X = [irradiance, temperature, cloud cover] as input, a quantile regression model is constructed:

[0026]

[0027] Among them, the regression coefficient By minimizing the quantile loss function, the values ​​of the regression coefficients at that quantile level are obtained after iterative convergence.

[0028]

[0029]

[0030] In the formula: Quantile level, For indicator functions;

[0031] Based on this, a dynamic confidence interval is generated:

[0032] .

[0033] Furthermore, in step (2), the static voltage stability margin constraint is:

[0034]

[0035] In the formula: Calculated from the distribution network power flow Jacobian matrix, This is the photovoltaic output adjustment coefficient. This represents the minimum static voltage stability margin.

[0036] Furthermore, in step (2),

[0037] The upper-level model aims to maximize the available photovoltaic capacity.

[0038]

[0039] The constraints of the lower-level model also include safety constraints such as node voltage limits, line power limits, and equipment capacity limits, which are used to ensure the dynamic operational stability of the distribution network under distributed photovoltaic access; the basic system and specific constraints are as follows:

[0040] The power flow model of the distribution network is as follows:

[0041]

[0042]

[0043]

[0044] In the formula: and They are respectively The active and reactive power flowing through line ij at any given time; P jk,t and Q jk,t Let them represent the active power and reactive power on line j→k (flowing from node j to node k) at time t, respectively; and They are respectively From the node Injected active and reactive power; for Time Node The voltage amplitude; and These are the resistance and reactance of line ij, respectively; For nodes The set of all child nodes that have a line connection relationship;

[0045] Distributed photovoltaic power generation system:

[0046]

[0047]

[0048] In the formula: for Time Node The active power output of a distributed photovoltaic power generation system; For nodes The installed capacity of distributed photovoltaic power generation systems; for Time Node The reactive power output from the inverter side of the distributed photovoltaic power generation system; and These are the phase angles corresponding to the upper and lower limits of the inverter's operating power factor, respectively.

[0049] The node voltage constraint is:

[0050]

[0051] In the formula: This is the lower limit of voltage. This is the lower limit of voltage. Number the nodes. A set of nodes;

[0052] The line power constraint is:

[0053]

[0054] In the formula: For line power exceeding the limit, For line numbering, This is a set of routes.

[0055] Equipment capacity constraints are:

[0056]

[0057] In the formula: For equipment capacity exceeding the limit, k For equipment number, This refers to the set of photovoltaic access points.

[0058] Furthermore, in step (3),

[0059] The optimistic subproblem is to maximize the available photovoltaic capacity. Assuming optimal grid stability, the optimistic subproblem can be expressed as:

[0060]

[0061] The pessimistic subproblem is to minimize the available photovoltaic capacity. Considering the worst-case scenario, the pessimistic subproblem can be expressed as:

[0062]

[0063] Where, η min =3.6%, therefore The problem can be transformed into a linear complementarity problem using KKT conditions:

[0064]

[0065] Introducing auxiliary variables Linearization using the Big M method:

[0066]

[0067] in b For binary variables, M =100 is a sufficiently large constant.

[0068] Furthermore, in step (3),

[0069] The method of using deep neural networks to quickly filter the feasible solution space is as follows:

[0070] Constructing a deep neural network (DNN) structure:

[0071] The input layer includes photovoltaic output. Node voltage Line load rate ;

[0072] The hidden layers consist of three fully connected layers with ReLU activation function.

[0073] The output layer represents the binary classification result indicating whether the candidate solution satisfies the constraints.

[0074] The loss function used is cross-entropy loss:

[0075]

[0076] in, This represents the true label of the sample, i.e., whether the solution is feasible; Both represent the sample labels predicted by the neural network model and are 0 / 1 variables.

[0077] After training, DNN can quickly eliminate those that do not meet the requirements. or Candidate solutions.

[0078] Furthermore, in step (4), the improvement strategy for the particle swarm algorithm includes:

[0079] (a) Dynamic inertia weight adjustment: inertia weight It decreases linearly with the number of iterations t:

[0080]

[0081] in, This represents the maximum number of iterations.

[0082] (b) Adaptive mutation strategy: When the particle swarm fitness variance is below a threshold When this occurs, mutation is triggered; that is:

[0083]

[0084]

[0085] In the formula: The average fitness of the population. Let N be the variance of population fitness, and N be the population size in generation t. For the t-th generation population particles i The fitness of;

[0086] The mutation is performed according to the following formula:

[0087]

[0088] In the formula: For particles i The fitness of U is given by U(·), which is a random vector that follows a uniform distribution within a specified interval.

[0089] Mutation probability Adaptive adjustment based on iteration count:

[0090] .

[0091] Furthermore, in step (4), considering capacity maximization and voltage stability, the fitness function of the improved particle swarm optimization algorithm is designed as follows:

[0092]

[0093] Where: weighting coefficient , , ;

[0094] Solve the optimistic subproblem Solution to the pessimistic subproblem Merge and generate the optimal open capacity range: .

[0095] The beneficial results of this invention are as follows: A dynamic photovoltaic output confidence interval is generated through kernel density estimation and quantile regression methods, accurately quantifying the randomness of distributed photovoltaics, and an open capacity interval model is constructed by integrating voltage stability margin constraints; based on interval analysis theory, it is decoupled into optimistic and pessimistic subproblems, and solved in parallel using KKT equivalent transformation and an improved particle swarm optimization algorithm. This improves computational efficiency by 40% while outputting an optimal capacity interval that balances safety and economy, reducing the voltage exceedance probability to below 3%; this method provides real-time decision support for high-penetration photovoltaic access scenarios, effectively balancing the safe operation of the distribution network with the demand for photovoltaic consumption, and promoting the large-scale grid connection of distributed photovoltaics and the intelligent upgrading of the distribution network under the "dual carbon" objective. Attached Figure Description

[0096] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0097] Figure 2 The probability prediction results obtained by the method of the present invention are compared with the prediction results of the traditional method and the actual output (24h).

[0098] Figure 3 This is a distribution map of the optimal range of photovoltaic openability for each node in the system obtained by the method of the present invention. Detailed Implementation

[0099] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention provide a dynamic assessment method for the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization, as follows: Figure 1 As shown.

[0100] (1) Collect historical photovoltaic power output data and meteorological data for the past year, and use a combination of kernel density estimation and quantile regression to generate the probability distribution and dynamic confidence interval of distributed photovoltaic power output, and quantify its uncertainty.

[0101] We collected 35,040 sets of annual photovoltaic (PV) output data (15-minute time resolution) and meteorological data (irradiance, temperature, cloud cover) for a specific location. Data cleaning was performed to remove outliers (such as zero values ​​at night or sensor malfunction data), and missing values ​​were filled using linear interpolation. The dataset was divided into three parts: 75% training set (26,280 sets), 15% validation set (5,256 sets), and 15% test set (5,256 sets), used for training and parameter tuning of the distributed PV output probability distribution and dynamic confidence interval generation model.

[0102] A Gaussian kernel function is used to fit the probability density function of photovoltaic power output. Given historical photovoltaic power output samples... The probability density function is:

[0103]

[0104] In the formula: P is the sample size; pv It is the independent variable, and belongs to the continuous variable category; P i These are the actual historical photovoltaic power output values ​​obtained from actual measurements, which are discrete variables. They are obtained using discrete samples {P}. i To estimate the continuous variable P pv In the entire interval [0, max(P) i The probability density on [ )]; For the bandwidth parameter, the Silverman criterion is used for optimization:

[0105]

[0106] In the formula: is the sample standard deviation, and IQR is the interquartile range.

[0107] Using meteorological variables X = [irradiance, temperature, cloud cover] as input, a quantile regression model is constructed:

[0108]

[0109] Among them, the regression coefficient By minimizing the quantile loss function, the values ​​of the regression coefficients at that quantile level are obtained after iterative convergence.

[0110]

[0111]

[0112] In the formula: Quantile level, This is an indicator function.

[0113] Based on this, a dynamic confidence interval is generated (taking a 95% confidence level as an example):

[0114]

[0115] (2) Construct a two-layer photovoltaic open capacity analysis and optimization model. The upper layer takes maximizing the photovoltaic open capacity as the objective function, and the lower layer introduces static voltage stability margin constraints on the basis of traditional safety constraints to ensure the safe and stable operation of the distribution network under photovoltaic power output fluctuations.

[0116] The upper-level model aims to maximize the available photovoltaic capacity.

[0117]

[0118] The lower-level model is a distribution network model with distributed photovoltaics deployed, with added security constraints and static voltage stability constraints. The basic system and specific constraints are as follows:

[0119] The power flow model of the distribution network is as follows:

[0120]

[0121]

[0122]

[0123] In the formula: and They are respectively The active and reactive power flowing through line ij at any given time; P jk,t and Q jk,t Let them represent the active power and reactive power on line j→k (flowing from node j to node k) at time t, respectively; and They are respectively From the node Injected active and reactive power; for Time Node The voltage amplitude; and These are the resistance and reactance of line ij, respectively; For nodes The set of all child nodes that have a line connection relationship.

[0124] Distributed photovoltaic power generation system:

[0125]

[0126]

[0127] In the formula: for Time Node The active power output of a distributed photovoltaic power generation system; For nodes The installed capacity of distributed photovoltaic power generation systems; for Time Node The reactive power output from the inverter side of the distributed photovoltaic power generation system; and These are the phase angles corresponding to the upper and lower limits of the inverter's operating power factor, respectively.

[0128] The node voltage constraint is:

[0129]

[0130] In the formula: This is the lower limit of voltage. This is the lower limit of voltage. Number the nodes. It is a set of nodes.

[0131] The line power constraint is:

[0132]

[0133] In the formula: For line power exceeding the limit, For line numbering, This is a set of routes.

[0134] Equipment capacity constraints are:

[0135]

[0136] In the formula: For equipment capacity exceeding the limit, k For equipment number, This refers to the set of photovoltaic access points.

[0137] The static voltage stability margin constraint is:

[0138]

[0139] In the formula: Calculated from the distribution network power flow Jacobian matrix, This is the photovoltaic output adjustment coefficient. This represents the minimum static voltage stability margin.

[0140] (3) The two-layer model is decomposed into optimistic sub-problems (upper limit of computational capacity) and pessimistic sub-problems (lower limit of computational capacity) by interval decoupling technology, and the feasible solution space is quickly screened by deep neural network to improve the solution efficiency.

[0141] Optimistic subproblem: Maximizing the available photovoltaic capacity, assuming optimal grid stability, can be expressed as:

[0142]

[0143] Pessimistic subproblem: Minimize the available photovoltaic capacity, considering the worst-case scenario:

[0144]

[0145] Considering the most pessimistic scenario, based on industry experience and national standards, ηmin = 3.6%. Therefore, the original model contains nonlinear constraints. To further improve the efficiency of solving the problem using mature linear or mixed-integer linear solvers, the problem is transformed into a linear complementarity problem using the KKT conditions:

[0146]

[0147] Introducing auxiliary variables Linearization using the Big M method:

[0148]

[0149] in b For binary variables, M =100 is a sufficiently large constant.

[0150] Then, a neural network is used to filter feasible solutions, and a deep neural network (DNN) structure is constructed:

[0151] Input layer: Photovoltaic output Node voltage Line load rate

[0152] Hidden layers: 3 fully connected layers, with ReLU activation function.

[0153] Output layer: Binary classification (feasible / infeasible)

[0154] The loss function used is cross-entropy loss:

[0155]

[0156] in, This represents the true label of the sample, i.e., whether the solution is feasible; The labels represent the sample labels predicted by the neural network model; both are 0 / 1 variables.

[0157] After training, DNN can quickly eliminate those that do not meet the requirements. or The candidate solutions reduce the search space by more than 50%.

[0158] (4) An improved particle swarm optimization (PSO) algorithm is used to solve the optimistic / pessimistic subproblems in parallel, and the fusion results generate the optimal range of photovoltaic open capacity.

[0159] Set dynamic inertia weight, inertia weight It decreases linearly with the number of iterations t:

[0160]

[0161] In the formula: setting , , .

[0162] When the particle swarm fitness variance is below the threshold At that time, that is:

[0163]

[0164]

[0165] In the formula: The average fitness of the population. Let N be the variance of population fitness, and N be the population size in generation t. For the t-th generation population particles i The degree of adaptability.

[0166] Triggering mutation:

[0167]

[0168] In the formula: For particles i The fitness of U is given by U(·), which is a random vector that follows a uniform distribution within a specified interval.

[0169] Mutation probability Adaptive adjustment based on iteration count:

[0170]

[0171] Taking into account both capacity maximization and voltage stability, the fitness function is designed as follows:

[0172]

[0173] Where: weighting coefficient , , .

[0174] Solve the optimistic subproblem Solution to the pessimistic subproblem Merge and generate the optimal open capacity range: .

[0175] The IEEE 33-node system was selected as an example. The system has a reference voltage of 12.66kV, contains 33 nodes and 32 lines, and distributed photovoltaic power is connected at nodes 6, 13, 18, 25 and 31 (single point capacity 0.7MW, total capacity 3.5MW).

[0176] The probability prediction results obtained by the method of this invention are compared with the actual output (24h) as follows: Figure 2 As shown in the figure. The black curve in the figure represents the actual photovoltaic output; the dark blue area represents the 95% dynamic confidence interval of the method of this invention ([Q...). 0.05Q 0.95 The red dashed line represents the result of the deterministic point prediction method (support vector regression); the gray area represents the 95th percentile interval of the Monte Carlo scene method. As shown in the figure, at 12:00 (peak irradiance), the interval width of the method of this invention is 126kW, and the actual value is close to the median; at 15:30 (cloud cover), the point prediction deviation reaches 68kW, and the interval of this invention completely covers the actual fluctuations; at 18:00 (sunset), the interval of this invention narrows in time to avoid over-conservatism.

[0177] Table 1 shows a comparison of the indices between the method of this invention and traditional prediction methods:

[0178] Table 1 Comparison of forecasting indicators for different forecasting methods

[0179]

[0180] In the table, RMSE is the root mean square error, which measures the deviation between the predicted and actual values; the lower the better. MAE is the mean absolute error, which, like above, is not sensitive to outliers. Interval coverage rate represents the proportion of actual output falling within the predicted interval; the closer to 95%, the better. Interval average width represents the average span of the predicted interval; the narrower the better for the same coverage rate. Calculation time is the time taken for a single prediction.

[0181] The data in the table show that the RMSE (28.5kW) of the method of this invention is 20.4% lower than that of the optimal comparison method (Gaussian mixture model), and the accuracy is higher. While ensuring a coverage of 96.3% (closest to the target of 95%), the interval width of the method of this invention is reduced by 16.8% compared with the Monte Carlo method, and the interval is better. The calculation time of the method of this invention is only 3.8 seconds, less than 5% of that of the Monte Carlo method, which is more efficient and meets the requirements of real-time evaluation.

[0182] Table 2 shows a comparison of the computational efficiency and optimization performance between the method of this invention and the traditional method:

[0183] Table 2 Comparison of computational efficiency and optimization performance of different optimization methods

[0184]

[0185] The data in the table show that the neural network screening method used in this invention reduces the search space by 50%, improves the PSO parallel optimization speed by 40%, and increases the static voltage stability margin (η) by 27.8%, thereby improving voltage stability and verifying the effectiveness of the two-layer model constraint.

[0186] Table 3 shows a comprehensive comparison of the overall evaluation results of the method of this invention and the traditional method:

[0187] Table 3. Overall Comparison of Evaluation Results of Different Methods

[0188]

[0189] The data in the table shows that the method of this invention improves the upper limit of the photovoltaic (PV) capacity that can be opened up by 3.2% (compared to the Monte Carlo method) and the lower limit by 8.5% (compared to traditional methods), while controlling the voltage over-limit probability to within 3% while expanding the grid connection capacity. The neural network screening used in this invention reduces invalid searches by 51.7% and improves the PSO algorithm by 41.7% (compared to suboptimal methods). In the IEEE 33-bus system, this invention increases PV grid connection capacity by 11.6% while reducing the voltage instability risk from the industry average of 6.8% to below 0.9%.

[0190] The available capacity ranges of the photovoltaic access nodes in the system at different times, calculated by the method of this invention, are as follows: Figure 3 As shown, the optimal range of predicted available capacity for each photovoltaic (PV) node in the distribution network is visually presented at three representative times: 12:00, 15:30, and 18:00. The horizontal axis represents the node number, and the vertical axis represents the available PV capacity. The figure compares the two evaluation results using colored bars (the method of this invention) and gray bars (the traditional method). The range calculated by the method of this invention is a dynamic evaluation result based on probabilistic prediction and voltage stability constraints, clearly defining the minimum and maximum capacity for each node to safely connect to PV at the current time. For critical nodes that are more sensitive to voltage stability (nodes 18 and 25 highlighted in light red in the figure), the method of this invention, by fully considering the static voltage stability margin, significantly raises the lower limit of its safe capacity range, thus ensuring that even in pessimistic scenarios with fluctuating PV output or heavy loads, the system voltage stability is not threatened.

[0191] Figure 3 The invention clearly demonstrates the time-varying characteristics of available capacity: during the peak solar radiation period at 12:00, nodes generally exhibit high photovoltaic absorption potential with a relatively wide range; as sunlight weakens at 15:30, the capacity range narrows and shifts downwards; by 18:00, at sunset, the available capacity shrinks sharply to near zero, which closely matches actual solar radiation patterns. The advantages of this invention are particularly prominent compared to traditional methods. For most nodes, the available capacity range assessed by this invention is typically wider, thanks to the refined probabilistic modeling and optimized solution of photovoltaic uncertainties, thereby uncovering greater absorption potential while ensuring safety. More importantly, when dealing with nodes constrained by voltage stability, the available capacity range determined by this invention is significantly higher than that of traditional methods, which may underestimate risk due to model simplification. This indicates that this invention can more accurately identify and strengthen the system's safety boundaries, avoiding the overly optimistic or conservative assessment biases that may exist in traditional methods.

Claims

1. A dynamic assessment method for the exploitable photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization, characterized in that, Includes the following steps: (1) Collect historical photovoltaic power output data and meteorological data to generate the probability distribution and dynamic confidence interval of distributed photovoltaic power output; (2) Construct a two-layer photovoltaic open capacity range analysis model. The upper layer model takes maximizing the open capacity of photovoltaic power distribution network as the objective function, and the lower layer model has constraints including static voltage stability margin constraints. (3) The photovoltaic open capacity range analysis model is decomposed into optimistic sub-problems and pessimistic sub-problems, and the feasible solution space is quickly screened using deep neural networks; (4) An improved particle swarm optimization algorithm is used to solve the optimistic and pessimistic subproblems in parallel, and the fusion results generate the optimal range of photovoltaic open capacity.

2. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization as described in claim 1, characterized in that, In step (1), the meteorological data includes irradiance, temperature, and cloud cover; The method for generating the probability distribution of distributed photovoltaic power output is to fit the probability density function f(P) of the photovoltaic power output using a Gaussian kernel function. pv ): In the formula: The number of samples; Given a sample of historical photovoltaic power output, P i It is the actual historical photovoltaic power output value obtained from actual measurements, and belongs to discrete variables; P pv It is the independent variable, a continuous variable, using discrete samples. To estimate continuous variable P pv In the entire interval [0, max(P) i The probability density on [ )]; For the bandwidth parameter, the Silverman criterion is used for optimization: In the formula: The standard deviation is the sample value, and the interquartile range is the interquartile range. The method for generating dynamic confidence intervals is as follows: Using meteorological data X = [irradiance, temperature, cloud cover] as input, a quantile regression model is constructed: Among them, the regression coefficient By minimizing the quantile loss function, the values ​​of the regression coefficients at that quantile level are obtained after iterative convergence. In the formula: Quantile level, For indicator functions; Based on this, a dynamic confidence interval is generated: 。 3. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization as described in claim 1, characterized in that, In step (2), the static voltage stability margin constraint is: In the formula: Calculated from the distribution network power flow Jacobian matrix, This is the photovoltaic output adjustment coefficient. This represents the minimum static voltage stability margin.

4. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization as described in claim 3, characterized in that, In step (2), The upper-level model aims to maximize the available photovoltaic capacity. The constraints of the lower-level model also include safety constraints such as node voltage limits, line power limits, and equipment capacity limits, which are used to ensure the dynamic operational stability of the distribution network under distributed photovoltaic access; the basic system and specific constraints are as follows: The power flow model of the distribution network is as follows: In the formula: and They are respectively The active and reactive power flowing through line ij at any given time; P jk,t and Q jk,t Let them represent the active power and reactive power on line j→k (flowing from node j to node k) at time t, respectively; and They are respectively From the node Injected active and reactive power; for Time Node The voltage amplitude; and These are the resistance and reactance of line ij, respectively; For nodes The set of all child nodes that have a line connection relationship; Distributed photovoltaic power generation system: In the formula: for Time Node The active power output of a distributed photovoltaic power generation system; For nodes The installed capacity of distributed photovoltaic power generation systems; for Time Node The reactive power output from the inverter side of the distributed photovoltaic power generation system; and These are the phase angles corresponding to the upper and lower limits of the inverter's operating power factor, respectively. The node voltage constraint is: In the formula: This is the lower limit of voltage. This is the lower limit of voltage. Number the nodes. A set of nodes; The line power constraint is: In the formula: For line power exceeding the limit, For line numbering, For the set of routes; Equipment capacity constraints are: In the formula: For equipment capacity exceeding the limit, k For equipment number, This refers to the set of photovoltaic access points.

5. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization according to claim 4, characterized in that, In step (3), The optimistic subproblem is to maximize the available photovoltaic capacity. Assuming optimal grid stability, the optimistic subproblem is expressed as follows: The pessimistic subproblem is to minimize the available photovoltaic capacity. Considering the worst-case scenario, the pessimistic subproblem is expressed as: Where, η min =3.6%, therefore The problem can be transformed into a linear complementarity problem using KKT conditions: Introducing auxiliary variables Linearization using the Big M method: in b It is a binary variable.

6. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization according to claim 5, characterized in that, In step (3), The method of using deep neural networks to quickly filter the feasible solution space is as follows: Constructing a deep neural network (DNN) structure: The input layer includes photovoltaic output. Node voltage Line load rate ; The hidden layers consist of three fully connected layers with ReLU activation function. The output layer represents the binary classification result indicating whether the candidate solution satisfies the constraints. The loss function used is cross-entropy loss: in, This represents the true label of the sample, i.e., whether the solution is feasible; Both represent the sample labels predicted by the neural network model and are 0 / 1 variables. After training, DNN can quickly eliminate those that do not meet the requirements. or Candidate solutions.

7. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization as described in claim 6, characterized in that, In step (4), the improvement strategies for the particle swarm algorithm include: (a) Dynamic inertia weight adjustment: inertia weight It decreases linearly with the number of iterations t: in, This represents the maximum number of iterations. (b) Adaptive mutation strategy: When the particle swarm fitness variance is below a threshold When this occurs, mutation is triggered; that is: In the formula: The average fitness of the population. Let N be the variance of population fitness, and N be the population size in generation t. For the t-th generation population particles i The fitness of; The mutation is performed according to the following formula: In the formula: For particles i The fitness of U is given by U(·), which is a random vector that follows a uniform distribution within a specified interval. Mutation probability Adaptive adjustment based on iteration count: 。 8. The method for dynamic evaluation of the available photovoltaic capacity of a distribution network that integrates voltage stability margin and neural network optimization according to claim 7, characterized in that, In step (4), considering capacity maximization and voltage stability, the fitness function of the improved particle swarm algorithm is designed as follows: Where: weighting coefficient , , ; Solve the optimistic subproblem Solution to the pessimistic subproblem Merge and generate the optimal open capacity range: .

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by a processor, it implements the steps of the method according to any one of claims 1-8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-8.

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