Active power distribution network bearing capacity probability modeling method and device involving virtual power plant demand response, equipment and storage medium

Abstract

The invention discloses an active power distribution network bearing capacity probability modeling method related to virtual power plant demand response, and aims to solve the problems that in the prior art, evaluation of photovoltaic bearing capacity depends on certainty, and an uncertainty processing method and an efficient probability evaluation framework are lacked. According to the method, uncertainty is quantified through a probability density function, a complex random problem is converted into a multi-scene deterministic optimization problem containing key uncertainty information by utilizing Monte Carlo simulation and scene reduction technologies, and demand response of a virtual power plant is integrated as an active control means. And finally, accurately calculating the photovoltaic bearing capacity and the system performance index of the active power distribution network under the condition of meeting multiple security constraints.

Description

Technical Field

[0001] This application relates to the field of power system operation and control technology, specifically to a method, apparatus, equipment, and storage medium for probabilistic modeling of active distribution network carrying capacity involving virtual power plant demand response. Background Technology

[0002] With the advancement of the "dual carbon" target, the penetration rate of distributed photovoltaic (PV) systems in active distribution networks is continuously increasing. However, the inherent intermittency and volatility of PV power generation, coupled with the randomness of load demand, pose a severe challenge to the safe and stable operation of distribution networks. Against this backdrop, accurately assessing the PV hosting capacity (HC) of distribution networks becomes crucial. PV hosting capacity is generally defined as the maximum PV power generation capacity that a distribution network can accommodate without violating standard limits for voltage, protection, and power quality. Existing PV hosting capacity assessment methods mainly suffer from the following limitations:

[0003] Over-reliance on deterministic methods: Most studies use deterministic hourly photovoltaic and load typical curves for carrying capacity calculations. This method ignores the dramatic random fluctuations in photovoltaic output and load demand over short timescales, leading to overly optimistic (underestimating risk) or overly conservative (wasting grid potential) assessments, failing to provide a reliable basis for refined planning and operation.

[0004] Limitations of uncertainty handling methods: Although some studies have attempted to introduce sensitivity analysis or robust optimization to handle uncertainty, the former cannot perform optimization design under uncertainty conditions, while the latter may lead to overly conservative results due to considering the worst case and is not suitable for carrying capacity assessment that requires long-term statistical characteristics, making it difficult to fully characterize the stochastic behavior of photovoltaics and loads.

[0005] The lack of an efficient probabilistic evaluation framework is a significant challenge. Probabilistic evaluation is considered an effective approach to addressing the aforementioned problems. Monte Carlo (MC) simulation, as a mature stochastic analysis method, can resolve the distribution of uncertain parameters through the generation and simulation of a large number of scenarios. However, directly applying the Monte Carlo method would result in an excessive computational burden due to the sheer number of scenarios, making it difficult to promote its application in engineering practice. Therefore, there is an urgent need for an efficient scenario generation and reduction technique to reduce massive amounts of scenarios into a representative set of a small number of scenarios while ensuring evaluation accuracy. Summary of the Invention

[0006] The main objective of this application is to provide a probabilistic modeling method for the carrying capacity of an active distribution network involving virtual power plant demand response, comprising the following steps:

[0007] Step S10: Based on historical monitoring data or forecast data, construct probability density functions for photovoltaic power generation, load demand, and demand response of virtual power plants at each node in the active distribution network.

[0008] Step S20: Using the Monte Carlo method, generate an initial scenario set based on the probability density function. The initial scenario set includes the power range identifiers and corresponding probabilities of photovoltaic power generation, load demand, and demand response of the virtual power plant.

[0009] Step S30: Compress the initial scene set using scene reduction technology to obtain a representative subset of scenes and their corresponding probability weights;

[0010] Step S40: Based on the representative subset of scenarios, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints and virtual power plant demand response constraints, the maximum photovoltaic capacity that the active distribution network can carry is solved by optimization calculation, and the carrying capacity result and system performance indicators are output.

[0011] In one embodiment, the step of generating an initial scenario set based on the probability density function using the Monte Carlo method, wherein the initial scenario set includes power range identifiers and corresponding probabilities for photovoltaic power generation, load demand, and demand response of the virtual power plant, includes:

[0012] The load demand is modeled, and the probability density function of the load demand adopts a normal distribution, with the mean being the predicted load value and the standard deviation being the prediction error.

[0013] The photovoltaic power generation is modeled, and the probability density function of the photovoltaic power generation adopts a Beta distribution;

[0014] The demand response is modeled, and the probability density function of the demand response is fitted to a normal distribution or a Beta distribution based on historical response data.

[0015] In one embodiment, the step of generating an initial scene set based on the probability density function using the Monte Carlo method, and compressing the initial scene set using scene reduction techniques to obtain a representative subset of scenes and corresponding probability weights, includes:

[0016] For each time step, generate a random number that is uniformly distributed within the interval for each uncertain variable;

[0017] By using a roulette wheel betting mechanism, the random number is mapped to the probability density function, and the specific values ​​of photovoltaic power generation, load demand, and demand response of the virtual power plant at that moment are derived.

[0018] The probability of each scenario is calculated by normalizing the joint probability of the power interval identifiers at each time step;

[0019] Combine all time step values ​​into a complete daily scene, and repeat this process to generate the initial scene set.

[0020] In one embodiment, the step of compressing the initial scene set using scene reduction techniques to obtain a representative subset of scenes and corresponding probability weights includes:

[0021] Calculate the Euclidean distance between the initial scene sets as a similarity index;

[0022] Iteratively delete the scene in the initial scene set that has the smallest Euclidean distance to other scenes and the smallest probability weight, and transfer its probability weight to the nearest neighbor retained scene, until the number of scenes is reduced to a preset size, thus obtaining a representative subset of scenes.

[0023] In one embodiment, the step of calculating the maximum photovoltaic capacity that the active distribution network can support based on the representative subset of scenarios, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints, and virtual power plant demand response constraints, and outputting the carrying capacity result and system performance indicators, includes:

[0024] Construct a stochastic optimization model with the objective of maximizing photovoltaic carrying capacity;

[0025] Define and apply multidimensional safe operation constraints, which include node voltage constraints, transformer capacity constraints, line capacity constraints, and demand response constraints of the virtual power plant;

[0026] By integrating a fully local reactive power regulation strategy and a virtual power plant demand response mechanism, the maximum photovoltaic capacity that the distribution network can support is calculated, and the carrying capacity results and system performance indicators are output.

[0027] In one embodiment, the step of defining and applying multidimensional safe operation constraints, which include node voltage constraints, transformer capacity constraints, line capacity constraints, and virtual power plant demand response constraints, includes:

[0028] The node voltage constraint requires all nodes to maintain their voltage within a preset limit under all scenarios, and the degree of exceeding the limit is quantified by a penalty term.

[0029] The transformer capacity constraint requires that the apparent power not exceed the rated capacity;

[0030] The line capacity constraint requires that the current load rate not exceed the thermal stability limit.

[0031] The demand response constraints of the virtual power plant require that the power adjustment amount be within its dispatchable range and meet the response rate limit.

[0032] In one embodiment, the output system performance indicators include, but are not limited to, the sum of expected total network loss, voltage over-limit penalty terms, total response of the virtual power plant, maximum transformer load rate, and maximum line load rate; wherein the expected total network loss calculation formula is a probabilistic weighted sum of branch active power losses under all scenarios.

[0033] An active distribution network carrying capacity probabilistic modeling device involving virtual power plant demand response includes:

[0034] The data acquisition and probabilistic modeling module is used to construct probability density functions for photovoltaic power generation, load demand, and demand response of virtual power plants at each node in the active distribution network based on historical monitoring data or forecast data.

[0035] The scenario generation and management module is used to generate an initial scenario set based on the probability density function using the Monte Carlo method. The initial scenario set includes the power range identifiers and corresponding probabilities of photovoltaic power generation, load demand, and demand response of the virtual power plant.

[0036] The optimization calculation and evaluation module is used to compress the initial scene set using scene reduction technology to obtain a representative subset of scenes and corresponding probability weights.

[0037] The human-computer interaction and result output module is used to calculate the maximum photovoltaic capacity that the active distribution network can carry based on the representative scenario subset, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints and virtual power plant demand response constraints, and output the carrying capacity result and system performance indicators.

[0038] Therefore, this application has the following beneficial effects:

[0039] This application provides a probabilistic modeling method for the carrying capacity of an active distribution network involving virtual power plant demand response, comprising the following steps: constructing probability density functions for photovoltaic power generation, load demand, and virtual power plant demand response at each node in the active distribution network based on historical monitoring data or forecast data; generating an initial scenario set according to the probability density functions using the Monte Carlo method, the initial scenario set including power range identifiers and corresponding probabilities for photovoltaic power generation, load demand, and virtual power plant demand response; compressing the initial scenario set using scenario reduction technology to obtain a representative subset of scenarios and corresponding probability weights; and, based on the representative subset of scenarios, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints, and virtual power plant demand response constraints, solving for the maximum photovoltaic capacity that the active distribution network can carry through optimization calculations, and outputting the carrying capacity results and system performance indicators. This application aims to address the problems in existing technologies for assessing photovoltaic carrying capacity, which rely on deterministic methods, lack uncertainty handling methods, and lack efficient probabilistic assessment frameworks. By quantifying uncertainty through probability density functions, and utilizing Monte Carlo simulation and scenario reduction techniques, the complex stochastic problem is transformed into a multi-scenario deterministic optimization problem containing key uncertainty information. Furthermore, the demand response of a virtual power plant is integrated as an active control mechanism. Ultimately, under the condition of satisfying multiple security constraints, the photovoltaic carrying capacity and system performance indicators of the active distribution network are accurately calculated. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a system flowchart of the probabilistic modeling method for active distribution network carrying capacity based on virtual power plant demand response;

[0042] Figure 2 This is an example of the output and load conditions of the active distribution network carrying capacity probabilistic modeling method for virtual power plant demand response;

[0043] Figure 3 It is the expected value result of the test feeder line of the active distribution network carrying capacity probabilistic modeling method of virtual power plant demand response. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0045] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this application.

[0046] Traditional deterministic assessment methods use typical daily curves, which fail to reflect the stochastic fluctuations in photovoltaic (PV) output and load demand, leading to overly optimistic or conservative results. While direct application of Monte Carlo simulation can handle uncertainty, its computational complexity makes it impractical. To address these shortcomings, this application provides a probabilistic modeling method for active distribution network carrying capacity involving virtual power plant demand response. Simulation experiments on the IEEE 33-bus system validate the effectiveness of this method. Results show that, compared to traditional PF-Power and Q-Voltage control strategies, the proposed strategy significantly reduces reactive power dependence on the upstream grid, lowers network losses, ensures equipment safety, and successfully increases PV carrying capacity constrained by branch power flow by approximately 20%-30%, demonstrating its significant advantages in unlocking grid acceptance potential.

[0047] This application provides an active distribution network carrying capacity probabilistic modeling method involving virtual power plant demand response, including steps S10-S40, referring to... Figure 1 , Figure 1 This is a system flowchart of the active distribution network carrying capacity probabilistic modeling method for virtual power plant demand response.

[0048] Step S10: Based on historical monitoring data or forecast data, construct probability density functions for photovoltaic power generation, load demand, and demand response of virtual power plants at each node in the active distribution network.

[0049] Step S20: Using the Monte Carlo method, generate an initial scenario set based on the probability density function. The initial scenario set includes the power range identifiers and corresponding probabilities of photovoltaic power generation, load demand, and demand response of the virtual power plant.

[0050] Step S30: Compress the initial scene set using scene reduction technology to obtain a representative subset of scenes and their corresponding probability weights;

[0051] Step S40: Based on the representative subset of scenarios, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints and virtual power plant demand response constraints, the maximum photovoltaic capacity that the active distribution network can carry is solved by optimization calculation, and the carrying capacity result and system performance indicators are output.

[0052] Specifically, in this embodiment, a systematic process transforms the uncertainties of photovoltaic power generation, load, and demand response into a calculable and optimizable deterministic problem. This process includes the following four key steps:

[0053] Step S10: Construct the probability density function of the uncertain variable.

[0054] This step forms the statistical foundation of the entire modeling process, aiming to transform random phenomena in the physical world into computable mathematical models. The system first collects historical operational monitoring data or high-precision short-term forecast data from each node in the active distribution network. Based on this data, specific probability density functions (PDFs) are constructed for three key uncertainty sources. For load demand, its fluctuations are typically caused by the superposition of numerous independent random events (such as user electricity consumption behavior). According to the central limit theorem, its prediction error follows a normal distribution (Gaussian distribution), and its PDF is completely determined by the prediction mean (μ) and standard deviation (σ). For photovoltaic power generation, its output is directly affected by solar irradiance, exhibiting significant non-negativity, boundedness (0 to maximum output P_max), and asymmetry. The Beta distribution, due to its flexible shape, accurately characterizes these properties and is therefore chosen as the modeling tool; its shape parameters α and β can be obtained by fitting historical data. A virtual power plant (VPP) is not a physical power plant, but an intelligent energy management system that aggregates a large number of dispersed energy resources, such as distributed power sources (e.g., rooftop photovoltaics, small wind turbines), flexible loads (e.g., adjustable air conditioners, charging piles), and energy storage systems, through advanced information and communication technologies and software systems, and coordinates, manages, and optimizes them in a unified manner.

[0055] For virtual power plants, their demand response capability is affected by the physical characteristics of aggregated resources (such as controllable loads and energy storage) and user willingness to respond, resulting in execution deviations. Therefore, based on the deviation data between historical dispatch instructions and actual response quantities, a probability distribution of the response quantity can be fitted (typically a normal distribution or a Beta distribution can also be used) to quantify its dispatchable range and response reliability. Through this step, the three major sources of uncertainty are given precise statistical characterization, providing a foundational basis for subsequent scenario simulations.

[0056] Step S20: Generation of the initial scene set based on the Monte Carlo method

[0057] After obtaining the probabilistic models of each node and variable, this step utilizes the Monte Carlo method to sample from the probability space, generating a massive initial scenario set covering all possible future scenarios. Specifically, for a complete daily operating cycle (e.g., divided into 96 15-minute time slots), the system independently generates a random number u uniformly distributed in the interval [0,1] for each uncertain variable (PV, load, VPP response) in each time slot t. Subsequently, using the inverse transformation sampling method (i.e., roulette wheel mechanism), this random number u is substituted into the cumulative distribution function (CDF) of the corresponding variable to solve the equation u = F(x), thereby retrieving the specific physical quantity value x (unit: kW) at that moment. Concatenating the sampling results of all T time slots within a day in chronological order constitutes a complete "daily scenario". Repeating the sampling-inversion process N times (N is usually on the order of 1000 to 10000) generates an initial scenario set containing N daily scenarios. Each scenario not only fully records the power time-series curves of photovoltaic, load, and VPP response within a day, but its generation process itself also implies the relative probability of the scenario occurring, thus comprehensively and realistically reproducing the random panorama of system operation.

[0058] Step S30: Extraction of a representative subset based on scene reduction techniques

[0059] Directly using the massive initial scene set generated in step S20 for subsequent optimization calculations would result in exponentially increasing computational complexity due to the sheer number of scenes, making it difficult to apply in engineering practice. Therefore, this step introduces an efficient scene reduction technique (such as the classic synchronous back-substitution reduction method) to intelligently compress the initial scene set. The core objective of this algorithm is to refine N scenes into K (K is typically 5 to 20) of the most representative scenes while minimizing information loss. The operation process is as follows: First, calculate the Euclidean distance between all scene pairs in the initial scene set and construct a distance matrix to quantify the similarity between scenes; then, iteratively identify the scene with the smallest average distance to other scenes (i.e., the most "common") and the lowest probability of occurrence, and remove it from the set; simultaneously, transfer and accumulate its probability weight to the nearest retained scene. This "delete-merge" process is repeated until the total number of scenes is reduced to a preset value of K. The final output of K scenarios constitutes a representative subset of scenarios. Each scenario is accompanied by a recalibrated probability weight, ensuring that the subset closely approximates the original massive scenario set in terms of key features such as statistical expectation and variance. This greatly reduces the computational burden while effectively preserving the core information of uncertainty analysis.

[0060] Step S40: Solving and Outputting Optimization Results for Multi-Constraint Bearing Capacity

[0061] This step is the core of the entire method, aiming to solve a rigorous multi-scenario deterministic optimization problem based on the representative scenario subset obtained in step S30, in order to accurately calculate the maximum photovoltaic carrying capacity of the active distribution network. The objective function of this optimization problem is to maximize the total installed photovoltaic capacity of the entire network. Its constraint system is extremely strict, requiring that at every time t in all K representative scenarios, the following four types of constraints must be satisfied simultaneously:

[0062] Node voltage constraints ensure that the voltage amplitude of all nodes is strictly maintained within the national standard limits (e.g., 0.9 pu to 1.1 pu);

[0063] Transformer capacity constraints prevent any distribution transformer from being damaged due to overload;

[0064] Line capacity constraints ensure that the current in all feeder branches does not exceed their thermal stability limits;

[0065] The virtual power plant demand response constraint ensures that the VPP's response is within its preset technically feasible range, and that the adjustment rate between adjacent time periods does not exceed the physical limits of the equipment. During the solution process, the model collaboratively utilizes the local reactive power and voltage regulation capabilities of the photovoltaic inverters and the flexible power dispatch capabilities of the VPP as active control measures to alleviate network pressure. Ultimately, the system not only outputs the core quantitative result of the maximum photovoltaic carrying capacity, but also simultaneously generates a series of system performance indicators, such as expected total grid loss, voltage over-limit risk probability, maximum load rate of key equipment, and total VPP call volume, providing grid planners with comprehensive, reliable, and actionable decision support.

[0066] Further, in this embodiment, the step of generating an initial scenario set based on the probability density function using the Monte Carlo method, wherein the initial scenario set includes power range identifiers and corresponding probabilities for photovoltaic power generation, load demand, and demand response of the virtual power plant, includes:

[0067] The load demand is modeled, and the probability density function of the load demand adopts a normal distribution, with the mean being the predicted load value and the standard deviation being the prediction error.

[0068] The photovoltaic power generation is modeled, and the probability density function of the photovoltaic power generation adopts a Beta distribution;

[0069] The demand response is modeled, and the probability density function of the demand response is fitted to a normal distribution or a Beta distribution based on historical response data.

[0070] Specifically, in this embodiment, the process of generating the initial scene set using the Monte Carlo method begins with refined probabilistic modeling of the three core uncertainty variables—load demand, photovoltaic power generation, and the demand response of the virtual power plant. This modeling process does not employ a uniform distribution; instead, it tailors the most suitable probability density function based on the physical characteristics and statistical laws of each variable, thereby ensuring that the generated scene is highly statistically close to the real world.

[0071] First, for load demand modeling, this embodiment adopts a normal distribution (Gaussian distribution). This choice has a solid physical and statistical basis. Load demand is formed by the random superposition of the electricity consumption behavior of a large number of users in a region. According to the Central Limit Theorem, the distribution of the sum of a large number of independent and identically distributed random variables tends to a normal distribution. Therefore, the prediction error of load demand usually exhibits symmetrical and unimodal characteristics. In specific modeling, the mean (μ) of the normal distribution is directly taken from the predicted value given by the load forecasting system, representing the most likely load demand level; while the standard deviation (σ) is calculated from the historical prediction error sequence and is used to quantify the degree of uncertainty in the prediction. The larger the standard deviation, the more drastic the fluctuation of load demand, and the higher the dispersion of the load value in the generated scenario.

[0072] Secondly, for modeling photovoltaic power generation, this embodiment uses the Beta distribution. This stems from the unique physical constraints of photovoltaic power generation: its output power strictly lies between 0 (no sunlight) and a maximum value (sunny midday), and its probability distribution is usually asymmetric, with power frequently switching rapidly between low and high values ​​under cloudy weather. The Beta distribution is defined in the [0,1] interval. By adjusting its two shape parameters α and β, various shapes (such as U-shaped, bell-shaped, and skewed shapes) can be flexibly fitted, perfectly matching the bounded, asymmetric, and multi-peaked stochastic characteristics of photovoltaic power output. In practice, historical photovoltaic power data must first be normalized to the [0,1] interval, and then the optimal α and β parameters are fitted using methods such as moment estimation or maximum likelihood estimation to construct an accurate Beta distribution model.

[0073] Finally, for virtual power plants, this embodiment fits their historical response data. The response behavior of virtual power plants is influenced by both the physical characteristics of aggregated resources (such as air conditioning, energy storage, and electric vehicles) and user participation intentions, resulting in a random deviation between the actual response and dispatch instructions. If historical data shows that this deviation distribution is approximately symmetrical, a normal distribution is used for modeling; if the data shows that the response has obvious upper and lower limits and the distribution is skewed, a Beta distribution is more appropriate. By analyzing the difference sequence between historical dispatch instructions and actual response, the best-matching distribution type can be determined and its parameters estimated.

[0074] After constructing the dedicated PDFs for the three types of variables, the Monte Carlo method uses them as a basis for random sampling. At each time step, a sample value is independently extracted from each of the three PDFs, representing the load, photovoltaic output, and VPP response power at that moment, respectively. Combining the sample values ​​from all time steps within a day forms a complete "daily scenario." Repeating this process thousands of times generates a large initial scenario set, where each scenario is a complete set of time-series power curves, implicitly containing the probability information of its occurrence, providing rich input data for subsequent scenario reduction and carrying capacity assessment.

[0075] Further, in this embodiment, the step of generating an initial scene set according to the probability density function using the Monte Carlo method, and compressing the initial scene set using scene reduction technology to obtain a representative subset of scenes and corresponding probability weights, includes:

[0076] For each time step, generate a random number that is uniformly distributed within the interval for each uncertain variable;

[0077] By using a roulette wheel betting mechanism, the random number is mapped to the probability density function, and the specific values ​​of photovoltaic power generation, load demand, and demand response of the virtual power plant at that moment are derived.

[0078] The probability of each scenario is calculated by normalizing the joint probability of the power interval identifiers at each time step;

[0079] Combine all time step values ​​into a complete daily scene, and repeat this process to generate the initial scene set.

[0080] Specifically, in this embodiment, Monte Carlo scene generation and subsequent scene reduction are key to connecting uncertainty modeling and efficient optimization computation. This process first constructs a massive initial scene through high-fidelity random sampling, and then extracts the most representative core scene subset through intelligent compression. The specific steps are as follows:

[0081] First, we move into the refined scene generation stage. For a complete daily operating cycle (e.g., divided into 96 15-minute periods), we independently perform sampling operations for each time step t. For each uncertain variable at that moment—including photovoltaic power generation, load demand, and the demand response of the virtual power plant—an independent random number u uniformly distributed in the interval [0,1] is generated. Mathematically, this random number u represents a probability quantile on the cumulative distribution function (CDF).

[0082] Next, a precise numerical inversion is performed using a roulette wheel sampling mechanism (i.e., inverse transformation sampling). The core of this mechanism is to take a random number *u* as input and substitute it into the cumulative distribution function (CDF) corresponding to the probability density function constructed for the corresponding variable in step S10. By solving the equation *u = F(x), where F is the CDF, the specific physical value *x* of the variable at that moment is inverted. For example, if *u* = 0.85, the inverted value is the power value (unit: kW) corresponding to the 85th percentile of the variable. Through this operation, the photovoltaic power generation, load demand, and VPP response are obtained for each time step *t*.

[0083] Subsequently, the system performs scene construction and probability assignment. The values ​​retrieved from all T time steps within a day are concatenated chronologically to form a complete daily scene. The joint probability of this scene occurring is theoretically equal to the product of the probabilities of the power interval identifiers (implied by the random number u) for each time step. In practice, because Monte Carlo sampling is uniform, each scene is initially assigned the same probability 1 / N (where N is the total number of scenes), and precise normalization and weight adjustments are performed in subsequent scene reduction steps.

[0084] By repeating the above "sampling-inversion-combination" process thousands of times (e.g., N=5000 times), the system generates a large initial scenario set. This set comprehensively covers the joint probability space constituted by the uncertainties of photovoltaic, load, and VPP response.

[0085] Finally, to address the computational burden of the initial scene set, the system employs scene reduction techniques (such as synchronous back-substitution reduction). This algorithm iteratively eliminates redundant scenes by calculating the similarity between scenes (e.g., Euclidean distance) and transfers their probability weights to the nearest retained scenes. After multiple rounds of reduction, the initial N scenes are compressed into a representative subset containing only K scenes (e.g., K=10). Each retained scene ξ^(k) is assigned a precise probability weight, with the sum of all weights being 1. This refined subset highly approximates the initial scene set in terms of statistical properties (e.g., expectation, variance).

[0086] Furthermore, in this embodiment, the step of compressing the initial scene set using scene reduction technology to obtain a representative subset of scenes and corresponding probability weights includes:

[0087] Calculate the Euclidean distance between the initial scene sets as a similarity index;

[0088] Iteratively delete the scene in the initial scene set that has the smallest Euclidean distance to other scenes and the smallest probability weight, and transfer its probability weight to the nearest neighbor retained scene, until the number of scenes is reduced to a preset size, thus obtaining a representative subset of scenes.

[0089] Specifically, in this embodiment, scene reduction is the core step in achieving efficient probabilistic assessment. Its goal is to compress the massive initial scene set (typically containing thousands of scenes) generated by the Monte Carlo method into a scalable and computationally friendly representative subset without significantly losing the original uncertainty information. This embodiment employs the classic Simultaneous Backward Reduction method to achieve this goal. This method quantifies the similarity between scenes and intelligently merges redundant scenes, ensuring that the final subset represents both the overall distribution characteristics and covers key extreme cases. This process begins with the quantification of similarity. The system first performs pairwise comparisons of all scenes in the initial scene set. Each scene can be considered a high-dimensional vector, with dimensions equal to the total number of time periods in the daily time series (e.g., 96 dimensions). The value of each dimension represents the power of the photovoltaic, load, or VPP response during that time period. To measure the similarity between any two scenes ξ(i) and ξ(j), the system calculates their Euclidean distance. The smaller the Euclidean distance, the more similar the power change trajectories of the two scenes throughout the daily cycle; conversely, the greater the difference. By calculating the distances between all scene pairs, a complete distance matrix is ​​constructed, providing an objective basis for subsequent reduction decisions.

[0090] Next, the system enters an iterative cycle of scene merging and deletion. In each iteration, the algorithm performs the following key operations: First, it finds the pair of scenes with the smallest distance in the distance matrix. This pair of scenes is the most similar in the current set. Then, among these two most similar scenes, their respective probability weights are further compared (initially, all scene weights are equal). The algorithm selects the scene with the smaller probability weight as the "deleted" object. This strategy ensures that when merging similar scenes, scenes that are more representative and have a higher probability of occurrence are retained first. The entire probability weight carried by the deleted scene is transferred to its "nearest neighbor"—the retained scene with the smallest distance. This weight transfer operation guarantees the conservation of the overall probability mass of the entire scene set (always 1) and allows the retained scenes to more accurately represent the statistical characteristics of the similar scenes that were merged around them.

[0091] The above process constitutes a complete iteration, and this iteration continues multiple times, reducing the number of scenes by one in each round while updating the distance matrix and probability weights. This process continues until the total number of scenes is reduced to a preset size (e.g., K=10). At this point, the algorithm terminates, outputting a final representative subset of scenes. Each scene in this subset has been enhanced, not only possessing its own typicality but also aggregating probabilistic information from multiple similar scenes, and its associated probability weights have been precisely calibrated. This refined subset efficiently carries the core uncertainty information of the initial scene set within a very small size.

[0092] Further, in this embodiment, the step of calculating the maximum photovoltaic capacity that the active distribution network can support based on the representative subset of scenarios, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints, and virtual power plant demand response constraints, and outputting the carrying capacity result and system performance indicators, includes:

[0093] Construct a stochastic optimization model with the objective of maximizing photovoltaic carrying capacity;

[0094] Define and apply multidimensional safe operation constraints, which include node voltage constraints, transformer capacity constraints, line capacity constraints, and demand response constraints of the virtual power plant;

[0095] By integrating a fully local reactive power regulation strategy and a virtual power plant demand response mechanism, the maximum photovoltaic capacity that the distribution network can support is calculated, and the carrying capacity results and system performance indicators are output.

[0096] Specifically, in this embodiment, based on the representative scenario subset obtained in the aforementioned steps, the system enters the final capacity calculation stage. The core of this stage is to construct and solve a rigorous multi-scenario deterministic optimization model to accurately quantify the maximum capacity of the active distribution network to accommodate photovoltaic power generation while fully ensuring grid security.

[0097] First, an optimization model is constructed, transforming the original stochastic optimization problem into a deterministic equivalent problem that must satisfy constraints under all representative scenarios. The optimization objective is explicitly set as maximizing the total installed capacity of the entire photovoltaic grid. Second, multi-dimensional safety operation constraints are defined and applied to ensure the robustness of the obtained solution under any anticipated uncertainty scenarios. These constraints cover key aspects of distribution network operation:

[0098] Node voltage constraint: It is mandatory to ensure that the voltage value of all nodes is strictly maintained within the national standard limit (e.g., 0.9 pu ≤ VV ≤ 1.1 pu) in all time periods and under all scenarios to prevent voltage exceeding the limit from damaging user equipment.

[0099] Transformer capacity constraints: Ensure that the load rate of all distribution transformers does not exceed their rated capacity under any circumstances to avoid equipment overheating and lifespan loss.

[0100] Line capacity constraint: Limit the current of all feeder branches to below their thermal stability limit under any circumstances to prevent line overload from causing faults.

[0101] Virtual power plant demand response constraints: The response behavior of the VPP is standardized, including that its response amount must be within the upper and lower limits of technical feasibility, and the adjustment rate between adjacent time periods must not exceed the maximum value allowed by its physical equipment, so as to ensure the executability of response commands.

[0102] To enhance system flexibility and unlock greater carrying capacity, the model deeply integrates two active control mechanisms. The first is a fully local reactive power regulation strategy, where each photovoltaic inverter independently and autonomously adjusts its reactive power output based solely on local voltage measurements at its grid connection point, providing rapid voltage support without relying on any communication or central commands. The second is a virtual power plant demand response mechanism, which uses the VPP's response as a core optimization variable. When high photovoltaic power generation leads to voltage spikes or line overloads, it actively balances power by reducing controllable loads or scheduling energy storage charging, thereby alleviating network pressure.

[0103] Finally, a high-efficiency mathematical programming solver is invoked to solve the above model. Once the optimal solution is obtained, key results will be output: the core carrying capacity results (i.e., the maximum total photovoltaic capacity and its node distribution), as well as a series of system performance indicators, such as the expected total grid loss under all scenarios, voltage over-limit risk, maximum load factor of key equipment, and total VPP call volume. These results together constitute a comprehensive, reliable, and operable evaluation report, providing a basis for decision-making for the scientific planning and safe operation of the power grid.

[0104] Furthermore, in this embodiment, the step of defining and applying multi-dimensional safe operation constraints, which include node voltage constraints, transformer capacity constraints, line capacity constraints, and virtual power plant demand response constraints, includes:

[0105] The node voltage constraint requires all nodes to maintain their voltage within a preset limit under all scenarios, and the degree of exceeding the limit is quantified by a penalty term.

[0106] The transformer capacity constraint requires that the apparent power not exceed the rated capacity;

[0107] The line capacity constraint requires that the current load rate not exceed the thermal stability limit.

[0108] The demand response constraints of the virtual power plant require that the power adjustment amount be within its dispatchable range and meet the response rate limit.

[0109] Specifically, in this embodiment, to ensure that the solved photovoltaic carrying capacity has high engineering practicality and operational safety, a rigorous and comprehensive multi-dimensional safety operation constraint system is defined and applied in the optimization model. This system covers the core elements of the steady-state operation of the distribution network and handles potential over-limit risks through quantitative means, specifically including the following four levels:

[0110] 1. Node voltage constraints and their over-limit penalty mechanisms

[0111] Voltage quality is a primary indicator for distribution network operation. This embodiment requires that, at every time step t in all representative scenarios k, the voltage value Vn,t(k) of any node n must be strictly maintained within the preset limits specified by national or industry standards, typically between 0.9 and 1.1 pu. To flexibly handle minor limit violations during optimization and guide the solver to avoid high-risk areas, a quadratic penalty term is introduced into the model. Specifically, to accurately quantify the degree of limit violation, the following indicators are defined:

[0112] Maximum voltage over-limit penalty:

[0113] Minimum voltage limit violation penalty:

[0114] The optimization objective is to minimize the sum of these penalty terms and dynamically adjust load and generation through virtual power plant demand response to maintain voltage stability.

[0115] in and This indicates the upper and lower voltage limits, for example, values ​​of 1.1 pu and 0.9 pu respectively; Representing a scene The probability of. It is the set of all nodes; and Indicates in the scene Next node The maximum and minimum voltage values; in addition, the penalty term is multiplied by 100 to amplify the degree of exceeding the limit, making it easier for the optimization algorithm to handle.

[0116] 2. Transformer capacity constraints

[0117] Distribution transformers are critical devices connecting the main grid and the distribution network; overload of these transformers can accelerate insulation aging and even cause faults. This embodiment imposes a hard constraint on this: for each transformer tr in the network, the apparent power flowing through it under any scenario k and any time period t is... The product of the effective values ​​of voltage and current must not exceed the rated capacity indicated on its nameplate. This constraint ensures that the transformer operates within its designed safe thermal load range, guaranteeing the long-term reliability of the equipment.

[0118] 3. Line capacity constraints.

[0119] The current carrying capacity of feeder lines is limited by their conductor materials and heat dissipation conditions, exhibiting a definite thermal stability limit. This embodiment transforms this physical limitation into a current load factor constraint. Specifically, for each feeder branch b, the effective value of its actual current under any scenario k and any time period t must not exceed its thermal stability limit current. Through this constraint, the model can effectively prevent line overload problems caused by excessive photovoltaic backfeed power, a typical bottleneck in high-penetration photovoltaic access scenarios.

[0120] 4. Demand Response Constraints of Virtual Power Plants

[0121] As a actively controlled resource, the scheduling of a virtual power plant must conform to physical feasibility. This embodiment imposes two constraints for this purpose:

[0122] Dispatchable range constraint: The power adjustment amount DRt(k) of VPP in any time period t and scenario k (positive value represents load reduction or power generation increase, negative value is the opposite) must be within the upper and lower limits specified in its agreement with the grid.

[0123] Response rate constraint: Considering the physical inertia of aggregated resources (such as air conditioning and energy storage) within the VPP, the power adjustment between adjacent time periods cannot be too drastic.

[0124] Through the synergistic effect of the above four types of constraints, this embodiment constructs a safety boundary that is both strict and flexible, ensuring that the final calculated maximum photovoltaic carrying capacity is a safe, reliable, and executable engineering solution under multiple uncertainties.

[0125] Furthermore, in this embodiment, the output system performance indicators include, but are not limited to, the sum of expected total network loss, voltage over-limit penalty terms, total response of virtual power plant, maximum transformer load rate, and maximum line load rate; wherein the expected total network loss calculation formula is the probabilistic weighted sum of branch active power loss under all scenarios.

[0126] Specifically, in this embodiment, to comprehensively and quantitatively evaluate the overall performance of the obtained maximum photovoltaic carrying capacity scheme, the system not only outputs the core carrying capacity value, but also simultaneously calculates and outputs a series of key system performance indicators. These indicators provide in-depth auxiliary decision-making information for power grid planners and operators from multiple dimensions such as economy, safety, and flexibility. Specifically, the system performance indicators include, but are not limited to, the following five items:

[0127] Expected Total Network Losses: This metric reflects the economic performance of the solution. It is calculated by taking a probability-weighted average of the total active power loss across all representative scenarios. The specific formula is:

[0128]

[0129] Where K is the number of scene subsets, pk is the probability weight of the k-th scene, B is the set of all branches, and T is the set of all time periods. The active power loss of branch b under scenario k and time period t is given. The lower this indicator, the better the economic efficiency of operation.

[0130] Sum of Voltage Violation Penalty Terms: This metric is a crucial quantitative representation of safety, directly derived from the penalty mechanism in the optimization model. It summarizes the total penalty costs incurred across all scenarios, nodes, and time periods due to voltage exceeding preset limits (e.g., 0.9-1.1 pu). A near-zero sum of penalty terms indicates that the capacity scheme can perfectly maintain voltage stability under all anticipated scenarios, demonstrating extremely high robustness and safety.

[0131] Total VPP Response Quantity: This metric measures the flexibility value of virtual power plants in supporting high-proportion solar PV grid connection. It is calculated as the expected sum of the absolute values ​​of the VPP response across all scenarios, i.e.:

[0132]

[0133] The magnitude of this value directly reflects the degree of dependence on VPP adjustment capability to achieve this carrying capacity, and is a key basis for evaluating the efficiency of flexibility resources.

[0134] Maximum Transformer Loading Rate: This metric is used to assess the safety margin of the main equipment. By traversing all scenarios and time periods, the maximum load rate (the ratio of actual apparent power to rated capacity) of all transformers is identified. This metric ensures that no transformer is on the verge of overload under extreme conditions, guaranteeing the safe operation of the equipment.

[0135] Maximum Line Loading Rate: Similar to transformer metrics, this metric is used to assess bottlenecks in feeder networks. It is determined by identifying the maximum current load rate (the ratio of actual current to thermal stability limit) across all feeder branches across all scenarios and time periods. This metric directly reveals the most strained link in the network and is a core basis for determining whether the carrying capacity is limited by line constraints.

[0136] This embodiment constructs an improved IEEE 33-node distribution test system in power system simulation software to verify the effectiveness of the proposed method. The test system is configured with photovoltaic power generation units at each node to simulate a high-penetration photovoltaic access scenario, with a system baseline power of 5750 kW. It also integrates virtual power plant demand response resources, including controllable loads and energy storage systems, enabling dynamic adjustment in response to grid signals. Figure 2 This is an example of photovoltaic power generation output and load conditions for the active distribution network carrying capacity probabilistic modeling method based on virtual power plant demand response. To comprehensively evaluate performance, the strategy proposed in this application, which combines a fully local reactive power and voltage coordination control strategy based on probabilistic assessment with virtual power plant demand response, is compared with two advanced local voltage control strategies in the current literature: PF-Power and Q-Voltage. All comparisons are conducted within a probabilistic assessment framework, based on the expected values ​​of 10 representative scenarios generated by Monte Carlo simulation and then reduced, thus ensuring the fairness and robustness of the comparisons. Traditional Q-Voltage and PF-Power strategies require the absorption of a large amount of reactive power from the upstream grid to support voltage, while the strategy in this application achieves local reactive power balance and offset by optimizing the reactive power capacity of the local photovoltaic inverter, significantly reducing the reactive power dependence on the upstream grid and improving the autonomous operation capability of the distribution network. Figure 3 These are the expected values ​​for test feeder lines using the probabilistic modeling method for active distribution network carrying capacity based on virtual power plant demand response. Throughout the day, the network active power loss under the strategy presented in this application remains at a minimum level. This indicates that precise reactive power coordination control effectively optimizes the system's power flow distribution, reduces unnecessary energy transmission losses, and thus improves the overall operational economy of the system.

[0137] An active distribution network carrying capacity probabilistic modeling device involving virtual power plant demand response includes:

[0138] The data acquisition and probabilistic modeling module is used to construct probability density functions for photovoltaic power generation, load demand, and demand response of virtual power plants at each node in the active distribution network based on historical monitoring data or forecast data.

[0139] The scenario generation and management module is used to generate an initial scenario set based on the probability density function using the Monte Carlo method. The initial scenario set includes the power range identifiers and corresponding probabilities of photovoltaic power generation, load demand, and demand response of the virtual power plant.

[0140] The optimization calculation and evaluation module is used to compress the initial scene set using scene reduction technology to obtain a representative subset of scenes and corresponding probability weights.

[0141] The human-computer interaction and result output module is used to calculate the maximum photovoltaic capacity that the active distribution network can carry based on the representative scenario subset, under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints and virtual power plant demand response constraints, and output the carrying capacity result and system performance indicators.

[0142] In this embodiment, the device achieves an efficient and accurate probability modeling and evaluation process through the collaboration of software and hardware. Its core components are as follows:

[0143] 1. Data Acquisition and Probabilistic Modeling Module

[0144] This module forms the basis for the device's data input and processing, and is responsible for mathematically quantifying all sources of uncertainty.

[0145] Data acquisition interface: It has communication interfaces with power distribution network monitoring systems, weather forecasting platforms, and virtual power plant control centers, and is used to acquire the required historical and forecast data streams in real time or near real time.

[0146] Data processing and feature extraction: The collected raw data is cleaned, aligned and normalized, and key statistical features are extracted, such as the mean and variance of photovoltaic output and load, as well as the statistical regularity of the historical response behavior of the virtual power plant.

[0147] Probabilistic model building unit:

[0148] Photovoltaic model unit: Based on the processed solar irradiance or photovoltaic power output data, the maximum likelihood estimation method or the method of moments is used to fit the probability density function of the Beta distribution for each photovoltaic node to characterize the random characteristics of its power output fluctuating between zero and the maximum value.

[0149] Load model unit: Based on load data, assuming that its prediction error follows a normal distribution, and using the mean of the prediction value and the standard deviation of the prediction error as the variance, the probability density function of each load node is constructed.

[0150] Virtual power plant model unit: Based on the historical response records of the virtual power plant, a probabilistic model of its dispatchable power is constructed using parametric estimation or non-parametric kernel density estimation techniques to quantify the uncertainty of user response behavior.

[0151] Output: The output of this module is a set of probability density functions with defined parameters for all uncertain nodes (photovoltaics, loads, virtual power plants) in the entire network, providing a sampling basis for scenario generation.

[0152] 2. Scene Generation and Management Module

[0153] This module is responsible for transforming continuous probabilistic models into discrete sets of scenarios that can be processed by computers.

[0154] The Monte Carlo simulation engine is the core computational unit of the module. It employs a roulette wheel selection mechanism as its random sampler. Specifically, for each time step, it generates a uniformly distributed random number for each PDF and generates the specific power value of the corresponding variable by solving the inverse function of the cumulative distribution function.

[0155] Structural Unit: The time-series power values ​​obtained from the above sampling are discretized and divided into several power intervals, which are then encoded using binary identifiers. Ultimately, a complete daily scenario is constructed as a structured high-dimensional data vector, containing power interval identifiers for load, photovoltaic, and demand response at all points in time throughout the day.

[0156] Initial probability calculation unit: According to the law of probability multiplication, calculate the original joint probability of each initial scenario and normalize it to ensure that the sum of the probabilities of all scenarios is 1, forming a complete initial scenario library.

[0157] 3. Optimize the calculation and evaluation module

[0158] This module is the brain of the device, responsible for transforming probabilistic problems into solvable optimization problems and determining the final carrying capacity.

[0159] Scene Reduction: Employs a synchronous back-substitution reduction algorithm. This component first calculates the Euclidean distance between all scene pairs to construct a distance matrix. Then, it iteratively calculates the distance index for each scene, thereby removing redundant scenes and transferring the probability weights of the removed scenes to their nearest neighbor scenes. Finally, it outputs a small but representative subset of scenes and their corrected probability weights.

[0160] Optimize model building and solver:

[0161] Objective function setting: The optimization objective is defined as maximizing the sum of the rated capacities of all photovoltaic units in the distribution network.

[0162] Voltage safety constraints: Introduce over-limit penalties based on maximum / minimum voltage to ensure that the voltage of all nodes remains within safe limits in all scenarios throughout the day.

[0163] Equipment safety constraints: The apparent power of the transformer and the line current are strictly limited to their rated capacity and thermal stability limits.

[0164] Virtual power plant operation constraints: Set the upper and lower limits of its power adjustment and the maximum adjustment rate for adjacent time periods.

[0165] Active control integration: In the optimization model, the reactive power regulation capability of the photovoltaic inverter (following its capacity constraints) and the active power regulation capability of the virtual power plant are used as core optimization variables to achieve coordinated control.

[0166] Solution engine: Integrates mathematical programming solvers (such as CPLEX, Gurobi, or intelligent optimization algorithms) to efficiently solve the deterministic optimization problems constructed above.

[0167] Performance evaluation unit: After solving, it calculates system performance indicators such as expected total network loss and probability of constraint overrun risk, and quantitatively evaluates the response effect of the virtual power plant.

[0168] 4. Human-computer interaction and result output module

[0169] This module serves as the user interface between the device and the user, responsible for transforming complex calculation results into intuitive decision support information.

[0170] Visual Interface: Provides a graphical user interface for displaying:

[0171] Key findings: The specific value of the maximum photovoltaic carrying capacity and the main limiting factors.

[0172] System status: voltage curves of key nodes, and probability distribution of transformer and line load rates under different scenarios.

[0173] Comparative analysis: The carrying capacity, network loss, reactive power demand, and other indicators of the method of this invention are intuitively compared with those of traditional methods in the form of charts.

[0174] Report Generator: Automatically generates structured assessment reports, including input parameters, a summary of the calculation process, final carrying capacity, detailed performance data, and risk assessment conclusions.

[0175] Data Interface: Provides standardized data output interfaces (such as API or file export functions) that can transmit key results to the distribution network management system or planning platform to provide data support for subsequent decision-making.

[0176] Other embodiments or specific implementations of the active distribution network carrying capacity probabilistic modeling device based on virtual power plant demand response in this application can be found in the above-described method embodiments, and will not be repeated here.

[0177] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0178] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0179] It should be particularly noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, or of course, by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0180] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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 this application.

Claims

1. An active distribution network carrying capacity probabilistic modeling method related to virtual power plant demand response, characterized in that, The method comprises the following steps: Step S10: Constructing probability density functions for photovoltaic power, load demand and demand response of virtual power plants in the active power distribution network based on historical monitoring data or prediction data; Step S20: Generating an initial scenario set according to the probability density functions by using a Monte Carlo method, wherein the initial scenario set comprises power interval identification and corresponding probabilities of photovoltaic power, load demand and demand response of virtual power plants; Step S30: Compressing the initial scenario set by using a scenario reduction technique to obtain a representative scenario subset and corresponding probability weights; Step S40: Based on the representative scenario subset, solving the maximum photovoltaic capacity that can be carried by the active power distribution network by optimization calculation under the conditions of satisfying node voltage constraints, transformer capacity constraints, line capacity constraints and demand response constraints of virtual power plants, and outputting the carrying capacity result and system performance index.

2. The method of claim 1, wherein, The step of generating an initial scenario set according to the probability density functions by using a Monte Carlo method, wherein the initial scenario set comprises power interval identification and corresponding probabilities of photovoltaic power, load demand and demand response of virtual power plants, comprises: Modeling the load demand, wherein the probability density function of the load demand adopts a normal distribution, the mean value is a load prediction value, and the standard deviation is a prediction error; Modeling the photovoltaic power, wherein the probability density function of the photovoltaic power adopts a Beta distribution; Modeling the demand response, wherein the probability density function of the demand response is fitted into a normal distribution or a Beta distribution based on historical response data.

3. The method of claim 1, wherein, The step of generating an initial scenario set according to the probability density functions by using a Monte Carlo method, and compressing the initial scenario set by using a scenario reduction technique to obtain a representative scenario subset and corresponding probability weights, comprises: For each time step, generating a random number uniformly distributed in an interval for each uncertain variable; Mapping the random number to the probability density function by using a roulette mechanism to inverse the specific values of photovoltaic power, load demand and demand response of virtual power plants at this moment; The probability of each scenario is calculated by normalizing the joint probability of power interval identification at each time step; Combining the values of all time steps into a complete daily scenario, and repeating the process to generate an initial scenario set.

4. The method of claim 1, wherein, The step of compressing the initial scenario set by using a scenario reduction technique to obtain a representative scenario subset and corresponding probability weights, comprises: Calculating the Euclidean distance between the initial scenario set as a similarity index; Iteratively deleting the scenario in the initial scenario set with the smallest Euclidean distance to other scenarios and the smallest probability weight of itself, and transferring the probability weight to the nearest neighbor reserved scenario until the number of scenarios is reduced to a preset size to obtain a representative scenario subset.

5. The method of claim 1, wherein, The step of calculating the maximum photovoltaic capacity that the active distribution network can bear and outputting the bearing capacity result and system performance index based on the representative scenario subset under the conditions of meeting the node voltage constraint, transformer capacity constraint, line capacity constraint and demand response constraint of the virtual power plant, comprises: A random optimization model is constructed to maximize the photovoltaic bearing capacity; Multi-dimensional safe operation constraints are defined and applied, including node voltage constraints, transformer capacity constraints, line capacity constraints and demand response constraints of the virtual power plant; The maximum photovoltaic capacity that the distribution network can bear is calculated by integrating the completely local reactive power regulation strategy and the demand response mechanism of the virtual power plant, and the bearing capacity result and system performance index are output.

6. The method of claim 5, wherein, The step of defining and applying multi-dimensional safe operation constraints, including node voltage constraints, transformer capacity constraints, line capacity constraints and demand response constraints of the virtual power plant, comprises: The node voltage constraint requires that the voltage of all nodes in all scenarios is maintained within the preset limit, and the out-of-limit degree is quantified by a penalty term; The transformer capacity constraint requires that the apparent power does not exceed the rated capacity; The line capacity constraint requires that the current load rate does not exceed the thermal stability limit; The demand response constraint of the virtual power plant requires that the power adjustment amount is within its adjustable range and meets the response rate limit.

7. The method of claim 6, wherein, The output system performance index includes but is not limited to expected total network loss, sum of voltage out-of-limit penalty terms, total response amount of virtual power plant, maximum load rate of transformer and maximum load rate of line; wherein the expected total network loss calculation formula is the probability weighted sum of branch active power loss in all scenarios.

8. An apparatus for proactive power distribution network carrying capacity probabilistic modeling involving virtual power plant demand response, characterized by, It comprises: A data acquisition and probability modeling module is used to construct probability density functions for photovoltaic power generation, load demand and demand response of the virtual power plant in the active distribution network based on historical monitoring data or predicted data; A scenario generation and management module is used to generate an initial scenario set by the Monte Carlo method according to the probability density functions, which includes power interval identification and corresponding probability of photovoltaic power generation, load demand and demand response of the virtual power plant; An optimization calculation and evaluation module is used to compress the initial scenario set by using scenario reduction technology to obtain a representative scenario subset and corresponding probability weight; A human-computer interaction and result output module is used to calculate the maximum photovoltaic capacity that the active distribution network can bear based on the representative scenario subset under the conditions of meeting the node voltage constraint, transformer capacity constraint, line capacity constraint and demand response constraint of the virtual power plant, and output the bearing capacity result and system performance index.

9. An electronic device, comprising: It comprises: One or more processors; Memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the electronic device implements the method of any one of claims 1-7.

10. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method of any one of claims 1-7.

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