Power distribution network weak link early warning method, device and storage medium

Abstract

The application relates to the technical field of power grids, and discloses a power distribution network weak link early warning method, equipment and a storage medium. The method obtains power distribution network parameters, constructs a planning scene set and a probability model to distinguish uncertainty types, constructs a probability power flow model based on this, and obtains probability representation results by using an efficient solving method, and then calculates an out-of-limit risk index to identify weak links, so that the weak links of the power distribution network can be efficiently and accurately identified, the new energy consumption capacity can be improved, and the safe and stable operation of the power distribution network can be ensured.

Description

Technical Field

[0001] This invention relates to the field of power grid technology, and in particular to a method, device and storage medium for early warning of weak links in a distribution network. Background Technology

[0002] With the rapid popularization of distributed renewable energy, especially distributed photovoltaic (PV), in distribution networks, the operating environment of distribution networks has undergone profound changes. Renewable energy power generation output is highly random and intermittent, influenced by meteorological conditions and geographical factors. This fluctuation, combined with the random variations in traditional load power, easily leads to abnormal operating phenomena such as distribution network node voltage exceeding safety thresholds, branch current exceeding thermal stability limits, and excessive three-phase load imbalance, seriously threatening the safe and stable operation of the distribution network. Therefore, accurate identification and timely early warning of potential weaknesses in the distribution network during the renewable energy planning and integration phase or in actual operation have become key technical requirements for ensuring reliable operation of the distribution network and improving the renewable energy absorption capacity.

[0003] In existing technologies, the assessment of risks associated with the integration of new energy sources into distribution networks mainly employs deterministic analysis methods and probabilistic analysis methods. Deterministic analysis methods typically perform power flow calculations based on typical operating conditions or extreme boundary conditions. Although the calculation process is relatively simple, it cannot effectively characterize the stochastic nature of new energy output and load fluctuations. This leads to assessment results that are either too conservative, limiting the scope for new energy integration, or too optimistic, ignoring potential operational risks. Consequently, it is difficult to accurately reflect the actual operating status of the distribution network under complex and uncertain environments.

[0004] To overcome the aforementioned limitations, some existing technologies have introduced probabilistic power flow analysis methods. These methods generate numerous operational scenarios by stochastically modeling historical load and irradiance data and employing techniques such as Monte Carlo sampling, thereby calculating risk indicators such as voltage exceedance probability or branch overload probability. However, these methods have significant drawbacks: they conflate renewable energy access planning schemes (such as access scale and location) with operational randomness (such as load fluctuations and irradiance variations), performing unified sampling and joint analysis. This fails to distinguish between the different characteristics of planning-level uncertainty (affecting renewable energy access scheme selection) and operational-level uncertainty (affecting real-time operational status). This hybrid modeling approach makes it impossible for the evaluation results to clearly reveal the independent impact of specific renewable energy access schemes on distribution network operational risks, resulting in a lack of specificity and scientific basis for planning decisions.

[0005] Furthermore, probabilistic analysis methods based on Monte Carlo simulations require generating massive amounts of samples to ensure statistical reliability. In complex distribution network scenarios, the computational complexity increases dramatically, leading to excessive time consumption and making it difficult to meet the real-time computational efficiency requirements of engineering applications. To reduce the computational burden, some existing methods have had to simplify the distribution network topology model or reduce the sampling scale, but this ignores the dynamic changes in load and renewable energy output over short timescales, resulting in distorted risk assessment results. More critically, existing technologies mostly focus on assessing the upper limit of the overall renewable energy access capacity, lacking a systematic identification mechanism for specific over-limit locations (such as specific nodes or branches). This fails to provide operators with intuitive and actionable early warning information on weak points, severely restricting the refined operation management and risk control capabilities of the distribution network. Summary of the Invention

[0006] To address one or more of the aforementioned technical problems, this invention proposes a method, device, and storage medium for early warning of weak links in power distribution networks.

[0007] The technical solution provided by this invention: a method for early warning of weak links in a power distribution network, comprising:

[0008] The topology parameters, feeder parameters, historical operating data, and new energy planning parameters to be connected to the distribution network are obtained. Based on the types of uncertainties in the distribution network, a set of planning scenarios and a probability model are constructed. The set of planning scenarios is used to characterize different new energy access schemes for uncertainties at the planning level, and the probability model is used to characterize the random fluctuation characteristics of load power and new energy output in uncertainties at the operation level.

[0009] Based on the set of planning scenarios and the probability model, a probabilistic power flow model of the distribution network is constructed, and a non-intrusive generalized multinomial chaos method is used to solve the probabilistic power flow model to obtain the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario.

[0010] Based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, combined with the preset distribution network operation safety constraints, the probability of exceeding the limit under different time sections of each planning scenario is calculated, and the corresponding limit exceeding risk index is generated.

[0011] Based on the aforementioned over-limit risk indicators, compliance screening is performed on each planning scenario to determine the critical renewable energy consumption scenario with the largest renewable energy access capacity under the condition of meeting the preset risk threshold. In the critical renewable energy consumption scenario, weak links in the distribution network that cause the over-limit risk to reach the threshold are identified and warnings are issued.

[0012] Furthermore, the construction of a set of planning scenarios and a probabilistic model based on the types of uncertainties existing in the distribution network includes:

[0013] Based on the new energy planning parameters, uncertainty parameters are extracted according to the uncertainty type of the planning layer. The uncertainty parameters of the planning layer include the scale of new energy access, the number of accesses, the access location, and the access phase.

[0014] According to the type of operational layer uncertainty, operational layer uncertainty parameters are extracted based on the historical operational data, wherein the operational layer uncertainty parameters include historical load data and historical irradiance data;

[0015] Based on the planning layer uncertainty parameters, the topology parameters, and the feeder parameters, a set of planning scenarios is constructed.

[0016] A probabilistic model is constructed based on the uncertainty parameters of the operating layer.

[0017] Furthermore, the construction of a planning scenario set based on the planning layer uncertainty parameters, the topology parameters, and the feeder parameters includes:

[0018] Determine the range of values ​​for the installed capacity of individual new energy units;

[0019] The access locations of the new energy sources are classified according to whether they are single-phase or three-phase new energy sources;

[0020] Determine the step size for changes in the penetration rate of new energy access;

[0021] Based on the scale of new energy access, the number of accesses, the access location, and the access phase, and using the value range and the change step size as constraints, multiple discrete new energy access planning scenarios are randomly combined according to the access type of the new energy to obtain a planning scenario set.

[0022] Furthermore, the construction of the probabilistic model based on the uncertainty parameters of the operating layer includes:

[0023] The maximum likelihood estimation method is used to fit the probability distributions of the historical load data and historical irradiance data to obtain a probability model.

[0024] In one feasible implementation, the step of employing the maximum likelihood estimation method to fit the probability distributions of the historical load data and historical irradiance data to obtain a probability model includes:

[0025] Distribution network users are clustered and grouped according to their annual electricity consumption or contracted power.

[0026] At a preset time granularity, the probability distribution of the historical load data corresponding to each user group is fitted to obtain the probability density function of the load power.

[0027] At the same time granularity, the historical irradiance data is fitted with a probability distribution to obtain the probability density function of new energy output.

[0028] Furthermore, the construction of a probabilistic power flow model for the distribution network based on the planning scenario set and the probabilistic model includes:

[0029] For each new energy access planning scenario in the planning scenario set, a corresponding distribution network deterministic topology model is constructed based on the topology parameters and the feeder parameters.

[0030] The load power and new energy output, which represent the uncertainty of the operation layer in the probabilistic model, are introduced into the deterministic topology model and set as random input variables.

[0031] The voltage amplitude of each node in the distribution network and the current magnitude of each branch are set as random output variables;

[0032] Based on the power flow constraint equations of the distribution network, a probabilistic power flow model of the distribution network is constructed, which simultaneously includes the random input variables and the random output variables.

[0033] Furthermore, the non-intrusive generalized multinomial chaotic method is used to solve the probabilistic power flow model to obtain probabilistic characterization results of distribution network node voltages and branch currents under each planning scenario, including:

[0034] Based on the probability distribution type of the random input variables in the probability model, select an orthogonal polynomial basis function that matches the probability distribution type;

[0035] Set the order of the chaotic expansion of the generalized polynomial basis function, and construct a polynomial function expression between random input variables and distribution network node voltages and branch currents;

[0036] Based on the aforementioned polynomial function expression, multiple test points are generated in the probability space of random input variables using low-discrepancy sequences.

[0037] Using the values ​​of random input variables corresponding to each test point as input, a deterministic power flow calculation is performed on the probabilistic power flow model to obtain the calculation results of the distribution network node voltage and branch current at each test point;

[0038] Based on the calculation results of node voltage and branch current corresponding to each test point, the chaotic expansion coefficients of the generalized polynomial basis function are solved to obtain the probabilistic characterization results of distribution network node voltage and branch current under each planning scenario.

[0039] Furthermore, based on the probabilistic characterization results of distribution network node voltages and branch currents under each planning scenario, and combined with preset distribution network operation safety constraints, the probability of exceeding limits under different time sections for each planning scenario is calculated, and corresponding limit-exceeding risk indicators are generated, including:

[0040] Define undervoltage, overvoltage, and branch overcurrent limit-exceeding events;

[0041] Based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, random sampling calculations are performed on each over-limit event to obtain the over-limit occurrence probability corresponding to each time segment;

[0042] Statistical analysis is performed on the probability of exceeding limits at each time segment to generate corresponding limit-exceeding risk indicators.

[0043] Another technical solution provided by the present invention is an electronic device comprising: a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to cause the electronic device to execute the above-mentioned method for early warning of weak links in the power distribution network.

[0044] Another technical solution provided by the present invention is a computer-readable storage medium storing instructions that, when run on a computer, cause the computer to execute the aforementioned method for early warning of weak links in the power distribution network.

[0045] The technical solution provided by this invention acquires the topology parameters, feeder parameters, historical operating data, and new energy planning parameters of the distribution network to be connected to the distribution network. Based on the types of uncertainties existing in the distribution network, a set of planning scenarios and a probability model are constructed. The set of planning scenarios characterizes different new energy access schemes for different uncertainty types at the planning layer, while the probability model characterizes the random fluctuation characteristics of load power and new energy output for uncertainties at the operating layer. Based on the set of planning scenarios and the probability model, a probabilistic power flow model of the distribution network is constructed, and a non-intrusive generalized multinomial chaos method is used to solve the probabilistic power flow model, obtaining the probabilistic characterization results of distribution network node voltage and branch current under each planning scenario. Based on the probabilistic characterization results of distribution network node voltage and branch current under each planning scenario, combined with preset distribution network operation safety constraints, the probability of exceeding limits under different time sections for each planning scenario is calculated, and corresponding exceedance risk indicators are generated. Based on the exceedance risk indicators, compliance screening is performed on each planning scenario to determine the critical new energy consumption scenario with the largest new energy access capacity under the preset risk threshold condition. In the critical new energy consumption scenario, weak links in the distribution network that cause exceedance risks to reach the threshold are identified and warnings are issued.

[0046] This method is based on obtaining the topology parameters, feeder parameters, historical operating data and new energy planning parameters of the distribution network to be connected to the distribution network, and constructs a set of planning scenarios and probability models according to the types of uncertainties in the distribution network. This enables effective differentiation and modeling of uncertainties from different sources, avoiding the problem of unclear risk attribution caused by mixed uncertainty analysis.

[0047] Furthermore, based on the planning scenario set and probability model, a probabilistic power flow model of the distribution network is constructed, and a non-intrusive generalized multinomial chaos method is used to solve the probabilistic power flow model to obtain the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario. This improves the computational efficiency of distribution network probabilistic power flow analysis while considering the random fluctuation characteristics of load power and renewable energy output, making it applicable to engineering application needs of multiple scenarios and multiple time sections.

[0048] Finally, calculating the risk index of exceeding limits to identify weak links can efficiently and accurately identify weak links in the distribution network, improve the capacity for renewable energy absorption, and ensure the safe and stable operation of the distribution network. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of one embodiment of the early warning method for weak links in the power distribution network according to the present invention;

[0050] Figure 2 This is a schematic diagram of another embodiment of the early warning method for weak links in the power distribution network in this invention;

[0051] Figure 3 This is a schematic diagram of one embodiment of the electronic device in this invention.

[0052] Figure 4 This is a simulation of the undervoltage congestion probability diagram in an embodiment of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] This invention proposes an early warning method for weak links in distribution networks based on new energy consumption and over-limit conditions. The aim is to accurately identify risk points when a distribution network accepts photovoltaic (PV) power, thereby improving the operational safety of the distribution network. The steps are as follows: First, classify the types of uncertainties in the distribution network. Decouple the planning-level uncertainties such as PV scale, quantity, and location from the operational-level uncertainties such as load and PV output. Generate multiple sets of probability density functions for planning and operational scenarios using an algorithm. Then, construct a probabilistic power flow model (GPC). Use Sobol sequences to generate test points, and combine load and irradiance data fitted with Beta distributions to solve the power flow equations under each planning scenario, obtaining key indicators such as node voltage and branch current. Second, determine the risk of distribution network limit violations. Calculate the overvoltage, undervoltage, and overcurrent probabilities at each time point, and statistically analyze the maximum probability and 95th percentile of the total probability throughout the day to achieve early warning for the distribution network. Finally, screen the critical scenarios under maximum PV conditions. Locating weak links such as voltage over-limit and current overload provides a basis for distribution network upgrades and PV integration planning, solving at least one of the following technical problems:

[0055] (1) How to effectively distinguish and model uncertainties from different sources when new energy access planning schemes and random fluctuations in operating status coexist, so as to avoid unclear risk attribution problems caused by mixed uncertainty analysis;

[0056] (2) How to improve the computational efficiency of probabilistic power flow analysis of distribution network while considering the random fluctuation characteristics of load power and new energy output, so that it can be applied to engineering application needs of multiple scenarios and multiple time sections;

[0057] (3) How to transform the probability analysis results of the distribution network operation status into quantifiable over-limit risk indicators, so as to achieve an objective assessment of the distribution network operation risk;

[0058] (4) How to identify key nodes or branches when the capacity of new energy access reaches the critical state under the premise of meeting the safety constraints of distribution network operation, so as to achieve accurate positioning and early warning output of weak links in distribution network.

[0059] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0060] It is understood that the executing entity of this invention can be an enterprise electricity load forecasting device, a terminal, or a server; no specific limitation is made here. This embodiment of the invention will be described using a server as an example.

[0061] Based on the above problems, a method for early warning of weak links in the distribution network is proposed below. The method assesses the operating status of the distribution network based on the absorption of new energy sources and over-limit, identifies nodes or branches that may have safety risks such as voltage over-limit and current overload during the access or operation of new energy sources, and issues early warning information in a timely manner to support the safe and stable operation and planning management of the distribution network.

[0062] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 One embodiment of the early warning method for weak links in the power distribution network in this invention includes:

[0063] 110. Obtain the topology parameters, feeder parameters, historical operating data, and new energy planning parameters of the distribution network to be connected to the distribution network, and construct a set of planning scenarios and probability models according to the types of uncertainties existing in the distribution network.

[0064] It should be noted that this set of planning scenarios is used to characterize different renewable energy access schemes under the uncertainty type of the planning layer; this probabilistic model is used to characterize the random fluctuation characteristics of load power and renewable energy output under the uncertainty type of the operation layer. The topology parameter refers to the connection relationships and physical layout between various devices (such as transformers, lines, nodes, etc.) in the distribution network. The feeder parameter refers to the electrical characteristics of transmission lines in the distribution network, such as resistance, reactance, and length. The historical operating data includes load data, renewable energy output data, voltage data, and current data of the distribution network over a past period, used to analyze the operating patterns and uncertainty characteristics of the distribution network. The renewable energy planning parameter refers to the planning information of renewable energy projects (such as distributed photovoltaics, wind power, etc.) to be connected to the distribution network, including their access capacity, number of projects, access location, and access phase. This uncertainty type is mainly divided into planning layer uncertainty (such as the diversity of renewable energy access schemes) and operation layer uncertainty (such as random fluctuations in load and renewable energy output). This set of planning scenarios consists of multiple possible renewable energy access schemes, each representing a specific configuration under a planning layer uncertainty type, used to evaluate the impact of different planning schemes on the operation of the distribution network. This probabilistic model is used to describe the stochastic fluctuation characteristics of load power and new energy output in the uncertainty type of the operation layer, and is usually characterized by probability density function or cumulative distribution function.

[0065] Specifically, topology parameters and feeder parameters can be exported from the distribution network's Geographic Information System (GIS) or obtained through manual measurement and recording. Historical operating data can be obtained from the distribution network's Supervisory Control and Data Acquisition (SCADA) system or smart meter system; for example, historical curves of load and renewable energy output can be exported periodically. Renewable energy planning parameters can be provided by the planning department; for example, by manually inputting the expected location, capacity, and connection point information of photovoltaic power plants. Based on this, a set of planning scenarios and a probabilistic model need to be constructed according to the types of uncertainties existing in the distribution network. The set of planning scenarios can be manually compiled by planners based on experience, listing several typical renewable energy access schemes; for example, considering photovoltaic power plants of different capacities at different feeder ends. The probabilistic model can approximate load and renewable energy output based on historical data through simple statistical averaging or empirical distribution; for example, by simply averaging historical load data and assuming it follows a normal distribution. This set of planning scenarios is used to characterize different renewable energy access schemes for uncertainties at the planning level, while the probabilistic model is used to characterize the random fluctuation characteristics of load power and renewable energy output for uncertainties at the operational level.

[0066] In practical applications, at the level of uncertainty in planning, a set of planning parameters is formed by determining the key parameters of photovoltaics, including installation scale, number of grid connections, installation location, and grid connection phase.

[0067] At the level of operational uncertainty, by focusing on load and photovoltaic output fluctuations, collecting historical data of the target distribution network, and clustering users according to their annual power consumption and contracted power, users are divided into 25 user groups, and the differences in load characteristics of each user group are clarified.

[0068] When constructing the planning scenario set, the system inputs basic feeder data, photovoltaic (PV) scale / type / location ranges, etc. The PV scale is defined as 1-15 kWp, categorized by single-phase / three-phase type, and 10 PV specifications are determined. Using a 5% penetration rate step, 20 different PV penetration rate scenarios are generated. Combining PV scale, penetration rate, and location parameters, a discrete planning scenario set is generated, with each scenario corresponding to a unique "PV installation plan."

[0069] In constructing the probabilistic model, historical load data for typical days in spring and summer, 25 user groups, and corresponding regional irradiance historical data are input. Then, typical day load data is extracted, and for each 15-minute load value of the group data, a Beta distribution is fitted using maximum likelihood estimation to obtain the load PDF for each time period. Similarly, a Beta distribution is fitted for the 15-minute irradiance data of typical days to obtain the irradiance PDF for each time period. The load PDF and irradiance PDF for the 25 user groups are output, forming a probabilistic representation of operational uncertainty.

[0070] 120. Based on the planning scenario set and probability model, construct a probabilistic power flow model for the distribution network, and use a non-intrusive generalized multinomial chaos method to solve the probabilistic power flow model to obtain the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario.

[0071] In this step, the probabilistic power flow model, based on the traditional deterministic power flow model, introduces random variables (such as load and renewable energy output) to calculate the probability distribution of node voltages and branch currents in the distribution network under uncertain conditions. This non-intrusive generalized polynomial chaos method is an efficient probabilistic power flow solution technique. By representing random variables as orthogonal polynomial chaotic expansions, it transforms the stochastic power flow problem into a series of deterministic power flow calculations, thereby obtaining the probabilistic representation of the output variables.

[0072] In this embodiment, for each renewable energy access scheme in the planning scenario set, a corresponding deterministic distribution network model can be constructed. Then, the load power and renewable energy output, which represent operational layer uncertainties in the probabilistic model, are introduced as random input variables into this deterministic model, forming a power flow equation set containing random variables. Subsequently, a non-intrusive generalized multinomial chaos method is used to solve this probabilistic power flow model, obtaining the probabilistic representations of node voltages and branch currents under each planning scenario. As an alternative, Monte Carlo simulation can be used to calculate the power flow through a large number of random samples and statistically analyze the probability distribution of the results. Specifically, a large number of load and renewable energy output samples can be randomly drawn from the probabilistic model, deterministic power flow calculations can be performed on each sample, and then statistical analysis can be performed on all calculation results to obtain the probability distributions of node voltages and branch currents. The final probabilistic representation results refer to the probability distribution information of node voltages and branch currents, such as mean, variance, and probability density function.

[0073] 130. Based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, and combined with the preset distribution network operation safety constraints, calculate the probability of exceeding the limit under different time sections for each planning scenario, and generate the corresponding limit exceeding risk index.

[0074] In this embodiment, based on the probability characterization results, it is directly determined whether the node voltage or branch current exceeds the limit within a certain confidence interval, and the number of exceedances is simply counted as a risk indicator. Specifically, the voltage amplitude can be set to be between 0.95 and 1.05 per unit, and the branch current should not exceed 1.2 times the rated capacity. For each planning scenario and each time segment, the probability of exceeding these constraints is calculated by analyzing the probability distribution of node voltage and branch current. Subsequently, a weighted average or maximum value selection can be performed on these exceedance probabilities to generate a comprehensive exceedance risk indicator.

[0075] 140. Based on the over-limit risk index, conduct compliance screening for each planning scenario, determine the critical renewable energy consumption scenario with the largest renewable energy access capacity under the condition of meeting the preset risk threshold, and identify the weak links in the distribution network that cause the over-limit risk to reach the threshold in the critical renewable energy consumption scenario, and issue an early warning.

[0076] In this embodiment, scenarios with lower risks are manually selected based on over-limit risk indicators, and then the scenario with the largest renewable energy capacity is chosen from among them. Specifically, a risk threshold can be set, for example, the probability of over-limit occurrence should not exceed 5%. The over-limit risk indicators of all planned scenarios are compared with this threshold, and all compliant scenarios that meet the threshold are selected. Among these compliant scenarios, the one with the largest total renewable energy access capacity is selected as the critical renewable energy consumption scenario. Subsequently, in this critical renewable energy consumption scenario, the weak links in the distribution network that cause the over-limit risk to reach the threshold are identified and warnings are issued. For example, based on the over-limit risk indicators, it is possible to manually check which nodes or branches have the highest risk in the critical scenario and manually generate warning information. Specifically, in the critical renewable energy consumption scenario, the over-limit risk indicators of each node and branch are analyzed to determine which nodes or branches have over-limit risk indicators that are closest to or have already reached the risk threshold. These nodes or branches are then identified as weak links in the distribution network, and corresponding warning information is generated, for example, indicating the location of the weak link, the type of over-limit (such as overvoltage, undervoltage, or overcurrent), and the time interval in which an over-limit may occur.

[0077] The following is a practical scenario to illustrate the above technical solution in more detail:

[0078] Suppose that a batch of distributed photovoltaic power stations are planned to be connected to a distribution network feeder at location A. This feeder connects multiple users whose loads exhibit random fluctuations.

[0079] First, obtain the feeder's topology parameters (e.g., line length, connection relationships), feeder parameters (e.g., line impedance), historical load data and historical irradiance data from the past year, as well as the planning parameters of the photovoltaic power station to be connected (e.g., potential connection location and capacity range of the photovoltaic power station). Based on this data, construct a set of planning scenarios. For example, consider connecting photovoltaic power stations of different capacities at different nodes of the feeder, forming dozens or even hundreds of different renewable energy connection planning scenarios. Simultaneously, based on historical load data and historical irradiance data, construct a probabilistic model of load power and photovoltaic output, for example, by obtaining its probability density function through statistical analysis.

[0080] Then, for each new energy access planning scenario in the planning scenario set, a corresponding deterministic topology model of the distribution network is constructed based on its topology and feeder parameters. Subsequently, the load power and photovoltaic output probability models constructed in step S1 are introduced into this deterministic topology model and set as random input variables, thereby constructing a probabilistic power flow model of the distribution network. For example, the voltage amplitude of each node and the current magnitude of each branch in the distribution network can be set as random output variables. Then, a non-intrusive generalized polynomial chaos method is used to solve the probabilistic power flow model. Specifically, according to the probability distribution type of load and photovoltaic output, the corresponding orthogonal polynomial basis functions are selected, and the order of the chaotic expansion is set. Next, based on the polynomial function expression, multiple test points are generated in the probability space of the random input variables using low-discrepancy sequences. Using the values ​​of the random input variables corresponding to these test points as input, deterministic power flow calculations are performed on the probabilistic power flow model to obtain the calculation results of the distribution network node voltage and branch current at each test point. Finally, based on these calculation results, the chaotic expansion coefficients of the generalized polynomial basis functions are solved, thereby obtaining the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario, such as their mean, variance and probability density function.

[0081] Furthermore, based on the probabilistic characterization results of distribution network node voltages and branch currents under various planning scenarios, and combined with preset distribution network operation safety constraints (e.g., node voltage amplitude should be between 0.95 and 1.05 per unit, and branch current should not exceed 1.2 times the rated capacity), the probability of exceeding limits at different time sections for each planning scenario is calculated. For example, undervoltage, overvoltage, and branch overcurrent limit events can be defined. By randomly sampling the probabilistic characterization results of node voltages and branch currents, the probability of exceeding limits at different time sections of the day (e.g., 10:00 AM, 2:00 PM, etc.) is obtained. Subsequently, these limits are statistically analyzed to generate corresponding limit risk indicators, such as a comprehensive risk index or the maximum probability of occurrence of each limit event.

[0082] Finally, based on this over-limit risk indicator, compliance screening is performed on all planning scenarios. For example, a preset risk threshold is set, such as the probability of any over-limit event not exceeding 3%. The over-limit risk indicator corresponding to each planning scenario is compared with this probability threshold to screen out all planning scenarios that meet operational safety constraints. Among these compliant scenarios, they are sorted according to the total capacity of renewable energy access, and the planning scenario with the largest total renewable energy access capacity is selected as the critical renewable energy consumption scenario. For example, if scenario X connects 5MW of photovoltaic power while meeting the risk threshold, while scenario Y only connects 4MW, then scenario X is selected as the critical renewable energy consumption scenario. Subsequently, under this critical renewable energy consumption scenario, the weak links in the distribution network that cause the over-limit risk to reach the threshold are identified. For example, by analyzing the over-limit risk indicators of each node and branch in this scenario, it is found that a certain node at the end of the feeder has an overvoltage risk during the peak photovoltaic output period at noon, and its over-limit probability just reaches the 3% threshold. This node is then identified as a weak node in the distribution network. Finally, an early warning message is generated and sent to the distribution network operators. For example, the early warning message may include the location of the weak node, the type of over-limit (overvoltage), and the time interval during which the over-limit risk occurs (12 noon to 2 pm).

[0083] The method provided in this embodiment effectively solves the problems of existing technologies, such as the difficulty in clearly reflecting the specific impact of renewable energy planning schemes on distribution network operation risks, as well as the high computational complexity and long processing time, by distinguishing and modeling planning-level uncertainties (renewable energy access schemes) from operational-level uncertainties (load and renewable energy output fluctuations), and employing an efficient, non-intrusive generalized multinomial chaos method for probabilistic power flow calculation. By constructing a set of planning scenarios and a probabilistic model, different renewable energy access schemes and operational randomness can be comprehensively considered, thereby obtaining a more accurate risk assessment.

[0084] The further adopted non-intrusive generalized polynomial chaos method transforms the stochastic power flow problem into a series of deterministic power flow calculations by representing random variables as orthogonal polynomial chaotic expansions. This significantly reduces computational complexity, improves computational efficiency, and meets the computational efficiency requirements of engineering applications.

[0085] Finally, the specific weak links in the distribution network that cause the risk of exceeding the limit to reach the threshold are identified, and early warning information is generated. This makes up for the shortcomings of existing technologies, which mostly focus on assessing the capacity of new energy access and lack systematic identification of specific nodes or branches that exceed the limit.

[0086] Please see Figure 2 Another embodiment of the early warning method for weak links in the power distribution network in this invention includes:

[0087] 201. Obtain the topology parameters, feeder parameters, historical operating data, and new energy planning parameters of the distribution network to be connected to the distribution network;

[0088] 202. Based on the uncertainty type of the planning layer, extract the uncertainty parameters of the planning layer from the new energy planning parameters;

[0089] In this step, the uncertainty type at the planning level refers to the future uncertainty introduced during the distribution network planning stage due to the diversity of new energy access schemes. Specifically, it is obtained by analyzing the design of the distribution network; however, the distribution network itself is an inherent uncertainty.

[0090] The extraction of uncertainty parameters at the planning level is specifically based on new energy planning parameters, such as government policies, market demand, and technological development trends.

[0091] Specifically, the uncertainties in this planning layer include the scale, number, location, and phase of new energy access. Examples include total installed capacity, the number of photovoltaic inverters or wind turbine generators, which node or branch of the distribution network it connects to, and whether it's single-phase or three-phase access.

[0092] 203. Extract operational layer uncertainty parameters based on historical operational data according to the type of operational layer uncertainty;

[0093] The extraction of operational layer uncertainty parameters is specifically based on historical operational data. These parameters include historical load data and historical irradiance data. Specifically, the historical load data for each node in the distribution network can be hourly or moment-by-moment load curves over a past period; and the historical irradiance data for the renewable energy generation side can be historical solar irradiance intensity data for the area where the photovoltaic power station is located. This historical data is a crucial basis for constructing the operational layer uncertainty probability model, reflecting the stochastic fluctuation characteristics of load and renewable energy output.

[0094] 204. Based on the uncertainty parameters, topology parameters, and feeder parameters of the planning layer, construct a set of planning scenarios;

[0095] In this step, the construction of the planning scenario set is actually based on the extracted planning layer uncertainty parameters, combined with the distribution network topology parameters and feeder parameters, and obtained by randomly constructing parameters. By combining and discretizing parameters such as the scale, quantity, location, and phase of new energy access, a series of planning scenarios representing different new energy access schemes can be generated.

[0096] 205. Construct a probabilistic model based on the uncertainty parameters of the runtime layer;

[0097] In this step, the construction of the probabilistic model is actually based on fitting the extracted operational uncertainty parameters using a fitting algorithm. For example, historical load data and historical irradiance data can be used to establish a probabilistic distribution model of load power and renewable energy output through statistical analysis and probability distribution fitting methods.

[0098] In this embodiment, two main types of uncertainty in the distribution network are systematically identified and quantified, namely, planning-level uncertainty and operational-level uncertainty, wherein:

[0099] To determine the uncertainties at the planning level, key uncertainty parameters are extracted from the renewable energy planning parameters, including the scale, number, location, and phase of renewable energy access. These parameters are the core elements defining future renewable energy access schemes. Subsequently, these uncertainty parameters are discretized and combined in conjunction with the distribution network topology and feeder parameters to construct a set of planning scenarios that comprehensively covers various renewable energy access possibilities. Each scenario in this set represents a specific renewable energy access configuration, providing a discretized analytical object for assessing the operational risks of the distribution network under different access schemes.

[0100] To determine the operational layer uncertainty, specific uncertainty parameters are extracted from historical operational data, namely historical load data and historical irradiance data. This historical data accurately reflects the random fluctuations in load and renewable energy output during actual distribution network operation. Subsequently, based on these operational layer uncertainty parameters, a probabilistic model that accurately characterizes the random fluctuations in load power and renewable energy output is constructed through statistical analysis and probability distribution fitting. This probabilistic model provides a statistical description of the random input variables for subsequent probabilistic power flow calculations.

[0101] Through this hierarchical and step-by-step parameter extraction and model building mechanism, this application can decompose the complex uncertainty problem of distribution network into manageable planning scenarios and quantifiable random variables, so that the subsequent probabilistic power flow calculation can more accurately assess the operation risk of distribution network under different new energy access schemes, and thus more effectively identify weak links.

[0102] Suppose a power distribution network plans to connect distributed photovoltaic power generation within the next five years. The specific construction of its planning scenario set and probability model is as follows:

[0103] First, when extracting the uncertainty parameters at the planning level, based on national or local new energy development plans, it can be determined that the scale of new energy access may be between 5MW and 20MW, the number of accessed may be between 10 and 40 distributed photovoltaic power stations, the access locations may be distributed across multiple different distribution network nodes, and the access phase may be single-phase or three-phase. These parameters constitute the uncertainty parameters at the planning level.

[0104] Secondly, when extracting operational uncertainty parameters, hourly load data of the distribution network over the past three years and hourly solar irradiance data from the local meteorological station can be collected. These historical load and irradiance data constitute the operational uncertainty parameters.

[0105] Next, based on the aforementioned planning-level uncertainty parameters, the distribution network topology, and feeder impedance parameters, a series of planning scenarios can be constructed. For example, one planning scenario could be "connecting 10MW of photovoltaic power at node A, consisting of 20 three-phase photovoltaic power plants of 500kW each," while another scenario could be "connecting 5MW and 8MW of photovoltaic power at nodes B and C respectively, consisting of different numbers of single-phase and three-phase power plants." Simultaneously, based on historical load data, kernel density estimation or parameter fitting (such as Gaussian or Weibull distributions) can be used to obtain the probability density function of the total load of the distribution network or the load of each region. Similarly, based on historical irradiance data, the probability density function of photovoltaic output (or irradiance) can be fitted, for example, using a Beta distribution to describe its randomness between 0 and 1. These probability density functions collectively constitute the probabilistic model of operational-level uncertainty.

[0106] Through the aforementioned technical solutions, this method can clearly classify and quantify the complex uncertainties at the planning and operational levels in the distribution network. By systematically extracting planning-level uncertainty parameters such as the scale, quantity, location, and phase of new energy access, and combining them with network topology and feeder parameters to construct a diverse set of planning scenarios, it can comprehensively simulate various possibilities for future new energy access. Simultaneously, by utilizing historical operational data to extract operational-level uncertainty parameters such as historical load data and historical irradiance data, and constructing corresponding probabilistic models, it can accurately capture the random fluctuation characteristics in distribution network operation. This refined parameter extraction and model construction process provides more accurate and representative input for subsequent probabilistic power flow calculations, thereby significantly improving the accuracy and reliability of early warning of weak links in the distribution network, enabling the early warning results to more realistically reflect the potential risks of the distribution network under different new energy access and operational conditions.

[0107] Step 204 can be implemented in the following way:

[0108] Determine the range of values ​​for the installed capacity of individual new energy units;

[0109] The access locations of the new energy sources are classified according to whether they are single-phase or three-phase new energy sources;

[0110] Determine the step size for changes in the penetration rate of new energy access;

[0111] Based on the scale of new energy access, the number of accesses, the access location, and the access phase, and using the value range and the change step size as constraints, multiple discrete new energy access planning scenarios are randomly combined according to the access type of the new energy to obtain a planning scenario set.

[0112] It should be noted that each planning site in the planning scenario set includes the following information: new energy access node number, corresponding new energy installation capacity, new energy access phase, new energy access type, and the above information constitutes a unique new energy access scheme identifier.

[0113] The purpose of defining the range of installed capacity for individual renewable energy units is to set reasonable upper and lower limits for the capacity of a single renewable energy grid connection unit. This range can be determined based on mainstream product specifications, national or local grid connection standards, and economic evaluation results. For example, for distributed photovoltaic systems, the installed capacity of a single unit can be set in the range of 5kW to 50kW; for small wind turbines, it can be set in the range of 100kW to 500kW. By setting this range, it can be ensured that the generated planning scenarios are practically feasible in terms of capacity.

[0114] The classification of renewable energy sources by their connection location (single-phase or three-phase) is intended to differentiate the impact of different connection methods on power flow and voltage distribution in the distribution network. Single-phase renewable energy typically refers to renewable energy connected to a single-phase line or a single-phase load side in a three-phase four-wire system, while three-phase renewable energy refers to renewable energy connected to a three-phase line or a three-phase load side. This classification can be based on the rated power of the renewable energy equipment, the voltage level of the connection point, or the topology of the distribution network. For example, smaller residential photovoltaic systems typically use single-phase connection, while larger-scale industrial and commercial photovoltaic systems or small wind farms use three-phase connection.

[0115] Determining the step size for the renewable energy integration penetration rate is crucial for systematically examining the operational characteristics of the distribution network under different renewable energy integration levels. The step size can be a fixed percentage increment, such as 5% or 10%, or it can be dynamically adjusted based on the distribution network characteristics and research needs. By setting the step size, the proportion of renewable energy integration can be gradually increased, thereby comprehensively assessing the carrying capacity and weaknesses of the distribution network under different integration rates.

[0116] Based on the scale, number, location, and phase of the renewable energy access, and using the value range and step size as constraints, multiple discrete renewable energy access planning scenarios are randomly combined according to the access type of the renewable energy source to obtain a set of planning scenarios. The aim is to generate a set of planning scenarios that is both diverse and conforms to practical constraints. Random combination can be achieved using methods such as Monte Carlo simulation and Latin hypercube sampling to ensure the randomness and representativeness of the scenarios. Discrete planning scenarios mean that each scenario is a specific and independently analyzable renewable energy access scheme.

[0117] This application addresses the potential blindness and incompleteness of traditional methods in scenario generation by implementing refined and systematic management of the construction of the planning scenario set. First, by defining the value range of the installed capacity of individual renewable energy units, reasonable boundaries are set for the capacity of individual renewable energy devices, avoiding unrealistic capacity settings. Second, by classifying renewable energy access locations according to single-phase and three-phase renewable energy, the application ensures that subsequent scenario combinations accurately reflect the impact of different access methods on the distribution network, which is crucial for accurate power flow calculations and weak link identification. Third, by determining the step size of renewable energy access penetration rate changes, the generated planning scenarios systematically cover various renewable energy access levels from low to high, thereby comprehensively assessing the operational risks of the distribution network under different penetration rates. Finally, based on the aforementioned defined parameters and constraints, multiple discrete renewable energy access planning scenarios are generated using a random combination method, ensuring the breadth and depth of the planning scenario set. This systematic scenario construction method enables the generated planning scenario set to more realistically and comprehensively reflect the various possibilities of future renewable energy access to the distribution network, providing a solid foundation for subsequent probabilistic power flow calculations and weak link early warning, significantly improving the accuracy and reliability of early warning.

[0118] The following is a concrete example to illustrate this. When constructing a set of planning scenarios, the range of individual renewable energy installation capacity can be determined first. For example, for distributed photovoltaic (PV), the individual installation capacity can be set to 5kW to 50kW. Simultaneously, the access type of renewable energy is classified according to its access location, categorized as single-phase or three-phase. For instance, PV systems with an access capacity less than 10kW are classified as single-phase access, while those with an access capacity greater than 10kW are classified as three-phase access. Furthermore, the step size for the renewable energy access penetration rate can be determined, for example, set to a 5% increment, gradually increasing from 5% to 50%. Based on this, and considering the uncertainty parameters of the distribution network's renewable energy access scale, number of accesses, access location, and access phase, using the capacity range and the step size for penetration rate change as constraints, and combining the single-phase or three-phase access type, multiple discrete renewable energy access planning scenarios are randomly generated using Monte Carlo simulation. For example, in a certain planning scenario, a 20kW three-phase PV unit might be accessed at one node, and two 5kW single-phase PV units might be accessed at another node, reaching a certain penetration rate level for the total access capacity. By repeating this process, a set of planning scenarios containing hundreds or even thousands of different renewable energy access schemes can be obtained, each scenario representing a possible future distribution network state.

[0119] Step 205 can be implemented in the following way:

[0120] The maximum likelihood estimation method is used to fit the probability distributions of the historical load data and historical irradiance data to obtain a probability model.

[0121] Maximum likelihood estimation is a statistical method used to estimate model parameters. Its core idea is: given a probability distribution model and a set of observed data, the model parameters are adjusted to maximize the probability of these observed data occurring.

[0122] Specifically, after obtaining the topology parameters, feeder parameters, historical operating data, and new energy planning parameters to be connected to the distribution network, historical load data and historical irradiance data are first extracted from the historical operating data as operational uncertainty parameters, based on the type of operational uncertainty. Then, for these extracted historical load data, the maximum likelihood estimation method is used to select an appropriate probability distribution type (e.g., a normal or log-normal distribution can be considered for load data). By maximizing the likelihood function of the observed data, the parameters of this distribution are estimated, thereby obtaining the probability distribution function of the load power.

[0123] Similarly, for historical irradiance data, the maximum likelihood estimation method is also used to fit the probability distribution to obtain the probability distribution function of renewable energy output. In this way, discrete historical observation data is transformed into a continuous probability distribution with a clear mathematical form, thereby constructing a probabilistic model that can accurately characterize the random fluctuation characteristics of load power and renewable energy output in the uncertainty of the operation layer.

[0124] The method employing maximum likelihood estimation to fit probability distributions to the historical load data and historical irradiance data respectively, resulting in a probability model, includes:

[0125] Distribution network users are clustered and grouped according to their annual electricity consumption or contracted power.

[0126] At a preset time granularity, the probability distribution of the historical load data corresponding to each user group is fitted to obtain the probability density function of the load power.

[0127] At the same time granularity, the historical irradiance data is fitted with a probability distribution to obtain the probability density function of new energy output.

[0128] Understandably, when clustering distribution network users based on their annual electricity consumption or contracted power, clustering algorithms such as K-means and DBSCAN can be used, with the users' annual electricity consumption or contracted power as features. Alternatively, users can be grouped manually or based on rules, according to their industry type (e.g., industrial, commercial, residential), geographical location, or electricity usage characteristics. At a preset time granularity, the historical load data corresponding to each user group is fitted with a probability distribution to obtain the probability density function of the load power.

[0129] The preset time granularity can be set to hours, half hours, 15 minutes, etc. For the data at each time granularity, probability distribution fitting is performed for each user group, using methods such as Gaussian mixture models and kernel density estimation. At the same time, different time granularities can also be selected for segmented fitting based on periodic characteristics such as seasons and weekdays / weekends to reflect the periodic changes in load.

[0130] At the same time granularity, probability distribution fitting is performed on the historical irradiance data to obtain the probability density function of new energy output. The same time granularity as the load power fitting can be used to perform statistical analysis on the historical irradiance data, and a suitable probability distribution (such as Beta distribution, Weibull distribution, etc.) can be selected for fitting. Alternatively, nonparametric methods, such as kernel density estimation, can be used to directly estimate the probability density function of irradiance from historical data.

[0131] For example, firstly, users in the distribution network are clustered and grouped according to their annual electricity consumption or contracted power, dividing heterogeneous user groups into several homogeneous subgroups. Then, at a preset time granularity, historical load data for each user group is fitted with a probability distribution to obtain a more targeted and accurate load power probability density function. Simultaneously, at the same time granularity, historical irradiance data is fitted with a probability distribution to obtain the probability density function of renewable energy output. This refined modeling approach, which involves clustering and time-segmentation, fully considers the differences in electricity consumption characteristics among different user groups and the temporal fluctuations in load and renewable energy output, avoiding the errors caused by simply fitting the overall data. Through this method, the constructed probabilistic model can more realistically and accurately reflect the random fluctuation characteristics of load power and renewable energy output in the distribution network, providing high-quality random input variables for subsequent probabilistic power flow calculations, thereby improving the accuracy and reliability of the entire weak link early warning method.

[0132] 206. Based on the planning scenario set and probability model, construct a probabilistic power flow model for the distribution network;

[0133] In this embodiment, for each new energy access planning scenario in the planning scenario set, a corresponding deterministic topology model of the distribution network is constructed based on the topology parameters and the feeder parameters; the load power and new energy output, which represent the uncertainty of the operation layer in the probabilistic model, are introduced into the deterministic topology model and set as random input variables; the voltage amplitude of each node of the distribution network and the current magnitude of each branch are set as random output variables; based on the distribution network power flow constraint equation, a probabilistic power flow model of the distribution network that simultaneously includes the random input variables and the random output variables is constructed.

[0134] Understandably, for each new energy access planning scenario in the planning scenario set, the steps of constructing a corresponding deterministic distribution network topology model based on topology parameters and feeder parameters can be achieved by using professional power system simulation software (such as DIgSILENT PowerFactory or PSS / E) to build a network model for each planning scenario, or by generating the network's admittance matrix or impedance matrix based on topology parameters and feeder parameters through programming (such as using Python combined with Pandas and NumPy libraries).

[0135] The step of introducing load power and renewable energy output, which characterize operational uncertainty in probabilistic models, into deterministic topology models and setting them as random input variables can be achieved by using probability distribution functions (such as normal distribution, Beta distribution, Weibull distribution, etc.) to describe the stochastic characteristics of load power and renewable energy output. These distribution functions can be obtained based on historical operating data through statistical methods (such as maximum likelihood estimation). In the power flow model, these random variables will replace the traditional deterministic load and power supply values.

[0136] In the step of constructing a probabilistic power flow model of a distribution network that simultaneously includes the random input variables and the random output variables based on the distribution network power flow constraint equations, the distribution network power flow constraint equations are the fundamental mathematical expressions describing the physical operation of the power grid, including Kirchhoff's laws, power balance equations, etc. Specifically, when constructing the probabilistic power flow model, the random input variables and random output variables can be substituted into a nonlinear power flow equation system to form a stochastic nonlinear equation system. Solving this equation system can be done using various methods, such as Monte Carlo simulation, point estimation, or polynomial chaotic expansion, to obtain the probabilistic representation of the random output variables.

[0137] In practical applications, assuming a distribution network plans to connect to photovoltaic power generation, there are multiple planning schemes for connection capacity and connection location.

[0138] First, for each planning scheme (i.e., each renewable energy access planning scenario), for example, Scheme 1 involves connecting 5MW of photovoltaic power at node A, and Scheme 2 involves connecting 8MW of photovoltaic power at node B, a corresponding deterministic topology model is constructed based on the distribution network's topology parameters and feeder parameters. This model includes the line resistance, reactance, transformer parameters, and the connection relationships of each node.

[0139] Next, the probability distribution models of load power and photovoltaic output (new energy output) extracted from historical data are introduced into the deterministic topological model constructed above. For example, the load power of node A may follow a normal distribution, while the photovoltaic output may follow a Beta distribution. These probability distributions are set as random input variables of the model.

[0140] Then, the voltage magnitude of all nodes and the current magnitude of all branches in the distribution network are set as random output variables of the probabilistic power flow model, which means that we expect to obtain the probability distribution information of these voltages and currents.

[0141] Finally, based on the power flow constraint equations of the distribution network (such as the nodal power balance equations), a probabilistic power flow model is constructed that includes these random input and output variables. For example, for a node i, its injected power Pi and Qi will be random, and its voltage Vi will also be random. These random variables are interconnected through the power flow equations.

[0142] 207. The probabilistic power flow model is solved using a non-intrusive generalized polynomial chaos method to obtain the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario.

[0143] In this step, based on the probability distribution type of the random input variables in the probability model, an orthogonal polynomial basis function matching the probability distribution type is selected; the order of the chaotic expansion of the generalized polynomial basis function is set, and a polynomial function expression between the random input variables and the distribution network node voltage and branch current is constructed; based on the polynomial function expression, multiple test points are generated in the probability space of the random input variables using a low-discrepancy sequence; using the random input variable values ​​corresponding to each test point as input, deterministic power flow calculation is performed on the probabilistic power flow model to obtain the calculation results of the distribution network node voltage and branch current under each test point; based on the calculation results of the node voltage and branch current corresponding to each test point, the chaotic expansion coefficients of the generalized polynomial basis function are solved to obtain the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario.

[0144] Understandably, the random input variables in the step of selecting orthogonal polynomial basis functions that match the probability distribution type of the random input variables in the probability model are actually load power and new energy output, which typically have specific probability distribution types such as normal distribution, Beta distribution, etc. Orthogonal polynomial basis functions are mathematical tools used to approximate functions of random variables, and their selection is closely related to the probability distribution type of the random variable to ensure the accuracy and efficiency of the approximation. Selecting a matching basis function can more effectively capture the statistical characteristics of the random variable. This can be done by consulting a table of correspondences between standard orthogonal polynomial families and common probability distributions. For random variables following a Gaussian distribution, Hermite polynomials can be used; for random variables following a uniform distribution, Legendre polynomials can be used. Alternatively, the probability distribution of the random input variables can be fitted, and then the most suitable orthogonal polynomial basis function can be selected based on the fitting result. For example, if the fitting result is close to a Gamma distribution, Laguerre polynomials can be considered.

[0145] In the step of setting the order of the chaotic expansion of the generalized polynomial basis functions and constructing the polynomial function expression of the random input variables and the node voltages and branch currents of the distribution network, the generalized polynomial chaos expansion (gPC) is a method to represent random variables as a linear combination of orthogonal polynomial basis functions. The order of the expansion determines the approximate accuracy and computational complexity. By setting an appropriate order, the complex nonlinear relationship between random input variables (load power, renewable energy output) and random output variables (node ​​voltage, branch current) can be transformed into an easily tractable polynomial function form, thereby avoiding the direct processing of complex stochastic differential equations. The order can be set according to the required computational accuracy and computational resources. Generally, the higher the order, the higher the accuracy, but the greater the computational burden. For example, it can be set to the second or third order to achieve a balance between accuracy and efficiency. The order can also be selected through trial and error or based on empirical rules. For example, a lower order can be used for random variables with a small range of variation, and a higher order can be used for random variables with a large range of variation or a high degree of nonlinearity.

[0146] Based on the polynomial function expression, multiple test points are generated in the probability space of the random input variable using low-discrepancy sequences. The polynomial function expression establishes the relationship between the input and output. To solve for the coefficients of this polynomial function, calculations need to be performed at a series of specific points. Low-discrepancy sequences (LDS), such as Halton sequences and Sobol sequences, are quasi-random sequences whose distribution in multidimensional space is more uniform than that of pseudo-random sequences, and can more effectively cover the probability space of the random input variable. Using low-discrepancy sequences to generate test points can improve sampling efficiency and computational accuracy while reducing the number of samples required. For example, Sobol sequences can be used to generate test points. Sobol sequences have good uniformity and converge quickly in multidimensional space, making them suitable for sampling high-dimensional random variables. Halton sequences can also be used to generate test points. Halton sequences are another common low-discrepancy sequence, and their generation method is relatively simple, also providing a more uniform distribution of sampling points than the Monte Carlo method.

[0147] Using the random input variable values ​​corresponding to each test point as input, deterministic power flow calculations are performed on the probabilistic power flow model to obtain the calculated results of the distribution network node voltages and branch currents at each test point. This step is crucial in transforming the probabilistic problem into a series of deterministic problems for solution. Each test point represents a specific combination of random input variables (load power, renewable energy output). For each such combination, the probabilistic power flow model degenerates into a standard deterministic power flow model. By performing deterministic power flow calculations, the specific values ​​of the distribution network node voltages and branch currents under that specific input condition can be obtained. Deterministic power flow calculations can employ classic power flow calculation algorithms such as the Newton-Raphson method, the fast decoupling method, or the Gauss-Seidel method. Alternatively, matrix factorization-based power flow calculation methods can be used, for example, by utilizing sparse matrix techniques to improve computational efficiency.

[0148] Based on the calculated node voltages and branch currents at each test point, the chaotic expansion coefficients of the generalized polynomial basis functions are solved to obtain the probabilistic representations of the distribution network node voltages and branch currents under each planning scenario. The chaotic expansion coefficients are the core of the generalized polynomial chaos method. Once deterministic power flow calculation results (i.e., sample values ​​of random output variables) are obtained at multiple test points, these sample values ​​and the corresponding orthogonal polynomial basis functions can be used to solve for the chaotic expansion coefficients of the generalized polynomial basis functions using techniques such as least squares, projection, or regression. These coefficients fully characterize the probability distribution information of the random output variables (node ​​voltages, branch currents), including their mean, variance, and higher-order statistical moments. For example, the least squares regression method can be used to solve for the chaotic expansion coefficients, which determines the coefficients by minimizing the sum of squared errors between the predicted and actual calculated values. Alternatively, the projection method can be used, utilizing the orthogonality of orthogonal polynomials, to directly calculate the chaotic expansion coefficients through integration.

[0149] For example, when solving the probabilistic power flow model of a distribution network, one can first analyze the historical data of load power and renewable energy output in the probabilistic model to determine their probability distribution type. For instance, if the load power approximately follows a truncated normal distribution and the renewable energy output approximately follows a Beta distribution, then corresponding orthogonal polynomial basis functions, such as Hermite polynomials and Jacobi polynomials, can be selected respectively. Subsequently, the order of the generalized polynomial chaotic expansion can be set to second order to achieve a balance between computational accuracy and efficiency, thereby constructing a polynomial function expression of the random input variables and node voltages and branch currents. To generate test points, a Sobol sequence can be used to generate, for example, 100 test points in the probability space of the multidimensional random input variables. These test points will be evenly distributed within the possible range of load power and renewable energy output values. For each test point, its corresponding load power and renewable energy output values ​​are substituted into the deterministic power flow model of the distribution network, and the Newton-Raphson method is used to perform power flow calculations to obtain the values ​​of all node voltages and branch currents at that test point. Finally, the calculation results of these 100 sets of node voltages and branch currents are combined with the previously selected orthogonal polynomial basis functions, and the chaotic expansion coefficients of the generalized polynomial basis functions are solved by the least squares regression method.

[0150] In another embodiment, the step of generating multiple test points in the probability space of random input variables using a low-discrepancy sequence based on the polynomial function expression includes: using the polynomial function expression as input, mapping the probability space of each random input variable based on the probability distribution type of the random input variable to construct a unified standard random variable space; generating multiple sampling points with uniform distribution characteristics in the standard random variable space using a low-discrepancy sequence; and mapping the sampling points back to the probability space of the random input variables to obtain multiple test points for probability power flow calculation.

[0151] Specifically, based on the established polynomial function expression and the specific probability distribution type of the random input variables, probability space mapping is performed on each random input variable. This step transforms random variables with different distribution characteristics into a standardized space, such as a standard normal distribution or a standard uniform distribution space, thus laying the foundation for subsequent unified sampling. Next, in the constructed unified standard random variable space, a series of sampling points with good uniform distribution characteristics are generated using low-discrepancy sequences. Compared with traditional random sampling, this sampling method can more effectively cover the entire random variable space, ensuring the representativeness and comprehensiveness of the sampling points, thereby improving computational accuracy. Finally, these sampling points generated in the standard space are transformed back to the probability space of the original random input variables through an inverse mapping operation, obtaining a series of specific combinations of input values ​​that can be used for deterministic power flow calculations, i.e., the required test points. Through this systematic sampling strategy, this application can obtain representative samples of random input variables more efficiently and accurately, providing high-quality input data for solving non-intrusive generalized polynomial chaos methods, thereby improving the reliability of the probability characterization results of distribution network node voltages and branch currents.

[0152] For example, in constructing a probabilistic power flow model for gPC, the generalized multinomial chaotic gPC expansion will use random input vectors Mapping to key outputs. This is achieved by fitting the key outputs to an equivalent polynomial on an orthogonal polynomial derived from the random input. Random key outputs It is represented as a weighted sum of random input polynomial basis functions, where each coefficient is its corresponding weight.

[0153] The series is truncated to a length of This reduces the computational burden. The reduced-dimensional basis vectors... sum coefficient vector The dimension depends on the order of the polynomial basis. and the number of random input variables , Represents a vector of multivariate basis polynomials, which are derived from random input variables. It is composed of the tensor product of each univariate polynomial.

[0154] The random input parameters in the model. These orthogonal polynomials are well-defined in most continuous univariate distributions. The basis polynomials in the expression are mutually orthogonal with respect to the probability density function PDF, i.e., 𝑓(𝜉), and satisfy the following properties: .

[0155] It employs non-intrusive gPC expansion. The core idea of ​​the non-intrusive method is: for random input vectors... Calculate attention from a specific selected sample Generate test points Several different methods exist. Sampling techniques based on ordinary Monte Carlo, Sobol sequences, and Halton sequences were evaluated for polynomials of different orders. Results show that the test points based on Sobol and Halton sequences... By combining second-order polynomials, its performance is superior to the gPC method based on ordinary Monte Carlo.

[0156] Test points based on Sobol sequences were used. And second-order polynomials. In this method, the number of deterministic power flow calculations required is equal to the coefficient vector. Dimensions. The calculation is done by solving The attention vector, obtained by completing a linear equation, is based on the following formula. and the orthogonal polynomial basis at each test point The value at that location.

[0157] ,

[0158] ,

[0159] ,

[0160] In the formula, Expressed as a power flow equation, This represents the voltage value at each node in the feeder. This indicates the current value of each branch in the feeder. Indicates the first Each test point is a random input variable. A specific sample, It is the coefficient vector of the gPC expansion. This represents the basis function vector of a multivariable orthogonal polynomial.

[0161] Deterministic power flow calculation: For each selected test point, perform a deterministic power flow calculation to obtain the system state.

[0162] Extracting attention volume: Based on the results obtained from the previous trend calculation. Through a defined operator Calculate the system performance metrics that we are truly concerned with. .

[0163] Constructing a system of fitting equations: This is the core step of the gPC non-intrusive method. The goal is to find a set of coefficients. This allows us to use these coefficients and the orthogonal polynomial basis. The resulting polynomial best fits the attention values ​​calculated from all test points. .

[0164] 208. Based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, and combined with the preset distribution network operation safety constraints, calculate the probability of exceeding the limit under different time sections for each planning scenario, and generate the corresponding limit exceeding risk index.

[0165] This step first defines undervoltage, overvoltage, and branch overcurrent exceeding events. Then, based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, random sampling calculations are performed on each exceeding event to obtain the probability of exceeding the limit at each time segment. Finally, statistical analysis is performed on the probability of exceeding the limit at each time segment to generate corresponding exceeding risk indicators. The exceeding risk indicators include at least one of the following: the maximum probability of exceeding the limit at each time segment, the median probability of exceeding the limit at each time segment, and the preset quantile of the probability of exceeding the limit at each time segment.

[0166] Understandably, defining undervoltage, overvoltage, and branch overcurrent limit events in the process aims to clearly define the types of safety issues that may arise in the operation of the distribution network, providing a basis for subsequent risk quantification. Specifically, upper and lower limits of voltage amplitude (e.g., ±5% or ±7% of the rated voltage) can be set as the criteria for judging undervoltage and overvoltage, based on national or industry standards; simultaneously, an upper limit of the rated current carrying capacity of a branch (e.g., 1.2 times the rated current carrying capacity) can be set as the criteria for judging branch overcurrent. Alternatively, more refined voltage and current limit thresholds can be customized based on the actual operating experience and equipment tolerance of a specific distribution network.

[0167] Based on the probabilistic representation results of distribution network node voltages and branch currents under various planning scenarios, random sampling calculations are performed on each limit-exceeding event to obtain the probability of limit exceeding at each time segment. This process transforms the probabilistic representation results into specific limit-exceeding probabilities, thereby quantifying the risk. One approach is to use Monte Carlo sampling, drawing a large number of samples from the probability distributions of node voltages and branch currents, and statistically analyzing the proportion of samples that meet the conditions for limit-exceeding events as the probability of limit exceeding. Another approach is to use more efficient sampling methods such as Latin hypercube sampling, which reduces computational load and quickly obtains the probability of limit exceeding while ensuring sample representativeness.

[0168] In the step of statistically analyzing the probability of exceeding limits at various time points to generate corresponding risk indicators, the aim is to integrate the probability of exceeding limits at different time points into a comprehensive risk assessment indicator. Specifically, the probability of exceeding limits at various time points can be weighted and averaged, where the weights can be determined based on the importance or duration of the time period, thus obtaining a comprehensive risk indicator. Alternatively, the risk indicator can be defined as the number of time points within a specific time period where the probability of exceeding limits exceeds a certain threshold, or the maximum probability of exceeding limits.

[0169] In practical applications, step 208 is actually an estimation of the risk indicators of exceeding limits in the planning scenario, which can be achieved through the following two methods:

[0170] (1) Use a kernel density estimator;

[0171] (2) For random input vectors Sampling was performed, and the sample points were substituted into the representative... The output is calculated in the polynomial proxy model.

[0172] The choice of specific method depends on the nature of the desired final output. As a trade-off between computational accuracy and time, a sampling method was adopted, with the final sample size set at 1000. These samples were used to calculate the violation probabilities of three power grid limits, namely:

[0173] (a) Undervoltage probability The probability that the minimum voltage of the feeder is lower than 0.95 pu;

[0174] (b) Overvoltage probability The probability that the feeder's maximum voltage exceeds 1.05 pu;

[0175] (c) Overcurrent probability The probability that the maximum current is greater than 1 per unit relative to the branch rating.

[0176] These probabilities of violating power grid limits are collectively referred to as congestion probabilities and are calculated for each planning scenario obtained from Algorithm 1. These probabilities are recorded for each time period of the day. The final congestion probability for a day can be represented by the following statistics:

[0177] (a) Median: This indicates that the probability of congestion is lower than this value 50% of the time during the day.

[0178] (b) 75th percentile: This indicates that the probability of congestion is below this value for 75% of the time of day.

[0179] (c) 95th percentile: This indicates that the probability of congestion is below this value for 95% of the time of day.

[0180] (d) Maximum probability of the day: The highest probability of congestion observed on the day.

[0181] Once these congestion probabilities are calculated, scenarios with probabilities exceeding the set random grid limit are filtered out. The final step in decoupling PV carrying capacity calculation is to scan all scenarios falling within the specified random grid limit and identify the scenario with the highest total connected PV capacity. This total connected PV capacity is considered the PV carrying capacity of the feeder under study. This is the complete workflow of this gPC-based tool for decoupling PV carrying capacity.

[0182] Numerical simulations were conducted based on the actual feeder proposed in [the paper / model / etc.]. Historical irradiance measurements from the site and user load data were used to fit the probability distribution function for each user group. It was assumed that the power generation of different photovoltaic panels was correlated. Users were divided into 25 groups, and users of the same type were considered correlated.

[0183] The irradiance curve and load for each user group every 15 minutes are characterized using a Beta distribution by fitting historical curves from similar dates. Since low-voltage user data is not readily available, cluster analysis of historical loads is necessary. The reason for choosing the Beta distribution to characterize user load and irradiance is that the photovoltaic power generation of all users is fully correlated. A second-order non-intrusive generalized multinomial chaotic method based on Sobol sequences is used for photovoltaic carrying capacity calculation.

[0184] Three feeders were chosen to represent typical types of low-voltage feeders:

[0185] Feeder 1 is a typical residential feeder, characterized by a high load power factor, a large number of users, and a high total line impedance but a low average path impedance.

[0186] Feeder 2 is a hybrid feeder for residential users and small and medium-sized enterprises in a single apartment building.

[0187] Feeder 3 is a typical feeder for commercial / industrial / SME users, characterized by high energy consumption, a small number of users, and low total impedance.

[0188] In the decoupled PV carrying capacity calculation, only rooftop PV scenarios are considered, and the maximum number of PV installations equals the number of users in the feeder. For each 5% increase in PV penetration, there are ten possible capacities and types of PV installations. The PV locations are uniformly distributed along the feeder length, and it is assumed that the phase of PV access is the same as the phase of the user's location. The carrying capacity boundary due to location uncertainty can be obtained by concentrating all PV installations at the end of the feeder or near the substation.

[0189] Using a decoupled generalized multinomial chaos (gPC) tool, the congestion probability at 15-minute intervals was calculated for each planning scenario under average summer / spring conditions. Recording the probability at each timestamp provides higher-resolution time-series impact analysis and helps to gain a deeper understanding of the impact of different performance indicators on carrying capacity calculations.

[0190] In calculating the photovoltaic carrying capacity, the probability at each time point was not analyzed individually. Instead, the median, 75th percentile, 95th percentile, and maximum probability were considered comprehensively. The maximum congestion probability was used as the reference benchmark for calculating the decoupled photovoltaic carrying capacity of the entire network.

[0191] 209. Based on the over-limit risk index, conduct compliance screening for each planning scenario, determine the critical renewable energy consumption scenario with the largest renewable energy access capacity under the condition of meeting the preset risk threshold, and identify the weak links in the distribution network that cause the over-limit risk to reach the threshold in the critical renewable energy consumption scenario, and issue an early warning.

[0192] Specifically, based on the aforementioned risk indicators, compliance screening is performed on each planning scenario to determine the critical renewable energy consumption scenario that maximizes renewable energy access capacity while meeting preset risk thresholds, including:

[0193] The risk indicators for exceeding limits corresponding to each planning scenario are compared with preset probability thresholds to select planning scenarios that meet operational safety constraints; the planning scenarios that meet operational safety constraints are sorted according to the total capacity of new energy access; and the planning scenario with the largest total capacity of new energy access is selected as the critical new energy consumption scenario.

[0194] For example, the first step is to compare the risk indicators corresponding to each planning scenario with preset probability thresholds to determine whether the scenario meets the preset operational safety constraints. This comparison process effectively filters out all planning scenarios that are safe at the operational level, ensuring that all scenarios analyzed subsequently are within acceptable risk ranges. Then, these planning scenarios that meet operational safety constraints are ranked according to their respective total renewable energy access capacity. This ranking aims to quantify the renewable energy penetration level of each compliant scenario. Finally, the planning scenario with the largest total renewable energy access capacity is selected from the ranking results and identified as the critical renewable energy absorption scenario. This critical scenario not only meets all operational safety constraints but also represents the maximum renewable energy capacity that the distribution network can accept under current conditions. Through this systematic screening and ranking mechanism, this solution can accurately locate the operating status of the distribution network under maximum renewable energy absorption capacity, thus providing the most critical and representative analytical basis for subsequently identifying weak links that cause the risk of exceeding the threshold.

[0195] For example, the system stipulates that the probability of voltage exceeding the limit at any node must not exceed 5%, and the probability of current exceeding the limit in any branch must not exceed 3%. The system will iterate through all planning scenarios. For each scenario, it will check whether the over-limit risk indicators of voltage at all nodes and current in each branch are lower than or equal to the corresponding thresholds. For example, if the voltage over-limit risk of scenario A is 4% and the current over-limit risk is 2%, then scenario A is determined to meet the operational safety constraints. If the voltage over-limit risk of scenario B is 6% and the current over-limit risk is 2%, then scenario B is determined not to meet the operational safety constraints and is excluded. After filtering out all planning scenarios that meet the operational safety constraints, the system will obtain the total renewable energy access capacity for each compliant scenario. For example, scenario A accesses 10MW of renewable energy, scenario C accesses 8MW of renewable energy, and scenario D accesses 12MW of renewable energy. Subsequently, the system will sort these compliant scenarios in descending order of their total renewable energy access capacity, resulting in D (12MW), A (10MW), C (8MW), etc. Finally, scenario D with the largest total renewable energy access capacity in the sorted results will be selected as the critical renewable energy consumption scenario.

[0196] In this embodiment, the step of identifying and issuing early warnings about weak links in the distribution network that cause the risk of exceeding limits to reach a threshold in the critical renewable energy consumption scenario includes:

[0197] In the critical renewable energy consumption scenario, the nodes or branches that cause the risk index of exceeding the limit to reach the probability threshold are identified; the nodes or branches are marked as weak nodes or weak branches of the distribution network, and early warning information is generated for early warning.

[0198] In the critical renewable energy consumption scenario, the step of identifying the nodes or branches that cause the over-limit risk index to reach the probability threshold essentially involves an in-depth analysis of the probabilistic representation results of the voltage of each node and the current of each branch under the critical renewable energy consumption scenario. For example, by calculating the individual over-limit probability of each node or branch and comparing it with a preset probability threshold, nodes or branches whose over-limit probabilities reach or exceed the threshold can be identified. Alternatively, sensitivity analysis can be used to assess the contribution of each node or branch in the distribution network to the overall over-limit risk index, identifying the nodes or branches with the greatest impact on the risk index and determining them as the key links causing the over-limit risk to reach the probability threshold.

[0199] The step of identifying the nodes or branches as weak nodes or branches in the distribution network and generating early warning information involves visually marking the identified nodes or branches on the distribution network's geographic information system (GIS) or topology map. This can be done by changing colors, flashing, or adding special symbols to make them stand out among other devices and visually display their weak state. Simultaneously, based on preset early warning rules, an early warning report or message containing detailed information such as the location of the weak link, the type of over-limit (e.g., undervoltage, overvoltage, overcurrent), and the risk level can be automatically generated and sent to the distribution network's operation and maintenance personnel or dispatch center via various methods such as SMS, email, system pop-ups, or audible and visual alarms.

[0200] Specifically, in critical renewable energy consumption scenarios, although the overall renewable energy access capacity is at its maximum and the risk is within an acceptable range, this does not mean that all local areas are in an absolutely safe state. By identifying the nodes or branches that cause the over-limit risk indicators to reach the probability threshold, the system can use the previously calculated probability characterization results of the distribution network node voltage and branch current to conduct a detailed risk assessment of each node and branch, identifying those key points where local risks have reached or exceeded the preset probability threshold. Subsequently, these identified key points are formally named as weak nodes or weak branches of the distribution network and transformed into intuitive and understandable early warning information. For example, for a node in the distribution network, the probability distribution of its voltage shows that at a certain time segment in the future, the probability of its voltage being lower than 0.95 pu is 6%, while the preset probability threshold is 5%. At this time, this node is identified as the node that causes the over-limit risk to reach the probability threshold. Subsequently, the system will identify the node as a weak node in the distribution network and highlight it in red on the monitoring interface of the distribution network dispatch system. At the same time, it will automatically generate an early warning message, such as: "Warning: Node X has an undervoltage risk, and the probability of exceeding the limit has reached 6%. Please pay attention." This early warning message can also be sent to the on-duty engineer via SMS so that he / she can be informed in a timely manner and take appropriate countermeasures.

[0201] In this embodiment, generating early warning information includes: determining the location of the weak node or weak branch, the corresponding over-limit type, and the time interval of the over-limit risk, and generating early warning information of the weak link of the distribution network based on the location of the weak node or weak branch, the corresponding over-limit type, and the time interval.

[0202] Specifically, in critical renewable energy consumption scenarios, once the specific nodes or branches causing the risk of exceeding limits to reach the probability threshold are identified, the system further analyzes the specific location of these weak nodes or branches in the distribution network topology. Simultaneously, based on probabilistic power flow calculations, the type of electrical quantity causing the limit exceedance is determined, such as overvoltage, undervoltage, or branch current overload. Furthermore, by statistically analyzing the probability of limit exceedances at different time points, the time periods in which these risks are most likely to occur can be precisely defined. Finally, this key information—the location of the weak link, the type of limit exceedance, and the time interval of occurrence—is integrated and packaged into a structured or visualized early warning message. This detailed early warning message enables maintenance personnel to quickly locate the problem, understand its nature, and predict when it will occur, thus allowing them to develop and implement targeted response strategies in advance, effectively avoiding or mitigating potential operational risks to the distribution network under high renewable energy penetration rates.

[0203] Suppose that in a critical renewable energy consumption scenario, analysis reveals that the over-limit risk of a certain node (e.g., node numbered "N001") and a certain branch (e.g., branch "L005" connecting nodes "N002" and "N003") in the distribution network has reached a preset probability threshold. In this case, the solution proposed in this application will further determine the detailed information of these vulnerable links. For node N001, its location can be determined by geographical coordinates (e.g., longitude XXX degrees East, latitude YYY degrees North) or its unique identifier in the distribution network geographic information system (GIS). Through probability distribution analysis of the voltage at this node, its over-limit type is found to be "overvoltage". Furthermore, by statistically analyzing the voltage over-limit probability at different time sections, it can be determined that this overvoltage risk mainly occurs between 11:00 and 14:00 daily. Similarly, for branch L005, its location can be identified as the line segment connecting N002 and N003, with an over-limit type of "overcurrent," and this overcurrent risk mainly occurs between 10:30 and 15:00 daily. Based on this detailed information, the system can generate an early warning report containing information such as "Weak node: N001, Location: [Geographic coordinates / GIS identifier], Over-limit type: Overvoltage, Expected occurrence time: Daily 11:00-14:00" and "Weak branch: L005, Location: [Connecting nodes N002-N003], Over-limit type: Overcurrent, Expected occurrence time: Daily 10:30-15:00," etc. This early warning information can be sent to relevant maintenance personnel via email, SMS, or system pop-up, or displayed in a highlighted manner on the power distribution network monitoring screen.

[0204] In practical applications, a critical scenario refers to a planning-operation combination scenario where, under the existing control and infrastructure configuration of a low-voltage distribution network (LVDS), the total PV access capacity reaches its maximum, and the probability of grid operation indicators violating the pre-set random limits is exactly met. Its core characteristic is the balance between "capacity maximization" and "risk controllability," meaning that the total PV capacity in the scenario is the maximum value among all compliant scenarios, and the probability of overvoltage is ≤5%, the probability of undervoltage is ≤5%, and the probability of overcurrent is ≤5%.

[0205] Screening principles:

[0206] Uncertainty decoupling principle: Separate the uncertainty at the planning level from the uncertainty at the operational level to avoid the ambiguity of risk attribution caused by the superposition of the two types of uncertainty.

[0207] The principle of prioritizing probabilistic constraints: taking the statistical indicators of congestion probability at each time segment as the core constraint, and prioritizing the use of maximum value indicators to ensure power grid safety under extreme operating conditions.

[0208] Capacity maximization principle: Among all planning scenarios that satisfy probability constraints, select the scenario with the largest total PV access capacity as the critical scenario.

[0209] Congestion probability quantification and scenario selection:

[0210] Probabilistic flow calculation: The non-intrusive gPC tool, which uses second-order Sobol sequence sampling, is used to calculate the three types of congestion probabilities for each planning scenario across the entire time cross section.

[0211] Constraint compliance verification: Filter out all compliant scenarios whose congestion probability statistics do not exceed the preset random limit, and exclude overpressure-dominated non-compliant scenarios.

[0212] Capacity maximization sorting: Compliant scenarios are sorted in descending order of total PV access capacity, with the top scenario being the critical scenario under maximum PV access.

[0213] Constraint priority confirmation: If there are multiple types of constraints that are in effect at the same time, the scenario corresponding to the most stringent constraint shall be the final critical scenario.

[0214] In this embodiment of the invention, by acquiring distribution network parameters and constructing a set of planning scenarios and a probability model to distinguish uncertainty types, a probabilistic power flow model is constructed based on this and a probabilistic characterization result is obtained by using an efficient solution method. Then, the over-limit risk index is calculated to identify weak links. This can efficiently and accurately identify weak links in the distribution network, improve the renewable energy absorption capacity, and ensure the safe and stable operation of the distribution network.

[0215] Table 1 Simulation Data Results

[0216]

[0217] Simulation results show that, as shown in Table 1, the three-phase photovoltaic (PV) capacity of the three test feeders is approximately twice that of the single-phase PV on average. In Feeder 1, the single-phase PV capacity is limited by overvoltage; a penetration rate of only 5% triggers the 5% congestion probability threshold, while the three-phase PV capacity only reaches the congestion threshold due to overcurrent when the penetration rate reaches 45%. Combined with… Figure 4 The trend of undervoltage probability shows that single-phase photovoltaic (PV) grid connection causes undervoltage problems in non-connected phases, and its undervoltage congestion probability increases significantly with the increase of PV penetration. In contrast, three-phase PV grid connection does not pose a significant undervoltage risk, and the undervoltage congestion probability remains at a low level until the penetration rate exceeds 60%, at which point the undervoltage congestion probability of single-phase PV gradually declines. This fully demonstrates that three-phase PV has better congestion robustness in low-voltage distribution networks, and the three-phase imbalance problem of single-phase PV is the core reason for its limited capacity.

[0218] See Figure 3 As shown, the electronic device includes a processor 300 and a memory 301. The memory 301 stores machine-executable instructions that can be executed by the processor 300. The processor 300 executes the machine-executable instructions to implement the aforementioned early warning method for weak links in the power distribution network.

[0219] Furthermore, Figure 3 The electronic device shown also includes a bus 302 and a communication interface 303. The processor 300, the communication interface 303 and the memory 301 are connected via the bus 302.

[0220] The memory 301 may include high-speed random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device. Communication between this system network element and at least one other network element is achieved through at least one communication interface 303 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc. The bus 302 may be an ISA bus, PCI bus, or EISA bus, etc. The bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 3 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0221] The processor 300 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of the processor 300 or by instructions in software form. The processor 300 may be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this disclosure. The general-purpose processor may be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this disclosure can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules may reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. The storage medium is located in memory 301. The processor 300 reads the information in memory 301 and, in conjunction with its hardware, completes the method steps of the aforementioned embodiment.

[0222] The present invention also provides an electronic device, the computer device including a memory and a processor, the memory storing computer-readable instructions, which, when executed by the processor, cause the processor to perform the steps of the power distribution network weak link early warning method provided in the above embodiments.

[0223] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the distribution network weak link early warning method provided in the above embodiments.

[0224] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0225] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0226] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for early warning of weak links in a power distribution network, characterized in that, include: The topology parameters, feeder parameters, historical operating data, and new energy planning parameters to be connected to the distribution network are obtained. Based on the types of uncertainties in the distribution network, a set of planning scenarios and a probability model are constructed. The set of planning scenarios is used to characterize different new energy access schemes for uncertainties at the planning level, and the probability model is used to characterize the random fluctuation characteristics of load power and new energy output in uncertainties at the operation level. Based on the set of planning scenarios and the probability model, a probabilistic power flow model of the distribution network is constructed, and a non-intrusive generalized multinomial chaos method is used to solve the probabilistic power flow model to obtain the probabilistic characterization results of the distribution network node voltage and branch current under each planning scenario. Based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, combined with the preset distribution network operation safety constraints, the probability of exceeding the limit under different time sections of each planning scenario is calculated, and the corresponding limit exceeding risk index is generated. Based on the aforementioned over-limit risk indicators, compliance screening is performed on each planning scenario to determine the critical renewable energy consumption scenario with the largest renewable energy access capacity under the condition of meeting the preset risk threshold. In the critical renewable energy consumption scenario, weak links in the distribution network that cause the over-limit risk to reach the threshold are identified and warnings are issued.

2. The method for early warning of weak links in a power distribution network according to claim 1, characterized in that, The process of constructing a set of planning scenarios and a probability model based on the types of uncertainties existing in the distribution network includes: Based on the new energy planning parameters, uncertainty parameters are extracted according to the uncertainty type of the planning layer. The uncertainty parameters of the planning layer include the scale of new energy access, the number of accesses, the access location, and the access phase. According to the type of operational layer uncertainty, operational layer uncertainty parameters are extracted based on the historical operational data, wherein the operational layer uncertainty parameters include historical load data and historical irradiance data; Based on the planning layer uncertainty parameters, the topology parameters, and the feeder parameters, a set of planning scenarios is constructed. A probabilistic model is constructed based on the uncertainty parameters of the operating layer.

3. The method for early warning of weak links in a power distribution network according to claim 2, characterized in that, The process of constructing a set of planning scenarios based on the uncertainty parameters of the planning layer, the topology parameters, and the feeder parameters includes: Determine the range of values ​​for the installed capacity of individual new energy units; The access locations of the new energy sources are classified according to whether they are single-phase or three-phase new energy sources; Determine the step size for changes in the penetration rate of new energy access; Based on the scale of new energy access, the number of accesses, the access location, and the access phase, and using the value range and the change step size as constraints, multiple discrete new energy access planning scenarios are randomly combined according to the access type of the new energy to obtain a planning scenario set.

4. The method for early warning of weak links in a power distribution network according to claim 2, characterized in that, The construction of the probabilistic model based on the uncertainty parameters of the operating layer includes: The maximum likelihood estimation method is used to fit the probability distributions of the historical load data and historical irradiance data to obtain a probability model.

5. The method for early warning of weak links in a power distribution network according to claim 4, characterized in that, The method employs maximum likelihood estimation to fit probability distributions to the historical load data and historical irradiance data, respectively, to obtain a probability model, including: Distribution network users are clustered and grouped according to their annual electricity consumption or contracted power. At a preset time granularity, the probability distribution of the historical load data corresponding to each user group is fitted to obtain the probability density function of the load power. At the same time granularity, the historical irradiance data is fitted with a probability distribution to obtain the probability density function of new energy output.

6. The method for early warning of weak links in a power distribution network according to claim 1, characterized in that, The construction of a probabilistic power flow model for the distribution network based on the planning scenario set and the probability model includes: For each new energy access planning scenario in the planning scenario set, a corresponding distribution network deterministic topology model is constructed based on the topology parameters and the feeder parameters. The load power and new energy output, which represent the uncertainty of the operation layer in the probabilistic model, are introduced into the deterministic topology model and set as random input variables. The voltage amplitude of each node in the distribution network and the current magnitude of each branch are set as random output variables; Based on the power flow constraint equations of the distribution network, a probabilistic power flow model of the distribution network is constructed, which simultaneously includes the random input variables and the random output variables.

7. The method for early warning of weak links in a power distribution network according to claim 6, characterized in that, The non-intrusive generalized multinomial chaotic method is used to solve the probabilistic power flow model to obtain probabilistic characterizations of distribution network node voltages and branch currents under various planning scenarios, including: Based on the probability distribution type of the random input variables in the probability model, select an orthogonal polynomial basis function that matches the probability distribution type; Set the order of the chaotic expansion of the generalized polynomial basis function, and construct a polynomial function expression between random input variables and distribution network node voltages and branch currents; Based on the aforementioned polynomial function expression, multiple test points are generated in the probability space of random input variables using low-discrepancy sequences. Using the values ​​of random input variables corresponding to each test point as input, a deterministic power flow calculation is performed on the probabilistic power flow model to obtain the calculation results of the distribution network node voltage and branch current at each test point; Based on the calculation results of node voltage and branch current corresponding to each test point, the chaotic expansion coefficients of the generalized polynomial basis function are solved to obtain the probabilistic characterization results of distribution network node voltage and branch current under each planning scenario.

8. The method for early warning of weak links in a power distribution network according to claim 1, characterized in that, Based on the probabilistic characterization results of distribution network node voltages and branch currents under each planning scenario, and combined with preset distribution network operation safety constraints, the probability of exceeding limits under different time sections for each planning scenario is calculated, and corresponding limit-exceeding risk indicators are generated, including: Define undervoltage, overvoltage, and branch overcurrent limit-exceeding events; Based on the probability characterization results of distribution network node voltage and branch current under each planning scenario, random sampling calculations are performed on each over-limit event to obtain the over-limit occurrence probability corresponding to each time segment; Statistical analysis is performed on the probability of exceeding limits at each time segment to generate corresponding limit-exceeding risk indicators.

9. An electronic device, characterized in that, The electronic device includes: a memory and at least one processor, wherein the memory stores instructions; The at least one processor invokes the instructions in the memory to cause the electronic device to execute the power distribution network weak link early warning method as described in any one of claims 1-8.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instruction is executed by the processor, it implements the early warning method for weak links in the power distribution network as described in any one of claims 1-8.

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