Branch risk ranking method and system for power distribution network facing high penetration rate of new energy

Abstract

This invention relates to the field of power system technology. To address the problem that existing technologies cannot meet the requirements of conservative dispatching and risk ranking for sensitivity to tail risks, it provides a method and system for risk ranking of distribution network branches for high-penetration renewable energy sources. The method for risk ranking of distribution network branches for high-penetration renewable energy sources includes: constructing a steady-state closed-loop relationship considering electro-thermal coupling; establishing a load factor-failure rate mapping model based on renewable energy and load uncertainty models, while simultaneously considering the steady-state closed-loop relationship of electro-thermal coupling, to obtain the branch failure rate; constructing a joint optimization model of risk-aware minimum load shedding and network reconfiguration to obtain the accident consequence assessment result; constructing accident landing point weights based on the branch failure rate, and then calculating the EVAR (Effective Value Assigned) branch risk contribution and ranking each branch based on the accident consequence assessment result to obtain a list of high-risk branches. This method can achieve the screening and ranking of high-risk branches while maintaining the feasibility of the engineering process.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method and system for risk ranking of distribution network branches for high-penetration renewable energy sources. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] With the high penetration of distributed renewable energy sources such as wind power and photovoltaics into the distribution network, the net power injected into distribution network nodes exhibits significant volatility and randomness. During operation, dispatching and safety verification typically use short-term forecasts as the nominal operating benchmark. However, actual output and load deviate from these forecasts, resulting in node voltage, branch power flow, and branch current exhibiting random variables within a single timeframe. To support day-ahead, intraday, and real-time rolling operation and online safety verification, projects often require rapid assessment within a single timeframe or rolling time window: the probability of voltage exceeding limits, the probability of branch overload, and the resulting list of high-risk branches and their consequences. This further leads to accident set screening and risk ranking results, providing a basis for operational decisions such as reactive power and voltage control, network reconfiguration, and flexible load adjustment.

[0004] While scenario simulation-based methods, such as the Monte Carlo method, are intuitive in existing stochastic power flow and risk assessment methods, their computational cost is high in scenarios involving high-dimensional uncertain injections, requiring rolling updates, and online output. The semi-invariant propagation approach offers higher computational efficiency and has therefore attracted attention in engineering applications. However, in distribution network scenarios characterized by high volatility of renewable energy and frequent switching of operational constraints, existing technologies still have the following shortcomings: Some semi-invariant methods rely on single-base-point first-order linearization. When prediction errors are large or control constraint switching causes power flow to cross multiple nonlinear regions, the first-order approximation error is difficult to control, easily leading to unreliable estimations of small-probability, large-deviation tail regions, thus affecting the credibility of over-limit probability and risk ranking results. Under conditions of high-volatility renewable energy penetration, protection actions and secondary cascading effects may cause accident consequences to exhibit heavy-tailed characteristics. Using only expected indicators easily underestimates the risk of small-probability, large-consequence outcomes, making it difficult to meet the requirements of conservative scheduling and risk ranking for sensitivity to tail risks. Summary of the Invention

[0005] To address the aforementioned technical issues, this invention provides a risk ranking method and system for distribution network branches oriented towards high-penetration renewable energy sources. It is applicable to online / rolling assessment scenarios, improves the reliability of tail probability estimation across nonlinear operating zones and ensures the physical consistency of the output probability density function while maintaining the feasibility of the engineering process. It also incorporates electrothermal feedback and multi-index failure rate mapping into a unified framework, and introduces a risk metric that is more sensitive to the tail to achieve the screening and ranking of high-risk branches.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The first aspect of this invention provides a risk ranking method for distribution network branches oriented towards high-penetration renewable energy sources.

[0008] In one or more embodiments, a risk ranking method for distribution network branches oriented towards high-penetration renewable energy sources is provided, including:

[0009] A model for uncertainty of new energy sources and loads is constructed. Without explicitly introducing external meteorological variables, the heat dissipation effect is represented by a constant parameter equivalent linear heat dissipation term, forming a closed-loop coupling of the algebraic power flow on the electric side and the slow dynamic equilibrium on the thermal side, and establishing a steady-state closed relationship that considers the electrothermal coupling.

[0010] Based on the uncertainty model of new energy and load, the probability density functions of node voltage amplitude, branch active power and branch current square are calculated, and then the current load rate, power load rate and node voltage over-limit probability are calculated. The current load rate is used to characterize the thermal stress inlet and the power load rate is used to characterize the operational constraint tension. The node voltage over-limit probability is introduced as a secondary correction term. At the same time, the steady-state closed relationship of electrothermal coupling is considered to establish a load rate-failure rate mapping model to obtain the branch failure rate.

[0011] The tail probability of the branch failure rate is engineered and embedded into the risk accident set for screening. The three sources of load shedding consequences after the accident are decomposed into direct load shedding due to line outage, load shedding triggered by low voltage over-limit, and load shedding triggered by active power over-limit. A joint optimization model of risk perception minimum load shedding and network reconfiguration is constructed to obtain the load loss results after the accident.

[0012] Based on the branch failure rate, the accident landing point weight is constructed. Then, combined with the load loss results after the accident, the EVAR branch risk contribution is calculated and each branch is ranked to obtain a list of high-risk branches.

[0013] As one implementation method, the process of calculating the probability density functions of node voltage magnitude, branch active power, and branch current square is as follows:

[0014] Based on the uncertainty model of new energy and load, the predicted net injection vector of new energy and load and its prediction error statistics are obtained, the injection disturbance random vector is constructed, and the disturbance scenario set is generated.

[0015] Adaptive clustering is performed on the set of perturbation scenarios to divide the perturbation space into several clusters, resulting in the cluster set, cluster weights, and cluster centers;

[0016] For each cluster center, perform an electrothermal consistent closed-loop iterative power flow solution to form a closed-loop iteration of power flow - branch current square - steady-state temperature rise - temperature-related admittance update - power flow until the temperature rise converges, and obtain an electrothermal consistent cluster base point that simultaneously satisfies electrical power flow balance and thermal steady-state balance.

[0017] At the cluster base point, the AC power flow equation and output mapping are localized to the first order, establishing a linear mapping from intra-cluster injected disturbances to output disturbances. The higher-order intra-cluster moments of node voltage magnitude, branch active power, and branch current square are obtained by semi-invariant propagation.

[0018] The global higher-order moments are obtained by synthesizing the higher-order moments of each cluster with full probability, and the probability density functions of each output are reconstructed based on the maximum entropy principle of the physical support domain constraint.

[0019] As one implementation method, the process of performing adaptive clustering segmentation on the perturbed scene set includes:

[0020] Deterministic power flow is solved and first-order linearization is completed at the center of each cluster. Several direction vectors are selected and finite difference calculation is performed along each direction with a preset step size. The maximum value of the second-order difference value in each direction is obtained for each output component and used as the upper bound estimate of the second-order nonlinear intensity of the output component in the cluster.

[0021] Calculate the distance from all scene points within the cluster to the cluster center, and take the maximum value as the cluster radius; take half of the product of the second-order nonlinear intensity upper bound estimate and the square of the cluster radius as the worst linearization error upper bound for the output component of the cluster;

[0022] Take the maximum value of the worst linearization error upper bound among all output components and compare it with the preset linearization error threshold: if the former does not exceed the latter, the cluster passes the acceptance criterion and remains unsubdivided; otherwise, the cluster is further split into smaller clusters, and the above steps are repeated until all clusters meet the acceptance criterion.

[0023] As one implementation method, the process of performing electrothermal consistent closed-loop iterative power flow solution for each cluster center includes:

[0024] The conductor temperature offset of all branches is initialized to zero, and the initial impedance of each branch is calculated according to the temperature-dependent resistance model. The initial temperature-dependent node admittance matrix is ​​then assembled.

[0025] Using the current temperature-dependent admittance matrix as a parameter, the AC power flow equations are solved under the injection conditions corresponding to the center of the cluster to obtain the node voltage magnitude and phase angle of the current iteration;

[0026] The current phasor of each branch is calculated from the node voltage magnitude and phase angle of the current iteration, and then the square current of each branch is obtained and substituted into the steady-state thermal equilibrium closed solution.

[0027] Update the conductor temperature offset of each branch, select the maximum difference between the updated temperature offset and the temperature offset of the previous iteration from all branches, and determine whether the maximum value is less than the preset temperature rise convergence threshold. If so, output the current power flow solution and temperature as the electrothermal consistent cluster base point. Otherwise, recalculate the impedance and admittance of each branch based on the updated temperature, reassemble the node admittance matrix, and continue iterative solution until convergence.

[0028] The process of reconstructing the probability density function of each output quantity based on the maximum entropy principle constrained by the physical support domain includes:

[0029] Based on the physical characteristics of the output, support domain constraints are set for various variables: the support domain for node voltage magnitude is set to a non-negative real domain, the support domain for branch active power flow is set to a fully real domain, and the support domain for branch current square is set to a non-negative real domain.

[0030] For node voltage magnitude and branch active power flow, a maximum entropy optimization problem is directly constructed within their respective support domains with global higher-order moments as constraints. By introducing Lagrange multipliers, the parametric form of the exponential probability density function is obtained. Numerical integration is used to calculate the constraint residuals and Jacobians of each moment, and Newton iteration is used to solve the multiplier parameters to obtain the corresponding probability density function.

[0031] For the square of the branch current, a logarithmic transformation is first applied to map it to the entire real number domain. The transformed variable is then reconstructed using maximum entropy in the entire real number domain to obtain the probability density function of the transformed domain. Finally, the probability density function is mapped back to the original non-negative domain by multiplying it by the Jacobian factor through the inverse transformation of the variable. This ensures that the reconstructed probability density function is strictly non-negative in the entire domain and does not assign probability mass to the physically infeasible domain.

[0032] As one implementation method, the process of establishing a load rate-failure rate mapping model to obtain the branch failure rate includes:

[0033] The statistical description of the current load factor is obtained from the probability density function of the square of the branch current, and the statistical description of the power load factor is obtained from the probability density function of the branch active power. The current load factor is mapped to the corresponding conductor temperature using the steady-state closed relationship of electrothermal coupling, and a deterministic mapping from current load factor to temperature is established.

[0034] Set piecewise amplification functions in the temperature domain and power load rate domain respectively: when the value is below the alarm threshold, the value is 1 to indicate no amplification; the value increases linearly between the alarm threshold and the limit threshold; and the value continues to increase with a larger slope after the limit threshold is exceeded.

[0035] The piecewise amplification function in the temperature domain is substituted back through the mapping from current load rate to temperature, and then integrated with the probability density function of the square of the branch current in the non-negative domain to obtain the expected amplification factor of the current / temperature channel; the piecewise amplification function in the power load rate domain is integrated with the probability density function of the active power of the branch in its domain to obtain the expected amplification factor of the power channel.

[0036] The marginal contribution of each branch to the two types of expected amplification factors relative to the baseline value of 1 is calculated separately. The two types of contributions are then aggregated at the level of all branches in the network, and normalized according to the aggregation ratio to obtain the current / temperature channel weight and the power channel weight.

[0037] In the logarithmic domain, the two types of expected amplification factors are combined convexly according to their weights to obtain the comprehensive load amplification factor; the voltage over-limit probability of each node is calculated by the probability density function of the node voltage amplitude, and the larger over-limit probability of the nodes at both ends of the branch is taken as the comprehensive voltage over-limit index of the branch, and the coefficient controlled by the upper bound is used as the secondary correction term; the reference failure rate, the comprehensive load amplification factor and the voltage over-limit correction term are multiplied to output the failure rate of each branch.

[0038] As one implementation method, the process of constructing a joint optimization model of risk-aware minimum load shedding and network reconfiguration to obtain the load loss results after an accident includes:

[0039] Using the branch failure rate or the time window failure probability derived from it, all branches are sorted from highest to lowest failure probability, and branches with failure probabilities higher than a preset threshold are retained to form a set of incidents to be evaluated;

[0040] For each faulty branch in the incident set, the incident consequences are decomposed into three sources and calculated separately:

[0041] The first item is the direct load shedding amount due to line outage, which is obtained by determining the power outage status of each node based on the topological connectivity after the accident, and then summing the load demand and importance coefficient of each node. The second item is the load shedding amount triggered by low voltage over-limit, which is obtained by integrating the probability density function of the voltage amplitude of each node after the accident with the segmented undervoltage load shedding trigger function to obtain the expected undervoltage load shedding ratio, and then summing it with the guaranteed load. The third item is the secondary load shedding amount triggered by active power over-limit protection tripping, which is obtained by calculating the tail probability of exceeding the protection threshold using the active power probability density function of each branch still in operation after the accident, obtaining the tripping probability of the branch within the evaluation time window, multiplying it by the downstream power outage load after the branch tripping, and then summing it up branch by branch.

[0042] Using the weighted sum of the above three terms as the objective function, constraints are set and jointly optimized to obtain the optimal load shedding scheme and the corresponding risk perception target value, which serves as the result of the corresponding post-accident load loss.

[0043] As one implementation method, the risk contribution of the EVAR branch is:

[0044] ;

[0045] ;

[0046] In the formula, Contribution to EVAR branch risk; For the worst-case accident landing point weights in the dual sense of EVAR; For branch index; For branch set; branch road As a normalized weight for a single fault landing point; Let branch k be the normalized weight of a fault landing point; For the faulty branch Risk perception target value; For the faulty branch Risk perception target value; v It is the optimal auxiliary variable.

[0047] A second aspect of the present invention provides a risk ranking system for distribution network branches oriented towards high-penetration renewable energy sources.

[0048] A risk ranking system for distribution network branches oriented towards high-penetration renewable energy sources includes:

[0049] The electrothermal coupling closed-loop module is used to construct a new energy and load uncertainty model. Without explicitly introducing external meteorological variables, the heat dissipation effect is represented by a constant parameter equivalent linear heat dissipation term, forming a closed-loop coupling of the electric side algebraic power flow and the thermal side slow dynamic balance, and establishing a steady-state closed relationship considering electrothermal coupling.

[0050] The failure rate calculation module is used to calculate the probability density functions of node voltage amplitude, branch active power and branch current square based on the new energy and load uncertainty model. Then, it calculates the current load rate, power load rate and node voltage over-limit probability. The current load rate is used to characterize the thermal stress inlet and the power load rate is used to characterize the operational constraint tension. The node voltage over-limit probability is introduced as a secondary correction term. At the same time, the steady-state closed relationship of electrothermal coupling is considered to establish a load rate-failure rate mapping model to obtain the branch failure rate.

[0051] The accident consequence assessment module is used to engineer the tail probability of the branch failure rate into the risk accident set for screening, decompose the three sources of the load shedding consequence after the accident into direct load shedding due to line outage, load shedding triggered by low voltage over-limit and load shedding triggered by active power over-limit, construct a joint optimization model of risk perception minimum load shedding and network reconfiguration, and obtain the load loss result after the accident.

[0052] The branch risk ranking module is used to construct the accident landing point weight based on the branch failure rate, and then combine it with the load loss results after the accident to calculate the EVAR branch risk contribution and rank each branch to obtain a list of high-risk branches.

[0053] A third aspect of the present invention provides an electronic device.

[0054] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the risk ranking method for distribution network branches for high-penetration renewable energy described above.

[0055] Compared with the prior art, the beneficial effects of the present invention are:

[0056] This invention provides a method and system for risk ranking of distribution network branches for high-penetration renewable energy sources. It can be applied to online / rolling assessment scenarios, improve the reliability of tail probability estimation across nonlinear operating zones and ensure the physical consistency of the output probability density function while maintaining the feasibility of the engineering process. It also incorporates electrothermal feedback and multi-index failure rate mapping into a unified framework, and introduces a risk metric that is more sensitive to the tail to achieve a method for screening and ranking high-risk branches. Attached Figure Description

[0057] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0058] Figure 1 This is a flowchart of the risk ranking method for distribution network branches for high-penetration new energy sources according to an embodiment of the present invention;

[0059] Figure 2 This is a schematic diagram of the risk ranking system structure for distribution network branches oriented towards high-penetration new energy sources according to an embodiment of the present invention. Detailed Implementation

[0060] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0061] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0062] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0063] As can be seen from the background technology, in distribution network scenarios with high volatility of new energy sources and frequent switching of operating constraints, existing stochastic power flow and risk assessment methods still have the following problems:

[0064] Probability density approximations are prone to non-physical phenomena: probability density approximations based on series expansion, truncation, or fitting may produce oscillations or even negative probabilities at the tail end; this is particularly prominent for variables that should be strictly non-negative, such as the square of current, which in turn affects the engineering usability of over-limit probability calculation, failure rate mapping, and subsequent accident screening.

[0065] Ignoring electrothermal feedback leads to parameter drift and risk underestimation: When the distribution network is operating at high load rate, the temperature rise of the conductor causes changes in resistance and further changes the power flow distribution; if the closed-loop feedback of "electrical power flow - thermal temperature rise - electrical parameter update" is not reflected in the probabilistic power flow calculation, the power flow deviation and risk accumulation under high load conditions are easily underestimated.

[0066] The mapping from probabilistic output to reliability parameters lacks a unified and calibrable model: In engineering, it is often necessary to convert probabilistic power flow results into branch failure rates or failure probabilities to screen accident sets and determine maintenance priorities. However, existing practices are often based on single indicators or empirical coefficients, lacking a unified mapping framework that integrates multi-source risk evidence such as current / temperature, power constraint tension, and voltage over-limit, and also lacking a transferable determination mechanism for weights and parameters.

[0067] Therefore, there is an urgent need for a method that can improve the reliability of tail probability estimation across nonlinear operating regions, ensure the physical consistency of the output probability density function, incorporate electrothermal feedback and multi-index failure rate mapping into a unified framework, and introduce a risk metric that is more sensitive to the tail to achieve high-risk branch screening and ranking, while maintaining the feasibility of the engineering process for online / rolling evaluation scenarios.

[0068] Figure 1 A schematic diagram of the risk ranking method for distribution network branches oriented towards high-penetration renewable energy sources, according to an embodiment of the present invention, is provided. Figure 1 The risk ranking method for distribution network branches for high-penetration new energy sources in this embodiment may include the following steps S101 to S104.

[0069] The specific implementation process of steps S101 to S104 is as follows:

[0070] Step S101: Construct an uncertainty model for new energy sources and loads. Without explicitly introducing external meteorological variables, represent the heat dissipation effect as a constant parameter equivalent linear heat dissipation term, forming a closed-loop coupling of the electric side algebraic power flow and the thermal side slow dynamic balance, and establishing a steady-state closed relationship considering the electrothermal coupling.

[0071] In the specific process of step S101, the steps for constructing the uncertainty model of new energy sources and load are as follows:

[0072] Wind power output model:

[0073] wind speed It follows a Weibull distribution with the following probability density function:

[0074] (1);

[0075] In the formula, >0 represents wind speed. >0 is a scale parameter, representing the average wind speed in the region. >0 represents the shape parameter, indicating the distribution characteristics of wind speed.

[0076] Expected active power of wind farm The relationship with wind speed is as follows:

[0077] (2);

[0078] In the formula, To cut into wind speed, Rated wind speed, To cut off the wind speed, The rated active power of the wind turbine. , .

[0079] In power distribution networks, distributed wind turbines are often treated as PQ nodes and constant power factor control is used. Therefore, the reactive power output is:

[0080] (3);

[0081] In the formula, For the expected active power of the wind farm, For the expected reactive power of the wind farm, The power factor angle.

[0082] Photovoltaic power output model:

[0083] The probability density function of the output power of a solar cell array is commonly described by a Beta distribution on short timescales. The expression is:

[0084] (4);

[0085] In the formula: Solar radiation intensity; The maximum solar radiation intensity within a given time period; It is the gamma function; β and β are both shape parameters of the Beta distribution.

[0086] (5);

[0087] In the formula, , The expected value and standard deviation of light intensity over a certain period of time.

[0088] The power of a photovoltaic array can be represented by an irradiance-area-efficiency map:

[0089] (6);

[0090] In the formula, The effective area of ​​the photovoltaic panel. This refers to the photoelectric conversion efficiency.

[0091] As can be seen from the above, the active power output of photovoltaic power generation is directly proportional to the solar radiation intensity. Therefore, the active power output of photovoltaic power generation also follows a Beta distribution, and its probability density function is:

[0092] (7);

[0093] In the formula, This refers to the active power output of the photovoltaic array under maximum solar radiation intensity.

[0094] Load uncertainty model:

[0095] The fluctuations in active and reactive power loads are commonly described by the normal distribution.

[0096] (8);

[0097] In the formula, For active power load demand, For reactive load demand, These are the expected value and standard deviation of the active power of the load, respectively. These are the expected value and standard deviation of the reactive power of the load, respectively.

[0098] In short-term or online analysis and evaluation studies considering the uncertainties of renewable energy and load output, the results of short-term power forecasts are often combined with the prediction error due to random fluctuations to describe the uncertainty. The uncertainty of renewable energy and load output is mainly reflected in the random fluctuations of the prediction error, which can be modeled as follows:

[0099] (9);

[0100] In the formula, For prediction error, This represents the standard deviation of the prediction error. The error distribution can be estimated from historical data, providing input statistics for subsequent propagation of the semi-invariants.

[0101] Under the influence of uncertainties in new energy sources and loads, the power fluctuations in distribution network branches intensify, and high load rates lead to changes in conductor temperature rise and consequently, changes in line resistance. To reflect the closed-loop feedback of "electrical power flow – thermal temperature rise," this section, without explicitly introducing external meteorological variables (ambient temperature, solar irradiance, etc.), represents the heat dissipation effect as a constant-parameter equivalent linear heat dissipation term, forming a closed-loop coupling of "electrical algebraic power flow – thermal slow dynamic equilibrium."

[0102] Temperature-dependent line impedance and admittance:

[0103] The temperature-dependent resistance model for line (i, j) is as follows:

[0104] (10);

[0105] In the formula, This is the offset relative to the reference temperature. The AC resistance of the line at the reference temperature. is the temperature coefficient of resistance.

[0106] The series impedance of the line is:

[0107] (11);

[0108] In the formula, For the collection of branch lines, Let be the series reactance of line (i, j).

[0109] The series admittance is:

[0110] (12);

[0111] The real and imaginary parts are respectively:

[0112] (13);

[0113] (14);

[0114] In the formula, For series conductance, It is a series susceptance.

[0115] Temperature-dependent nodal admittance matrix :

[0116] To embed the temperature-controlled resistor into the power flow equation, a temperature-dependent node admittance matrix obtained from the line admittance assembly is introduced. ;make:

[0117] (15);

[0118] In the formula, Indicates the temperature offset of all lines. A set of vectors stacked in a fixed order.

[0119] Considering only the series branches of the line, the nodal admittance matrix can be expressed in a compact form by summing the outer products as follows:

[0120] (16);

[0121] In the formula, , These are the standard basis vectors corresponding to nodes i and j, respectively.

[0122] Will Decompose into real and imaginary parts:

[0123] (17);

[0124] In the formula, Let be the real part of the nodal admittance matrix. This represents the imaginary part of the nodal admittance matrix.

[0125] Temperature-dependent AC power flow model:

[0126] The injected active power at node i can be obtained from the calculated temperature-dependent Y(T). With no merit satisfy:

[0127] (18);

[0128] (19);

[0129] In the formula, N is the set of distribution network nodes. , Each is a matrix , The (i, k)th element, This represents the phase angle difference at the nodes.

[0130] Branch current square and current load factor:

[0131] In the series model of the line ignoring parallel branches, the branch current phasor of line (i, j) is:

[0132] (20);

[0133] In the formula, and These are the voltage phasors of nodes i and j, respectively.

[0134] Define the square of the current and the current load factor:

[0135] (twenty one);

[0136] (twenty two);

[0137] In the formula, The square of the line current amplitude. For line current load factor, The rated current amplitude of line (i, j) is selected from the rated parameters of the conductor.

[0138] Thermal dynamics and steady-state thermal equilibrium of conductors:

[0139] Without explicitly introducing meteorological variables, the heat dissipation effect between the conductor and the outside environment is equivalent to a constant-parameter linear heat dissipation term, resulting in a first-order thermal dynamic model:

[0140] (twenty three);

[0141] In the formula, For time variables, Let (i, j) be the temperature offset of line (i, j) at time t. Equivalent heat capacity of the conductor This is the equivalent heat dissipation coefficient.

[0142] When the hot side reaches a steady state, i.e., the slow dynamic approximation, Therefore:

[0143] (twenty four);

[0144] Substituting into the resistance-temperature model and rearranging, we obtain the steady-state temperature rise with respect to... Explicit functions:

[0145] (25);

[0146] To ensure consistency with subsequent temperature thresholds and failure rate mappings, the absolute temperature of the conductor is introduced:

[0147] (26);

[0148] In the formula, Let (i, j) be the absolute temperature of the conductor in line (i, j). To and The corresponding reference temperature.

[0149] Further utilization ,available Regarding load rate The function expression:

[0150] (27);

[0151] To ensure the existence of a steady-state solution and that the denominator is positive, the following must be satisfied:

[0152] (28);

[0153] Step S102: Based on the uncertainty model of new energy and load, calculate the probability density functions of node voltage amplitude, branch active power and branch current square, and then calculate the current load rate, power load rate and node voltage over-limit probability. Use the current load rate to characterize the thermal stress inlet and the power load rate to characterize the operational constraint tension. Introduce the node voltage over-limit probability as a secondary correction term. At the same time, consider the steady-state closed relationship of electrothermal coupling and establish a load rate-failure rate mapping model to obtain the branch failure rate.

[0154] Specifically, based on the uncertainty model of new energy sources and loads, the process of calculating the probability density functions of node voltage amplitude, branch active power, and branch current square is as follows:

[0155] Step a: Based on the uncertainty model of new energy and load, obtain the predicted net injection vector of new energy and load and its prediction error statistics, construct the injection disturbance random vector, and generate the disturbance scenario set;

[0156] Step b: Perform adaptive clustering segmentation on the perturbation scene set to divide the perturbation space into several clusters, and obtain the cluster set, cluster weights and cluster centers;

[0157] The process of performing adaptive clustering segmentation on the perturbation scene set includes:

[0158] Step b1: Solve the deterministic power flow at the center of each cluster and complete the first-order linearization. Select several direction vectors and perform finite difference calculations along each direction with a preset step size. For each output component, find the maximum value of the second-order difference value in each direction and use it as the upper bound estimate of the second-order nonlinear intensity of the output component in the cluster.

[0159] Step b2: Iterate through all scene points within the cluster and calculate their distance to the cluster center, taking the maximum value as the cluster radius; take half of the product of the second-order nonlinear intensity upper bound estimate and the square of the cluster radius as the worst linearization error upper bound for the output component of the cluster;

[0160] Step b3: Take the maximum value of the worst linearization error upper bound among all output components and compare it with the preset linearization error threshold. If the former does not exceed the latter, the cluster passes the acceptance criterion and remains unsubdivided. Otherwise, the cluster is further split into smaller clusters. Repeat the above steps until all clusters meet the acceptance criterion.

[0161] Step c: Perform electrothermal consistent closed-loop iterative power flow solution for each cluster center to form a closed-loop iteration of power flow - branch current square - steady-state temperature rise closed update - temperature-related admittance update - re-power flow until the temperature rise converges, and obtain the electrothermal consistent cluster base point that simultaneously satisfies electrical power flow balance and thermal steady-state balance.

[0162] The process of performing electrothermal consistent closed-loop iterative power flow solution for each cluster center includes:

[0163] Step c1: Initialize the conductor temperature offset of all branches to zero, calculate the initial impedance of each branch according to the temperature-dependent resistance model, and assemble the initial temperature-dependent node admittance matrix.

[0164] Step c2: Using the current temperature-related admittance matrix as a parameter, solve the AC power flow equation under the injection conditions corresponding to the cluster center to obtain the node voltage magnitude and phase angle of the current iteration;

[0165] Step c3: Calculate the current phasor of each branch from the node voltage magnitude and phase angle of the current iteration, and then obtain the square current of each branch, and substitute it into the steady-state thermal equilibrium closed solution.

[0166] Step c4: Update the conductor temperature offset of each branch. Select the maximum value of the difference between the updated temperature offset and the temperature offset of the previous iteration from all branches, and determine whether the maximum value is less than the preset temperature rise convergence threshold. If so, use the current power flow solution and temperature as the electrothermal consistency cluster base point output. Otherwise, recalculate the impedance and admittance of each branch based on the updated temperature, reassemble the node admittance matrix, and continue iterative solution until convergence.

[0167] Step d: Perform first-order local linearization on the AC power flow equation and output mapping at the cluster base point to establish a linear mapping from intra-cluster injected disturbance to output disturbance, and use semi-invariant propagation to obtain intra-cluster higher-order moments of node voltage magnitude, branch active power, and branch current square.

[0168] Step e: Synthesize the higher-order moments of each cluster according to the full probability to obtain the global higher-order moments, and reconstruct the probability density function of each output quantity based on the maximum entropy principle of the physical support domain constraint.

[0169] The process of reconstructing the probability density function of each output quantity based on the maximum entropy principle constrained by the physical support domain includes:

[0170] Step e1: Set support domain constraints for various variables according to the physical characteristics of the output: set the support domain of node voltage magnitude to non-negative real number domain, set the support domain of branch active power flow to all real number domain, and set the support domain of branch current square to non-negative real number domain.

[0171] Step e2: For node voltage magnitude and branch active power flow, construct the maximum entropy optimization problem directly in their respective support domains with global higher-order moments as constraints. By introducing Lagrange multipliers, obtain the parametric form of the exponential probability density function. Calculate the constraint residuals and Jacobians of each moment using numerical integration. Solve the multiplier parameters using Newton iteration to obtain the corresponding probability density function.

[0172] Step e3: For the square of the branch current, first apply a logarithmic transformation to map it to the entire real number domain. Then, perform maximum entropy reconstruction on the transformed variable in the entire real number domain to obtain the probability density function of the transformed domain. Finally, multiply the variable by the Jacobian factor through the inverse transformation to map the probability density function back to the original non-negative domain, thereby ensuring that the reconstructed probability density function is strictly non-negative in the entire domain and does not assign probability mass to the physically infeasible domain.

[0173] Define the injection of wind power, solar power, and load at node i:

[0174] (29);

[0175] (30);

[0176] (31);

[0177] In the formula, , The active and reactive power injected into the wind power at node i , The predicted active and reactive power values ​​are injected into the wind power at node i. , Inject random disturbances, both active and reactive, into the nodes; , The active and reactive power injected into the photovoltaic system at node i , The predicted active and reactive power values ​​are injected into the photovoltaic system at node i. , Inject random disturbances, both active and reactive, into the nodes; , The active and reactive power consumed by the node load. , The predicted active and reactive power consumption values ​​for node i are given. , The random disturbances that consume active and reactive power for node loads.

[0178] From this, we can obtain the predicted net active and reactive power injection values ​​and the net injection disturbance at node i:

[0179] (32);

[0180] (33);

[0181] Uncertain disturbances, both active and reactive, injected into nodes are uniformly represented as random vectors:

[0182] (34);

[0183] In the formula, To inject a perturbation random vector, For the set of nodes that are modeled as having uncertain injection, For the perturbation dimension, This is a column vector stacking operator.

[0184] Let the deterministic prediction injection vector be:

[0185] (35);

[0186] In the formula, Inject vectors to predict (nominal) This is the actual injected vector.

[0187] Generate a set of injected perturbation scenarios :

[0188] (36);

[0189] In the formula, For a set of perturbation scenarios, For the number of scenes, Let s be the s-th perturbation sample.

[0190] And define cluster weights With cluster center for:

[0191] (37);

[0192] (38);

[0193] In the formula, This represents the number of samples contained in the k-th scene cluster.

[0194] Define an intra-cluster centralization perturbation for each cluster k:

[0195] (39);

[0196] In the formula, For the perturbation relative to the cluster center, This is the conditional expectation.

[0197] To incorporate the impact of temperature rise feedback on power flow into the cluster base point, the deterministic power flow base point is solved using the following electro-thermal consistent closed-loop iterative method at each cluster center:

[0198] First initialize , and by Assembly ;

[0199] Then inject The temperature-dependent AC power flow is then solved to obtain the nodal states. ;

[0200] Depend on Calculate branch current

[0201] Finally, the temperature rise is updated using the steady-state closed-form solution:

[0202] (40);

[0203] like If the iteration stops, then stop; otherwise, continue iterating from t to t+1.

[0204] In the formula, >0 represents the temperature rise convergence threshold. After convergence, electrically and thermally consistent cluster base points are obtained. and Then, subsequent linearization and moment propagation are performed on this base point.

[0205] Solving for the deterministic AC power flow at the cluster center yields the cluster baseline operating point:

[0206] satisfy:

[0207] (41);

[0208] In the formula, For the injection-state power flow equation mapping, This is the baseline power flow solution for cluster k. This is the baseline output for cluster k.

[0209] For the above formula in ( , Performing first-order linearization at ) gives:

[0210] (42);

[0211] Thus, the intra-cluster state sensitivity matrix is ​​obtained:

[0212] (43);

[0213] In the formula, For cluster state perturbation, To facilitate the exchange of trends, the Jacobi matrix, The sensitivity matrix for injecting perturbations into the state perturbations within the cluster.

[0214] Similarly, for the output mapping y=h(x) in linearization yields

[0215] (44);

[0216] Substituting into the intra-cluster state sensitivity matrix yields the linear mapping of "injected perturbation → output perturbation" within the cluster:

[0217] (45);

[0218] In the formula, To output the Jacobian matrix for each state, The equivalent sensitivity matrix from intra-cluster injected perturbation to output perturbation.

[0219] If for each output component The true nonlinear mapping is twice differentiable within the cluster, and it is also differentiable within the cluster. The upper bound of the norm of the second derivative on is Then for any The linearized remainder term satisfies:

[0220] (46);

[0221] In the formula, for The OK, This indicates that the solution to the power flow equations Substituting the r-th scalar value into the output function h, output the value. for The r-th component, It is an upper bound estimate of the second-order nonlinear intensity within the cluster.

[0222] To make the above formula computable in engineering calculations, this invention employs a finite difference construction. Select a set of direction vectors For each direction Define second-order difference:

[0223] (47);

[0224] In the formula, >0 represents a finite difference step size.

[0225] Based on this, take:

[0226] (48);

[0227] Define cluster radius:

[0228] (49);

[0229] In the formula, This indicates the extent of disturbance coverage within the cluster.

[0230] Then output components The upper bound of the worst linearization error within the cluster can be written as:

[0231] (50);

[0232] Given a linearization error threshold The present invention adopts the following adaptive segmentation criterion:

[0233] (51);

[0234] If cluster Accept, otherwise Further subdivision. In the formula, To determine the output dimension, the above error engineering upper bound subdivision upgrades the clustering segmentation from an empirical strategy to an adaptive mechanism with controllable accuracy, thereby steadily improving the reliability of tail probability estimation when experiencing large fluctuations across operating regions.

[0235] Semi-invariant (cumulative) moment propagation, from input moment to output moment:

[0236] For any cluster k and any input components Define its v-th order central moment:

[0237] (52);

[0238] In the formula, For cluster-centered input perturbation components, Let its v-th order central moment be... The highest moment order (n≥2) used for subsequent maximum entropy reconstruction.

[0239] Define the v-th order semi-invariant (i.e., v-th order cumulant) operator for a random variable. (·), and give the recursive transformation from central moments to semi-invariants. For a zero-mean variable, let:

[0240] (53);

[0241] The recurrence relation from central moments to semi-invariants is:

[0242] (54);

[0243] The recurrence relation from semi-invariants to central moments in reverse order is:

[0244] (55);

[0245] In the formula, Let v be the v-order semi-invariant of the input components within the cluster.

[0246] Output components for any scalar within cluster k It can be written as:

[0247] (56);

[0248] In the formula, for The (r, i)th element.

[0249] In one embodiment, it is assumed that the intra-cluster perturbation vector Since the components are independent of each other, the homogeneity and additivity of the semi-invariants can be used to propagate higher-order statistics, thus obtaining the v-order semi-invariant of the output perturbation:

[0250] (57);

[0251] In the formula, Output perturbation within cluster k The v-th order semi-invariant.

[0252] definition:

[0253] (58);

[0254] And define the Hadamard exponentiation (element-wise exponentiation) operator for matrices:

[0255] (59);

[0256] Then the v-th order semi-invariant can be equivalently expressed as:

[0257] (60);

[0258] In the formula, For the cluster, input semi-invariant vector, The output perturbation semi-invariant vector within the cluster. for The element-wise exponentiation matrix.

[0259] For each cluster k and each output component ,Will Recursive conversion to output disturbance center moment :

[0260] (61);

[0261] In the formula, Output perturbation within cluster k of The first-order central moment, because of its zero mean, is also the moment about 0 at the origin.

[0262] Within cluster k and Therefore, the conditional central moments of the output within the cluster satisfy:

[0263] (62);

[0264] In the formula, Output components within cluster k Regarding its conditional mean of The central moment of the order.

[0265] Full probability synthesis, obtaining the global output moment from the cluster moments:

[0266] For any output component Its global mean is obtained from the total expectation formula:

[0267] (63);

[0268] In the formula, For output components The global mean.

[0269] Furthermore, to use the global central moment in maximum entropy reconstruction, the global order central moment is defined as follows:

[0270] (64);

[0271] In the formula, For output components Regarding the global mean of The central moment of the order.

[0272] By using the law of total probability and binomial expansion, for any This yields a consistent synthesis formula for the "higher-order moments within the cluster after piecewise linearization" to the "global higher-order moments":

[0273] (65);

[0274] When K=1 The above formula can be degenerated into .

[0275] The maximum entropy principle with physical support domain constraints reconstructs the output probability density function:

[0276] For any output component Let its range be... Given the constraints of the first n central moments, the maximum entropy reconstruction is defined as:

[0277] (66);

[0278] In the formula, For output components The probability density function, It is an integral infinitesimal element.

[0279] Introducing Lagrange multipliers into the above equation Its stationary solution satisfies:

[0280] (67);

[0281] In the formula, For output components In the maximum entropy model, the first The Lagrange multiplier parameters. Substituting the stationary point solution into the constraints of the maximum entropy reconstruction model, we can obtain the following about... The (n+1)-dimensional nonlinear equation system: ,have:

[0282] (68);

[0283] In the formula, For output components The maximum entropy parameter vector.

[0284] The above equation can be solved using Newton's iteration method, by applying numerical integration to calculate the residuals and Jacobians of each order of moment constraints, thereby obtaining... The probability density function.

[0285] This invention explicitly sets the physical domain for different output quantities:

[0286] Node voltage amplitude physical domain :

[0287] (69);

[0288] Branch Roads Have Merits and Trends physical domain :

[0289] (70);

[0290] Branch current square physical domain :

[0291] (71);

[0292] For targeting The nonnegativity of >0 allows this invention to provide a maximum entropy reconstruction implementation of the logarithmic transform, further improving numerical stability and physical consistency. Branch impedance is defined. :

[0293] (72);

[0294] In the formula, >0 is a small constant to prevent ln(·) from becoming singular.

[0295] First to In the full real domain Reconstruction Then, through variable transformation, we obtain:

[0296] (73);

[0297] This guarantees and The support domain strictly conforms to the physical feasible domain.

[0298] PDF output of probability density functions for node voltage, branch power, and branch current:

[0299] For any node With any branch From the cluster central moments to the global central moments, we can obtain... and Then from the output components The probability density function can be obtained as follows:

[0300] (74);

[0301] (75);

[0302] (76);

[0303] In the formula, Let PDF be the probability density function of the voltage magnitude at node i. for The global mean, for The maximum entropy parameter, for Domain; Let PDF be the probability density function of the active power of branch (i,j). for The global mean, for The maximum entropy parameter, for Domain; The logarithmic square of the current in branch (i, j) The probability density function PDF, for The global mean, for The maximum entropy parameter, for The domain of definition. It is obtained by variable substitution from equation (73).

[0304] Current load factor and power load factor:

[0305] (77);

[0306] (78);

[0307] In the formula, , Let be the current load factor and active load factor of branch (i, j), respectively. Let the square of the branch current be a random variable. This is the upper limit of the allowable current for the branch. This is the upper limit of the active power of the branch circuit.

[0308] Electrothermal coupling: Temperature varies with load rate;

[0309] (79);

[0310] This formula forms a mapping from "current load rate to temperature". The subsequent temperature threshold and failure rate amplification segment can be set directly in the temperature domain and returned to the load rate domain through the above mapping.

[0311] Segmented mapping of "load rate → failure rate":

[0312] (a) A piecewise amplification function dominated by current / temperature, used to represent the increase in failure rate caused by thermal stress:

[0313] (80);

[0314] In the formula, This is the failure rate amplification function in the temperature domain. , These are the temperature alarm threshold and the temperature limit threshold, respectively. This represents the gain coefficient for the alarm segment. is the over-limit slope coefficient of the limit segment.

[0315] The equivalent amplification function in the current load factor domain can be obtained from the temperature mapping:

[0316] (81);

[0317] In the formula, This is the failure rate amplification function in the current load factor domain. The independent variable is the current load factor.

[0318] (b) A piecewise amplification function dominated by power load rate, used to reflect the increase in failure rate due to power constraint stress:

[0319] (82);

[0320] In the formula, This is the failure rate amplification function in the power load rate domain. , These are the power load rate alarm threshold and the extreme threshold, respectively. , These are the alarm segment gain coefficient and the limit segment over-limit slope coefficient, respectively.

[0321] The equivalent amplification factor is obtained from the probability density function PDF, and "uncertainty" is explicitly incorporated into the failure rate;

[0322] The amplification effect caused by random load factor is incorporated in the desired form. The equivalent amplification factor of the current path is defined as:

[0323] (83);

[0324] In the formula, Indicates will Substitute the temperature value obtained from the closed-form temperature mapping.

[0325] The equivalent amplification factor of the power channel is defined as:

[0326] (84);

[0327] Voltage over-limit indicators are adjusted for a slightly lower failure rate using a probabilistic approach.

[0328] (85);

[0329] In the formula, Let be the probability of voltage exceeding the limit at node i. Node voltage amplitude PDF, , These are the lower and upper limits of the allowable node voltage, respectively. for The range of values, It is a comprehensive index for the voltage exceeding the limit at both ends of the branch (i, j).

[0330] Logarithmic domain fusion and slight voltage correction: output branch failure rate;

[0331] To avoid fusion bias caused by differences in the scales of different amplification functions and to ensure that the fusion result is strictly positive, this invention performs a convex combination of the current and power amplification factors in the logarithmic domain to obtain the comprehensive load amplification factor:

[0332] (86);

[0333] In the formula, Let (i, j) be the overall load amplification factor of the branch. and These are the combined weights for current / temperature and power load rate, respectively. Based on this, a branch failure rate model is constructed, and voltage exceedance is introduced as a secondary correction term:

[0334] (87);

[0335] In the formula, Failure rate of branch (i, j) The branch reference failure rate, This is a minor correction factor for voltage exceeding limits.

[0336] For weights , , The selection of weights begins by constructing initial unlabeled weights using the output of the probability model itself. Two types of load metrics are defined as having a "marginal contribution" to the increase in failure rate:

[0337] (88);

[0338] (89);

[0339] In the formula, , These represent the marginal contributions of branch (i, j) current / temperature and power load rate to the amplification of the failure rate, respectively.

[0340] The contributions are aggregated and normalized at the network level to obtain the adaptive fusion weights:

[0341] (90);

[0342] (91);

[0343] In the formula, For the number of branch roads, >0 is a small constant to prevent the denominator from being zero.

[0344] For the voltage over-limit correction coefficient, to ensure the location of "minor effects" and avoid overfitting, an empirical setting of the upper bound constraint can be used, or it can be calibrated using data; in unlabeled scenarios, the following values ​​can be taken:

[0345] (92);

[0346] In the formula, This is the upper limit of the allowable voltage over-limit correction factor.

[0347] If high-risk branch screening is required within time window t, the failure probability can be further obtained:

[0348] (93);

[0349] In the formula, Let be the failure probability of branch (i, j) within the time window t. To evaluate the length of the time window.

[0350] Step S103: The tail probability in the branch failure rate is engineered and embedded into the risk accident set for screening. The three sources of load shedding consequences after the accident are decomposed into load shedding directly caused by line outage, load shedding triggered by low voltage over-limit, and load shedding triggered by active power over-limit. A joint optimization model of risk perception minimum load shedding and network reconfiguration is constructed to obtain the load loss results after the accident.

[0351] When a branch fault occurs in the system and a tripping is possible, load loss may occur. To assess the consequences of the incident, this invention constructs a risk-aware minimum load shedding-reconstruction joint optimization model consisting of "deterministic AC power flow feasibility constraints + PDF-driven probabilistic consequence terms". A more reliable tail probability is obtained from the foregoing and engineered into a risk incident set for screening, proposing a three-source decomposition of the load shedding consequences after an incident: direct load shedding due to line outage, load shedding triggered by low voltage exceeding limits, and load shedding triggered by active power exceeding limits; the latter two can be decomposed by... , By directly calculating the expected consequences, the "probability → consequence" relationship is unified, thereby improving the engineering consistency of risk ranking.

[0352] The risk-aware minimum load shedding-reconfiguration joint optimization model consists of a risk-aware objective function and constraints.

[0353] Risk perception objective function establishment:

[0354] Constructing a network and incident set:

[0355] (94);

[0356] In the formula, This is a diagram of the power distribution network topology. For a set of nodes, For branch road collection, For a fault branch index, Let be the set of directed arcs induced by each undirected branch. For node indexing.

[0357] Establish accident Risk perception objective function:

[0358] (95);

[0359] In the formula, For the accident The set of all decision variables, For the accident Lower the risk perception target value. , , The consequences of line outages resulting in direct load loss, undervoltage secondary load shedding, and branch overload tripping resulting in secondary load loss are measured respectively. >0 represents the weighting of the three types of consequences.

[0360] The direct consequences of service interruption and loss of supply:

[0361] (96);

[0362] In the formula, >0 represents the load importance coefficient of node i. The load supply ratio at node k after the accident. The active power load requirement for node i.

[0363] For the consequences of undervoltage-triggered secondary load shedding driven by voltage PDF:

[0364] (97);

[0365] In the formula, Let be the expected cutoff ratio triggered by undervoltage and load shedding at node i under accident k. The set of nodes participating in the undervoltage load reduction assessment.

[0366] (98);

[0367] In the formula, Let i be the random variable representing the voltage amplitude at node i under accident k. for The probability density function, It is the integral variable.

[0368] For undervoltage load shedding trigger function:

[0369] (99);

[0370] In the formula, This represents the lower limit of the allowable voltage at node i. Set the threshold for triggering "full cut-off" of node undervoltage load reduction.

[0371] The consequences of secondary power supply failure triggered by the overload protection tripping of the branch active power PDF:

[0372] (100);

[0373] In the formula, For branch index, This represents the on / off state of branch e after accident k (1 closed, 0 open). The probability of branch e's protection tripping within the evaluation time window after accident k. This measures the downstream load loss caused by the tripping of branch line e.

[0374] (101);

[0375] In the formula, The active power exceeding the limit tail probability index for branch e. The risk intensity coefficient for branch circuit e tripping. This refers to the length of the risk assessment time window.

[0376] (102);

[0377] In the formula, The active power threshold for protection tripping of branch e in the reference direction. Let e ​​be the active power flow random variable in the reference direction of branch e under accident k. for The probability density function, It is the integral variable.

[0378] (103);

[0379] In the formula, This refers to the set of downstream nodes in the power supply structure after accident k that are disconnected by branch e. This is the boundary for the load supply guarantee ratio.

[0380] The constraints in the risk-aware minimum load shedding-reconfiguration joint optimization model include: branch on / off status and switch operability constraints, post-fault AC power flow equation constraints, node power balance constraints, reactive power compensation equipment model and state variable constraints.

[0381] (a) Regarding the on / off state of the branch circuit and the operability of the switch:

[0382] (104);

[0383] (105);

[0384] In the formula, , is a set of fixed closed branches; This is a collection of interconnecting switch branches.

[0385] (106);

[0386] (107);

[0387] In the formula, Let e ​​be the change in the switching state of branch e after accident k. These are the on / off state parameters of branch e before the accident. This is an auxiliary variable for the switching operation of branch e after accident k.

[0388] (108);

[0389] In the formula, This is the parameter representing the maximum number of switching operations allowed after accident k.

[0390] (b) Post-accident AC power flow equation constraints:

[0391] (109);

[0392] In the formula, For the active power flow at the transmitting end of branch (i, j) after the accident k, Let be the voltage amplitude at node i. The nominal voltage phase angle at the node. , These are the real and imaginary parameters of the series admittance of branch (i, j), respectively.

[0393] (110);

[0394] In the formula, Let (i, j) be the reactive power flow at the transmitting end of the branch (i, j) after the accident (k).

[0395] (c) Node power balance:

[0396] (111);

[0397] This represents the total number of nodes in the distribution network. , These represent the active and reactive power of the generator node, respectively. , These represent the active and reactive power of each load node. For each load node i, the active load is removed under accident k. The voltage phase angle difference between node i and node j. , These are the conductance and susceptance values ​​when the transformation ratio between nodes i and j is 1, respectively. Here, fault k refers to the faulty branch k.

[0398] (d) Reactive power compensation equipment model:

[0399] (112);

[0400] In the formula, For the net reactive power injection after a fault in the reactive power compensation device at node i, The reactive power injection decision quantity for the SVG at node i. This is a set of switchable groups for node capacitor banks. Let m be the switching state of the capacitor at node i. The rated reactive power capacity parameter of the m-th capacitor at node i.

[0401] (113);

[0402] In the formula, , These are the lower and upper bounds for reactive power injection in node SVG / SVC, respectively.

[0403] (114);

[0404] In the formula, This represents the upper limit of the active power output of new energy at node i after the accident (k). The upper limit of reactive power output of new energy at node i after the accident k. The upper limit parameter of the rated apparent power of the node new energy inverter.

[0405] (e) State variable constraints:

[0406] (115);

[0407] In the formula, , These are the lower and upper limits of the node voltage i, respectively.

[0408] (116);

[0409] In the formula, The upper limit parameter for the apparent power capacity of the thermal stability of branch (i, j) is given.

[0410] Step S104: Construct accident landing point weights based on branch failure rates, and then combine them with the post-accident load loss results to calculate the EVAR branch risk contribution and sort each branch to obtain a list of high-risk branches.

[0411] When high-volatility renewable energy penetration, protective actions, and secondary chain reactions are significant, accident losses exhibit heavy-tailed characteristics, and relying solely on expected-type indicators may underestimate the risk of low-probability, high-consequence outcomes. Therefore, this invention introduces Entropic Value-at-Risk (EVaR) to construct a system risk indicator, using branch failure rate as a benchmark. By assigning weights to accident landing points, a unified approach to "probability and consequence" is achieved.

[0412] The total failure rate is obtained by summing the failure rates of each branch in the accident set. The failure rate of each branch is divided by the total failure rate to obtain the normalized weight of that branch as a failure point. Thus, a discrete random variable is defined: its value is the risk perception target value of each accident, and the corresponding probability is the normalized weight.

[0413] The moment generating function of discrete random variables is calculated using the weights of each accident landing point and the risk perception target value; the tail probability parameter is given. The dual expression of EVAR is transformed into a one-dimensional convex optimization problem with respect to the auxiliary variable v. The optimal auxiliary variable v is obtained by one-dimensional search or Newton's method. ;

[0414] Utilizing the optimal auxiliary variable In the original normalized weights of each branch Performing an exponential tilt transformation, we obtain the worst-case accident landing weights in the dual sense of EVAR. This weight automatically amplifies the proportion of branches corresponding to high-consequence accidents compared to the original weight, making risk measurement more sensitive to extreme tail accidents.

[0415] Weight the worst-case scenario for each branch. Its risk perception target value Multiply the results to obtain the EVAR risk contribution of the branch; sort the branches by contribution from largest to smallest and output a list of high-risk branches.

[0416] Normalized weights for accident landing points are constructed from the failure rate:

[0417] (117);

[0418] In the formula, For the accident set, classify the branch faults as one fault. The total failure rate at any given time.

[0419] (118);

[0420] In the formula, Let branch k be the normalized weight of a fault landing point. ≥0, and .

[0421] Baseline system risk indicator, i.e., expected power loss:

[0422] (119);

[0423] In the formula, Let be a random variable representing the system load loss under a single branch fault condition.

[0424] (120);

[0425] In the formula, It is an expected systemic risk indicator used to characterize baseline risk.

[0426] EVaR system risk indicators and contribution ranking:

[0427] Construct the moment generating function:

[0428] (121);

[0429] In the formula, For random variables The moment generating function, These are auxiliary optimization variables for EVAR.

[0430] Define EVAR risk metrics:

[0431] (122);

[0432] In the formula, EVAR system risk indicators For the tail probability parameter, The smaller the value, the more conservative the risk measurement and the more emphasis is placed on extreme accidents.

[0433] (123);

[0434] In the formula, For The KL relative entropy uncertainty set centered on, The weight of the accident landing point after the disturbance within the set.

[0435] (124);

[0436] Allow in information budget The internal probability is redistributed in the worst case, making it more sensitive to tail events and more in line with the conservative scheduling requirements in high-volatility scenarios.

[0437] The EVAR risk index can be obtained by using an algorithm:

[0438] (125);

[0439] This is the optimal solution to a one-dimensional convex optimization problem.

[0440] (126);

[0441] In the formula, For the "worst-case" incident landing point weights in the dual sense of EVAR, Branch index used for summation.

[0442] Therefore, the risk contribution of EVAR is:

[0443] (127);

[0444] according to Sort the branches from largest to smallest to obtain the "tail risk-dominant branch list", which can be used to screen high-risk branches.

[0445] like Figure 2 As shown, the risk ranking system for distribution network branches oriented towards high-penetration new energy sources provided in this embodiment of the invention can be implemented in software. The risk ranking system for distribution network branches oriented towards high-penetration new energy sources includes the following software modules: electrothermal coupling closed-loop module 201, failure rate calculation module 202, accident consequence assessment module 203, and branch risk ranking module 204.

[0446] The following is an introduction to the functions of each software module in the risk ranking system for distribution network branches oriented towards high-penetration renewable energy:

[0447] The electrothermal coupling closed-loop module 201 is used to construct a new energy and load uncertainty model. Without explicitly introducing external meteorological variables, the heat dissipation effect is represented by a constant parameter equivalent linear heat dissipation term, forming a closed-loop coupling of the electric side algebraic power flow and the thermal side slow dynamic balance, and establishing a steady-state closed relationship considering electrothermal coupling.

[0448] The failure rate calculation module 202 is used to calculate the probability density functions of node voltage amplitude, branch active power and branch current square based on the new energy and load uncertainty model, and then calculate the current load rate, power load rate and node voltage over-limit probability. The current load rate is used to characterize the thermal stress inlet and the power load rate is used to characterize the operational constraint tension. The node voltage over-limit probability is introduced as a secondary correction term. At the same time, the steady-state closed relationship of electrothermal coupling is considered to establish a load rate-failure rate mapping model to obtain the branch failure rate.

[0449] The accident consequence assessment module 203 is used to engineer the tail probability of the branch fault rate into the risk accident set for screening, decompose the three sources of the load shedding consequences after the accident into direct load shedding due to line outage, load shedding triggered by low voltage over-limit and load shedding triggered by active power over-limit, construct a joint optimization model of risk perception minimum load shedding and network reconfiguration, and obtain the load loss results after the accident.

[0450] The branch risk ranking module 204 is used to construct the accident landing point weight based on the branch failure rate, and then combine it with the load loss results after the accident to calculate the EVAR branch risk contribution and rank each branch to obtain a list of high-risk branches.

[0451] It should be noted that each module in the risk ranking system for distribution network branches of high-penetration renewable energy in this embodiment corresponds one-to-one with each step in the risk ranking method for distribution network branches of high-penetration renewable energy in the above embodiment, and their specific implementation processes are the same, so they will not be repeated here.

[0452] The structure of the electronic device according to embodiments of the present invention is described in detail below. The electronic device provided in embodiments of the present invention includes: at least one processor, a memory, a user interface, and at least one network interface. The various components in the risk prioritization system for distribution network branches oriented towards high-penetration renewable energy are coupled together through a bus system. It can be understood that the bus system is used to realize the connection and communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus. The user interface may include a display, keyboard, mouse, trackball, click wheel, buttons, a touchpad, or a touch screen, etc.

[0453] It is understood that the memory can be volatile memory or non-volatile memory, or both. The memory in this embodiment of the invention is capable of storing data to support the operation of the terminal. Examples of this data include any computer programs used to operate on the terminal, such as operating systems and applications. The operating system includes various system programs, such as the framework layer, core library layer, driver layer, etc., used to implement various basic services and handle hardware-based tasks. Applications can include various applications.

[0454] In some embodiments, the risk ranking system for distribution network branches oriented towards high-penetration renewable energy provided by this invention can be implemented using a combination of hardware and software. For example, the risk ranking system for distribution network branches oriented towards high-penetration renewable energy provided by this invention can be a processor in the form of a hardware decoding processor, programmed to execute the risk ranking method for distribution network branches oriented towards high-penetration renewable energy provided by this invention. For instance, the processor in the form of a hardware decoding processor can employ one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0455] As an example, a processor can be an integrated circuit chip with signal processing capabilities, such as a general-purpose processor, a digital signal processor (DSP), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., where a general-purpose processor can be a microprocessor or any conventional processor, etc.

[0456] As an example of the hardware implementation of the risk ranking system for distribution network branches with high penetration of new energy provided in this embodiment of the invention, the device provided in this embodiment of the invention can be directly executed by a processor in the form of a hardware decoding processor. For example, it can be executed by one or more application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components to implement the risk ranking method for distribution network branches with high penetration of new energy provided in this embodiment of the invention.

[0457] The memory in this embodiment of the invention is used to store various types of data to support the operation of a risk prioritization system for distribution network branches oriented towards high-penetration renewable energy, or to store data for execution. Figure 1 The program code for the method shown. Examples of this data include: any executable instructions for operation on a risk prioritization system for distribution network branches oriented towards high-penetration renewable energy, such as executable instructions. A program implementing the risk prioritization method for distribution network branches oriented towards high-penetration renewable energy according to embodiments of the present invention can be contained in executable instructions.

[0458] Specifically, according to embodiments of this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program including functions for executing... Figure 1 The program code for the method shown. In such an embodiment, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by the central processing unit, it performs the various functions defined in the apparatus of this application.

[0459] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart. Figure 1 One or more processes and / or boxesFigure 1 A device that provides the functions specified in one or more boxes.

[0460] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A risk ranking method for distribution network branches oriented towards high-penetration renewable energy sources, characterized in that, include: A model for uncertainty of new energy sources and loads is constructed. Without explicitly introducing external meteorological variables, the heat dissipation effect is represented by a constant parameter equivalent linear heat dissipation term, forming a closed-loop coupling of the algebraic power flow on the electric side and the slow dynamic equilibrium on the thermal side, and establishing a steady-state closed relationship that considers the electrothermal coupling. Based on the uncertainty model of new energy and load, the probability density functions of node voltage amplitude, branch active power and branch current square are calculated, and then the current load rate, power load rate and node voltage over-limit probability are calculated. The current load rate is used to characterize the thermal stress inlet and the power load rate is used to characterize the operational constraint tension. The node voltage over-limit probability is introduced as a secondary correction term. At the same time, the steady-state closed relationship of electrothermal coupling is considered to establish a load rate-failure rate mapping model to obtain the branch failure rate. The tail probability of the branch failure rate is engineered and embedded into the risk accident set for screening. The three sources of load shedding consequences after the accident are decomposed into direct load shedding due to line outage, load shedding triggered by low voltage over-limit, and load shedding triggered by active power over-limit. A joint optimization model of risk perception minimum load shedding and network reconfiguration is constructed to obtain the load loss results after the accident. Based on the branch failure rate, the accident landing point weight is constructed. Then, combined with the load loss results after the accident, the EVAR branch risk contribution is calculated and each branch is ranked to obtain a list of high-risk branches.

2. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 1, characterized in that, The process of calculating the probability density functions of node voltage magnitude, branch active power, and branch current square is as follows: Based on the uncertainty model of new energy and load, the predicted net injection vector of new energy and load and its prediction error statistics are obtained, the injection disturbance random vector is constructed, and the disturbance scenario set is generated. Adaptive clustering is performed on the set of perturbation scenarios to divide the perturbation space into several clusters, resulting in the cluster set, cluster weights, and cluster centers; For each cluster center, perform an electrothermal consistent closed-loop iterative power flow solution to form a closed-loop iteration of power flow - branch current square - steady-state temperature rise - temperature-related admittance update - re-power flow until the temperature rise converges, and obtain the electrothermal consistent cluster base point that simultaneously satisfies electrical power flow balance and thermal steady-state balance. At the cluster base point, the AC power flow equation and output mapping are localized to the first order, establishing a linear mapping from intra-cluster injected disturbances to output disturbances. The higher-order intra-cluster moments of node voltage magnitude, branch active power, and branch current square are obtained by semi-invariant propagation. The global higher-order moments are obtained by synthesizing the higher-order moments of each cluster with full probability, and the probability density functions of each output are reconstructed based on the maximum entropy principle of the physical support domain constraint.

3. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 2, characterized in that, The process of performing adaptive clustering segmentation on the perturbed scene set includes: Deterministic power flow is solved and first-order linearization is completed at the center of each cluster. Several direction vectors are selected and finite difference calculation is performed along each direction with a preset step size. The maximum value of the second-order difference value in each direction is obtained for each output component and used as the upper bound estimate of the second-order nonlinear intensity of the output component in the cluster. Calculate the distance from all scene points within the cluster to the cluster center, and take the maximum value as the cluster radius; take half of the product of the second-order nonlinear intensity upper bound estimate and the square of the cluster radius as the worst linearization error upper bound for the output component of the cluster; Take the maximum value of the worst linearization error upper bound among all output components and compare it with the preset linearization error threshold: if the former does not exceed the latter, the cluster passes the acceptance criterion and remains unsubdivided; otherwise, the cluster is further split into smaller clusters, and the above steps are repeated until all clusters meet the acceptance criterion.

4. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 2, characterized in that, The process of performing electrothermal consistent closed-loop iterative power flow solution for each cluster center includes: The conductor temperature offset of all branches is initialized to zero, and the initial impedance of each branch is calculated according to the temperature-dependent resistance model. The initial temperature-dependent node admittance matrix is ​​then assembled. Using the current temperature-dependent admittance matrix as a parameter, the AC power flow equations are solved under the injection conditions corresponding to the center of the cluster to obtain the node voltage magnitude and phase angle of the current iteration; The current phasor of each branch is calculated from the node voltage magnitude and phase angle of the current iteration, and then the square current of each branch is obtained and substituted into the steady-state thermal equilibrium closed solution. Update the conductor temperature offset of each branch, select the maximum difference between the updated temperature offset and the temperature offset of the previous iteration from all branches, and determine whether the maximum value is less than the preset temperature rise convergence threshold. If so, output the current power flow solution and temperature as the electrothermal consistent cluster base point. Otherwise, recalculate the impedance and admittance of each branch based on the updated temperature, reassemble the node admittance matrix, and continue iterative solution until convergence.

5. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 2, characterized in that, The process of reconstructing the probability density function of each output quantity based on the maximum entropy principle constrained by the physical support domain includes: Based on the physical characteristics of the output, support domain constraints are set for various variables: the support domain for node voltage magnitude is set to a non-negative real domain, the support domain for branch active power flow is set to a fully real domain, and the support domain for branch current square is set to a non-negative real domain. For node voltage magnitude and branch active power flow, a maximum entropy optimization problem is directly constructed within their respective support domains with global higher-order moments as constraints. By introducing Lagrange multipliers, the parametric form of the exponential probability density function is obtained. Numerical integration is used to calculate the constraint residuals and Jacobians of each moment, and Newton iteration is used to solve the multiplier parameters to obtain the corresponding probability density function. For the square of the branch current, a logarithmic transformation is first applied to map it to the entire real number domain. The transformed variable is then reconstructed using maximum entropy in the entire real number domain to obtain the probability density function of the transformed domain. Finally, the probability density function is mapped back to the original non-negative domain by multiplying it by the Jacobian factor through the inverse transformation of the variable. This ensures that the reconstructed probability density function is strictly non-negative in the entire domain and does not assign probability mass to the physically infeasible domain.

6. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 1, characterized in that, The process of establishing a load rate-failure rate mapping model to obtain the branch failure rate includes: The statistical description of the current load factor is obtained from the probability density function of the square of the branch current, and the statistical description of the power load factor is obtained from the probability density function of the branch active power. The current load factor is mapped to the corresponding conductor temperature using the steady-state closed relationship of electrothermal coupling, and a deterministic mapping from current load factor to temperature is established. Set piecewise amplification functions in the temperature domain and power load rate domain respectively: when the value is below the alarm threshold, the value is 1 to indicate no amplification; the value increases linearly between the alarm threshold and the limit threshold; and the value continues to increase with a larger slope after the limit threshold is exceeded. The piecewise amplification function in the temperature domain is substituted back through the mapping from current load rate to temperature, and then integrated with the probability density function of the square of the branch current in the non-negative domain to obtain the expected amplification factor of the current / temperature channel; the piecewise amplification function in the power load rate domain is integrated with the probability density function of the active power of the branch in its domain to obtain the expected amplification factor of the power channel. The marginal contribution of each branch to the two types of expected amplification factors relative to the baseline value of 1 is calculated separately. The two types of contributions are then aggregated at the level of all branches in the network, and normalized according to the aggregation ratio to obtain the current / temperature channel weight and the power channel weight. In the logarithmic domain, the two types of expected amplification factors are combined convexly according to their weights to obtain the comprehensive load amplification factor; the voltage over-limit probability of each node is calculated by the probability density function of the node voltage amplitude, and the larger over-limit probability of the nodes at both ends of the branch is taken as the comprehensive voltage over-limit index of the branch, and the coefficient controlled by the upper bound is used as the secondary correction term; the reference failure rate, the comprehensive load amplification factor and the voltage over-limit correction term are multiplied to output the failure rate of each branch.

7. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 1, characterized in that, The process of constructing a joint optimization model for risk-aware minimum load shedding and network reconfiguration to obtain post-accident load loss results includes: Using the branch failure rate or the time window failure probability derived from it, all branches are sorted from highest to lowest failure probability, and branches with failure probabilities higher than a preset threshold are retained to form a set of incidents to be evaluated; For each faulty branch in the incident set, the incident consequences are decomposed into three sources and calculated separately: The first item is the direct load shedding amount due to line outage, which is obtained by determining the power outage status of each node based on the topological connectivity after the accident, and then summing the load demand and importance coefficient of each node. The second item is the load shedding amount triggered by low voltage over-limit, which is obtained by integrating the probability density function of the voltage amplitude of each node after the accident with the segmented undervoltage load shedding trigger function to obtain the expected undervoltage load shedding ratio, and then summing it with the guaranteed load. The third item is the secondary load shedding amount triggered by active power over-limit protection tripping, which is obtained by calculating the tail probability of exceeding the protection threshold using the active power probability density function of each surviving branch after the accident, obtaining the tripping probability of that branch within the evaluation time window, multiplying it by the downstream power outage load after the branch tripping, and then summing it up branch by branch. Using the weighted sum of the above three terms as the objective function, constraints are set and jointly optimized to obtain the optimal load shedding scheme and the corresponding risk perception target value, which serves as the result of the corresponding post-accident load loss.

8. The risk ranking method for distribution network branches oriented towards high-penetration new energy sources as described in claim 1, characterized in that, The risk contribution of the EVAR branch is: ； ； In the formula, Contribution to EVAR branch risk; For the worst-case accident landing point weights in the dual sense of EVAR; For branch index; For branch set; branch road As a normalized weight for a single fault landing point; Let branch k be the normalized weight of a fault landing point; For the faulty branch Risk perception target value; For the faulty branch Risk perception target value; v It is the optimal auxiliary variable.

9. A risk ranking system for distribution network branches oriented towards high-penetration renewable energy sources, characterized in that, The risk ranking method for distribution network branches oriented towards high-penetration new energy sources, based on any one of claims 1-8, includes: The electrothermal coupling closed-loop module is used to construct a new energy and load uncertainty model. Without explicitly introducing external meteorological variables, the heat dissipation effect is represented by a constant parameter equivalent linear heat dissipation term, forming a closed-loop coupling of the electric side algebraic power flow and the thermal side slow dynamic balance, and establishing a steady-state closed relationship considering electrothermal coupling. The failure rate calculation module is used to calculate the probability density functions of node voltage amplitude, branch active power and branch current square based on the new energy and load uncertainty model. Then, it calculates the current load rate, power load rate and node voltage over-limit probability. The current load rate is used to characterize the thermal stress inlet and the power load rate is used to characterize the operational constraint tension. The node voltage over-limit probability is introduced as a secondary correction term. At the same time, the steady-state closed relationship of electrothermal coupling is considered to establish a load rate-failure rate mapping model to obtain the branch failure rate. The accident consequence assessment module is used to engineer the tail probability of the branch failure rate into the risk accident set for screening, decompose the three sources of the load shedding consequence after the accident into direct load shedding due to line outage, load shedding triggered by low voltage over-limit and load shedding triggered by active power over-limit, construct a joint optimization model of risk perception minimum load shedding and network reconfiguration, and obtain the load loss result after the accident. The branch risk ranking module is used to construct the accident landing point weight based on the branch failure rate, and then combine it with the load loss results after the accident to calculate the EVAR branch risk contribution and rank each branch to obtain a list of high-risk branches.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the risk ranking method for distribution network branches for high-penetration new energy sources as described in any one of claims 1-8.

Images