Extreme scene cascading failure modeling method considering new energy uncertainty

Abstract

The invention relates to an extreme scene cascading failure modeling method considering new energy uncertainty, and belongs to the field of power system disaster simulation early warning. The extreme scene of the method is a typhoon scene, and the method comprises the steps: carrying out the cascading fault simulation of a power grid in the typhoon scene, determining the disconnection condition of a line at each time point based on the wind-induced fault rate of each line at each time point in the typhoon scene, and forming a wind-induced fault set; the wind-induced fault set is traversed, cascading faults caused by the wind-induced faults at each time point are calculated based on the disconnection condition of each line and the corresponding wind power output, and the cascading faults comprise the wind-induced faults and line disconnection faults caused by one or more thermal overload; and determining a key line in the power grid based on cascading failures in multiple simulations. According to the method, cascading failures under typhoon weather are simulated through double time scales (the typhoon scale and the cascading failure time scale), and the influence of the cascading failures caused by typhoon on the power grid is accurately evaluated.

Description

Technical Field

[0001] The present invention relates to the technical field of power system disaster simulation and early warning, and in particular to a method for modeling extreme scenario cascading failures taking into account the uncertainty of new energy sources. Background Art

[0002] As global climate change intensifies, extreme weather events such as typhoons, heavy rains, and high temperatures are increasingly impacting power systems. Typhoon-prone regions, in particular, face significant challenges. Typhoons not only directly damage infrastructure such as transmission lines and substations but can also impact the output of renewable energy sources like wind power, increasing system uncertainty and potentially triggering cascading failures. Furthermore, with the large-scale integration of renewable energy sources, particularly wind power, the operating characteristics of the power system have changed significantly. The intermittent and uncertain nature of these changes poses new challenges to the system's stable operation.

[0003] In the field of power system disaster simulation and early warning, research on the impact of extreme weather and the uncertainty of renewable energy sources is gradually increasing. Existing research mainly focuses on the direct impact of extreme weather such as typhoons on the physical facilities of the power system, while there is relatively little research on the uncertainty of renewable energy output such as wind power and its impact on system cascading failures. In addition, existing assessment methods often lack dynamic simulation of the evolution process of cascading failures, making it difficult to accurately assess the impact of failures on the system. In summary, the existing power system cascading failure assessment methods have the following main shortcomings: First, there is a lack of comprehensive consideration of the impact of extreme weather, especially the assessment of the uncertainty of renewable energy output such as wind power; second, there is a lack of dynamic simulation of the evolution process of cascading failures, making it difficult to accurately assess the impact of failures on the system; third, there is a lack of identification of key components, making it difficult to provide a scientific basis for the reinforcement and optimization of the power grid. Summary of the Invention

[0004] In view of the above analysis, the present invention aims to disclose a method for modeling cascading failures in extreme scenarios that takes into account the uncertainty of new energy sources, simulate the impact of extreme weather such as typhoons on the power system, evaluate the uncertainty of the output of new energy sources such as wind power, and accurately evaluate the impact of failures on the system by dynamically simulating the evolution process of cascading failures.

[0005] The present invention discloses a method for modeling cascading failures in extreme scenarios taking into account the uncertainty of new energy sources, which specifically includes the following steps:

[0006] S1. Simulate cascading failures of the power grid under a typhoon scenario. Determine the disconnection status of each line at each time point based on the wind-induced failure rate of each line at each time point under the typhoon scenario. Construct a wind-induced fault set based on the disconnection status of each line at each time point.

[0007] S2. Traverse the wind-induced fault set and calculate the cascading faults caused by the wind-induced faults at each time point based on the disconnection status of each line and the corresponding wind power output. The cascading faults include wind-induced faults and line disconnection faults caused by thermal overload.

[0008] A critical line in the power grid is determined based on the calculated cascading failures.

[0009] Furthermore, determining the disconnection status of each line at each time point based on the wind-induced failure rate of each line at each time point in the typhoon scenario, and forming a wind-induced fault set based on the disconnection status of each line at each time point includes:

[0010] An improved Batts interval model is constructed based on the Batts typhoon model;

[0011] The wind-induced failure rate of each line at each time point is calculated based on the Batts interval model, and a failure rate matrix is ​​constructed based on the wind-induced failure rate of each line at each time point;

[0012] Randomly generate a sampling matrix that follows a uniform distribution and has the same size as the failure rate matrix, and determine whether the line is disconnected at each time point based on the subtraction result of the sampling matrix and the failure rate matrix; wherein, if the subtraction result is less than zero, it is determined that the corresponding line at the corresponding time point is disconnected;

[0013] A wind-induced fault set is constructed based on the disconnection conditions of the corresponding lines at the corresponding time points.

[0014] Furthermore, the wind-induced failure rate of each line at each time point calculated based on the Batts interval model includes:

[0015] Each route is divided into multiple segmented routes, and the effective wind speed at the center point of each segment of the route at each time point is calculated based on the Batts interval model;

[0016] Calculating the wind-induced failure rate of each segmented line at each time point based on the effective wind speed;

[0017] The wind-induced failure rate of each line at each time point is calculated based on the wind-induced failure rate of all segmented lines of each line at each time point.

[0018] Furthermore, the traversal of the wind-induced fault set and the calculation of the chain failures caused by the wind-induced faults at each time point based on the disconnection status of each line and the corresponding wind power output at each time point include:

[0019] Traverse each time point of the wind-induced fault set and perform the following steps at each time point:

[0020] a. Determine whether the power grid system is disconnected based on the disconnection status of each line;

[0021] b. Divide the power grid into at least one independent network based on the split situation, and calculate the random power flow of each independent network at the time corresponding to the split situation based on the wind power output and the minimum load shedding of each independent network;

[0022] c. calculating the disconnection time of each thermally overloaded circuit based on the random power flow;

[0023] d. Based on the comparison of the next time point of the wind-induced fault set with the disconnection time of each thermally overloaded circuit, the earliest time point is selected as the time point of the next disconnected circuit. If the next disconnected circuit is still a thermally overloaded circuit, execute steps a to b; otherwise, start traversing the next time point of the wind-induced fault set.

[0024] Furthermore, the calculation method of the wind power output corresponding to each time point includes:

[0025] Determine the wind speed range at the location of the wind turbine based on the Batts interval model;

[0026] Determine a probability density function of wind power output based on the wind speed range, the cut-in wind speed, and the cut-out wind speed of the wind turbine;

[0027] The wind power output at each time point is determined based on the probability density function.

[0028] Furthermore, the calculating the disconnection time of each thermally overloaded circuit based on the random power flow includes:

[0029] Based on the semi-invariant method, the probability density function of the active power of each line is obtained;

[0030] Based on the probability density function of the active power, an inverse transformation method is used to sample and obtain the active power of each sampling point of each line;

[0031] The disconnection time corresponding to each sampling point is calculated based on the active power of each sampling point of each line and the rated power of the corresponding line;

[0032] The disconnection time of the corresponding thermal overload circuit is determined based on the disconnection time corresponding to each sampling point.

[0033] Furthermore, the probability density function p(x) of the active power of each line is expressed as:

[0034]

[0035] in, is the standard normal probability density function; is a standardized random variable, μ and σ are the expected value and standard deviation of the random variable distribution respectively; g v, v∈[3,4,5,6...] is the standardized semi-invariant, H r (x), r=3,4,5,6,... are Hermite polynomials.

[0036] Furthermore, the disconnection time of the thermal overload circuit is calculated as follows:

[0037]

[0038] Where, Δt cut,j represents the disconnection time of the thermal overload line; lh is the simulation step length of the interval of statistical sampling points; i is the i-th sampling point of line j; SA is the sampling point set; function is an indicator function, which is 1 when SA∈[i·lh,(i+1)·lh), otherwise it is 0; (Δt cut,i,j ) is the disconnection time of the i-th sampling point of line j, o j,max is the power flow limit of line j, that is, the active power limit; j (t, Δt) is the heat accumulation of line j from time t to Δt; X s,i,j is the active power of the i-th sampling point of line j; C j Indicates the rated power of line j.

[0039] Furthermore, determining a critical line in the power grid based on the calculated cascading failures includes:

[0040] Based on the calculated cascading failures, a plurality of index values ​​are calculated, wherein the index values ​​include a probability of occurrence of a cascading failure, a number of occurrences of a kr-order cascading failure, an average cascading failure order, an average number of failure paths, an average number of load losses, and a maximum number of load losses;

[0041] Calculating an importance metric value for each route based on any of the index values;

[0042] Critical lines in the power grid are determined based on the importance metrics of the lines.

[0043] Furthermore, the calculating of the importance metric value of each route based on any of the indicator values ​​includes:

[0044]

[0045] Among them, FV j is the importance metric value of line j; RM0 is any of the above index values; RM j In each simulation, line j is set to the corresponding index value calculated so that the line will never be disconnected due to thermal overload.

[0046] The present invention can achieve at least one of the following beneficial effects:

[0047] By constructing a Batts interval model based on the Batts typhoon model, the impact of typhoon weather on power system lines and wind turbines is simulated, accurately describing the effect of typhoons on grid components and the uncertainty of wind power output, laying the foundation for subsequent simulation analysis and improving the accuracy of simulation analysis results.

[0048] By using the semi-invariant method to model the random power flow, the impact of the randomness of wind power output on the system power flow is considered. Through random power flow analysis, a line overload time accumulation model is established to determine the line overheating tripping situation.

[0049] By combining the typhoon time scale with the cascading failure time scale, the evolution process of cascading failures is dynamically simulated, and the impact of wind power uncertainty and cascading failures on the power system under typhoon conditions is effectively evaluated.

[0050] By identifying critical lines (components) based on the Fussell-Vesely (FV) importance metric, a basis is provided for the reinforcement and optimization of the power grid.

[0051] Other features and advantages of the present invention will be described in the following description, and some advantages may become apparent from the description or be understood through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0053] Figure 1 Flow chart of the method of the present invention;

[0054] Figure 2 This is a schematic diagram of the typhoon wind field structure under the Batts model;

[0055] Figure 3 Schematic diagram of the interaction between typhoons and transmission lines. DETAILED DESCRIPTION

[0056] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0057] Example 1

[0058] One embodiment of the present invention discloses a method for modeling cascading failures in extreme scenarios that takes into account the uncertainty of new energy sources, wherein the extreme scenario refers to a typhoon scenario, and specifically includes steps S1 and S2.

[0059] S1. Perform a cascading failure simulation on the power grid under a typhoon scenario. Determine the disconnection status of the line at each time point based on the wind-induced failure rate of each line at each time point under the typhoon scenario. Construct a wind-induced fault set based on the disconnection status of each line at each time point.

[0060] It should be noted that the method of the present invention performs multiple cascading failure simulations on the power grid under a typhoon scenario, and the operation of step S1 needs to be performed in each simulation.

[0061] Specifically, step S1 includes steps S11-S14.

[0062] S11. Construct an improved Batts interval model based on the Batts typhoon model.

[0063] Specifically, in the Batts model (such as Figure 2 As shown in the figure, an asymmetric auxiliary function is added to convert it into interval form to obtain the improved Batts interval model, which is expressed as:

[0064]

[0065] in, and They are the distances from the typhoon center less than R in the improved Batts interval model. max and the distance from the typhoon center is greater than R max The wind speed at the point; V r,in With V r,out The distance from the typhoon center to the Batts model is less than R max and the distance from the typhoon center is greater than R max The wind speed at the point is r, and r is the distance between the studied location and the typhoon center.

[0066] ψ f (r) is an asymmetric rational function, which is expressed as:

[0067]

[0068] in, Both are shape parameters, which can be obtained by fitting the wind speed of actual typhoon records and the Batts typhoon model.

[0069] Furthermore, the wind speed V in the Batts typhoon model r,in With V r,out The calculation method is:

[0070]

[0071] Among them, R max is the typhoon's maximum wind speed radius, is the maximum wind speed of the typhoon, that is, within the maximum wind speed radius R max χ is the wind speed decreasing index, which is used to describe the rate at which the wind speed decreases with increasing distance from the typhoon center.

[0072] S12: Calculate the wind-induced failure rate of each line at each time point based on the Batts interval model, and construct a failure rate matrix consisting of the wind-induced failure rate of each line at each time point. This specifically includes S121-S214.

[0073] S121. Each line is divided into multiple segmented lines, and the effective wind speed at the center point of each segmented line at each time point is calculated based on the Batts interval model. Specifically, each line refers to a line connecting two power grid system nodes. Each line is divided into multiple segmented lines according to the number of wires that make up each line, that is, each segmented line corresponds to one wire. For each line, its failure rate is composed of the failure rates of the corresponding multiple segmented lines. The failure rate of each segmented line is determined by the effective wind speed at the midpoint of the segmented line.

[0074] Specifically, for time point t, the calculation method of the effective wind speed at the center point of each segment line is:

[0075]

[0076] in, is the lower limit of the effective wind speed at the nth segment line; is the upper limit of the effective wind speed at the nth segment line; R a The radius inside the typhoon is selected for auxiliary calculation; R max is the maximum wind speed radius of the typhoon; r n (t) is the distance between the typhoon center and the center point (x, y) of the nth segment transmission line at time t; ζ 1,max and ζ 1,min is the upper and lower limits of the wind speed on the maximum wind speed radius of the time section t; 2,max and ζ 2,min are the upper and lower limits of the wind speed along the radius in the time section t; sinβ(t) is the coefficient of the influence of wind direction on wind load; β(t) is the angle between the typhoon wind direction and the transmission line (such as Figure 3 shown); The coordinates of the center of the typhoon wind circle.

[0077] S122. Calculate the wind-induced failure rate of each segmented line at each time point based on the effective wind speed.

[0078] Specifically, the calculation method of the wind-induced failure rate of the nth segment line is:

[0079]

[0080] Among them, λ n (t) represents the wind-induced failure rate of the nth segment line at time t; represents the calculated value of the wind-induced failure rate of the nth segment line at time t, without minimum value processing; v d represents the design wind speed, i.e. the wind speed value used as a reference during line design; φ1 and φ2 are model parameters used to calculate the wind-induced failure rate; and They represent the typical maximum and minimum values ​​of wind load on the n-th line at time t respectively; It represents the wind load impact factor of the n-th line, which is used to calculate the failure rate.

[0081] S123. Calculate the wind-induced failure rate of each line at each time point based on the wind-induced failure rate of all segmented lines of each line at each time point.

[0082] Specifically, for each line, the method for calculating the wind-induced failure rate of the line is:

[0083]

[0084] Among them, λ l represents the wind-induced failure rate of line l; i represents the i-th segment line of line l.

[0085] It should be noted that the wind-induced failure rates at each time point obtained at this time are used as typhoon time-scale data in this application for application in subsequent simulations.

[0086] S124. Construct a failure rate matrix based on the wind-induced failure rate of each line at each time point.

[0087] Each element in the failure rate matrix represents the wind-induced failure rate of line l at time point t.

[0088] S13. Use a randomly generated sampling matrix that obeys a uniform distribution and has the same size as the failure rate matrix, and determine whether the line is disconnected at each time point based on the subtraction result of the sampling matrix and the failure rate matrix. If the subtraction result is less than zero, it is determined that the corresponding line at the corresponding time point is disconnected.

[0089] Specifically, when randomly generating a sampling matrix that obeys a uniform distribution, the size of each matrix element depends on the range of the specified uniform distribution. For example, the distribution range is [0, 1].

[0090] S14. Construct a wind-induced fault set based on the disconnection status of the corresponding lines at each time point.

[0091] Specifically, the positions where the subtraction result in the matrix is ​​less than zero are marked as 0, indicating that the corresponding line is disconnected at the corresponding time point, and the other positions are marked as 1, indicating that the corresponding line has no fault. The resulting matrix is ​​used as the wind-induced fault set obtained in this simulation.

[0092] S2. Traverse the wind-induced fault set and calculate the cascading faults caused by the wind-induced faults at each time point based on the disconnection status of each line and the corresponding wind power output at each time point. The cascading faults include wind-induced faults and line disconnection faults caused by thermal overload; determine the critical lines in the power grid based on the calculated cascading faults.

[0093] Specifically, step S2 includes steps S21-S22.

[0094] S21. Calculating the wind power output at each time point based on the Batts interval model, specifically including S211-S213.

[0095] S211, determining the wind speed range at the location of the wind turbine based on the Batts interval model;

[0096] Specifically, the wind speed range at the location of the wind turbine is calculated according to step S11.

[0097] S212: Determine a probability density function of wind power output based on the wind speed range, the cut-in wind speed, and the cut-out wind speed of the wind turbine generator.

[0098] Specifically, let time point T typoon,i When the fan Wind k The wind speed range is [v pmin ,v pmax ].

[0099] The output model of the wind turbine is expressed as:

[0100]

[0101] Among them, P wv is the target wind turbine output power; P n,wind is the target wind turbine rated power; v ci is the target wind turbine cut-in wind speed; v r The target wind turbine cut-out wind speed.

[0102] In the case of a typhoon, the output power of the wind farm will fluctuate greatly due to the drastic change in wind speed, and is directly related to the typhoon intensity, movement path and wind speed distribution. Therefore, the output model is expanded to an interval output model. At the i-th time point T during the typhoon, the output power of the wind farm will fluctuate greatly.typoon,i , the power model of wind turbines affected by typhoon is derived as follows:

[0103] First, transform the wind speed interval into a normal distribution with mean and standard deviation:

[0104]

[0105] Furthermore, the wind turbine output probability P is calculated wind,out , P wind,out It is divided into two parts: the continuous part and the continuous part.

[0106] Among them, the discrete part is the value when the wind power is 0, P wind,out (p=0) represents the probability that the wind turbine output power is 0, and its probability mass is:

[0107]

[0108] Where Φ() is the cumulative distribution function of the standard normal distribution.

[0109] The continuous part describes the output power belonging to (0,P n,wind ], its probability density is:

[0110]

[0111] in, φ is the probability density function of the standard normal distribution, P n Indicates the rated power of wind power.

[0112] Furthermore, the power distribution has both discrete and continuous parts. Considering the computational cost of the subsequent cascading failure modeling process, the power distribution is simplified here and the converted wind turbine output load beta distribution is directly assumed, which is expressed as:

[0113]

[0114] Where Γ(*) is the gamma function.

[0115] P wind,out Perform nw random samplings to obtain the sample set {x wind,out,1 ,x wind,out,2 ,...,x wind,out,nw}, construct the maximum likelihood function to estimate it:

[0116]

[0117] Taking the logarithm and finding the maximum gives the parameter estimate Finally, we get the wind power at typhoon time point T typoon,iThe probability density function of the wind turbine output power is expressed as:

[0118]

[0119] S213: Determine the wind power output at each time point based on the probability density function.

[0120] Specifically, based on Determine the wind power output at each time point.

[0121] It should be noted that the probability density function comprehensively considers the coupling effect of extreme meteorological conditions on wind speed fluctuations and wind turbine output, and can more accurately reflect the power output characteristics of wind turbines under typhoon interference.

[0122] S22. Traverse the wind-induced fault set, and calculate the chain failure caused by the wind-induced fault at each time point based on the disconnection status of each line at each time point and the corresponding wind power output.

[0123] Specifically, traverse each time point of the wind-induced fault set and perform the following steps (ad) at each time point:

[0124] a. Determine whether the power grid system is disconnected based on the disconnection status of each line;

[0125] b. Divide the power grid into at least one independent network based on the splitting condition, and calculate the random power flow of each independent network at the time point corresponding to step a based on the wind power output and the minimum load shedding of each independent network; that is, when there is no splitting condition, the power grid is regarded as an independent network; when there is a splitting condition, the power grid is divided into two or more independent networks based on the disconnection condition;

[0126] c. calculating the disconnection time of each thermally overloaded circuit based on the random power flow; specifically, determining whether the circuit is overheated based on a comparison of the random power flow with the maximum allowable load of the circuit, and calculating the disconnection time of the thermally overloaded circuit;

[0127] d. Based on the comparison of the next wind-induced fault time point in the wind-induced fault set with the disconnection time of each thermally overloaded circuit, the earliest time point is selected as the time point of the next disconnected circuit. If the next disconnected circuit is still a thermally overloaded circuit, steps ad are executed; otherwise, the next time point of the wind-induced fault set is traversed.

[0128] Specifically, in step c, the calculation of the disconnection time of each thermal overload circuit includes c1-c4:

[0129] c1. Obtain the probability density function of the active power of each line based on the semi-invariant method;

[0130] c2. Based on the probability density function of the active power, an inverse transformation method is used to sample and obtain the active power of each sampling point of each line;

[0131] c3. Calculate the disconnection time corresponding to each sampling point based on the active power of each sampling point on each line and the rated power of the line;

[0132] c4. Determine whether the line is a thermally overloaded line based on the disconnection time corresponding to each sampling point, and calculate the disconnection time of the line.

[0133] Specifically, in C1, the semi-invariant method is used to quantify the uncertainty brought by renewable energy and load. In power system analysis, the linearized polar coordinate node power equation can be simplified as:

[0134]

[0135] Where ΔX is the change in node state, including node voltage and node phase angle; J0 is the Jacobian matrix; S0 is the sensitivity matrix; ΔW is the disturbance of node injection power, which is the difference between the active and reactive power input in the power flow calculation and the active and reactive power during the iterative process of the power flow calculation.

[0136] Similarly, the branch power flow equation can be simplified as:

[0137] ΔZ=G0S0ΔW=T0ΔW;

[0138] Where ΔZ is the change in branch state, including line active and reactive power; G0 is the first-order partial derivative of the branch power flow vector with respect to the node state vector; and T0 is the coefficient matrix of the line power flow with respect to the change in injected power.

[0139] The k-order semi-invariants of state variables such as voltage amplitude and line active power can be calculated by the following formula:

[0140]

[0141] Where ΔX (k) The kth-order semi-invariant representing state variables such as voltage amplitude and line active power; represents the kth-order derivative of the sensitivity matrix, which is used to describe the sensitivity of the state variable to the power disturbance injected by the node; ΔW (k) represents the kth order disturbance of the node injection power; ΔZ (k) Represents the kth order semi-invariant of the branch state quantity; The k-th derivative of the coefficient matrix representing the line power flow to the injection power change is used to describe the sensitivity of the branch state quantity to the node injection power disturbance.

[0142] Furthermore, the Gram-Charlie series expansion is used to obtain the probability density function of the active power of each line, which is expressed as:

[0143]

[0144] in, is the standard normal probability density function; is a standardized random variable, μ and σ are the expected value and standard deviation of the random variable distribution respectively; g v , v∈[3,4,5,6...] is the standardized semi-invariant, H r (x), r=3,4,5,6,... are Hermite polynomials.

[0145] Specifically, in c2, for the jth line at time t, the inverse transformation method is used for sampling, that is, Z is uniformly sampled in the interval [0,1]. c data points, and calculate the sampling point X through the inverse function of the probability distribution function s,i,j (i∈SA=[1,2,3,...,Z c ]), where s indicates that this is a sampling point, i indicates that this is the i-th sampling point, and j indicates line j.

[0146] Specifically, in c3, the disconnection time corresponding to each sampling point is calculated based on the active power of each sampling point of each line and the rated power of the line;

[0147]

[0148] Δt cut,i,j is the disconnection time of the i-th sampling point of line j, o j,max is the power flow limit of line j, that is, the active power limit; j (t, Δt) is the heat accumulation of line j from time t to Δt; X s,i,j is the active power of the i-th sampling point of line j; C j Indicates the rated power of line j.

[0149] Further,

[0150] It means that when the line current exceeds the current limit by 50% and lasts for 5s, it is considered to have reached the breaking limit.

[0151] Further,

[0152] o j (t, Δt) is the cumulative heat of line j from time t to Δt; F j(t) is the line active power value of line j at time t; Δt is the cumulative time from the occurrence of overload on line j to the current time section.

[0153] Specifically, in c4, whether the line is a thermally overloaded line is determined based on the disconnection time corresponding to each sampling point, and the disconnection time of the line is calculated.

[0154] Specifically, if the calculation results of each sampling point are all ∞, it means that the line is not thermally overloaded. Otherwise, the line is a thermally overloaded line, and the disconnection time of the thermally overloaded line is calculated as follows:

[0155]

[0156] Where, Δt cut,j represents the disconnection time of the thermal overload line; lh is the simulation step length of the interval of statistical sampling points; i is the i-th sampling point of line j; SA is the sampling point set; function is an indicator function, which is 1 when SA∈[i·lh,(i+1)·lh), and 0 otherwise.

[0157] Specifically, in step S22, the above are all steps for calculating the chain failures caused by wind-induced faults at each time point based on the disconnection status of each line and the wind power output at each time point. During the calculation process, the time corresponding to the chain failure (the chain failure includes the wind-induced fault and the line disconnection fault caused by one or more thermal overloads) is obtained (the sum of the time intervals of the wind-induced fault and the line disconnection fault caused by one or more thermal overloads), which is called the chain failure time scale in this application.

[0158] Furthermore, the method for modeling cascading failures in extreme scenarios taking into account the uncertainty of new energy sources disclosed in the present invention also includes step S3, determining the critical lines in the power grid based on the calculated cascading failures.

[0159] It should be noted that steps S1 and S2 represent a single simulation of cascading failures in a power grid under a typhoon scenario. In the present invention, multiple Monte Carlo simulations are performed based on steps S1 and S2. The sampling matrix randomly generated using a uniform distribution in S13 is different in each simulation, and the result obtained by subtracting the failure rate matrices is also different. By performing multiple simulations, bias can be avoided, more scenarios can be covered, statistical reliability can be improved, and the robustness of the simulation can be further enhanced.

[0160] Specifically, step S3 includes S31-S32.

[0161] S31. Calculate the importance metric of each line based on all cascading failures in the simulation, including:

[0162] Based on all the cascading failures in the simulation, multiple index values ​​are calculated, including the probability of cascading failures, the number of kr-order cascading failures, the average cascading failure order, the average number of failure paths, the average number of load losses, and the maximum number of load losses;

[0163] An importance metric value of each route is calculated based on any of the index values.

[0164] Furthermore, the probability of cascading failures N err The calculation method is:

[0165]

[0166] Among them, n turn is the total number of simulations, Co1 i Indicates whether a cascading failure occurs during the i-th Monte Carlo simulation. It is 1 if a cascading failure occurs, otherwise it is 0.

[0167] Furthermore, the number of occurrences of kr-order cascading failures N kr The calculation method is:

[0168]

[0169] Among them, Co2 kr,i is the count of kr-order cascading failures during the i-th Monte Carlo simulation; kr refers to the sum of all fault lines from the initial fault line, the middle fault lines to the last fault line in the fault chain, that is, the lowest-order 2-order cascading failure.

[0170] Furthermore, the average cascading failure order The calculation method is:

[0171]

[0172] kr max is the highest order of cascading failures that occur during the simulation process; the average cascading failure order represents the ratio of the sum of the lengths of all fault chains in all Monte Carlo simulations to the total number of Monte Carlo simulations.

[0173] Furthermore, the average number of failure paths is calculated as follows:

[0174]

[0175] N we,i is the number of disconnections caused by wind failure in the i-th simulation; N ce.i is the number of disconnections caused by cascading failures in the i-th simulation.

[0176] Furthermore, the average load loss number The calculation method is:

[0177]

[0178] ΔP loss,i is the number of load losses in the i-th simulation; L i is the set of load nodes of the system in the initial state in the i-th simulation; L' i is the set of load nodes of the system after the simulation ends in the i-th simulation; P l,i and P l',i are the system loads at the initial and final states in the i-th simulation, respectively.

[0179] Furthermore, the maximum load loss number ΔP loss，max The calculation method is:

[0180]

[0181] Specifically, the calculation formula for calculating the importance metric value (FV metric) of each line based on any of the index values ​​is:

[0182]

[0183] Among them, FV j is the importance metric value of line j; RM0 is any of the above index values; RM j The corresponding index value is calculated so that in each simulation, line j is set to never be disconnected due to thermal overload, that is, when traversing the wind-induced fault set in step S2 in each simulation, line j is set to never be disconnected due to thermal overload.

[0184] S32. Determine a critical route in the power grid based on the importance metric value of each route.

[0185] Specifically, the FV measurement results can directly reflect the criticality of components. The larger the FV measurement, the more critical the line is. By selecting lines with significantly higher FV measurements than other lines for upgrade and maintenance, the network's resistance to typhoons can be improved.

[0186] This embodiment constructs a Batts interval model based on the Batts typhoon model to simulate the impact of extreme weather such as typhoons on power system lines and wind turbines. It accurately describes the effects of typhoons on grid components and the uncertainty of wind power output, lays the foundation for subsequent simulation analysis, and improves the accuracy of simulation analysis results.

[0187] By using the semi-invariant method to model the random power flow, the impact of the randomness of wind power output on the system power flow is considered. Through random power flow analysis, a line overload time accumulation model is established to determine the line overheating tripping situation.

[0188] By combining the typhoon time scale with the cascading failure time scale, the evolution process of cascading failures is dynamically simulated, and the impact of wind power uncertainty and cascading failures on the power system under typhoon conditions is effectively evaluated.

[0189] By identifying critical lines (components) based on the Fussell-Vesely (FV) importance metric, a basis is provided for the reinforcement and optimization of the power grid.

[0190] Example 2

[0191] A specific embodiment of the present invention discloses simulation results of a method for modeling extreme scenario cascading failures that takes into account the uncertainty of new energy sources.

[0192] Specifically, to study the impact of wind farms on cascading failures during typhoon-induced disasters, an original IEEE RTS79 system without wind farms was set up as a control group. Simulation conditions for both scenarios were identical, except for the grid structure. 5,000 cascading failure simulations were performed in each scenario under a typhoon background. The simulation results are shown in Table 1.

[0193] Table 1 Statistics of impact of cascading failures

[0194]

[0195] Specifically, statistical results show that compared to traditional power systems, power systems with wind power experience an increase in both the frequency and complexity of cascading failures under typhoon conditions. The probability of cascading failures increases by 74.73% when wind power is included. Under typhoon conditions, the uncertainty of wind power affects the power flow transfer process, increasing the likelihood of overload on the transferred lines.

[0196] Statistical results show that the average cascading failure order in the wind power scenario is 14% higher than in the scenario without wind power. The distribution of cascading failure orders shows an increase in the number of fault chains of all orders when wind power is added. The number of fault chains of order 2 and 3 increases by approximately 3,000 and 1,800, respectively, compared to the scenario without wind power. The number of higher-order fault chains increases by dozens of times. In terms of the probability of occurrence of each order of fault chain, the highest probability in both scenarios is the second-order fault chain, with a rate of 76% and 60%, respectively, in the absence and presence of typhoons. This means that the cascading process stops after affecting the next component, demonstrating that the traditional power system's resilience to extreme disasters remains somewhat effective. However, in the wind power system, the probability of fault chains of order 5, 6, 7, and above is 3, 21, and 23 times higher, respectively. The addition of wind power increases the frequency of faults while making higher-order faults more likely to occur. This suggests that the impact of wind power on cascading failures is not limited to the overload value but also exhibits more complex multidimensional characteristics in terms of time and space.

[0197] Judging from the average number of fault paths, the number of faulty lines without wind power is about 6, while the number of faulty lines reaches 8 when wind power is included, which also reflects that the chain failure situation will be more complicated when affected by wind power.

[0198] From the perspective of the average number of load losses, since the proportion of major power outages during the fault simulation process is small, the average number of load losses is small, but the average number of load losses in the scenario with wind power impact is still higher than that without wind power impact.

[0199] Judging from the records of the maximum number of load losses, the most serious losses recorded in the scenario with wind power are five times that of the scenario without wind power, that is, the wind power access system is more affected by the typhoon, which will cause more serious chain failure consequences.

[0200] This embodiment simulates a method for modeling cascading failures in extreme scenarios that takes into account the uncertainty of new energy sources. Using a control group without wind power, the simulation verifies that when the power system includes wind turbines, the uncertainty of wind power under the influence of typhoons will affect the power flow transfer process, increasing the frequency of failures while making high-order failures more likely to occur, and exhibiting more complex multi-dimensional characteristics in time and space dimensions. Therefore, the present invention provides a method for modeling cascading failures in extreme scenarios that takes into account the uncertainty of new energy sources, evaluates the uncertainty of the output of new energy sources such as wind power, and dynamically simulates the evolution of cascading failures. It has a positive effect on simulating the impact of typhoon extreme weather on the power system, and provides a scientific basis for identifying key lines through simulation and strengthening and optimizing the power grid.

[0201] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A method for modeling extreme scenario cascading failures taking into account the uncertainty of new energy sources, characterized by: The extreme scenario is a typhoon scenario, which includes the following steps: S1. Simulate cascading failures of the power grid under a typhoon scenario. Determine the disconnection status of each line at each time point based on the wind-induced failure rate of each line at each time point under the typhoon scenario. Construct a wind-induced fault set based on the disconnection status of each line at each time point. S2. Traverse the wind-induced fault set and calculate the cascading faults caused by the wind-induced faults at each time point based on the disconnection status of each line and the corresponding wind power output. The cascading faults include wind-induced faults and line disconnection faults caused by thermal overload. A critical line in the power grid is determined based on the calculated cascading failures.

2. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy according to claim 1 is characterized in that: The determining of the disconnection status of each line at each time point based on the wind-induced failure rate of each line at each time point in the typhoon scenario, and forming a wind-induced fault set based on the disconnection status of each line at each time point include: An improved Batts interval model is constructed based on the Batts typhoon model; The wind-induced failure rate of each line at each time point is calculated based on the Batts interval model, and a failure rate matrix is ​​constructed based on the wind-induced failure rate of each line at each time point; Randomly generate a sampling matrix that follows a uniform distribution and has the same size as the failure rate matrix, and determine whether the line is disconnected at each time point based on the subtraction result of the sampling matrix and the failure rate matrix; wherein, if the subtraction result is less than zero, it is determined that the corresponding line at the corresponding time point is disconnected; A wind-induced fault set is constructed based on the disconnection conditions of the corresponding lines at the corresponding time points.

3. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy according to claim 2 is characterized in that: The wind-induced failure rates of each line at each time point calculated based on the Batts interval model include: Each route is divided into multiple segmented routes, and the effective wind speed at the center point of each segment of the route at each time point is calculated based on the Batts interval model; Calculating the wind-induced failure rate of each segmented line at each time point based on the effective wind speed; The wind-induced failure rate of each line at each time point is calculated based on the wind-induced failure rate of all segmented lines of each line at each time point.

4. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy according to claim 1 is characterized in that: The traversal of the wind-induced fault set and the calculation of the chain failures caused by the wind-induced faults at each time point based on the disconnection status of each line and the corresponding wind power output at each time point include: Traverse each time point of the wind-induced fault set and perform the following steps at each time point: a. Determine whether the power grid system is disconnected based on the disconnection status of each line; b. Divide the power grid into at least one independent network based on the decoupling condition, and calculate the random power flow of each independent network at the time point corresponding to step a based on the wind power output and the minimum load shedding of each independent network; c. calculating the disconnection time of each thermally overloaded circuit based on the random power flow; d. Based on the comparison of the next time point of the wind-induced fault set with the disconnection time of each thermally overloaded circuit, the earliest time point is selected as the time point of the next disconnected circuit. If the next disconnected circuit is still a thermally overloaded circuit, execute steps a to b; otherwise, start traversing the next time point of the wind-induced fault set.

5. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy according to claim 4 is characterized in that: The calculation method of the wind power output corresponding to each time point includes: Determine the wind speed range at the location of the wind turbine based on the Batts interval model; Determine a probability density function of wind power output based on the wind speed range, the cut-in wind speed, and the cut-out wind speed of the wind turbine; The wind power output at each time point is determined based on the probability density function.

6. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy sources according to claim 4 is characterized in that: The calculating the disconnection time of each thermal overload line based on the random power flow includes: Based on the semi-invariant method, the probability density function of the active power of each line is obtained; Based on the probability density function of the active power, an inverse transformation method is used to sample and obtain the active power of each sampling point of each line; The disconnection time corresponding to each sampling point is calculated based on the active power of each sampling point of each line and the rated power of the corresponding line; The disconnection time of the corresponding thermal overload circuit is determined based on the disconnection time corresponding to each sampling point.

7. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy sources according to claim 6 is characterized in that: The probability density function p(x) of the active power of each line is expressed as: in, is the standard normal probability density function; is a standardized random variable, μ and σ are the expected value and standard deviation of the random variable distribution respectively; g v , v∈[3,4,5,6...] is the standardized semi-invariant, H r (x), r=3,4,5,6,... are Hermite polynomials.

8. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy sources according to claim 6 is characterized in that: The calculation method of the disconnection time of the thermal overload circuit is: Where, Δt cut,j represents the disconnection time of the thermal overload line; lh is the simulation step length of the interval of statistical sampling points; i is the i-th sampling point of line j; SA is the sampling point set; function is an indicator function, which is 1 when SA∈[i·lh,(i+1)·lh), otherwise it is 0; (Δt cut,i,j ) is the disconnection time of the i-th sampling point of line j, o j,max is the power flow limit of line j, that is, the active power limit; j (t, Δt) is the heat accumulation of line j from time t to Δt; X s,i,j is the active power of the i-th sampling point of line j; C j Indicates the rated power of line j.

9. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy sources according to claim 1 is characterized in that: Determining a critical line in the power grid based on the calculated cascading failures includes: Based on the calculated cascading failures, a plurality of index values ​​are calculated, wherein the index values ​​include a probability of occurrence of a cascading failure, a number of occurrences of a kr-order cascading failure, an average cascading failure order, an average number of failure paths, an average number of load losses, and a maximum number of load losses; Calculating an importance metric value for each route based on any of the index values; Critical lines in the power grid are determined based on the importance metrics of the lines.

10. The extreme scenario cascading failure modeling method taking into account the uncertainty of new energy sources according to claim 9 is characterized in that: Calculating the importance metric value of each link based on any of the indicator values ​​includes: Among them, FV j is the importance metric value of line j; RM0 is any of the above index values; RM j In each simulation, line j is set to the corresponding index value calculated so that the line will never be disconnected due to thermal overload.

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