Elastic evaluation and improvement method for power transmission system under debris flow effect

Abstract

The invention discloses an elasticity evaluation and improvement method for a power transmission system under the action of debris flow, is used for solving the technical problem of single fault rate consideration factor in the prior art, and belongs to the technical field of evaluation of anti-disaster capability and recovery capability of the power transmission system under extreme natural disasters (such as debris flow). The method comprises the following specific steps: step 1, constructing a debris flow model considering an impact force attenuation effect; s11, describing the influence area of the debris flow by using the three parameters; s12, carrying out stress analysis on the tower impacted by the debris flow; 2, constructing a fault model considering the accumulated impact process of debris flow on the power transmission element; s21, calculating a tower failure probability; s22, calculating the failure probability of the power transmission line; s23, calculating the overall failure probability of the power transmission line; 3, sampling at a constant time interval delta t based on the solved failure probability of the power transmission line within the debris flow duration delta T; 4, drawing an expected power supply power curve of the power transmission system; and 5, calculating an elastic index.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of evaluating the disaster resistance and recovery ability of power transmission systems under extreme natural disasters such as mudslides, and particularly relates to a method for evaluating and improving the resilience of power transmission systems under the action of mudslides. BACKGROUND

[0002] Mudslides are a typical extreme geological disaster with strong impact and destructive power, which can pose a serious threat to power transmission systems. When a mudslide occurs, the failure probability of an element is strongly related to the impact force it withstands. The greater the impact force, the higher the failure probability. The impact force model is directly related to the accuracy of the resilience evaluation. Various models for analyzing the impact force of mudslides have been constructed at home and abroad. Classic models include the Rickenmann model, the Voellmy-Salm model, and the FLO-2D model, etc. Different models have different advantages in terms of disaster intensity characterization, motion path prediction, and impact force estimation. The Rickenmann model estimates the maximum flow rate and impact force through flow rate and slope; the Voellmy-Salm model simulates the propagation process of mudslides based on the basic equations of fluid mechanics; the FLO-2D model can analyze the propagation path and flow rate distribution of mudslides based on DEM (Digital Elevation Model) terrain data. However, the above models cannot be directly used for resilience evaluation of power transmission systems under mudslides. The reasons are as follows: these models generally focus on the process of mudslide movement itself, without fully considering the change of impact force over time. In view of the above shortcomings, a mudslide model considering the impact force attenuation effect is proposed by introducing factors such as path length, terrain roughness, and mudslide density.

[0003] The element failure model is the basis of resilience evaluation, and without accurate failure probability, it will be difficult to quantify the resilience of the system. In order to integrate the disaster intensity into the evaluation system, it is necessary to establish a quantitative relationship between the failure probability of system elements and the impact force of mudslides. In recent years, researchers have linked mudslide parameters such as flow rate and density to the damage of power transmission elements to assess the damage caused by mudslides to power transmission systems. Song et al. studied the impact of impact load on the stability of power transmission towers, simulating the damage degree of towers under different impact velocities, impact durations, etc.; Yu et al. analyzed the main failure mechanisms of power transmission towers under the action of landslides, and quantitatively evaluated the overturning risk of towers; Yue et al. discussed the influence of flow rate, mass, and impact position on the dynamic response of power transmission towers during the process of rockfall or mudslide debris impacting the tower body. However, the above studies mainly focus on the damage analysis of structures under specific loads, and have not yet established a quantitative relationship between mudslide parameters and the failure probability of power transmission elements from a probabilistic perspective. Therefore, a failure model considering the cumulative impact process of mudslides on power transmission elements is proposed.

[0004] The existing evaluation method has the following defects:

[0005] I, the towers are widely distributed, and not all towers are affected when the debris flow occurs, so it is necessary to analyze the influence range of the debris flow. The influence range of the debris flow is described by three parameters, i.e. the length, width and depth of the debris flow.

[0006] II, the sediment will continuously impact the base of the transmission tower and even the tower body. In most cases, the debris flow mainly destroys the tower foundation, causing the tower to fail.

[0007] III, the failure rate described by the bathtub curve only considers the aging factor of the element itself. Since the aging process of the element during stable operation is very slow, it is considered that the failure rate of the element is constant. However, under the action of the debris flow, the failure rate may increase significantly, so the failure probability evaluation of the power transmission element cannot directly use the constant failure rate. Therefore, it is necessary to establish a quantitative relationship between the impact force of the debris flow and the failure rate of the power transmission element to lay a foundation for subsequent failure probability analysis. SUMMARY

[0008] The purpose of the present application is to provide a flexible evaluation and improvement method for a power transmission system under the action of a debris flow, which solves the technical problem of single consideration of the existing failure rate.

[0009] The present application is realized by adopting the following technical solutions:

[0010] The flexible evaluation and improvement method for a power transmission system under the action of a debris flow comprises the following specific steps:

[0011] Step 1, constructing a debris flow model considering the impact force attenuation effect;

[0012] S11, describing the influence area of the debris flow by three parameters;

[0013] S111, calculating the length L of the debris flow;

[0014] S112, calculating the width w of the debris flow;

[0015] S113, calculating the depth h of the debris flow;

[0016] S12, force analysis of the tower impacted by the debris flow

[0017] S121, calculating the overall flow rate v of the debris flow;

[0018] The average flow rate of the debris flow is taken to represent the overall flow rate of the debris flow, which is calculated by the following formula:

[0019]

[0020] In the formula, v is the overall flow rate of the debris flow;

[0021] S122, calculate the flow head impact force F0;

[0022] The formula for calculating the impact force of the flow head is as follows: F0=κFcosβ=κmacosβ=κρLhwacosβ

[0023] In the formula, κ is the dynamic pressure coefficient; F is the impact force along the mountain direction; m is the debris flow mass; a is the debris flow acceleration; β is the slope angle, i.e. the angle between the mountain slope and the horizontal direction; and ρ is the debris flow density.

[0024] S123, calculate the impact force F(t) at time t after the tower is hit by a debris flow;

[0025] The formula for calculating the impact force of a tower at time t after it has been hit by a debris flow is as follows:

[0026]

[0027] In the formula, γ is the terrain roughness; δ is the fluid density coefficient;

[0028] S124, calculate the impact time of the tower;

[0029] The calculation formula is: ΔT = L / v

[0030] Step 2: Construct a fault model that considers the cumulative impact of debris flow on power transmission components;

[0031] S21, Calculate the failure probability of the tower;

[0032] S211, the maximum impact force F that the tower can withstand at different locations. max The calculation formula is:

[0033]

[0034] In the formula, E t Let ω be the elastic modulus of the tower; I be the moment of inertia of the tower's cross section; ω lim This is the deflection limit; when the actual deformation exceeds ω... lim It is assumed that the transmission tower will be completely destroyed; x is the height of the impact point above the ground; H is the height of the transmission tower;

[0035] S212, the formula for calculating the impact force that the tower can withstand at x = h is:

[0036] S213, calculate the failure rate of the tower;

[0037] The calculation expression is:

[0038] In the formula, τ is the tower failure rate coefficient, which is taken as 0.11;

[0039] S214, calculate the failure probability of the tower;

[0040] Based on mathematical formulas, considering the continuous impact of the flow head and body within the debris flow duration ΔT, the failure probability of the tower is:

[0041] S22, calculate the failure probability of the transmission line;

[0042] S221, the total tension T borne by the transmission line I It is the sum of normal tension and tension increment;

[0043] S222, calculate the failure rate of the transmission line;

[0044] The calculation expression is:

[0045] In the formula, X is the transmission line failure rate coefficient, taken as 0.13; T max This is the maximum tension that a power transmission line can withstand.

[0046] S223, calculate the failure probability of the transmission line;

[0047] Based on mathematical formulas, the probability of power transmission line failure due to accumulated tension within the debris flow duration ΔT is:

[0048]

[0049] S23, calculate the overall failure probability of the transmission line;

[0050] According to reliability analysis theory, the failure probability of a transmission line is the product of the failure probabilities of each transmission component, and the calculation formula is as follows:

[0051] Step 3: During the duration ΔT of the debris flow, sampling is performed at constant time intervals δt based on the calculated failure probability of the transmission line.

[0052] The sampling method is as follows:

[0053] In the formula, S k The state of line k; ε k P is a random number within the interval [0,1]. k Let k be the failure probability of line k.

[0054] Step 4: Plot the expected power supply curve of the power transmission system;

[0055] S41. Calculate the expected power supply of the transmission system under each state based on the sampling results of step three. Repeat step three until the debris flow disaster ends. Plot the expected power supply curve of the transmission system during the debris flow disaster.

[0056] S42, After the debris flow ends and the power transmission components are repaired, the power supply of the power transmission system gradually recovers after the power transmission components repair time Tr. At the same time, the expected power supply of the power transmission system during the recovery phase is plotted.

[0057] Step 5: Calculate the elasticity index;

[0058] The resilience index is defined as the ratio of the area under the actual power supply curve to the area under the normal power supply curve. The larger the index, the higher the system resilience. The calculation formula is as follows:

[0059] R0 represents the power supply under normal operation; t1 is the moment the mudslide occurs; and t4 represents the moment when the power supply is restored to normal.

[0060] Traditional methods focus on analyzing the impact force of the flow head, which is clearly much greater than that of the flow body. However, the prolonged impact force of the flow body can still cause tower failure and therefore cannot be ignored. This invention focuses on the impact of both the flow head and body on the tower, analyzing the continuous effect of the entire debris flow impact process on the tower. Since the damage to the tower caused by debris flow is achieved by the horizontal force during the debris flow impact process, this invention only considers the horizontal force of the debris flow when considering the tower impacted by the debris flow.

[0061] Typically, debris flows cause tower failures, while transmission line failures are caused by tower tilting or displacement. Failure probability is a core parameter in resilience assessment methods; without it, the resilience of the transmission system cannot be quantified.

[0062] The failure rate of the tower depends on the debris flow impact force F and the maximum impact force F that the tower can withstand. max The difference between the two is defined as tension. Clearly, the failure rate is related to tension; the greater the tension, the higher the failure rate of the tower. According to DL / T5154-2012 "Technical Specifications for Structural Design of Overhead Transmission Line Towers," if... Figure 8 As shown, the square areas represent debris flows. The debris flows impact different locations on the tower, and the impact resistance varies at each location. The impacted areas of the tower can be considered a "series structure"; once the impact force exceeds the bearing capacity of a certain location, the tower collapses. Therefore, the tower's failure rate depends on the weakest location within the impacted area, i.e., F. max The smallest position.

[0063] Depend on Figure 9It can be seen that the denominator function is monotonically increasing in the interval (0, 2H). Since the height of the pole tower is H and the depth of the debris flow is much less than the height of the pole tower, the impact range of the debris flow is 0 < x ≤ h < H. The pole tower can withstand the impact force F max The minimum position appears at the height h of the pole tower from the ground.

[0064] According to the actual situation of the pole tower suffering from debris flow disasters, when F ≤ F h，max , the failure rate of the pole tower increases exponentially; when F > F h，max , the cumulative number of pole tower failures in the power transmission system increases by 1.

[0065] According to the actual situation of the transmission line suffering from debris flow disasters, when T I ≤ T max , the failure rate of the transmission line increases exponentially; when T I >T max , the number of transmission line failures in the power transmission system increases by 1.

[0066] The power transmission line is a series system composed of multiple pole towers and transmission lines. When any power transmission component fails (in this invention, the power transmission component specifically refers to the pole tower and the transmission line), the entire power transmission line fails. Suppose a certain power transmission line includes i pole towers and j transmission lines, and the failure probability of each pole tower is P tower，1 , P tower，2 , …, P tower，i ; the failure probability of each transmission line is P line，1 , P line，2 , …, P line,j , and then the overall failure probability of the power transmission line is calculated.

[0067] The resilience index is used to quantify the functional degradation and recovery ability of the power transmission system under debris flow. Based on the resilience trapezoid theory, the resilience index is evaluated according to the determined power supply power curve.

[0068] As Figure 12 shown, the power transmission system goes through two stages of resistance and recovery under the action of debris flow. R0 represents the power supply power under normal operation; R min represents the minimum value of the power supply power during the disaster; t1 is the moment when the debris flow occurs, t2 is the moment when the debris flow disaster ends, t1~t2 represents the resistance stage; t3 is the end moment of the minimum power supply power, t2~t3 represents the repair process of the failed component, and t2~t4 represents the recovery stage.

[0069] Further preferably, since the debris flow density is relatively fixed and M reflects the total mass of the debris flow, obviously, the debris flow length L is proportional to these two parameters. The specific formula: L = b(MH m ) c

[0070] In the formula, b and c are empirical coefficients, which are related to the sand or soil information at the debris flow site; the formula for calculating the debris flow length L takes into account the total amount of debris flow deposits M and the height difference H between the debris flow site and the tower base. m .

[0071] In a further preferred embodiment, b and c in S111 are 0.9 and 0.33, respectively.

[0072] Furthermore, the debris flow width w is mainly determined by the debris flow rate Q and the slope S of the mountain. The formula for calculating the debris flow width w is as follows:

[0073] In the formula, r, μ and The value is an empirical coefficient and is related to the geology of the debris flow location. The width is proportional to the flow rate Q, and the slope S determines the flow velocity of the debris flow. A smaller slope results in a relatively slower flow velocity, making it easier for debris to accumulate and thus resulting in a wider flow.

[0074] Further preferred, in S112 r, μ and The values ​​are 0.6, 0.5, and 0.3.

[0075] Further preferred, the depth of the debris flow head is directly proportional to the slope, and the depth of the tail is inversely proportional to the slope. The debris flow depth h is the average depth of the entire debris flow, not the depth at a specific location. The calculation formula is as follows:

[0076] In the formula, h is the debris flow depth; N is the drag coefficient; the calculation of the debris flow depth h is based on the assumption of constant flow, that is, the total volume of sediment flowing through the debris flow cross section per unit time remains unchanged, and the average depth is widely used to describe debris flows.

[0077] A further preferred embodiment of the formula derivation in step 214 is as follows:

[0078] Under the influence of debris flow, the fault-free operating time T of a power transmission component is represented by a continuous random variable. In engineering, T is usually assumed to follow an equal probability model, such as an exponential distribution or a Weibull distribution. The probability distribution function of T is defined as: F p (t)=P(T≤t)

[0079] The probability density function of T is defined as follows:

[0080] Based on reliability theory, within the duration ΔT of the debris flow, an arbitrary time interval Δt is taken, λ tower (t) represents the probability of a power transmission component failing during the period Δt, assuming it operates normally before time t. Δt is a local minimum. Since the decay of the impact force over time is considered, the failure rate λ... tower(t) is a quantity that changes with time;

[0081]

[0082] According to the conditional probability formula:

[0083]

[0084] Combining the above two equations, we get:

[0085] Based on mathematical relationships, we can obtain:

[0086] Combining the above two equations, we get:

[0087] Therefore, considering the continuous impact of the flow head and body forces within the debris flow duration ΔT, the failure probability of the transmission tower is:

[0088] In a further preferred embodiment, the expected power supply of the transmission system in each state calculated in step four is quantified using a power flow analysis algorithm, such as... Figure 11 As shown in the first half of the figure, each purple line segment represents the power supplied by the system during the time interval δt.

[0089] A further preferred approach is to utilize power flow analysis algorithms to generate the expected power supply during the power transmission system recovery phase. After the debris flow ends, the repair team repairs the transmission components, and the power transmission system enters the recovery phase. For example... Figure 11 As shown by the blue curve in the latter half, after the transmission component repair time Tr, the power supply during the transmission system recovery phase is generated using a power flow analysis algorithm. Because the repair of transmission components occurs sequentially, the power supply of the transmission system recovers gradually, rather than instantaneously.

[0090] Not all power towers are impacted during a debris flow; the location and number of towers affected need to be determined based on the area of ​​impact. For example... Figure 1 As shown, the impact area of ​​a debris flow is described using three parameters: the length, width, and depth of the debris flow.

[0091] Traditional power transmission networks often experience outages when damaged by natural disasters, relying solely on relay protection devices to restore power over the largest possible area. This can lead to prolonged periods without power restoration in affected areas, or even cause the outage area to expand. Research on power transmission network resilience primarily considers the network's ability to withstand natural disasters, with resilience indicators quantitatively describing its elasticity. During natural disasters, the performance of the power transmission network changes in response to variations in the disaster's impact. Attached Figure Description

[0092] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0093] Figure 1 This diagram illustrates the debris flow impact area of ​​the present invention.

[0094] Figure 2 This is a schematic diagram showing the depth of debris flow according to the present invention.

[0095] Figure 3 This invention illustrates the geographical spatial relationship between debris flows and power transmission systems.

[0096] Figure 4 This diagram illustrates the flow of debris along a mountainside according to the present invention.

[0097] Figure 5 This diagram illustrates the force analysis of the tower according to the present invention.

[0098] Figure 6 A schematic diagram illustrating the duration of debris flow impact on the tower of the present invention.

[0099] Figure 7 This is a schematic diagram showing the curve of the bathtub of the present invention.

[0100] Figure 8 This diagram illustrates the debris flow impact tower of the present invention.

[0101] Figure 9 This invention represents 3Hx 2 -x 3 Graph of the function.

[0102] Figure 10 This is a schematic diagram illustrating the tension resistance of the power transmission line of the present invention.

[0103] Figure 11 This diagram shows the expected power supply curve of the power transmission system under debris flow impact according to the present invention.

[0104] Figure 12 This diagram shows the power supply curve of the power transmission system of the present invention.

[0105] Figure 13 This represents the IEEE-30 node topology diagram of Embodiment 2 of the present invention.

[0106] Figure 14 This is a geographical location map of the power transmission system according to Embodiment 2 of the present invention.

[0107] Figure 15 This is a schematic diagram showing the location of the tower affected by a debris flow in Embodiment 2 of the present invention.

[0108] Figure 16 This indicates the impact force of debris flow borne by each tower in Embodiment 2 of the present invention.

[0109] Figure 17 This indicates the failure probability of each tower in Embodiment 2 of the present invention.

[0110] Figure 18 This is a power supply curve diagram of the power transmission system in Embodiment 2 of the present invention.

[0111] In the diagram: 1-tower, 2-tower base, 3-mountain, 4-impact force along the mountain direction, 5-transmission line, 6-mudslide, 7-transmission line, 8-contact surface. Detailed Implementation

[0112] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0113] Example 1: A method for assessing and improving the resilience of a power transmission system under debris flow, including the following specific steps: Step 1: Construct a debris flow model 6 that considers the impact force attenuation effect;

[0114] S11, using three parameters to describe the area affected by debris flow 6;

[0115] For the power company, the coordinates of pole 1 are known. By analyzing the location information of pole 1 and the affected area of ​​debris flow 6, the number and location of pole 1 affected by debris flow 6 can be determined. Figure 3 As shown in the figure, there are a total of 4 towers 1. The subsequent fault analysis only focuses on towers 1, ①, ② and ③, which are affected by debris flow 6.

[0116] S111, calculate the length L of the debris flow 6;

[0117] Since the density of debris flow 6 is relatively constant, M reflects the total mass of debris flow 6. Clearly, the length L of debris flow 6 is proportional to these two parameters, specifically: L = b(MH). m ) c

[0118] In the formula, b and c are empirical coefficients, which are related to the sand or soil information at the location of debris flow 6. b and c take values ​​of 0.9 and 0.33, respectively.

[0119] S112, calculate the width w of the debris flow 6;

[0120] The width w of debris flow 6 is mainly determined by the debris flow flow rate Q and the slope S of the mountain 3. The formula for calculating the width w of debris flow 6 is as follows:

[0121] In the formula, r, μ and These are empirical coefficients, related to the geology of the debris flow location, r, μ, and The values ​​are 0.6, 0.5, and 0.3. S113, calculate the depth h of the debris flow at point 6;

[0122] The depth of the head of debris flow 6 is directly proportional to the slope, while the depth of the tail is inversely proportional to the slope. The depth h of debris flow 6 is the average depth of the entire debris flow 6, not the depth at a specific location. The calculation formula is as follows:

[0123] In the formula, h is the depth of the debris flow; N is the drag coefficient.

[0124] S12, Stress analysis of tower 1 subjected to debris flow 6.

[0125] S121, Calculate the overall flow velocity v of debris flow 6;

[0126] The impact force of debris flow 6 is strongly correlated with its flow velocity. When debris flow 6 flows on mountain 3, its flow velocity is uneven due to the unevenness of mountain 3. For example... Figure 4 As shown, it is clear that at the same location, the velocity near the surface of mountain 3 is lower than the velocity further away from the ground. The average velocity of debris flow 6 is used to represent the overall velocity of debris flow 6, calculated using the following formula:

[0127]

[0128] In the formula, v is the overall velocity of the debris flow.

[0129] S122, calculate the flow head impact force F0;

[0130] According to Newton's second law, force equals mass multiplied by acceleration. Therefore, along the direction of mountain 3, the impact force of debris flow 6 is the mass of debris flow 6 multiplied by its acceleration. Figure 5 As shown, the force along the mountain 3 direction is decomposed into horizontal and vertical directions. The horizontal force is the impact force that caused the failure of tower 1.

[0131] The formula for calculating the impact force of the flow head is as follows: F0=κF cosβ=κma cosβ=κρLhwa cosβ

[0132] In the formula, κ is the dynamic pressure coefficient; F is the impact force along the mountain direction; m is the mass of the debris flow; a is the acceleration of the debris flow; β is the slope angle, i.e., the angle between the mountain slope and the horizontal direction; and ρ is the density of the debris flow.

[0133] S123, calculate the impact force F(t) at time t after tower 1 is hit by debris flow 6;

[0134] During the flow of debris flow 6, its impact force decreases with time or distance due to factors such as friction and resistance. Clearly, the rougher the terrain, the faster the impact force of debris flow 6 decreases; the lower the density of debris flow 6, the greater the decrease in impact force. Assuming that the impact force on the contact surface 8 between debris flow 6 and tower 1 is equal when debris flow 6 impacts tower 1, the formula for calculating the impact force of tower 1 at time t after being impacted by debris flow 6 is:

[0135]

[0136] In the formula, γ is the terrain roughness; δ is the fluid density coefficient;

[0137] S124, calculate the impact time of tower 1;

[0138] The calculation formula is: ΔT = L / v

[0139] Step 2: Construct a fault model that considers the cumulative impact process of debris flow on the power transmission components.

[0140] S21, calculate the failure probability of tower 1;

[0141] S211, the maximum impact force F that tower 1 can withstand at different positions. max The calculation formula is:

[0142]

[0143] In the formula, E t Let ω be the elastic modulus of tower 1; I be the moment of inertia of the cross section of tower 1; ω lim This is the deflection limit; when the actual deformation exceeds ω... lim It is assumed that the transmission tower will be completely destroyed; x is the height of the impact point above the ground; H is the height of transmission tower 1.

[0144] S212, the formula for calculating the impact force that tower 1 can withstand at x = h is:

[0145] S213, calculate the failure rate of tower 1;

[0146] The calculation expression is:

[0147] In the formula, τ is the failure rate coefficient of tower 1, which is taken as 0.11;

[0148] S214, calculate the failure probability of tower 1;

[0149] Based on mathematical formulas, considering the continuous impact of the flow head and body during the duration ΔT of debris flow 6, the failure probability of tower 1 is:

[0150] The formula derivation is as follows:

[0151] Under the action of debris flow 6, the fault-free operating time T of the transmission element is represented by a continuous random variable. In engineering, T is usually assumed to follow an equal probability model such as an exponential distribution or a Weibull distribution. The probability distribution function of T is defined as: F p (t)=P(T≤t)

[0152] The probability density function of T is defined as follows:

[0153] Based on reliability theory, within the duration ΔT of debris flow 6, an arbitrary time interval Δt is selected, λ tower (t) represents the probability of a power transmission component failing during the period Δt, assuming it operates normally before time t. Δt is a local minimum. Since the decay of the impact force over time is considered, the failure rate λ... tower (t) is a quantity that changes with time;

[0154]

[0155] According to the conditional probability formula:

[0156]

[0157] Combining the above two equations, we get:

[0158]

[0159] Based on mathematical relationships, we can obtain:

[0160]

[0161] Combining the above two equations, we get:

[0162]

[0163] Therefore, considering the continuous impact of the flow head and body forces during the duration ΔT of debris flow 6, the failure probability of transmission tower 1 is: S22, calculate the failure probability of transmission line 5;

[0164] S221, the total tension T borne by transmission line 5 I It is the sum of normal tension and tension increment;

[0165] S222, calculate the failure rate of transmission line 5;

[0166] The calculation expression is:

[0167] In the formula, X is the failure rate coefficient of transmission line 5, which is taken as 0.13; Tmax This is the maximum tension that transmission line 5 can withstand;

[0168] S223, calculate the failure probability of transmission line 5;

[0169] Based on mathematical formulas, the probability of power transmission failure caused by accumulated tension during the duration ΔT of debris flow 6 is:

[0170]

[0171] S23, calculate the overall failure probability of transmission line 7;

[0172] Suppose a transmission line consists of i towers and j transmission lines, and the failure probability of each tower is P. tower，1 P tower，2 , ..., P tower,i The probability of failure for each transmission line is P. line,1 P line,2 , ..., P line，j This allows for the calculation of the overall failure probability of the transmission line.

[0173] According to reliability analysis theory, the failure probability of transmission line 7 is the product of the failure probabilities of each transmission component, and the calculation formula is as follows:

[0174] Step 3: During the duration ΔT of debris flow 6, sampling is performed at constant time intervals δt based on the calculated failure probability of transmission line 7.

[0175] The sampling method is as follows:

[0176] In the formula, S k The state of line k; ε k P is a random number within the interval [0, 1]. k Let k be the failure probability of line k.

[0177] Step 4: Plot the expected power supply curve of the power transmission system;

[0178] S41, calculate the expected power supply of the transmission system under each state based on the sampling results of step three, repeat step three until the debris flow 6 disaster ends, and plot the expected power supply curve of the transmission system during the debris flow 6 disaster; the expected power supply of the transmission system under each state is quantified by the power flow analysis algorithm.

[0179] S42, After the debris flow 6 ends, and after the repair of the transmission components, the power supply of the transmission system gradually recovers after the repair time Tr of the transmission components. At the same time, the expected power supply of the transmission system during the recovery phase is plotted. The expected power supply of the transmission system during the recovery phase can be generated using power flow analysis algorithms.

[0180] Step 5: Calculate the elasticity index;

[0181] The resilience index is defined as the ratio of the area under the actual power supply curve to the area under the normal power supply curve. The larger the index, the higher the system resilience. The calculation formula is as follows:

[0182] The specific details are as follows:

[0183] A stress analysis was conducted on tower 1 impacted by debris flow 6. Traditional methods focus on analyzing the impact force of the flow head, which is clearly much greater than that of the flow body. However, the impact force of the flow body over a long period can still cause tower 1 to fail, and therefore cannot be ignored. The following analysis focuses on the impact of both the flow head and flow body on tower 1, examining the overall impact of debris flow 6 on tower 1.

[0184] Duration refers to the time from when tower 1 begins to be impacted by debris flow 6 to when the impact ends. The longer the duration, the higher the probability of tower 1 failing. Figure 6 As shown, a debris flow 6 of length L flows over tower 1 at a velocity v.

[0185] The transmission components studied include tower 1 and transmission line 5. Typically, the impact of debris flow 6 causes tower 1 to fail, while the failure of transmission line 5 is due to the tilting or displacement of tower 1. Failure probability is a core parameter in resilience assessment methods; without it, the system's resilience cannot be quantified.

[0186] Example 2,

[0187] Taking the IEEE 30-bus transmission system as an example, this paper considers the impact of debris flow 6 and quantifies the resilience of the transmission system. This example uses the MATLAB R2018b software platform and the MATPOWER 7.1 toolkit for power flow calculations. All simulations were performed on a Windows 10 computer equipped with an Intel Core i5-8300H processor and 16GB of memory.

[0188] like Figure 13 As shown, the transmission system comprises 30 bus nodes, 41 branch lines, and is planned to have 1500 towers, a total load power of 189.2MW, and a total generating capacity of 1120MW. This ensures that the transmission system can maintain power supply even in the event of partial transmission component failure, meaning that the reduction in resilience is not due to insufficient generating capacity. However, the actual geographical location of tower 1 in the IEEE 30-node transmission system is not provided. For ease of analysis, tower 1 of this node transmission system is placed in a mountainous area in northern my country to simulate the impact of a debris flow 6 on the transmission system.

[0189] The geographical orientation and distribution of each transmission line 7 are as follows:Figure 14 As shown, the areas where transmission system nodes 6 to 15 are located are steep mountains (3), typical high-risk areas for debris flows (6). Nodes 1 to 5 and 16 to 30 are located in relatively gentle hills and plains with good geological stability. It is assumed that debris flows (6) occur at nodes BUS6, 9, 10, and 12. To better reflect the complex terrain conditions in actual engineering, this embodiment selects four representative mountains (3). These mountains (3) have diverse terrains, covering different slope variations and landforms, including typical valley types, steep slope types, multi-peak hills, and gentle slopes. The location information of towers (1) affected by debris flows (6) at each node is as follows: Figure 15 As shown.

[0190] The main power transmission components in the disaster-stricken area (affected by debris flow 6) include Q345 type tower 1 and LGJ-240 / 30 type conductors. Tower 1 is made of high-strength angle steel, with an overall height of 35 meters and a front width of 4 meters; the conductors are made of high-strength aluminum alloy. The specific structural parameters of tower 1 and transmission line 5 are shown in Tables 1 and 2.

[0191] Table 1 Structural parameters of transmission tower 1

[0192]

[0193] Table 2 Structural parameters of transmission line 5

[0194]

[0195] The parameters for debris flow 6 are based on typical experimental data from both domestic and international sources. Specific parameters are shown in Table 3, including debris flow 6 density, depth, cross-sectional area, ground friction coefficient, and slope angle. Due to space limitations, only information related to BUS6 is listed. Clearly, tower 1 on the mountaintop will not be impacted by debris flow 6. Therefore, the debris flow 6 information given in this example does not include towers 3 and 7 (tower 1).

[0196] Table 3 shows the information on the debris flow suffered by tower 1 in BUS6.

[0197]

[0198] Based on Table 3, the impact forces experienced by each tower 1 were obtained according to the proposed debris flow model considering the impact force attenuation effect. The impact forces experienced by towers 1-9 in BUS6 are as follows: Figure 16As shown in the diagram, tower 1 located on the mountaintop will not be impacted by debris flow 6. Examples include towers 3 and 7 in Bus 6, and towers 3 and 8 in Bus 9. Except for tower 1 on the mountaintop, the closer the other towers 1 are to the mountaintop, the earlier they will be impacted by debris flow 6. For example, the impact on towers 2, 4, 6, and 8 in Bus 6 begins on average 18.71 minutes earlier than that on towers 1, 5, and 9. Towers 1 located in valleys will be impacted by debris flows 6 from both sides. For example, tower 6 in Bus 6 will experience two impacts with maximum values ​​of 136.32 kN and 130.25 kN respectively. In conclusion, the impact force experienced by each tower 1 is highly dependent on its geographical location and the path of debris flow 6, with the maximum and minimum impact forces differing by approximately 1.46 times.

[0199] Based on the impact force of debris flow 6 on tower 1, the failure probability of each transmission tower 1 is calculated. Figure 17 The failure probabilities of transmission tower 1 under different node impacts by debris flow 6 are listed. The blue portion in the figure represents the failure probability of transmission tower 1 considering the attenuation of the impact force of debris flow 6, while the red portion represents the increase in failure probability without considering impact force attenuation (traditional method). Clearly, the failure probability without considering impact force attenuation is higher; the results show that ignoring impact force attenuation leads to an average increase in failure probability of 31.46%. Therefore, the method proposed in this invention solves the problem of overly conservative assessment of failure probability of traditional transmission components under debris flow 6.

[0200] In addition, through observation Figure 17 It can be observed that the changes in each factor affect the failure probability of tower 1: 1. Only the depth of debris flow 6 differs; for example, the depth of debris flow 6 differs by 0.12m between towers 4 and 5 in BUS6, resulting in a 4-fold difference in failure probability; 2. Only the cross-sectional area of ​​debris flow 6 differs; for example, the cross-sectional area of ​​debris flow 6 differs by approximately 10% between towers 2 and 4 in BUS6, resulting in failure probabilities of 0.1120 and 0.4038, respectively; 3. Under the same conditions, the slope angle of tower 1's location differs; for example, the slope angle of towers 1 and 6 in BUS6 differs, resulting in failure probabilities of 0.2560 and 0.5242, respectively. The comparison shows that the impact of each factor's change on the failure probability of tower 1 is not negligible.

[0201] The failure probability of each transmission line 5 was calculated. Table 4 lists the failure probabilities of the affected transmission lines 5 at each node. Overall, the failure probabilities fluctuated between 0.02 and 0.40, with the highest failure probability (0.3991) for lines 6-7 in BUS12 and the lowest (0.0269) for lines 5-6 in BUS9.

[0202] Table 4 shows the failure probability of each node's affected transmission line 5.

[0203]

[0204] Based on the obtained failure probabilities of each transmission component, the failure probability of transmission line 7 is calculated. Then, in the simulation software, the non-sequential Monte Carlo method is used to sample the state of the transmission system multiple times within one simulation step. When using the Monte Carlo method for simulation, the convergence of the elasticity index directly determines the number of samplings. In this embodiment, the elasticity index is evaluated according to different sampling numbers, and finally, considering both convergence and computational efficiency requirements, 921 samplings are selected. During each sampling, based on the failure probability of each transmission line 7, it is determined whether transmission line 7 is in a normal or failed state, thereby generating a transmission component state combination. Subsequently, the transmission component state combination is input into the MATPOWER power flow calculation tool to calculate the power supply of the transmission system under each state. The above process is repeated to obtain the expected power supply curve of the transmission system under the debris flow 6 disaster, as shown below. Figure 18 As shown.

[0205] Depend on Figure 18 It can be seen that the system operated normally because debris flow 6 did not propagate to the power transmission system in the early stage; as debris flow 6 moved, a power shortage occurred at 0.87h; as the number of faulty components increased, the system load loss reached its peak at 1.28h, at which time the system's power supply was 115.95MW, accounting for 61.26% of the total power demand; at 24.19h, power supply began to be restored, and the system was fully restored at 25.28h, so the system recovery time was 24h.

[0206] Furthermore, the system's power supply capacity experienced a maximum drop of over 38%, and the extended component repair time led to a prolonged period of low power consumption. According to... Figure 18 The curve shown indicates that the resilience of the power transmission system under debris flow 6 is 0.6463, meaning that it can maintain an average of 64.63% of the power supply demand during debris flow 6.

[0207] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the present invention. Although detailed descriptions have been provided with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments, and they should all be covered within the protection scope of the claims.

Claims

1. A method for elastic assessment and improvement of power transmission systems under debris flow, characterized in that: The specific steps include the following: Step 1: Construct a debris flow (6) model that considers the impact force attenuation effect; S11, using three parameters to describe the area affected by debris flow (6); S111, calculate the length L of the debris flow (6); S112, calculate the width w of the debris flow (6); S113, calculate the depth h of the debris flow (6); S12, stress analysis of tower (1) subjected to debris flow (6); S121, calculate the overall flow velocity v of the debris flow (6); The average velocity of the debris flow (6) is used to represent the overall velocity of the debris flow (6), and is calculated using the following formula: In the formula, v is the overall velocity of the debris flow (6), and S is the slope of the mountain. S122, calculate the flow head impact force F0; The formula for calculating the impact force of the flow head is as follows: F0=κF cosβ=κma cosβ=κρLhwa cosβ In the formula, K is the dynamic pressure coefficient; F is the impact force along the mountain direction (4); m is the mass of the debris flow (6); a is the acceleration of the debris flow (6); β is the slope angle, that is, the angle between the mountain slope and the horizontal direction; ρ is the density of the debris flow (6); S123, calculate the impact force F(t) at time t after the tower (1) is hit by the debris flow (6); The formula for calculating the impact force of tower (1) at time t after it is hit by debris flow (6) is: F(t)=F0e -2γt (1+δ·t) In the formula, γ is the terrain roughness; δ is the fluid density coefficient; S124, calculate the impact time of tower (1); The calculation formula is: ΔT = L / v Step 2: Construct a fault model that considers the cumulative impact of debris flow (6) on power transmission components; S21, calculate the failure probability of tower (1); S211, the maximum impact force F that the tower (1) can withstand at different positions. max The calculation formula is: In the formula, E t Let ω be the elastic modulus of tower (1); I be the moment of inertia of the cross section of tower (1); ω lim This is the deflection limit; when the actual deformation exceeds ω... lim It is assumed that the transmission tower will be completely destroyed; x is the height of the impact point from the ground; H is the height of the transmission tower (1); S212, the formula for calculating the impact force that tower (1) can withstand at x=h is: S213, calculate the failure rate of tower (1); The calculation expression is: In the formula, τ is the failure rate coefficient of the tower (1), which is taken as 0.11; S214, calculate the failure probability of tower (1); Based on mathematical formulas, considering the continuous impact of the flow head and body during the duration ΔT of the debris flow (6), the failure probability of the tower (1) is: S22, calculate the failure probability of transmission line (5); S221, the total tension T1 borne by the transmission line (5) is the sum of the normal tension and the tension increment; S222, calculate the failure rate of the transmission line (5); The calculation expression is: In the formula, X is the failure rate coefficient of the transmission line (5), which is taken as 0.13; T max The maximum tension that the power transmission line (5) can withstand; S223, calculate the failure probability of transmission line (5); Based on mathematical formulas, the probability of transmission line (5) failure due to accumulated tension within the duration ΔT of the debris flow (6) is: S23, calculate the overall failure probability of the transmission line (7); Suppose a transmission line consists of i towers and j transmission lines, and the failure probability of each tower is P. tower,1 P tower,2 , ..., P tower,i The probability of failure for each transmission line is P. line,1 P line,2 , ..., P line,j Then, the overall failure probability of the transmission line can be calculated. According to reliability analysis theory, the failure probability of the transmission line (7) is the product of the failure probabilities of each transmission component, and the calculation formula is as follows: Step 3: During the duration ΔT of the debris flow (6), sampling is performed at constant time intervals δt based on the calculated failure probability of the transmission line (7); The sampling method is as follows: In the formula, S k The state of line k; ε k P is a random number within the interval [0, 1]. k Let k be the failure probability of line k. Step 4: Plot the expected power supply curve of the power transmission system; S41, calculate the expected power supply of the power transmission system under each state based on the sampling results of step three, repeat step three until the debris flow (6) disaster ends, and draw the expected power supply curve of the power transmission system during the debris flow (6) disaster. S42, After the debris flow (6) ends, after the repair of the power transmission components, the power supply of the power transmission system gradually recovers after the repair time Tr of the power transmission components. At the same time, the expected power supply of the power transmission system during the recovery stage is plotted. Step 5: Calculate the elasticity index; The resilience index is defined as the ratio of the area under the actual power supply curve to the area under the normal power supply curve. The larger the index, the higher the system resilience. The calculation formula is as follows: R0 represents the power supply under normal operating conditions; t1 is the moment the mudslide occurred, and t4 represents the moment when normal power supply was restored.

2. The method for elastic assessment and improvement of power transmission systems under debris flow as described in claim 1, characterized in that: Since the density of the debris flow (6) is relatively fixed, M reflects the total mass of the debris flow (6). Obviously, the length L of the debris flow (6) is proportional to these two parameters, specifically: L = b(MH) m ) c In the formula, b and c are empirical coefficients, which are related to the sand or soil information at the location of the debris flow (6), and H m The height difference between the location of the debris flow (6) and the base (2) of the tower (1).

3. The method for elastic assessment and improvement of power transmission systems under debris flow as described in claim 2, characterized in that: In S111, b and c take values ​​of 0.9 and 0.33, respectively.

4. The method for elastic assessment and improvement of power transmission systems under debris flow as described in claim 3, characterized in that: The width w of a debris flow (6) is mainly determined by the flow rate Q of the debris flow (6) and the slope S of the mountain (3). The formula for calculating the width w of the debris flow (6) is as follows: In the formula, r, μ and It is an empirical coefficient, which is related to the geology of the debris flow (6) location.

5. The method for elastic assessment and improvement of power transmission systems under debris flow as described in claim 4, characterized in that: In S112, r, μ and The values ​​are 0.6, 0.5, and 0.

3.

6. The method for elastic assessment and improvement of power transmission systems under debris flow as described in claim 5, characterized in that: The depth of the head of a debris flow (6) is directly proportional to the slope, and the depth of the tail is inversely proportional to the slope. The depth h of the debris flow (6) is the average depth of the entire debris flow (6), not the depth at a specific location. The calculation formula is as follows: In the formula, h is the depth of the debris flow (6); N is the resistance coefficient.

7. The method for elastic assessment and improvement of power transmission systems under debris flow according to claim 6, characterized in that: The formula derivation in step 214 is as follows: Under the action of debris flow (6), the fault-free operating time T of the transmission element is represented by a continuous random variable. In engineering, it is usually assumed that T follows an exponential distribution or a Weibull distribution probability model. The probability distribution function of T is defined as: F p (t)=P(T≤t) The probability density function of T is defined as follows: Based on reliability theory, within the duration ΔT of the debris flow (6), an arbitrary time interval Δt is selected, λ tower (t) represents the probability of a power transmission component failing during the period Δt, assuming it operates normally before time t. Δt is a local minimum. Since the decay of the impact force over time is considered, the failure rate λ... tower (t) is a quantity that changes with time; According to the conditional probability formula: Combining the above two equations, we get: Based on mathematical relationships, we can obtain: Combining the above two equations, we get: Therefore, considering the continuous impact of the flow head and body during the duration ΔT of the debris flow (6), the failure probability of the transmission tower (1) is:

8. The method for elastic assessment and improvement of power transmission systems under debris flow as described in claim 7, characterized in that: In step four, the expected power supply of the transmission system under each state is calculated and quantified using a power flow analysis algorithm.

9. The method for elastic assessment and improvement of a power transmission system under debris flow as described in claim 8, characterized in that: The expected power supply during the power transmission system recovery phase can be generated using power flow analysis algorithms.

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