Substation earthquake risk fast assessment method based on minimal cut sets

Abstract

This invention discloses a rapid seismic risk assessment method for substations based on minimum cut sets. First, a fault tree model is used to find the minimum cut set of the system, and a network model of the substation system is constructed. Given the reliability of various equipment, the failure probability of the system is quickly assessed based on the probability of each path. Then, the seismic resistance capability of the substation system and the seismic risk probability are combined to propose a quantitative index of seismic risk based on the key functional characteristics of the system. The rapid assessment of the seismic risk of the substation system is achieved through the minimum cut set algorithm. The advantages of this invention are improved data accuracy, achieving high-precision calculation in a short time, efficient risk assessment of lifeline engineering projects, and effective fulfillment of practical engineering needs.

Description

Technical Field

[0001] This invention relates to the field of functional status, seismic resistance, and seismic risk assessment of substation systems, and particularly to a rapid seismic risk assessment method for substations based on minimal cut sets. Background Technology

[0002] Substations are power system networks composed of various electrical equipment connected by busbars. They possess high redundancy and interconnectivity, ensuring continued operation even after an earthquake. However, substations have suffered extensive damage in numerous major earthquakes both domestically and internationally. The resulting power outages caused by their malfunctions have led to significant direct and indirect economic losses. In the 1994 Beiling earthquake, widespread substation damage caused power outages, directly impacting the power supply to 1.1 million people and resulting in severe economic losses. In the 2008 Wenchuan earthquake, the Sichuan power grid was severely damaged, with over 170 substations of 35kV and above damaged, and it took several months for them to return to normal operation. In the 2011 Great East Japan Earthquake, 67 substations were severely damaged, and it took 10 days for 95% of the power system to return to normal. This demonstrates that for sudden and destructive natural disasters like earthquakes, it is extremely difficult to accurately predict and effectively defend against them before they occur. Meanwhile, China is located on two major seismic belts in the world, with high seismic activity and intensity. This places higher demands on substation systems, requiring them not only to maintain necessary stability during normal operation but also to ensure the reliability of system functions during earthquakes. In addition, current research is mostly limited to the seismic performance of individual equipment in substations. Therefore, there is an urgent need to conduct seismic risk assessments for various types of substations in different regions, analyze and understand the functional reliability and failure probability of substation systems during earthquakes, and clarify strategies to reduce seismic risks in substations, thereby achieving the overall goal of reducing human, material, and economic losses.

[0003] In 1973, the concept of resilience first appeared in ecology. It refers to the ability of a system to resist and recover to its original normal functional level after being subjected to external disturbances. Since then, with in-depth research, the scope of resilience research has expanded to fields such as medicine, transportation, and urban pipeline networks. In the field of power systems, seismic resilience is theoretically summarized into five key characteristics: reliability, robustness, redundancy, resourcefulness, and speed. Reliability refers to the probability that a system will maintain its function reliably under earthquake loading; it is one of the key characteristics for measuring the seismic resistance of substations. Robustness refers to the system's ability to resist damage and maintain its functional level under earthquake loading. Redundancy refers to the excess capacity of substation system structural connections or equipment functional levels, ensuring that the system can still maintain normal functional status even when a few components are damaged. Resourcefulness refers to the coordination and linkage capabilities of various resources in the system. Speed ​​refers to the substation's ability to quickly recover from functional losses after an earthquake. These five characteristics well explain the important role of seismic resilience in practical engineering.

[0004] Current research progress reveals extensive studies on seismic hazard analysis for specific regions, while disaster risk assessment at the power grid level is also advancing. However, risk assessment in power systems primarily considers system operation and functionality, such as grid frequency and voltage stability, with slower progress in seismic hazard-level risk assessment. Furthermore, substation systems differ from power grid systems in key characteristics, structural forms, and research focus; many theories and methods applicable to the power grid are not suitable for substation systems. Additionally, current research methods largely rely on Monte Carlo sampling, where higher sampling rates yield more accurate data, but also significantly increase data processing time, hindering the current goal of rapid seismic risk assessment.

[0005] This is an area that needs significant improvement in this application. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a rapid assessment method for seismic risk of substations based on minimal cut sets, which realizes accurate and rapid assessment of substation system functions and seismic risk.

[0007] To address the aforementioned technical issues, this invention provides a rapid substation seismic risk assessment method based on minimum cut sets. This method first finds the minimum cut set of the system using a fault tree model and constructs a network model of the substation system. Given the reliability of various equipment types, it rapidly assesses the system's failure probability based on the probability of each path. Then, it combines the substation system's seismic resistance capability with the seismic risk probability, proposing a quantitative seismic risk index based on the system's key functional characteristics. The rapid assessment of substation system seismic risk is achieved through a minimum cut set algorithm, including the following specific steps: S1: Determine the seismic intensity of the area where the substation is located, and clarify the type, number, and system connection method of the substation equipment; S2: Seismic hazard analysis is performed, and the conditional probability of seismic risk is obtained by combining the seismic reliability analysis of the substation as follows: in: The conditional probability of seismic risk function failure in the substation system; This represents the failure probability of the substation system under a specific earthquake intensity. This represents the probability of an earthquake of a specific magnitude occurring in the area where the substation is located, where the earthquake magnitude is represented by the peak ground acceleration (PGA). S3: Set the peak ground acceleration To reflect the seismic intensity and peak ground acceleration in areas with different seismic intensities As shown in the following formula: in These respectively represent frequent earthquakes, earthquakes designed for earthquake resistance, and rare earthquakes; Indicates the earthquake intensity level; This represents the maximum horizontal seismic influence coefficient, obtained according to the Chinese Code for Seismic Design of Buildings. This represents the power amplification factor, which is generally taken as... ; S4: Establish a fault tree network model of the substation system, arrange and combine various basic events to obtain the minimum cut set of the event tree model, and transform the fault tree model into the equivalent model of the substation through the minimum cut set algorithm. S5: Establish earthquake risk quantification indicators; conduct a quantitative assessment of the earthquake risk of the substation system from the two aspects of key functional characteristics, namely reliability and robustness. The goal of quantitatively assessing the earthquake resistance of the substation is achieved by clarifying the normal operation probability of the substation system and establishing the remaining functional indicators of the substation system.

[0008] Furthermore, in step S1, the seismic intensity of the area where the substation is located is represented by peak ground acceleration (PGA) and used as an indicator to measure the intensity of the earthquake.

[0009] Furthermore, in step S2, the seismic risk function failure condition probability of the substation system is the product of the seismic failure probability of the substation and the probability of earthquake occurrence.

[0010] Furthermore, the fault tree model in step S4 satisfies the following assumptions: 1) Assume each unit in the substation system as a basic event in the fault tree model, and assume the connection method of each unit in the substation system as the logical relationship of each basic event in the fault tree. 2) Assume the functional state of each unit as the conditional probability of the basic event; 3) The series and parallel connections between units are made through AND gates and OR gates in the fault tree; 4) The probability of the outgoing unit working normally is assumed to be the conditional probability parameter of the output event.

[0011] Furthermore, in step S4, the reliability of various types of equipment is expressed in the form of seismic vulnerability curves. These seismic vulnerability curves follow a log-normal cumulative distribution with a median of λ and a log-standard deviation of λ, as shown in the following formula: .

[0012] Furthermore, in step S4, given the known probabilities of various basic events, the conditional probability of the output event is quickly calculated using the minimum cut set algorithm; when there are repeated events in each minimum cut set, the probability of the output time is calculated using the following formula: in: This indicates the probability of the output event W occurring; Indicates the minimum number of cut sets in the system; This represents the number of basic events in the i-th minimum cut set; This represents the probability of the j-th basic event occurring in the i-th minimum cut set of the system; This represents the union of the basic events in the r-th minimum cut set and the s-th minimum cut set in the system.

[0013] Furthermore, in step S5, robustness refers to the substation system's ability to resist damage and maintain its functional level under earthquake conditions. Since the number of outgoing units in the substation system determines its power transmission level, a system residual function index is established considering the outgoing units and their corresponding weights. The functional level of a substation system is quantitatively assessed using the following formula: ; in: This represents the failure probability of the nth outgoing line unit in the substation system. This represents the weighting coefficient of the nth outgoing line unit in the substation system. N This represents the number of outgoing units in the substation system.

[0014] The superior effects of this invention are as follows: 1) This invention constructs a probability-based system network model, which simplifies the complex network model into the probability and logical connection relationship of each basic event, greatly reducing the amount of data input and processing of the network model. Therefore, it is not necessary to perform multiple samplings to improve the accuracy of the data results, and at the same time avoids long-term data processing, thus achieving the goal of high-precision calculation in a short time. 2) For network models with complex connections but with correlation patterns, the minimum cut set can be obtained directly by finding the key features in the substation system, and the conditional probability of the output event can be quickly obtained by using the minimum cut set algorithm. This avoids the process of building a complex network model, thus enabling more efficient and rapid risk assessment of lifeline projects. 3) Conditional constraints are imposed on any node in the network model, while satisfying the multi-state probability design of each node, effectively meeting the actual needs in engineering. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a rapid substation seismic risk assessment method based on minimum cut sets, according to a specific embodiment of the present invention. Figure 2a This is a general plan view of a 220kV substation according to a specific embodiment of the present invention; Figure 2b This is a side view of the high-voltage side equipment of a 220kV substation according to a specific embodiment of the present invention; Figure 2c This is a side view of the low-voltage side equipment of a 220kV substation according to a specific embodiment of the present invention; Figure 3 This is a specific embodiment of the invention: a fault tree network model of a 220kV substation. Figure 4 This is a fault tree equivalent model of a 220kV substation according to a specific embodiment of the present invention; Figure 5 This is a specific embodiment of the seismic risk assessment index for a 220kV substation. Detailed Implementation

[0016] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0017] Figure 1 A flowchart illustrating a rapid substation seismic risk assessment method based on minimal cut sets, according to a specific embodiment of the present invention, is shown. Figure 1 As shown, this invention provides a rapid substation seismic risk assessment method based on minimal cut sets, comprising the following steps: S1: Determine the seismic intensity of the area where the substation is located, and clarify the type, number, and system connection method of the substation equipment; In step S1, the seismic intensity of the area where the substation is located is represented by the peak ground acceleration (PGA) and used as an indicator to measure the intensity of the earthquake.

[0018] S2: Seismic hazard analysis is performed, and the conditional probability of seismic risk is obtained by combining the seismic reliability analysis of the substation as follows: in: The conditional probability of seismic risk function failure in the substation system; This represents the failure probability of the substation system under a specific earthquake intensity. This represents the probability of an earthquake of a specific magnitude occurring in the area where the substation is located, where the earthquake magnitude is represented by the peak ground acceleration (PGA). In step S2, the conditional probability of the substation system's seismic risk function failure is the product of the substation's seismic failure probability and the probability of an earthquake occurring.

[0019] S3: Set the peak ground acceleration To reflect the seismic intensity of different seismic intensity zones, and since the power system is a crucial component of lifeline engineering, the seismic design code for power facilities requires an increased seismic fortification level of one degree, including peak ground acceleration. As shown in the following formula: in These respectively represent frequent earthquakes, earthquakes designed for earthquake resistance, and rare earthquakes; Indicates the earthquake intensity level; This represents the maximum horizontal seismic influence coefficient, obtained according to the Chinese Code for Seismic Design of Buildings. This represents the power amplification factor, which is generally taken as... .

[0020] S4: Establish a fault tree network model of the substation system, arrange and combine various basic events to obtain the minimum cut set of the event tree model, and transform the fault tree model into the equivalent model of the substation through the minimum cut set algorithm. The fault tree model in step S4 satisfies the following assumptions: 1) Assume each unit in the substation system as a basic event in the fault tree model, and assume the connection method of each unit in the substation system as the logical relationship of each basic event in the fault tree. 2) Assume the functional state of each unit as the conditional probability of the basic event; 3) The series and parallel connections between units are made through AND gates and OR gates in the fault tree; 4) The probability of the outgoing unit working normally is assumed to be the conditional probability parameter of the output event; In step S4, the reliability of various types of equipment is expressed in the form of seismic vulnerability curves. These curves follow a log-normal cumulative distribution with a median of λ and a log-standard deviation of λ, as shown in the following formula: ; In step S4, given the known probabilities of various basic events, the conditional probability of the output event is quickly calculated using the minimum cut set algorithm. When there are repeated events in each minimum cut set, the probability of the output event is calculated using the following formula: in: This indicates the probability of the output event W occurring; Indicates the minimum number of cut sets in the system; This represents the number of basic events in the i-th minimum cut set; This represents the probability of the j-th basic event occurring in the i-th minimum cut set of the system; This represents the union of the basic events in the r-th minimum cut set and the s-th minimum cut set in the system.

[0021] S5: Establish earthquake risk quantification indicators; conduct a quantitative assessment of the earthquake risk of the substation system from the two aspects of the key functional characteristics of the substation system, namely reliability and robustness. The goal of quantitatively assessing the seismic resistance of the substation is achieved by clarifying the normal operation probability of the substation system and establishing the remaining functional indicators of the substation system. In step S5, robustness refers to the substation system's ability to resist damage and maintain its functional level under earthquake conditions. Since the number of outgoing units in the substation system determines its power transmission level, a system residual function index is established considering the outgoing units and their corresponding weights. The functional level of a substation system is quantitatively assessed using the following formula: ; in: This represents the failure probability of the nth outgoing line unit in the substation system. This represents the weighting coefficient of the nth outgoing line unit in the substation system. N This represents the number of outgoing units in the substation system.

[0022] To gain a fuller understanding of the features of this invention and its applicability to practical engineering, this invention targets... Figures 2a-2cThe 220kV substation shown is assessed using a rapid seismic risk assessment method based on minimum cut sets. According to China's seismic classification, the structural fortification intensity for this region is 7 degrees (0.1g). Based on the importance of the power system, the fortification intensity needs to be increased by one degree, with a basic design seismic acceleration of 0.2g. The substation is mainly divided into five parts: 6 incoming line units, 2 high-voltage busbar units, 3 transformer units, 2 low-voltage busbar units, and 12 outgoing line units. Electrical energy enters the substation system through the incoming line units, is transmitted to the transformer units via the high-voltage busbar units, and then to the power users via the outgoing line units through the low-voltage busbar units. The substation has six types of equipment: DS-H, DS-V, CT, CB, TF, and PI, representing horizontal telescopic disconnect switches, vertical telescopic disconnect switches, current transformers, circuit breakers, transformers, and post insulators, respectively. The seismic intensity, substation equipment types, numbers, and system connection methods are determined to complete the initial conditions setting in step S1.

[0023] Based on this, step S2 was performed, and the failure probability under three different earthquake risk conditions was obtained by combining the seismic reliability of the 220kV substation system, as shown in Table 1. Table 1: Based on this, step S3 is performed. Since the structural fortification intensity of this area is 7 degrees (0.1g), the fortification intensity needs to be increased by one degree according to the importance of the power system. The basic design seismic acceleration is 0.2g, thus obtaining the peak ground acceleration under frequent earthquakes, fortified earthquakes, and rare earthquakes. As shown in Table 2; Table 2: Based on this, step S4 is performed, combining the key structural features of the substation, namely equipment type, equipment quantity, and equipment connection method, to obtain the system fault tree model, as follows: Figure 3 As shown; where IN, BUS220, TR, BUS110, and OUT represent the incoming line unit, high-voltage side busbar unit, transformer unit, low-voltage side busbar unit, and outgoing line unit, respectively; XI1-XI6 represent the normal operation probability of the six incoming line units; XP1-XP2 represent the normal operation probability of the two high-voltage side busbar units; XT1-XT3 represent the normal operation probability of the three transformer units; XB1-XB2 represent the normal operation probability of the two low-voltage side busbar units; by arranging and combining various basic events, the minimum cut set set of the event tree model is obtained, and the fault tree model is transformed into the equivalent model of the substation using the minimum cut set algorithm, as shown. Figure 4As shown in Table 3, the functional model of the substation system was established; the median and logarithmic standard deviation parameters of various equipment are shown in Table 3. Table 3: Based on this, step S5 is performed to analyze the post-earthquake functional level of the substation system and obtain the remaining seismic risk function of the system, as shown in Table 4. Table 4: The failure probability and remaining function of the substation system due to seismic risk are plotted as follows: Figure 5 As shown, from Figure 5 The study found that as earthquake intensity increased, the trends of system failure probability and remaining function were exactly opposite, but both reflected the changing law of substation system with earthquake intensity, proving the consistency and effectiveness of risk assessment indicators.

[0024] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A rapid seismic risk assessment method for substations based on minimal cut sets, characterized in that: First, the minimum cut set of the system is found using a fault tree model, and a network model of the substation system is constructed. Given the reliability of various equipment, the failure probability of the system is quickly assessed based on the probability of each path. Then, combining the seismic resistance of the substation system with the seismic risk probability, a seismic risk quantification index based on the key functional characteristics of the system is proposed. The minimum cut set algorithm is used to achieve rapid assessment of the seismic risk of the substation system. The method includes the following specific steps: S1: Determine the seismic intensity of the area where the substation is located, and clarify the type, number, and system connection method of the substation equipment; S2: Seismic hazard analysis is performed, and the conditional probability of seismic risk is obtained by combining the seismic reliability analysis of the substation as follows: ； in: The conditional probability of seismic risk function failure in the substation system; This represents the failure probability of the substation system under a specific earthquake intensity. This represents the probability of an earthquake of a specific magnitude occurring in the area where the substation is located, where the earthquake magnitude is represented by the peak ground acceleration (PGA). S3: Set the peak ground acceleration To reflect the seismic intensity and peak ground acceleration in areas with different seismic intensities As shown in the following formula: ； in These respectively represent frequent earthquakes, earthquakes designed for earthquake resistance, and rare earthquakes; Indicates the earthquake intensity level; This represents the maximum value of the horizontal earthquake influence coefficient. Indicates the power amplification factor; S4: Establish a fault tree network model of the substation system, arrange and combine various basic events to obtain the minimum cut set of the event tree model, and transform the fault tree model into the equivalent model of the substation through the minimum cut set algorithm. S5: Establish quantitative indicators for earthquake risk; conduct a quantitative assessment of the earthquake risk of the substation system from the perspectives of reliability and robustness, and achieve quantitative assessment of the substation's seismic resistance by clarifying the normal operation probability of the substation system and establishing indicators of the remaining functions of the substation system.

2. The rapid substation seismic risk assessment method based on minimum cut sets according to claim 1, characterized in that: In step S1, the seismic intensity of the area where the substation is located is represented by the peak ground acceleration (PGA) and used as an indicator to measure the intensity of the earthquake.

3. The rapid substation seismic risk assessment method based on minimum cut sets according to claim 1, characterized in that: In step S2, the conditional probability of the substation system's seismic risk function failure is the product of the substation's seismic failure probability and the probability of an earthquake occurring.

4. The rapid substation seismic risk assessment method based on minimum cut sets according to claim 1, characterized in that: The fault tree model in step S4 satisfies the following assumptions: 1) Assume each unit in the substation system as a basic event in the fault tree model, and assume the connection method of each unit in the substation system as the logical relationship of each basic event in the fault tree. 2) Assume the functional state of each unit as the conditional probability of the basic event; 3) The series and parallel connections between units are made through the "AND gate" and "OR gate" logic gates in the fault tree; 4) The probability of the outgoing unit working normally is assumed to be the conditional probability parameter of the output event.

5. The rapid substation seismic risk assessment method based on minimum cut sets according to claim 1, characterized in that: In step S4, the reliability of various types of equipment is expressed in the form of seismic vulnerability curves. These curves follow a log-normal cumulative distribution with a median of λ and a log-standard deviation of λ, as shown in the following formula: 。 6. The rapid substation seismic risk assessment method based on minimum cut sets according to claim 1, characterized in that: In step S4, given the known probabilities of various basic events, the conditional probability of the output event is quickly calculated using the minimum cut set algorithm. When there are repeated events in each minimum cut set, the probability of the output time is calculated using the following formula: ； in: This indicates the probability of the output event W occurring; Indicates the minimum number of cut sets in the system; This represents the number of basic events in the i-th minimum cut set; This represents the probability of the j-th basic event occurring in the i-th minimum cut set of the system; This represents the union of the basic events in the r-th minimum cut set and the s-th minimum cut set in the system.

7. The rapid substation seismic risk assessment method based on minimum cut sets according to claim 1, characterized in that: In step S5, robustness refers to the substation system's ability to resist damage and maintain its functional level under seismic loading, establishing a system residual function index. The functional level of a substation system is quantitatively assessed using the following formula: ； in: This represents the failure probability of the nth outgoing line unit in the substation system. This represents the weight coefficient of the nth outgoing line unit in the substation system; N represents the number of outgoing line units in the substation system.

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