Abstract
In terms of earthquake disaster loss modeling research, the main international research lies in disaster loss risk assessment, which studies the risk of damage outcomes and their impacts with an indicator system model.
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4.1 Current Status of Disaster Loss Modeling Research
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In terms of earthquake disaster loss modeling research, the main international research lies in disaster loss risk assessment, which studies the risk of damage outcomes and their impacts with an indicator system model. From the 1970s to the present, various governments have made great progress in disaster risk research and application, while many scholars have conducted in-depth research on disaster risk. A series of global and regional comprehensive disaster risk assessment programs, such as the Disaster Risk Indicator Initiative (DRI), the Multi-Period Indicator Program (HotsPot), and the American Programme (AP), have been carried out internationally for the first time, and corresponding results have been achieved. In the 1990s, the Scientific and Technical Committee of the United Nations International Decade for Disaster Reduction approved the Global Earthquake Hazards Assessment Program to reduce earthquake disaster losses, and the United States, France, and several other countries conducted risk assessment and risk management studies for different spatial scale regions and domains such as entire countries, regions, states, provinces, and societies. In 2005, the Organization for Economic Cooperation and Development (OECD), in order to reduce earthquake losses, proposed the development of a global risk assessment, using the Global Earthquake Model (GEM) as the authoritative standard for earthquake hazards and risks. In 1985, the Applied Technology Council (ATC) completed and published the ATC-13 (Vulnerability Inventory Method) report, which proposed a set of expert experience-based seismic hazard assessment (ATC-13) methods. In 1997, FEMA and NIBS developed a GIS-based seismic hazard damage assessment software that included seismic hazard, structural vulnerability, and economic and social vulnerability (HAZUS). In 1999, HAZUS99 was further improved, and in 2004, the ability to estimate losses from floods and hurricanes was added, resulting in a multi-hazard disaster loss assessment software (HAZUS-MH) that can quickly and accurately assess human casualties, building (structure) damage conditions, economic losses, and secondary hazards caused by earthquakes. At present, HAZUS-MH has been widely used. In 1951, Kawasumi showed that there was a linear correlation between the magnitude and intensity of earthquakes, and in 1970, Lomnitz explored the relationship between earthquake casualties and the time of the earthquake based on the data of the Chilean earthquake. In 1976, Westgate and O'Keefe, geographers at the University of Bradford, UK, were the first to explore the correlation between vulnerability and population and economy. In 1983, Ohta, et al. identified a mathematical model of the number of earthquake fatalities and the amount of building damage, and in 1983, Rachel Davidson proposed the first earthquake disaster risk index (EDRI) to quantify the level of earthquake risk among cities and to compare the relative severity of potential earthquake hazards and the contribution of different factors to earthquake risk. The first earthquake damage assessment was conducted after the 1989 Datong earthquake in Shanxi Province, and the first earthquake damage analysis of the Tangshan earthquake was conducted by Liu Chuoxian in 1986. Huang Chongfu and Shi Peijun established a mathematical model for urban seismic hazard risk evaluation using fuzzy set method, and gave a model of earthquake incubation environment, a model of earthquake intensity decay, and a formula for calculating urban hazard risk. Fu Zhengxiang and Li Ge Ping analyzed the relationship between the number of earthquake fatalities and the magnitude, seismic intensity, and damage state of houses. Yin Zhiqian et al. proposed the relationship between building vulnerability and seismic hazard loss, and at the same time gave a dynamic building damage matrix based on time change, and established the link between future building damage matrix and current existing building damage. The seismic damage matrices for single and group buildings were established by Sun, Baotao et al. Jane You et al. applied the information diffusion method to analyze the seismic hazard risk in the western region from two aspects: annual maximum magnitude and annual frequency of seismic hazard at all levels, respectively, and the overall feature is that the smaller the seismic hazard level is, the larger the occurrence probability value is. Some other scholars have carried out the work of seismic hazard damage assessment by combining the secondary development of RS and GIS with a series of software. For power grids, researchers elaborated the mechanism and analysis methods of the impact of seismic hazard on power grids from the perspective of equipment vulnerability or resilience by calculating the ground shaking intensity at the location of power grid equipment. Shouxiang Wang studied the damage probability of towers under seismic hazards and assessed the resilience of distribution networks; Tianhua Li studied the vulnerability of grid nodes under seismic effects using a variable fuzzy clustering model; Han Wang conducted a study on the seismic impact of electrical interconnection systems and assessed the resilience of electrical interconnection systems under earthquakes. Among the existing studies, the research on electrical system vulnerability or toughness helps to identify the risk of the grid system, which has a certain effect on improving the resilience of the grid system from the perspective of precautionary measures, and it is difficult to accurately predict the occurrence of earthquakes with today's technical means, while the completion of the disaster damage prediction in the first time after the earthquake is beneficial for the emergency commanders to make timely decisions and deployments, and to carry out emergency repair for the possible key loss equipment. This is of great significance for post-disaster emergency response and recovery. Many scholars at home and abroad have conducted a series of studies on earthquake damage prediction from the perspective of theoretical and mathematical models, but the overall research on earthquake damage assessment and prediction of power grid equipment is still in the initial stage, and the mechanism and assessment methods need to be further explored.
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In terms of typhoon disaster loss model research, although in recent years, China has attached importance to the assessment of typhoon disaster risk and organized experts, scholars and research institutions to find solutions, a unified and comprehensive assessment method has not yet been formed and is still at the stage of mapping and discussion. Early studies on typhoon disaster risk assessment, early warning and damage assessment were mainly based on historical statistics, using mathematical statistics and data mining methods. Such methods select assessment factors from disaster-causing factors, disaster-bearing bodies, and disaster-inducing environments, and use historical data to train the selected models, which are then used for disaster assessment. In terms of risk assessment, a more representative one using mathematical statistical methods is the risk assessment of typhoon disasters in Guangdong and Zhejiang by Ding Yan, Peijun Shi, and Yafei Zhou, respectively. Mathematical statistics and data mining methods require a large amount of accurate historical typhoon disaster data as support, while the early data have certain defects due to many reasons such as backward technology, and even the monitoring data in recent years have been questioned, which seriously affects the accuracy of the assessment; typhoon disaster-causing principles are complex, so the disaster assessment also requires a high level of modeling methods, as far as the modeling methods used by scholars are concerned The results of the disaster assessment are simple, but with only a set of overall data of the disaster, such as the amount of economic loss, the number of casualties, etc., which cannot reflect the spatial and temporal distribution of the disaster. With the popularization of GIS application, its powerful spatial analysis and mapping capabilities, fine grid processing and visualization results display, more and more scholars at home and abroad apply it in the study of typhoon disasters. With the help of GIS tools, these methods are combined with system tools to input hazard system data such as hazard-causing factor hazard, disaster-inducing environment sensitivity, and vulnerability of disaster-bearing bodies, and to use GIS spatial up-and-down superposition operations to map out the regional risk and disaster distribution in the form of heat maps. GIS software is also suitable for risk assessment of typhoon hazards by overlaying typhoon wind and rain intensity and frequency with environmental sensitivity and vulnerability of disaster-bearing bodies in GIS to obtain risk distribution maps. The GIS-based analysis method has also replaced the mathematical and statistical methods as the mainstream of current research. However, the problem of such methods is that the rationality of the simple GIS spatial overlay method is doubtful, and the accuracy and stability of the research results have not been tested by cases. In terms of disaster assessment method applications, although China's Central Weather Bureau and Shanghai Typhoon Institute also have advanced typhoon information systems, these systems tend to focus on weather forecasting and the impact of weather factors, and do not assess disasters or generate countermeasure recommendations. The IMASH intelligent integrated dynamic information management tool in the United States, which can provide comprehensive data and emergency response plans for relevant hurricane hazards, can be considered as a disaster assessment system in the true sense. Scholars in China have also done a lot of research and accumulated many results. For example, with Zhejiang, Hainan, Anhui, Taizhou and other regions as research objects, they are making attempts to apply wind hazard assessment methods in practice. However, in typhoon risk planning and disaster assessment, research results in Guangdong Province are relatively scarce. The budget models studied by many scholars in the past are almost all based on a single linear regression model. Whereas the influence factors of natural disasters (typhoon intensity factors, geographic environment and socio-economic conditions) and disaster situations have highly uncertain non-linear relationships, traditional mathematical models can hardly solve such problems satisfactorily. After the accumulation of research and improvement of methods, the current disaster loss prediction methods can be broadly divided into two categories: one is to construct nonlinear prediction model methods (such as neural network, SVM, etc.) for disaster loss prediction; and the other is to make comprehensive use of geographic information system (GIS), remote sensing (RS), numerical simulation and other technologies for disaster loss prediction. In the power grid, typhoon-induced transmission tower collapse and wind deflection discharge have attracted a lot of attention from researchers. Regarding the analysis of downed towers of transmission towers, the finite element method is generally used for structural modeling Kitipornchai used the beam-column model to derive the geometric nonlinear stiffness matrix with only one unit representing one rod, used the concept of concentrated plasticity analysis and yield surface for material nonlinearity, considered the nonlinear properties of shear bolts, and analyzed the nonlinear morphology of transmission towers under static forces. The curve of displacement of the top node of the tower versus the applied load is used to determine the damage of the transmission tower. Jinwen Wang established a structural finite element model and finite element model modification for a towering transmission tower structure, proposed a dynamic analysis method for the tower-line coupled system under the action of ordinary near-ground wind loads, a fatigue life estimation method for high circumferential crack sprouting caused by long-term wind vibration, studied the mechanical model for down-strike storm loads and the method of simulation, a plastic fatigue damage model for spatial steel structure rods, and considered the fatigue damage model to simulate the transmission tower structure under strong wind.Irvine used two methods, considering transmission line stiffness and not considering transmission line stiffness, to build a continuum model of the structure and analyze the dynamic characteristics of the structural model of the cable tower structure under wind loads. Tsujimoto et al. proposed a multi-degree-of-freedom spring-mass calculation model of the conductor, and calculated the wind deflection response of a single-span conductor and compared it with the measured results of the line. The current code in China uses a single pendulum model to calculate the wind deflection of the conductor by the static method. Some researchers have established the static and dynamic models of the conductor respectively, simulated and compared the dynamic characteristics of different conductors in different wind speeds, and proposed that with the increase of the file distance, the focus of suppressing the asynchronous wind deflection protection is the horizontal interphase, and the analysis shows that the contribution of multi-order vibration type must be considered in the calculation of dynamic wind deflection of the conductor, and the current transmission line design does not consider the value of wind deflection pulsation as the main cause of wind deflection flashing under high wind. The failure to consider the wind deflection pulsation value in current transmission line design is one of the main causes of wind deflection flashover under high wind. So far, based on the development of meteorological science, typhoon paths and wind speeds have been predicted by scholars, which lays the foundation for the scientific, accurate and quantitative development of typhoon damage prediction for power grid equipment. Today's research focuses on the impact of typhoons on lines and towers, as well as the impact of secondary typhoon hazards, such as high winds and strong convection and other extreme weather, on power grid equipment, and the corresponding damage mechanisms and assessment models need to be studied in depth.
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In terms of flooding, developed countries started to carry out relevant flood damage calculation work at a very early stage. Developed countries such as the U.S., Japan, and France have carried out meticulous and comprehensive research and survey projects for the evaluation of flood losses. In developed countries and regions, flood insurance is widely purchased, and statistical information such as socio-economic information and information on the vulnerability of various industrial assets necessary for flood damage assessment is more complete, which provides data support for timely and efficient evaluation of flood damage. Since the 1960s, the U.S. government has carried out extensive research on floodplain management and developed a comprehensive approach to flood damage assessment. In 1978, based on the simulation model developed by his predecessors, Professor Lee in the U.S. solved a new curve for many different types of properties, which is called the average curve. This curve was widely used in the calculation of flood damage. In the 1990s, Jonge used GIS to study the evaluation and calculation methods of flood losses; in the same period, proferi used Landsat remote sensing data to carry out flood damage assessment; Srikantha Herath in Japan used geographic information technology and remote sensing technology combined with distributed hydrological models to carry out flood inundation calculation and related damage The insurance companies in Munich, the second largest city in Germany, firstly researched a set of flood damage assessment model that can be used in the whole country according to the willingness to insure, which provides data support for insurance payouts in flood disasters and provides new ideas for the development of the insurance industry. Compared with the perfection of foreign flood evaluation system, the research of flood damage assessment tools in China started later, and along with the global scientific research on flood prevention and mitigation, the results of flood damage calculation gradually appeared in China until the 1980s. In the loss assessment of flash floods, Huang Wei, Nie Hua, Zhang Jieyun and others have carried out many mapping research works. For example, in 2005, Huang Wei et al. systematically analyzed and organized the existing flood disaster investigation and assessment methods at home and abroad, and explored the method of using the frequency method to assess the benefits of flash flood disaster control. In 2006, Nie Hua et al. used the pilot flash flood control carried out in 2002 in Washing Horse Township, Hongjiang City, Hunan Province, as an example, and elaborated from two parts: disaster loss assessment and study of prevention and control benefits. In 2000, Feng Wei et al. et al. explored the losses in urban flooding, summarized the loss laws, and established a flood disaster loss simulation and early warning model; Wang Waxchun et al. studied the typical flood disasters in Taihu Lake area by combining socio-economic information analysis, and obtained a flood disaster prediction and early warning model and a water body overflow range model for the area; in 2012, Zhang Jieyun et al. used remote sensing technology combined with information grid technology to establish a model for damage assessment of flood disasters, taking into full consideration the uneven distribution of socio-economic data. In terms of power grid, Alexis Kwasinski et al. conducted a study on the reliability of power system operation in the Garner region of the U.S. By collecting meteorological data under the local floods caused by heavy rainfall and the damage data of major power equipment such as transformers and insulators, and based on BP neural network theory, they analyzed the impact of rainfall intensity on major power equipment such as transformers and insulators. Xin Miao et al. collected meteorological, geographic and electric power data under 18 floods in Wilmington area from 1985 to 2005 for the safe operation of electric power system, and based on statistical analysis theory, they established a linear Hybrid model, which also uses the feature quantity extraction method to extract feature quantities from meteorological factors, geographic factors and electric power factors to establish a model of the impact of flooding on electric power equipment and to test the fit of the model. They also established a probability model of rainfall intensity, estimating the probability of insulator flashover and the probability of transformer failure, and calculating the probability of transmission and substation line outage failure under flooding, and based on this, they completed the power system load cutting. On this basis, the calculation of power system load shedding and economic loss evaluation of power outage are completed. For the prediction of grid damage in flooding, a comprehensive judgment should be given with the local geological and hydrological information of the equipment. In recent years, with the continuous development of fluid mechanics, seepage mechanics and CFD technology, the research results of heavy rainfall and flooding disaster loss have emerged. In addition, the 7–20 extreme rainstorm disaster in Henan Province has also sounded an alarm to emergency responders that the mechanism of damage to different power grid equipment by heavy rainfall and flooding varies, and the existing damage assessment methods are subjective and quantitative and accurate evaluation methods need to be further explored.
4.2 Typical Disaster Event Loss Model
4.2.1 Earthquake Disaster Damage Model
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Ground vibration parameters and their attenuation relations
PGA is the first and most widely used strength indicator in most countries, but PGA mainly reflects the amplitude characteristics of the local high frequency components of seismic waves, and the high frequency components do not play a key role in the seismic response of the structure. PGV is another important ground-vibration strength index, which is used in Japanese seismic design codes to guide the seismic design of engineering structures in correspondence with the seismic intensity:
where \(a(t)\) is the acceleration of ground shaking at time \(t\); \(v(t)\) is the velocity of the ground shaking at time \(t\); \(d(t)\) is the displacement of ground shaking at time \(t\).
The ground shaking attenuation relationship is a functional relationship that characterizes the variation of ground shaking parameters with magnitude, distance, site and other factors. Common ground shaking parameters in engineering include seismic intensity, acceleration, velocity, displacement peak, as well as ground shaking response spectrum, ground shaking holding time and ground shaking envelope function, etc., while the more common name for the attenuation relationship in the international arena is the ground shaking prediction equation.
The attenuation relationship describes the different effects of earthquakes on sites under different conditions, and has a wide range of uses in seismic zoning, seismic safety evaluation of engineering sites and earthquake damage prediction, and is of great research importance in engineering. Both seismic zoning and small-area zoning require the use of attenuation relations to determine ground-motion input parameters. Strong ground shaking attenuation relations can roughly determine the impact of engineering sites during earthquakes based on the characterized earthquake source, propagation path and local site conditions, and therefore have an important role in seismic risk assessment.
The earliest documented empirical decay relationship was proposed by Esteva and Rosenblueth in 1964:
where \(a\) is the peak acceleration of ground shaking in cm/s2. The two used data from the western U.S. ground shaking record to determine the coefficients in the attenuation relationship: \(c=2000, \alpha =0.8,\) and \(\beta =2\).
Due to the historical conditions, the initial attenuation relationships were often very simple and were based on a relatively small number of observation records. With the gradual accumulation of ground-motion records and the gradual improvement of observation means, attenuation relations that take into account more complex conditions began to appear.
Campbell C selected 229 horizontal acceleration records from 27 earthquakes worldwide and regressed the peak accelerations using a weighted least squares method. The peak acceleration was regressed using the weighted least squares method to obtain the decay relationship.
\(Y\) is the peak acceleration, \(M\) is the magnitude, and \(D\) is the epicenter distance.
The records he selected do not impose restrictions on seismic magnitude, fault type, or geological conditions at the record site, but they do provide a more detailed classification of the previous simple method of site delineation, i.e., bedrock and overlying layers, respectively. The importance and necessity of this classification idea is pointed out in the subsequent comparison in his paper.
In contrast, J.R. Huo selected 329 acceleration records from 41 earthquakes in the western United States and mixed them with single and multiple random variable regressions of peak and absolute acceleration response spectra without distinguishing between bedrock and upper layers:
In addition, they weighted the information to ensure that the sum of the weight coefficients was uniformly distributed in the M-R plane, and the magnitude and distance were graded.
In general, the attenuation relationship is the variation of peak ground acceleration with seismic intensity and epicenter distance, mostly obtained by fitting. Yu Yanxiang and Xiao Liang et al. gave the Seismic ground motion parameters zonation map of China (GB18306-2015) in the research results from the eastern strong seismic region:
When the earthquake magnitude \(M<6.5\):
where \(Y\) represents the peak ground acceleration, \(R\) is the epicenter distance, \(M\) is the magnitude, \({A}_{1}\), \({B}_{1}\) \({A}_{2}\), \({B}_{2}\), \(C\), \(D\), and \(E\) are the regression coefficients, and \(\varepsilon \) is the standard deviation.
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Ground shaking of power grid equipment causes disaster mechanism
The probability of different degrees of damage to the grid equipment can be described by the cumulative log-normal distribution function as:
In the formula, k = 1, 2, 3, 4, respectively, indicates four damage states: minor damage, moderate damage, server damage, and complete damage. \({p}_{k}^{\mathrm{DMG}}\) is the probability of the equipment reaching the \(k\)th damage state, which is related to the intensity of ground shaking in its area; \({\lambda }_{k}\) and \({\xi }_{k}\) are the log mean and standard deviation of the vulnerability curve of the equipment in the \(k\)th limit damage state, respectively. This formula is a common formula for analyzing the damage degree of building facilities, transportation systems, lifeline systems, etc. under earthquakes, and is widely used worldwide for calculating the damage rate of facilities under earthquake hazards.
For some of the grid equipment, the damage curves are shown in Figs. 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, and the peak ground acceleration decay relationship in the eastern part of China is shown in Fig. 4.13.
Damage curves for low-voltage substations with seismic-resistant components
Damage curves for medium voltage substations with seismic-resistant components
Damage curves of high-voltage substations with seismic-resistant components
Damage curves of low-voltage substations without seismic elements
Damage curves of medium voltage substations without seismic elements
Damage curves of high-voltage substations without seismic elements
Damage curves of distribution lines with seismic-resistant components
Damage curves of distribution lines without seismic elements
Damage curves for small power generation facilities with fixed components
Damage curves for small power generation facilities with unfixed components
Damage curves of medium and large power generation facilities with all fixed components
Damage curves for medium and large power generation facilities with unfixed components
Decay relationship of peak ground acceleration in eastern China
The combined percentage of damage to grid equipment in a single earthquake can be expressed as:
where
where \({\omega }_{k}\) is the weight coefficient of grid equipment in the kth extreme damage state, which is dynamically set according to the size of the regional PGA in proportion to the vulnerability curve; \({Z}_{k}\) is the percentage of damaged grid equipment corresponding to the \(k\)th extreme damage state. The proportions of light, moderate, high and complete damage of the equipment are 4%, 12%, 50% and 80% respectively, i.e. \({Z}_{1}\) = 4%, \({Z}_{2}\) = 12%, \({Z}_{3}\) = 50% and \({Z}_{4}\) = 80%. As an example, the percentage of damaged distribution lines is shown in the figure. As seen in Fig. 4.14, the proportion of faults in distribution lines increases as the magnitude increases or the epicenter distance decreases, and when the magnitude is >6.5, the proportion of damaged distribution lines increases sharply regardless of the epicenter distance.
Degree of damage to distribution network lines
The research in this section shows that earthquake damage analysis can be used to quantitatively describe the degree of damage to grid equipment under a certain intensity earthquake by combining the calculation of peak ground acceleration (PGA) with a loss probability function to provide assistance to emergency commanders.
4.2.2 Landslide Disaster Damage Model
The common theory of slope stability analysis in engineering is the limit equilibrium method based on the strength criterion of Moore and Coulomb. The limit equilibrium method has two basic characteristics. Firstly, it only considers the mechanical equilibrium condition and the Mohr–Coulomb law. The second is that by introducing some simplifying assumptions, the problem becomes static and solvable. The expressions are:
where \({\tau }_{f}\) is the shear stress on the damage surface; \({c}^{\mathrm{^{\prime}}}\) is the effective cohesion of the soil; \(\sigma ,\sigma^{\prime}\) are the total stress on the damage surface; \({\phi }^{\mathrm{^{\prime}}}\) is the effective internal friction angle of the soil; \(u\) is the pore water pressure.
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Seepage slope instability
The root cause of slope instability is that the shear stress is located on a certain surface inside the soil exceeds or is at the critical value of its shear or crack strength, resulting in the loss of balance inside the soil. Due to the increase of shear stress or the weakening of the shear strength of the soil itself, the shear stress reaches or even exceeds its own shear or crack strength, and this damage and sliding will be increased by the effect of rainfall infiltration. For example, the infiltrated rainwater makes the soil, which is unsaturated at the beginning, reach saturation, thus causing its capacity to increase, which makes the shear stress inside the soil increase, and along with the increasing infiltration of rainfall, the water content of the soil continues to increase, and the strength will also change. Under the infiltration of rainfall, the pore water pressure, that is, the fluid in the soil particles between the pores of the seepage water pressure, in the calculation of its stability, along the arc sliding surface of the pore water pressure, despite all through the sliding circle resulting in no sliding moment, can reduce the effective stress to a certain extent so that the shear strength is reduced, and therefore has a great impact on stability.
To analyze the influence of rainfall infiltration on slope stability, we focus on the effect of seepage water body on slope, including dynamic water load and static water load. With the dynamic water load, that is, the flow of water in the soil, for the fluid on the soil particles have a certain impact or tug force and exert adverse impact on the stability of the slope, especially when the slope has downhill outflow, while with the existence of infiltration force, the stability of the slope is greatly unfavorable. The so-called hydrostatic load, results from the situation where the water content of the soil in the unsaturated area of the slope increases continuously with the infiltration of rainfall, the capacitance increases, and the pore water pressure may also increase, which leads to an increase in shear stress or a decrease in the shear strength of the soil itself.
In general, unsaturated soils of the same nature exceed saturated soils in strength. Only when the water content of unsaturated soils increases do the suction force and the strength of the soil decrease substantially. However, the effective internal friction angle \({\varnothing }^{\prime}\) of both saturated and unsaturated clay soils is less affected by external forces or matrix suction.
The soil in the unsaturated zone will increase in water content with the infiltration of rainfall, which makes part of the unsaturated soil transform to saturated soil and makes the shear strength decrease, while the matrix suction decreases, which further makes the shear strength of the unsaturated soil decrease. For several years, studies have shown that the loss or reduction of matrix suction in unsaturated soils caused by infiltration of rainwater has a great influence on the shear strength of unsaturated soils, and the matrix suction affects the stability of slopes by influencing the shear strength of slope soils.
The infiltration of rainwater first increases the saturation of the soil in the surface layer, then gradually moves to the lower part and accumulates in the impermeable layer at the foot of the slope first, making the infiltration line form at the foot of the slope, which is due to the short infiltration path at the foot of the slope and the fast increase of saturation at the foot of the slope. After that, as the rainfall continues, the infiltration line at the foot of the slope rises and moves continuously. The increase of soil water content, i.e., the transformation of soil from unsaturated state to saturated state, mainly occurs within the infiltration line. Of course, the rise of pore water pressure, the decrease of soil strength and the increase of soil capacity are also the direct causes of slope instability.
Through the above analysis, it can be seen that different slope gradient and soil quality are greatly affected by rainfall, and soil slopes are also affected to different degrees with different rainfall intensity and types. Different soils have different permeability, and the mechanism of influence on slope stability is also different; the larger the slope is, the smaller the stability under rainfall is; the larger the average daily rainfall intensity is, the lower the safety coefficient of soil slope is (since the surface layer of soil slope will form a transient saturation zone when encountering strong rainfall, thus making the infiltration capacity of soil body lower, and rainwater cannot infiltrate and overflow); the smaller the rainfall intensity change is, the lower the corresponding safety factor is.
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Seismic slope instability
The current seismic slope stability analysis is mainly based on limit equilibrium theory and stress-deformation analysis. For saturated state soil, because the water in the soil cannot provide shear strength, according to the Mohr–Coulomb law and the effective stress principle, the factors affecting the soil strength from the above equation of soil shear strength are the effective stress \(\sigma^ {\prime}\), cohesion \(c^{\prime}\) and the angle of internal friction \(\phi^{\prime}\). In general, earthquakes last from a few seconds to several tens of seconds, and the water pressure \(u\) generated by the earthquake in such a short time does not dissipate in time. The effective stress \(\sigma^{\prime}\) in the soil is reduced because it does not dissipate in time. At the same time, there is a seismic action to cause super pore water pressure, which will make the soil content. The increase of water content will weaken the soil cohesion \(c^{\prime}\) and the angle of internal friction \(\phi ^{\prime}\). These are the reasons for the decrease of soil shear strength due to earthquake.
Earthquake has always been one of the factors to be considered in slope stability analysis. The main research concerns of slope stability analysis under the effect of earthquake are: (a) how to calculate the seismic force; (b) the location and shape of slope instability; (c) the possibility and factors to judge the slope instability under the effect of earthquake; (d) the calculation of permanent deformation or permanent displacement of slope instability. The first two are the prerequisites of the study, and the last one is the key research concern. The main causes of slope instability under earthquake action are inertia force caused by seismic force and reduction of shear capacity due to cyclic degradation. Usually, the seismic slope instability includes inertial instability and attenuation instability.
Seismic dynamics is very complex, so in order to simplify the calculation, it is unified and simplified into horizontal seismic dynamics and vertical seismic dynamics, and the following are their effects on the slope soil stress respectively. For the horizontal seismic force, it is assumed that the seismic wave is simple harmonic (mainly for the quantitative expression of the earthquake), and the seismic dynamics is shown in Fig. 4.15.
Horizontal seismic dynamics (harmonic wave)
For a simple slope, before the earthquake, the stress state of a soil unit within the slope soil is shown in Fig. 4.16, where \({\sigma }_{1}=\gamma h\), \({\sigma }_{3}={k}_{0}\gamma h\), which corresponds to the solid line circle in the Mohr stress circle. During the earthquake, the stress state of this soil unit at time \({t}_{2}\) is: \({\sigma }_{1}=\gamma h\), \({\sigma }_{3}^{\mathrm{^{\prime}}}={k}_{0}\gamma h{F}_{h}\), which corresponds to the dashed circle in the Mohr stress circle, as shown in Fig. 4.17. The dashed circle is closer to the strength damage line than the solid circle, indicating that the horizontal component of the seismic dynamics can make the soil stress state close to the damage.
Soil unit stress state diagram
The effect of horizontal seismic dynamics on the stress state of the soil unit
Near the top of the slope and the slope face, because h is smaller, when the earthquake is strong, the main stress \({\sigma }_{3}^{\prime} \,={ k}_{0}\gamma h{F}_{h}<0\), that is, the slope top and slope face parts are likely to have tension, which well explains why the slope first appears at the slope face and the top of the slope.
Vertical seismic dynamics is caused by the longitudinal waves in seismic waves, and its destructive force cannot be ignored. The vertical seismic force analysis can be carried out in the same way as the above-mentioned analysis of the effect of horizontal seismic dynamics on the force state of soil units, i.e., the vertical seismic force where the change with time is also in the form of simple harmonic waves. Before the earthquake, the stress state of a unit in the slope soil body is shown as the solid circle in Fig. 4.18, \({\sigma }_{1}=\gamma h\), \({\sigma }_{3}={k}_{0}\gamma h\). During the earthquake, the stress state of the unit at \({t}_{1}\) time is: \({\sigma }_{1}^{\prime} \, = \, \gamma h+{F}_{h}\), \({\sigma }_{3}={k}_{0}\gamma {h}_{h}\), as the dashed circle in the next. The dashed circle is also closer to the strength damage line (solid line) than the solid circle, indicating that the vertical component of the seismic force makes the increase of the first principal stress, which causes the stress state of the soil unit to be on the verge of damage. \({t}_{2}\), \({F}_{h}\) is reversed with gravity, \({\sigma }_{1}^{\prime} \, = \, \gamma h-{F}_{h}\), and the shear strength of the soil unit can be expressed as the dashed line in the figure at this time. It can be seen that the vertical seismic force at time \({t}_{2}\) also leads to the reduction of soil strength and causes the slope instability damage. Therefore, the influence of the vertical seismic force should be fully considered in the seismic slope stability analysis.
The effect of vertical seismic dynamics on the stress state of the soil unit
In summary, rainfall will reduce the strength of the slope body, while seismic forces (including seismic horizontal and vertical dynamics) likewise have an effect on the strength of the slope soil body. Under some specific conditions, such as continuous rainfall after a major earthquake, when a mega-earthquake occurs in an area with abundant rainfall, aftershocks and continuous rainfall after a major earthquake, the continuous influence effect of earthquake and rainfall may have a scourge weakening effect on the stability of the slope body, resulting in a huge landslide disaster.
The Newmark slider displacement method was first proposed based on the limit equilibrium theory for analyzing the stability of dams under the action of earthquakes, and was widely used in slope stability analysis due to the clear physical meaning of the model and the simplicity of the principle in subsequent studies. In order to make the model simple and easy to operate, only horizontal ground vibration is considered and acts in the direction of the slope, and the slider is displaced only when sliding downward, and the critical acceleration is kept constant.
The displacement principle of the Newmark slider is shown in Fig. 4.19. Assume that a slider of mass \(m\) is located on a slope with a slope of \(\theta^\circ \). The slider is subjected to both the anti-slip force \({F}_{f}\) along the upward slope and the downward sliding force \({F}_{S}\) along the slope, where \(\sigma \) is the positive stress generated by gravity \(mg\); σ is the positive stress generated by gravity mg; \(\tau \) is the shear stress generated by gravity \(mg\); \(\gamma \) is the weight of the slider soil, the thickness of the sliding block is \(h\), and \(a\) is the critical acceleration.
Newmark slider force analysis
The positive and shear stresses satisfy \(\sigma =\gamma h\mathrm{cos}\theta \,\mathrm{ and }\,\tau =\gamma h\mathrm{sin}\theta \), respectively. Since the anti-slip force is influenced by the shear strength of the soil, \({F}_{f}=TA\), \(T\) is the shear strength, \(T=C+\sigma \mathrm{tan}\varphi \), \(C\) is the equivalent cohesive force of the slide drawing, \(\varphi \) is the equivalent the effective internal friction angle, and \(A\) is the sliding block bottom area, then the anti-slip force can be written as:
The downward sliding force can be expressed as \(FS = \tau A\), which can be further expressed as:
According to the equation of motion it is known that \({F}_{f}-{F}_{S} = ma\), where \(m = hA (\gamma /g),\) combined with the above equation it is known that the critical acceleration is:
Let \({F}_{S}= a/a\mathrm{^{\prime}}\), where \(a\mathrm{^{\prime}}\) is the acceleration of ground shaking at any moment, then:
If the effect of pore water is considered, the safety factor equation can be rewritten as:
where \({t}_{w}\) denotes the ratio of the thickness of saturated water in the slide to the thickness of the slide, \({\gamma }_{w}\) denotes the weight of water (\(N/{m}^{3}\)), \({F}_{S}\) is the safety factor at this time, \({F}_{S}>1\) means the slope is in stable state, equal to 1 is the ultimate equilibrium state, when \({F}_{S}<1\), the slope is unstable. According to the analysis of rainfall, river runoff statistics and water content of sampling points in the study area, the water content of slopes in the study area is low, and the \({t}_{w}\) follows the normal distribution with the mean value of 0.3 and variance of 0.15. For the value of landslide thickness, the Newmark is applied to the natural shallow slope. As Newmark is applicable to the evaluation of natural shallow landslide hazard, Wang Tao et al. analyzed the landslide caused by the Hanchuan earthquake by taking the value of 4 m. When the value is 4 m, the physical properties of the strata in the study area are similar to those in the study area of the paper. Liu Jiamei evaluated the landslide hazard in Tianshui area. In the evaluation of landslide hazard in Tianshui area, the value of landslide thickness is 3 m. Considering the geographical proximity and the similarity of lithological and physical parameters of the strata with the study area, it is possible to evaluate the thickness of landslide in the study area. Taking into account the geographical proximity and the similarity of the physical parameters of the formation with the study area, the thickness of the landslide body h = 3 m can be taken as a reference.
When the slope is subjected to seismic action, the input ground shaking is greater than the critical acceleration, which will lead to instability of the slope and displacement along the slope surface. After stopping the input of ground shaking, the total displacement occurring in the landslide can be obtained by quadratic integration of the part of ground shaking acceleration \(a^{\prime}\left( t \right)\) greater than the critical acceleration \(a\):
Since the site type has little effect on the regression coefficients in the cumulative displacement model, the cumulative displacement is related to the ground vibration parameter PGA and the critical acceleration a is related as in Eq. (4.18):
where \(D\) is measured in \(cm\), and the coefficient of determination is \({R}^{2} = 91.4\%\), showing that the model has good correlation with the regression data. The correlation between the model and the regression data is good. The cumulative displacement of D characterizes the degree of damage to the slope caused by ground shaking. In general, 5 cm can be considered as the critical value of cumulative displacement for slope instability. Thus the probability of instability of a slope with critical acceleration a under the action of ground shaking with intensity value x can be expressed as:
where \(P(D\ge 5\, \mathrm{cm}|x,a)\) represents the probability that the slope produces \(a\) displacement \(D\) greater than 5 cm after a critical acceleration of a and an input ground vibration of \(x\).
The above analysis shows that researchers have analyzed the impact and influence of earthquakes on soil slopes with the help of NewMark theory and Mohr-Column damage criterion, and the evaluation and mechanism of earthquake-induced landslides have gradually changed from being qualitative to becoming quantitative.
Considering the impact damage process of the tower due to the instability of the rock slide, we aim to establish the mathematical model of the tower deformation due to the landslide, and the deformation process of the tower due to the rock slide is shown in Fig. 4.20.
Rock slide deformation process of the tower
From the energy point of view, the landslide body from high potential energy position to low potential energy position sliding process will be accompanied by a huge energy release, based on the landslide body movement energy consumption mechanism that can be obtained from the landslide body acting on the transmission tower equivalent impact force \(F = \sqrt {\frac{{6mgh \cdot E_{1} \left( {1 - \mu \cdot {\text{cot}}\theta } \right)}}{{x^{3} }}}\) \(x\) is the equivalent height from the base of the tower when \(F\) acts on the transmission tower; \(m\) is the total mass of the landslide body, \(h\) is the vertical height of the center of mass of the landslide from the base of the tower, \({E}_{1}\) is the bending stiffness of the transmission tower, \(\mu \) is the coefficient of friction of the sliding surface; \(\theta \) is the inclination angle of the slope body; \(g\) is the acceleration of gravity, often taken as 9.8 N/kg.
The linear displacement of the axis of an object such as a vertical tower in the direction perpendicular to the axis is defined as the deflection in structural mechanics, which is used to measure the degree of bending deformation of the object. Therefore, the deflection of the transmission tower is used as the control index and based on the cantilever beam. The top deflection of the transmission tower with flexural stiffness of \({E}_{1}\) is, which is based on the simplified method of cantilever beam: \(\omega (x)=-\frac{F{x}^{2}}{6{E}_{1}}(3H-x)\) where \(H\) is the overall height of the transmission tower; \(\omega \) value is negative; the smaller the value is, the greater the tower deflection is. It has been pointed out that the normal distribution can accurately express the deformation of transmission towers caused by landslides of the probability distribution. The deflection at the midpoint of the elastic cantilever beam, \({\omega }_{c}\) and the coefficient of variation \(\delta \) can be written as:\(f(\omega )=\frac{1}{\sqrt{2\pi \sigma }}\mathrm{exp}[-\frac{{(\omega -\mu )}^{2}}{2{\sigma }^{2}}]\), where \(\omega \) is the actual deflection degree; \(\mu \) is the mean value, often taken as\({\omega }_{c}\); \(\sigma \) is the standard standard deviation, often taken as\(\delta {\omega }_{\mathrm{max}}\). As the transmission towers are located in different environments and under different rainfall meteorological conditions, the coefficient of variation is 0.02~0.12.
The probability density function \(f(r,\omega )\) of transmission tower damage is a conditional probability density function, and the geotechnical landslide event and the tower deformation caused by the landslide are independent of each other. The events of landslide and tower deformation due to landslide are independent of each other, therefore, the transmission tower damage density function \(f(r,\omega )\) is the product of the probability density function of landslide and tower deformation,, i.e.,
Then the transmission tower damage probability \(F(r,\omega )\) is:
A transmission line consists of dozens or even hundreds of towers, a rainfall may cover multiple towers, the line Any tower damage in the line will result in the entire line out of service, and then the probability of loss of \({P}_{k}\) for line \(k\) is:
where \({F}_{m}\left(r,\omega \right)\) indicates the probability of damage of the mth transmission tower; \(n\) is the number of stalls of the \(k\)th transmission line.
This section of the study allows quantitative assessment of the impact of landslide hazards on transmission towers, calculation of the probability of line damage, and assistance in the development of emergency repair decisions.
4.2.3 Typhoon Disaster Damage Model
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Typhoon wind field calculation model
At present, the methods for solving the circulation wind speed component of tropical cyclone wind field can be broadly divided into two categories: the first category of methods is to solve the tropical cyclone pressure distribution first, and then derive the circulation wind speed distribution of tropical cyclone according to the gradient wind speed formula. The second method is based on the empirical model of tropical cyclone circulation wind speed distribution, which is given directly by the parameters of maximum wind speed and maximum wind speed radius, without solving the barometric distribution. This method is based on an empirical model of the tropical cyclone circulation wind distribution, which is given directly by parameters such as maximum wind speed and maximum wind radius, without solving the pressure distribution. The empirical model of circulation wind speed distribution in this type of method reflects the wind speed of tropical cyclone along the radial direction from the eye area to the cloud wall area (caused by the intersection of cold and warm air peaks), and the wind speed from the cloud wall area to the outer area gradually decreases. Commonly used empirical models of circulation wind speed distribution include Rankine model, Jelesnianski (1965) model, Jelesnianski (1966) model, Miller model, Chan and Williams model, etc.
The method of solving tropical cyclone wind field based on the empirical model of tropical cyclone circulation wind velocity distribution does not need to solve the pressure distribution first, so it has the advantages of simple principle and easy calculation. However, since both the circulation wind speed model and the moving wind speed model contain the key parameter of the maximum wind speed radius, it is necessary to identify the maximum wind speed radius more accurately first.
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Circulating wind speed calculation model
In general, typhoon transit will lead to the collapse of a large number of towers. After analysis, it is found that tower collapse is related to wind, the tower design strength, tower structure, geographic location and other factors.
Typical models for calculating the circulating wind speed are:
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a)
Rankine Model
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b)
Jelesnianski (1965) Empirical Model
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c)
Jelesnianski (1966) Empirical correction Model
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d)
Chen, Kongmo (1994) Empirical Model
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e)
Miller Model
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f)
Chan and Williams(1987) Model
In the above equations: \({V}_{\text{r}}\) is the circulation wind speed at a point in the tropical cyclone wind field, and \({V}_{\text{rmax}}\) is its maximum value; \(x\) and \(d\) are the shape parameters of the model.
If \(r/{R}_{\text{max}}\) is taken as the horizontal axis and \({V}_{\text{r}}/{V}_{\text{rmax}}\) as the vertical axis, the distribution of the circulation wind speed for each of the above models is shown in Fig. As can be seen from the figure, the general trend of the circulation wind speed distribution of each model is the same: as the observation point gradually moves away from the center of the tropical cyclone, the circulation wind speed increases first, and then gradually decreases after increasing to the maximum circulation wind speed at the radius of the maximum wind speed. The difference between the models is the speed of increase or decay of the circulation wind speed, as shown in Fig. 4.21.
Comparison of circulating wind speed models
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Maximum wind speed radius calculation model
Graham and Nunn studied tropical cyclones along the U.S. East Coast and in the Gulf of Mexico, plotted the effects of central pressure, geographic latitude, and migrating winds on the radius of maximum wind speed, and proposed a parameterization scheme for the radius of maximum wind speed.
where \(\varphi \) is the geographic latitude; \(V\) is the speed of the migrating wind; \({P}_{c}\) is the central pressure of the tropical cyclone.
Jiang Zhihui’s study, based on the “Tropical Cyclone Yearbook” central pressure and maximum wind speed radius information, analyzed the average trend of the maximum wind speed radius, giving the maximum wind speed radius of the tropical cyclone central pressure of the power exponential empirical formula.
Willoughby obtained an exponential relationship between the radius of maximum wind speed and the variation of maximum wind speed in the flight level and geographical latitude based on the flight sounding records of tropical cyclones in the Atlantic and Eastern Pacific Ocean from 1977 to 2000 published by the National Oceanic and Atmospheric Administration (NOAA).
where \({V}_{f{\text{max}}}\) is the maximum wind speed in the flight level; \(\varphi \) is the geographical latitude.
Kato, in his work on the simulation and evaluation of storm surges off the coast of Japan, pointed out that the linear expression for the radius of maximum wind speed versus the central pressure of a tropical cyclone:
The typhoon wind field model gives information on cyclone direction, wind speed and movement path in the local area, which can provide support and prerequisite for the establishment of typhoon disaster assessment model for power grid equipment.
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Wind speed and wind direction variation study
The non-uniformity of horizontal wind is an important source of danger in engineering construction, which is related to the wind-excited vibration and deformation of the structure. Wind shear can indicate the non-uniformity of horizontal wind. Both horizontal wind shear and vertical wind shear have the effect of structural damage. For engineering construction, horizontal wind shear can cause more severe damage than vertical wind shear, especially near the maximum wind speed radius and eye wall area. The main concern here is horizontal wind shear, and the equation is as in Eq. (4.33).
\({V}_{h}\) is the horizontal wind, \(u\) and \(v\) are the \(x\) and \(y\) components of the horizontal wind, and \({S}_{h}\) denotes the horizontal wind speed shear module, which reflects the reflects the horizontal non-uniformity of wind field. The wind speed run diagram and the maximum 10-m horizontal wind speed shear diagram are shown in Figs. 4.22 and 4.23.
Typhoon wind speed run chart
Maximum 10 m horizontal wind speed shear
The maximum horizontal wind speed shear Qiongzhou Strait during the passage of the typhoon is shown in the figure above. The prominent difference between these two typhoons is due to their different structures. Figure 4.23 shows that the horizontal wind speed shear is most significant in the area of the eye wall and the spiral rain band, while its horizontal wind speed shear is most significant near the eye wall because of its stronger and more compact structure.
The non-uniformity of the wind field is manifested not only in space but also in time. As in a moving and rotating rotating system, changes in the wind vector of a tropical cyclone can cause temporal variations and thus anomalies. Wind speed and wind direction are used to quantify these abrupt changes. They are defined as the difference between the wind speed and direction at time \(t\) and the previous time \((t-1)\), as shown in Fig. 4.24.
Maximum time variation of wind speed
It is clear from Fig. 4.24 that for tropical cyclones, the maximum values mainly vary from 15 to 35 m/s, distributed along the trajectory. In contrast, for typhoons, the greater the intensity is, the more drastic the temporal variation in wind speed is, arriving at 50 m/s before landfall. For the 30 min wind variation, the maximum values are mainly distributed in the typhoon eye area.
In summary, the temporal variation of wind speed is most significant in the spiral rainband area on the eye wall, while for wind direction the greatest temporal variation occurs in the eye area. The largest temporal variation in wind direction is in the eye region. Both parameters reflect the rapid changes in the core wind speed of tropical cyclones. These areas are particularly dangerous for engineering structures. In addition, the high values of the temporal variation of wind direction allow to visually track the tropical cyclone eye, where the risk is expected to be high.
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(3)
Construction of a disaster damage assessment model for typhoon disaster power grid equipment
In the course of typhoon, the risky towers in different geographical locations will last for a period of time from the beginning to the end of the typhoon impact. Under the cumulative effect of the growing duration, the reliability of the tower will be continuously reduced with the increase of plastic fatigue damage of the tower. At the same time, during this duration, the relative position of the typhoon center and the tower changes constantly, and the wind field strength of the typhoon itself also changes constantly, which leads to the constant changes in the wind speed of the tower.
As shown in Fig. 4.25, \(O^{\prime}\) and \({O}^{{\prime}{\prime}}\) with a risk tower distance from the risk wind circle radius \({R}_{risk}\) are the initial impact and end impact tower typhoon center points.
Short-term forecast under the tower affected by the typhoon diagram
Under the short-term linear forecast path, the latitude and longitude of the two intersections of \(O^{\prime}\) and \(O^{\prime}{\prime}\) can be calculated jointly, where the latitude and longitude coordinates of the risk tower are \(({x}_{g},{y}_{g})\), the latitude and longitude coordinates of the typhoon center \({O}_{1}\) and \({O}_{2}\) are\(\left({x}_{{O}_{1}},{y}_{{O}_{1}}\right),({x}_{{O}_{2}},{y}_{{O}_{2}})\), respectively, and \((x,y)\) are the coordinates of a point where the typhoon center is between \({O}_{1}\) and\({O}_{2}\).
where \(R\) is the radius of the earth, generally taken as 6371 km.
When \(O^{\prime}\) and \(O^{\prime}{\prime}\) latitudes and longitudes are the same, the tower is only affected by the wind speed of the typhoon risk circle, and there is no time cumulative effect. Otherwise, the tower is affected by the typhoon for the duration of:
where \(\mid {O}^{\prime}{O}^{{\prime}{\prime}}\mid \) is the length of the risk area from the beginning to the end of the typhoon effect on the tower; \(\mid {O}_{1}{O}_{2}\mid \) is the distance between \({O}_{1}\) and \({O}_{2}\), the short-term center points of the typhoon; \(\Delta T\) is the length of short-term forecast time.
During the typhoon, the distance between the tower and the typhoon center changes continuously due to the movement of the typhoon, and the wind speed of the tower also changes. According to the historical typhoon information, the typhoon's moving wind speed is generally much smaller than its circulation wind speed, especially in the high-grade wind speed component, the proportion of the circulation wind speed is more obvious, so it can be approximated that the typhoon circulation wind speed of the tower is constant within 10 min, and the duration of the tower by the typhoon is divided into n time intervals with 10 min as the span, that is:
Let \(({x}_{0},{y}_{0})\) be the latitude and longitude coordinates of the center \({O}^{\prime}\) where the typhoon begins to act on the tower, and assume that the typhoon at the short-term forecast time \(\Delta T\), the longitude and latitude of the typhoon center after the \(i\)-th time interval \(({x}_{i},{y}_{i})\) is:
Using the Rankine model, the wind speed to which the tower is subjected is related to the distance from the tower to the eye of the typhoon, and the different time intervals can be approximated by the distance:
The above equation is an expression for the distance from the typhoon center to the risk tower at the beginning of the \(i\)th time interval, and is an expression for the distance from the typhoon center to the risk tower at the end of the \(i\)th time interval. \({r}_{i}^{i+1}\) is the approximate distance from the tower to the typhoon eye in the \(i\)th time interval. Considering the radius of maximum wind speed and maximum wind speed of the typhoon under typhoon movement as linear changes, the typhoon circulation wind speed of the tower at different time intervals under the predicted typhoon path can be obtained.
Strong typhoons generally maintain high winds for about two days after landfall, and due to their strong destructive force, low circumferential fatigue damage will be brought to the towers for a number of hours before and after landfall, and the towers are prone to enter a plastic state thus generating fatigue failure problems. According to the analysis of literature experimental results, the fatigue damage of the structure and the wind load show an exponential relationship, and the wind load is proportional to the square of the wind speed, then the fatigue damage model of the tower under strong typhoon can be given by the wind speed of the tower:
where a and b are the model coefficients, varying according to different tower material strength, since different materials have different fatigue damage values, even if the wind speed is the same, and therefore the size of the coefficient is different, for the specific material of the tower can use the tower production design fatigue experimental data to determine the a, b coefficients. \({V}_{i}\) is the typhoon wind speed for the tower at time \(i\); \({V}_{0}\) is the critical wind speed when the typhoon begins to hit the tower and causes low cycle fatigue damage; \({V}_{m}\) is the extreme wind speed when the typhoon reaches a load failure on the tower; \({D}_{i}\) denotes the low cycle fatigue damage of the tower per unit minute.
According to the Palmgren–Miner linear fatigue damage criterion, the total accumulated fatigue damage D of the rod can be obtained by superimposing the single fatigue damage. When D equals to 0, the rod is considered to have no damage; when D equals to 1, the rod is considered to have fatigue damage.
The failure rate of transmission towers under strong typhoon weather is related to the accumulated time of fatigue damage, and considering that Poisson model can effectively predict the failure rate of components under short time weather conditions, the probability model that a tower does not collapse in the first \(i\) time intervals can be modified as:
Then the probability of the inverted tower occurring in the first \(i\) time intervals is:
where \(\Delta t\) is the length of each time interval. As can be seen from the equation, when \({D}_{j}=0\), regardless of how long the typhoon acts on the tower, the tower collapse is an impossible event; when \({D}_{j}=1\), the tower collapse is an inevitable event.
This section suggests the calculation and evaluation methods of typhoon disaster impact on transmission towers. Based on the conclusion of typhoon wind field analysis and comprehensive consideration of wind speed and wind direction changes, a transmission tower damage assessment model is constructed, which can give the probability of transmission tower damage after typhoon disasters and provide assistance for emergency relief decisions.
4.2.4 Heavy Rainfall and Flooding Disaster Damage Model
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(1)
Rainfall prediction model
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1)
Based on historical rainfall extrapolation model
Considering that heavy rainfall will affect the safety of the power grid directly or through secondary disasters, urban flooding is mainly caused by short-term heavy precipitation, landslides, mudslides, etc., which is related to the 24 h daily rainfall and the accumulated rainfall in the previous 10 d. In the real-time assessment of the risk of disaster-causing factors, the previous day's 1 h \({P}_{1h}\), 3 h rainfall maximum \({P}_{3h}\), the previous day's daily rainfall \({P}_{1d}\), the current day's rainfall (forecast value) \({P}_{1df}\), and the previous 10 days’ effective rainfall \({P}_{10d}\) are extracted for calculation, and the calculation expressions are as follows:
where \({X}_{1h}\), \({X}_{3h}\), \({X}_{1d}\), \({X}_{1\mathrm{df}}\), \({X}_{10\mathrm{d}}\) are the normalized indices of 1 h, 3 h, 1d actual, 1d forecast, and the first 10 days, respectively. The normalized index of effective rainfall.
The effective rainfall \({P}_{10\mathrm{d}}\) for the first 10 days is calculated as follows:
where \(t\) is the number of days before the current moment of the assessment calculation: i.e., \(t=0\) is the day; \({P}_{t}\) is the rainfall amount \(t\) days ago, and \(f(t)\) is the weight of rainfall \(t\) days ago.
Factors that play an important role in the process of rainfall and flood redistribution are considered: the height and undulation of the terrain, the density of the river network, and the vegetation coverage. The damage caused by rainstorm disaster is eventually reflected in the disaster-bearing body, and the disaster-bearing body of the grid rainstorm disaster is the grid facilities. The more concentrated the grid facilities are, the lower the height from the ground is, and the greater the damage caused by the storm is.
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2)
POT model based on statistical theory
The meteorological conditions that lead to insulator flashover and transformer water ingress and moisture failure are usually severe weather such as heavy rainfall or rainstorm. Therefore, heavy precipitation is the direct cause of insulator flashover and transformer water ingress. Considering that the probability of failure prediction of power equipment under flooding can be equated to the probability of rainfall intensity exceeding a certain threshold value (above which the equipment will fail), the extreme value theory model POT (Peaks over threshold) is available for its analysis. The model takes all the individual exceedance samples of rainfall intensity observations that reach or exceed a certain threshold value as the analysis sample and fits Generalized Pareto Distribution (GPD). The theory proves that the tail distribution of all distributions approximates GPD as the selected threshold increases. The POT model is a model based on GPD, in which the number of samples of the rainfall intensity \(V\) sequence \(\{vt\}\) is assumed to be \(N\), and \(F(v)\) is its distribution function. Define \(F(w)\) as the Conditional Excess Distribution Function (CEDF) of the rainfall intensity, which is the conditional distribution function of the rainfall intensity exceeding the threshold value \(u\), and can be expressed as:
When \(u\) is large enough, there exists a GPD such that:
where \(\xi \) is the shape parameter; \(\frac{1}{\xi }\) is the tail index; σ is the scale parameter. When \(\xi =0\), \({F}_{u}\) is the Gumbel distribution; When \(\xi <0\), \({F}_{u}\) is weibull distribution; When \(\xi >0\), \({F}_{u}\) is Frechet distribution.
And the density function of rainfall intensity greater than \(u\):
The real-time risk assessment index system of the power grid is constructed by considering four factors, namely, the risk of disaster-causing factors, the sensitivity of disaster-inducing environment, the exposure of disaster-bearing body and the disaster prevention and mitigation capability. The real-time assessment model of grid rainstorm disaster is based on the four elements of risk assessment; the classification of the impact of rainstorm on grid security is carried out; the index method is used to calculate.
Among them, FDRI is the storm disaster risk assessment index of the grid. The larger its value is, the higher the risk to the grid is, and failure is more likely to occur. \(H\), \(S\), \(E\), and \(R\) denote hazard factors, disaster-pregnant environment sensitivity, exposure of disaster-bearing bodies, and disaster prevention and mitigation capability, respectively, and \({W}_{h}\), \({W}_{s}\), \({W}_{e}\), and \({W}_{r}\) are the weights of the corresponding indicators, as shown in Table 4.1. All indicators are classified into 5 levels: very low, low, medium, high, and very high; disaster-causing factors are graded according to rain, heavy rain, rainstorm, heavy rainstorm, and megastorm; except for disaster-causing factors, all other indicators are graded by the natural breakpoint method. The grading criteria are shown in Table 4.2.
Precipitation is a key parameter of heavy rainfall and flooding, and the precipitation prediction model can support the subsequent disaster damage assessment in this section.
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Construction of disaster damage assessment model for power grid equipment in heavy rainfall disaster
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1)
Insulator flashover
The insulator is a special insulating control that supports the wire and prevents the current from returning to the ground in overhead transmission lines. Once an insulator flashover occurs in a high-voltage grid, it will cause a short-circuit fault in the transmission line, resulting in a transmission line outage. Insulator flashover is one of the main causes of transmission line outages under flooding caused by heavy rainfall and other adverse weather conditions.
The influence of altitude on the flashover characteristics of insulators lies mainly in the influence of atmospheric pressure on the flashover characteristics of insulators. As the atmospheric pressure decreases, the DC and AC flashover voltages of insulators decrease, and the flashover voltage \({U}_{f}\) is non-linearly related to the air pressure \(P\) linear relationship, i.e.,
where \({P}_{0}\) is the standard atmospheric pressure layer; \({U}_{0}\) is the flashover voltage of insulator under standard atmospheric pressure; \(n\) is the drop index reflecting the influence of atmospheric pressure on the flashover voltage.
The atmospheric pressure intensity is mainly related to the altitude of the location, and the function can be expressed as
where \(H\) is the elevation of the insulator.
When the rain falls on a clean, dry insulator surface for an extended period of time, the conductivity fluctuates more strongly. The conductance of insulators subjected to rain fluctuates greatly. When the rainwater on the insulator surface reaches stability, the conductance will also reach stability. The surface resistance of the insulator when the rainfall surface reaches stability can be expressed as:
where \(c\) is a constant; \(\rho \) is the rain resistivity; \(A\) is the rainfall intensity. The above formula shows that the insulator reaches a stable wetting after the insulator reaches the stable wet state, its surface resistance is more influenced by the rain resistivity than by the rain intensity. For the insulator flashing mechanism and characteristics, the surface resistance of the insulator is influenced by the rain resistance. For the mechanism and characteristics of insulator flashover, the exponential function of insulator flashover voltage and rain surface resistance under standard atmospheric pressure is linear. The insulator flashover voltage at standard atmospheric pressure is linearly related, i.e., the insulator flashover voltage at standard atmospheric pressure is
where a and b are constants.
Combining the above equations, the flashover voltage of the insulator can be expressed as
In addition, under flooding, when the combined force of water and wind exceeds the resistance capacity of the transmission line or pole hitch, it will cause damage such as broken lines and fallen poles. Some cross-river transmission lines with poles built on the river are easily submerged or even washed away. Under the action of heavy rain and wind, tree branches are easy to be broken. Some of the broken branches pressed on the overhead transmission lines, causing transmission line disconnection. In addition, heavy rainfall has different degrees of impact on overhead equipment such as reactors, lightning arresters, capacitors, transformers and fuses on transmission and substation lines.
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2 )
Transformer failure
Power transformer is one of the core equipment of the power grid; transformer is the node of the transmission and transformation network; its safe and reliable operation is a prerequisite for the power system to provide reliable power to the load. Transformer failure has been the main factor that endangers the safety of the power grid. Transformer failure rate of the largest part is the transformer's internal insulation, the main failure characteristics of the transformer insulation material moisture. Under the flood disaster, there are two main reasons for causing the transformer to enter water and moisture: a) Under the flood disaster, the air humidity is extremely high, due to poor sealing of the top connection cap of the casing. Moisture in the air enters the winding insulation along the lead wire, causing a breakdown accident; b) in the transformer operation, if the desiccant filled in the breathing apparatus fails, the explosion-proof tube is not tightly sealed, or the suction side of the submersible pump is leaking, external rainfall or humid air will enter the transformer through these ways, resulting in the insulation material moisture and thereby insulation accidents.
For the transformer operating characteristics, the insulating oil moisture content \({W}_{1}\) and oil-impregnated paper moisture content \({W}_{2}\) in the transformer under heavy rainfall disaster can be expressed as follows:
where \(N\) is the duration of rainfall, \(A\) is the intensity of rainfall; \(P\) is the atmospheric pressure at the location of the transformer; \({P}_{0}\) is the standard atmospheric pressure; \({a}_{1}\), \({a}_{2}\), \({b}_{1}\), \({b}_{2}\), \({n}_{1}\), \({n}_{2}\) are constants.
Both transmission line faults and transformer faults can lead to outage faults on transmission and substation lines. Therefore, it is possible to calculate the probability of the outage fault probability of transmission and transformation line under rainstorm disasters by studying insulator flashover probability and transformer fault probability of transmission line. If the insulator flashover critical value \({U}_{\zeta }\) is calculated, the critical value of rainfall intensity \({A}_{\zeta }\) can be expressed as:
If the rainfall intensity density function is \(f(x)\), the individual insulator flashover probability can be obtained as
Assuming that the rainfall time is a constant, the critical rainfall intensity \({A}_{1\zeta }\) of insulating oil spark discharge and the critical rainfall intensity of oil-impregnated paper being broken through can be expressed as:
Based on the transformer operating characteristics, the transformer failure probability can be expressed as:
where the probability of spark discharge of insulating oil and the probability of oil-impregnated paper being struck can be obtained as:
Assume that the number of insulators of the transmission line in the affected area is \(n\). When the value is more than n, \(s\%\) of the insulators develops a flashover, the transmission line will experience a shutdown fault. Let
where \([]\) denotes rounding to positive infinity.
If the impact of other equipment on the transmission line is not considered, there will be at least s insulators flashing before the transmission line is out of service. From the Bernolli probability model, the probability that at least m of the n insulators will flash is
where Pinsulator is the individual insulator flashover probability.
The occurrence of either of these events, insulator flashover and transformer failure, will result in the shutdown of the transmission and substation line. Assume that insulator flashover and transformer failure are mutually independent events, the transmission line outage probability is:
The storm disaster seriously affects the normal operation of transmission lines and transformers, and the damage probability of transmission lines and transformers can be calculated by Eqs. (4.52) to (4.68), and then we can quantitatively analyze and assess the impact on the power grid system to provide support for emergency decision-making.
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Construction of disaster damage assessment model for flooded power grid equipment
The analysis of the impact of flooding on power systems is the key to assess the damage of power system equipment under flooding. With the advancement of technology, the technology of collecting meteorological data, geographic data and power data under floods has also developed greatly. The statistical modeling is the most effective means to deal with this problem.
When modeling the impact of flooding on power systems, usually as many impact factors as possible are selected to reduce model bias due to the lack of important factors. However, in the actual modeling process, it is necessary to find the subset of influence factors that are most explanatory to the equipment influence variables, i.e., feature quantity extraction (or model selection, variable selection), in order to improve the explanatory and prediction accuracy of the model. Under the flood disaster, selecting the feature quantity among the many influencing factors that lead to the failure of power equipment is the key to reasonably analyze the failure of power equipment. Considering to the complexity and randomness of flooding itself, this project establishes a model of the impact of flooding on power system equipment based on the analysis of the impact of flooding on the power system, and uses the least squares method to obtain the parameters.
Floods have a significant impact on the power generation, transmission and distribution equipment of the power system. Power equipment is widely distributed and diverse, and the impact of flooding on it is highly complex. The degree of damage to the power system by flooding is mainly determined by the severity of flooding and the characteristics of the power system itself. On the one hand, the generation and development of flood disasters are mainly influenced and constrained by meteorological and geographical factors. Therefore, meteorological and geographic factors are indispensable in analyzing the impact of flooding on the power system, including the meteorological factors such as rainfall amount and rainfall intensity under flooding. On the other hand, the power equipment's own conditions (including operation status, operation age, etc.) are also the main factors affecting the disaster loss of electric power equipment.
The specific definitions and descriptions of the variables of flooding impact and its influencing factors are shown in Table 4.3.
Let \(y=\mathrm{ln}\frac{P}{1-P}\), the relationship between \(y\) and the influencing variables in the above table can be written as:
\({\beta }_{0},\ldots ,{\beta }_{16}\) are statistical parameters and \(\varepsilon \) is the model error without bias, variance and correlation.
For power equipment in different areas, select suitable and representative influence factors from \({x}_{1}, \ldots, {x}_{16}\) as the set of influence factors according to the characteristics of the environment in which they are located {\({a}_{1},\ldots ,{a}_{n}\)}, describe the impact of flooding on electrical equipment impact. The observations of the set of power equipment disaster impact variables y and impact factors under \(N\) floods were collected as the sample set\(\{({A}_{t},{Y}_{t}), t=\mathrm{1,2},\ldots,n\}\). Each set of sample values satisfies the following relationship:
where \({y}_{t}\) is the influence variable of power equipment under the \(t\) th flood; \({a}_{t,n}\) is the value of the \(n\) th influence factor under the tth flood.
If the above equation is written in matrix form, we have
where
Let \(Q\) be the error sum of squares of the model, and then we have:
The smaller \(Q\) is, the more accurate the model is. Therefore, let \(Q\) reaches the minimum value of \({\beta }_{0},{\beta }_{1},{\beta }_{2},\ldots,{\beta }_{n}\), which is the best estimate of the model parameters and use the least squares method to estimate the model parameters. Consequently, the following optimization problem is solved:
Taking the partial derivative of the above equation \({\beta }_{i}\) and making the partial derivative equal to 0, we obtain:
Solution:
where \({L}^{-1}={A}^{T}A\). The solution is brought into (4.70), which yields the influence factor \({a}_{1},\ldots ,{a}_{n}\) impact on electrical equipment.
Equations (4.69) to (4.79) give the impact of flooding on the power grid. The method of flooding power grid equipment damage assessment involves various factors such as terrain conditions, precipitation intensity, geohydrology, as well as equipment and facilities resilience, emergency response capability, etc. Overall, the analysis of flooding power grid equipment damage requires comprehensive consideration of the impact of multiple types of parameters.
4.2.5 Freezing Rain and Snow Disaster Damage Model
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Meteorological causes of ice cover
The cold air in the north of China and the warm air with high temperature and humidity in the south often intersect each other to form “stationary peaks” and their extensions “quasi-stationary peaks” from the severe winter to the early spring each year. Usually the warm and humid airflow rise through the cold airflow, often at high altitude due to the drop in temperature; they contain water molecules that break down in large numbers and continue to freeze and condense, producing fog; at the same time, when the cold air flow is relatively strong, it will lead to cold front meteorological conditions, and then the rising warm and moist air will dilute a large number of water molecules; when they are located above the 0 ℃ temperature line or just above the frozen altitude layer, they will change to produce snowflakes, ice crystals and supercooled water droplets (also known as supercooled clouds).
Previous studies have shown that although the occurrence of water and ice clouds is temperature dependent, the “dust” that can be used as ice cores is the central link between them. At temperatures above −18 to 20 °C, most clouds are composed of subcooled water droplets below, and below −25 °C, most are ice clouds. Supercooled water droplets in the sub-steady state (relatively unstable), in contact with the surface of the object, will freeze in the body and form ice. The existence of many dangerous weather phenomena is caused by an excessive number of supercooled water droplets (clouds), such as rain-song and ice accumulation in aircraft clouds. In southwestern and central China, “stationary fronts” and “quasi-stationary fronts, ‘often can maintain a very long time; generally, the area covered by the front will appear continuous rain “freezing rain” weather. This is because the cold air mass in the north is like a wedge to the south and inserted under the warm and humid air mass and the temperature inversion phenomenon begins to appear in the atmosphere, first from the ground up; the temperature below 0 ℃ rises with the temperature reaching above 0 ℃; if it continues to rise, the temperature will fall below 0 ℃, and then it begins to contact the condensation height. Usually ice crystals or snowflakes both appear on top of the condensation height. At this time, ice crystals, snowflakes and the height of the supercooled water droplets are in the atmosphere above 0 ℃; once the temperature of the supercooled water droplets have increased, ice crystals, snowflakes or all melted, or partially melted (if the temperature is not high enough in the atmosphere above 0 ℃). If it continues to fall until the atmosphere is below 0 ℃, the over-cooled water droplets with a large contact surface will encounter the dust that can be used as ice nuclei (such as volcanic dust, meteorite ash) on the way down and thus form ice grains, falling to the ground, called “snow”. However, snow on transmission lines cannot be firmly attached to them, so they do not pose a major hazard to overhead transmission lines. If the supercooled water droplets are relatively small, their radius and surface area are small, and “dust” is difficult to be completely contained in it; in addition, their curvature and surface tension are relatively large; consequently their structure is difficult to be changed, so even in the temperature below 0 ℃, they still fall to the ground in the form of supercooled water droplets, called “freezing rain”. These supercooled water droplets are in a sub-stable state, if the colder objects on the ground meet them, the water molecules will gain energy due to collision vibration, resulting in the “activation” of some water molecules to form an ice nucleus, and solid ice will be transformed by the supercooled liquid water. Also, water droplets will be deformed due to collision, the surface bending degree becomes smaller, causing the surface tension to become smaller at the same time, and the surface of the transmission line wire has the function of capturing water droplets, so the supercooled water droplets will freeze into ice on the surface of the wire. Generally, the smaller the supercooled water droplets are, the easier it is to freeze into rime. Fog and drift can often be seen in plateau areas at an altitude of over 1000 m, such as the Yunnan-Guizhou plateau in China. When the altitude reaches or exceeds 2000 m or more, this situation is very common. In contrast, glaze usually appears in the area at a lower altitude, because the supercooled water droplets at this altitude are usually larger and easy to freeze. Glaze is often seen in the mountainous areas of Hunan, Hubei, Henan and Guizhou in China. In the north of China, because it is not within the influence of stationary fronts, the overhead conductor ice is presented as the phenomenon of snow or rime, such as in northeastern, northern and northwestern China. The stationary front is not the only means to produce freezing rain supporting ice, as there is another important form of icing, cloud supercooling and condensation on wires, which is also common in the southwest plateau of our country. In some mountainous areas of Sichuan, Guizhou, Yunnan and other places, if there is no wind at night in the severe winter and spring season, the sublimation ice will appear because of radiation cooling, resulting in the formation of crystalline rime, but the crystalline rime growth is slow, and generally does not pose a great harm to the overhead line. The process and conditions for the formation of ice cover are as follows:
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1)
Formation process
When winter is cold and spring comes, in the −10 to −0 ℃ temperature, the wind reaches 1–10 m/s, the transmission line operating environment encounters fog or light rain, the wire will produce rime or glaze; if the climate becomes clear, the temperature rises; the ice begins to melt, the climate has been clear, and the ice on the wire will completely melt. However, in the process of ice melting, the climate suddenly becomes colder and the temperature drops, and the water film that has just melted on the rime will freeze on the wire and become a dense rime layer. Then the temperature continues to decrease, the ice will keep changing, and the surface of the wire will be covered with a layer of fog. Continuously alternating, it leads to the production of mixed silt on the surface of the wire, and it is a mixed frozen substance caused by repeated cascading of fog silt and rain silt. When icing occurs on the wire, it often appears on the windward side at first. At this time, if the wind direction does not change arbitrarily, the ice frozen on the windward side of the wire surface will increase in thickness with the change of wind speed and temperature. When they reach a significant thickness, the eccentric weight of the ice itself will cause a change in torque, which in turn makes the wire twist. After the wire is twisted, the originally leeward side of the wire slowly turns into the windward side, and this process occurs so that the side of the wire with less ice can capture the cooling water droplets, eventually leading to an increase in ice cover and the eventual formation of round or oval ice on the wire surface. Under most conditions, the resistance of small-section wires to torsion is weak, so the ice covering on their surface is generally round, while the resistance of large-section wires is strong, so their surface ice cover type is mainly oval or crescent-shaped.
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Basic conditions of formation
The basic conditions for ice cover include (Table 4.4):
Usually, the water droplets with larger diameter have a relatively low transition process of overcooling, and the water droplet collision rate is also relatively high, and when encountering a higher surrounding temperature, it is found that the potential heat of the water droplets evaporates very slowly at this time, and the probability of forming a rime in this case is great. If the diameter of water droplets is relatively small, the transition process of over-cooling is relatively high, and the collision rate of water droplets is relatively small, and when the surrounding temperature is low, the latent heat of water droplets evaporates quite rapidly at this time, and the probability of forming rime in this case is great. Of course, in the actual environment, the above two transformations are mutually controlled and influenced by each other, so often we can see that the surface of transmission line conductor also produces a frozen mixture, which is called mixed rime.
There are many factors that affect the ice on the wire, including meteorological conditions, topography and geography, altitude and conductors themselves, etc.
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a)
Meteorological factors
The meteorological factors affecting the wire icing mainly include temperature, air humidity, wind speed, wind direction, diameter of supercooled water droplets in the cloud and condensation height and other parameters, as shown in Table 4.5.
When glaze is covered with ice, the diameter of supercooled droplets is large, at about 10–40 μm, and the median volume droplet diameter is about 25 μm, a light rain; when rime is covered with ice, the droplet diameter is between 1 and 20 μm, and the median volume droplet diameter is about 10 μm; while for mixed rime, its droplet diameter is between 5 and 35 μm, and the median volume diameter is 15–18 μm.
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b)
Terrain type, geographical conditions
The prominent terrain with good wind conditions, such as mountain tops, narrow mountain passes, wind channels and windward slopes, and air water more adequate rivers, lakes, reservoirs and cloud-encircled mountainsides, mountain tops, etc. are all locations where night ice is extremely easy, and the degree of ice cover is also more serious.
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c)
Altitude and wire suspension height
Under normal circumstances, the icing of the wire is closely related to the altitude of the environment; the higher the altitude is, the thicker the ice is, and most of the frozen material is rime; if the altitude of the line is relatively low, then the ice thickness of the wire is also small, and most of the frozen material is glaze or mixed rime. At the same time, with the increase of the suspended point height of the wire, the ice thickness will increase, because the wind speed and fog density in the near ground will increase with the increase of the height of the ground. The law of ice thickness with height can be expressed by multiplying the power law: \(\frac{{b}_{z}}{{b}_{0}}=(\frac{Z}{{Z}_{0}}{)}^{\alpha }\), where \(b\) is the thickness of ice cover; \(Z\) is the height.
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d)
Wire
The conditions of the wire itself include the diameter of the wire, stiffness, the size of the current through the wire and other factors. For the diameter of the wire, its influence on the ice coating of the wire is mainly manifested in the effectiveness of the wire to capture supercooled water droplets in the air, that is, the effect of the collection coefficient. According to the theory of fluid dynamics, the Stokes number of supercooled water droplets in the air stream can be expressed as: \(St=\frac{2{\rho }_{d}{r}^{2}\nu }{9\mu R}\), where \(\rho d\) is the density of air and water droplets; r is the radius of water droplets; \(v\) is the wind speed; \(R\) is the radius of the wire; \(\mu \) is the dynamic viscosity constant of air.
As can be seen from the above equation, the number of Stokes into the cooling water droplet and R is inversely proportional, that is, the larger the radius of the wire is, the smaller the Stokes number of the cooling water droplet is. And the impact rate of overcooling droplets hitting the wire is related to the Stokes of overcooling droplets: the smaller the Stokes number of overcooling droplets is, the smaller the average rate of the impact wire is. Therefore, the larger the radius of the wire is, the smaller the impact rate is. The impact rate is an important factor affecting the growth of the wire ice:
where \({\alpha }_{1}{,\alpha }_{2},{\alpha }_{3}\) are the collision rate, capture rate and freezing coefficient, respectively; \(\omega \) is the liquid water content in the air. From the above formula, it can be seen that the smaller the collision rate is, the slower the growth of the wire ice is. Previous studies have obtained the relationship between ice thickness and wire radius as shown in Fig. 4.26.
Relationship between conductor ice thickness and conductor radius
Wire resistance to torsion depends on its own rigid strength, and it is the main factor affecting the shape of the wire section ice. The one with less rigidity strength is generally thin wire, easy to twist, while the cross section of the ice covered wire is generally circular. Transmission lines around the electric field will exist on the surrounding air droplet particles of attraction and polarization, regardless of the changes in the internal charge of the droplet particles with the changes in the electric field their force is always an attractive force of the reference wire. Therefore, when the surrounding is a thick fog or light rain, due to the existence of this attraction, there are more water droplet particles towards the surface of the wire. The thickness of the ice on the wire surface increases. At the same time the wire ice is also related to the passing load current; when the load current is not large enough, the current generated by the Joule heat is not able to maintain the wire surface temperature above 0 ℃, and this situation will exacerbate the growth of the wire ice thickness. If the passing load current is large enough, the Joule heat generated by the current can maintain the wire surface temperature to be above 0 ℃; under this condition, the thickness of the wire surface ice will be reduced, and the reduction in the amount of ice can be enlightened to the effect of natural anti-icing transmission lines.
In summary, the icing of the wire is affected by many factors, such as wind speed, temperature and humidity, and precipitation type, and the type of ice formation also varies according to different environmental conditions. It is necessary to consider the influence of many types of factors when constructing the ice growth model.
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Transmission line ice cover model
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Chaine and Skeates models
For a horizontal surface, assuming that the temperature is near or below zero, \({L}_{H}\) represents the amount of precipitation observed during the entire freezing rainfall process and assuming that it is completely frozen as ice, then: \({L}_{H}=P\times t\), where \(P\) is the precipitation rate; \(t\) is the precipitation time. However, when the surface is at a certain angle to the wind direction, the amount of glaze ice cover on the surface will exceed the precipitation rate. In order to calculate the vertical ice cover thickness \({L}_{v}\), it is assumed that the mass growth rate of the glaze layer formed on a 1 \({m}^{2}\) flat surface perpendicular to the wind direction is related to the precipitation rate as follows:
where \(v\) is the average wind speed; \(E\) is the collection factor, which is assumed to be 1 for a vertical flat plate. When the ice is generated on the wire, the concept of equivalent radial thickness is borrowed, i.e., the ice is assumed to be uniformly distributed on the wire. Then the equivalent radial thickness \(\Delta R\) of the wire glaze ice is:
where \(K\) depends on the wire diameter ice shape correction factor, as shown in Table 4.6; \({R}_{0}\) is the wire radius.
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2)
Lenhard Model
Lenhard proposed a simple model based on empirical data where the ice weight M per meter of wire can be written as:
where \(Hg\) is the total precipitation during ice cover; \({C}_{3}\) and \({C}_{4}\) are constants. This model ignores all effects of parameters such as wind velocity, air temperature, and other parameters are neglected in this model.
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3)
Goodwin Models
Goodwin et al. assumed that all the supercooled water droplets collected or captured by the wire freeze to ice on the wire surface. In other words, the ice cover is a dry growth model. Therefore, the ice cover rate per meter of conductor is
where \(w\) is the liquid water content in the air; \({\nu }_{i}\) is the impact velocity of the supercooled water droplets. At the moment \(t\), the amount of ice covering the length of a single long conductor is:
where \({\rho }_{i}\) is the density of ice, generally \(0.8\sim 0.9 g/c{m}^{3}\).
Combining the above equations, there are:
Integrating the above equation, the radial ice thickness \(\Delta R=R-{R}_{0}\) of the ice over the conductor in time period \(t\) is obtained as
The raindrop impact velocity is:
where \({v}_{d}\) is the falling speed of raindrops, generally 6–13 m/s. Here the wind direction is assumed to be perpendicular to the wire frame direction. The liquid water content \(w\) in the air can be related to the thickness of precipitation measured during the ice cover time \(t\):
Combining the above equations, we have:
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4)
McComber and Govoni model of fog and drift ice cover
McComber and Govoni conducted a fog experiment on Mount Washington, New Hampshire, from 1978 to 1980. The experimental conductor was a 64-mm diameter steel wire set at 2.5 m above ground level and oriented perpendicular to the prevailing wind direction. Temperature, wind speed, liquid water content, droplet diameter, ice weight, and maximum ice cover diameter were measured. In all five sets of ice cover data selected for analysis, it was found that the ice cover rate increased with time. Therefore, McComber and Govoni suggested the use of an exponential growth model, namely,
where \(M\) is the ice weight per meter of conductor; \({M}_{0}\) is the average initial ice weight per meter of conductor; \(k\) is a constant; \(t\) is the ice-covering time, which can be written as
The factor \(4\times 1{0}^{-2}\) in the above equation includes the conversion relationship from seconds to hours and the correction of the average typical ice diameter, the correction of \({v}_{m}\) is the average wind speed; \({D}_{0}\) is the wire diameter.
McComber and Govoni found that the data they measured in their experiments fit well with the exponential growth model.
Overall, line ice cover involves a phase change process, which is influenced by a variety of factors, and the ice cover growth mechanism is complex. When faced with practical problems, it is necessary to consider the type of ice cover, meteorological conditions and line type to select a suitable ice cover growth model.
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5)
Modification of a disaster damage assessment model for power grid equipment in rain and snow freezing disasters considering the ice melting process
Ice melting process on the wire can be divided into 2 stages, as shown in Fig. 4.29, a) ice cylinder and wire close contact, when the highest rate of ice melting, and then, b) a thin liquid film on the surface of the wire, and ice and wire in the upper part of the liquid film is isolated. The lower part is separated by water and air space, and the melting rate decreases. The left side of Fig. 4.29 is the first stage of ice melting diagram; because the upper part of the wire has been in full contact with the ice, the melting rate is high; the right side of Fig. 4.27 is the second stage of ice melting diagram; only a small amount of ice surface contact with the wire, and as time passes its contact area is getting smaller, so the melting rate is low. As long as the current wire melts the ice cylinder, with the continuous reduction of the contact area between the ice and the wire, after a period of time, the residual ice hanging on the wire will be separated under the action of wind and gravity.
Schematic diagram of the ice melting stage of conductors
During ice melting, the heat balance expression can be written as:
where \({q}_{J}={I}^{2}R\), being the Joule heat generated per unit length of wire; \(I\) is the ice melting current; \(R\) is the resistance per unit length of wire; \(\Delta t\) is the ice melting time; \({q}_{c}\) is the convective heat exchange between the outer surface of the ice and the surrounding air; \({Q}_{Melt}\) is the heat required to melt the ice; \(\rho \) is the average density of the ice; \(l\) is the latent heat of melting of the ice; \({c}_{p}\) is the specific constant pressure heat capacity of the ice; \({t}_{0}\) is the ice melting temperature; \({t}_{s}\) is the average surface temperature of the ice; and \({V}_{Melt}\) is the volume of ice melting. Also, according to the cylindrical thermal conductivity model in heat transfer, the \({q}_{c}\) can be written as follows:
where \({t}_{0}^{\prime}\) is the atmospheric temperature; \({r}_{i}\) is the radius of the ice-covered column of the wire; \({r}_{c}\) is the radius of the wire; \(h\) is the convective heat transfer coefficient of air flow across the frozen wire, and its value is related to the diameter of the ice cylinder, surface roughness and wind speed; \({k}_{i}\) is the thermal conductivity of the ice cover.
Combining (4.92) and Eq. (4.93), it is known that the volume of ice melt can be written as:
In this section, a variety of ice growth models are presented to calculate the ice growth over time. If ice melting measures have been taken during the actual disaster damage analysis process, the relevant research conclusions of Eqs. (4.92), (4.93), and (4.94) can be used as a supplement to the ice cover growth model, and the ice melting process can be considered in the calculation of ice cover growth. Construction of disaster damage assessment model for power grid equipment in rain, snow and ice disaster.
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1)
Hazardous forms of grid ice damage
The operational impact of ice and snow events on the power system is a gradual process with time scales ranging from a few hours to several days. When there is a severe ice and snow disaster weather, the surface ice thickness of the main equipment that is exposed to the environment such as lines, towers, and insulators increases, the corresponding mechanical components subject to external forces increase, including the gravity of the ice and increased wind due to the increase in the wind area of the line, and the insulation level of the insulator reduces; these factors will jointly lead to a reduction in the level of safety of the main equipment of the system.
The ice on the insulator will lead to a reduction in insulator strength, as it will cover the insulator surface with a water film, making the insulator susceptible to surface flashover which will cause tripping and lead to a further reduction in strength, thus forming a vicious cycle. For lines and towers, the continuous increase of ice cover will eventually make the corresponding power components unable to withstand the weight of ice cover and breakage or collapse of the tower and other accidents. Whether it is insulator flashover tripping, line breakage or tower collapse, it will cause changes in the system tide, the impact on power transmission. Also a long time and wide range of ice damage will affect transportation and may lead to insufficient fuel supply and limited power generation in thermal power plants, posing a great threat to the power system in terms of power supply.
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2)
Calculation model of transmission line load under ice-cover disaster
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a)
Line failure rate calculation
According to the principle of strength and stress interference model, when the ice-covered line is subjected to a load greater than its own strength; the line will fail. First define the limit state equation as:
where \(R(t)\) represents the line strength at time t and \({\text{S}}\left(t\right)\) is the total load on the ice-covered line at time t. Then, according to Stress and interference theory, \(Z\left(t\right)\) is greater than 0 when the line is reliable; \(Z\left(t\right)\) is less than 0 when the line out of operation.
According to the stress and strength interference model, the dynamic reliability index \(\beta (t)\) of the line at time \(t\) can be calculated:
where \(\overline{R}\left( t \right)\) is the standard deviation of the predicted strength of the line at time \(t\); \(\overline{S}\left( t \right)\) is the predicted t moment of the total load carried by the line; \({\sigma }_{R(t)}\) is the standard deviation of the predicted strength; \({\sigma }_{S(t)}\) is the standard deviation of the predicted total load.
The span rate indicates the probability that the component is operating normally at time \(t\) and is withdrawn from operation due to a fault after time \(\Delta t\), and can be written as:
The span rate calculated by this formula is actually the aforementioned transmission line failure rate, characterized by the transmission line. The average failure rate in \([t, t+\Delta t]\) where \(\Phi \) is a 2D standard normal distribution function; \(\beta (t)\) denotes the dynamic reliability index at time \(t\) and \(\beta (t+\Delta t)\) denotes the dynamic reliability index at time \(t+\Delta t\); \({\rho }_{z}\left(t,t+\Delta t\right)\) is the correlation coefficient of the limit state equation at the corresponding two times.
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b)
Load calculation for ice-covered lines
The total load borne by the transmission line in the ice disaster climate includes ice load caused by snow and ice, wind load caused by wind speed and wind direction, and gravity load caused by its own weight. Among them, the calculation formula for wind load is:
where \(\left(d+2\Delta r\right)\) is the ice thickness; \(\alpha \) is the wind speed unevenness coefficient, as in Table 4.7; \(v\) is the wind speed; \(d\) is the wire diameter.
The ice load on the transmission line is:
where \({\mathrm{F}}_{i}\) denotes the ice load in \(kN\); \({\rho }_{i}\) is the ice density; \(d\) is the diameter of the conductor; \({L}_{h}\) denotes the tower’s vertical stall distance.
When the wind direction is the same as the ice load direction, the total load is maximum with:
where \(G\) is the gravity load and \(Q(t)\) is the ice and wind load at time \(t\). Theoretically, the ice and wind load \(Q(t)\) obeys a normal distribution, and its predicted value at time \(t\) is expressed as \({\overline{Q} }_{t}\); the load uncertainty due to the prediction error is characterized by \({\sigma }^{2}R\). In general, it can be considered that \({\sigma }_{Q\left(t\right)}=0.15{\overline{Q} }_{t}\). In addition, since the load values of the line other than the ice and wind load are more stable, the total line load obeys a normal distribution and satisfies \({\sigma }_{S\left(t\right)}=0.15Q(t)\).
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c)
Iced line strength treatment
Line strength \(R\) also follows a normal distribution with a standard value of \(\overline{R }\). The line inevitably deviates from the standard due to errors in the production and installation process. There are errors causing the strength to deviate from the standard, and the uncertainty of the line strength is expressed as \({\sigma }_{R}\). The snow on the transmission line during the ice storm of snow and strong winds in the natural environment can affect the strength of the line, causing the line strength to decrease, and this change is time-dependent, so the line strength calculation formula is written:
where \(R\left(0\right)\) stands for the line design strength, \({S}_{i}\) indicates the total load on the line; \({t}_{i}\) is the line to withstand the load duration; \(T\) is the line design input life, in years; \(c\) takes a constant greater than \(i\). Compared to the long design life of the transmission line, the duration of the line’s ice cover appears insignificant; the ratio of \({t}_{i}\) to \(T\) is the minimal value, so the strength loss of the line during ice cover can be ignored, i.e., when calculating the reliability of ice-covered lines, the strength of the lines is considered to be a time-invariant parameter:
The line strength is calculated by the formula:
where \(R\) is the line strength; \(Td\) is the line maximum use tension; \(Tm\) is the pull-off tension; \(k\) is the safety factor, with a general value of 2.5.
When the total load S > R, the line is destroyed.
In summary, in this section, the ice growth rate model is constructed according to the ice type and meteorological conditions, the wind and ice load of the line is calculated, the damage discrimination conditions of the line are given in combination with the design carrying capacity of the line, and the damage assessment model of the line under the rain and snow freezing disaster is constructed.
4.3 Disaster Loss Model Validation and Optimization
4.3.1 Earthquake Disaster Cases
The model is constructed based on statistical principles based on existing data, and the model can be modified according to the actual disaster damage data of the grid equipment. In this project, the model was modified and optimized based on the actual damage data from the Ya’an earthquake in Sichuan, the Aba earthquake in Aba, and the rainstorm in Fujian and Jiangxi.
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1)
Earthquake of magnitude 6.1 in Lushan, Sichuan Province on June 1, 2022 and the damage caused
At 17:00 on June 1, a 6.1 magnitude earthquake was recorded in Lushan County, Ya’an City, Sichuan Province (30.40° N latitude, 102.99° E longitude), with a depth of 20 km. At 17:03; a 4.5 magnitude earthquake occurred in Baoxing County, Ya’an (30.37° N, 102.94° E). The earthquake was of magnitude 4.5 in Baoxing County, Ya’an (latitude 30.37° N, longitude 102.94° E). After the earthquake, State Grid Sichuan Power started the earthquake disaster level II emergency response at 17:20. After the earthquake, State Grid Sichuan Power started the earthquake disaster level II emergency response at 17:20, and carried out emergency disposal work according to the earthquake emergency plan, whose seismic intensity distribution map is shown in Fig. 4.28.
Intensity distribution of the Lushan 6.1 magnitude earthquake in Sichuan Province on June 1, 2022
The impact of this earthquake on equipment above 35 kV is shown in Table 4.8.
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2)
Sichuan Markang 6.0 magnitude cluster earthquake on June 10, 2022
On June 10, 2022, at 00:03, a 5.8 magnitude earthquake occurred in Markang, Aba Prefecture, Sichuan Province (32.27° N latitude, 101.82° E longitude), with a depth of 10 km. An earthquake with a magnitude of 5.8 occurred at a depth of 10 km in Markang, Aba Prefecture, Sichuan Province, at 01:28 on June 10. A magnitude 6.0 earthquake occurred at a depth of 13 km in Malkang, Aba Prefecture, Sichuan Province (32.25° N, 101.82° E) at 1:28 a.m. on June 10, 2022. An earthquake with a magnitude of 5.2 occurred at 3:27 p.m. on June 10, 2022 in Markang, Aba Prefecture, Sichuan Province (32.24° N latitude, 101.85° E longitude), with a depth of 15 km. State Grid Sichuan Power upgraded its earthquake disaster level III emergency response to earthquake disaster level II at 02:40 on the 10th. The seismic intensity distribution map of the earthquake cluster is shown in Fig. 4.29.
Intensity distribution of the earthquake swarm of magnitude 6.0 in Markang, Sichuan, on June 10, 2022
The impact of the earthquake on equipment above 35 kV is shown in Table 4.9.
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3)
Model Comparison and Optimization
The model prediction results were compared with the damage of the power grid in the June 1, 2022, 6.1 earthquake in Ya’an, Sichuan, and the June 10, 2022, series of earthquakes in Markang, Aba, Sichuan, and the results showed that the information of equipment damage locations was generally consistent, and the damaged equipment predicted by the model also included the actual earthquake damaged equipment. In the next step, it is necessary to optimize the earthquake damage models of power grid equipment at different voltage levels to improve the accuracy of the models (Fig. 4.30).
Comparison analysis of earthquake damage model and actual damage data
In general, the probability of earthquake damage to power grid equipment can be described by the cumulative log-normal distribution function, as shown in Eq. (4.9). This project studied the effects of the 2008 Wenchuan earthquake, the 2013 Lushan earthquake and the current earthquake disaster, improved the prediction model for substation and line damage, and optimized the model parameters, as follows.
According to Tables 4.10 and 4.11, combined with Eqs. (4.9)~(4.11), the seismic damage of the grid equipment can be evaluated based on the optimized parameters calculation.
4.3.2 Storm Disaster Cases
In this section, the corresponding disaster damage models are modified and optimized based on the actual disaster damage data from the Ya’an earthquake in Sichuan, the Aba earthquake, and the rainstorm disasters in Fujian and Jiangxi.
At 18:00 on May 26, 2022, the Ministry of Natural Resources and the China Meteorological Administration (CMA) jointly issued a Geological Hazard Meteorological Risk Warning; the Ministry of Water Resources and the CMA jointly issued a Blue Flash Flood Meteorological Warning. At 18:00 on May 28, 2022, the Ministry of Natural Resources and the China Meteorological Administration jointly issued a meteorological risk warning for geological disasters; the Ministry of Water Resources and the China Meteorological Administration jointly issued an orange meteorological warning for flash floods; from 18:00 on May 28 to 6:00 on May 29, 2022, the Central Weather Station continuously issued a yellow warning for fog, a blue warning for rainstorm, a blue warning for strong convection, and a yellow warning for high temperature.
The model prediction results were verified by comparing the model prediction results with the damage to the power grid caused by the heavy rainfall in Fujian and Jiangxi on May 27–29, 2022, and the results showed that the model prediction location information was generally consistent, as in Fig. 4.31. However, some of the damage in the actual disaster was caused by secondary hazards (such as landslides and geological hazards), so it is necessary to construct a chain hazard model for the process of landslides induced by rainstorm. Therefore, it is necessary to construct a chain hazard model for the process of storm-induced landslides.
A comparison analysis of landslide disaster damage model and actual disaster damage data
Precipitation is a key factor leading to the occurrence of landslides. Statistics show that the frequency of rainfall meteorology occurs during the flood season is significantly greater than other periods, and a large amount of rainfall plays a driving role in the breeding of geological hazards. Landslide hazards often occur during or after rainfall, and the degree of landslide development is enhanced with the increase of rainfall. Generally, the landslide probability density after precipitation can be written as:
where \(\sigma \) is the standard deviation; \(\mu \) is the expectation, and \(Rr\) is the effective precipitation, calculated from the daily average precipitation over a period of time, which can be written as
\({R}_{0}\) is the precipitation of the day; \({R}_{i}\) is the precipitation of the previous \(i\) days; \(\omega \) is the weight; if for the first 10 days of precipitation \(i=\mathrm{1,2},3,\ldots,10\) and \({\omega }_{1}\sim {\omega }_{10}\) can be written as 0.84, 0.71, 0.59, 0.50, 0.42, 0.35, 0.30, 0.25, 0.21, 0.18.
Combining Eqs. (4.105) and (4.106), we can calculate the probability of rainstorm-induced landslide, and combined with the contents of Sect. 3.2, we can deduce and predict the disaster damage of power grid equipment in the “rainstorm-landslide” disaster chain.
4.4 Grid Loss Forecasting Technology
4.4.1 Overview
Based on the type of information, the fusion method is selected, the information integration and fusion method of disaster loss multiple information collection-disaster loss model library-emergency command comprehensive database is proposed, the information fusion technology of power grid emergency command comprehensive database and disaster loss model, fuzzy dynamic power grid loss prediction technology are studied, and the following conclusions are obtained:
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(1)
According to the data types, the multiple data fusion technology is studied, the information integration and fusion method of disaster damage multiple information collection-disaster damage model library-emergency command comprehensive database is proposed, the information integration and fusion technology scheme of multiple information collection-disaster damage model library-emergency command comprehensive emergency command comprehensive database is proposed, and the function and positioning of emergency command comprehensive data analysis module in emergency command system is designed.
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(2)
The proposed prediction model of disaster damage assessment under the combined effect of multi-hazard concurrency and disaster chains improves the accuracy of damage assessment of grid equipment by disasters and enables rapid damage assessment of grid equipment under multi-hazard concurrency, which provides a basis for emergency decision-making.
4.4.2 Grid Emergency Database Fusion Technology and Methods
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Data fusion techniques and methods
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1)
Artificial neural network (ANN)
The human brain is an extremely complex signal processing system composed of a very large number of neurons, which are interconnected in a very complex way and use a highly complex, nonlinear and parallel processing method to process signals. The artificial neural network (ANN) is a dynamic system that interconnects the nodes in a mathematical way to form a nonlinear, parallel processing system, drawing on the way and characteristics of signal processing by neurons in the human brain. Although artificial neural network is said to be a computing model that imitates the brain, it is not comparable to the neural operation of the brain, which is extremely complex to the extent that it is not yet clear to humans. The artificial neural network is an abstraction and simplification of the information processing of the neuronal network of the human brain, and the corresponding mathematical model is formulated and then simulated by computer technology. After the abstraction and simplification of the brain nerves, they become the nodes (also called elements) of the model; neurons are the basic processing unit of artificial networks, a large number of simple connections to form parallel distribution; this connection between neurons is the core idea of signaling and the key is the variable weights between neurons. BP neural network (Back Propagation neural network) means that the error is back propagated in the system according to the input layer of the network side, which is equivalent to the outside world. In fact, it means that the input layer of the error according to the network is equivalent to the external stimulus in the system, and the hidden layer in the middle region is the hidden layer of the signal transmission in the neural network to represent the outside world, and the result of the signal transmission in the neural network to represent the external element after multiple propagation. BP neural network architecture diagram is shown in Fig. 4.32.
Back Propagation neural network
The variables in Fig. 4.32 are defined as follows.
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\({x}_{j}\) represents the input of the jth node in the input layer.
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\({v}_{ij}\) represents the weight from the ith node in the hidden layer to the \(j\)th node in the input layer.
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\({\theta }_{i}\) represents the threshold value of the \(i\)th node in the hidden layer.
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Φ(x) represents the activation function of the hidden layer in the neural network.
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\({w}_{ki}\) represents the weight value from the kth node in the output layer to the \(i\)th node in the hidden layer.
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\({a}_{k}\) represents the threshold of the \(k\)th node in the output layer.
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Ψ(x) represents the activation function of the output layer.
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\({o}_{k}\) represents the output of the kth node in the output layer.
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2)
Particle Swarm Optimization (PSO)
PSO model: Particle Swarm Optimization (PSO) was introduced by Eberhart and Kennedy in 1995, and its basic idea is inspired by the foraging behavior of birds. Imagine a scene where a group of birds are randomly searching for food, assuming that there is only one food (optimal point) in the foraging area. Initially, all the birds do not know the location of the food, but they know the distance from their current position to the food. So what is the optimal method for searching for this food? The direct method is to focus on the bird that is currently closest to the food, and move to the surrounding area of that bird to search. In the PSO algorithm, particles represent individual birds in a flock and can be a number or vector, among other possibilities. Each particle is evaluated for its fitness through a fitness function. Each particle in PSO has a position and a flight velocity value. \({X}_{i}=({x}_{i1},{x}_{i2},...,{x}_{in})\) represents the current position of particle \(i\), \({V}_{i}=({v}_{i1},{v}_{i2},...,{v}_{in})\) represents the current flight velocity of particle \(i\), and \({P}_{i}=({p}_{i1},{p}_{i2},...,{p}_{in})\) represents the best position where particle \(i\) has experienced the highest fitness value. During the search process, the particle updates its velocity and position according to the following formulas:
The position of a particle is represented by a position vector xid, and its velocity by a velocity vector vid. The particle’s personal best position is represented by pid, and the global best position by pgd. The acceleration factors c1 and c2, as well as the random numbers randid and randpd, are also involved in the update formula for each particle. Based on its personal best and global best positions, each particle dynamically adjusts its position and velocity until the optimal solution is found.
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3)
Data Cleaning Techniques
The huge scale, rapid growth, variety of types and differences in structure of big data of power disasters have become a practical problem that has to be faced. It is especially important to convert potentially valuable data into effective data that can be used, and data cleansing is essential to solve this problem. “Dirty data” can affect the quality of data, so data cleaning is an essential step. Only through cleaning technology to obtain clean and meaningful data and improve the quality of data, is it possible to obtain reassuring and specific intelligence through subsequent analysis and mining technology.
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a)
An overview of Data Cleaning Techniques
Statistical data on electric power disasters needs to be extracted from multiple business systems, which may bring erroneous or conflicting data that is clearly not usable, known as “dirty data”. There may be intuitive and transparent “dirty data” in the database, which usually manifests as follows: incorrect values, duplicate records, spelling issues, values that do not meet requirements, null values, inconsistent values, destruction of data entity integrity, referential integrity, and user-defined integrity, etc. In addition, when data are extracted from multiple database sources, there may be inconsistent or redundant information due to the different design of the logical and physical structures of the databases. If not cleaned, this “dirty data” will contaminate the stored information, reduce the database’s performance, disrupt the consistency between data, and affect the practical value of the data warehouse.
People have different research focuses on data cleaning techniques, so their understanding of it cannot be completely unified. In different fields, data cleaning has different status: in short, the process of improving data quality through detecting and processing “dirty data”, synthesizing and resolving some data can be considered as data cleaning techniques.
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The Basic Process of Data Cleaning
The core idea of data cleaning is to backtrack. Generally speaking, the basic process of data cleaning mainly includes four parts. The flowchart is shown in Fig. 4.33.
Data cleaning process
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①
Data Analysis
Data analysis refers to the analysis of the causes, types, and definition rules of “dirty data” in a database. It involves identifying constraint relationships among data attributes. In short, data analysis techniques can correct erroneous values, fill in missing values, and identify duplicate records caused by multiple data sources.
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②
Defining and Validating Cleaning Transformation Rules
Data cleaning rules are defined according to the number of data sources, the number of “dirty data” in the data sources and the appropriate algorithm. Of course, it is also necessary to validate and evaluate the correctness and efficiency of the defined rules. Cleaning experiments can be performed on small-scale data samples, and the rules can be continuously adjusted and improved based on the feedback results of the cleaning.
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③
Cleaning dirty data
To prevent excessive cleaning and errors, it is necessary to back up the source data before cleaning. Then, based on the characteristics and properties of the “dirty data”, different steps of cleaning work should be carried out.
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The return flow of clean data
Once data is cleaned, the “clean” data can represent the entire dataset. This can improve data quality, reduce duplicated efforts, and save material and labor costs.
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⑤
Objects for data cleaning
The main objects of data cleaning can be categorized into two types distinguished by pattern concept: one related to pattern-level data and the other related to instance-level data. The techniques used for data cleansing may differ depending on which of the two types is being targeted.
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⑥
Data cleaning methods for pattern layer
Pattern-level data mainly include naming conflicts, attribute conflicts, and structural conflicts.
Naming conflicts can be divided into two parts: homonymy and synonymy. Homonymy refers to the situation where different data objects with different meanings adopt the same name in different applications, while synonymy refers to the situation where data objects with the same meaning have different names in different applications. Naming conflicts may occur in entities, relationships, or attributes. Naming conflicts may occur in entities, relationships, or attributes.
Attribute conflicts can be divided into two categories: conflicts related to attribute domain and conflicts related to attribute value units. Conflicts related to attribute domain may include conflicts related to the type of attribute values as well as conflicts related to the range of attribute values.
Structural conflicts refer to the situation where the same data object is represented differently in multiple data sources, which can result from inconsistencies such as differences in data types, keywords, violations of unique value constraints, violations of referential integrity constraints, or violations of user-defined integrity constraints.
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⑦
Data cleaning methods for instance layer
There are mainly two types of methods for cleaning “dirty data” at the instance level, which are dealing with incorrect attribute values and handling duplicate records.
Attribute value errors mainly include empty values and erroneous values. Empty values can be divided into two categories: one is that the data exist but have not been stored in the database, and the other is that the data do not exist at all. Erroneous values refer to errors generated during the recording of original data or due to other reasons that cause the data to be incorrect.
Duplicate records are one of the most common problems in data cleaning, often caused by multiple data sources. Redundant data can affect the efficiency of querying and updating data warehouses, significantly reducing the value of database usage. Similarly, according to the number of data sources, the objects of data cleaning can be divided into two aspects: single data source data and multi-data source data. After simple combination with the pattern layer and instance layer data mentioned above, data quality problems can be classified into four categories: single data source pattern layer problems, single data source instance layer problems, multi-data source pattern layer problems, and multi-data source instance layer problems.
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c)
Attribute value cleaning
Data cleaning mainly includes methods for detecting and cleaning attribute value errors, as well as algorithms for detecting and cleaning duplicate records. The specific division of data cleaning work is shown in Fig. 4.34.
Data cleaning work division
To clean up attribute value errors, it is necessary to first detect the existing errors, convert erroneous values to null values, and then handle null values. When the dataset is large in scale, this can greatly reduce the workload and improve the efficiency of cleaning attribute value errors.
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①
Attribute value cleaning
There are roughly three methods for detecting attribute value errors: clustering algorithms, association rule algorithms, and probability-based statistical methods.
The clustering algorithm, also known as cluster analysis, is a method for categorizing multiple factors. Its core idea is to use mathematical methods based on various similarity and difference indicators to determine the closeness of samples based on their attributes, and to use different algorithms to cluster samples based on their closeness.
The association rule algorithm consists of two steps: the first step is to modify the rules using known knowledge, and an iterative algorithm is used to find all frequent, precise, and possible rule sets; the second step is to construct a classification using a heuristic method.
The most common method based on probability statistics is Chebyshev’s theorem. The essence of Chebyshev’s theorem is that for any data set, after calculating its mean and standard deviation, the proportion of data points that fall within n standard deviations from the mean is always at least \(1-1/{n}^{2}\) (\(n\) is any positive number greater than 1), or equivalently, the proportion of data points outside of n standard deviations from the mean is no more than \(1/{n}^{2}\). To illustrate, for a given dataset, if \(n=2\), it means at least 75% of the data fall within 2 standard deviations from the mean of the dataset; if \(n=3\), at least 88.9% of the data fall within 3 standard deviations from the mean. The formula for Chebyshev's theorem is usually represented as \(P(\mu -n\alpha <X<\mu +n\alpha )\ge 1-1/{n}^{2}\), where \(X\) represents the dataset, \(n\) is the number of standard deviations,\(\mu \) represents the mean of the dataset, and \(\alpha \) represents the standard deviation of the dataset.
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②
Comparison of Algorithms for Detecting Attribute Value Errors
Cluster algorithms group a dataset into multiple clusters based on certain criteria, with highly similar data usually grouped into the same cluster and significant differences between clusters. Cluster algorithms are often used to detect isolated points that deviate significantly from normal data. Association rule algorithms are not easily affected by data distribution; although they can detect more “dirty data,” it is difficult to detect exceptional isolated points. To balance the ability of cluster algorithms to detect isolated points and the characteristics of association rule algorithms to detect large amounts of data, a probability statistical method can be used, which can quickly and efficiently detect these “dirty data.”
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d)
Duplicate record cleaning
Strictly speaking, in the real world, each entity can have a record that matches it. However, when there are multiple data sources, input errors and variations in data format and spelling may occur during the integration process, causing the database management system to fail to recognize multiple duplicate records of an entity. This can greatly reduce the value of the database's data utilization.
The harm caused by duplicate records mainly includes two aspects. Firstly, it destroys consistency. The use of different keywords to identify the same record in the database may complement each other to some extent, but it will cause data redundancy and even lead to data inconsistency. When the state of the entity changes, database administrators or database management systems may only update part of the duplicate records in some cases, leaving the remaining records unchanged. This may cause multiple records of the same entity to have inconsistent meanings, destroy information consistency, and make it inconvenient and inefficient to use data in the future. Secondly, it wastes resources. Duplicate records not only bring data redundancy but also waste valuable storage space of the database, increase management costs, reduce the cost-effectiveness of the database, and even cause dissatisfaction among data users.
In essence, cleaning duplicate records means deleting data, which has extremely important theoretical and practical significance for improving and optimizing the storage efficiency, operational performance, utilization value, and efficiency of storage systems. Firstly, duplicate records are detected, and after the screened dataset is obtained, only the first record of each batch of duplicate records is retained, and the rest of the duplicate records are directly deleted. The simplest and most primitive detection method is to directly compare each record in the data warehouse with every other record, but this algorithm is too cumbersome and resource-intensive, with a time complexity of \(O({N}^{2})\), for example, if the total number of records is \(N\), detecting duplicate records alone requires \(N\times (N-1)/2\) comparisons. Therefore, the “sort and merge” method is used, which is also simple and clear. Its core idea is to first sort the dataset to be detected, and then compare adjacent records for equality. If they are equal, the records are merged or deleted.
The Sorted-Neighborhood Method (SNM) consists of three steps: selecting keywords from the data warehouse for sorting, sorting the records, and finally conducting the detection process by sequentially moving a sliding window over the sorted record set and comparing only the records within the window to determine if they are duplicates.
The first step of sorting is to select keywords from the data warehouse, in this case, five evaluation indicators are chosen as keywords. Secondly, radix sort is used to sort the keywords. Because the electric power disaster data being analyzed is roughly within the same range and the five indicators are used as keywords for sorting, and because the electricity consumption data have temporal characteristics, the statistical data roughly increases over time and is already roughly ordered, so radix sort is chosen for its convenience and efficiency.
The radix sort uses two basic operations, “distribution” and “collection”, to perform the sorting. Here, we only introduce the least significant digit first sorting method: assuming that the record table to be sorted is composed of nodes a0, a2, …, an–1, each node has a d-tuple (kjd–1, kjd–2, …, kj1, kj0) as its key, where 0 ≤ kji ≤ r–1 (0 ≤ j < n, 0 ≤ i ≤ d–1). During the sorting process, r queues \({Q}_{0},{Q}_{1},...,{Q}_{r-1}\) are used.
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① The sorting process involves “distribution” and “collection” steps for each\(i = 0, 1, ..., d-1\).
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② distribution: At the beginning, the queue \({Q}_{0},{Q}_{1},...,{Q}_{r-1}\) is cleared, and then each node \(aj(j=\mathrm{0,1},...,n-1)\) in the linear table is examined in turn. If the key of node \(\mathrm{aj}\) is equal to k, then the node \(\mathrm{aj}\) is put into the queue \(\mathrm{Qk}\).
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③ collection: After allocating each node to corresponding queues, we concatenate the nodes in each queue in order, forming a new linear list. The auxiliary space required for each sorting pass is r (the number of queues), so the space complexity of radix sort is O(r). Next, considering the time complexity, radix sort requires d passes of allocation and collection, each allocation pass takes O(n) time, and each collection pass takes O(r) time, and therefore the total time complexity of radix sort is O(d(n + r)).
A judgment window is set in a pre-sorted dataset, with a size smaller than the dataset size, for the purpose of searching and identifying duplicate records. Each time, only the records inside the sliding window are compared one by one to determine if they are duplicates. If the window size is w records, when the window moves, the first record in the original window is removed, and the new incoming record is compared with the original w-1 records to determine if it is a duplicate. After the use of the SNM algorithm to identify duplicate records, the first duplicate record is retained, and the remaining records are merged and deleted directly. The SNM duplicate record identification algorithm is shown in Fig. 4.35.
SNM algorithm for determining duplicate records
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4)
Research on Integrated Fusion Technology for Multi-Source Data
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a)
Basic Principles of Data Fusion
The fusion of multi-source information is a fundamental function that is commonly found in human or other biological systems. Humans utilize this ability to combine information from various sensors (eyes, ears, nose, limbs) in the body and use prior knowledge to statistically understand the surrounding environment and events occurring. The basic principles of multi-sensor information fusion technology are similar to the way the human brain integrates and processes information, making full use of resources from multiple sensors. By reasonably managing and using the observations and information from these sensors, we combine the redundant or complementary information in time and space from multiple sensors according to certain criteria to obtain a consistent interpretation or description of the observed object.
A data fusion system refers to the reasonable allocation and use of various types of real-time, non-real-time, accurate, fuzzy, fast-changing, slowly-changing, similar, or conflicting data from various data sources. Based on specific rules, redundant or complementary information is comprehensively analyzed and processed to obtain a comprehensive description of the measured object.
Specifically, the principles of multi-source data fusion are as follows:
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① Collecting multiple types of data on the target.
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② Extracting features from the collected data, where the feature extraction represents the characteristic vector of the target measurement data.
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③ Utilizing artificial intelligence or other methods that can transform the target's characteristic vector into attribute decision mode recognition to effectively recognize and process the characteristic vector, in order to provide an explanation of the measured target based on the data collected from each sensor.
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④ Based on the results of the previous step, the description data of the target is grouped together based on their associations.
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⑤ By using appropriate fusion algorithms, the grouped data for each target can be synthesized to obtain a more accurate and consistent interpretation and description of the measured target.
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b)
Data Fusion Hierarchy
Based on the identification and alarm results data obtained by various warning and monitoring methods, the comprehensive data library and disaster-damage model library for power grid emergency command are constructed. The data are classified into unstructured, semi-structured, and structured data according to its characteristics, and information fusion technology is used to complete the fusion of the two. Structured data consists of clearly defined data types, and its pattern makes it easy to search. For computers, reading and processing structured data is relatively easy. Unstructured data has internal structure, but it is not structured through predefined data models or patterns. Semi-structured data, although it does not conform to the form of the relational database or other data table's structured data model structure, it includes relevant marks used to separate semantic elements and layer records and fields. For the data of the power grid emergency command comprehensive database and disaster-damage model library, various types of data information are automatically analyzed, synthesized, dominated, and used according to certain criteria, with full utilization of multi-source information resources at different times and spaces to obtain consistent descriptions and explanations with the tested object, in order to complete the required decision-making and estimation tasks, and to enable the system to perform data processing processes with better performance than its various components. According to the level of data abstraction, data fusion is classified into three levels: data-level fusion, feature-level fusion, and decision-level fusion.
Taking multi-sensor data fusion as an example, the data-level fusion process is shown in Fig. 4.36. Firstly, all sensor observation data are fused, and then feature vectors are extracted from the fused data and used for recognition and identification. Data-level fusion is the fusion and analysis of data directly on the collected raw data layer, before various sensor measurements are processed. This is the lowest level of fusion.
Data-level fusion
The advantage of data-level fusion is that it can maintain as much on-site data as possible and provide fine-grained information that other fusion levels cannot provide. However, it involves a large amount of basic data processing, which incurs high processing cost, long processing time, and poor real-time performance. This type of fusion is carried out at the lowest level of information, which requires high error-correcting ability in the fusion process due to the uncertainty, incompleteness, and instability of the sensor's raw information. Data-level fusion is carried out after a small degree of processing on the raw data, thus preserving as much raw information as possible. The fusion result has the best accuracy and can provide more intuitive and comprehensive understanding. However, this fusion method involves a large amount of data processing and has poor real-time performance.
The process of feature-level fusion is shown in Fig. 4.37. Representative features are extracted from the raw data provided by various sensors, and these features are fused into a single feature vector, which is then processed using pattern recognition methods. Therefore, some information compression is carried out before fusion, which is beneficial for real-time processing. At the same time, this fusion can preserve important features of the target, and the fused features provided are directly related to decision reasoning, based on which the properties of the target can be estimated. Its fusion accuracy is lower than that of pixel-level fusion.
Feature-level fusion
The process of decision-level fusion is shown in Fig. 4.38. Decision-level fusion refers to the transformation of each sensor data source and obtaining independent identity estimates before fusion. Information is fused based on certain criteria and the reliability of the decision to integrate the attribute decision results of each sensor, and ultimately obtain a consistent overall decision. The fusion data used at this level is relatively the highest level of attributes. This fusion method has good fault tolerance and real-time performance, and can be applied to heterogeneous sensors, and can also work normally when one or more sensors fail. However, its disadvantage is the high cost of pre-processing.
Decision-level fusion
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c)
Multi-source information fusion
Multi-source information fusion, also known as multi-sensor information fusion, refers to the process of fully utilizing information resources from different sensors at different times and spaces, using computer technology to automatically analyze, synthesize, and control multi-sensor observation information obtained according to a certain criteria, in order to complete the required decision-making and estimation tasks. Figure 4.39 shows the multi-source information fusion system, with the fusion subject represented by the dotted box.
multi-source information fusion system
Multi-source information fusion system fully utilizes and reasonably allocates multi-sensor resources, detects and extracts observation data, and then guides and manages sensors to achieve the best energy efficiency ratio for fusion based on relevant criteria and domain knowledge. Compared with individual sensors and subsets of system components, the entire system not only has more precise and clear reasoning and superior performance, but also has the characteristics of reducing the dimension of state space, improving measurement accuracy, reducing uncertainty, enhancing decision robustness, solving conflict problems, and saving costs. Therefore, it can be seen that the multi-sensor system is the hardware basis of multi-source information fusion, multi-source information is the processing object, and coordinated optimization and integrated processing are the core. Multi-source information fusion emphasizes the full spatiality, comprehensiveness, and complementarity of information.
Multi-source information fusion can be achieved through data-level fusion, feature-level fusion, and decision-level fusion. Data-level fusion directly processes the observation data from multiple sensors and performs feature extraction and decision-making are based on the fused results. Feature-level fusion involves each sensor abstracting its own feature vectors, which are then fused by the fusion center. Decision-level fusion involves each sensor making local decisions based on its own data, which are then combined by the fusion center. The hierarchical model diagram of the data fusion level, as well as its advantages and disadvantages are shown in Fig. 4.40 as below.
Data fusion hierarchy model diagram
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2)
Multi-source Information Collection—Disaster Damage Model Library—Integrated Information Integration and Fusion Technology Scheme for Emergency Command Comprehensive Database
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1)
Research on Multidimensional Information Collection
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a)
On-site information collection
Field information includes equipment status, disaster damage, and environmental parameters. In this research project, field data will mainly be collected through sensors and image recognition.
The common information collection methods for power sensors and power transmission and transformation equipment include monitoring the operation and operating environment of the transmission equipment, which can effectively improve the perception and early warning capabilities when the transmission lines are covered with ice, tower inclination, and wire wind deflection arc. It plays an important role in realizing dynamic and full-time monitoring of the operating status of transmission equipment. For substation equipment, it mainly includes the core current of transformers, oil chromatography, GIS partial discharge, and insulation of lightning arresters. Online monitoring based on power IoT sensor technology not only can realize high-sensitivity collection of equipment operation information, but also realize the online management of pre-commissioning projects of substation equipment, so as to diagnose and evaluate the online operating status of equipment.
Image recognition technology is mainly used for identifying the overall damage of power equipment. The research on recognition algorithms is mainly based on emergency needs, and the results of the algorithm will be used to estimate the required resources for repairing power equipment and provide direct reference information for emergency decision-making. The process of using image information to identify electrical equipment is presented as follows, including image preprocessing, image registration, and image feature extraction. The image analysis process is affected by noise and other factors that are not conducive to image analysis during the image acquisition and transmission process. Therefore, the first step in image analysis is preprocessing to improve the quality of the image. The main method is to use a low-pass filter to remove image noise and improve the quality of the image. Image registration is not only necessary for the recognition of electrical equipment from infrared images to visible light images, but also for the comparison of images obtained during inspections with images in historical databases. Due to differences in angles and local regions during image capture, it is necessary to perform image registration for subsequent feature extraction. Feature matching based on the SIFT algorithm can be used to extract stable feature points and handle matching problems between two images that have undergone translation, rotation, affine transformation, and perspective transformation. The SIFT algorithm is robust to changes in illumination and can achieve high probability matching. Image features refer to the original characteristics or attributes of an image field. Some of them are natural features directly perceived by the image, while others are artificial features that need to be obtained through transformation or measurement. In inspection, the color, shape, and texture of the image can all be used as natural features, while grayscale, histograms, and infrared temperature differences can be used as artificial features for identification. Feature extraction should focus on the benefits of the extracted features for the accuracy and speed of the subsequent recognition process.
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b)
Public information collection
In this research project, it is proposed to collect data distributed in departments related to emergency power work, exchange data through the data center, and then integrate the data through a data exchange and sharing system. Governmental departments’ warning and alert data (such as meteorology, land, forestry, and other related data from government functional departments) will be accessed through a data access platform. Afterwards, data exchange and review will be conducted through a data exchange and sharing system to provide effective technical solutions for data integration of the system.
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2)
Construction of Disaster Damage Model Library
Based on the disaster damage assessment models for earthquake, landslide, typhoon, heavy rain and flood, snow and ice disasters of power grid equipment developed in Chap. 3, mathematical model code implementation was carried out using Python language. Disaster-related multidimensional information is used as input parameters to the disaster damage assessment model to analyze the impact of disasters on power grid equipment. The input of multidimensional information and disaster damage assessment model library are shown in Fig. 4.41. The collected on-site and public emergency information are used as input parameters. According to the type of disaster, corresponding disaster damage assessment models are inputted to obtain the assessment results, providing data support for emergency command.
Schematic diagram of disaster loss assessment model library
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3)
Research on Integrated Database and Command System for Emergency Response
Based on the basic information of emergency command and disaster loss assessment, an emergency command comprehensive database is established as shown in Fig. 4.42. It comprehensively analyzes disaster site information, public emergency information, disaster loss information, power grid information, user information, emergency team and resource allocation, as well as public opinion and sentiment. The study focuses on the integration and fusion method of multi-dimensional information collection, disaster loss model library, and emergency command comprehensive database. A disaster loss prediction and analysis function module is designed and developed, which can be integrated into the power grid disaster situation intelligent perception and emergency command system.
Schematic diagram of emergency command data analysis
The system provides modules for viewing warning and monitoring information, typhoon monitoring information, heavy rain and flood information, rain and snow and freezing information, earthquake information, landslide information, emergency response, work communication, public information, etc.
Typhoon monitoring includes typhoon path, satellite cloud image, radar image, nationwide power grid information, disaster information updates, and disaster damage perception. The typhoon path module allows users to view real-time and predicted paths, as well as information such as wind speed, air pressure, and movement speed. The satellite cloud image module displays current satellite cloud image information, overlaid with typhoon path information to assist in determining the current typhoon's development trend. The radar image module displays current radar image information, also overlaid with typhoon path information. The nationwide power grid information module shows the power grid GIS station line information. By analyzing the typhoon’s path and predicted path, it is possible to assess the impact on substations, transmission lines, and power users, and predict the disaster damage. The disaster information updates include information bulletins and emergency situation alerts. Information bulletins report current disaster damage information using fixed templates, while emergency situation alerts allow for rapid reporting of on-site emergency situations via mobile devices. The disaster damage perception module includes both statistics and detailed information on disaster damage perception. Through unmanned aerial vehicle (UAV) images, the current status of equipment damage can be intelligently determined.
The monitoring of heavy rain and flood includes prediction of rainstorm damage, satellite cloud images, radar images, power grid GIS site information, disaster situation updates, and disaster damage perception. The rainstorm damage prediction provides information on current precipitation areas, effective precipitation amounts, and the probability of precipitation-related disasters. Satellite cloud images can be used to view current satellite cloud image information and assist in determining the current development trend of precipitation. Radar images can be used to view current radar image information and assist in determining the current development trend of precipitation. Power grid GIS site information can be displayed through the power grid GIS website, and the impact on substations, power lines, and distribution network customers can be analyzed based on the precipitation range and predicted precipitation amount. Disaster situation updates include information bulletins and risk situation updates. Information bulletins mainly report current disaster information through fixed information templates, while risk situation updates are mainly implemented through mobile devices to quickly report on-site risk situations. Disaster damage perception is divided into disaster damage perception statistics and disaster damage perception details. By using drone images, the current equipment damage can be intelligently determined.
The freezing rain and snow monitoring system includes snow disaster prediction, satellite cloud imagery, radar maps, power grid monitoring, disaster information updates, and damage assessment. Among them, the snow disaster prediction provides information on current snowfall areas, ice thickness, and total load rates per unit length. The satellite cloud imagery displays current satellite cloud information, overlaid to assist in determining the current snowfall trend. The radar maps provide current radar information, overlaid to assist in determining the current snowfall trend. The power grid monitoring system displays the GIS station and line information, and by analyzing the range and predicted snowfall, it can assess the impact on substations, power lines, and users in the area. The disaster information updates include both information bulletins and hazardous situation reports. Information bulletins report current disaster information using a fixed information template, while hazardous situation reports are submitted quickly through mobile devices to report on-site hazardous situations. The damage assessment includes both disaster assessment statistics and detailed disaster assessment. By using drone footage, the system can intelligently assess the damage to current equipment.
The earthquake information can be viewed based on different time periods of 3, 7, or 15 days, as well as based on different earthquake magnitudes, such as below 4.0, between 4.0 and 6.0, and above 6.0. The earthquake disaster situation report provides information on the affected area, including longitude and latitude, and predicts potential damage to equipment, such as substations and poles. The satellite cloud map displays current satellite cloud information, which can assist in determining the current weather conditions. The radar map shows current radar information and can assist in determining the current weather trends. The power grid GIS information system displays the power grid GIS station line information. By using the earthquake information, it is possible to analyze the impact on substations, power lines, and customers in the affected area. The disaster damage report is divided into information bulletins and risk reports. The information bulletin reports the current disaster damage information based on a fixed information template. The risk report provides a quick report of on-site disaster risks through a mobile device. The disaster damage perception system includes both statistics and detailed information. Through the use of unmanned aerial vehicles (UAVs), the system can intelligently determine the current equipment damage situation.
Landslide disasters include landslide damage prediction, satellite cloud maps, radar maps, power grid GIS site information, disaster situation updates, and disaster damage perception. Among them, landslide damage prediction can check current rainfall in landslide-prone areas, landslide disaster probability, and other information. Satellite cloud maps can display current satellite cloud map information and assist in judging the development trend of current rainfall and analyzing the possibility of landslide triggering. Radar maps can show current radar map information, assist in judging the development trend of current rainfall, and analyze landslide situations. Power grid GIS site information can display the site information of the power grid GIS, and through rainfall-induced landslides, analyze the affected situation of substations, lines, and user areas. Disaster situation updates include information bulletins and hazard situation alerts. Information bulletins mainly report current disaster damage information through fixed information templates, while hazard situation alerts mainly achieve rapid reporting of on-site hazard situations through mobile devices. Disaster damage perception includes disaster damage perception statistics and disaster damage perception details. Through pictures taken by drones, the current equipment damage can be intelligently judged.
In summary, this section has studied data fusion technology and methods, and proposed a technology scheme for integrating and fusing multi-source information from data collection, disaster damage model library, and comprehensive emergency command database. The functional design and positioning of the emergency command comprehensive data analysis module in the emergency command system have also been presented. This can provide data support and auxiliary reference for emergency command and decision-making.
4.4.3 Fuzzy Dynamic Grid Multi-Hazard Loss Prediction Technology
In recent years, meteorological and geological disasters such as typhoons, heavy rains, snow and ice, earthquakes, and landslides have occurred frequently, with strong destructive power and significant chain reactions, posing a great threat to power grid equipment such as towers, lines, and substations. Meteorological and geological disasters often do not occur alone, but are accompanied by secondary disasters or occur simultaneously with other disasters. For single meteorological and geological disasters, current power equipment damage prediction technologies, such as grey correlation degree, Petri networks, fuzzy evaluation, and artificial neural networks, can obtain relatively accurate prediction results. However, for power equipment damage prediction under multiple disasters or comprehensive disaster chains, such models are rare. After a disaster occurs, it is necessary to study multi-disaster fusion damage prediction models to quickly assess the extent of damage to power grid equipment under the combined effects of multiple disasters and disaster chains, predict the load loss and economic loss caused by the affected power grid equipment, and provide a basis for emergency decision-making.
Fuzzy dynamic power grid loss prediction can be divided into evaluations of multiple concurrent disasters and evaluations of comprehensive disaster chain effects. As shown in Fig. 4.43, multiple sources of information, such as meteorology, equipment, environment, and disasters, are fused with power grid equipment damage assessment models to evaluate the damage of power grid equipment under the concurrent effects of multiple disasters and under the comprehensive effects of disaster chains. The data fusion technology and methods as well as the disaster damage assessment model have been described earlier and will not be repeated here. This section will analyze and explore the fuzzy dynamic prediction of power grid equipment damage under the concurrent effects of multiple disasters and under the effects of disaster chains.
Schematic diagram of fuzzy dynamic power grid loss prediction technology based on multi-source data
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(1)
Multi-hazard synergistic effects on power grid equipment damage prediction under fuzzy and dynamic conditions
A method of expert evaluation is used to predict the fuzzy and dynamic damage caused by multi-hazard synergistic effects on power grid equipment. Taking into account the actual conditions of power equipment design, construction and use, meteorological conditions, terrain and geological conditions, power equipment use time, maintenance frequency, disaster-resistant protective structures, etc. in a certain region, the degree of damage to power equipment (poles, lines, substations) caused by earthquakes, landslides, typhoons, heavy rain and flooding, and snow and ice disasters in the disaster-stricken area is evaluated. The weight value \({\omega }_{ij}\) of a single disaster damage is determined using the Pythagorean fuzzy set, and then the prediction result \({P}_{{d}_{i}}\) of a single type of power grid disaster damage is obtained. The specific process is shown as follows:
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(a)
For power equipment within a certain region, the weight values of single disaster damage caused by typhoons, heavy rain, snow and ice, earthquakes, and landslides are evaluated separately. The membership degree \({\mu }_{i}\) and non-membership degree \({V}_{i}\) of each disaster evaluation index are determined (where i = 1,2,3,4,5 represents earthquakes, landslides, typhoons, heavy rain and flooding, snow and ice, and j = 1,2,… represents different equipment), combined with Pythagorean fuzzy set theory, the hesitation degree and Pythagorean fuzzy entropy are calculated, and then the weight value of single disaster damage \({\omega }_{i}\) is obtained.
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(b)
The severity of damage caused by earthquakes, landslides, typhoons, heavy rain and flooding, and snow and ice to power grid equipment is separately predicted and calculated, and the results \({P}_{ij}\) are obtained.
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(c)
Calculate the predicted damage of a single disaster to the power grid equipment.
$$ P_{{d_{i} }} = \left[ {1 - \mathop \prod \limits_{j = 1,23} \left( {1 - P_{ij} } \right)} \right] \times \omega_{i} $$(4.109)
After the analysis of the occurrence of two or more disasters in the area, based on disaster rapid report information from meteorological agencies, earthquake bureaus, etc., the type of disaster is determined, basic information about the disaster is collected, and the impact range of a single disaster is assessed to predict the degree of damage to the power grid equipment. With the use of the single disaster damage weight value, the degree of equipment damage under the combined effect of multiple disasters is evaluated. For power grid equipment in a certain area, the overall probability of damage under the combined effect of multiple disasters can be expressed as \(\mathrm{P}\):
In the equation, the value of \(i\) is determined by the actual type of disaster, with \(i=1, 2, 3, 4, 5\) representing earthquake, landslide, typhoon, torrential rain and flood, and rain and snow and ice disasters respectively. For a certain equipment, the degree of damage under the combined effect of multiple disasters can be expressed as:
In summary, based on the research in Chap. 3, the degree of damage to power grid equipment caused by a single disaster can be evaluated. On this basis, the probability of damage to power grid equipment under the combined effect of multiple disasters can be calculated using Eqs. (4.109) to (4.111), and the prediction and assessment results of power grid equipment disaster damage under the combined effect of multiple disasters can be obtained.
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(2)
Chain-type disasters, combined with fuzzy dynamic prediction of power grid equipment damage
For the fuzzy dynamic prediction of the cascading effects of chain disasters on power grid equipment damage, based on the degree of power equipment damage \({P}_{d}\) caused by a particular disaster, the probability \(\upvarepsilon \) of triggering secondary disasters or disaster chains is analyzed. With the results of the single disaster damage prediction combined, the damage degree of power grid equipment under the comprehensive effect of the disaster chain can be evaluated and expressed as \({P}_{H}\).
where \({P}_{{d}_{i}}^{\prime}\) is the degree of damage of the secondary disaster grid equipment; \({\varepsilon }^{\prime}\) and \({P}_{{d}_{i}}^{{\prime}{\prime}}\), is the prediction of the possibility of secondary disaster and the degree of damage of the equipment.
Equipment failure rate varies depending on the time of use, considering that the accuracy of equipment failure rate prediction can be improved. The distribution of equipment life cycle can be described by the Weibull distribution, and the failure rate function can be written as:
where \(h(t)\) denotes the failure rate of the equipment at \(t\) years of operation, \(\alpha \ge 0\), \(\beta \ge 0\) is the shape parameter, and \(\lambda \ge 0\) is the acceleration parameter. Then the degree of damage \({P}_{S}^{*}\) of a certain equipment considering the equipment failure rate can be written as:
The above analysis shows that for chain disasters, in addition to analyzing the damage of primary and secondary disasters to power grid equipment, it is also necessary to consider the causal relationship between primary and secondary disasters and establish a relationship formula for the primary-secondary disaster chain. The comprehensive evaluation of the impact of chain disasters on power grid equipment is then carried out.
In summary, this section has studied the fuzzy dynamic prediction technology for electric power grid equipment disaster damage under multiple concurrent disasters and chain disasters. A disaster damage assessment model has been constructed, which can achieve rapid assessment of electric power grid equipment disaster damage under multiple concurrent disasters and chain disasters.
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Yu, Z., Feng, J., Tang, S., Liu, Z., Yan, Y., Luo, N. (2024). Grid Disaster Information Fusion and Integrated Prediction Technology. In: Disaster Intelligent Perception and Emergency Command of Power Grid. Springer, Singapore. https://doi.org/10.1007/978-981-99-7236-4_4
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DOI: https://doi.org/10.1007/978-981-99-7236-4_4
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