A hurricane is one of the major natural hazards that cause dramatic economic, social, and environmental loss. In the 2018 Atlantic hurricane season, Hurricane Michael caused approximately $25 million damage estimated by the National Oceanic and Atmosphere Administration [1]. Widespread power outages affected 1.7 million customers in six states [2]. Meanwhile, power outage also indirectly impacts communication, transportation, medical, and all other lifeline systems. As Abedi et al. [3] summarized in the review, the natural hazard is a significant cause of the power system failure and leave a long-duration impact. Therefore, the reliability analysis of the power system during extreme events draw a lot of researchers' attention: (1) some mathematical approaches such as the sequence operation theory, the fault tree analysis are implemented to evaluate the power system reliability [4,5]; (2) maintenance optimization and hardening strategies are proposed based on the system reliability [6][7][8]; (3) some comprehensive frameworks are developed to provide the vulnerability indicators [9], rank the critical components [10], and compare different power flow-based models [11]. However, limited research reveals the physical damage in the transmission system infrastructure and also the further impact on the power network performance during a hurricane.
Previous studies of the hurricane impact power system were mainly conducted through statistical analysis to explore key impact factors, including environmental variables or structural variables. Environmental variables include hurricane wind speed, hurricane rainfall, land cover type, tree type, and so on. Liu et al. [12] employed the negative binomial regression model to predict the power outage. They concluded that several important influence factors such as the maximum gust wind speed and affected companies instead of land cover type and soil drainage level. Han et al. [13] also used this regression model to consider both local climatology and geography information. Nateghi et al. [14] examined the environmental variables by random forest method to develop a simplified hurricane power outage forecasting model with fewer variables. Several other statistical analysis models including the spatial generalized linear mixed modeling approach [15] the classification and regression trees approach [16], the quantile regression forests and Bayesian additive regression trees method are also employed to determine the important variables like company indicator covariates, the influence of soil and elevation characteristics and local conditions. Structural variables include the power system components like the transmission line, transmission tower, wood pole, etc. Guikema et al. [17] employed the regression and data mining to estimate the damaged utility poles for the prestorm estimation of a power outage. Liu et al. [18] used a fuzzy inference system combined with the regional weather model to obtain the increment multipliers of the failure rate of transmission lines during the hurricane. However, most research above utilizes a data-based approach to predict the hurricane-induced power outage based on the environmental or structural variable analysis.
Limited research demonstrates the physical laws that govern the hurricane's impact on the power system components and eventual impact on the power outage. A Power system's failure and damage during a hurricane are led by the failures of the physical structural components supporting the power transmission and distribution system [19]. The main structural components of a power system include power plants, substations, transmission towers, transmission lines, and distribution lines [20]. The structural damages in the system during a hurricane can be induced by either heavy wind or flood [21]. Substations are vulnerable due to the flood or storm surge during a hurricane [22]. Transmission tower-line structure system has complex vibration modes; they span a vast geographical region and therefore are fully exposed to the wind field during a hurricane. North American Electric Reliability Corporation (NERC) reports show that Electric Reliability Council of Texas (ERCOT) experienced 106 transmission line outages (138 kV and above) after Hurricane Harvey made landfall [23]. Similarly, Hurricane Sandy caused the outage of over 218 high-voltage (115 kV and above) transmission lines [24]. It can be concluded that the transmission tower-line system is vulnerable to the extensive dynamic wind loading. Among the limited research which predicts the power system performance considering the structural physical damage, Winkler et al. [25] considered power system components' impact on the power outage by HAZUS while they did not involve the critical coupling effect between the transmission tower-line system.
This paper presents a physical based simulation process that estimates the damage and failure of bulk power system, taking the transmission tower-wire structural interaction into account. Previous research about the transmission tower-line system's structural behavior during large wind loadings can be divided into deterministic analysis and probabilistic analysis [26][27][28][29]. Deterministic analysis conducted through finite element modeling demonstrates the transmission towerline structural behavior by static nonlinear analysis [30,31] and windinduced vibration dynamic analysis [32]. However, the finite element method can only reflect an individual structure's behavior under a certain wind load in a deterministic way. For a specific hurricane event, obtaining the responses of each structure requires a set of simulations for each individual tower. The average response can further take random wind time histories at each tower location into account. However, for a system-level simulation, which hundreds of thousands of towers are included in a target region, such intensive simulation is computationally expensive. It is necessary to reflect the transmission tower-line's structural behavior in a probabilistic way by fragility analysis.
Wind fragility modeling is the most common probabilistic approach utilized [33][34][35]. The wind fragility model expresses the likelihood of structural damage under different wind intensities and directions [31,[36][37]. After the fragility model is developed, the user can rapidly calculate the transmission tower-line system's failure probability with given wind speed and attack angle. The state-of-the-art investigation on the probabilistic performance of transmission tower-line system can be divided into three categories: (1) the fragility model considering only a single tower response; (2) the fragility model only considering a transmission line response; and (3) the fragility model that captures the interaction between transmission tower and line. Fu et al. [38] conducted the single transmission tower's fragility analysis subject to the wind and rain loads. Ma et al. [39] presented a conductor's fragility analysis during a hurricane for the probabilistic simulation of the power system. Fu et al. [40] considered the coupling effect between the transmission tower and line by a simplified model. Cai et al. [41] developed the fragility modeling framework for a transmission tower-line system by considering the line load. However, the fragility analysis considering the coupling effect of the transmission tower-line system is limited.
Challenges exist in developing a fragility model for a transmission tower-line system. These include: (1) due to unevenly distributed stiffness of a transmission tower and the largely geometrical nonlinearity of the long transmission line, the transmission tower-line system's dynamic response is complex; the model reduction and simplification are challenging to achieve with high fidelity. (2) The dynamic analysis of the transmission tower-line system during intensive wind is usually realized by implicit Newmark-β method in ANSYS [32]; when solving the nonlinear problem, this integration method is difficult to converge. (3) As fragility analysis shows the structure's failure probability subject to a certain wind load, a set of simulations is needed for the probabilistic analysis. To obtain the transmission tower-line system's high order response, each simulation case takes several hours to run. The fragility analysis is computationally expensive [42][43][44].
To address the aforementioned challenges, this paper uses an explicit integration method to analyze the transmission tower-line system's dynamic response under intensive wind loads. Meanwhile, the computational efficiency of the fragility analysis is improved by wind speed conversion and optimal sample size selection. The transmission tower-line system fragility model is compared to the fragility model of only the transmission tower. We further investigate the impact of the transmission tower-line interaction on the system level performance of a transmission power network. A benchmark problem that simulates the performance of a synthetic power network during Hurricane Harvey is used to conduct the system-level analysis.
The objective of the structural model is to map the damage condition of a transmission tower to the wind field information (wind speed, wind direction), which enables the performance analysis of the power system. To develop a wind fragility model which represents the failure probability of the transmission tower due to different loading conditions, the first task is to analyze the dynamic response, failure modes, and limit states of a transmission tower during intense winds considering the tower-line interaction (Fig. 1).
The transmission tower investigated in this paper is a suspension tower designed for Texas with a height of 31.5 m, steel-made members (ASTM A-36), and L-shaped cross-sections. The transmission tower is initially described by Tort et al. [45] and redesigned based on ASCE Manual 74 Guidelines for Electrical Transmission Line Structural Loading [46] using the industry-standard software PLS-TOWER. Based on research by Zhang et al. [32], a three-tower two-line model is a good representation of the transmission tower-line system. Hence, this paper develops a prototype three-tower two-line model to capture the interaction between the transmission tower and line. In the prototype simulation, the span between the two towers is determined at 200 m. The maximum sag of the ground line and the conductor is 2.9 m and 3.7 m, respectively. Fig. 2 displays the finite element model of a transmission tower-line system. Design details of the transmission tower-line system are provided on the WeatherG website [47].
We used ANSYS LS-DYNA to develop the finite element model of this transmission tower-line system. ANSYS LS-DYNA is a commonly used explicit dynamic response analysis program to model the mechanical phenomena with high nonlinearity [48]. Compared with the implicit integration, based on commercial software using the transient analysis and implicit integration, the explicit integration method does not need to form the global stiffness matrix, which facilitates convergence. It is a proper way to simulate a complex and nonlinear structural dynamics system [49]. The tower members are modeled as beam 161, and the line members are considered as truss elements.
Determining the initial configuration of the transmission line is significant for developing a finite element model for it. The spatial shape equation of the transmission line can be determined by Eq. (1) [32,50], as the span sag ratio of the transmission line is less than
where z and x are the spatial coordinates, q is the line weight, H is the initial horizontal tension, l is the span, c is the height difference, and f is the sag of the transmission line, respectively.
The dynamic wind, composed of the mean and fluctuating wind, is simulated and added on the transmission tower-line system as input loading. The fluctuating wind is simulated based on the mean wind. In ASCE 7-93, mean wind profile changes over height by a power law [38,51].
where V ¯is the mean wind speed along with the height; V ¯10 is the mean wind speed at 10 m height; z is the height of the mean wind speed and z 10 is the reference height, 10 m; α is the surface roughness coefficient for the open terrain.
As the mean wind is obtained by the power law, the fluctuating wind can be expressed as a Gaussian stationary random process. For an n-dimensional zero-mean stationary Gaussian random process
, the spectral density matrix is shown in (3).
Davenport spectrum is used to obtain the power spectrum of fluctuating wind [38,40,52]. It is a spectrum implemented to generate the dynamic wind on the transmission tower or line [38,40] when the local measured spectrum is not available. The auto power spectrum of fluctuating wind is obtained by (4).
(1 )
where S v (f) is the auto power spectrum of the fluctuating wind at frequency f. κ is the surface drag coefficient.
The spatial correlation of the fluctuating wind is obtained by its cross-spectral density spectrum S ij (r, f) based on each panel's auto power spectrum from Eq. ( 4). . y i , y j , z i and z j are the spatial coordinate. It is decomposed by Cholesky decomposition.
Fluctuating wind v j (y j , z j, t) can be obtained after this.
where H(ω) is the decomposed matrix by Cholesky decomposition; Δω is the frequency increment; N is a large positive integer. Since there are 5403 nodes in the transmission tower-line system, it is necessary to select several representative nodes to generate the wind speeds and add the wind load. As demonstrated in Fig. 2, we divided each transmission tower and each transmission line into several parts, respectively. The generated point wind loads will be added on the selected nodes of the transmission tower-line system. Fig. 3(a) demonstrates the simulated wind speed at the top of the first tower when the mean wind speed is 30 m/s at 10 m height. Fig. 3(b) is the comparison between the simulated spectrum and the Davenport spectrum.
Wind pressure in a wind field is calculated as Eq. ( 11) [53].
Wind load is related to the wind pressure, air density, and drag coefficient in Eq. (12).
where ρ is the air density, chosen as 1.195 kg/m 3 . V(t) is wind time history, obtained from Eqs. (2) to (10). C f is the drag coefficient, and A is the projected area. Drag coefficients of the transmission tower are calculated based on the solidity of transmission tower from Tables 2 to 4 in ASCE Manual 74 [46]. The drag coefficient of the transmission line is recommended as 1.0.
In order to conduct the fragility analysis of the transmission towerline system, the failure criterion of the tower-line system should be identified first. This paper employs the nonlinear static pushover (NSP) method [54] to obtain the transmission tower's capacity curve, which is then used as the reference to generate the fragility curve. Static wind load is calculated in Eq. ( 13) and ( 14) based on ASCE Manual [46].
where γ w equals 1.0 in this paper, which is the load factor related to wind return period; Q is a numerical constant, 0.00256; K zt is the topographic effect coefficient, which equals 1.0 in a plain area; V is the wind speed and G t is the gust response factor; Ψ is the yaw angle in a horizontal plane. C ft and C fl are drag coefficients related to the face of structure, which is parallel and perpendicular to the line. A mt and A ml are all member areas in the face of structure, which are parallel and perpendicular to the line, respectively.
To consider the power system's performance during a hurricane, five wind attack angles Ψ: 0 ∘ , 30 ∘ , 45 ∘ , 60 ∘ and 90 ∘ are chosen. Degree of 0 ∘ is the wind direction along the axis of the transmission line (x-axis) and an attack angle of 90 ∘ is for the case, where the wind direction acts perpendicular to the line direction (y-axis) as Fig. 2 displays. By monotonically increasing wind load, the force and deformation curve, i.e., the capacity curve is obtained, as shown in Fig. 4.
The top displacement of the transmission tower is always considered as a convenient index to reflect the tower's dynamic response [55]. In addition, the transmission line rarely gets pulled apart during hurricanes [56]. Hurricane's impact on the transmission tower-line system is the tension on the tower caused by the lines. Therefore, this paper chooses the top displacement of the middle tower, as N1 in Fig. 2, to evaluate the transmission tower-line system's limit state. As Fig. 4 shows, the failure of the transmission tower occurs when the capacity curve reaches its limit [54]. Hence, at these five wind attack angles, the transmission tower reaches its limit state when the top displacement is around 0.27 m to 0.35 m, which is equivalent to a drift ratio between 0.86% to 1.1%. This paper chooses the top drift 1% of the transmission tower as the limit state to evaluate the failure of the tower.
Since the transmission tower-line system's dynamic response is complex and computationally burdensome, the computational efficiency improvement for the fragility analysis of the transmission towerline system is critical.
As stated above, the fragility curve displays the likelihood of damage of the structure as a function of different wind speeds. Thus, this paper investigates the transmission tower-line system's failure probability from the mean wind speed at 10 m height changing from 15 m/s to 70 m/s with 5 m/s intervals. There are 12 groups of mean wind speed. At each mean wind speed group, a set of mean wind speed in a ± 2 m/s range by Monte-Carlo simulation is considered for the stochastic process.
To determine the computational time in running each dynamic response simulation, a test was conducted on a computer with an Intel (R) Core (TM) i7-8700 CPU and 64.0 GB RAM. The results show that more than 9 h are needed to calculate the dynamic response of the transmission tower-line system under a 60 s wind loading input. Meanwhile, using Monte-Carlo simulation, to take the stochastic effect of wind loading into account, results in hundreds of simulations at each wind speed. Considering different attack angles will only add to the computational burden of developing the fragility model. Consequently, it is critical to find a computationally efficient way to generate the fragility curve. This paper focuses on two aspects: wind speed conversion and determining the optimal sampling size for the Monte-Carlo simulation.
According to ASCE Manual 74 [46], the wind speed values depend on the wind speed record on the averaging time. Higher wind speed corresponds to a shorter averaging time, and lower wind speed corresponds to a longer time. Therefore, it is reasonable to employ the mean conversion figure, reported by Durst [57] to transfer the mean wind speed from 600 s to a shorter time. Here in Fig. 5 the horizontal axis is the averaging time of the wind speed, and the vertical axis is the ratio V t /V h , as the wind speed is averaged in t seconds to hourly mean wind speed. Therefore, a ratio of 3-second wind speed V 3s to 10-minute wind speed V 10min at 10 m, V 3s /V 10min is roughly 1.43 (where V 3s /V h =1.526, V 10min /V h =1.067 from Fig. 5).
To obtain a proper short time period with higher accuracy, we generated 100 samples for the mean wind speed ranging from 25 m/s to 75 m/s with different time windows: 3 s, 5 s, 10 s, 15 s, 20 s, and 600 s. We further investigated the mean maximum top displacement of the tower by averaging the maximum displacement of the tower during each wind loading sample with different time windows. Table 1 illustrates the mean top displacement results of this comparison. As the Davenport spectrum used to simulate the fluctuating wind is obtained in 8-10 min time period [52], this paper takes 600 s as a reference to compare the result. It clearly shows that when transferring the wind speed in 600-5 s, the absolute errors of the tower's top displacement are all below 10%. The mean absolute error (MAE) is only 3.81%. Thus, it is reasonable to employ this wind speed conversion from 600 s to 5 s to simulate the transmission tower-line system's dynamic response in a short period with high accuracy.
Another way to reduce the calculation time is to choose a proper sample size to capture the stochastic wind loading through Monte-Carlo simulation. This paper compares the results from 20, 50, 80, 100, and 200 samples for the transmission tower's fragility curve. Fig. 6 displays the results, which show that the fragility curves of the five sample sizes are similar. According to the sample size 20, 50, 80, 100, 200 of the Monte-Carlo simulation, the failure probability resolution of each sample size is 0.05 (1/20 samples), 0.02(1/50 samples), 0.0125(1/80 samples), 0.01(1/100 samples), and 0.005(1/200 samples). The discrepancy of different sample size's failure probability at 40 m/s and 50 m/s is mainly because of this resolution difference: 0.05, 0.02, 0.0125, 0.01, and 0.005 from the sample size. Besides, the difference is also acceptable because the fragility curve for the same tower in the same sample size will get slightly different fragility curve when running Monte-Carlo simulation several times.
Based on the effective fragility analysis stated above, the fragility curve of the transmission tower-line system can be calculated. In structural wind fragility analysis, the damage and failure probability F R (V) under a given wind speed V is determined by Eq. ( 15):
where LS is the limit state discussed in Section 2.3; l is the simulated response compared with the limit state; in the development of the transmission-line system fragility curve, l is the top displacement of the middle tower in this analysis. V ¯10 is the mean wind speed at 10 m ranging from 15 m/s to 70 m/s with 5 m/s increase. At each wind speed, the sample size is 20, as discussed in Section 3.1. If the top displacement of the middle tower is larger than the limit state 1% drift at each case, it is considered failed. The failure probability is calculated as the number of failed transmission towers over total 20 cases at each wind speed. The fragility curve is formed based on all the failure probabilities of each wind speed. The fragility curve of the transmission tower-line system is presented in Fig. 7(a). Developing the fragility curve of a stand-alone transmission tower (not considering the towerwire interaction) is a standard process [58]. Fig. 7(b) is a comparison between the stand-alone transmission tower's fragility curve with the transmission tower-line system's fragility curve. It demonstrates that the interaction between the transmission tower and line impacts the performance of the transmission tower significantly. Stand-alone Fig. 5. Regeneration of the wind speed conversion [57].
transmission tower starts to fail much later than the transmission towerline system, which can lead to overly optimistic results for the power system performance assessment.
In order to investigate the impact of transmission infrastructure performance on transmission power network during the hurricanes, the structural model should be integrated into a system-level simulation platform. We utilized a wind-impacted power system performance simulator in this research. The simulator includes four modules: (1) a hurricane wind field information module, which produces the realistic wind data, including the wind speed and direction, in a grid format in the region of the study; (2) a physical power system module which maps a power network to the physical region of the study; the physical power system infrastructure includes generators, substations, and transmission towers and lines designed for the study region; (3) a transmission system structural performance analysis module which integrates the physical transmission system infrastructure, the structural models, and the wind field information to estimate the damage and failure likelihood of each individual structure inside the study region; for individual transmission tower-line structural systems (three-tower two-line system), the component failure probability will be converted to the failure and damage of a transmission line (which is composed of hundreds of towers); (4) power network simulation module which utilizes stochastic analysis to simulate the probabilistic power outage and economic loss due to the physical damage to the infrastructure, after obtaining the damage and failure probability of the physical Note: Coefficient 1 is the ratio, V V / t h (Durst,19,610); Conversion coefficient 2 is to consider 600 s as the reference time period, the conversion factor converts the wind speed in other time period to 600 s; MAE is the mean absolute error. components in the transmission power system. The workflow of the wind-impacted power system performance simulator is demonstrated in Fig. 8.
In the benchmark problem, the simulator evaluates the performance of a synthetic power network during Hurricane Harvey. In the wind filed information module, the wind field is calculated based on the observed wind speed and direction for Hurricane Harvey. We mapped the designed transmission-line structural system is mapped to a synthetic Texas 2000-bus network model [59] to the footprint of Texas.
The damage and failure probabilities of the transmission-line system are predicted, and the element failure of transmission-line is estimated according to both (1) the structural model only considering individual towers and (2) structural models considering the tower-line interaction. To investigate the system-level performance, the power network simulation module predicts the power outage and economic loss for both cases. To be noted, multiple designs and multiple spans are not yet fully considered in the study. The main reason is due to the missing design blueprints of transmission tower in different voltage, and the span variation and performance of the transmission tower would be affected to the detailed topography. However, as the objective of this study is to evaluate the impact of the transmission tower-line interaction, the simplified assumption of using a universal tower and span design throughout the entire system is considered to be valid. The detailed results in each module are presented in the following subsections.
To obtain a high-resolution hurricane wind field information, a mesoscale community Weather Research and Forecasting (WRF) Model (https://www.mmm.ucar.edu/weather-research-and-forecastingmodel), which is a numerical weather prediction system designed for both atmospheric research and operational forecasting applications, is employed to simulate the hurricane during its landfall period. The National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) final analysis (FNL) are used to generate meteorological input data for the WRF model. These NCEP 0.25-degree by 0.25-degree grid (about 27.8 km × 27.8 km) FNL data is produced from the Global Data Assimilation System (GDAS), which continuously collects observational data from the Global Telecommunications System (GTS) and other sources for analyses. To produce flexible meteorological data for this study, the FNL data, as well as Moderate Resolution Imaging Spectroradiometer (MODIS) collected land cover data are input into the WRF model during the simulation. The WRF model generates a meteorological field data hourly with a horizontal resolution of 1 km. Fig. 9 displays a sample of the wind field of Hurricane Harvey.
Hurricane Harvey mainly attacked the coastal area, and the wind speed inland was relatively small, compared with the wind speeds when it had been over the ocean. Hurricane wind field is simulated from 26 ∘ N to 36 ∘ N and 94 ∘ W to 100 ∘ W. This wind field information includes the mean wind speed at 10 m height and the movement from August 25th 4:00 p.m. to August 26th 4: 00 p.m. Fig. 9 demonstrates the hurricane wind field data in Texas at 1 a.m., August 26th.
According to the hurricane's landfall position and influenced area, the local power system should be mapped to the corresponding geographical location. Power networks are usually described by three elements: (1) the network bus, which describes nodes in the system; (2) the generator, which contains information of the generator's nodal location, limits and cost data; and (3) the transmission data, which describes the links connecting two nodes of the network. To simulate a more realistic power outage case, this paper employs the ACTIVSg 2000: a synthetic 2000-bus Texas power system test case, to conduct the simulations [59], as demonstrated in Fig. 10. This Texas 2000-bus system is built on the footprint of the Electric Reliability Council of Texas (ERCOT) to provide similar generation and load profiles while it has no relation to the actual grid in Texas. In this power system, every point represents a substation, and each transmission line links the substations. The locations of the substations are provided by this test
As the simulated wind field and the power system in the hurricane influenced area is determined, the mean wind speed and wind attack angle on each transmission tower is obtained (Fig. 11). The arrows represent the wind direction. Assuming that the longitude is the horizontal direction, the wind direction and the transmission line's direction to the horizontal direction are β and α, respectively. The wind attack angle to the transmission tower-line system is θ.
By giving the wind attack angle and the wind speed from the hurricane wind field, the damage probability for each transmission tower can be estimated based on the structural fragility model of the transmission tower-line structural system, as developed in Section 3.2. A transmission line is composed with hundreds of towers, which is a serial system. The transmission line survives a wind load only if all of its towers withstand the wind. Each transmission line's current failure is calculated based on the m th individual transmission tower's failure probability
from previous fragility model. The Kth transmission line's ith current independent failure probability is denoted by P[FL, k] i and its survival probability is P[SL, k] i . FL is each transmission line's failure probability, and k represents the transmission line's index. Thus, the failure probability is calculated as:
Meanwhile, the passage of the hurricane is a stochastic process. Each transmission line's failure probability at the current time step is dependent on its failure probability in the previous time step. Here, t i represents the current time step and t i 1 is the previous time step. Therefore, each transmission line's dependent failure probability is demonstrated in Eq. ( 17):
There are 3206 transmission lines and transformers in Texas 2000 bus system. The failure probability of each transmission line at different time intervals is shown in Fig. 12. After Hurricane Harvey makes landfall, with the movement of the hurricane, transmission lines are damaged gradually. The green line means the transmission line survives the wind. With the color turning red, the failure probability of the transmission line increases. Table 2 summarizes the number of failed transmission lines during different time periods. There are 51 transmission lines with failure probability larger than 90% when the hurricane passes the coastal area of Texas, the failure ratio (failed transmission line over the total transmission lines) is 1.59%.
If the system-level modeling only considers the stand-alone transmission tower performance without the tower-line interaction, and uses the fragility model of the stand-alone transmission tower, only 2 transmission lines are damaged. The calculated probability of failure of these two lines is about 0.6%, as demonstrated in Fig. 13. Such results severely underestimate the damage of the power system. Therefore, it is essential to consider the coupling effect of the transmission tower-line system from the system-level analysis.
North American Electric Reliability Corporation (NERC) reports show that Electric Reliability Council of Texas (ERCOT) experienced 106 transmission line outages (138 kV and above) after Hurricane Harvey made landfall [14]. Texas 2000 bus system is a synthetic system, developed from public data, where the grid location and the number of lines is different from the real system. The realistic Texas system has 7800 transmission lines, and the damage ratio of the transmission line is 1.35%. The percentage of damaged transmission lines, in our simulations, matches the realistic condition.
The power outage simulator estimates the power outage (unserved load) based on the predicted damage to the power system components. Temporal and geographical distribution of power outage depends on the generation dispatch as well as the level of damage to the network. Generation dispatch simply identifies the commitment status (on or off) as well as the production level of those generators that are on, throughout the duration of operation, which in this paper is a full day. Different dispatch combinations will use the transmission network differently, and thus, will result in different outage distribution even with the same level of damage. In power system operation, day-ahead generation dispatch is calculated using a unit commitment model, which minimizes the cost of operation by finding the cheapest dispatch, while considering the physical constraints of the system. One set of such constraints include the modeling of power flows on transmission lines and the capacity constraints of the transmission system.
To properly estimate the power outages induced by the hurricane, we first solve a unit commitment model, without considering the hurricane impacts. This is referred to as the business as usual scenario. Using the commitment results (hourly generation status and production for each generating unit), the hurricane is simulated in the next stage. Please note that the operators cannot change the status of the generators in real-time, as starting up new generation can take hours depending on the type of the generator. However, the operators can adjust the production levels in response to real-time conditions, such as the damages induced by the hurricane, as long as the changes are within the ramping capabilities of the generators. As the hurricane damages more transmission lines, the operator will change the generation dispatch, without changing the commitment, to minimize the power outage and serve as much load as possible. With few damaged lines, there is a chance to keep the balance and serve the majority of the electricity demand. However, during major hurricanes, the number of damaged lines is too large, and some level of a power outage is unavoidable.
The temporal failure probability for each transmission line is given in the results of the previous section. Considering that there are many transmission lines in this test case (3206 lines), and time resolution of power simulator (3 h), the number of possible network topologies that can emerge due to the hurricane damage is an extremely large number. Here, each unique possibility is referred to as a "future". It is not possible to simulate each feature to evaluate the unserved load in all of the futures, because of the large number of possible futures. As an alternative solution, Monte Carlo simulation is used to simulate as many futures as possible. In this process, thousands of those futures are selected randomly, and the expected value of power outage is calculated for each future. We stop the Monte Carlo simulations once the average value of the power outage stays stable for at least more than half of the simulations. In Monte Carlo simulations, for each unique network topology (caused by the hurricane), the commitment status of generating units is fixed. The simulator, then minimizes the unserved load, by adjusting the dispatch within the ramping limits. The unit commitment solution, obtained for business, as usual, would result in no power outage, if the network is not damaged. The power system performance for the business as usual case is shown in Table 3, considering no damage.
During the hurricane, the network will be partially damaged, and some transmission lines will go out of service. The total number of lines with a nonzero damage probability is 174 according to Table 2. Moreover, the hurricane can create islands in the network, which would divide the network into regions that are not connected to each other, with the main network and a number of small islands. Under such conditions, avoiding unserved load and/or over-generation will not be possible. The results of over 1000 Monte Carlo simulations, are presented in Table 4, evaluating the power system performance using the damage probabilities calculated in the previous section.
Table 4 shows that the hurricane leads to high levels of unserved load and over-generation. The total level of load shedding and overgeneration is more than 4.4% of the total load in the network. Moreover, the operation cost in this case increased substantially, due to the high penalty for unserved load, which here is considered to be $30,000 per MWh.
Hurricane-induced power network damage is a severe issue. Although there is some research about the bulk power system performance analysis during a hurricane, there is limited research that considers the physical laws governing the power outage and system-level performance. In this paper, we presented the physical-based process in estimating the bulk power system performance during a severe wind.
Through this framework, we investigated one of the most vulnerable structural components in the bulk power system during a hurricane, which is the transmission tower-line system. We considered the transmission tower-line interaction and studied its impact on the power system performance during a hurricane. A benchmark problem evaluated a synthetic power network in Texas during Hurricane Harvey. The results indicate that the damage of the power system is massively underestimated if only isolated and stand-alone transmission tower or line structural models are considered. It is necessary to take the interaction between towers and line into consideration. In summary, the contributions of this work include:
(1) The fragility model of the transmission tower-line system is developed to probabilistically describe the power system component's failure and damage state. (2) The computational efficiency of the fragility analysis of the transmission tower-line system is improved. By the error analysis of the wind speed conversion and the sensitivity analysis of the sample size choice, the effective method can largely improve the computational efficiency. (3) Realistic hurricane wind field information from Hurricane Harvey is utilized in the benchmark problem. Combining with the realistic wind field information, the transmission tower-line structural system fragility model predicted the damage state of the physical elements in the transmission system. (4) At the system level, the results from the benchmark problem are comparable to the recorded failure in the NERC reports, which validates the developed fragility model of the transmission towerline structural system. (5) Results from both the element and system level indicate that the coupling effect between the transmission tower-line system is not negligible.
In this research, the structural response of the transmission towerline is considered to be affected by the dynamics of the transmission tower and the transmission tower-line interaction. In the future, the authors plan to refine the simulator by considering more structural influence factors of the power system, such as the breakage of the insulator, the airborne debris, and the impacts from the foundation. Meanwhile, the impact of the different types of transmission towers and spans will be investigated to simulate the system level performance and obtain more realistic and accurate results. Besides, the multi-hazards influence on the power system will be explored to consider the comprehensive impact of the hurricane, rain, and flood on the substations and other power system equipment.