Framework for Measuring the Resilience of Utility Poles of an Electric Power Distribution Network

As the severity and frequency of natural hazard-induced disasters increase year by year (NOAA 2017), utility companies are very keen to develop resilient power distribution systems. An electric pole-based resilience assessment can establish a strong base for prestorm planning. The literature shows a variety of definitions of resilience, and there is no consensus on the one accepted definition of the term. Resilience can be simply defined as the capability of a system to anticipate and absorb threats to mitigate adverse effects as well as develop response and recovery actions to resume its normal operations (Eren Tokgoz and Gheorghe 2013). According to Hosseini et al. (2016, p. 4), resilience is “the ability of an entity or system to return to normal condition after the occurrence of an event that disrupts its state.” Similarly, Nan and Sansavini (2017, p. 36) define resilience capability as “the ability of the system to withstand a change or a disruptive event by reducing the initial negative impacts, by adapting itself to them and by recovering from them.” Haimes (2009, p. 498) also defines resilience as “the ability of the system to withstand a major disruption within acceptable degradation parameters and to recover with a suitable time and reasonable costs and risks.”

The concept of resilience is multidimensional, and the quantification of it depends on several factors (MacKenzie and Zobel 2016). It is hard to consider all possible factors and vulnerabilities against various disasters, but preparation, response, recovery, and mitigation efforts, which are resilience strategies, can reduce the adverse consequences of disasters (Eren Tokgoz et al. 2017). Carlson et al. (2012) claimed that the concept of resilience plays a vital role in assessing the threats for various entities, such as owners and operators of critical infrastructures, communities, regions, and the nation. Resilience can be assessed at the asset/facility level and critical infrastructure level to develop methodologies that provide resilience-related information to critical infrastructure owners, operators, state, and local partners. Power distribution systems are complex systems and increasing their resilience by implementation of some mitigation actions could be costly. Moreover, investment in increased resilience of power distribution systems involves several complexities, such as a lower rate of future return, strict regulatory restrictions by the Public Utility Commission (PUC), lack of strong value propositions, and inadequate incentives (Mukhopadhyay and Hastak 2016). Mukhopadhyay and Hastak stated that the present investment analysis framework has flaws; hence it is not cogent and persuasive to PUC. A report published by the U.S. Executive Office of the President mentioned that investment in electric grid modernizations and increased resilience of the electric grids would reduce hardship and recovery time during weather-related disasters as well as cut down the costs associated with damages based on these disasters over time (Executive Office of the President 2013). According to this report, the annual cost of lost power due to outage consists of foregone output and wages, spoiled inventory, delayed production, inconvenience, and damage to the electric grid itself.

Several studies have been conducted on the failure of utility poles in the power distribution system. Shafieezadeh et al. (2013) found that wooden poles often fail due to a wind load greater than the flexural capacity of a pole. Han (2008) examined two mechanisms that cause the failure of poles—flexural failure due to the wind load and foundation failure. A structural analysis involving wind loads and the probabilities of failure has been conducted in the Caribbean Disaster Mitigation Project (1996). In this project, the wooden pole was assumed to be a cantilever beam that will fail if the bending stress exceeds the modulus rupture of a pole. Taras et al. (2004) argued that the strength of a pole is subject to decay over time and a pole may fail due to lateral bending. United States utility companies have struggled to strike a balance between over- and under-preparation because they lack a rigorous methodology with which to estimate the damage caused by hurricane winds (Guikema et al. 2010). Various methods have been proposed by researchers to increase the reliability of power distribution systems under wind-related disasters and to decrease the time required to restore damaged systems. These efforts can be largely divided into two groups: predictive models and storm hardening models (Salman et al. 2015; Wanik et al. 2015). Predictive models are popular because they can support pre-event activities for better resource allocations. Some of the notable previous works that proposed predictive models are:

In contrast to Darestani and his colleagues, the present study is focused on the evaluation of the condition of individual poles. In our study, the angular deflection of a pole due to wind force is considered as damage to the pole, and a damage prediction model is proposed to predict pole failure based on its angular deflection.

Several studies have been conducted to perform a cost–benefit analysis on upgrading the electric power distribution network. In the Caribbean Disaster Mitigation Project (1996), a cost–benefit analysis was conducted on the replacement of wooden poles to mitigate damage due to hurricanes. The results of the analysis revealed that the replacement of the wooden poles in a high voltage network with Class 1 poles results in a significant cost saving, but the same action with the lower voltage network is over investment. Taras et al. (2004) considered the cost of poles, labor expenses, and power outage cost as the cost of pole replacement. Quanta Technology (2009) conducted a cost–benefit analysis of utility infrastructure upgrades and storm hardening programs based on data collected from several utility companies. In Quanta report, the estimated benefits were calculated against the duration of a power outage and the projected rate of failure or damage. Results were evaluated by selecting and strengthen 10% of distribution poles in Texas, the United States. The potential net benefit from the hardening was estimated as well. However, it did not show how the most vulnerable part of the distribution network was selected for strengthen purpose. Chang (2003) developed a framework of extended life-cycle cost to evaluate efforts for mitigating the impact of disaster on infrastructure systems. This framework consists of four major costs—planned cost, associated cost imposed on the society, unplanned cost, and societal cost due to a power outage. Salman et al. (2015) adopted Chang’s framework to evaluate the cost-effectiveness of a targeted hardening strategy for a power distribution system that is susceptible to the impact of hurricane damage under both probabilistic and scenario-based hurricane conditions.

The photogrammetry-based technique is utilized to measure the current angle of a pole. Given the determined angle and the properties of a pole, two types of force that are exerted—gravitational force and wind force—are calculated. The total force, which is the summation of gravitational and wind forces, is defined as a resilience metric in this study. Figure 2 illustrates the two forces (Eren Tokgoz et al. 2017).

The gravitational force is perpendicular to the ground. Thus, the component of gravitational force acting perpendicular to the pole can be expressed aswhere \(F_{g}\) = gravitation force acting on the center of a pole. The wind force is parallel to the ground and uniformly distributed on the pole and can be expressed aswhere \(F_{w}\) = uniformly distributed wind force, \(P\) = wind pressure, \(A\) = cross-sectional area, and \(C\) = a constant converting the wind force from pound-force (lbf) to Newton (N). \(C\) is needed since the wind force and the height of a pole were considered as miles per hour and feet, respectively, at the beginning of the calculations. According to the Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals (AASHTO 2013), the wind pressure on the pole can be calculated aswhere \(V\) is the 3-second peak gust wind speed in the region where the pole is located, \(K_{z}\) is the exposure coefficient, \(G_{h}\) is the gust response factor, and \(C_{d}\) is the drag coefficient. Meanwhile, the uniformly distributed force, \(F_{w}\), can be converted into a concentrated load at the center of a pole.

Thus, the component of wind force acting perpendicular to the pole can be expressed as

Therefore, the total force due to the gravitational and wind forces can be expressed as

The mathematical model, Eq. 5, can be used to predict the force acting on a pole under various conditions of wind speeds and material properties of a pole.

A three-dimensional finite element analysis is performed to analyze the mechanical properties and capacity of a wooden pole. ANSYS^® Workbench¹ is used as a platform for the finite element analysis. Input data for the analysis include the varying wind speeds and pole angles as well as the properties of the material. Table 1 presents the material properties of a southern yellow pine pole. The output of the analysis is the amount of angular deflection of a pole for each combination of a certain force.

In this analysis, the resilience conditions of a pole are defined based on the angular deflection of a pole—the angle (θ) range 0 ≤ θ < 15, 15 ≤ θ < 25, and 25 ≤ θ corresponds to healthy (resilient), critical (moderately resilient), and unhealthy (non-resilient), respectively (Alam et al. 2018). The angle range for each resilient condition is an expert judgment-driven parameter and the range values were determined by an expert with more than 25 years of experience in the management of a power distribution system at a major utility company. The range values and corresponding resilient conditions were reviewed and accepted by additional two experts working at the same company. It is worth noting that there are no standard values of the angle range. Thus, the parameter values can vary depending on the choice of a utility company. Eren Tokgoz et al. (2017) proposed a set of recommended actions per the resilience conditions as follows. If a pole is in a healthy condition, then an immediate mitigation action is not needed. If a pole is in a critical condition, then an examination should follow to determine whether a corrective action must take place immediately or not. Lastly, if a pole is in an unhealthy condition, then an immediate corrective action, that is, maintenance or complete replacement of the pole, is needed.

There are a few previous studies that produced a resilience model or framework. Willis (2014) argued that resilience could be evaluated for different systems, disruptions, responses, and time-scales based on inputs, capacities, capabilities, and performance or outcomes. Phillips and Tompkins (2014) defined the resilience of critical infrastructure as preparedness, mitigation, response, and recovery. The Sandia National Laboratories (2014) have maintained that a resilience metric is an effective tool for quantifying uncertainty, making decisions for planning and operation, and examining the validity of the decisions.

In our study, a resilience model was developed taking into consideration the angular deflection of a pole (Fig. 3). The model consists of four sequential components of resilience—anticipate, absorb, response, and recovery. This model can address multiple aspects through a proactive approach rather than a reactive one. As part of the proactive approach, the potential wind-related disaster is anticipated. Based on the existing pole angle and calculated wind load, the most vulnerable part of the distribution systems can be detected. Once the threats and vulnerable parts are identified, the capacity of the systems needs to be measured. This capacity can be called an absorptive capacity of the system, which is the ability of the system to withstand damage during a disruptive event without any significant deviation from its normal condition. To the greatest possible extent, the uncertainties about pole damage due to wind force need to be quantified. In this case, the angular deflection of the pole from its original position is considered as damage to the pole. Based on the angular deflection, the pole’s resilience condition can be evaluated. The response to any wind-related disaster can be compared at two situations: (1) with corrective action; and (2) without corrective action before the disaster. The last step of this model is recovery, which refers to how quickly and cost effectively the system can return to its normal operative condition. The availability of the resources and their better distribution can ensure a quick recovery with low cost. Using the model, decision makers can produce an effective plan for preparation, mitigation, and recovery. It also allows decision makers to effectively prioritize required actions and allocate limited resource according to the prioritization results.

The total cost of damage due to wind-related events can be found by summing the cost of a pole replacement, revenue loss of the utility company, and economic loss of the customers (Taras et al. 2004). The replacement cost is a fixed cost for removing the existing pole and installing a new pole. The fixed cost is usually higher when the replacement of a damaged pole is done after an event has occurred (Quanta Technology 2009). The revenue loss of utility companies and loss of societal economy due to the interrupted power supply are the power interruption costs (Chang 2003; Quanta Technology 2009). The cost of revenue loss to the utility company is the volume of unmet demand due to the system’s delivery failure and the unit price of electric power (Chang 2003). The volume can be determined by the number of the customers without power, their average consumption rate, and the time needed to restore power. Chang (2003) demonstrated this cost for an earthquake disaster, which was adopted here for a wind-related disaster. The expected cost of revenue loss can be expressed aswhere \(C_{v}\) = the cost of revenue loss of the utility company, \(T_{r}\) = the time to restore power after a disaster, \(N_{out}\) = the number customers without power, \(P_{avg}\) = the average power consumption per customer, and \(r\) = the unit price of electric power. The output of the economic activities can be measured by gross domestic product (GDP) of the region or country. Thus, the cost of economic loss can be measured by the loss of economic activities due to the interrupted power supply and economic shutdown time (Quanta Technology 2009). The expected cost of economic loss can be expressed aswhere \(C_{e}\) = the cost of economic loss to the customer, \(T_{e}\) = the economic shutdown time, and \(E\) = the economic loss due to power interruption based on GDP. The expected benefit is calculated against the amount of expected damage and the duration of a power outage. Pre-event actions for upgrading the poles would reduce the severity of damages, and thus the avoided cost can be considered as a benefit. Therefore, investment for the corrective action is considered as pre-event action cost.

Twenty-two electric poles were selected as samples for a case study. The poles are located along the two major transit roads—S. Martin Luther King Jr Parkway and Highway 69—in the city of Beaumont, Texas. This area is very prone to hurricanes. The area experienced a devastating flood caused by the largest amount of rainfall recorded in the United States during Hurricane Harvey in 2017. Other most recent hurricanes that affected the same area were Hurricane Rita and Hurricane Ike in 2005 and 2008, respectively. Thus, the selected area for a case study well represents areas for which the developed methodology is intended to be implemented. The angular deflection (θ) of poles was found by using photogrammetry technology (Table 2). Given the small size of the original sample (pole angles of 22 poles) and the large sample variance, the sample was propagated from 22 to 1000 using the negative binomial distribution to perform a finite element analysis. A finite element analysis was performed using ANSYS^® Workbench to evaluate the resilience condition of the 1000 poles based on their angular deflection. Wind speeds of 90, 100, 120, 140, and 160 mph were selected and applied to each pole within each hurricane category, which is determined by the Saffir-Simpson hurricane category scale. The amount of angular deflection of each pole was then calculated for each wind speed and represented as θ₁, θ₂, θ₃, θ₄, and θ₅. These calculated angular deflections were added to the selected angles of 5°, 10°, 15°, 20°, and 25°. Table 3 presents the partial results. Figure 4 presents an example of the results of the finite element analysis. Various pole failure testing methods are available. Among them “setting poles in the earth and applying load at the middle of the pole height” was selected and applied using ANSYS^® Workbench. Figure 4 shows that the maximum deflection occurs at the top of a pole and the minimum deflection at its bottom.

Figure 5 presents the percentages of the resilient (green), moderately resilient (yellow), and non-resilient (red) conditions of the poles. The results show that the initial wind thrust caused a significant problem to the poles. The number of poles moved from moderately resilient region to non-resilient region was comparatively more than the number of poles moved from resilient to moderately resilient region. There is no significant change to those numbers as the wind speed increases due to a few reasons. For instance, the data points might be very close to a maximum value of the resilient angle range (0 ≤ θ < 15). So, once they moved from the maximum value of resilient angle to the minimum value of moderately resilient angle range (15 ≤ θ < 25), they need more forces to move to the non-resilient region. Table 4 shows the percentages of poles of that shifted in resilience condition from resilient to moderately resilient and from moderately resilient to non-resilient.

Cost–benefit analysis was conducted to show the merits of a resilience metric. It compares losses and savings for different pole conditions and corrective actions. Three strategies have been considered:

The total cost of damage was calculated based on a cost–benefit analysis approach. The replacement cost per pole was determined to be USD 2500 before a disaster event and USD 4000 after a disaster event based on Quanta Technology (2009) and the experts’ assessment. Three types of customer groups were considered—residential, commercial, and industrial customers. Each customer group has an average power consumption rate and an average economic loss due to a disaster event, which is different for each group. The size of the customer groups was assumed in this analysis to be 80% residential, 10% commercial, and 10% industrial. This cost–benefit analysis was conducted for a wind speed of 120 mph, which represents a Category 3 hurricane. The resulting damages were limited to wind-related damage to poles only.

Table 5 summarizes the data set used for the cost–benefit calculations. Tables 6, 7, and 8 present the results of the cost–benefit analysis for three corrective action strategies, respectively. Table 6 shows that 11.60% of poles is in non-resilient condition, which was originally 6.3%. Approximately 5.3% of poles was predicted to fall in non-resilient condition under a Category 3 wind speed. Thus, the total percentage of non-resilient poles is 11.60% (5.3 + 6.3). When Strategy 1 is implemented, all unhealthy poles were assumed to fail, and the total incurred cost is about USD 8.5 million. If decision makers decide to invest money into the corrective action only for existing non-resilient poles, which is Strategy 2 in this study, then the avoided cost may be considered as a benefit. In Strategy 2, USD 0.16 million investment is required to replace the existing non-resilient poles, which can reduce the initial loss down to around USD 3.6 million instead of USD 8.5 million. This saving is calculated to be approximately USD 4.9 million (USD 8.5–USD 3.6) as shown in Table 7. If decision makers choose to invest money into the corrective action to replace both existing and predicted non-resilient poles, which is Strategy 3 in this study, then, there is theoretically no loss. The predicted non-resilient poles are the ones moving from moderately resilient condition to non-resilient condition under Category 3 wind speed. Table 8 shows the results of Strategy 3 implementation, requiring approximately USD 0.3 million investment to avoid loss to the distribution network due to the pole inclination angle. It should be noted that these results do not account for other causes of pole damages such as falling trees or branches on a pole and foundation failures.

Figure 6 illustrates the results of the cost–benefit analysis of the three predetermined corrective action strategies presented in Tables 6, 7, and 8. Since the strategies are set with the number of vulnerable poles, the cost–benefit analysis can be effectively used to evaluate different resilience actions for future events. For example, using the analysis method, decision makers can set how much resilience they want to gain or how much money they want to invest to strengthen their distribution system against no corrective action option.

Figure 6 graphically presents the result of cost–benefit analysis in which a Category 3 hurricane wind speed was considered. The results show that if a decision maker follow Strategy 1, the damage cost will be approximately USD 8.5 million. Strategy 2 shows that an investment of around USD 0.16 million can reduce the damage cost from USD 8.5 million to USD 3.6 million, which can save USD 4.9 million. Strategy 3 shows that an investment of about USD 0.3 million is needed to take care all non-resilient poles, which can save USD 8.5 million damage cost.