Original article
A comprehensive assessment of power system resilience to a hurricane using a two-stage analytical approach incorporating risk-based index

https://doi.org/10.1016/j.seta.2020.100831Get rights and content

Highlights

  • A two-stage resilience assessment method includes snapshot and overall assessment.

  • Snapshot resilience assessment means measuring it at a single event intensity.

  • Risk is incorporated into snapshot resilience indices using the measure of CVaR.

  • Overall resilience assessment means measuring it on a range of event intensities.

  • The two-stage resilience assessment provides an accurate picture of resilience.

Abstract

Sustainability of power systems is a vital need for modern societies. The occurrence of extreme weather events, such as hurricanes, may lead to blackouts. Hence, power systems resilience is a critical issue for experts. The main focus of this paper is on how to assess power system resilience comprehensively. In this regard, a two-stage framework is proposed. In the first stage, an approach is presented to evaluate power system resilience against a single intensity of a hurricane, which is called snapshot resilience assessment. The Cost of Energy Not Supplied (CENS) is regarded as a primary criterion. A risk measure called Conditional Value at Risk (CVaR) is incorporated into this approach to manage the risk of experiencing unfavorable failure scenarios. Accordingly, CVaR of CENS is proposed as an index in this stage. In the second stage, an approach for comprehensive resilience assessment is proposed, which is based on the trend of changing the values of snapshot resilience indices over a range of intensities of the event. The applicability of the proposed framework is tested in the IEEE 24-bus system. Finally, to examine the accuracy of the framework, the resilience of the test system is re-evaluated after applying a resilience improvement method.

Introduction

Today, modern societies, one of the pillars of which is technology, are heavily dependent on power systems as one of the most vital infrastructures. Hence, power systems blackout is one of the most critical challenges for all stakeholders, including electrical-based industries and consumers, because of the costly and time-consuming procedures of power systems restoration after collapsing. Study on the consequences of the events with High Impact and Low Probability (HILP events), as one of the leading causes of power systems blackout, is included in resilience studies. The US National Infrastructure Advisory Council (NIAC) presented a definition of resilience as the ability to decrease the extent and the duration of the consequences of catastrophic events [1]. Resilience has four main features, including resourcefulness, robustness, adaptability, and rapid recovery, as described in Table 1.

The US Department of Energy (DOE) has conducted extensive studies on the origins of the major outages in power systems. It can be derived from these studies that natural disasters are the most common cause of power systems blackouts [2]. Weather events are increasing across the world due to climate changes of the Earth over the last few decades [3]. These kinds of events cause severe damage. For example, in the US, the cost of damage due to weather events is about $ 25–$ 70 billion a year [4]. Therefore, power systems resilience to extreme weather events is a critical issue that has attracted the attention of most experts in the field nowadays. In the face of a HILP event, a power system at each state experiences a different level of performance, as shown in Fig. 1. In a non-resilient power system, the performance level of the system may drop to such an extent that it causes a blackout. However, if the system is resilient to that event, it can continue to its performance even at a lower than ideal level.

Methods for assessing power systems resilience comprise of qualitative and quantitative methods [5], [6]. Also, measures used to improve power systems resilience generally fall into two categories; preventive measures which are carried out before the occurrence of an event and recovery measures which are executed after the event [7]. In this paper, a quantitative approach is presented to assess power system resilience from a new perspective. Then, a preventive measure is utilized to improve power system resilience. It should be noted that power system resilience against a hurricane is studied in this paper. However, the proposed framework for resilience assessment is of general validity for other types of HILP events.

Here, the literature on power system resilience has been surveyed in two subsections. First, resilience assessment approaches and then resilience improvement techniques are reviewed. It has to be noted that since the focus of this paper is on the resilience-oriented operation of power systems, only short-term solutions to resilience enhancement are surveyed.

As mentioned earlier, the methods used in the literature for evaluating system resilience are generally divided into two groups, namely qualitative approaches and quantitative approaches [5], [15], that are surveyed in the following, respectively.

  • A.

    Qualitative Assessment of Power System Resilience

The qualitative assessment approaches are based on evaluating the features of resilience, including preparedness, absorption capacity, resourcefulness, robustness, adaptability, consequence mitigation capacity, and recovery capacity [16]. There are various methods for this type of assessment. For example, a conceptual framework has been used in [17], which is formed by designing appropriate questionnaires that examine different features of resilience. Authors of [18] have presented a comparative assessment approach in which a weighted score is assigned to each of the main features of resilience. Then for comparative resilience assessment of different systems, a scoring matrix is used that consists of all the weighted values of features in each system. Since such qualitative approaches can provide a good picture of a system's long-term behavior, they can be used to design and plan power systems [19]. However, for short-term decisions and accurate evaluation of system resilience, quantitative assessment approaches are preferred.

  • B.

    Quantitative Assessment of Power System Resilience

Quantitative approaches can be used to provide appropriate indices for quantitative comparison of the resilience of different systems and also to measure the efficiency of resilience enhancement methods. In these kinds of approaches, resilience is evaluated by quantifying some system performance metrics, e.g., the resilience drop rate in the event-progress state, the duration of the post-event degraded state, and the outage recovery capacity in the recovery state.

In view of the interdependency between the critical infrastructure systems, some of the quantitative methods developed for resilience assessment of a particular infrastructure can also be applied to other infrastructures. The idea of developing the quantitative resilience assessment methods, so that are applicable to different critical infrastructures has been proposed in [20], [21], [22]. According to[23], the resilience capacity of any kind of supply chain system, including critical infrastructure systems, can be assessed by quantifying the absorptive, adaptive, and restorative capacities of supply chain systems. As pointed out in [24], a significant number of valuable scientific work has been done on the development of quantitative methods for assessing the resilience of a supply chain system. Some of these studies have provided general models that can be used for evaluating the resilience of different critical infrastructure systems and their components (e.g., those general frameworks organized based on Bayesian networks theory)[20], [23], [24], [25]. For example, in both research works [20], [25], the Bayesian networks technology has been used to model a general framework for resilience assessment. However, in the first work, the test case is an intermodal transportation system, and in the latter, an interdependent electrical infrastructure system has been used as the case study. It worth noting that any Bayesian network used in the mentioned frameworks can be modeled as a directed graph and a set of node probability tables [23].

Generally speaking, the quantitative resilience assessment approaches can be classified into statistical methods, analytical methods, and simulation-based methods [26]. In [27], [28], [29], statistical methods are used to forecast the restoration time of a power system and the system recovery rapidity, respectively. In addition, different analytical methods have been proposed in the literature to evaluate power systems resilience that most of them are based on calculating the probability of system failure in case of severe external disruption. For example, in [30], the probability of a power system performance at its desired level while some components of the system have been failed due to external events is proposed as an index to assess its resilience. In [31], an analytical approach based on the analytical hierarchical process (AHP) has been used to evaluate the topological resilience of power systems. Among all quantitative approaches, the simulation-based methods are the most common methods for evaluating power system resilience. These types of methods fall into three general categories: I) Methods that calculate the ratio of the real performance level of a system in the face of an event to the desired performance level of that system [32]. In most studies that use this type of method for assessing resilience, system performance is evaluated using reliability metrics. However, this type of criteria cannot be comprehensive and accurate indices for system resilience. For example, the loss of load expectation (LOLE) and the loss of load frequency (LOLF), which are, in fact, reliability metrics, are used in [33] as resilience indices; II) Methods that are based on evaluating the network connectivity. In this light, authors in [34] presented a graph theory-based approach to provide a set of possible paths that causes loss-of-generation. The simulation results demonstrate that the resilience of a power distribution network is dependent on the number of paths connecting a source node to a sink node. Indeed, resilience is proportional to path redundancy which defined as the ratio of the total number of available paths to the total number of critical loads; III) Methods that calculate the cost of damages to a system due to weather events, such as presented in [35].

By surveying the literature, it can be seen that the resilience indices presented so far measure a system's ability to deal with a HILP event at a single forecasted intensity. Hence, these indices are not helpful for a comprehensive assessment of resilience as a concept that indicates the system's ability to cope with a HILP event over a wide range of intensities. To further clarify the issue, for example, in all studies that have assessed the resilience of a power system against a hurricane, the system's ability to withstand a single probable hurricane speed, e.g., 40 m/s, 50 m/s, etc., has been evaluated. This way of evaluation does not give a comprehensive picture of the overall resilience of a system. Accordingly, indices that evaluate the resilience of a system over a range of intensities of an event are more suitable to assess the concept of resilience.

In general, short-term resilience enhancement strategies depending on whether they can be used before or after the occurrence of a HILP event fall into categories of preventive and emergency measures, respectively. As the scope of this paper is the day-ahead operation of power systems, so only the preventive strategies for resilience improvement are surveyed here. There are many strategies for improving operational resilience, e.g., resilience-based unit commitment, network reconfiguration, utilizing microgrids, defensive islanding, and resilience-based demand response (DR) programs.

The technique of resilience-based unit commitment has been implemented in [36], [37] using a preventive algorithm and a decentralized algorithm, respectively. In [38], [39], a security-based unit commitment model has been presented that can be modified in such a way to be appropriate for enhancing the operational resilience of a power system against cascading failures that occur after a HILP event.

It has been demonstrated in many studies that utilizing the controllable and islandable microgrids can be a useful solution to improve the resilience of both distribution and transmission networks. Authors in [31] have presented a technique based on percolation theory that uses the method of AHP to utilize microgrids to improve the resilience of distribution systems. In [40], a method for improving the resilience of distribution networks has been presented that is based on sectionalizing the networks into multiple interconnected microgrids. It has been demonstrated in [41] that utilizing networkable microgrids facilitates the transaction of energy, and leads to increased resilience.

Authors in [42] have proposed a defensive islanding-based approach to boost the resilience of transmission systems. In this approach, an adaptive algorithm has been used to isolate vulnerable components of a power system whose outages may result in cascading failures or blackouts.

In [43], a network reconfiguration approach has been implemented to improve resilience. In this method, the power flow of networks reroutes by temporarily switching of transmission lines in such a way that the operational resilience increases.

The novel contributions of the paper are as follows:

  • In this paper, the resilience assessment is performed from a new perspective. In this light, the snapshot assessment of resilience at only a single possible intensity of an event cannot provide an accurate picture of the resilience of a system. Hence, a comprehensive assessment, which indicates the overall resilience of the system, should also be performed. It is claimed in this paper that the lower is the change in the snapshot values of resilience in a wide range of intensities of an event, the greater the overall resilience of the system. In this regard, a resilience graph is introduced in this work whose smoothness is proposed as an index for a comprehensive assessment of power system resilience.

  • The proposed optimization problem formulation for resilience assessment in this paper incorporates an acceptable number of failure scenarios. While, in previous studies, the objective functions of resilience assessment were not formulated in such a way to include a set of failure scenarios, so system resilience was assessed for each scenario separately.

  • In this paper, the decision maker's risk aversion to experiencing the worst failure scenarios is incorporated in the objective function of resilience evaluation through modeling it using a risk assessment measure called CVaR.

  • The severity of a hurricane changes as it passes across different climate zones of a power system, and over time. Taking this into account can lead to a more accurate model of the hurricane impact on power systems. Thus, the under-study power network has been divided into an arbitrary number of climate zones so that a distinct value is assigned to each zone indicating the Hurricane Spatio-Temporal Propagation factor (HSTP factor) of that zone.

Although the HILP event studied in this paper is a hurricane, the proposed framework for resilience assessment is of general validity for other types of HILP events. The steps of modeling of the proposed framework are pointed out in the following, as shown in Fig. 2:

Step 1: Modeling the uncertain impacts of a hurricane on a power system using stochastic methods

Step 2: Snapshot assessment of the system resilience using an index that does not take into account the level of risk aversion of the decision-maker to face with the worst failure scenarios

Step 3: Modifying the snapshot assessment of the system resilience to manage the risk of experiencing the unfavorable failure scenarios by incorporating the risk measure of CVaR with the index mentioned in the previous step

Step 4: Assessing the overall resilience of a system by presenting a resilience index that evaluates system resilience comprehensively for a range of hurricane speeds

In this paper, after accomplishing these steps for resilience assessment, an approach for resilience improvement is applied to a test system. Then the resilience of the system is reassessed to examine the accuracy of the proposed framework.

The rest of this paper is structured as follows. In Section 2, the impact of an upcoming hurricane is modeled. First, the concept of the fragility curve of transmission lines, which is used to identify vulnerable components of a power system, is described. Then, how to generate failure scenarios using a sequential Monte Carlo method is detailed in this section. Section 3 describes how to assess the resilience of power systems properly. First, appropriate indices that are useful for snapshot resilience assessment are provided. Next, an approach for a comprehensive assessment of resilience is introduced. In Section 4, a model of optimal transmission switching that can increase power system resilience is described. The numerical and graphical results of applying proposed approaches for resilience assessment and improvement on a test system are given in Section 5. Conclusions of the paper and the trend of future research are brought up in Section 6.

Section snippets

Modeling the impact of a hurricane on a power system

To model the impact of a weather-related event on the resilience of power systems, the vulnerability of the power system’s components in the face of different intensities of an event must be estimated. In this paper, only the vulnerability of transmission lines is regarded as the most vulnerable component of a power grid against events such as a hurricane. In the current study, it is assumed that the only part of the power system that may fail due to the hurricane is the transmission lines.

Power system resilience assessment

As mentioned, since a power system may face different severities of a HILP event, a distinct evaluation of its resilience to each of these intensities (snapshot assessment) does not give an accurate resilience metric in practice. In this light, the proposed framework for resilience assessment comprises two stages. First, a snapshot assessment of resilience is accomplished, and appropriate indices are provided. After that, an approach is presented to assess the overall resilience of power

Enhancement of power system resilience using transmission line switching

In order to prevent blackouts or reduce major outages caused by HILP events, the resilience of power systems must be enhanced using appropriate solutions. A technical solution to this end is reconfiguring the network topology via transmission line switching (TLS) [46]. Indeed, TLS is an approach to utilize the flexibility feature of a power system that may also lead to increased resilience of the system. In the literature, TLS is studied as a corrective technique as well as a control method to

Case study application

In this section, the proposed approaches for resilience assessment and improvement are applied to the IEEE 24-bus test system to investigate their applicability. The day-ahead operation of the test system is simulated for a 24-hour period when a hurricane has been predicted to occur. In this paper, it is assumed that the power system is impacted by the hurricane for all the 24 h ahead. According to meteorological studies, the minimum intensity of the hurricane phenomenon is 30 m/s. On the other

Conclusion and future trend of research

Resilience is a multi-dimensional concept that its definition, according to NIAC, is the ability of a system to alleviate the amount and duration of the destructive consequences of a HILP event. The HILP events, especially the weather-related types of them, can pose a severe threat to the sustainability of power systems. Hence, many experts have been working on approaches for evaluating this concept. Most of the indices presented in the literature to assess resilience are not appropriate enough

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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