Abstract
Large-scale electricity outages have the potential to result in substantial business interruption losses. These losses can be reduced through a number of tactics within the broader strategies of mitigation and resilience. This paper presents a methodology for analyzing the tradeoffs between mitigation and three categories of resilience. We derive optimality conditions for various combinations of strategies for a Cobb-Douglas damage function and then explore implications of a less restrictive Constant Elasticity of Substitution damage function. We also calibrate the model and perform Monte Carlo simulations to test the sensitivity of the results with respect to changes in major parameters. Simulation results highlight the possibility that substitution away from mitigation towards resilience may lower total expected costs from large-scale outages for a given level of risk reduction expenditure when the marginal benefit of resilience is high relative to the expected marginal benefit of mitigation.
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Notes
Dozens of definitions of resilience have been offered along several dimensions. One important distinction is between definitions that consider resilience to be any action that reduces risk (e.g., Bruneau et al. 2003), including those taken before, during and after an unforeseen event, such as a power outage, and those that use the term narrowly to include only actions taken after the event has commenced, acknowledging, however, that resilience is a process. The latter definition does not ignore pre-event actions, but prefers to refer to them as mitigation, and emphasizes that the intent of these actions is to make a system more resistant, robust or reliable (in standard engineering terminology). Our definition simply chooses to focus on the basic etymological root of resilience, “to rebound”, and thus emphasizes system or business continuity in the static sense and recovery in the dynamic one (see also Greenberg et al. 2007). The distinction between reliability (as promoted by mitigation) and resilience is poignantly stated in a recent NRC report: “Resilience is not the same as reliability. While minimizing the likelihood of large-area, long-duration outages is important, a resilient system is one that acknowledges that such outages can occur, prepares to deal with them, minimizes their impact when they occur, is able to restore service quickly, and draws lessons from the experience to improve performance in the future” (NRC 2017, p. 10)
Keogh and Cody (2013; p. 1) have suggested that the term “resilience” might be considered as covering both “robustness and recovery characteristics of utility infrastructure and operations, both of which avoid or minimize interruptions of service during an extraordinary and hazardous event.” As such, it is intended to be broader than the term “reliability”, in that they do not consider reliability to be sufficiently meaningful to handle large-scale disruptions. However, we contend that this juxtaposition is confusing, and prefer to refer to reliability as a goal of pre-event mitigation and resilience as activities to be implemented to reduce losses once the event has commenced.
“Speed” here is short-hand for the entire time-path of the recovery. This has two important dimensions: the shape of the entire time-path and its duration. Jump-starting the recovery and shortening its duration can both reduce BI losses, though the former is likely to have the greater effect (see Xie et al. 2018).
Note that this paper encompasses only the electricity generation and utilization stages of electricity. It omits the distribution aspect, where several tactics, including many market-oriented ones such as dispatchable ancillary services and black start services, could reduce losses. While these are beyond the scope of our paper, the modeling framework can be adapted to include various alternative mitigation and resilience tactics.
While mitigation and inherent static resilience expenditures are often large investments that are paid for over many years, the decision to make these investments is made prior to the realization of whether an outage occurs so the costs can be viewed by discounting the stream of future payments to the time that the investment decision was made. Further, while utilities can recoup some of these costs through rate of return regulation we abstract away from these details because their inclusion does not alter our analysis. While there are complex situations related to electricity storage where modification in investment timing are possible during the course of an outage, these complications are beyond the scope of our paper.
This problem could also be formulated based on minimizing expenditure given a targeted level of loss reduction. The resulting optimal levels of mitigation and resilience would be equivalent to the model that we present according to duality theory.
While we focus on business interruption as measured by decrease in GDP (Sanstad 2013), there are several alternative ways to measure losses from electric power outages including Value of Lost Load (VOLL), System Average Interruption Duration Index (SAIDI), and expenditure on backup generation (See, e.g., Keogh and Cody 2013, Matsukawa and Fuji 1994; Beenstock et al. 1997). There are also distinction between “direct” and “indirect” losses, where the former term refers to losses in revenue and lost consumer output while the latter term refers to supply chain losses. Our modeling framework is sufficiently general to cover these alternative definitions of losses.
Production rescheduling would best be modeled with 2 periods following the onset of the outage.
The mitigation BCR stems from Rose et al. (2007a, b), and the resilience BCR from Dormady et al (2018a). We note a major distinction between the benefits of investment in mitigation and dynamic resilience versus benefits of investment in inherent and adaptive static resilience. The former has public good attributes, in that reducing the magnitude or duration of the outage benefits all customers. However, the latter is a private good, in that it only directly benefits the firm undertaking the investment. Our BCRs factor this into their numerical values (see Rose 2017). Note also that distinctions made above pertain to partial equilibrium analyses; general equilibrium analysis, which would include supply-chain effects, include spillover effects that cannot be captured by either the utility or individual firms (see also Sue Wing and Rose 2018).
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Funding
The work described in this study was funded by the Transmission Planning and Technical Assistance Division of the U.S. Department of Energy’s Office of Electricity Delivery and Energy Reliability under Lawrence Berkeley National Laboratory (LBNL) Contract No. DE-AC02-05CH11231. This paper benefited from helpful comments from Ben Hobbs and participants at the LBNLWorkshop on The Economics of Long Duration, Widespread Power Interruptions, Washington, DC, March 4, 2018.
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Eyer, J., Rose, A. Mitigation and Resilience Tradeoffs for Electricity Outages. EconDisCliCha 3, 61–77 (2019). https://doi.org/10.1007/s41885-018-0034-5
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DOI: https://doi.org/10.1007/s41885-018-0034-5