key: cord-0593966-gx5zouzo authors: Gargani, Julien title: Impact of major hurricanes on electric energy production date: 2021-03-19 journal: nan DOI: nan sha: fa2861ac41baff081240c332f8b28935a1af5e7e doc_id: 593966 cord_uid: gx5zouzo After major hurricanes, electric production is significantly reduced owing to not only electric infrastructure destruction, but also the economic crisis associated with damage to private and public activities. The full restoration of the electric infrastructure is not always simultaneously performed with the full restoration of electric production. Here, we describe the electric production curves for the islands of Saint-Martin, Saint-Barthelemy, and Puerto Rico in the Caribbean, where two major hurricanes occurred in 2017. After the major hurricanes, the electric energy production was characterised by a slow recovery followed by a stable phase during several months, corresponding to approximately $75%$ of the initial electric production. A resilience time of several months (1 month $ a > b. The amplitude of the combined parameter a + b influences the loss of energy from the initial stable condition until the new equilibrium, after which the electric production collapses. t represents time, and  is a characteristic time and a state variable (a state variable can be used to describe the state of a dynamical system; see for example Scholz, 1998) of the system defined by : First, at the equilibrium / dt = 0, and thus 1 -V× / L = 0 Including it in Equation (1), the electric production at the equilibrium becomes Consequently, at equilibrium, the competition between the rate of electric production V a and the rate of electric energy consumption V0 b is described by a power law (Equation 3) . Post-cyclonic-electric-energy production is a non-linear process. Second, when the hurricane occurs and the electric system collapses, there is a discrepancy between the electric energy production and electric energy consumption. The condition necessary to restore the electric system is that the rate of the electric production V a be greater than the rate of electric energy consumption V0 b . According to Equation (1), the following can be written: During the collapse, the electric energy is not at equilibrium. There is a relaxation of the system. After the collapse, during the restoration of the electric energy production, an intermediate phase of equilibrium is observed (for example, in Figure 2 ). During this phase, the ratio between the electric production and the maximum capacity of the electric energy production E / Emax is constant and equal to 0. Consequently, from Equation (4) we obtain a×ln(V/V0) + b×ln(V0×/L ) = 0. Thus, during the restoration of the electric energy production, the rate of the electric energy production is equivalent to Let us describe some basic consequences of Equation (5). First, the rate of the electric energy production V a and the rate of electric energy consumption V0 b are generally not equal. Second, if  / L > 1, then the rate of the electric energy production V a is greater than the rate of the electric energy consumption V0 b because a / b < 1. Under these conditions, the electric system will have no risk of collapse during the restoration of the system. Conversely, if 0 <  / L < 1, the rate of electric energy consumption V0 b will be greater than the rate of electric energy production V a , and a blackout can be expected. Third, in our model, the values of V a and V0 b are relative to each other, as given in Equation (5). In this approach, only the relative values between V a and V0 b play a role and not the absolute values. From Equation (3), it is possible to estimate the value of the rate of the electric energy consumption V0 b at equilibrium. In the transient state, it is necessary to use Equation (5). A numerical code was developed in Fortran to solve Equations (1) and (2) using a finite-difference method. The electric production is relaxed by a change in the rate of electric production. For example, in Saint-Martin, the rate of the electric production V a before the hurricane was 1.65 MWh/h, whereas the rate of electric production V a after the hurricane was 1.08 MWh/h. An abrupt change in the rate of the electric production is necessary to simulate the observed trend. The spatial dimensions of the restoration will not be investigated. The daily electric production of Saint-Martin, Saint-Barthelemy, and Puerto Rico has been quantified before and after the occurrence of a major hurricane during a period of time of 8 months. In the island of Saint-Martin, the electric network was critically damaged by Hurricane For Saint-Martin, the simulation of the daily electric production was performed using Equation (1), considering that the electric production capacity is Emax = 56.6 MW. A value of effective electric production ratio 0 of 0.30 was considered. In the modelling of Saint-Martin, the rate of electric energy production was V a = 1.65 MWh/h, the rate of electric consumption was V0 b = 1.08 MWh/h, and the electric power was L= 0.09 MWh. Using these parameters, the model could fit the electric production for 8 months before and after the impact of Hurricane Irma (Figure 2 ). Even in the island of Saint-Barthelemy, located approximately 10-15 km east of Saint-Martin, the electric network was damaged by Hurricane Irma. The general trend of daily electric production shows the same pattern in Saint-Barthelemy than that in Saint-Martin. Two stable periods can be observed in the daily electric production of Saint-Barthelemy, the first before the blackout and the second one month after the main blackout (Figure 3 ). The resilience time is approximately 1 month from the blackout until the new stable equilibrium is reached. The first initial stable daily electric production Ei is approximately 16.5 MW. The second intermediate stable equilibrium of the daily electric production Eis is of 12 MW for at least 3 months. In Puerto Rico, the transient state between Hurricane Maria and the new equilibrium extended over 5 months. Equations (1) and (2) provide the estimates of electric production before and after the hurricane at each time step (Figure 4) . Before Hurricane Maria, the daily electric production was approximately 400 MW, whereas the daily electric production after the hurricane was 300 MW in the stable state. Rico and Saint-Barthelemy was higher than that of Saint-Martin (Table 1) . The electric production restoration rate is estimated using the ratio between the intermediate electric production (Eis) and resilience time (tr). This rate represents the velocity of the system to reach a new equilibrium. Puerto Rico and Saint-Barthelemy have a higher rate of restoration of electric energy production than Saint-Martin (Table 1 ). The electric production restoration rate is not strictly proportional to the electric power capacity (i.e., the initial electric production Ei) of the territory, as shown by the comparison between Saint-Barthelemy and Saint-Martin (Table 1) . Saint-Martin has a lower electric production restoration rate, whereas the electric power capacity of Saint-Martin is higher than that of Saint-Barthelemy. Figure 4) . The smaller the system size (i.e., initial energy distribution) is, the higher is |b|. There is an effect of |b| on the increase in the electric production rate after the collapse. The higher |b| is, the higher will be the increase in electric production after the hurricane. The higher |a| is, the higher will be the offset between the two stable values of the electric production Ei and Eis ( Figure 6B ). The higher the parameter V is, the faster the electric production reaches the intermediate stable electric production Eis ( Figure 7A ). The resilience time of the system increases when V increases. In the calculation, V = 0.25 (MWh/h) 1/a . However, the absolute value of V is less important in the model than the ratio between V and V0. There is an analytic relation between these two parameters at equilibrium, or when 0 = E / Emax is constant. V0 is always smaller than V in the three cases studied, and the ratio V / V0 ranges from 9.1 to 10 ( Table 2 ). The variation in V0 generates a translation of the electric production. The higher the value of V0 is, the higher will be the electric production E ( Figure 7B ). The influence of this parameter can apparently be counterintuitive. However, this can be interpreted considering that a bigger country with a higher electric production E has a higher rate of electricity consumption as well. In Puerto Rico, the influence of two hurricanes was observed in 2017 ( Figure 4 ). The electric production was reduced by 30% of the initial electric capacity of Puerto Rico after Hurricane Irma (6 September) and it appeared to return "elastically" (i.e., linearly and rapidly) to the initial state ( Figure 4) . This was not the case following Hurricane Maria. The electric production was reduced by more than 90% in this second case. The electric network and economic activities were not completely destroyed by the first hurricane. This could explain why two weeks after the first hurricane, the electric production was at the same level of 400 MW as the initial one ( Figure 4 ). In the second case, the collapse was complete (i.e., the reduction in the electric production was above 90%) and the restoration was slower. The electric production was not impacted in the same way by the two hurricanes. The higher the lowering of the electric production during the hurricane, the longer the time required to reach the new equilibrium. The restoration rate of the electric production depends on the electric production capacity as well as the rate of electric production and consumption (see Equation 1 and Figures 5 to 7) . The results suggest that the restoration of the electric production is not linear and that the restoration rate of the electric production depends on the amount of initial destruction. Furthermore, it depends on the adaptation and coping capacities as well (Medina et al., 2020) . After one year of Hurricane Maria, electric production of Puerto Rico attained the same values of approximately 400 MW (Figure 1) . Nevertheless, the gross domestic product (GDP) of Puerto Rico was slightly lower in 2017 and 2018 than in 2016, suggesting that economic activity was not fully re-established to the level before Hurricane Maria [The World Bank, 2020], even if the electric production was almost completely restored (Figure 1 ). A decrease of approximately 25% of the electric production was observed in Saint-Barthelemy and Puerto Rico, from the initial stable phase when E = Ei until the new equilibrium phase after the collapse when E = Eis (Figure 3 and 4 ; Table 1 ). In both cases, there was an approximate constant number of inhabitants before and after the hurricane. This reduction can be explained by a reduction in the activity of restaurants and shops, along with other social and individual activities (schools, administration, etc.). Buildings where these activities take place had been damaged (Rey et al., 2019) . Migration, Remittances, and Children's Schooling in Haiti. The annals of the American academy of political and social science Saint-Martin, un pôle d'attraction migratoire dans la Caraïbe : contexte, logiques et insertion économique. Écologie et progrès, juillet The determinants of vulnerability and adaptive capacity at the national level and the implications for adaptation Resilience and capital flows in the Caribbean. Economic Commission for Latin America and the Caribbean Washington office A decade of weather extremes. Nature climate change Evaluating the Implementation of the "Build-Back-Better" Concept for Critical Infrastructure Systems: Lessons from Saint-Martin's Island Following Hurricane Irma Les défis soulevés par la reconstruction post-Irma. Actualité de la catastrophe Le système du risque à Saint-Martin (Petites Antilles françaises High human influence on beach response to tropical cyclones in small islands: Saint-Martin Island Systèmes énergétiques insulaires de Saint-Martin: bilan prévisionnel de l'équilibre offre/demande d'électricité 2018a Systèmes énergétiques insulaires de Saint-Barthélemy: bilan prévisionnel de l'équilibre offre/demande d'électricité 2018b Les liens entre Société, Nature et Technique durant les derniers 200 ans : analyse dans deux vallées françaises Crises environnementales et crises socio-économiques Prévenir les catastrophes naturelles ou alibi de réorganisation urbaine en faveur des plus riches ? Revue du MAUSS permanente How hurricanes influence social and economic changes? EGU Vienna Cyclones and Societies in the Mascarene Islands 17th-20th Centuries Les îles de Saint-Martin et de Saint-Barthelemy, un an après Irma. Bilan d'une année de reconstruction des îles du Complex rupture during the 12 Le réchauffement climatique actuel influence-t-il l'activité des ouragans extrêmes de l'Atlantique Nord Déstabilisation sociétale dans la caraïbe française Post-disaster recovery: how to encourage the emergency of economic and social dynamics to improve resilience? Stratégie d'adaptation et réduction de la vulnérabilité : exemple de l'évolution des rives dans la vallée du Rhône et de la Saône. Espace populations sociétés Recovery of the Island of Saint Martin after Hurricane Irma : An Interdisciplinary Perspective Mortality in Puerto Rico after Hurricane Maria Projecting future costs to US electric utility customers from power interruptions. Energy Complexity of coupled human and natural systems Assessing Socioeconomic Vulnerability after a Hurricane: A Combined Use of an Index-Based approach and Principal Components Analysis Interaction nature/société de 1947 à 2017 : processus, caractéristiques et vulnérabilité à Saint-Martin, Proceding of the Vulnérabilité et Résilience Conférence The impact of hurricanes on the island of Saint-Martin (French West Indies) from 1954 to 2017: how are our society changes? EGU Vienna Engineering Perspectives on Reducing Hurricane Damage to Housing in CARICOM Caribbean Islands Saint-Martin/Sint-Maarten, une petite île divisée pour de grands enjeux Coastal Processes and Influence on Damage to Urban Structures during Hurricane Irma Satellitebased assessment of electricity restoration efforts in Puerto Rico after Hurricane Maria National and Local Vulnerability to Climate-Related Disasters in Latin America: The Role of Social Asset-Based Adaptation Hurricane Wind and Storm Surge Earthquakes and friction laws Terre d'accueil et de contrastes. n°24. Guadeloupe, Antilles-Guyane The Hurricane Disaster Potential Scale, Weatherwise following-hurricanes-irma-and-maria/, data from the U.S. Department of Energy Office and Puerto Rican's Government Portal -StatusPR Resilience, adaptability and transformability in social-ecological systems Identifying Risk Indicators for Natural Hazard-Related Power Outages as a Component of Risk Assessment: An Analysis Using Power Outage Data from Hurricane Irma Acknowledgement: This study has been funded by an ANR grant (French National Agency for Research, RELEV). The funding source had no involvement in the design and interpretation of the data in the writing of the report.