Resilience to storm conditions of power systems with large dependencies on offshore wind

The ongoing transition towards large installations of offshore wind and the electrification of the transport sector and other critical infrastructures introduce new vulnerabilities to the society. Large dependencies of power production from offshore wind are expected in the next decades, but there are large knowledge gaps regarding the power production reliability under severe weather conditions. Simultaneously, weather extremes may increase in frequency and intensity, driven by climate change. In this paper we investigate the resilience of a power system subject to a hurricane event. The power system is based on the IEEE39-bus New England system but with different scenarios for increasing penetration of offshore wind. We find that an offshore wind penetration level of 30% or less results in a power system resilient to hurricane events, with no need for load disconnection. However, when increased to 40% offshore wind penetration, 650 MW corresponding to 10% of the total load demand gets disconnected during the storm peak. With a penetration of 50% offshore wind, the disconnected load ranges from 2.2 GW of load corresponding to 1/3 of the total load demand, to a total power system blackout.


Introduction
Globally, a fast transition to renewable energy sources is needed to cover the increasing electricity demands and to reach the targets on reduction of fossil fuels to combat climate change.A large portion of the future energy mix is expected to be covered by offshore renewable energy sources, in particular offshore wind.At the US Pacific coast alone, the potential for offshore wind is expected to be 8750 MWh [1], and the goals are to reach 22 GW of installed capacity by 2030 and 86 GW by 2050 [2].In Sweden, an extension of the offshore wind capacity to 167 TWh until 2050 is seen as the most costeffective approach to meet the growing electricity demand [3].The large-scale installation has already begun; globally, 17 GW of offshore wind was installed in 2021, and 29 GW is expected to be installed in Europe alone during 2022-2026 [4].In the US, the first commercial offshore wind farm was installed in 2016.The Block Island Wind Farm outside Long Island has a capacity of 30 MW. Due to the abundant wind resources and load demand along the northern US coast, several offshore wind farms are being planned and constructed in the region, with a total capacity of 2.3 GW.
Most installations are made with towers fixed at the seabed in shallow waters, but emerging technologies, such as floating offshore wind, are seen as promising and enable installations in deep water [5].Even if offshore wind technology is based on the established onshore wind technology, its vulnerability to extreme weather conditions is expected to be higher than onshore wind [6].Several authors have pointed out the risk related to hurricane impact on the wind turbines [7,8].Wang et al. (2019) studied the resilience of an IEEE-RTS24 node grid with power generated by offshore wind farms, hydropower plants, and nuclear power plants during a typhoon event, and proposed an improved curtailment strategy to avoid severe power shortages and reduce the operational costs [9].Repair costs and capacity loss in the Texas power system, subject to hurricane wind conditions, was studied by Watson and Etemadi (2019) [10], and it was seen that when the penetration increases from today's level of 20% to 80%, the system become more vulnerable to hurricanes.In [11], the vulnerability of the same Texas power system was studied in a situation with 3 large wind farms of a total of 317 wind turbines.Fragility curves of the wind turbines were combined with Monte-Carlo simulations to assess the probability of component failures due to the wind loading.All simulations resulted in a disconnected graph for the grid, highlighting the vulnerability in the system to external weather hazards.
Hashemi et al. ( 2021) assessed hurricane generated loads on offshore wind farms in New England [12].A combined wind-wave model was first validated with data from the 2012 Sandy Hurricane, and then used to reproduce the most severe hurricanes recorded in the area: the 1938 hurricane and the 1954 hurricane Carol.Both were seen to represent extreme wind speeds with a 500-year return period.The wind and wave loading were used to model the structural response of a 5 MW offshore wind turbine in parked condition.It was seen that the results were sensitive to the input loads, concluding that the prediction of wind turbines to extreme weather conditions is associated with large uncertainties.Mattu et al. (2022) considered four potential wind farm sites in Mexico; two in the Pacific Ocean and two in the Gulf of Mexico on the Atlantic side, and aimed to quantify the potential hazard posed by tropical cyclones [13].Assuming threshold for cut-out and failures, and investigating measured wind data at the four locations, they concluded that Category 4 and 5 hurricanes have the potential to cause periods of low power generation due to wind speed cut-out at all four sites.However, the likelihood of cut-out conditions occurring simultaneously at the four geographically separated sites was found to be very low.
The risks related to hurricane impact of offshore wind turbines, the uncertainty related to extreme weather events (in particular due to the ongoing climate change), and the increased societal dependency of electricity generated by wind turbines, constitute three areas of knowledge gaps, and together make up a potential emerging vulnerability in our society.This paper contributes to filling these knowledge gaps by studying a power system with different penetration levels of offshore wind, under the impact of extreme wind scenarios.The system properties during these events are examined, and potential scenarios where the power system fails to deliver the demand load to the customers are identified.According to Hallowell et al. (2018), the majority of the wind energy areas in the US are exposed to hurricane hazards [14].The US coast has been chosen in this study due to the planned large expansion of offshore wind installations, in combination with the presence of hurricane conditions.
The rest of the paper is organized as follows.The methods including the power system setup and wind data are described in section 2. The results of the wind penetration scenarios subject to the storm conditions are shown in section 3, and the limitations of the study as well as suggestions for further research are discussed in section 4. Conclusions of the study are presented in section 5.

Power system
The power system under consideration in this work is a model of the New England power grid, which has been modified to accommodate scenarios of different penetration of offshore wind.Specifically, an increasing number of power generation facilities have been replaced by hypothetical wind power farms, for which the power output is dependent on the wind conditions at the respective offshore site.

Power grid model.
The IEEE39-bus system, also known as the New England power grid, is located in the North-Eastern US and shown in figure 1 (a).The same power system was studied by Jian et al. (2020) to obtain the optimal dispatch strategy if the grid was affected by wildfires [15].The model consists of 39 buses interconnected with transmission lines.In the original model, the generators consist of a combination of hydro, fossil, and nuclear power plants.In this paper, it is assumed that the power generation facilities along the southern New England coast are replaced by 1 up to 6 offshore wind farms at bus 31-36, respectively.These busses correspond to generator G2 to G7 in figure 1 (a).
In the original IEEE39 model, the loads are constant values, specifying active and reactive power demand.Thus, the load demand at the different busses is assumed constant in all simulated cases.In accordance with the original model, the slack bus is interpreted as the interconnection to the rest of the US as well as Canada.From the slack bus, power can be exchanged with the neighboring grid.

Figure 1. The 39 bus
New England power grid, as a map (a) [16] and as diagram (b) [17].On the map, red dots represent generators, blue dots represent loads and yellow lines represent transmission lines.2.1.2.Offshore wind farms.Six different penetration levels have been investigated, with 1-6 offshore wind farms integrated into the power system as shown in tables 1-2.Based on [9], every wind farm is assumed to reach its rated power capacity at wind speed of 12 m/s.As in [13], a cut-out wind speed of 25 m/s has been assumed.A power curtailment strategy has been applied to the offshore wind farms, reducing the power production to 75% and 50% of rated power for wind speeds U of 23 ≤ U < 24 m/s and 24 ≤ U < 25 m/s, respectively.The full relative power capacity curve is shown in figure 2.
The installed capacity of the offshore wind farms has been set to 4 times the installed capacity of the generators in the original model.This assumption is based on an average capacity factor of 33.2% for 22 wind farms presented in [18].Moreover, all wind turbines in a single offshore wind farm have been assumed to behave as one, and a start-up time of 12 minutes for the wind turbines has been applied.The actual power output P from the offshore wind farms is calculated as where  = 1.29 kg/m 3 is the air density, Cp = 6.8 • 10 -8 is the aerodynamic performance constant, Rb = 65 m is the wind turbine blade radius, U is the wind speed, Prated is the rated power capacity, Urated = 12 m/s is the wind speed where the wind turbine reaches its full capacity, U75 = 23 m/s, U50 = 24 m/s, and Ucutoff = 25 m/s is the cut-off wind speed.A similar approach for the power capacity as function of the wind speed was taken in [9] but has here been extended to include a curtailment strategy of reduced total farm capacity at 50% and 75% close to the cut-off wind speed.This is to better reflect a realistic scenario where all turbines in a farm would not be shut down at the same time.
The percental penetration level PL of offshore wind farms integrated into the system is  =   /  where Pwind is the installed offshore wind power capacity, CF = 0.332 is the capacity factor for offshore wind farms based on [18], and Pall is the total installed capacity of all generators.

Wind data
The two most severe hurricane conditions recorded in New England are the 1938 hurricane and the 1954 hurricane Carol, both Category 3 hurricanes, resulting in 600 and 65 deaths, respectively [12].In this paper, geospatial wind data from four more recent storm events has been used: the Hurricane Sandy (Oct 29-30, 2012), the Winter Storm Nemo (Feb 8, 2013), the 2018 nor'easter (March 1-3, 2018), and the 2021 nor'easter (Oct 27, 2021).The Hurricane Sandy inflicted damage measuring $70 billion USD and killed 233 people across eight countries from the Caribbean to Canada.When reaching the US coast, it had weakened to a Category 1-equivalent extratropical cyclone, but still recorded wind gusts of over 37 m/s and resulted in 300 000 customers without power in Massachusetts only.The Winter Storm Nemo caused heavy snowfall and hurricane-force wind gusts.The storm forced state governors to declare states of emergency, and travel bans were put in place in several US states.In total 700 000 customers were without electricity, mostly due to the wet snow.The 2018 nor'easter brought hurricaneforce winds to the coasts of New England, and caused 9 deaths, most due to falling trees or branches.Finally, the October 2021 nor'easter, which eventually became Tropical Storm Wanda, was an erratic nor'easter and tropical cyclone that struck the East Coast of the United States, causing significant flooding and strong winds.It left over 617 000 customers without electricity in the US and caused at least 2 deaths.Here, wind data during these four extreme weather events has been used as input to the wind power generation facilities.Wind gust data at 6 offshore locations with a time resolution of 6 minutes have been used, as listed in table 1, and shown in figure 3.Each location corresponds to the location of a hypothetical wind farm.Wind gust data profiles for the measurement sites during Hurricane Sandy are shown in figure 4. The wind data at the six stations have been measured at different altitudes, and have all been scaled to the same height of 100 m above ground using the relationship  100 =   (100/  )  , where Uref is the reference wind height measured at height zref above ground, and a is the Hellmann exponent.As the wind conditions are unstable above open water surface, the exponent is a = 0.06 [19].

Resilience
Resilience can be defined as the ability to withstand or recover quickly after a major disruption.In the context of power systems, Panteli and Mancarella (2015) described it as the ability to "anticipate extraordinary and high-impact, low-probability events, rapidly recover from these disruptive events, and absorbing lessons for adapting its operation and structure for preventing or mitigating the impact of similar events in the future" [20].Using dynamic game methodology, minimal load loss was used to optimize strategies to reduce the impact of wildfires on the New England 39-bus grid in [15].
An economic approach from the perspective of the distribution system operator and planner was taken by Nikkhah et al. (2018), who improved resilience by minimizing the costs for load shedding, purchasing power from substations, hardening of wind turbines, and hardening of power lines [21].For the present study, resilience is interpreted as the ability to handle loss of wind power generation caused by extreme wind speeds without having to disconnect load.

Numerical simulations
For the purpose of this study, quasi-dynamic simulations have been performed in terms of AC power flow analyses in each time step.To solve the power flow equations, the fast decoupled method FDXB has been used, implemented as a package in MATPOWER [22].The method is designed to perform fast and reliable load flow calculations [23] which is valuable in order to decrease the computation time.However, it is widely known that AC power flow analysis can lead to convergence issues, where no solution can be found which satisfies the power flow equations [24].In such cases, load shedding can be one strategy to find a converged solution [24].In this study, if a solution to the initial power flow problem was not found, four different strategies were applied in each time step in order to find a convergent solution.Each strategy was applied iteratively up to 70 times for each time step.Simulations showed that if the system did not converge within 70 iterations for a given strategy, the specific strategy would never be able to solve the convergence problem.If no converged solution could be found after applying all four strategies, the result was interpreted as a total power grid blackout.In the case of a blackout, all voltage levels and angles in the grid were set to the initial values and a flat start was applied.The procedure of the numerical simulations is shown in figure 5.The four convergence strategies applied in the algorithm were executed in consecutive order, from strategy 1 to strategy 4, and are formulated as follows: • strategy 1: reduce largest load with 10%, • strategy 2: reduce largest generator with 10%, • strategy 3: reduce largest generator with 10% with the same load profile as in the last converged solution, • strategy 4: reduce largest load with 10% with the same power generation profile as in the last converged solution for all generators that are not offshore wind farms.

Hurricane Sandy
From figure 6 (a)-(f), the sequences of events during Hurricane Sandy are shown for wind penetration level 1 to 6.It can be seen from figure 6 (a) that when the storm approaches its peak just before October 29, the wind turbines reach their cut-out wind speed and the power production from the wind farm drops down to 0 MW.As can be seen from figure 6 (a)-(c), the load connected to the grid stays at a constant value of 6.3 GW and is thereby unaffected by the lack of wind power generation during the storm peak.
The power import and generation from other generators in combination with a sufficient strong power grid are capable of compensating for the loss of wind power production.
As can be seen from figure 6 (d), when integrating 4 offshore wind farms into the system, the need for load disconnection rises during the storm peak.As all 4 offshore wind farms reach cut-out wind speeds at the same time, the system cannot fully compensate for the lack of power production and 650 MW of load gets disconnected.Neither is the power grid strong enough to fully compensate for the loss of power generation through power import from the neighboring grid.Furthermore, the disconnected load increases significantly for wind penetration level 5, as shown in figure 6 (e).When all 5 offshore wind farms are shut down during the storm peak, 2.2 GW of load gets disconnected.(2012).Sub figure (a) to (f) illustrate the time series applying wind penetration level 1 to 6 (offshore wind penetration of 13%, 21%, 30%, 40%, 50%, and 59 %), respectively.However, penetration level 6 shown in figure 6 (f) shows different characteristics than the other penetration levels.The wind power production as well as the power export profiles are oscillating right before the storm peak.These oscillations are caused by oscillating wind speeds below the rated wind speed at measurement site NWHC3, see figure 4. Furthermore, the actual power production from generator G2, which is the slack bus and gets its power production data from measurement site NWHC3, can be directly transferred to the neighboring grid through the slack bus.Thereby, the power production from this offshore wind farm does not need to be curtailed.Instead, surplus power can be exported via the slack bus without causing problems in the New England power grid itself.

Penetration levels
In figure 7, the disconnected load for all 4 storms and all 6 penetration levels are shown.It can be seen that no load gets disconnected in any of the storms for penetration level 1 to 3.However, for penetration level 4, a maximum of 650 MW load gets disconnected during the storm peaks for all 4 storms.However, the duration of the 650 MW power outages ranges from a total of 18 minutes during the 2021 nor'easter to 4.5 hours during the 2018 nor'easter.
For penetration level 5, the disconnected load profiles differ significantly between figure 7 (a) and (b) on the one hand, and (c) and (d) on the other hand.For Hurricane Sandy as well as the Winter Storm Nemo, a maximum load of about 2.2 GW gets disconnected for 4.5 hours and 5.5 hours, respectively.For the 2018 nor'easter and 2021 nor'easter, the power system undergoes a total blackout for 1.5 hours and 4 hours, respectively.The profiles of the disconnected load are identical for penetration level 5 and 6 in all storms studied.This is a result of the last added offshore wind farm which is connected to the slack bus.Since this wind farm is connected to the slack bus, it does not affect the results more than to increase or decrease power exchange with the neighboring grid.

Discussion and future work
A non-linear relationship between the number of offshore wind farms integrated into the grid and the disconnected load can be seen from figure 7.There is a threshold between penetration level 3 and 4 where the amount of offshore wind farms actually starts to affect the resilience of the power system.When the penetration of wind farms eventually starts to affect the power system, the increase is significant.However, this study is built upon simulations of a standard power grid model without any adaptions made to integrate a high penetration of intermittent and variable power production.It is likely that the penetration level threshold differs from grid to grid.Thus, the general conclusion is that thresholds exist and should be considered when integrating high penetrations of offshore wind.
Interestingly, there is a major difference in terms of disconnected load between penetration level 4 and 5 for the 2021 nor'easter storm as shown in figure 7 (d).This storm generates the smallest disconnected load for penetration level 4 but at the same time the largest blackout for penetration level 5, compared with the other storms.This is a consequence of the spreading in time and space of the 2021 nor'easter storm, forcing all offshore wind farms to be shut down for 4 hours which leads to a major blackout.Thus, it is important to geographically spread out the offshore wind farms to prevent a storm from shutting down all power production facilities simultaneously.The importance of a geographical spreading of the wind farms is also shown in figure 6, where the time when no power is produced by the farms decreases when the number and geographical spreading of the farms increase.
The New England power grid model, which has been under consideration in this work, has its interconnection to neighboring grids through one single node.This node constitutes a bottleneck, limiting the exchange of power between the New England grid and its neighboring grids.Without this bottleneck, surplus wind power could have been exported more efficiently.Furthermore, in a scenario of low wind power production due to wind speeds above the cut-out velocity, more power could have been imported from neighboring grids.This would have resulted in reduced, or even completely eliminated, power outages and thereby an increased power system resilience.However, the exchange of electric power is dependent on the power balance in the neighboring grids as well as the ability to transfer power within the present grid.Thus, adapting the power grid to facilitate power exchange with neighboring grids is crucial to improve the resilience of a power system.Based on the abovementioned reasoning, it can be argued that power grid adaptations and extensive interconnections to neighboring grids are important factors to successfully integrate large amounts of offshore wind power.
In this study, disconnection and reconnection of loads have been performed without considering any stability perspectives.In reality, both disconnection and reconnection of loads are performed stepwise to maintain the stability of the grid as long as possible.This means that situations when loads are to be reconnected to the grid, the reconnection will be done according to some stepwise, predefined strategy.This is not the case in the results presented in figure 7, where fast reconnections of loads are done.The most unrealistic situation is the one presented in figure 7 (d) where the grid oscillates between a fully connected system and a total blackout between 3 pm and 4 pm which is a result of the simplified simulation algorithm.However, even if rapid reconnections of large loads are unrealistic, the main features of the results are to be considered as reasonable.To implement a realistic strategy for reconnection of loads is a proposal for future work.Furthermore, the use of wind gust data might have generated overestimated power production profiles.However, the data used has been considered as reasonable with respect to the purpose of the study and further data processing is left for future studies.
In the current work, up to 6 electricity generation facilities in the studied power grid have been replaced by wind farms with an installed capacity factor of 4. In other words, when producing electricity at their rated capacity, the farms could generate four times more electricity than the traditional power plants they replaced.The installation capacity factor has been chosen based on an average capacity factor of 33.2% for 22 wind farms (in the range 11.8% to 41.9%) reported in [18].For a more thorough assessment of the required installed capacity, the energy systems, loads and grid performance should be modelled for an extended period using realistic input data for wind speeds and load requirements, and the resulting installation capacity should be defined such that the required electricity demand can be satisfied even during periods of little or no wind, while still avoiding overcapacity due to cost limitations.This is outside the scope of the present paper and is left for future work.Further suggestions of future work are to implement a dynamic and realistic load demand profile and to integrate energy storage facilities and reserve capacity in the model, and to formulate the strategies applied to disconnect and reconnect loads and generators more sophistically.Finally, one important question to investigate is how to expand existing power grids to increase the resilience in power systems with large dependencies on offshore wind and other renewable energy sources.
Only implicit vulnerability of the power system due to storm conditions has been considered here.The capacity to deliver electricity has been reduced only due to wind turbines ramping down at wind speeds above the cut-out velocity.In a real electric grid, both the electricity generating facilities as well as the transmission and distribution systems are explicitly exposed to the weather hazards.With this in mind, the results on disconnected load found in this paper should be regarded as conservative -in reality, blackouts of larger magnitude could be expected.

Conclusions
In this study, the resilience of a power system with varying dependencies on offshore wind has been investigated.Wind data from 4 historical extreme weather events; Hurricane Sandy (2012), Winter Storm Nemo (2013), the 2018 nor'easter, and the 2021 nor'easter has been used to generate power production profiles for 1 up to 6 offshore wind farms situated along the southern New England coast.The power generation data has been used in AC power flow simulations of the IEEE39-bus New England power grid model.The results show that the power grid has a good resilience to the storm conditions with a maximum wind power penetration level of 30%.With a wind power penetration level of 40%, about 650 MW of load has to be disconnected from the grid due to the lack of power production.When considering a penetration level of 50%, the Hurricane Sandy as well as the Winter Storm Nemo cause power outages of 2.2 GW which corresponds to 1/3 of the total load demand.Moreover, the 2018 nor'easter as well as 2021 nor'easter cause total blackouts for 1.5 hours and 4 hours, respectively.With a penetration level of 59%, where one of the wind farms is connected to the slack bus, the disconnected load profiles become identical as in the case of 50% penetration level.The results of this study highlight the importance of thorough grid analyses and well-suited grid adaptions to create a resilient power system capable of handling high dependencies on offshore wind.

Figure 2 .
Figure 2. Relative rated power output for a wind farm as function of wind speed.

Figure 3 .
Figure 3. Locations of the 6 measurement sites where the weather data was recorded.The map is adapted from the National Data Buoy Centre (NDBC).Yellow markers show measurement sites; the ones marked red are used for the present study.

Figure 4 .
Figure 4. Wind gust speeds during the Hurricane Sandy at the six measurement sites.

Figure 5 .
Figure 5. Illustration of the algorithm used to perform the numerical simulations.

Table 1 .
Specifications of the offshore wind farms and corresponding measurement sites.

Table 2 .
Penetration levels and corresponding integrated offshore wind farms.