10 A lack of winterization of power system infrastructure resulted in sig- 11 ni cant rolling blackouts in Texas in 2021. We therefore assess if incentives 12 for winterization on the energy only market have been sucient, combin- 13 ing power demand estimates with estimates of power plant outages to 14 derive power de cits and scarcity prices. The loss of load in 2021 was the 15 most severe in our simulation of 71 years. Expected pro ts from winteriza- 16 tion of a large share of existing capacity are positive. However, investment 17 risk is high due to the low frequency of freeze events, potentially explain- 18 ing under-investment, as do high discount rates and uncertainty about 19 power generation failure under cold temperatures. As the social cost of 20 power de cits is one to two orders of magnitude higher than winteriza- 21 tion cost, regulatory enforcement of winterization is welfare enhancing. 22 Current legislation can be improved by emphasizing winterization of gas 23 power plants and infrastructure. 24 Keywords| Texas, extreme event, power systems, winterization 25 Weather extremes such as storms can signi cantly a ect the reliability of power 26 systems [1]. The increasing use of variable renewable energies additionally exposes 27 power systems to hazards caused by weather extremes [2, 3]. However, recently a gas 28 power dominated system was deeply impaired by a weather extreme: a cold spell over 29 Texas, between February 10thand February 20th, 2021 with temperatures far below 30 0°C caused a failure of large parts of the Texan power system. The combination of 31 extraordinarily high winter electricity demand and more importantly the failure of 32 signi cant power generation capacities, both due to low temperatures, resulted in up 33 to 4.5 millions of Texans being cut-o from their electricity supply [4]. 34 A rst retrospective analysis of the event by Busby et al. [5] discusses the magni- 35 tude of the event and its causes, indicating that the total economic loss amounted to 36 130bn $and that the outage of gas power plants was mainly responsible for the high 37 1 de cits in power generation capacity. Wu et al. [6] provide a power grid simulation 38 to conduct a very detailed analysis of the 2021 event and, Doss-Gollin et al. [7] have 39 shown that lower temperatures than in February 2021 have been observed in the past 40 71 years, and heating demand predicted from temperature data would also have been 41 higher in the past, although the 2021 freeze event was comparably long. These previ- 42 ous studies indicate that there is a striking gap between the occurrence probability of 43 such an event, its large scale economic and social cost, and the lack in winterization 44 e orts. However, none of these studies assessed whether the economic incentives for 45 power companies to invest into winterization have been high enough, when the 2021 46 event is put into a long-term climatic context. 47 As winterization was not strongly enforced by regulation in Texas, power gener- 48 ators had to rely on the incentives provided by the energy only market to arrive at 49 investment decisions. These incentives consist mainly of regulated price spikes at the 50 spot market when generation capacity is scarce [8]. Hence, we assess here how revenues 51 from winterization compare to its cost for power companies. Technically, we combine 52 estimates of temperature dependent load with a model of power plant outages, tak- 53 ing into account 71 years (1950{2021) of past climate from reanalysis data. Climate 54 change, of course, may have an impact on temperatures. We therefore also assess if 55 trends in the occurrence of extremely cold temperatures and loss of load events can 56 be observed. Furthermore we conduct an extensive sensitivity analysis to show un- 57 certainties arising from our modelling choices. To put the event into context, we rst 58 discuss details of the relationship of temperatures, electricity load, and power plant 59 failures during the 2021 event. Subsequently, we analyze the long-term frequency of 60 such events. Finally, we determine revenues from and costs of winterization and discuss 61 potential reasons for underinvestment. 62 The 2021 event in a long-term climatic context 63 Starting on 10thof February 2021, temperatures in Texas began to fall, causing load 64 to increase from around 40 GW to over 70 GW by February 14th{15th. On February 65 15ththe freeze reached a critical level where substantial shares of generation capacities 66 began to fail. Available capacities dropped below demand leading to a sustained 67 power generation capacity de cit (Figure 1). Consequently, rolling blackouts had to 68 be implemented to stabilize the grid and scarcity prices at the power market increased 69 to the upper limit of 9000 $/MWh. The de cit event continued until 19thof February 70 when rising temperatures allowed the system to recover. 71 The highest predicted demand in the February 2021 event was well above the 72 highest load observed in winter in the period 2004{20201. Our estimate is in the range 73 of observed extreme summer loads (see Figure A.1). Our predicted demand matches 74 ERCOT forecasts of peak load during the cold spell well - ERCOT forecasts were only 75 about 0.26GW lower compared to our estimates[6]. 76 Besides leading to high electricity demand, the low temperatures also caused sub- 77 stantial outages of generation capacities. Gas capacity failures were responsible for the 78 largest share in power outages. As a result, loss of load occurred in 106 hours. Based 79 on the predicted demand and the observed load, we estimate that in total 1.45TWh of 80 1The values of loss of load, capacity failures, and demand prediction in this section rely on our simulation and may therefore di er from ERCOT reports to some extent. As we focus on estimating the long-term frequency of such events, we did not aim at reproducing the February 2021 event in highest detail. 2 4050607080GWPeriod of deficit event (ERCOT) Period of predicted deficit eventPower deficit Load (ERCOT) Predicted demand Predicted available capacity Predicted deficit 20 15 10 5 051015°CTemperature Average temperature weighted by Population Gas power plants Gasfields Coal power plants Wind parks North Wind parks South Feb-13 Feb-14 Feb-15 Feb-16 Feb-17 Feb-18 Feb-19 Feb-20 Feb-21010203040GWOutage capacity (ERCOT) Gas Coal Wind OtherFigure 1: The February 2021 event in retrospect Observed load, pre- dicted demand, available capacity, temperatures and capacity outages during the February 2021 event load were a ected by blackouts. Busby et al. [5] estimate the social costs of the power 81 outages to amount to 130bn $. Therefore, the de cit cost around 87,000 $/MWh, one 82 magnitude higher than the current Value of Lost Load (VOLL) used by the Texan 83 market regulator ERCOT, i.e. 9000 $/MWh. 84 Outages of gas generation capacities started to increase rapidly at a gas power plant 85 weighted temperature of -8.8 °C, which is a record low temperature in the past 17 years 86 (see Figure A.2). The outages were not only related to freezing of power plants, but 87 also of gas supply infrastructure, including gas production equipment at gas elds. 88 Power plants started failing rapidly when temperature weighted by gas elds dropped 89 below -10.9 °C. In the period 2004{2021, when no other outage events comparable to 90 the one in 2021 was observed, this is a record low gas eld weighted temperature (see 91 Figure A.2). Therefore, gas supply infrastructure played an important role in the 92 outage events. This is con rmed by ERCOT, which classi ed around 8GW of outages 93 being related to limited fuel supply [9]. 94 Coal generation capacity came oine at average temperatures weighted by coal 95 plant locations of below -10.2 °C. This temperature is at the very lower end of observed 96 temperatures in the period 2004{2020. For both technologies, coal and gas, recovery 97 time was substantial. Even when temperatures recovered back to over 0 °C, according 98 to ERCOT 11.3GW of thermal power plants, i.e. 18% of total available thermal 99 capacity, stayed oine for another 16 hours. 100 3 Temperatures weighted by wind power plant locations indicate that the failure of 101 wind power plants may be a more frequent event. While at the time of failure temper- 102 atures at wind parks in Southern Texas were at the very lower end of the temperature 103 range observed in the period 2004{2020, the average wind park temperature in North- 104 ern Texas when wind power plants started to fail was just below 0 °C and well within 105 the range of previously observed low temperatures. Later on, temperatures reached 106 record lows though at wind power plant sites. Compared to thermal power genera- 107 tion, wind power capacities began to fail much earlier and at higher temperatures. On 108 February 13th, when gas outages summed up to only 5GW, ERCOT already reports 109 13GW of wind capacity outages (Figure 1). This represented a loss of 3.3GW of wind 110 power production on average at the prevailing wind conditions. 111 Our simulations of loss of load events using climate data from 71 years shows 112 that the 2021 event was a record one. In total, we estimate that eight other severe 113 power de cit events would have occurred in the current system assuming climate from 114 the period 1950{2021 (see Figure 2). The second largest power de cit event at 1.26 115 TWh is predicted when using climate data from 1983 { assuming installed generation 116 capacities as in February 2021. Furthermore, we observe 17 minor events. However, 117 the sum of de cits of all 17 minor events is less than 1% of the sum of the de cit of 118 the 9 largest events. We therefore exclude them from the further analysis. 119 In our model predictions, the loss of load event has a duration of 106 hours, and 120 causes an aggregated de cit of 1.49TWh, at a peak capacity de cit of 31.3GW. There 121 are several events with similar peak capacity de cits identi ed in the 1950{2021 period, 122 and also events with a comparably long duration but none with a comparably high 123 amount of loss of load. In the largest event before 2021 (1962 and 1983), 250GWh 124 less lost load results from our simulation (Figure 2). 1989 was the last time a similar 125 freeze event occurred. This long break in freeze events of a signi cant magnitude may 126 explain why the recent event hit an insuciently winterized power production system. 127 The 2021 record high loss of load is not caused by the freeze magnitude alone but 128 by a combination of a long, relatively cold freeze event and an inopportune timing 129 of the freeze peak. According to Figure 1 the system failure occurred early and was 130 prolonged by a long freeze period afterwards. This is in contrast to other years when 131 temperatures recovered more quickly after temperature minima had been reached (e.g. 132 in 1951 and 1963). This nding is supported by the extreme value statistics of the 133 freeze spells shown in Figure 3. 2021 was the second longest freeze event in seven 134 decades. It has a return period of 37 years. Other events, however, were colder (1951, 135 1989) or had higher frost sums (1951, 1983). 136 In terms of load, the highest predicted winter load in 2021 was slightly lower than 137 the highest predicted winter load in the complete 71 year time series (Figure A.1), as 138 there were lower temperatures in earlier years during the 1989 event. 139 It may also have been expected that freeze events would have decreased due to 140 global warming. However, our analysis does not show any signi cant trend in the loss 141 of load time series (Figure A.12). Still, average temperatures in Texas signi cantly 142 increased due to climate change since 1951 (Figure A.13). This result is con rmed 143 by others, however, the increase in mean temperature is not genuinely transferable 144 to extreme temperatures [10]. A strati ed analysis of annual freeze events (minimum 145 annual temperature) below temperature thresholds from 0 to -10 °C reveals that there 146 is indeed no signi cant observed change of severe freeze events below -2 °C (section 147 A.9). Only very mild freeze events showed a signi cant attenuation (2.6 °C over the 148 past seven decades), but such events are irrelevant for freeze related failures of the 149 power system comparable to the 2021 event. 150 4 Overall, extreme value statistics show that the event of 2021 was severe because 151 of its long freeze duration and its freeze dynamics. Against the background of seven 152 decades of observed climate data, the freeze event had to be expected, especially as 153 we could not nd evidence for a decrease of severe freeze events due to climate change. 154 This suggests that similar events comparable to the one in 2021 need to be mitigated 155 even in a future, on average warmer climate. 156 −12.3 °CDuration: 129 h −20−1001020tempera− ture °CEvent 1 (1951) 29.4 GW Duration: 65 h −50−25025 Jan 27Jan 29Jan 31Feb 02Feb 04Feb 06capacity deficit GW−10.2 °CDuration: 85 hEvent 2 (1962) 29.1 GW Duration: 68 h Jan 06Jan 08Jan 10Jan 12Jan 14Jan 16−9.6 °CDuration: 77 hEvent 3 (1963) 27.5 GW Duration: 33 h Jan 21Jan 23Jan 25Jan 27Jan 29Jan 31 −8.6 °CDuration: 51 h −20−1001020tempera− ture °CEvent 4 (1979) 22.2 GW Duration: 36 h −50−25025 Dec 28Dec 30Jan 01Jan 03Jan 05Jan 07Jan 09capacity deficit GW−9.2 °CDuration: 72 hEvent 5 (1982) 27.2 GW Duration: 46 h Jan 07Jan 09Jan 11Jan 13Jan 15Jan 17−11.3 °CDuration: 200 hEvent 6 (1983) 28.4 GW Duration: 120 h Dec 20Dec 22Dec 24Dec 26Dec 28Dec 30 −9.3 °CDuration: 72 h −20−1001020tempera− ture °CEvent 7 (1985) 23.9 GW Duration: 48 h −50−25025 Jan 28Jan 30Feb 01Feb 03Feb 05Feb 07capacity deficit GW−14.2 °CDuration: 82 hEvent 8 (1989) 29.1 GW Duration: 73 h Dec 18Dec 20Dec 22Dec 24Dec 26Dec 28−12 °CDuration: 132 hEvent 9 (2021) 31.3 GW Duration: 106 h Feb 11Feb 13Feb 15Feb 17Feb 19Feb 21 Figure 2: Analysis of extreme temperatures and simulated loss of load events Population weighted temperature and predicted capacity de cit of se- vere freeze events within the 1950{2021 period. Labels in the graph refer to temperature minima and de cit maxima 5 1983 20211951 1973 19891.525102050100 050100150200return period in yearsfrost duration htemperature 1983 2021 19891962 19511.525102050100 050100return period in yearscapacity deficit duration hloss of load 1983 1951 20211962 1989 0300600900frost sum °C h2021 19831962 1989 1951 050010001500total loss of load GW h 198919512021198319620 −5 −10 −15 0.010.10.50.80.90.95 0.99 probabilitymin temperature °C2021195119891962 1983 0102030 0.010.10.50.80.90.95 0.99 probabilitymax capacity deficit GWFigure 3: Extreme value statistics of temperature and power de cits Population weighted temperature (left panels) and predicted capacity de cit (right panels) of freeze events in Texas from seven decades of of climate data. Shown are the empirical (circles) and theoretical (lines) quantile functions of the three de cit characteristics, duration (upper), severity (centre) and intensity (lower). The return period (inferred from a GEV distribution) and magnitude of the 2021 event are annotated in blue. Very small events lasting less than six hours are removed. Comparing revenues to costs of winterization 157 In the following, we assess how much revenues could have been earned by power 158 generators by winterizing their capacities under current regulation, assuming perfect 159 competition, and using the 71 past meteorological years in our simulation. The rev- 160 enues result from the scarcity price mechanism implemented by ERCOT: it increases 161 prices automatically, if spare capacity falls below a certain threshold [8]. The upper 162 price limit is set to 9000 $/MWh if spare capacity is below 2GW (Figure A.11). If 163 power operators winterize, they will be able to generate during times of high scarcity, 164 generating additional revenues. 165 6 Revenues from winterization are high, but show signi cant variability. For the 166 rst winterized GW of gas power capacity, expected revenues over a 30 years period 167 are at 1.06bn $/GW, but drop to 0.52bn $/GW at 14GW of winterization (see Figure 168 4). Revenues for coal power plant winterization are slightly lower per GW, and sig- 169 ni cantly lower for wind power. For all technologies, the spread of revenues is high: 170 The revenues at the 68% con dence interval are reduced or increased by half of the 171 expected revenues. In 1.2% of all cases, there is no de cit event in a 30 year period, 172 which is the worst case scenario in case of investment in winterization, because no 173 additional revenues from winterization can be earned at all. 174 Signi cant winterization measures can be implemented under our estimates of ex- 175 pected revenues, assuming that variable operating costs are low for power generators2. 176 In particular, we estimate that the winterization of gas wells { or building 250GWh 177 of pipe gas storage at gas power plant locations { in combination with winterization 178 of gas power plants will cost about 450M $/GW (see section A.10). This cost is below 179 the revenues up to the 15thGigawatt of winterized capacity. Winterization of coal and 180 wind power plants is signi cantly cheaper, as no or very limited fuel supply infras- 181 tructure would have to be winterized. Winterization costs assumed at 10% of initial 182 plant investments of coal power plants are far below revenues up to full winterization 183 of all failed coal capacity. In fact, one could even assume winterization cost of 30% of 184 initial plant investments and winterization cost would still be lower than the revenues 185 for the completely winterized capacity. For wind turbines, our estimates of revenues 186 are half those of coal, but are still substantially higher than the costs of winterization 187 which are reported to be 5% of investment costs [11]. 188 The assumed discount rate has a signi cant impact on results. When increasing 189 the rate from 5% to 10%, the revenues for winterizing the rst GW of gas power plants 190 are reduced from 1.06bn $to 0.65bn $. While winterization of coal and wind power still 191 fully pays o under these assumptions due to low winterization cost, the pro table 192 winterization of gas infrastructure and gas power is reduced from 15GW to 7GW. 193 Before 2021, these estimates might have been lower, as since 1989 no climatic event 194 of a similar magnitude was observed. When dropping 2021 from our set of events, our 195 estimates of expected revenues falls by 17.6% on average, causing only 13GW of gas 196 power to be pro tably winterized. Still, when taking into account expected revenues, 197 a signi cant amount of capacities should have been winterized. 198 Further assessments of the uncertainties in our modeling approach can be found 199 in Appendix A.2. 200 Potential reasons for the lack of winterization 201 We have shown that the Texas loss of load event in February 2021 was among the 202 top three extreme events when simulating the power generation system under climate 203 conditions of the last 71 years. Nevertheless, winterization of power generation infras- 204 tructure was already pro table before the event took place, taking into account the 205 past climate, potential climate-change impacts, and current regulatory conditions. So 206 why did power generators not winterize? We identify several possible reasons for this 207 gap between potential revenues and observed winterization e orts. 208 2This is true for nuclear, wind, PV, and coal power plants. However, gas power plants may face high gas spot market prices during cold spells, as observed during the 2021 event. We assume here that gas plant operators therefore have physically or nancially hedged against high gas prices. 7 2 4 6 8 10 12 Winterized capacity GW0.00.20.40.60.8bn$/GWWind North 2 4 Winterized capacity GW0.00.20.40.60.8Wind South 5 10 15 Winterized capacity GW0.00.51.01.52.02.5bn$/GWGas Expected revenue over a 30 year period CI=68% CI=95% Winterization cost1.0 1.5 2.0 2.5 3.0 Winterized capacity GW0.00.51.01.52.02.5CoalFigure 4: Revenues from winterization Comparison of revenues (bn $/GW of winterized capacity in a 30 year period) to marginal costs for winterizing existing power generation capacity First, while expected revenues are above winterization costs, their variance is high, 209 in particular for gas power plants: for this technology, for the winterization of the rst 210 GW in 16% and for the winterization of the 10th GW in 36.2% of all cases, the pro t 211 becomes negative. Additionally, gas power plant owners have to secure gas supply 212 and may be exposed to high gas prices during cold spells. However, the risk of not 213 investing into winterization is very low. Even if a catastrophic failure occurs, the 214 associated social cost is not born by power generators. Potential costs include minor 215 nes and damages to power plant equipment. A risk-averse investor may therefore 216 decide against winterization. For coal and gas power plant owners, another fact may 217 reduce expected revenues: we assumed a 30 year lifetime for all power plants, but 218 gas and coal generation infrastructure is partly old and winterization now may not 219 8 pay o as the plants may be retired soon anyhow. For wind power plant owners, we 220 see however the highest incentives and the lowest risk: the eet is comparably young, 221 winterization cost is low, and revenues are well above these costs. Even under relatively 222 high risk-aversion, winterization seems to be a rational choice for wind power plants 223 therefore, in particular if new wind parks are built. 224 Second, even though historical temperature time series clearly indicate that the 225 2021 event could have been expected, the associated outages of power plants may have 226 been underestimated by power generators. This is supported by King et al. [12] who 227 show that for a high number of plants, rated temperatures of failing power plants were 228 partly signi cantly lower than prevailing temperatures during outages in February 229 2021. As no major outage as the one in February 2021 was observed before, plant 230 owners may have assumed that current power plant standards are reliable enough. 231 Third, high discount rates also imply that winterization becomes signi cantly less 232 attractive. At a 10% discount rate, our estimates of revenues drop by about 38.8%. 233 Therefore, alternative investments with higher return on investment and potentially 234 lower risk may be preferred under limited capital availability, in particular for the 235 more costly winterization technologies necessary for gas power generation. 236 Fourth, our calculation only holds under perfect competition. Owners of large 237 generation assets have less incentives to additionally winterize, as this would partly 238 reduce scarcity prices for the already winterized part of their eet. However, there is 239 little concentration in the market in Texas and we therefore see strategic behaviour 240 potentially as less important reason (see Appendix A.3). 241 Conclusions 242 The total cost to society of extreme freeze events has to be expected to be at least 243 one order of magnitude higher than winterization cost. Winterization is therefore 244 highly welfare enhancing. We have shown that current regulation in principle gave 245 sucient incentives for a larger scale winterization, but risk aversion, lack of knowledge 246 about potential outages, or higher yielding alternative investments may have impeded 247 generators from taking more e orts. A more stringent regulation of winterization 248 therefore seems to be necessary. In June 2021, Senate Bills 2 and 3 became e ective. 249 They enforce winterization of power plant infrastructure. However, gas power plants 250 do not have to fully winterize but instead, a committee will de ne those assets which 251 have to do so [13]. As the failure of the gas power infrastructure by far has the largest 252 impact on de cits in our simulations, we emphasize here that this should be strongly 253 considered when de ning rules for enforcing winterization of a large share of gas power 254 plants and associated infrastructure. 255 Winterization of power generation units, however, may also come with its down- 256 sides during periods of warm temperatures, as measures used to increase performance 257 during cold weather, such as integrating gas turbines into insulated buildings, may 258 make the cooling of power plants more complex. Apart from winterization, other mit- 259 igation measures, in particular strong demand response programs and an expansion 260 of transmission capacities to neighbouring states may therefore become important [6]. 261 They may be signi cantly less costly, and they will be bene cial not only during cold 262 spells. Both options can make the system more resilient against other variations in 263 power generation, in particular taking into account the ongoing transition to a larger 264 share of renewable energies in the power generation mix. During extreme freeze events, 265 demand response may have to focus on industrial applications however, since electric 266 9 heating can hardly be postponed during freeze events. 267 Of course, our results have to be considered in the light of a continuously evolving 268 power system. We assume 30 years of lifetime for all installed capacities, however some 269 capacities, in particular coal power plants, may soon be retired and their winterization 270 may not be pro table therefore. As winterization of new capacity is cheaper and easier 271 to implement than winterization of existing one, winterization standards for installing 272 new power plants and associated infrastructure should have high priority. The ongoing 273 transformation of the Texan power system can therefore be considered an opportunity 274 to ensure robustness during future freeze events. 275 Methods 276 We use a chain of statistical and simulation models to derive loss of load events, and 277 revenues from winterization. The data sets which feed the models and model interac- 278 tions are shown in Figure 5. A detailed explanation of all involved models and data 279 sets is given below. 280 281 ResultsAggregated data Annual loss ofloadInput dataOutage data Per minute , per power plant Outage model HourlyDemand model HourlyTemperature ERA5, hourly , 0.25 °grid Simulated demand HourlySimulated outage HourlyWind speeds ERA5, hourly , 0.25 °grid Simulated wind power generation HourlyLoad data Hourly Data subset Data Output Model/ MethodAggregated outage data Hourly , per technology : coal, wind, gasPower plants Installed capacities and locations forcoal, wind, gas Available capacity HourlyForecasted thermal winter capacity Coal +gas + nuclear Population density 2020, 30‘‘ grid Aggregated temperature PopulationCoal, wind, gas capacity 20211950 -20212012 -2020 Bootstrapping Sets of30 years 10,000 iterationsExpected capacity deficit and expected revenue from winterizationFrequency ofdeficit events1950 -2021 Frequency offrost events2012 - 2020 Scarcity pricing Figure 5: Overview of data inputs and de cit model Estimation of temperature induced electricity de cits: To estimate the 282 amount of de cits in the power system, we simulate the di erence between the ex- 283 pected, temperature dependent electricity demand and the available generation ca- 284 pacity. 285 10 Formally this can be described by de ning the capacity de cit dy;has the di erence 286 between the demand y;hand the available generation capacity cy;hin yearyin hour of 287 yearh: 288 dy;h= demand y;hcy;h (1) The total loss of load dtot yin a year is the sum over dy;hfor all hours where capacity 289 de cit was larger than 0: 290 dtot y=X h; dy;h>0dy;h (2) Demand is simulated from load in the past using a linear regression model as 291 described below in more detail. Available generation capacity is obtained by reducing 292 the total available capacity by temperature dependent outages: 293 cy;h=cthermalogas y;hocoal y;h+wy;h cwind cwindowind y;h (3) wherecthermalis the total available thermal capacity in winter according to ER- 294 COT, andogas y;h,ocoal y;handowind y;h are the temperature dependent power plant outages, 295 respectively. Current wind power generation wy;h, simulated from wind speeds assum- 296 ing full capacity (for details refer to [14]), is used to calculate the capacity factor and 297 scale the working wind power capacity, i.e. the di erence between installed capacity 298 cwindand wind power outages owind y;h. We do not model nuclear and solar PV outages, 299 as their overall generation capacity and their contribution to outages was low (Figure 300 1). We also neglect transmission of power from neighbouring states, which is of minor 301 magnitude. 302 According to ERCOT [15], 67.5GW of capacity was available during the 2021 win- 303 ter, but 4GW of these may have been under maintenance. We therefore assume a 304 value of 63.5GW for cthermalto match our simulation with available capacity during 305 the event, as indicated by served load. 306 307 Demand prediction: We predict demand y;hfrom temperatures using a regres- 308 sion model (equation (4)). We estimate a model for demand in winter (December{ 309 February, the three coldest months on average) from load data in the years 2012{2020, 310 taking into account a linear time trend ly;h, seasonality (sine and cosine terms depend- 311 ing on the hour hof the year y), and the temperature ty;h. Furthermore, we include 312 dummy variables for the hour of day hod i;y;h, the weekdays dow i;y;h, and for holidays hold y;h. 313 To account for changes in the temperature dependency of load over time due to in- 314 stallment of increased shares of electrical heating, we include the interaction of the 315 linear time trend with temperature. We also include t2 y;handt4 y;hinto the equation 316 as with falling temperatures, load shows a highly non-linear increase (Figure A.5). In 317 order to avoid overestimation of loads at low temperatures with this model, a thresh- 318 old temperature at -8 °C was introduced, under which the temperature dependency of 319 11 the load was kept constant (see Figure A.5). 320 demand y;h= 0+7X i=1 idow i;y;h+31X j=8 jhod j;y;h+ 32hold y;h+ 33sin2h 8760 + 34cos2h 8760 + 35ly;h+ 36ly;hty;h+ 37ty;h+ 38t2 y;h+ 38t4 y;h(4) The model performs well for di erent temperature ranges in terms of average bias 321 (Figure A.6), although at low temperatures we slightly underestimate load. We there- 322 fore also ran the whole model with an alternative demand model where the temperature 323 impact does not atten o at -8 °C. The results are reported in our sensitivity analysis, 324 indicating that the estimated de cits do not strongly change when using a di erent 325 demand model ( <10% di erence). Testing the model out-of-sample for January 2021 326 delivers a high t with an R2of 0.92 and an RMSE of 1.31 GW. A cross-validation 327 for other years (see Table A.1) indicates a good t in general. 328 Temperature dependent generator outages: The power plant outages in 329 Texas were caused by a systemic failure, as a substantial amount of capacity tripped 330 in a short period of time [9]. Most of the capacity failed due to weather events, but 331 the lack of fuel supply was also relevant. Additionally, non- weather related equipment 332 failures and, to a smaller amount, frequency problems in the grid caused problems at 333 generation units. This implies that temperature at single power plants alone cannot 334 fully explain outages. We derived infrastructure fragility curves [16] from our data 335 and they show that 25% of gas power plants, about 30% of wind power plants, and 336 50% of coal power plants failed when temperatures were above 0 °C and in many cases 337 have not been below 0 °C in the days before failure. Other weather conditions besides 338 freezing temperatures may be partly responsible, but at least wind conditions at the 339 time of failure were not particularly extreme. Besides freezing temperatures, which 340 caused failure of power plant components and of gas production and gas distribution, 341 there are also systemic reasons for failure therefore. 342 We do not use infrastructure fragility curves for modeling outages, but estimate 343 threshold temperatures and outage capacities during catastrophic failure by technol- 344 ogy: we derive the temperature, at which the largest increase in outages occurred, 345 from the 2021 outage data. Furthermore, we estimate an outage level in terms of trip- 346 ping capacity. Finally, we also de ne a constant recovery rate, which describes how 347 outages decreased after the recovery temperature is reached. This is an aggregate ap- 348 proach and will omit smaller outages, but it accounts better for the inter-dependency 349 of failures. A detailed outline of how we derived the outage parameters from the 2021 350 data in Texas is given in section A.5. The resulting outage models are subsequently 351 applied to the 71 years of climate data to obtain capacity availability during this period. 352 353 Estimating revenues from winterization: We determine the revenues from the 354 scarcity price mechanism implemented by ERCOT [8]. This mechanism comes into 355 e ect, whenever spare capacity falls under 8GW. In this case, power market prices are 356 regulated and set to xed (high) values depending on the spare capacity. The lower 357 the spare capacity, the higher the price, reaching 9 000 $/MWh when spare capacity 358 falls under 2GW (see appendix A.6). We determine spare capacity sy;h;g;z ,gbeing 359 the technology used for power generation which is winterized (i.e. gas, coal or wind) 360 12 andzbeing the amount of winterized capacity, by 361 sy;h;g;z =cy;h+ay;h;g;z demand y;h; (5) whereay;h;g;z is the additional capacity available at a certain point in time. For 362 coal and gas, ay;h;g;z equals the amount of winterized capacity zwhen the outages are 363 larger than z. In periods without outages before winterization of power generation 364 capacity,ay;h;g;z is 0GW. During outage events, the available capacity is increased by 365 the amount of winterized capacity zfor gas and coal power plants. If the outage og y;his 366 smaller than winterized capacity z, then additional capacity corresponds to the outage 367 capacity, i.e. ay;h;g;z = min(z;og y;h). For wind power plants, the additional capacity is 368 calculated by multiplication with the capacity factor similarly to equation (3): 369 ay;h;wind;z=wy;h cwindmin z;owind y;h (6) We use temperature data for all years in the period 1950{2021 to determine 370 demand y;h, we use simulated wind power generation for the same years from ERA5 371 reanalysis wind speeds to obtain wy;h(for further details see [14]), and we use the 372 temperature dependent power plant outage functions to estimate og y;h. This allows 373 to simulate today's power system for 71 di erent weather years as a set of di erent 374 weather realisations. Consequently, we calculate the market price py;h;g;z by 375 py;h;g;z =f(sy;h;g;z ) (7) The function fmaps spare capacity to scarcity prices as used in the price regulations 376 by ERCOT (see Appendix A.6). We assume that the market price is 0 whenever 377 there is no capacity scarcity. This of course is a simpli cation, but is a suciently 378 precise approximation for our purpose3. We estimate the revenues from winterizing 379 one additional unit of capacity. This capacity may not fully be dispatched in all hours 380 with scarcity prices, we therefore determine cdispatch y;h;g;z as being the dispatched capacity 381 in a particular hour. Let dy;h;z be the de cit in winterization scenario z, where all 382 values<0 are set to 0. Then, cdispatch y;h;g;z =dy;h;z1dy;h;z, i.e. the dispatched capacity 383 is the di erence in capacity de cit between two consecutive winterization scenarios. 384 The revenue ry;g;z earned by that additional unit in a year yis hence de ned by 385 ry;g;z =X hpy;h;g;z cdispatch y;h;g;z (8) We further assume that additionally winterized capacities are dispatched last in the 386 merit-order during de cit events. This implies that additionally winterized capacities 387 can only earn revenues during de cit periods in former winterization scenarios, i.e. 388 when the price is at 9,000 $/MWh4. If the dispatch order would be changed by winter- 389 ization, this would imply higher revenues for winterization of new capacities, making 390 our estimates (slightly) conservative. 391 3We analyze only scenarios with winterization, no additional capacity is installed. Winter- ization will only a ect dispatch and market prices during outages of power plants, so market prices during other periods should remain una ected, implying no additional revenues from winterization during normal operation. 4We use, however, the same method also for determining marginal revenues in non- competitive markets in Appendix A.3. For that purpose, the full range of function fis relevant. 13 We then use the set of revenues ry;g;zderived from 71 di erent weather realizations 392 for a bootstrapping procedure. For each bootstrapping iteration b, we sample 30 years 393 of revenues rboot i;b;g;z fori= 1;:::; 30 from the set ry;g;z,y= 1950;:::; 2021. This is 394 done for 10 000 iterations, b= 1;:::; 10 000. Subsequently, total revenues Ry;g;z over a 395 typical investment period of 30 years are calculated, as shown in equation (9), i= 0:05 396 being the discount rate: 397 Rb;g;z=30X j=1rboot j;b;g;z (1 +i)j(9) This results in 10 000 di erent samples Rb;g;z, allowing to derive a distribution of 398 revenues from winterization. We emphasize here that this calculation only holds under 399 a perfectly competitive market, as we assume marginal winterization steps of 1GW. 400 For generators with large capacities, partly already winterized, additional winteriza- 401 tion may yield strongly negative revenues, as market prices for existing winterized 402 assets are reduced by the additional winterization. We discuss this in more detail in 403 appendix A.3. 404 405 Frequency analysis of freeze and power de cit events : The frequency analy- 406 sis of extreme events follows well-established methods of hydrological drought analysis 407 [17], where de cit events are de ned as periods when the variable of interest is below 408 a certain threshold. Here, we use two di erent threshold concepts. First, we anal- 409 yse temperature, and de ne a constant threshold of 0 °C to de ne de cit events in 410 analogy to drought events in drought statistics. De cit events in the power system, 411 resulting from low temperatures, are simply de ned for periods when the capacity 412 de cit>0GW (equation (1)). In each case, the result is a derived de cit time series, 413 which is further investigated using Yevjevich's theory of runs [18]. During a freeze pe- 414 riod, minor thaw episodes or other disturbances may split an event in several smaller 415 events. As a remedy, pooling procedures have been recommended [19]. In this study, 416 an inter-event time criterion of 1 day is used to de ne the de cit event series. In case 417 that multiple events occur in a year the event with the absolutely largest accumulated 418 de cit is used for further analysis. The series so derived are characterized by three 419 de cit characteristics: duration (measured in hours), intensity (minimum temperature 420 / maximum power de cit), and severity (aggregated frost sum / power de cit over the 421 event), each of which constitutes an annual extreme value series. These are further 422 analyzed using extreme value statistics to determine the return period of each freeze 423 and capacity de cit characteristic according to natural hazard management standards. 424 Minor capacity de cit events (with a duration <6 hours) are excluded as these are not 425 extreme events and would distort extreme value modeling. Our analysis was conducted 426 using the R-software package lfstat [20], which provides a collection of state-of-the-art 427 methods that are fully described in the World Meteorological Organization's manual 428 on low ow estimation and prediction [21]. The resulting winter power de cit events 429 are shown in Figure 2, their extreme value statistics are shown in Figure 3. 430 431 Data: Temperature at 2m above ground is taken from the ERA5 reanalysis [22]. 432 We weight temperature over Texas by population density [23] to derive a temperature 433 index for modeling electricity demand. For estimating outages in the power system 434 due to low temperatures, we also weight temperature by capacities of wind [24], coal 435 and natural gas power plants [25], which were the power generation technologies most 436 a ected by failure during the extreme temperature event of February 2021. For wind 437 14 power plants, we split into a North and South region (along the latitude of 30 °), 438 since temperatures at wind parks in the North and South of Texas di er substantially. 439 Since the failure of the power system might be related to infrastructure at gas elds 440 supplying these power plants [26], we also determine a gas eld weighted temperature 441 index, using the distribution of natural gas production by county [27] to complement 442 our analysis. Load data used for demand prediction were retrieved from ERCOT 443 [28] for the period 2004{2021/02. Since the focus of this study is on freeze events in 444 winter, only winter load data (Dec{Feb) is used. Outage data is provided in the period 445 since 10thof February 2021 by ERCOT [29] and is aggregated by power generation 446 technology for the analysis. 447 Data availability 448 We will provide aggregated climate data from ERA5 as well as gridded population data 449 necessary to derive population weighted temperatures openly to the community on 450 Zenodo. Data from public institutions, in particular ERCOT, the Energy Information 451 Administration, and the Texas Railroad Commission is not available under an open 452 license. However, we will provide, upon publication, links to data sources and the 453 whole code, including download scripts, so that our analysis, and in particular all 454 gures, can be fully reproduced. 455 Code availability 456 Code will be published in a Github repository and will be archived using Zenodo, 457 hence a DOI for the code can be provided too. 458 459 Corresponding author 460 Katharina Gruber 461 Acknowledgement 462 We gratefully acknowledge support from the European Research Council (\reFUEL" 463 ERC2017-STG 758149). We are grateful to Edgar Virg uez who provided spatial loca- 464 tions of power plant outages and discussed early results with us. 465 Contributions 466 Conceptualization: K.G., T.G., P.R., G.L., J.S.; Software: K.G., T.G., P.R., J.S.; 467 Investigation: K.G., T.G., P.R., G.L., J.S.; Writing - Original Draft: K.G., G.L., P.R., 468 J.S.; Writing - Review & Editing: K.G., T.G., , G.L., P.R., J.S.; Visualization: K.G., 469 T.G., P.R.; Supervision: J.S.; Funding acquisition: J.S.; 470 15