# Resilience of urban public electric vehicle charging infrastructure to flooding

### EV charging infrastructure

The locations of the public EV chargers in Greater London were taken from the website maintained by the Office of the Mayor of London51, which consists of the locations of slow (defined as < 43 kW) and rapid chargers (defined as ≥43 kW). Overall, we obtained data for 5925 chargers across the region as a .csv file from the ArcGIS platform, see Supplementary Note 4. Each charger was assumed to be connected to the node on the road network that is the closest to its location. According to a report from the International Council on Clean Transportation30, more than 40% of drivers in Greater London do not have off-street parking. Accordingly, we assume that 25% of BEVs each depend on public night-time charging and daytime workplace/commercial charging, and the rest 50% depend on residential charging. Since the actual charging power depends on the model of the BEV and the charger, for simplicity in our simulations, the slow chargers are assigned a power of 12.5 kW (the average of the reported lower and upper limits, respectively, 3 kW and 22 kW) and the rapid chargers, 43 kW, corresponding to the definitions from ref. 30. All the chargers added to mitigate the impact of flooding are considered to be rapid chargers to allow us to assess the best-possible outcome. We further assume 89% efficiency for all the chargers, similar to the approach adopted in ref. 1.

### Simulating rides

We simulated personal electric vehicle trips using MATLAB; the overall flowchart is shown in Supplementary Note 5. We selected the number of EVs to be between 6 and 8 times that of the chargers, based on the 2020 statistics for Greater London30. Results presented in the main article correspond to the value 6, whereas Supplementary Note 1 presents results for the value 8. Given that the share of BEVs over all EVs (which also includes hybrid EVs) is projected to reach 90% by 2025 and 100% by 203030, we assumed that the entire set of EVs in our simulations are comprised of BEVs. We consider three models of BEVs: Nissan Leaf (40 kWh battery), Nissan Leaf Plus (62 kWh battery), and Tesla Model S (100 kWh battery). In each simulation, the vehicles are assigned with equal probability one of these models.

The BEV trips were simulated according to the travel patterns reported by Transport for London52. This data pertains to a survey conducted until 2011, and reports details including the number, duration, and distribution of trips for the residents of Greater London. Vehicles begin and end at home (or a parking spot close to home), and the entire journey over 24 h is referred to as a tour. Each vehicle can make two or more trips in their tour, defined as starting from one location in Greater London and ending at another, during the day. The number of trips for each BEV is determined using the probabilities presented in Supplementary Table 1 in Supplementary Note 6. In our study, the average number of trips per BEV is 2.42, which matches closely with the surveyed data from ref. 52 which is 2.49. While the final trips for the BEVs terminate at home, the interim destinations in each BEV’s schedule are determined based on the purpose of each trip. Since particular destination locations are not specified in the survey, we selected them randomly across the region using available trip-purpose data, from the appropriate building type: (i) work or (ii) commercial (shopping, public spaces, leisure, escort or school); the probabilities for each are shown in Supplementary Table 2 in Supplementary Note 6. A previous study53 of EV users in the UK has shown that there is no seasonality in the charging behaviors. We therefore only consider trips on a typical weekday, and the probability distribution of the departure times of the BEVs are given in Supplementary Fig. 22 in Supplementary Note 6. The speed of vehicles through the day is taken from the Transport for London report54, within the ranges presented in Supplementary Table 3 in Supplementary Note 6. At each instant of the simulation, the average speeds of the vehicles are selected randomly between the minimum and maximum values specified. Based on these speed values, the arrival times of the BEVs are estimated for each trip, assuming that they traverse the shortest distance between the source and the destination. Overall, the average Haversine distance of a trip in our simulations is 15.8 km, which corresponds well to the value of 13.9 km obtained in prior surveys52,55. The BEVs begin with state-of-charge (SOC) values randomly selected in the interval [a, b], which depends on whether the BEV relies on residential charging or night-time public chargers close to home (a = 0.9, b = 1.0), or on public chargers during the day (a = 0.4, b = 0.6). The SOC of the ith BEV at the end of a trip of distance dtrip is calculated as follows:

$${{{{{{{{\rm{SOC}}}}}}}}}_{i,dest}={{{{{{{{\rm{SOC}}}}}}}}}_{i,source}-{{{{{{{{\mathcal{D}}}}}}}}}_{i}\cdot{d}_{trip}$$

(1)

where the discharge rate $${{{{{{{{\mathcal{D}}}}}}}}}_{i}$$ depends on the BEV model, see Supplementary Note 6.

The simulation of EV charger usage for 24 h is carried out using simulations with 1-min resolution. At every time step, an event-triggered algorithm generates arrival and departure events based on the estimated arrival and departure times for each trip.

#### Arrival event

A user decides to charge their BEV after a trip if the SOC falls below a threshold λ1 (taken here as 0.5). The user then drives to a charger that is closest to the destination and currently available, considering an upper limit on the distance between the destination and the charger to be 300 m. If the SOC falls below a lower and more critical threshold λ2 (taken here as 0.3), the user seeks the nearest available charger at any distance from the destination. The assignment of the chargers to the BEVs is carried out in a first-come-first-served basis. Charging only occurs if there remain at least 30 min to the departure time for the next trip in the BEV’s schedule.

#### Departure event

If a BEV charges at the completion of a trip, the charger’s location is updated as the actual location in the trip schedule instead of the intended destination; the difference between the two is noted as the ‘distance to the nearest available charger’ for that trip. During the charging process, the SOC of the BEV changes as follows:

$${{{{{{{{\rm{SOC}}}}}}}}}_{i,end}={{{{{{{{\rm{SOC}}}}}}}}}_{i,start}+{{{{{{{{\mathcal{C}}}}}}}}}_{i}\cdot{T}_{wait}$$

(2)

where Twait is the total charging time, and $${{{{{{{{\mathcal{C}}}}}}}}}_{i}$$, the charging rate; see Supplementary Note 6. The trip distance and actual arrival time are determined from the shortest distance from the origin of the trip to the destination. When a charging BEV departs, it releases that charger to be used by others.

Overall, a BEV is considered to have failed if its SOC falls below 0.2 at any time1. In addition, a BEV dependent on day-time public charging is considered to have failed if its SOC at the end of the day falls below 0.3, considering that the user must then drive to a nearby charger on the following day to charge.

### Flooding data

To obtain the regions in Greater London that are at risk from flooding, we used the tool developed by Climate Central43, which projects the land area under a given flood level considering sea level rise and coastal flooding. The following settings were used: Projection Type = sea level rise + moderate flood; Pollution Pathway = current trajectory; Luck = medium; Areas to show as threatened = exclude areas isolated by higher land; and Sea-level-projection source = leading Consensus (IPCC 2021). Specifically, we used projections for the year 2030, which is the closest available data point. Notably, other estimates of flood risk in Greater London, such as from the UK Environment Agency56, also present very similar results when other sources of flooding (river and surface water) and existing flood defenses are included, see Supplementary Note 7. The Climate Central data corresponds to a 10% risk per year over these areas, while the UK Environment Agency data projects anywhere from greater than 0.1% to greater than 3.3% per year.

We obtained the regions at risk in Greater London as a .png map image and utilized an open source tool57 to extract the coordinates of the regions at risk. Subsequently, we overlaid for simplicity a 42 × 86 grid on the geographical area of Greater London between the latitudes 51.280 and 51.692, and the longitudes −0.510 and 0.340. All grids which overlapped with the at-risk regions were considered to be at risk from flooding; we assume that the flooded grids do not change during the day. For each simulation, the public chargers within each at-risk grid are assumed to become unavailable for use with the probability pf, which is selected as 0.5, 0.7, and 0.9, and designated as flood scenarios-1, -2, and -3, respectively. We note that BEVs that depend on night-time public chargers within a flooded grid are assigned lower SOC values at the beginning of the day, in the range [0.4, 0.6], to reflect their inability to charge.

https://www.nature.com/articles/s41467-022-30848-w