**5. Discussion**

The risk of assets has been quantified in other studies and in several ways, but not in the same way it was conducted here. For example, a GIS-based method was proposed by JRC [7] to assess the electrical grid and the gas network in case of seismic events using seismic fragility curves proposed by FEMA-HAZUS [10], which is similar to what was done on the failure assessment of this study. However, it was not taken into account how to assess the economic losses, later releasing other studies, with methodologies to evaluate the economic losses caused by storms and floods to the electrical infrastructure in [12,13], but never fusing them in a complete methodology and using it in case of flooding. The case of [9] builds on FEMA-HAZUS methodology [10] and follows a much more detailed analysis by using interdependencies but with the single problem of the huge requirement of data and the added difficulty of creating the network topology, and in most of the cases that information is confidential. Considering other methodologies as the proposed in [8] only the probability of flooding is assessed and not the probability of failure neither the economic losses. The most similar methodology can be found at [11] where a GIS-based approach is taken for the assessment of the electrical sector in flooding events determining the system exposure and vulnerability of the grid to flooding, with the particularity of not using fragility curves. A good point here is that this study takes into account other ways to assess the economic losses considering the economic sectors involved in each area of study.

Regarding the points highlighted above and the new procedures developed, this is a novel process that allows an analytical interpretation not only of the risk that electrical assets are exposed to but also about the potential costs that these assets could produce in many different ways to the population and to the DSO company.

This process enables the user to find the distribution center most exposed to flooding within a set region, allowing them to then take preventive measures if necessary on behalf of the responsible organization or authority.

This study evaluated several scenarios by using different parameters. This allowed a check on the effectiveness of the process and to establish comparisons between the different scenarios proposed.

#### *5.1. Comparison between Fragility Curves*

The results produced in the different analyses, carried out by applying the different fragility curves modelled, offer a comprehensive view of the effect of changing the curve shape, as demonstrated in the results produced. The analysis made with FC1 (softened fragility curve) may overestimate the results because high failure rates at low water depths are considered. On the contrary, when using FC3 (hardened fragility curve) the results can be underestimated due to the curve considering zero failure probability up to water depths of 1.4m. Taking into account the results presented, FC3 is neither representative nor realistic because it omits a high number of DCs with a failure probability in the other FCs. As the arrangement of the electrical elements can vary heavily between DCs, a zero probability would be a great underestimation. In fact, taking the experiences of electrical companies' employees, a DC can fail from very low water depths and the threshold to identify the flood risk was set to 10 cm in the risk analysis.

In general, taking FC2 as a reference point, FC1 results in a 19% cost average increase caused by the sum of all the possible small losses produced by low failure probabilities, while FC3 results in a 9% cost average reduction, as it neglects all of the small losses and keeps the gross.

In the end, the variation in the fragility curves can be taken as a pessimistic, neutral or optimistic view if choosing from FC1 to FC3, although in general, FC3 is not representative.

#### *5.2. Comparison Between Current and BAU Scenario*

The first comparison made was between a current scenario, where different return periods based on historical data were modelled in flooding shape layers, and a BAU scenario considering climate change with an RCP 8.5, estimating the flooding that could occur in the year 2100. As is normal, in the results obtained, the BAU scenario introduced higher risk and consequently higher costs.

Depending on the fragility curve applied, the differences between both scenarios change, but counting the maximum change experienced in both cities, the maximum increase in the number of DCs affected goes in the LFP category with a 2.38% increment in Barcelona and 3.37% increment in Bristol. Also, big increases are presented for MFP with 1.64% rise in Barcelona and 1.12% in Bristol. These increments seem to be very low but when translated into cost, the average increase is a 22% respective difference to the current scenario, but depending on the case analyzed, the percentage can vary (Figure 17).

**Figure 17.** Radial chart that represents the cost increase provoked by climate change in a future scenario by taking into account all return periods for different fragility curves, scenarios and cities.

#### *5.3. Comparison between Cities*

It is difficult to make a complete comparison between both cities due to different return periods being analyzed (in Bristol these were lower than in Barcelona), and because of the context of each city. With regards to context, it has to be taken into account that the extent of both cities studied is more or less within the same scale (Bristol with 111 km<sup>2</sup> and Barcelona with 102 km2) but the effective territory studied is much less in Barcelona (only 32% which means 33km2) and also 326,000 inhabitants against 460,000 in Bristol. In this aspect, the number of inhabitants of both cities is also similar.

In addition, the hydraulic models that simulate the flooding are different. In Barcelona, the whole drainage system was included within the model, while in the underground Bristol sewer network only larger diameter pipes, although in Bristol this considered both pluvial and fluvial flood events, while in Barcelona, only the pluvial flooding was considered.

Bearing in mind the above statements and taking the unique return period (T100) run for both cities an analysis comparing the cities was performed, resulting in quite similar losses for each fragility curve applied but always resulting in Bristol being the city most affected by flooding. In Figure 18a the total costs are represented for both cities, for the two scenarios analyzed and the different fragility curves developed, showing a clear difference between cities in almost all cases analyzed. As this difference could be linked to the number of DCs analyzed in each city, the total cost has been unified taking into account the total number of DCs analyzed in each city (Figure 18b). In this case, the difference between cities is even more noticeable, which is something reasonable taking into account the great problem that Bristol has with flooding [14].

**Figure 18.** Radial chart that takes into account the return period T100 for different fragility curves and scenarios, comparing both cities taking into account (**a**) the total costs associated with risk and (**b**) the unified cost by DC.

#### **6. Conclusions**

This paper has gone through a methodology that aims to estimate and classify the DCs at risk of flooding in different classes set by failure probabilities, as well as the energy losses and their expenditures provoked by shortages caused by potential flooding. This methodology takes a probabilistic GIS-based approach to quantify the risk of electrical shortage in different areas caused by DCs flooded. In this research it has been demonstrated that it has become possible to implement this method to any city where the locations of the DCs and a flooding model are available.

The method used to go through different steps for each city, depending on the data availability for each one, offers several ways to estimate risk and electrical losses with, inevitably, different accuracy.

As a result, it can be drawn the potential losses incurred to put them into balance against the cost of taking protective measures if the assets analyzed are not already under protection.

**Author Contributions:** Conceptualization, D.S.-M. and J.L.D.-G.; Data curation, D.S.-M.; Formal analysis, D.S.-M.; Investigation, D.S.-M. and J.L.D.-G.; Methodology, D.S.-M. and J.L.D.-G.; Project administration, J.L.D.-G.; Resources, E.M.-G., B.R., J.S. and M.P.; Software, D.S.-M.; Supervision, J.L.D.-G.; Visualization, D.S.-M.; Writing—original draft, D.S.-M.; Writing—review and editing, J.L.D.-G., E.M.-G., B.R. and J.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the European Union's Horizon 2020 Research and Innovation Program (RESCCUE project), grant number 700174.

**Acknowledgments:** The authors want to acknowledge to the RESCCUE project where this research is framed. Also, to all the organizations that transferred the necessary data to carry out this study, in special, Western Power Distribution in UK and Endesa in Spain for the electrical data, Aquatec in Spain and Bristol City Council in UK for the flooding models and to the Bristol and Barcelona city councils for developing the Open Data Portals from where basic data was taken.

**Conflicts of Interest:** The authors declare no conflict of interest.
