*3.1. Risk Assessment*

For the electrical asset risk assessment, a novel procedure has been established. The first step was to create a sampling shape layer by using an average diameter of 20 meters for the electrical DCs wanted for evaluation, with the diameter based on recommendation in the Energy Networks Association article [19]. The diameter was used to define the influence area for each location and after that a uniformly distributed cloud of 106 sampling points was created all across the extent (Figure 4). It is worth noting that such areas allow the tool to cope with location uncertainty in GIS data.

**Figure 3.** Flowchart of the method followed in the analysis.

**Figure 4.** Non-affected area (**a**), partially affected area (**b**), fully affected area (**c**).

The second step consisted of the intersection of the sampling layer with the detailed flooding map that contained the water depth of each flooded area. After crossing both shapes, the following parameters were extracted:


The third step was to process the information obtained for every sampling point to calculate a representative figure for each location. In this way, the rate of the affected area and an average for the water depth for each location was calculated.

To calculate the Affected Area Rate (AAR), the number of sampling points affected were counted (*nY*) and later divided by the total number of sampling points (*ntotal*) (Equation (1)).

$$AAR = \frac{n\_Y}{n\_{\text{total}}} \times 100\tag{1}$$

Afterwards, the Water Depth Average (WDA) was calculated for the sampling points flood depth, obtaining a general representative number of each location (Equation (2)):

$$WDA = \frac{1}{n} \sum\_{i=1}^{n} \mathbf{Y}\_i \tag{2}$$

Once the water depth for each location was calculated, the fourth step was to introduce this parameter in the X-axis of each fragility curve represented in Figure 5**.** The failure probability was obtained and represented from 0 to 1 in the Y-axis.

**Figure 5.** Original flooding fragility curves for HV, MV and LV electrical substations and distribution centers (**b**) (adapted from FEMA, 2009). Softened fragility curve (**a**) and Hardened fragility curve for sensitivity analysis (**c**).

The original fragility curve (Figure 5b) used in this study was adapted from that of the Federal Emergency Management Agency of the United States [10], previously formed through data gathered from important disasters occurred in the US electrical grid. It must be remarked that the US grid can have different standards and protective measures compared to Europe and a different substation and DC topology. However, in further studies with more data available, the curves can be rebuilt to fit with the real conditions and features. Taking into account this dissimilarity with the grid established in Bristol or Barcelona, a sensitivity analysis was performed to assess the possible error caused by this. In this manner, it is possible to offer a better resolution by contemplating a wider spectrum (Figure 5a,c).

After obtaining the result from the fragility curves, the fifth step was to multiply the Fragility Curve Probability (FCP) by the AAR, obtaining a final probability of failure for each analysis performed for each return period given (Equation (3)).

$$P\_F = AAR \times FCP\tag{3}$$

The last step was to classify each location studied according to the *PF* calculated by following the categories established in Table 2.

**Table 2.** Different categories set for ranges of failure probabilities.

