3.2.3. Energy Non-Supplied Cost (ENSC)

In this section, the electrical supply losses caused by the shortage duration have been estimated by following some different steps for the two cities studied due to the data availability.

The first step was to estimate the power supplied at each DC. In Barcelona, this step was not necessary because the real parameter was known, making the analysis performed in the selected areas quite accurate.

However, in Bristol, the average electrical demand of each DC studied was estimated based on the GIS layer generated in "3.2.2. Cost Associated with Businesses Losses (BC)" where the consumers were associated with the different DCs. The power estimation consisted of the multiplication of the total number of consumers by an average consumption of 531 kWh gathered from the world data portal [22]. In this case, the power losses could be underestimated, due to the business locations, the industries and other possible sources of consumption were neglected.

Another important parameter required for the calculation of ENSC is the repair time (*tR*), which was calculated by associating the different damage categories to the repair time obtained from "power grid recovery after natural hazard impact" [6], creating in such a way a damage-time curve based on these categories (Figure 8). Because in this study the damage will never overpass the 50% mark (see Figure 8), the categories that could exceeded that mark were discarded for a better equation curve-fitting, and the rest of categories were represented in a scatter chart, looking for a trend line that really fits the curve. In this case, it was found that a polynomial curve fitted almost to the perfection with the damage-time curve (R<sup>2</sup> = 0.9987). Hence, it was possible to adapt from a categorical scale to continuous by using the trend line equation.

**Figure 8.** Repair time-damage curve obtained from deriving data from "power grid recovery after natural hazard impact" [6].

For those future cases in which 100% damage can be reached, it is suggested to consider a total replacement.

Thus, the equation obtained from Figure 8 was applied to the damage percentage calculated in the previous step for all locations analyzed to obtain the corresponding repair time of each one.

Thus, *DES* was applied to the trend line equation, obtaining the corresponding repair time of each location damaged.

Once the DCs power and the repair time were calculated, the energy losses were derived according to Equation (7).

$$ENSC \begin{cases} \ P\_F \cdot P\_{ES} \cdot t\_R \cdot p\_{E\_{\mathcal{H}}} \ t\_R \le t\_{WE} \\\ P\_F \cdot P\_{ES} \cdot t\_{WE} \cdot p\_{E\_{\mathcal{H}}} \ t\_R > t\_{WE} \end{cases} \tag{7}$$

where *PF* is the failure probability, *PES* is the DC power, *pE* is the energy price and *tWE* is the period without energy.

In such a way, the energy blackout will be extended up to the Auxiliary Generation systems that are put into operation. From this point onwards, the cost will be directly attached to the Auxiliary Generation Cost.
