3.2.4. Auxiliary Generation Cost (AGC)

In this section, the cost attached to the energy generation to avoid the prolongation of the shortage was estimated. The use of diesel emergency power generator support was assumed for when the repair time exceeded 9h of duration. This period was chosen as a hypothesis assuming the rainfall duration given for the flooding maps calculation (i.e., 3 hours) and 6h of response time to rent, transport and install the equipment. In this way, the calculation of the cost of penalties to the DSO company can be neglected in the analysis, although this, depending on the severity of the event experienced could be an underestimation.

It has been considered the transport of the equipment (*CAGT*) to the affected DC as 20€, and three different tranches of renting price depending on the number of days required. The first renting tranche (*CRt*1) has been set as 100€/day when the period is less than 1 week. The second tranche (*CRt*2) takes part when the problem is extended from one week to three weeks with a renting price of 50€/day and the third tranche (*CRt*3) when the repair tasks need more than three weeks, the price is reduced up to 40€/day. The prices used for this calculation have been taken from a company of machinery renting in Barcelona [23]. In addition, the fuel consumption cost (*CFC*) was added to the calculation as well as the number of auxiliary generators (*nAG*) (Equation (8)).

$$\text{AGC} \begin{cases} & \text{0, } t\_R \le t\_{W\text{E}} \\ & P\_F \cdot \text{C}\_{AGT} \cdot \eta\_{AG} + \text{C}\_{FC} + \text{C}\_{R1} \cdot \eta\_{AG}, \ t\_{WE} < t\_R < 1 \text{ week} \\ & P\_F \cdot \text{C}\_{AGT} \cdot \eta\_{AG} + \text{C}\_{FC} + \text{C}\_{R2} \cdot \eta\_{AG}, \ 1 \text{ week} < t\_R < 3 \text{ weeks} \\ & P\_F \cdot \text{C}\_{AGT} \cdot \eta\_{AG} + \text{C}\_{FC} + \text{C}\_{R13} \cdot \eta\_{AG}, \ t\_R > 3 \text{ weeks} \end{cases} \tag{8}$$

The number of auxiliary generators was calculated by dividing the DC power consumption (*PES*) by the maximum active power given by the generator (*PAG*) and rounding up the result to the whole number (Equation (9)).

$$m\_{AG} = \lceil \frac{P\_{ES}}{P\_{AG}} \rceil \tag{9}$$
