# Valuing Resilience Benefits of Microgrids for an Interconnected Island Distribution System
## 2 Valuation Approach
### Baseline Economic Consequence of Outage Events  
To apply the valuation methodology to the historic events, a few assumptions were made. The annual value of a resilience upgrade is equal to the expected annual avoided outage costs. This is equal to the sum of costs by outage scenario multiplied by the annual frequency of each scenario. The cost of a given outage scenario is determined by the number and type of customers impacted, as well as the outage duration. Table 3 displays the number of customers by island. The average load across Vieques and Culebra is 5.45 MW.  
The financial impact on a customer goes well beyond the cost of electricity that was not billed to that customer. In fact, there are different approaches to quantify the value of lost load (VOLL). This section introduces each valuation method's philosophy and results from performing a baseline economic loss calculation across the outage event categories.  
The four main economic loss evaluation methods are:  
1. A FEMA-assigned cost of USD 174 per person (not customer) per day [18].
2. A jurisdictional survey to obtain a blended cost per lost MWh assigns a cost of USD 31,895 per MWh, as a blended class rate for the islands [19].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Number of Customers**} \\ \hline
**Location** & **Residential** & **Commercial** & **Industrial** & **Total** \\ \hline Viewes & 4378 & 465 & 1 & 4863 \\ \hline Culebra & 1121 & 306 & 1 & 1449 \\ \hline Total & 5499 & 771 & 2 & 6312 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Customer Affected in Viewes and Culebra.  
Figure 2: Component outage, restoration, and resilience curves for the hurricanes, (**a**) outage count and (**b**) unserved customers.  
Using the Interruption Cost Estimate (ICE) Calculator [20] to estimate a cost of USD 40,430 per MWh, as a blended class rate for the islands.
4. Using a simple time-varying customer damage function, as described below, to estimate outage costs in each scenario.  
Costs from power outages may vary nonlinearly with outage durations. Factors such as food spoilage or limited fuel for backup generators can result in marginal outage costs increasing with outage duration. Meanwhile, mitigation steps can reduce the marginal cost of outages as outage duration increases. Such nonlinearities imply that it may be inappropriate to use a single per MWh value to outage cost. Instead, the per MWh cost of an outage may vary by outage duration.  
To incorporate nonlinearities in shorter duration outages, the ICE Calculator was used to estimate outage costs across outage durations from 1 to 16 h, and then multiplied by the frequency of outages of each duration to estimate an average cost of USD 48,940 per MWh, which is 20% higher than the ICE Calculator when average outage durations are used.  
The marginal costs (e.g., the additional outage cost per hour after already experiencing an outage of x hours) of long duration outages may be less than, or more than, the marginal costs of shorter duration outages. The results are presented for a range of potential costs for long duration outages. The low-end case sets the average per MWh cost of long duration outages to half of the per MWh cost of short duration outages (USD 24,470/MWh), the mid case sets the two equal (USD 48,940), and the high-end case sets the per MWh cost of long duration outages to double the per MWh cost of short duration outages (USD 97,880).  
These numbers result in the costs presented in Table 4, which displays estimates for the annual expected outage costs by event type. These results illustrate the local economic impact of both shorter duration grid outages and the potentially significant cost of low probability but high impact hurricane events.