## 3 Investigation of Resilience Investment Strategies
### Infrastructure Hardening  
Infrastructure hardening is a long-term strategy that involves replacing or reinforcing weaker infrastructure with more robust alternatives. While this approach can be effective, it requires substantial initial investment. As strategic hardening of selective sections can enhance system resilience at reduced costs, this study considers three hardening cases:  
**Case 1. **: undergrounding the network section that supplies power to the critical loads from bus 47 to bus 60. **Case 2. **: undergrounding the network section which forms a part of the main feeder from bus 1 to bus 8. **Case 3. **: replacing overhead distribution assets with a 30% robust infrastructure as an alternative investment to undergrounding. Cases 1 and 2 include a similar number of assets, requiring similar investment costs, thereby allowing for comparative cost/benefit analysis without requiring detailed cost calculations. Case 3 involves system-wide asset replacement and warrants further evaluation to enable a more accurate comparison. The results from these studies are compared to those for the base case in Figures 4-8. Figure 4 shows that the system EENS is reduced, and therefore, the system resilience is improved for all three cases of investment in infrastructure hardening. Case 3, in which the entire infrastructure is hardened, shows the greatest improvement,. Although the improvement from Case 2 is less than that of Case 3, the improvement is still quite significant and only requires hardening part of the system. The improvement in Case 2 was due to the strategic decision to harden the main feeder supplying the overall system. Case 1 results in the lowest improvement among the three cases, although the investment cost is comparable to that in Case 2. Case 1, however, significantly reduces the EENS of the critical loads from the base case, as shown in Figure 5. The reduction in EENS for critical loads in Cases 2 and 3 is less significant compared to the improvement observed in Case 1. The enhancements in system performance for critical loads are highly valuable, since the outages of critical loads result in relatively high outage costs. Figure 6 illustrates the DLH values for each of the hardening strategies relative to the base case, showing a similar pattern of resilience improvement consistent with the EENS metric. Figure 4: EENS for cases with infrastructure hardening. Figure 5: Critical load EENS for cases with infrastructure hardening. Figure 6: System DLH for cases with infrastructure hardening. Figure 7 compares the system EOD and the NDLH indices for the above case studies. It can be noted that the value of NDLH is less than that of the EOD. The difference indicates the resilience of the infrastructure to withstand the extreme events. It should be noted that the difference increases as system hardening rises. This highlights the effectiveness of the NDLH metric in capturing both the system's resilience and its vulnerability, unlike that noted for the EOD metric. The comparison of the three hardening cases with the base case using these two indices shows similar results to those obtained from the EENS index. The results for both the duration and energy metrics exhibit similar trends, although this correlation may not always hold true. In this study, the observed similarity can be attributed to the uniform load distribution and the specific topology of the network. Figure 8 illustrates the percentage change in EOD from the base case when the performance of critical and non-critical loads is analyzed separately for each of the hardening strategies. As anticipated, hardening the critical sections in Case 1 results in a substantial 30.9% reduction in EOD for critical loads compared to the results for the base case. Interestingly, this strategy also yields a 5.9% improvement in EOD for non-critical loads, despite no direct hardening applied to those sections.