“…However, to treat outages and reliability they require a number of simplifying linearizations and are commonly parameterized with assumptions of perfect DER reliability or a single prescribed (e.g., average) grid outage frequency and duration (Marnay et al, 2008) (Simpkins et al, 2014). It is known that these simplifications introduce inaccuracies in model results for optimal investment and resilience benefits (Marqusee et al, 2021a(Marqusee et al, , 2021b. More detailed reliability calculations can be made aside linear models, for example, via pre-processing (Laws et al, 2018) or post-processing (Mishra et al, 2021) routines that permit simulation of a wider array of moderate and long-duration outages, parameterized with full pdfs, or that ensure resilience constraints are met.…”