## 1 Introduction
### Operational Grid Resilience: Background and Definitions  
The U.S. National Academies define resilience as \"the ability to anticipate, prepare for, and adapt to changing conditions and withstand, respond to, and recover rapidly from disruptions\" [6]. NERC defines power grid resilience as \"the ability to reduce the magnitude and/or duration of disruptive events\" [3]. Complementary definitions and power system resiliency metrics are presented in [81; 82]: the power system is resilient if it operates reliably over range of operating conditions and has the capability to deliver power and absorb and to adapt to events of low probability and high consequence. The CIGRE C4.47 Power System Resilience Working Group defines power system resilience as the ability to limit the extent, severity, and duration of system degradation following an extreme event [83].  
Robust and resilient operation of a power grid requires anticipation of unplanned outages that could lead to cascading and blackouts. Planning and operation standards are designed so the power grid shall always be _operated_ such that instability, uncontrolled separation, cascading, or voltage collapse will not occur because of any single contingency or two sequential N-1 contingencies (N-1, time for readjustment, and another N-1). On the other hand, planning standards cover credible N-2 contingencies, such as double-circuit outages, circuits on common structures, or stuck breaker conditions. The specific NERC reliability standards that relate to the BPS capability to withstand events in anticipation of potential outages, manage the system after an event, and prepare to restore or rebound after an event are TPL-001-4, TOP-002, EOP-004-3, EOP-005-2, EOP-006-2, EOP-011-1, CIP-014-2, PRC-006-3, PRC-016-1, and TPL-007-1 [39]. While these criteria fulfill for example the NERC requirements to meet performance standards and operate securely under the N-1 contingency criterion, this is not a guarantee that the system is immune to multiple N-k outages. Detecting and preventing multiple outages is critical to maintaining power system reliability and resilience. Operation planning engineers, as well as control room operators, face complex situations resulting from these multiple events. When power grids have high volume of renewable energy sources or they are heavily stressed with high power transfers it becomes an increasingly challenging task to make electricity grids most efficient, reliable, and resilient.  
A growing body of publications in recent years presents the concept of resilience by assessing the impact and mitigation measures to major disturbances as result of adverse weather, natural disasters, hurricanes, earthquakes, and cyberattacks [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50]. Reference [3] emphasizes, \"To increase system resilience requires an understanding of a wide range of preparatory, preventive, and remedial actions, as well as how these impact planning, operation and restoration over the entire life cycle of different kinds of grid failures\".