# Quantification of the Benefits for Power System of Resilience Boosting Measures
## 2 A Framework to Model Power System Resilience
### The \"Three-Leg\" Model to Link Reliability and Resilience  
The Working Group C1 of CIGRE defined reliability as \"A measure of the ability of a power system to deliver electricity to all points of consumption and receive electricity from all points of supply within accepted standards and in the amount desired\" [13]. It is worth noticing that reliability definition does not refer to any specific application criterion (in particular, there is no reference to credible or extreme events). Currently, security and adequacy are necessary conditions to verify the classical property of \"reliability\" for a power system. However, assuring the security of the system in case of multiple outages such as the ones produced by extreme events, would lead to unbearable costs in terms of component design, grid redundancy, system operation, and maintenance. The resilience property addresses this aspect by imposing a less stringent requirement, i.e., to limit the degradation of the system. Accordingly, resilience can be added to reliability to characterize the system in the presence of any type of events. Under a broad perspective, reliability can be interpreted as a fundamental property which can be decomposed into three components: adequacy, security, and resilience (see Figure 1). Figure 1: Model of relationship between reliability and resilience: resilience as a third subproperty of reliability. A reliable system must have enough available generation and transmission resources to feed the load with a suitable margin (adequacy), in case of the most limiting contingencies; it must withstand disturbances (security), i.e., continue to supply all the customers fulfilling suitable requirements, at least for the category of contingencies which satisfy a credibility criterion; but it must also limit its functional degradation (resilience) for those contingencies which do not satisfy the credibility criterion adopted by the TSO (extreme events). This positioning of resilience as a sub-property of reliability is also justified by the following considerations. According to the classical reliability definition, a power system could not be defined reliable in case of extreme events. In fact, security, which requires no loss of load, is not assured for extreme events but only for credible contingencies. Instead, several advantages derive from stating that a necessary condition for a system to be reliable is that the system must have a sufficient resilience to extreme events:  
1. International definitions of reliability which do not include any references to the types of outages, are satisfied, including the recent definition proposed by CIGRE WG C1 [13]. 2. The definitions of security and adequacy remain unaltered. 3. A clear link between resilience and well-known, widely adopted concepts is established. This model is coherent with the definitions of FERC (Federal Energy Regulatory Commission of the US), NERC (North American Electric Reliability Corporation) and of the Italian national regulatory Authority, that considers both normal and exceptional (major force) events to evaluate the reliability. In particular FERC indicates that \"resilience is a component of reliability in relation to an event\" [14], and NERC states that \"a bulk power system that provides an adequate level of reliability is a resilient one\" [15]: This implies that resilience is a necessary condition for a reliable system. In 2013 NERC introduced the definition of ALR \"Adequate Level of Reliability\" [16] of a Bulk Electric System (BES): ALR definition includes the typical requirements requested to a resilient system. Reference [17] states \"Within the broad context of reliability defined by these indices, resiliency would appear as a component of reliability. Resilience relates to restorability and speed of restoration\", highlighting that available reliability tools should consider the resilience of the system, by adequately modeling repair and restoration processes [18].