# Review of Power System Resilience Concept, Assessment, and Enhancement Measures
## 4 Resilience Assessment and Metrics  
### Review of Resilience Curve  
[PERSON] et al. [18; 70] proposed the disturbance and impact resilience evaluation (DIRE) curve, which illustrates the relationship between time and performance levels for resilient and un-resilient systems, as shown in Figure 3. Additionally, several common terms have been presented, including robustness, agility, adaptive capacity, adaptive insufficiency, resiliency, and brittleness. In the DIRE curve, \(t_{i}\) represents the time when the disturbance  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Reliability** & **Robustness** & **Resilience** \\ \hline Objective disruptions & LIHP & LIHP, HILP & HILP \\ Specific threats & No & Yes & Yes \\ Network components & Independent & Independent & Interdependent \\ Reliance on historical data & Yes & No & No \\ Operation/Security method & Static & Passive & Dynamic/Active \\ Design for failures & Expected & Expected & Unexpected \\ Consider the probability of occurrence & Yes & Yes & No \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of the concepts of resilience, robustness, and reliability.  
starts; \(t_{Bi}\) indicates the duration during which the system performance is below the resilience threshold (i.e., minimum normal value); \(t_{R}\) is the time when the system reaches the minimum performance level; \(t_{Bf}\) signifies the time when the system performance returns to the resilience threshold; \(t_{f}\) represents the end time of the recovery process.  
[PERSON] et al. proposed the concept of a resilience trapezoid, illustrating the relationship between time and system states during and after disturbances, along with the available measures, as shown in Figure 4[6; 71]. Typical activities during each state are:  
* Pre-disturbance resilient state: Evaluation of information about the disturbance and pre-arranging resources needed after the event.
* Phase I (disturbance progress): The capacity of absorption is demonstrated in this phase. Smart grid technologies and distributed energy systems play a role in providing operational flexibility to cope with the disturbance. The goal of this phase is to decrease the level of system performance degradation (i.e., \(R_{o}\)-\(R_{pd}\)).
* Phase II (post-disturbance degraded state): The ability to adapt is demonstrated in this phase. Evaluation of losses caused by the disturbance, formulation of recovery strategies, and initiation of recovery measures as soon as possible. The goal of this phase is to shorten its duration (i.e., \(t_{r}\)-\(t_{ex}\)).
* Phase III (restorative state): The ability to recover is demonstrated in this phase. In order to restore system performance and load, measures such as repairing damaged components, restarting units, and re-energizing lines are taken. The purpose of these measures is to restore the load within a short period of time (i.e., \(T\)-\(t_{r}\)).
* Post-restoration state: Analysis of impacts of disturbances on the system and subsequent improvements to the system to better handle similar events in the future.  
[PERSON] et al. [72] decomposed the resilience curve \(C(t)\) into outage and restore processes to track the accumulation and restoration of outages during the event, as shown in Figure 5. \(O(t)\) and \(R(t)\) represent the cumulative number of outages and restores, respectively. The total number of outages increases from zero to ten over time for \(O(t)\) and \(R(t)\). The cumulative number of outages at time \(t\) can be expressed as \(O(t)-R(t)\). Therefore, the resilience curve \(C(t)\) can be defined as the negative of the cumulative number of outages at time \(t\), as shown in Equation (1).  
\[C(t)=R(t)-O(t) \tag{1}\]  
Figure 3: Disturbance and impact resilience evaluation (DIRE) curve [70].