# Review of Power System Resilience Concept, Assessment, and Enhancement Measures
## 4 Resilience Assessment and Metrics
### Metrics of Resilience Assessment
#### 4.3.2 Post-Event Estimation  
The variation in system performance is used to describe the load loss of resilient systems compared to traditional systems, as shown in Figure 6. The load loss of resilient  
Figure 6: Resilience assessment curve with associated characteristics. systems is relatively smaller than that of traditional systems. The resilience metrics can be determined by a function of load loss, and reducing the area of load loss can improve the resilience of power systems. Therefore, the event-related system resilience can be quantified as a reciprocal of load loss, as expressed in Equation (4) [12; 53]. \[Resilience=\frac{1}{Loss} \tag{4}\]  
The load loss can be calculated by integrating the relative deviation over the duration of performance degradation (from time \(t_{1}\) to time \(t_{4}\)), as shown in Equation (5). \[Loss=\int_{t_{1}}^{t_{4}}\biggl{[}\frac{Q_{0}-Q(t)}{Q(t)}\biggr{]}dt \tag{5}\]  
Based on this calculation, reducing the performance degradation (\(Q_{0}\)-\(Q_{min}\)) or decreasing the duration of performance degradation implies a smaller area of load loss, indicating better system resilience. After a disruptive event occurs, the system performance begins to decline. By increasing the strength of the infrastructure, the damage caused by external factors can be reduced. In practice, we do not want the performance degradation time (from time \(t_{1}\) to time \(t_{2}\)) to be too short. This indicates that the system has better reliability and robustness, enabling it to resist, withstand, and absorb the impacts caused by events. Moreover, it is crucial to have more time to take measures and mitigate the threats caused by events, thereby reducing the extent of the decline in system performance. In contrast, when the system performance reaches its lowest level, implementing recovery strategies and measures can help the system adapt to the impact of the event and quickly restore it to a normal state. We would therefore wish to reduce the adaptation and recovery phase times (from time \(t_{2}\) to time \(t_{4}\)), signifying a system that is more flexible and resilient. In other words, during the period when the system performance declines from a normal state to the lowest level, the rate of change in system performance can be relatively low. However, during the period when the system performance recovers from the lowest level to a normal state, the rate of change in system performance can be relatively high. For example, two systems with the same magnitude of load loss are depicted in Figure 7, but we consider the system in Figure 7 to have greater resilience potential compared to the system in Figure 7. This is because the system in Figure 7 has better capabilities of absorption and recovery, allowing it to have more time to absorb the impact of events and recover quickly from disruptions. Therefore, we take into account both the rate of performance degradation and the rate of performance recovery (indicated by a red dashed lines) and introduce a coefficient \(\gamma\) to the original resilience metric equation, as follows:  
\[\gamma=\left|\frac{t_{2}-t_{1}}{t_{4}-t_{2}}\right| \tag{6}\]  
\[R^{\prime}=\frac{\gamma}{Loss} \tag{7}\]  
where \(\gamma\) is the resilience coefficient and \(R^{\prime}\) is the optimized resilience assessment metric. The article proposes a new framework and metrics for resilience assessment that is related to resilience characteristics, as shown in Table 3. It shows the main characteristics of power system resilience, which summarizes the required capabilities of a resilient power system before, during, and after extreme events. Additionally, this paper proposed resilience curves related to the main features, as shown in Figure 6. After a severe event occurs, the capability to supply power to load consumers begins to decline. By increasing the strength of the power system infrastructures, the potential damages can be reduced.