*4.3. Evolution of the Risk Behaviors Considering Dual Interactions*

Section 4.2 quantitatively assessed the extent to which the risk factors, if functioning independently, would ultimately cause losses to the coupled natural gas–electric market. If we consider the dynamism further, Figure 5 displays the evolutionary behavior of the coupled markets' key indicators over time when each of the four risk factors occur alone and when all the risk factors operate in collaboration. In particular, we focused on three indicator variables: the natural gas market's satisfaction rate, the electricity market's satisfaction rate and the coupled markets' satisfaction rate, which was calculated by combining the first two.

**Figure 5.** Dynamic behavior of the key variables, considering multiple risks and dual interactions.

First, the satisfaction rate of the natural gas and electricity markets were investigated separately. Consistent with the previous discussion, it could be observed that the natural gas market was primarily influenced by three risk factors: pipeline failures, import shortages and extreme weather. In contrast, the electricity market was heavily influenced by the risks of extreme weather and damage to the infrastructure, whereas pipeline failures and import shortages had negligible effects. For the natural gas market, pipeline failures lowered the market satisfaction rate, but the emergence of import shortages caused the market satisfaction rate to drop rapidly, surpassing pipeline failures as the most significant risk factor after day 32. The disruption caused by extreme weather shifted from growing to decreasing. However, even when the temperature had almost returned to the initial level, the market satisfaction rate did not return to normal. Since import shortages persisted as the most prevalent risk factor, the natural gas market satisfaction rate continued to decline, reaching the lowest level of 50.40% at the end of the simulation. For the electricity market, while infrastructural damage did not occur until day 70, after the emergence of extreme weather, it soon became the dominant risk factor owing to the substantial damage. After recovery of the damaged infrastructure on day 130, the satisfaction rate of the electricity market progressively recovered after day 157. The satisfaction rate of the electricity market showed a pattern of declining and then rising, with the lowest value occurring on day 121, at around 76.90%.

We then looked into the coupled markets' satisfaction rate. Considering the behavior of both markets and their interactions, we could observe that as time progressed, the dominant risk factors evolved, inducing more complexity for decision-makers attempting to make an adequate risk assessment. First, the different risk factors had their own evolutionary patterns. While pipeline defects and import shortages occurred abruptly and then persisted, infrastructural damages and extreme weather both showed a recovery trend, and the recovery pattern of extreme weather was even more obvious than that in each individual market. Second, various risk factors could be emphasized at different times. For instance, after the import shortages exceeded pipeline defects as the dominant risk factor, the disruptions induced by infrastructural damage also surpassed those induced by pipeline defects for some time. Third, the aggregated effects of minor risks may have serious effects on the coupled systems. While the disruptions from the most severe risk factor caused a decline of 17.88%, the satisfaction rate of the coupled market dropped by as much as 35.60% (e.g., on day 125). Hence, to better prevent crises, a holistic and dynamic perspective is essential when monitoring the performance of energy markets.
