**2. Theoretical Framework**

A thorough analysis of the mechanism of evolution can reveal the internal structure of the natural gas and electricity markets, their interactions and the associated risks to facilitate the risk assessment of coupled markets. The key risk factors and dual interactions are depicted, with illustrative examples from real-world accidents. These risks and interactions were determined on the basis of the relevant literature, by tracking news stories and through expert interviews.

#### *2.1. Risk Evolution Mechanism*

Taking a systematic perspective, a risk evolution mechanism of a coupled natural gas– electricity market is presented in Figure 1. The risk system, the natural gas system and the electricity system constitute a massive system-of-systems (SoS) [35,36], in which multiple components in each market, multiple risks and multiple interactions among the risk factors and market interactions interweave and evolve simultaneously. A key component of assessing the impact of specific risks on the overall SoS is to quantify their potential impact and aggregate the cascading disruptions induced by the interactions. To better understand the development and characteristics of the complex risk evolution process, each system and the interactive effects can be described as follows.

**Figure 1.** Mechanism of risk evolution in a coupled natural gas–electricity market.

Each market can be viewed as a collection of components functioning to achieve the common goal of satisfying market demand. In a natural gas market, gas utilization may be diverse, with electricity generation accounting for one of the major demands [1]. Natural gas is derived from multiple sources, including international trade and domestic production. An electricity market must satisfy the electricity demand of residents and industries. A diverse portfolio of fuels serves to supply the electricity, including natural gas, oil, coal, wind, etc. As natural gas is the primary focus of this study, the other categories of fuel were classified as "other fuels" in terms of the total proportion of electricity generation.

Nonetheless, the stochastic occurrence of unanticipated risks may result in market chaos [35]. These risk factors may emerge externally or internally, interact with each other and experience a rise or a decline during a certain period. The market's reactions may create counterintuitive side effects and cause the emergence of new risk factors [11]. Distinct bidirectional interactions among the facilities from different markets also act as the most prominent feature of the mechanism, as these are at the core of the complex risk assessment process. Through these interactions, excessive risks on one market may cause system inefficiency and then be transferred to another market. For instance, natural disasters or attacks may damage part of the gas production facilities, resulting in a severe shortage in the gas supply, which, in turn, would reduce the gas needed for supplying electricity and hinder the electricity system.
