When the curtailed wind power is converted to hydrogen or methane through power to hydrogen facilities (P2H) or power to methane facilities (P2M), P2G which includes P2H and P2M is the load of power system and the gas source of natural-gas system. Meanwhile, the gas-fired units are the load of natural-gas system and the generators of power system. Obviously, operation parameters of P2G, power system and natural-gas system are interrelated and interactive which can affect the operation cost, CO\({}_{2}\) emissions, reliability, and stability of both systems. Therefore, how to deal with the interactive relationship between power system and natural-gas system and how to achieve coordinated optimal operation with economic environmental benefits are the key issues for the integrated power system and natural-gas system. For the integrated electricity-natural gas energy systems, the initial research is focused on optimal power flow [12; 13; 14; 15], unit commitment [16], optimal dispatch [17; 18; 19], steady-state analysis [20], and system planning [21]. For the calculation of optimal power flow, the total operation cost is usually considered as optimal objective and the dual interior point method [12], the Monte Carlo method [13] and the point estimation method [14] are adopted frequently. Some studies introduce an energy hub to deal with the translation of different energies in the hybrid electricity-natural gas energy systems [13; 17]. For the optimization of system operation, the operation of power system and the operation of natural-gas system are mostly optimized separately using the deterministic optimization methods or stochastic optimization methods [18]. For the steady-state analysis of the hybrid electricity-natural gas energy systems, based on the steady-state analysis of power system, the analysis model of natural-gas system is realized by analogy analysis between power system and natural-gas system, and then  
Figure 1: Diagram of integrated electricity and natural-gas energy systems with power to gas (P2G). the comprehensive steady-state analysis model of hybrid electricity-natural gas energy systems is given [20]. For the optimal system planning, a chance constrained programing approach is presented to minimize the investment cost of the integrated energy systems [21]. In these studies, P2G is not considered. As the coupling operation link of the power system and natural-gas system, P2G plays a more and more important role in wind power accommodation with broad prospects and potential for energy development [22; 23; 24]. Therefore, it is necessary to carry out the research on optimal operation of integrated electricity-natural gas energy systems considering P2G. The early studies on P2G are mainly focused on technology implementation and security application [6; 25; 26; 27; 28]. Recently, although some achievements about optimal operation of integrated electricity-natural gas energy systems considering P2G have been achieved [6; 7; 8; 24; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38], it still seems to be in the exploratory stage from the following aspects. (1) Optimal objectives: The minimum total operation cost is mostly adopted [6; 24; 29; 30; 31; 32; 37]. In only a few studies, the maximum wind power accommodation [33], the minimum energy purchase cost [34], or net power demand smoothness [38] is also considered as the objective. However, environmental benefit is rarely considered. As we know, the low-carbon and emission reduction requirements become more and more important. Therefore, it is necessary to take environmental benefit into consideration. (2) Optimal models: The operation model of power system and operation model of natural-gas system are mainly established separately based on the two-level optimal power flow structure [6; 30; 31; 32]. It seems that rare consideration is given to coordinated optimization between the two energy systems.