## 6 Discussions  
(1) The inner stochastic optimal dispatch model provides an optimal hourly dispatch plan for the integrated power and natural gas energy system considering the uncertain wind power and carbon trading costs. Photovoltaic power generation and other types of generators can also be well integrated into this model. Wind power was chosen in this article because of its reverse peak shaving characteristics. In China, the peak period of wind power at night is at a low electricity load, and wind power is difficult to absorb. At the same time, wind power accounts for the highest installed capacity of all renewable power sources in Europe. The natural gas network is the physical constraint of the inner model, and the natural gas network constraint can be ignored in the power system dispatch where the proportion of gas generators is not high.  
(2) This paper introduces the carbon trading mechanism into the energy power system with wind power and gas generators. The construction of the bi-layer model can obtain the optimal carbon price of the regional power system under a given carbon emission reduction control target and the day-ahead dispatching plan of the system at this time. It aims to find a carbon trading price and scheduling plan that meets the lowest cost and achieves carbon emission reduction targets. However, the method in this paper can be extended to other regional cases, as follows:  
The government's regulatory authority sets the carbon emission reduction targets (\(\lambda_{redu}\)) of the energy and power systems of the corresponding regions and the free carbon quota (\(Q_{c}^{i}\)) of the carbon emission sources. Whether the allocation object of free carbon emission quota is all generators or carbon emission source generating units in the region, such as thermal power, depends on the local carbon trading policy. The free carbon emission quota is mainly determined by the free carbon emission quota coefficient per unit of electricity allocation (\(\epsilon\)), which is obtained by the weighted average of the marginal emission factor of electricity and the marginal emission factor of capacity in the area. When regional clean generators account for a relatively high proportion, such as Europe, the free carbon emission quota per unit of electricity allocation will be lower. Under strong emission reduction requirements, gas-fired generators need to purchase carbon emission rights in the carbon trading market, and cleaner generators such as carbon capture power plants and nuclear power generators will sell carbon emission rights to make profits. Taking the above-mentioned parameters in a specific area as the input of the bi-level model in this article, the optimal carbon price of carbon trading and the day-ahead dispatching plan of the system at this time can be obtained according to the idea of the bi-level model in this article. Realize the reasonable allocation of carbon resources in the regional energy power system under consideration of dispatching economy and total carbon emission control. The method in this article can provide a certain reference, but the application of a specific area should also be combined with the regional policy situation.  
Figure 12: The carbon emissions of IPGES under different free carbon emission quota coefficient.  
(3) Energy and environmental issues are very complex. This paper only considers the carbon emissions of pollutants. Relevant studies also show that the carbon emissions of the power industry and other pollutants such as SO2 have certain roots and simultaneity, and other pollutants can be roughly controlled through the control of CO2 [33; 34]. However, in a more in-depth environmental analysis, we should also consider the emissions of other pollutants in power production.