In response to increasing environmental deterioration, the vigorous development of the integrated energy system is an important measure to achieve the goal of carbon neutrality. In order to ensure that the system takes into account the economic operation under the premise of low carbon and environmental protection, this paper proposes a bi-level optimal low-carbon economic operation model for the regional integrated energy system (RIES). At the upper level, the objective of the RIES is economic

more »

... optimization, which contains the carbon emission cost so that the system would change its preference for high-carbon energy to limit the carbon emission of the system. At the lower level, an electricity and natural gas pricing model is established, and a carbon emission flow (CEF) model is used to calculate the price of carbon emissions. This proposed bi-level optimization model is converted to a single-level mathematical problem with KKT (Karush–Kuhn–Tucker) conditions for efficient calculation. The proposed optimal model is tested on the five-bus power system and seven-node natural gas system, and numerical results indicate the optimal operating model with this proposed carbon pricing method can effectively reduce carbon emissions and minimize the total operating cost of RIES.