###### Abstract
So far, however, the general energy hub models seldom consider the influence of system uncertainties, which greatly reduce the practical application effect of the model. In the interaction process with the external multi-energy market, the role of the electric-gas interconnection system is not only the energy producer, but also the energy consumer [15]. When its internal energy supply cannot meet demand, it will purchase energy from the external natural gas market or the power market, and when its internal energy supply exceeds the demand, it can sell the surplus to the natural gas market or the power market. The particularity of its positioning makes its bidding behavior different from that of the traditional generation side or the user side market [11; 12; 13; 14; 15]. Meanwhile, due to the fact that the electric-gas interconnection system can flexibly participate in the purchase and sale of energy in the multi-energy system, it is necessary to make a coordinated bidding decision in the multi-energy market. So far, there have been many research works on the bidding strategy optimization for both generation side or user side in the power system, and the bidding decision-making subjects mainly include single energy generator, joint generator of renewable energy and traditional energy, joint generator of renewable energy and energy conversion unit, virtual power plant considering demand side resources, electricity seller of multi-type load aggregation, large consumer, micro-grid subject of paralleling in the network or off-network flexibly, etc.. All the bidding decision-making subjects except the micro-grid only participate in market transactions as a single buyer or a single seller. Due to the limitations of the decision-making subjects and market background, there are few studies on the optimization of energy bidding decision-making which consider the duality of the multi energy system's identity in the market and the differences of the multi energy market. When research into the bidding decision-making optimization method is carried out, according to the treatment of uncertain variables, optimization methods can be generally divided into two categories: stochastic optimization and robust optimization [16]. Stochastic optimization, depending on the probability distribution of uncertain variables, can transform uncertain optimization problems into deterministic optimization problems by describing the continuous or discrete probability distribution characteristics of uncertain variables. However, there are many problems in this method, such as the fact that it easily falls into dimension disaster, a high accuracy requirement for probability estimation, poor anti-noise ability and so on. Robust optimization is an optimization method that considers the influence of the worst-case on system decision-making. Compared with stochastic optimization, robust optimization focuses on the boundary condition of uncertain variables, so it is not necessary to obtain the accurate probability distribution of uncertain variables, and its conservatism can be controlledby adjusting the scale of uncertainty set [17]. A robust optimization method can effectively solve the problems such as high sensitivity of the model to the parameters and large influence of parameter estimation error on the model, which is widely used in the power system unit commitment [18] and economic dispatch [19; 20; 21], but seldom used in the multi-energy system. Based on the above background, this paper proposes a robust optimization model of energy purchase and sale for the electric-gas interconnection system in the multi-energy market. Firstly, the basic structure of the electric-gas interconnection system is introduced, and the steady-state model of energy flow in the system is built based on the energy hub model.