The transmission service of small and topology-complex natural gas pipeline networks can be provided using an Entry/Exit(E/E) tariff mode. The booking of gas transmission capacity under the E/E tariff mode does not consider the path of gas flow, and is charged according to injections and/or deliveries. The input/output capacity at an entry/exit in the E/E mode is defined as the maximum flow that can be booked by the shippers. The pipeline company initially determines the tentative input/output capacities at entries/exits in the pipeline network based on experience. If there exists at least one feasible operational plan for any input/output flow combination that does not exceed the capacities at the entries/exits in the pipeline network, the initially determined input/output capacities can be published and booked by shippers. The validation of input/output capacities requires finding an operational plan for the pipeline network when the actual input/output flows are uncertain parameters. Thus, the validation problem is an uncertainty optimization problem. In this work, a two-stage robust optimization model was established to transform the validation problem with uncertain parameters into a deterministic problem of verifying the worst-case scenarios. There were several sub-models in the first stage. In each sub-model, the input and output flows at the entries and exits of a gas network were decision variables, with the corresponding uncertainty set transformed into constraints. And the objective function is to minimize the inlet pressure of each compressor or delivery station to generate the worst-case scenarios. In the second stage, the minimum inlet/delivery pressures of the compressor/delivery stations under the worst-case scenarios were verified whether they meet the lower pressure limit constraints. The input and output capacities are feasible if all the constraints are satisfied. Compared to previous capacity validation methods that based on verifying multiple scenarios, the model proposed in this study eliminated the limitation of manually selecting scenarios, ensuring that the calculation results were reliable. The results indicated that in a complex pipeline network, the gas transmission cost under the E/E mode better reflects actual costs, comparing to that under the path-based tariff mode. However, the physical gas transmission capacity of a network cannot be fully utilized under this mode in most cases, resulting in capacity wastage. Based on the input/output capacities validation model, this paper explored the feasibility of applying the E/E tariff mode in regional gas pipeline networks in China, and it could also be referred for improving the open access regime for pipeline networks.

The “X+1+X” policy in the national natural gas industry has positioned the price of natural gas as a crucial factor for the development of the downstream customer market. The sales segment, which is directly exposed to market competition, heavily relies on this pricing strategy. In response to the shortcomings of the ladder gas price settlement contract signed between the natural gas sales company and downstream customers, which does not fully consider the customers' gas purchasing ability in the process of formulation, this paper analyzes the impact of customer volume-price relationship on the ladder price, and establishes a natural gas volume-price coupled nonlinear sales optimization model of the natural gas supply chain. The model takes the maximum total benefit of the natural gas sales company as the objective function, and takes the gas volume of each link in the natural gas supply chain, the natural gas supply and sales volume as well as the customers' ladder prices as the decision variables. The constraints of the model include the upper and lower limits of the gas volume of each link, pricing adjustment space constraints for each customer, the node flow balance constraints, the constraints of customers' volume-price relationship, the constraints of the ladder price, the constraints of the type of different customer, etc. The proposed complex mixed-integer quadratic optimization model is solved using the spatial branch and bound algorithm in the GUROBI solver. This method is applied to a large-scale multi-gas source and multi-customer supply and demand system (including 10 gas sources and 121 customers) within a provincial network. Remarkably, the computation time does not exceed 5 seconds, demonstrating the high efficiency of the model and algorithms. When compared to the current sales situation with a fixed ladder pricing scheme, the optimized sales volume and gas price scheme for each customer resulted in a total benefit increase of 17.2%. This significant improvement underscores the effectiveness of the proposed model. Importantly, the model and algorithm developed in this paper can be applied to a variety of customer types, ensuring that the interests of both customers and natural gas sales companies are considered. The model has shown promising application effects and can be used to recommend price adjustment plans in cases of price reconsideration between natural gas sales companies and downstream customers, and provides a solid foundation for natural gas sales companies to formulate more effective and beneficial ladder gas price sales schemes.