Pipe Sharing: A Bilevel Optimization Model for the Optimal Capacity Allocation of Natural Gas Network

The liberalization reform of the natural gas market has decoupled gas trading from storage and transportation services and introduced the new role, namely shippers. The shippers book network capacity from pipeline network operators (PNOs) by signing capacity contracts and nominate the gas of injection and withdraw in the day-ahead market. The PNOs then validate the feasibility of nominations and optimize the operation plan of gas network. How to efficient allocate the network capacity has become a new challenging subject due to the need to coordinate the interests of multiple market participants, including producers, merchants, local distribution companies and others. To address this issue, this paper established a bilevel optimization model for the optimal allocation of network capacity. Two approaches are proposed: (i) a single-level reformulation-based method (KKT reformulation), used as a benchmark, where a tailored outer approximation (OA) method is applied to handle the nonlinear constraints; (ii) a distributed method where a variant of Inexact-ADMM is proposed by exploiting the separable structure of coupling constraints. Case studies are performed on a real-life 352-node gas network. Initially, the proposed method is tested by a simplified 139-node gas network, showing that the solution speed of Inexact ADMM is 27.51 and 28.23 times faster than that of KKT-based method in two typical cases, while the objective value of the whole system only increased by 0.41% and 0.38%. Then, the Inexact-ADMM is successfully implemented in the whole size of the 352-node gas network by further decoupling the upper-level PNOs model into several sub-models. The maximal relative error of hydraulic was <0.4% in Case 1 and 0.7% in Case 2. This study demonstrates that the proposed ADMM-based distributed algorithm can guarantee the pipeline operation, safely and efficiently, by determining the suitable bookable capacities of the shippers.