A systematic two-stage optimization framework for congestion locating and multi-component expansion planning in natural gas pipeline networks

As global energy demand continues to rise, natural gas pipeline systems face significant challenges, including congestion during peak demand periods and the complexities of system expansion. This paper introduces an integrated congestion identification and expansion planning framework (ICIEPF) designed to enhance the hydraulic reliability of pipeline networks. The framework integrates two key models: a physics-based congestion location model (CL-Model) and a multi-component expansion optimization model (MCEO-Model). The CL-Model employs a flow relaxation variable to precisely identify congestion points, quantifying the severity of bottlenecks and providing a deterministic foundation for targeted investments. The MCEO-Model utilizes these insights to optimize expansion strategies—considering pipeline loops, new pipelines, and compressor station upgrades—while strictly enforcing equipment operational safety. The framework utilizes a two-stage sequential optimization strategy, incorporating convex relaxation and linearization techniques to enable a high-quality warm start, thereby accelerating solution speed and minimizing costs. Case studies demonstrate that, compared with the direct solving method, the ICIEPF achieves an average computational speedup of 12.37 times. Furthermore, it reduces expansion costs by 54.8% compared to single-component expansion strategies and significantly improves the compressor safety margins. These results demonstrate the framework's potential to address complex pipeline expansion challenges while improving system reliability and operational efficiency.