Battery as a lifter: Decoupling energy efficiency from deep tunneling in metro vertical alignment

Energy-saving vertical alignment (VA) design for underground metro systems favors deep V-shaped profiles that exploit gravitational potential energy, yet deeper tunnels are typically associated with greater construction effort, drainage burden, and flood vulnerability. This paper investigates whether regenerative braking train control (RBTC) with onboard energy storage devices (OESDs) can decouple this trade-off, enabling shallower alignments without sacrificing energy performance. We formulate the joint VA–RBTC design as a bi-objective mixed-integer linear program that simultaneously minimizes bidirectional net energy consumption and alignment buried depth. The Pareto frontier is traced via a depth-budgeted ɛ-constraint framework, supported by logic-based cuts, convex reformulation, and a shallow-to-deep sweep algorithm with warm starting and bound refinement. We test the model on a real-world section of Chengdu Metro Line 4 across four OESD technologies, five running-time settings, and three cyclic State-of-Energy (SOE) levels. For this section, the high-power flywheel and supercapacitor substantially decouple the energy–depth relationship, achieving average decoupling ratios of 58% and 44%, respectively; meanwhile, the marginal energy benefit of excavation beyond 12m drops to near zero. These findings indicate that, in the studied setting, the conventional energy–depth coupling is largely an artifact of neglecting regenerative braking, and that high-power OESDs can break it, enabling metro alignments that are simultaneously energy-efficient and shallower.