Coordination of Power and Natural Gas Systems: Convexification Approaches for Linepack Modeling

Utilizing operational flexibility from natural gas networks can foster the integration of uncertain and variable renewable power production. We model a combined power and natural gas dispatch to reveal the maximum potential of linepack, i.e., energy storage in the pipelines, as a source of flexibility for the power system. The natural gas flow dynamics are approximated by a combination of steady-state equations and varying incoming and outgoing flows in the pipelines to account for both natural gas transport and linepack. This steady-state natural gas flow results in a nonlinear and nonconvex formulation. To cope with the computational challenges, we explore convex quadratic relaxations and linear approximations. We propose a novel mixed-integer second-order cone formulation including McCormick relaxations to model the bidirectional natural gas flow accounting for linepack. Flexibility is quantified in terms of system cost compared to a dispatch model that either neglects linepack or assumes infinite storage capability.