Locational Marginal Pricing of Natural Gas subject to Engineering Constraints

We derive a price formation mechanism to maximize social welfare for a pipeline network that delivers natural gas from suppliers to consumers. The system is modeled as a metric graph subject to physical balance laws for steadystate hydraulic flow on edges and mass balance at nodes. The pricing mechanism incorporates engineering constraints on local pressures and energy applied by gas compressors. Optimality conditions yield expressions for locational marginal prices for gas (gLMPs) and a decomposition of gLMPs into components corresponding to energy, compression, and two types of congestion. We demonstrate that price and pressure differentials between nodes have the opposite sign, so that price cannot decline in the direction of flow, and prove that the pricing mechanism is revenue adequate. We also present computational examples of congestion pricing for a small test network and a large-scale case study.