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Center for Nonlinear Studies |
New emissions restrictions, the resulting push towards cleaner electric power, and increased supplies of natural gas have led to the installation of gas-fired power plants for most new generating capacity over the past 15 years. The growing interaction between electric power and natural gas infrastructures, which operate on different spatiotemporal scales, adds volume and volatility to gas consumption that significantly impacts gas network dynamics, causes gas price fluctuation, and thus affects electric generator dispatch and electricity prices. These disruptive challenges invalidate traditional operations and compel practical techniques for coordinated management of these systems, which requires a multidisciplinary approach from physics, mathematics, and engineering. I will present a model for compressible gas dynamics in pipeline networks with time-varying injections and pressure regulators. The 1D Euler PDE equations on each pipe segment, together with the set of boundary conditions, are simplified and reduced to a nonlinear ODE model that resolves the dynamics for conditions and time-scales of interest with accuracy comparable to traditional numerical PDE methods. I use the model to form dynamic constraints for computational solutions of optimal control problems involving gas networks, in which pseudospectral collocation schemes are used to represent functional optimizations as large-scale nonlinear programs. The efficient simulation technique and optimization method provide a practical, physics-based, tractable, reliable, and scalable framework for analysis and control of transient dynamics in gas pipeline systems. Infrastructure interaction problems arise during gas shortages on the coldest days, when gas utilities use their entire contracted capacity to meet heating demands, so deliveries to power generators with non-firm contracts get cut off. Electric generators are currently dispatched to meet power demands without using information about gas transmission systems, which are operated using steady-state assumptions and local controllers that cause instabilities to cascade system-wide. As a solution, I propose adjoining the dynamic gas network model and gas system limits as constraints to the day-ahead optimal power flow dispatch. I will show that such model-predictive power flow planning is tractable for various levels of integration of gas system information, from simulation to combined optimal control.
Host: Jeffrey D. Hyman