Efficient Dynamic Compressor Optimization in Natural Gas Transmission Systems

The growing reliance of electric power systems on gas-fired generation to balance intermittent sources of renewable energy has increased the variation and volume of flows through natural gas transmission pipelines. Adapting pipeline operations to maintain efficiency and security under these new conditions requires optimization methods that account for transients and that can quickly compute solutions in reaction to generator re-dispatch. This paper presents an efficient scheme to minimize compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flow. The optimization scheme relies on a compact representation of gas flow physics, a trapezoidal discretization in time and space, and a two-stage approach to minimize energy costs and maximize smoothness. The resulting large-scale nonlinear programs are solved using a modern interior-point method. The proposed optimization scheme is validated against an integration of dynamic equations with adaptive time-stepping, as well as a recently proposed state-of-the-art optimal control method. The comparison shows that the solutions are feasible for the continuous problem and also practical from an operational standpoint. The results also indicate that our scheme provides at least an order of magnitude reduction in computation time relative to the state-of-the-art and scales to large gas transmission networks with more than 6000 kilometers of total pipeline

Optimizing Nonlinear Dynamics in Energy System Planning and Control

Understanding the physical dynamics underlying energy systems is essential in achieving stable operations, and reasoning about restoration and expansion planning. The mathematics governing energy system dynamics are often described by high-order differential equations. Optimizing over these equations can be a computationally challenging exercise. To overcome these challenges, early studies focused on reduced / linearized models failing to capture system dynamics accurately. This thesis considers generalizing and improving existing optimization methods in energy systems to accurately represent these dynamics. We revisit three applications in power transmission and gas pipeline systems. Our first application focuses on power system restoration planning. We examine transient effects in power restoration and generalize the Restoration Ordering Problem formulation with standing phase angle and voltage difference constraints to enhance transient stability. Our new proposal can reduce rotor swings of synchronous generators by over 50\% and have negligible impacts on the blackout size, which is optimized holistically. Our second application focuses on transmission line switching in power system operations. We propose an automatic routine actively considering transient stability during optimization. Our main contribution is a nonlinear optimization model using trapezoidal discretization over the 2-axis generator model with an automatic voltage regulator (AVR). We show that congestion can lead to rotor instability, and variables controlling set-points of automatic voltage regulators are critical to ensure oscillation stability. Our results were validated against PowerWorld simulations and exhibit an average error in the order of 0.001 degrees for rotor angles. Our third contribution focuses on natural gas compressor optimization in natural gas pipeline systems. We consider the Dynamic Optimal Gas Flow problem, which generalizes the Optimal Gas Flow Problem to capture natural gas dynamics in a pipeline network. Our main contribution is a computationally efficient method to minimize gas compression costs under dynamic conditions where deliveries to customers are described by time-dependent mass flows. The scheme yields solutions that are feasible for the continuous problem and practical from an operational standpoint. Scalability of the scheme is demonstrated using realistic benchmark data

Optimal Control of Transient Flow in Natural Gas Networks

We outline a new control system model for the distributed dynamics of compressible gas flow through large-scale pipeline networks with time-varying injections, withdrawals, and control actions of compressors and regulators. The gas dynamics PDE equations over the pipelines, together with boundary conditions at junctions, are reduced using lumped elements to a sparse nonlinear ODE system expressed in vector-matrix form using graph theoretic notation. This system, which we call the reduced network flow (RNF) model, is a consistent discretization of the PDE equations for gas flow. The RNF forms the dynamic constraints for optimal control problems for pipeline systems with known time-varying withdrawals and injections and gas pressure limits throughout the network. The objectives include economic transient compression (ETC) and minimum load shedding (MLS), which involve minimizing compression costs or, if that is infeasible, minimizing the unfulfilled deliveries, respectively. These continuous functional optimization problems are approximated using the Legendre-Gauss-Lobatto (LGL) pseudospectral collocation scheme to yield a family of nonlinear programs, whose solutions approach the optima with finer discretization. Simulation and optimization of time-varying scenarios on an example natural gas transmission network demonstrate the gains in security and efficiency over methods that assume steady-state behavior

Pressure Fluctuations in Natural Gas Networks caused by Gas-Electric Coupling

The development of hydraulic fracturing technology has dramatically increased the supply and lowered the cost of natural gas in the United States, driving an expansion of natural gas-fired generation capacity in several electrical inter-connections. Gas-fired generators have the capability to ramp quickly and are often utilized by grid operators to balance intermittency caused by wind generation. The time-varying output of these generators results in time-varying natural gas consumption rates that impact the pressure and line-pack of the gas network. As gas system operators assume nearly constant gas consumption when estimating pipeline transfer capacity and for planning operations, such fluctuations are a source of risk to their system. Here, we develop a new method to assess this risk. We consider a model of gas networks with consumption modeled through two components: forecasted consumption and small spatio-temporarily varying consumption due to the gas-fired generators being used to balance wind. While the forecasted consumption is globally balanced over longer time scales, the fluctuating consumption causes pressure fluctuations in the gas system to grow diffusively in time with a diffusion rate sensitive to the steady but spatially-inhomogeneous forecasted distribution of mass flow. To motivate our approach, we analyze the effect of fluctuating gas consumption on a model of the Transco gas pipeline that extends from the Gulf of Mexico to the Northeast of the United States.Comment: 10 pages, 7 figure