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

Adjoint-based error control for the simulation and optimization of gas and water supply networks

In this work, the simulation and optimization of transport processes through gas and water supply networks is considered. Those networks mainly consist of pipes as well as other components like valves, tanks and compressor/pumping stations. These components are modeled via algebraic equations or {ODEs} while the flow of gas/water through pipelines is described by a hierarchy of models starting from a hyperbolic system of {PDEs} down to algebraic equations. We present a consistent modeling of the network and derive adjoint equations for the whole system including initial, coupling and boundary conditions. These equations are suitable to compute gradients for optimization tasks but can also be used to estimate the accuracy of models and the discretization with respect to a given cost functional. With these error estimators we present an algorithm that automatically steers the discretization and the models used to maintain a given accuracy. We show numerical experiments for the simulation algorithm as well as the applicability in an optimization framework