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One of the most common control decisions faced by power system operators is the question of how to dispatch generation to meet demand for power. This is a complex optimization problem that includes many nonlinear, non convex constraints as…
Incorporating renewable energy sources into modern power grids has significantly decreased system inertia, which has raised concerns about power system vulnerability to disturbances and frequency instability. The conventional methods for…
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this…
Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the…
Large-scale integration of renewables in power systems gives rise to new challenges for keeping synchronization and frequency stability in volatile and uncertain power flow states. To ensure the safety of operation, the system must maintain…
Stability of inviscid shear shallow water flows with free surface is studied in the framework of the Benney equations. This is done by investigating the generalized hyperbolicity of the integrodifferential Benney system of equations. It is…
The study of the response of amorphous materials to oscillatory strain is traditionally performed with many repeated cycles. We argue that it pays to consider carefully just one cycle (and may be a second), to reveal the rich physics that…
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
The objective of this paper is to improve the accuracy and robustness of optimal power flow (OPF) formulations for distribution systems modeled down to the low-voltage point of connection of individual buildings. An approach for addressing…
Optimization problems that involve topology optimization in scenarios with large scale outages, such as post-disaster restoration or public safety power shutoff planning, are very challenging to solve. Using simple power flow…
In this paper, we consider a chance-constrained formulation of the optimal power flow problem to handle uncertainties resulting from renewable generation and load variability. We propose a tuning method that iterates between solving an…
Power flow in a low voltage direct current grid (LVDC) is a non-linear problem just as its counterpart ac. This paper demonstrates that, unlike in ac grids, convergence and uniqueness of the solution can be guaranteed in this type of grids.…
We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i)…
Flexible transmission line impedances on one hand are a promising control resource for facilitating grid flexibility, but on the other hand add much complexity to the concerned optimization problems. This paper develops a convexification…
The coordination of cascading hydropower systems represents a fundamental challenge in modern energy systems engineering, requiring a sophisticated balance between multi-reservoir physics, stringent environmental regulations, and dynamic…
Robust network flows are a concept for dealing with uncertainty and unforeseen failures in the network infrastructure. They and their dual counterpart, network flow interdiction, have received steady attention within the operations research…
The method of flow tracing follows the power flow from net-generating sources through the network to the net-consuming sinks, which allows to assign the usage of the underlying transmission infrastructure to the system participants. This…
We derive the branch ampacity constraint associated to power losses for the convex optimal power flow (OPF) model based on the branch flow formulation. The branch ampacity constraint derivation is motivated by the physical interpretation of…
We formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…