Related papers: Exploiting Symmetry in the Power Flow Equations Us…
For a subvariety of a smooth projective variety, consider the family of smooth hypersurfaces of sufficiently large degree containing it, and take the quotient of the middle cohomology of the hypersurfaces by the cohomology of the ambient…
One common type of symmetry is when values are symmetric. For example, if we are assigning colours (values) to nodes (variables) in a graph colouring problem then we can uniformly interchange the colours throughout a colouring. For a…
Applications of the monodromy transform approach to construction of exact solutions of electrovacuum Einstein - Maxwell field equations are considered. Examples of new solutions are given.
The large penetration of distributed generations impacts both the secondary low-voltage (LV) and the primary medium-voltage (MV) segments of the distribution network. Optimizing power flow calculations for the integrated MV/LV networks is…
Recent advances have shown that the circuit simulation algorithms that allow for solving highly nonlinear circuits of over one billion variables can be applicable to power system simulation and optimization problems through the use of an…
Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…
We consider balanced flows in a natural gas transmission network and discuss computationally hard problems such as establishing if solution of the underlying nonlinear gas flow equations exists, if it is unique, and finding the solution.…
It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
We develop an algorithm that computes for a given undirected or directed network with flow-dependent piece-wise linear edge cost functions all Wardrop equilibria as a function of the flow demand. Our algorithm is based on Katzenelson's…
The solution to an optimal power flow (OPF) problem provides a minimum cost operating point for an electric power system. The performance of OPF solution techniques strongly depends on the problem's feasible space. This paper presents an…
Full-physics modeling of multiphase flow in porous media, e.g., for carbon storage and groundwater management, requires the nonlinear coupling of various physical processes. Industry standard nonlinear solvers, typically of Newton-type, are…
Synthesis problems for linkages in kinematics often yield large structured parameterized polynomial systems which generically have far fewer solutions than traditional upper bounds would suggest. This paper describes statistical models for…
Transmission system operators need to adapt their decision-making tools to the technological evolutions of the twenty first century. A computation inherent to most tools seeks to find alternating-current power flows that minimize power loss…
Formulating the alternating current optimal power flow (ACOPF) as a polynomial optimization problem makes it possible to solve large instances in practice and to guarantee asymptotic convergence in theory.
We link regularity and smoothness analysis of multivariate vector subdivision schemes with network flow theory and with special linear optimization problems. This connection allows us to prove the existence of what we call optimal…
The monodromy transform and corresponding integral equation method described here give rise to a general systematic approach for solving integrable reductions of field equations for gravity coupled bosonic dynamics in string gravity and…
We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…
The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and…
Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation,…