Related papers: Geometric Algebra Power Theory in Time Domain
In this paper, we examine a time-dependent family of two-dimensional algebras. We investigate the conditions under which any two algebras from this family, formed at different times, are isomorphic. Our findings reveal that the flow…
Quantifying the impact of inverter-based distributed generation (DG) sources on power-flow distribution system cases is arduous. Existing distribution system tools predominately model distributed generation sources as either negative PQ…
We show the link between U1 lattice gauge theories and the off-equilibrium thermodynamics of a large class of nonlinear oscillators networks. The coupling between the oscillators plays the role of a gauge field, or connection, on the…
Wegner's method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding…
A new graph dual formalism is presented for the analysis of line outages in electricity networks. The dual formalism is based on a consideration of the flows around closed cycles in the network. After some exposition of the theory is…
The impedances of cables and lines used in (multi-conductor) distribution networks are usually unknown or approximated, and may lead to problematic results for any physics-based power system calculation, e.g., (optimal) power flow. Learning…
In this work, we generalize the non-geometrical construction of gauge theories, due to S. Deser, to a noncommutative setting. We show that in a free theory, along with the usual local N\"{o}ther current, there is another conserved current,…
Part I of this paper embeds the AC power flow problem with voltage control and exponential load model in the complex plane. Modeling the action of network controllers that regulate the magnitude of voltage phasors is a challenging task in…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…
In this work, we investigate the heat flow of two interacting quantum systems on the perspective of noncommutativity phase-space effects and show that by controlling the new constants introduced in the quantum theory, due to a deformed…
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric…
We examine the dynamics of a free massless scalar field on a figure eight network. Upon requiring the scalar field to have a well defined value at the junction of the network, it is seen that the conserved currents of the theory satisfy…
Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associated with a time-dependent Riemannian metric by extremizing…
General physics approach is applied to analysis of power components in electrical systems under sinusoidal and non-sinusoidal conditions. Physical essence of active, reactive and distorting powers are determinate. It is shown that the all…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
Power flow calculation in EMS is required to accommodate a large and complex power system. To achieve a faster than real-time calculation, a graph based power flow calculation is proposed in this paper. Graph database and graph computing…
Geometric phases play a central role in a variety of quantum phenomena, especially in condensed matter physics. Recently, it was shown that this fundamental concept exhibits a connection to quantum phase transitions where the system…
Directed topology was introduced as a model of concurrent programs, where the flow of time is described by distinguishing certain paths in the topological space representing such a program. Algebraic invariants which respect this…
In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of `dark energy', `dark matter', and `dark flow'. Instead of assuming the existence of these theoretical concepts,…