Related papers: Geometric Algebra Power Theory in Time Domain
A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for…
This experiment demonstrates to engineering students that control system and power system theory are not orthogonal, but highly interrelated. It introduces a real-world power system problem to enhance time domain State Space Modelling (SSM)…
In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport)…
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…
This paper presents a perspective of functional analysis to analyze electric load and electricity pricing in the $L_2$ space and its isomorphic vector space, which also yields the general algebraic model of load and pricing associated with…
Classical phasor analysis is fundamentally limited to sinusoidal single-frequency conditions, which poses challenges when working in the presence of harmonics. Furthermore, the conventional solution, which consists of decomposing signals…
Power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). This complicates the analysis and mitigation of harmonics, whose creation and propagation are facilitated…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…
This paper presents exploratory investigations on the concept of generalized geometrical frequency in electrical systems with an arbitrary number of phases by using Geometric Algebra and Differential Geometry. By using the concept of…
The time-domain analysis of pulse width modulated (PWM) single-phase inverters is presented for different load circuits. It is demonstrated that this analysis can be reduced to the solution of linear simultaneous algebraic equations with…
Non-Hermitian systems exploiting the synergy between gain and loss have recently become the focus of interest to discover novel physical phenomena. The spatial symmetry breaking in such systems allows tailoring the wave propagation at will.…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We give a new approach to the study of statistical mechanical systems: algebraic topology is used to investigate the statistical distributions of stochastic currents generated in graphs. In the adiabatic and low temperature limits we will…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
Achieving robust and scalable convergence for simulation of realistic power flow cases can be challenging. One specific issue relates to the disconnected solution space that is created by the use of piecewise-discontinuous models of power…
We consider the electrodynamics of electric charges and currents in vacuum and then generalise our results to the description of a dielectric and magnetic material medium : first in spatial algebra (SA) and then in space-time algebra (STA).…
Modern power systems are at risk of largely reducing the inertia of generation assets and prone to experience extreme dynamics. The consequence is that, during electromechanical transients triggered by large contingencies, transmission of…
Synchronous generators and inverter-based resources are complex systems with dynamics that cut across multiple intertwined physical domains and control loops. Modeling individual generators and inverters is, in itself, a very involved…
The changing nature of power systems dynamics is challenging present practices related to modeling and study of system-level dynamic behavior. While developing new techniques and models to handle the new modeling requirements, it is also…