相关论文: A Review of Matrix Algebra for Power and Energy Ap…
Hierarchical optimization architectures are used in power systems to manage disturbances and phenomena that arise at multiple spatial and temporal scales. We present a graph modeling abstraction for representing such architectures and an…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
Many optimization problems in power transmission networks can be formulated as polynomial problems with complex variables. A polynomial optimization problem with complex variables consists in optimizing a real-valued polynomial whose…
In this paper, some real-world motivated examples are provided illustrating the power of linear algebra tools as the product of matrices, determinants, eigenvalues and eigenvectors. In this sense, some practical applications related to…
Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different…
We argue that the Julia programming language is a compelling alternative to implementations in Python and C++ for common data analysis workflows in high energy physics. We compare the speed of implementations of different workflows in Julia…
The Jacobian matrix is the core part of power flow analysis, which is the basis for power system planning and operations. This paper estimates the Jacobian matrix in high dimensional space. Firstly, theoretical analysis and model-based…
The state of numerical computing is currently characterized by a divide between highly efficient yet typically cumbersome low-level languages such as C, C++, and Fortran and highly expressive yet typically slow high-level languages such as…
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
In this paper we discuss the mathematical background and the computational aspects which underly the implementation of a collection of Julia functions in the MatrixPencils package for the determination of structural properties of polynomial…
In this article we discuss the application of the Heath-Jarrow-Morton framework Heath et al. [26] to energy markets. The goal of the article is to give a detailed overview of the topic, focusing on practical aspects rather than on theory,…
Modern electric power systems have an increasingly complex structure due to rise in power demand and integration of diverse energy sources. Monitoring these large-scale systems, which relies on efficient state estimation, represents a…
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…
In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the…
In this paper, the power flow in electrical systems is modelled in the time domain by using Geometric Algebra and the Hilbert Transform. The use of this mathematical framework overcomes some of the limitations shown by the existing…
Directed mixed graphs permit directed and bidirected edges between any two vertices. They were first considered in the path analysis developed by Sewall Wright and play an essential role in statistical modeling. We introduce a matrix…
Lagrangian modelling can be used to derive mathematical models for complex power electronic converters. This approach uses scalar quantities (kinetic and potential energy) to derive models, which is simpler than using (vector-based) force…
An introduction to the density matrix renormalization group is contained here, including coding examples. The focus of this code is on basic operations involved in tensor network computations, and this forms the foundation of the DMRjulia…