| 1. |
- Foskolos, Georgios, 1976-, et al.
(författare)
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The impact of aggregation interval on current harmonic simulation of aggregated electric vehicle loads
- 2020
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Ingår i: Proceedings of International Conference on Harmonics and Quality of Power, ICHQP. - : IEEE Computer Society. - 9781728136974
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Konferensbidrag (refereegranskat)abstract
- Electric vehicles (EVs) poses new challenges for the Distribution System Operator (DSO). For example, EVs uses power electronic-based rectifiers for charging their batteries, an operation that could significantly impact Power Quality (PQ) in terms of harmonic distortion. The DSO responsibilities include ensuring grid code compliance confirmed by PQ metering. In general, 10 min rms values are sufficient. However, the large scale integration of non-linear loads, like EVs, could lead to new dynamic phenomena, possibly lost in the process of time aggregation.This paper presents an analysis of the impact on time aggregation (3 s-, 1min-and 10 min rms), when modelling current harmonics of aggregated EV loads, using power exponential functions. The results indicate that, while3 s rms and 1 min rms marginally affect the outcome, 10 min rms aggregation will lead to a significant deviation (>30%) in terms of maximum current harmonic magnitude.
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| 2. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 - 9783030418502 ; , s. 761-789
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Bokkapitel (refereegranskat)abstract
- The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed visually. The extreme points of the ordinary Vandermonde determinant on finite-dimensional unit spheres are given as the roots of rescaled Hermite polynomials and a recursion relation is provided for the polynomial coefficients. Analytical expressions for these roots are also given for dimension three to seven. A transformation of the optimization problem is provided and some relations between the ordinary and generalized Vandermonde matrices involving limits are discussed.
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| 3. |
- Muhumuza, Asaph Keikara, 1975-
(författare)
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Extreme points of the Vandermonde determinant in numerical approximation, random matrix theory and financial mathematics
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis discusses the extreme points of the Vandermonde determinant on various surfaces, their applications in numerical approximation, random matrix theory and financial mathematics. Some mathematical models that employ these extreme points such as curve fitting, data smoothing, experimental design, electrostatics, risk control in finance and method for finding the extreme points on certain surfaces are demonstrated.The first chapter introduces the theoretical background necessary for later chapters. We review the historical background of the Vandermonde matrix and its determinant, some of its properties that make it more applicable to symmetric polynomials, classical orthogonal polynomials and random matrices.The second chapter discusses the construction of the generalized Vandermonde interpolation polynomial based on divided differences. We explore further, the concept of weighted Fekete points and their connection to zeros of the classical orthogonal polynomials as stable interpolation points.The third chapter discusses some extended results on optimizing the Vandermonde determinant on a few different surfaces defined by univariate polynomials. The coordinates of the extreme points are shown to be given as roots of univariate polynomials.The fourth chapter describes the symmetric group properties of the extreme points of Vandermonde and Schur polynomials as well as application of these extreme points in curve fitting.The fifth chapter discusses the extreme points of Vandermonde determinant to number of mathematical models in random matrix theory where the joint eigenvalue probability density distribution of a Wishart matrix when optimized over surfaces implicitly defined by univariate polynomials.The sixth chapter examines some properties of the extreme points of the joint eigenvalue probability density distribution of the Wishart matrix and application of such in computation of the condition numbers of the Vandermonde and Wishart matrices. The seventh chapter establishes a connection between the extreme points of Vandermonde determinants and minimizing risk measures in financial mathematics. We illustrate this with an application to optimal portfolio selection.The eighth chapter discusses the extension of the Wishart probability distributions in higher dimension based on the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions.The ninth chapter demonstrates the connection between the extreme points of the Vandermonde determinant and Wishart joint eigenvalue probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras that occur in both the discrete and continuous part of the Gindikin set.
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| 4. |
- Muhumuza, Asaph Keikara, et al.
(författare)
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Extreme points of the vandermonde determinant on surfaces implicitly determined by a univariate polynomial
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 791-818
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Bokkapitel (refereegranskat)abstract
- The problem of optimising the Vandermonde determinant on a few different surfaces defined by univariate polynomials is discussed. The coordinates of the extreme points are given as roots of polynomials. Applications in curve fitting and electrostatics are also briefly discussed.
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| 5. |
- Muhumuza, Asaph Keikara, et al.
(författare)
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Optimization of the wishart joint eigenvalue probability density distribution based on the vandermonde determinant
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 819-838
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Bokkapitel (refereegranskat)abstract
- A number of models from mathematics, physics, probability theory and statistics can be described in terms of Wishart matrices and their eigenvalues. The most prominent example being the Laguerre ensembles of the spectrum of Wishart matrix. We aim to express extreme points of the joint eigenvalue probability density distribution of a Wishart matrix using optimisation techniques for the Vandermonde determinant over certain surfaces implicitly defined by univariate polynomials.
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