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18 pages, 436 KiB

Open AccessArticle

by Tekin Dereli, Philippe Nounahon and Todor Popov

Universe 2024, 10(4), 172; https://doi.org/10.3390/universe10040172 - 7 Apr 2024

Cited by 2 | Viewed by 2132

The Landau problem and harmonic oscillator in the plane share a Hilbert space that carries the structure of Dirac’s remarkable

s o (2, 3)

representation. We show that the orthosymplectic algebra

o s p (1 | 4)

is [...] Read more.

The Landau problem and harmonic oscillator in the plane share a Hilbert space that carries the structure of Dirac’s remarkable

s o (2, 3)

representation. We show that the orthosymplectic algebra

o s p (1 | 4)

is the spectrum generating algebra for the Landau problem and, hence, for the 2D isotropic harmonic oscillator. The 2D harmonic oscillator is in duality with the 2D quantum Coulomb–Kepler systems, with the

o s p (1 | 4)

symmetry broken down to the conformal symmetry

s o (2, 3)

. The even

s o (2, 3)

submodule (coined Rac) generated from the ground state of zero angular momentum is identified with the Hilbert space of a 2D hydrogen atom. An odd element of the superalgebra

o s p (1 | 4)

creates a pseudo-vacuum with intrinsic angular momentum 1/2 from the vacuum. The odd

s o (2, 3)

-submodule (coined Di) built upon the pseudo-vacuum is the Hilbert space of a magnetized 2D hydrogen atom: a quantum system of a dyon and an electron. Thus, the Hilbert space of the Landau problem is a direct sum of two massless unitary

s o (2, 3)

representations, namely, the Di and Rac singletons introduced by Flato and Fronsdal. Full article

(This article belongs to the Special Issue The Languages of Physics—A Themed Issue in Honor of Professor Richard Kerner on the Occasion of His 80th Birthday)

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17 pages, 4945 KiB

Open AccessFeature PaperArticle

MMC-Based PV Single-Phase System with Distributed MPPT

by Simone Barcellona, Marzio Barresi and Luigi Piegari

Energies 2020, 13(15), 3964; https://doi.org/10.3390/en13153964 - 1 Aug 2020

Cited by 14 | Viewed by 3722

Abstract

The presence and evolution of static power converters in electric grids are growing on a daily basis. Starting from the most used voltage source converter (VSC), passing through the use of multilevel converters, the most recent configuration is the so-called modular multilevel converter (MMC). Because of its intrinsic advantages, it is used not only in high-voltage systems but also in low- and medium-voltage ones to interface renewable energy sources such as photovoltaic (PV) panels. Several configurations and maximum power point tracker (MPPT) algorithms have been proposed and analyzed for MMC-PV-based systems. However, when using distributed MPPTs, partial shading conditions cause a problem. The PV panel can be directly connected to the MMC using its dc link or submodule. Based on this configuration, this paper proposes a novel control strategy that tracks both the ac grid current and ac circulating current for a single-phase low-voltage system to obtain the maximum power under any irradiance condition. The effectiveness of the proposed control strategy is demonstrated through time-domain simulation results. Full article

(This article belongs to the Special Issue Recent Advances in Photovoltaic Systems Operation and Maintenance (O&M))

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11 pages, 277 KiB

Open AccessArticle

The Recognition of the Bifurcation Problem with Trivial Solutions

by Yanqing Li, Dejian Huang and Donghe Pei

Symmetry 2019, 11(7), 935; https://doi.org/10.3390/sym11070935 - 17 Jul 2019

Viewed by 1961

Abstract

This paper studies the recognition criterion of the bifurcation problem with trivial solution. The t-equivalence is different from the strong equivalence studied by Golubitsky et al. The difference is that the second component of the differential homeomorphism is not identical. Consider the [...] Read more.

P (h)

. In addition, we also explore the properties of intrinsic submodules and the finite determinacy of the bifurcation problem. Full article

30 pages, 5251 KiB

Open AccessArticle

A Novel Hybrid Interval Prediction Approach Based on Modified Lower Upper Bound Estimation in Combination with Multi-Objective Salp Swarm Algorithm for Short-Term Load Forecasting

by Jiyang Wang, Yuyang Gao and Xuejun Chen

Energies 2018, 11(6), 1561; https://doi.org/10.3390/en11061561 - 14 Jun 2018

Cited by 68 | Viewed by 4422

Abstract

Effective and reliable load forecasting is an important basis for power system planning and operation decisions. Its forecasting accuracy directly affects the safety and economy of the operation of the power system. However, attaining the desired point forecasting accuracy has been regarded as a challenge because of the intrinsic complexity and instability of the power load. Considering the difficulties of accurate point forecasting, interval prediction is able to tolerate increased uncertainty and provide more information for practical operation decisions. In this study, a novel hybrid system for short-term load forecasting (STLF) is proposed by integrating a data preprocessing module, a multi-objective optimization module, and an interval prediction module. In this system, the training process is performed by maximizing the coverage probability and by minimizing the forecasting interval width at the same time. To verify the performance of the proposed hybrid system, half-hourly load data are set as illustrative cases and two experiments are carried out in four states with four quarters in Australia. The simulation results verified the superiority of the proposed technique and the effects of the submodules were analyzed by comparing the outcomes with those of benchmark models. Furthermore, it is proved that the proposed hybrid system is valuable in improving power grid management. Full article

(This article belongs to the Special Issue Short-Term Load Forecasting by Artificial Intelligent Technologies)

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