Study of power management of standalone DC microgrids with battery supercapacitor hybrid energy storage system

<p>In the last years, renewable energy (RE) is increasing widely in the energy sector, and microgrid technology is overgrowing. In this paper, stand-alone microgrid using solar photovoltaic (PV) energy as a source of renewable energy is simulated to provide power for direct current (DC) loads with hybrid energy storage system (HESS) which consists of battery and supercapacitor bank. The proposed microgrid system is tested under various cases of load and variable irradiance to confirm and validate the proposed management strategy to remain the DC bus voltage within a stable limit. The performance of DC microgrid is comparing with and without supercapacitor (SC) bank and notes a desirable decrease in the magnitude of transient voltage when using HESS. The sun power SPR-E19-320 standard was simulated to analyze system performance taking into account the constant load demand. Note that HESS helps reduce transient of DC voltage very effectively in all situations. Very large transients arise due to sudden changes in load demand is also compensated by HESS. The results obtained indicate that the stand-alone DC microgrid with HESS is very beneficial for reducing transient of DC-link voltage that occurs due to sudden change in load or fault. The proposed system is performed by MATLAB/Simulink environment.</p>

Analysis of A Coendemic Model of COVID-19 and Dengue Disease

The coronavirus disease 2019 (COVID-19) pandemic continues to spread aggressively worldwide, infecting more than 170 million people with confirmed cases, including more than 3 million deaths. This pandemic is increasingly exacerbating the burden on tropical and subtropical regions of the world due to the pre-existing dengue fever, which has become endemic for a longer period in the same region. Co-circulation dengue and COVID-19 cases have been found and confirmed in several countries. In this paper, a deterministic model for the coendemic of COVID-19 and dengue is proposed. The basic reproduction ratio is obtained, which is related to the four equilibria, disease-free, endemic-COVID-19, endemic-dengue, and coendemic equilibria. Stability analysis is done for the first three equilibria. Furthermore, a condition for coexistence equilibrium is obtained, which gives a condition for bifurcation analysis. Numerical simulations were carried out to obtain a stable limit-cycle resulting from two Hopf bifurcation points with dengue transmission rate and COVID-19 transmission rate as the bifurcation parameter, representing a stable periodic coexistence of dengue and COVID-19 transmission. We identify the period of limit cycle decreases after reaching the maximum value.

Bifurcation analysis of the predator–prey model with the Allee effect in the predator

The use of predator–prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka–Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be subject to an Allee effect, where the per capita growth rate increases with the population density. Including an Allee effect has been shown to fundamentally change predator–prey dynamics and strongly impact species persistence, but previous studies mostly focused on scenarios of an Allee effect in the prey population. Here we explore a predator–prey model with an ecologically important case of the Allee effect in the predator population where it occurs in the numerical response of predator without affecting its functional response. Biologically, this can result from various scenarios such as a lack of mating partners, sperm limitation and cooperative breeding mechanisms, among others. Unlike previous studies, we consider here a generic mathematical formulation of the Allee effect without specifying a concrete parameterisation of the functional form, and analyse the possible local bifurcations in the system. Further, we explore the global bifurcation structure of the model and its possible dynamical regimes for three different concrete parameterisations of the Allee effect. The model possesses a complex bifurcation structure: there can be multiple coexistence states including two stable limit cycles. Inclusion of the Allee effect in the predator generally has a destabilising effect on the coexistence equilibrium. We also show that regardless of the parametrisation of the Allee effect, enrichment of the environment will eventually result in extinction of the predator population.

Comparison Between Different Growth Functions of the Jatropha Curcas Plant with Random Attack Pattern of Whitefly

We have proposed here two deterministic models of Jatropha Curcas plant and Whitefly that simulate the dynamics of interaction between them where the distribution of Whitefly on plant follows Poisson distribution.In the first model growth rate of the plant is assumed to be in logistic form whereas in the second model it is taken as exponential form. The attack pattern and the growth of the whitefly are assumed as Holling type II function.The first model results a globally stable state and in the second one we find a globally attracting steady state for some parameter values,and a stable limit cycle for some other parameter values. It is also shown that there exist Hopf bifurcation with respect to some parameter values. The paper also discusses the question about persistence and permanence of the model. It is found that the specific growth rate of both the population and attack pattern of the whitefly governs the dynamics of both the models.

Regularization of Planar Piecewise Smooth Systems with a Heteroclinic Loop

In this paper, we study bifurcations of the regularized systems of planar piecewise smooth systems, which have a visible fold-regular point and a sliding or grazing heteroclinic loop. Our results show that if the planar piecewise smooth system with a sliding heteroclinic loop undergoes sliding heteroclinic bifurcation, then the regularized system can bifurcate with a stable limit cycle passing through the regularized region and at most two limit cycles outside the regularized region. The regularized system can have at most three periodic orbits. When the upper subsystem is a Hamiltonian system, the regularized system can bifurcate with a semi-stable periodic orbit. Finally, we discuss two cases when the heteroclinic loop of a piecewise smooth system remains unbroken under a small perturbation. Our results show that the regularized system can bifurcate at most two limit cycles from an inner unstable grazing heteroclinic loop.

Asymptotics for the number of standard tableaux of skew shape and for weighted lozenge tilings

We prove and generalise a conjecture in [MPP4] about the asymptotics of $\frac{1}{\sqrt{n!}} f^{\lambda/\mu}$ , where $f^{\lambda/\mu}$ is the number of standard Young tableaux of skew shape $\lambda/\mu$ which have stable limit shape under the $1/\sqrt{n}$ scaling. The proof is based on the variational principle on the partition function of certain weighted lozenge tilings.

Study of internal oscillations in a dynamic system through an external signal implemented in circadian rhythms

Through the analysis carried out on a dynamic model that is represented as a system of ordinary differential equations that describes the behavior of the circadian cycles; we will show and analyze in the next document what are the conditions that allow the synchronization of the circadian clock oscillator with the external modification oscillator. The implementation of this type of techniques in anatomical problems is highlighted, which are rare in the literature. The implementations will be carried out through different simulations using numerical techniques and the way in which we will determine the coupling conditions of an internal cycle of the system versus external cycles will be detailed. In the final development of this work, we will be able to see in the model without an external modification signal the existence of stable limit cycles and discover the moment in which the synchronization of the internal oscillator and the external modification signal occurs. These types of problems are common when making biological models that are described by a physical analysis.

Modeling of Chaotic Processes by Means of Antisymmetric Neural ODEs

The main goal of this work is to construct an algorithm for modeling chaotic processes using special neural ODEs with antisymmetric matrices (antisymmetric neural ODEs) and power activation functions (PAFs). The central part of this algorithm is to design a neural ODEs architecture that would guarantee the generation of a stable limit cycle for a known time series. Then, one neuron is added to each equation of the created system until the approximating properties of this system satisfy the well-known Kolmogorov theorem on the approximation of a continuous function of many variables. In addition, as a result of such an addition of neurons, the cascade of bifurcations that allows generating a chaotic attractor from stable limit cycles is launched. We also consider the possibility of generating a homoclinic orbit whose bifurcations lead to the appearance of a chaotic attractor of another type. In conclusion, the conditions under which the found attractor adequately simulates the chaotic process are discussed. Examples are given.