A compact star model formed by quintessence and ordinary matter is presented, both sources have anisotropic pressures and are described by linear state equations, also the state equation of the tangential pressure for the ordinary matter incorporates the effect of the quintessence. It is shown that depending on the compactness of the star $u=GM/c^{2}R$ the constant of proportionality $\mu$ between the density of the ordinary matter and the radial pressure, $P_r=\mu c^2(\rho -{\rho }_b)$ , has an interval of values which is consistent with the possibility that the matter is formed by a mixture of particles like quarks, neutrons and electrons and not only by one type of them. The geometry is described by the Durgapal metric for $n=5$ and each one of the pressures and densities is positive, finite and monotonic decreasing, as well as satisfying the condition of causality and of stability $v_t^2-v_r^2<0$ , which makes our model physically acceptable. The maximum compactness that we have is $u\le 0.28551$ , so we can apply our solution considering the observational data of mass and radii $M=(2.01\pm 0.04)M_{\odot }$ , $R\in [12.062,12.957]$ km which generate a compactness $0.22448\le u\le 0.25448$ associated to the star PSR J0348$$ +$$ 0432. In this case, the interval of $\mu \in [0.78055,1]$ and its maximum central density ${\rho }_c$ and in the surface ${\rho }_b$ of the star are ${\rho }_c=7.0387\times 10^{17}\mathrm{\text{kg}}/{\mathrm{\text{m}}}^3$ and ${\rho }_b=4.6807\times 10^{17}\mathrm{\text{kg}}/{\mathrm{\text{m}}}^3$ , respectively, meanwhile the central density of the quintessence ${\rho }_{qc}=3.4792\times 10^{16}\mathrm{\text{kg}}/{\mathrm{\text{m}}}^3$ .

Starting from the construction of a solution for Einstein’s equations with a perfect fluid for a static spherically symmetric spacetime, we present a model for stars with a compactness rate of $u\le 0.114508$ . The model is physically acceptable, that is to say, its geometry is non-singular and does not have an event horizon, pressure and speed of sound are bounded functions, positive and monotonically decreasing as function of the radial coordinate, also the speed of sound is lower than the speed of light. While it is shown that the adiabatic index $\gamma >14.615$ , which guarantees the stability of the solution. In a complementary manner, numerical data are presented considering the star PSR J0737-3039A with observational mass of $1.3381M_{\odot }$ , for the value of compactness $0.105395$ , which implies the radius $R=18745.32\mathrm{\text{m}}$ and the range of the density ${\rho }_b=0.931561\times 10^{17}{\mathrm{\text{kg/m}}}^3$ $\le \rho \le 1.012207\times 10^{17}{\mathrm{\text{kg/m}}}^3={\rho }_c$ , where ${\rho }_c$ and ${\rho }_b$ are the central density and the surface density, respectively. This range is consistent with the expected values; as such, the model presented allows to describe this type of stars.

This paper proposes a hybrid active power filter for harmonic current mitigation in nonlinear loads. The hybrid system is composed of a shunt passive filter and an Active Power Filter (APF). The reactive power compensation is achieved by shunt passive filter banks. The scheme presented allows the reduction in size of the active power filter converter, as compared with the needs of a conventional active power filter. The instantaneous reactive power theory is used for this purpose as strategy of control to compensation in three-phase nonlinear loads, This control method allows a simple and effective way to determine compensation currents and achieve a remarkable performance in terms of harmonic mitigation. The authors present the modeling of shunt active power filter, and the simulation results obtained with MATLAB/Simulink®.

In this contribution, a harmonic domain (HD) model of grid-connected photovoltaic (PV) generation systems is proposed. The topology of the PV generation system contains a PV array connected to a DC/DC converter and a DC/AC converter, coupled to the grid through a filter. The individual components of the PV system are modeled in the HD. The PV array is represented as a Thevenin equivalent, whereas the DC/DC converter and the DC/AC converter are represented in the HD using switching function matrices. The periodic steady-state solution of the PV system is obtained through simple matrix/vector operations. The results obtained by the proposed model are validated against the response obtained with the PSCAD/EMTDC^® simulator, widely accepted by the power industry.

This paper proposes a Shunt Active Power Filter (SAPF) for harmonic mitigation based a selective harmonic current mitigation (SHCM) method. The proposed SHCM method improves the filtering efficiency and solves many issues existing in highly contaminated loads. The Fast Fourier Transform (FFT) is applied to a specific harmonic current detection of a three-phase circuit. A simulation study of a three-phase compensated system is carried out using Matlab/Simulink ^® to validate the proposed method.