Adding new capacity expansion alternatives using distributed generation (DG) technologies, particularly penetration of renewable energy, has several economical, and technical advantages such as the reduced system costs, the improved voltage profile, lower line loss and enhanced system's reliability. However, the DG units may lead to power quality, energy efficiency, and protection problems in the system when their penetration exceeds a particular value, generally called as the system's hosting capacity (HC) in the literature. In this paper, the HC determination of a distorted distribution system with Photovoltaic (PV)-based DG units is handled as an optimization problem by considering over and under voltage limitations of buses, current carrying capabilities of the lines, and harmonic distortion limitations as constraints. It is seen from simulation results that the HC is dramatically decreased with the increament of the load's nonlinearity level and the utility side's background voltage distortion. Accordingly, a C-type passive filter is designed to maximize the harmonic-constrained HC of the studied system while satisfying the constraints. The results indicate that higher HC level can be achieved using the proposed filter design approach compared to three conventional filter design approaches as voltage total harmonic distortion minimization, line loss minimization and power factor maximization.

In this paper, we establish the exact relationship between the continuous and the discrete phase difference of two shifted images, and show that their discrete phase difference is a two-dimensional sawtooth signal. Subpixel registration can, thus, be performed directly in the Fourier domain by counting number of cycles of the phase difference matrix along each frequency axis. The subpixel portion is given by the noninteger fraction of the last cycle along each axis. The problem is formulated as an overdetermined homogeneous quadratic cost function under rank constraint for the phase difference, and the shape constraint for the filter that computes the group delay. The optimal tradeoff for imposing the constraints is determined using the method of generalized cross validation. Also, in order to robustify the solution, we assume a mixture model of inlying and outlying estimated shifts and truncate our quadratic cost function using expectation maximization.

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Voltage sags can be symmetrical or unsymmetrical depending on the causes of the sag. At the present time, one of the most common procedures for mitigating voltage sags is by the use of dynamic voltage restorers (DVRs). By definition, a DVR is a controlled voltage source inserted between the network and a sensitive load through a booster transformer injecting voltage into the network in order to correct any disturbance affecting a sensitive load voltage. In this paper, modelling of DVR for voltage correction using MatLab software is presented. The performance of the device under different voltage sag types is described, where the voltage sag types are introduced using the different types of short-circuit faults included in the environment of the MatLab/Simulink package. The robustness of the proposed device is evaluated using the common voltage sag indices, while taking into account voltage and current unbalance percentages, where maintaining the total harmonic distortion percentage of the load voltage within a specified range is desired. Finally, several simulation results are shown in order to highlight that the DVR is capable of effective correction of the voltage sag while minimizing the grid voltage unbalance and distortion, regardless of the fault type.

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