This paper presents a new concept for finding saddle-node bifurcation (SNB) points in voltage stability analysis of power systems by applying the extended functional method (EFM). This method enables the finding of the SNB point of power systems by directly calculating the extreme values of a nonsmooth variational functional, which is obtained in its turn by the so-called nonlinear generalized Collatz-Wilandt formula. The main theoretical result establishes the EFM applicability for finding the maximum loading capacity of power systems. The maximum loading capacity of the power system is shown to be located at the maximizing point of the nonsmooth function of bifurcations. The subgradient method for nonsmooth functions was applied. The EFM was performed on various IEEE test systems to find SNB points, and the results were compared with those obtained with the Continuation Power Flow (CPF) and the Point of Collapse (PoC) method. The simulation results show that the proposed method is robust and, unlike the PoC method, finds the SNB point even when good guessing of the turning point is not available. Tasks such as tracking an SNB point displaced by a contingency and infeasible power flow were performed successfully by using the EFM.

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The sun is a plenty and popular source of renewable energy. To transform solar energy into electricity it is necessary to use photovoltaic (PV) panels which in turn have flow efficiency and therefore do not provide maximum power. Maximum power depends on temperature and solar radiation. Changes in these  environmental factors require an algorithm to find the Maximum Power Point (MPP) where maximum power can be extracted. The algorithm is called the Maximum Power Point Tracking (MPPT). Through MatLab=Simulink the MPPT algorithm based on the Kalman Filter was implemented. The MPPT algorithm is essential for the maximum use of solar energy and therefore plays an important role for the feasibility and competitiveness of PVs in renewable energy. This article proposes a MPPT based on the kalman filter that has the advantage of efficiently estimating variables based on measurements with statistical noise, in this case measurements of solar irradiation and temperature. The results show efficiency because the relative errors are less than 1.13% compared to results obtained from simulink.

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