Fourier Analysis for Harmonic Signals in Electrical Power Systems

The harmonic content in electrical power systems is an increasingly worrying issue since the proliferation of nonlinear loads results in power quality problems as the harmonics is more apparent. In this paper, we analyze the behavior of the harmonics in the electrical power systems such as cables, transmission lines, capacitors, transformers, and rotating machines, the induction machine being the object of our study when it is excited to nonsinusoidal operating conditions in the stator winding. For this, a model is proposed for the harmonic analysis of the induction machine in steady‐state regimen applying the Fourier transform. The results of the proposed model are validated by experimental tests which gave good results for each case study concluding in a model proper for harmonic and nonharmonic analysis of the induction machine and for “harmonic” analysis in an electrical power system

Vibration Measurement Using Laser Triangulation for Applications in Wind Turbine Blades

The blades in a wind turbine are currently manufactured with flexible and light materials, which make them more susceptible to the effects of vibrations when the wind speed is high enough, causing fatigue damage, affecting the functionality of its structure and aerodynamic efficiency. This work presents a comparison of the modal vibration parameters, applied to a cantilever beam, determined with two experimental methods—the use of accelerometers and a proposed optical non-contact method—based on the principle of laser triangulation and photogrammetry techniques. This technique uses the geometric symmetry of the equidistant displacements along the z axis of the beam to obtain the amplitude data. Parameters such as natural frequency and modal form are obtained by fitting the data to a nonlinear equation with a solution which is an exponential/harmonic equation. Also, analytically, these parameters are determined, and a comparison is made between the experimental methods. The result shows that the relative error of the first-order natural vibration frequency is below 1%. The proposed method is simple, efficient, reliable, and it is also a method that has not been applied to the test of wind turbine blades, so its implementation as this type of wind turbine component is an area of opportunity for the validation of modal vibration parameters in the wind industry. An analysis of results is presented showing benefits of the proposed method and its limitations

Angle Calculus-Based Thrust Force Determination on the Blades of a 10 kW Wind Turbine

In this article, the behavior of the thrust force on the blades of a 10 kW wind turbine was obtained by considering the characteristic wind speed of the Isthmus of Tehuantepec. Analyzing mechanical forces is essential to efficiently and safely design the different elements that make up the wind turbine because the thrust forces are related to the location point and the blade rotation. For this reason, the thrust force generated in each of the three blades of a low-power wind turbine was analyzed. The angular position (θ) of each blade varied from 0° to 120°, the blades were segmented (r), and different wind speeds were tested, such as cutting, design, average, and maximum. The results demonstrate that the thrust force increases proportionally with increasing wind speed and height, but it behaves differently on each blade segment and each angular position. This method determines the angular position and the exact blade segment where the smallest and the most considerable thrust force occurred. Blade 1, positioned at an angular position of 90°, is the blade most affected by the thrust force on P15. When the blade rotates 180°, the thrust force decreases by 9.09 N; this represents a 66.74% decrease. In addition, this study allows the designers to know the blade deflection caused by the thrust force. This information can be used to avoid collision with the tower. The thrust forces caused blade deflections of 10% to 13% concerning the rotor radius used in this study. These results guarantee the operation of the tested generator under their working conditions