This paper aims at summarizing various methods used for representing and estimating the power coefficient in wind turbines, such as exponential, sinusoidal and polynomial models, as well as mathematical tools known as state observers. We present an exhaustive bibliographic review of the models used to calculate the power coefficient, given that this type of studies are scarce nowadays. In addition, we propose models that can be satisfactorily used for various analyzes of wind energy conversion systems, such as the representation by a polynomial function of fourth degree and the models based on the stochastic probability function. The relevance of this work is supported by the advantages and disadvantages of the various models and estimators of the power coefficient, which are presented at the end of the article in a comparative table with the purpose of offering to the reader a general summary. Ultimately, this review aims at helping researchers, students, university professors and those who wish to venture into this field, even though they do not have much experience, to establish a quick synthesized understanding of the different models and representations of the power coefficient.

For decades, maximum power coefficient limit, known as the Betz limit, has been accepted as a theoretical optimum value for wind turbine power extraction; nevertheless, some reports, exceeding this limit, have already been published. To explain this phenomenon and show a different point of view, a novel theoretical and ideal analysis based on flow conservation law and areas’ quotient is presented, supported by a review of works related to surpassing the power coefficient limit approached from different perspectives.

Mathematical models and algorithms for maximizing power extraction have become an essential topic in renewable energies in the last years, especially in wind energy conversion systems. This study proposes maximum power point tracking using gain scheduling approximations for an emulated wind system in a direct-drive connection. Power extraction is obtained by controlling the duty cycle of a Multilevel Boost Converter, which directly varies the rotational speed of a permanent magnet synchronous generator directly coupled to a three-phase induction motor that emulates the wind turbine. The system’s complexity is linked to the inherent non-linearities associated with the diverse electrical, mechanical, and power electronic elements. In order to present a synthesized model without losing the system dynamic richness, several physical tests were made to obtain parameters for building several mathematical approaches, resulting in non-linear dynamic equations for the controller gains, which are dependant on wind speed. Thirty real operational wind speeds considering typical variations were used in several tests to demonstrate the mathematical models’ performance. Results among these gain scheduling approaches and a typical controller constant gains mathematical model were compared based on standard deviations, absolute error, and the time for reaching the optimum generator angular speed related to every wind speed.

Maximum power point tracking in wind turbines is a topic that has attracted many researchers' interest; however, the studies presented are usually carried out only at the simulation level, so they lack a verification in the system through real measurements. On the other hand, the system's modeling is usually quite complex, making it challenging to meet the control objectives. There are unified models in which the system is treated in a generalized way according to various research purposes. This work presents a methodology that simplifies the unified system through a series of dynamic tests that applied to obtained a simplified model much easier to handle without sacrificing the system's dynamic richness.

El Aprendizaje Basado en Problemas (ABP) es un método de enseñanza-aprendizaje centrado en el estudiante en el que éste adquiere conocimientos, habilidades y actitudes a través de situaciones de la vida real. En la Universidad Tecnológica de Altamira al ser parte de instituciones de educación superior tecnológica en México, incluye en sus programas de estudio el manejo de los controladores lógicos programables (PLC), lo cual constituye parte de su formación como mecatrónicos en la implementación de sistemas automatizados con aplicación industrial. La presente investigaciones propone el uso del método ABP para el aprendizaje de los PLC´s, mostrando los resultados que relacionan el desempeño académico de los alumnos de los grupos de experimentación.

La enseñanza de los sistemas algebraicos lineales, así como sus técnicas de solución, constituyen un eslabón importante en el desarrollo profesional de los alumnos de ingeniería y áreas afines, sin embargo, la asimilación de conceptos se ve afectada por la falta de vinculación entre la teoría y la práctica, de modo que gran parte de los estudiantes muestran con frecuencia poco interés en la explicación de los temas y esto da como resultado un bajo desempeño académico. Este trabajo presenta una propuesta de enseñanza de sistemas algebraicos lineales, en donde se verifican los resultados a través de simulación electrónica e implementación física de circuitos eléctricos para estudiantes de ingeniería.