Research Article
MaximumPowerCoefficientAnalysisinWindEnergyConversion
Systems: Questioning, Findings, and New Perspective
Jos´ e Genaro Gonz´ alez-Hern´ andez
1,2
andRub´ en Salas-Cabrera
1
1
Division of Graduate Studies and Research, Tecnol´ ogico Nacional de M´ exico, Instituto Tecnol´ ogico de Ciudad Madero,
Ciudad Madero 89440, Mexico
2
Mechatronics Department, Universidad Tecnol´ ogica de Altamira, Altamira 89603, Mexico
Correspondence should be addressed to Jos´ e Genaro Gonz´ alez-Hern´ andez; jggh77@hotmail.com
Received 3 April 2021; Accepted 12 July 2021; Published 20 July 2021
Academic Editor: Juan C. Jauregui-Correa
Copyright©2021Jos´ eGenaroGonz´ alez-Hern´ andezandRub´ enSalas-Cabrera.isisanopenaccessarticledistributedunderthe
CreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,provided
the original work is properly cited.
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 phe-
nomenon 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.
1. Introduction
Wind power has become an important source of energy for
humanity; in recent years, the installed capacity has grown
considerably to reach hundreds of Giga Watts as it was
reported in [1]. e importance of wind energy nowadays is
crucial to face the energetic problems around the world; as
established by [2], wind energy has evolved from an
emerging technology to a near-competitive technology. is
fact, combined with an increasing global focus on political
desire in the energy supply diversification and environ-
mental concern, promotes wind energy has an important
role in the future electricity market.
For example, in recent times, specialized methods in
aerostatic stability and wind fragility analysis have been
made as well as sophisticated methods based on aeroelastic
models to improve structural reliability have also been
proposed, for example [3–6]. Among all wind studies, en-
ergy efficiency is a highlight; because of this, new and so-
phisticated control equipment is currently developed to
extract the most energy from the wind, and several works
about overviews of emerging technologies of wind energy
conversion systems (WECS) have already been published in
recent years, for example [7–9], but it is necessary to move
back 100 years to the past to identify and understand the
origin of wind turbine power extraction limit, or at least, as it
has been known for decades.
A century has passed since the German scientist Albert
Betz published the results of the power coefficient (C
p
) limit
as approximately 0.593, a result whose authorship was the
subject of debate for years. According to [10], Lanchester
was very close to determining the famous wind turbine limit
efficiency in a paper that he published in 1915; unfortunately,
he did not include Froude’s result, which establishes that the
velocity in the disk is the average of velocities upstream and
downstream. Joukowsky and Betz used vortex theory to
support Froude’s result and obtained theoretical maximum
power coefficient simultaneously, just as Newton and
Leibnitz developed calculus theory simultaneously.
Betz deduction has been presented in several ways; for
example, Ochieng and Ochieng [11] present a mathematical
series power expansion method to obtain the Betz equation
functional form to determine optimum wind power coef-
ficient. It is important to note that Betz analysis supposes an
ideal turbine, which, according to [12], is the most efficient
wind turbine and has so many blades so that there will not be
Hindawi
Mathematical Problems in Engineering
Volume 2021, Article ID 9932841, 7 pages
https://doi.org/10.1155/2021/9932841