  Wind energy is an integral part of nowadays energy supply and one of the
fastest growing sources of electricity in the world today. Accurate models for
wind energy conversion systems (WECSs) are of key interest for the analysis and
control design of present and future energy systems. Existing control-oriented
WECSs models are subject to unstructured simplifications, which have not been
discussed in literature so far. Thus, this technical note presents are thorough
derivation of a physical state-space model for permanent magnet synchronous
generator WECSs. The physical model considers all dynamic effects that
significantly influence the system's power output, including the switching of
the power electronics. Alternatively, the model is formulated in the $(a,b,c)$-
and $(d,q)$-reference frame. Secondly, a complete control and operation
management system for the wind regimes II and III and the transition between
the regimes is presented. The control takes practical effects such as input
saturation and integral windup into account. Thirdly, by a structured model
reduction procedure, two state-space models of WECS with reduced complexity are
derived: a non-switching model and a non-switching reduced-order model. The
validity of the models is illustrated and compared through a numerical
simulation study.
