Performance and Operation Management - Wind Energy Systems for Electric Power Generation - page 130

Fig. 6.8 Model of intermediate circuit voltage source converter

6.2.5 Modeling the Drive Train

For investigating transient phenomena and stability problems a model of the me-
chanical drive train must be established. This is usually done by a lumped parameter
model of the rotating components. The one-mass system considered in the previous
chapters is not sufficient to study occurring oscillations and torsional stress. The
usual approach is to describe the rotating system by a multi-mass model.
A multi -inertia system is described by the differential matrix vector equation:

J ¨ + D ˙ ϕ ϕ + K ϕ = T (6.49)

where

φ is the vector of angular rotor positions,

J is the matrix of inertias,
D is a damping matrix,
K is the matrix of spring coefficients, and
T is the vector of torques acting on the inertias.

Note that angular velocities are / d t . In the present problem the inertia com-

ponents J are arranged in a line, coupled by shaft components characterized by
spring parameters K , while damping parameters D are attributed to losses in the
inertia components themselves and in the coupling shaft components. The system
(6.49) will be considered linear.
Considering a general wind energy system, the main components that make up
the rotating inertia are the wind turbine, the gear-box and the generator. Hence it
is advisable to model the system by three masses or, when there is no gear-box,
by two-masses. Such a representation does not take into account that the blades
(mostly 3) have their own degrees of freedom and may contribute differently to the
turbine torque. However, extension to a six-mass model is not necessary for shaft
oscillation and stability calculations.
Figure 6.9 is a sketch of a three-mass lumped parameter model. In simple rep-
resentation an inertia is modeled by a homogenous disk of radius R , length L and
a material density

Ω = d ϕ

. On the other hand the spring coefficient of a shaft segment is
described by its geometric dimensions and the shear modulus G . Disk mass inertia
moment and cylinder shaft stiffness become:

ρ