24-10-2016, 12:26 PM
Observer-Based Decentralised Control of a Wind Turbine with a Hydrostatic Transmission
1460786495-Varun.pdf (Size: 524.85 KB / Downloads: 5)
Abstract— In this paper, a decentralised control approach
for a 5 MW wind turbine with a hydrostatic transmission is
presented that covers the whole range from low to very high
wind speeds. In addition to a linear control of the pitch angle,
a multi-variable gain-scheduled PI state feedback control based
on LQR techniques is proposed for the angular velocities of both
the rotor and the generator. The sixth-order simulation model
comprises the complete drive train dynamics, the generator
torque dynamics as well as the rotor aerodynamics and is derived
from first principles. To reduce the implementation effort, the
multi-variable control structure is based on a simplified statespace
model with three states and two inputs. Moreover, a
reduced-order observer estimates the rotor torque as well as an
unknown leakage volume flow for a disturbance compensation.
The control performance is illustrated by simulation results,
which show an excellent tracking behaviour for the controlled
variables.
I. INTRODUCTION
The majority of modern wind turbines in operation today is
equipped with pitch actuators. Thereby, the generated power
can be kept constant by increasing the pitch angle of the
rotor blades at high wind speeds. Usually, the generator shaft
is mechanically connected to the rotor shaft via a gearbox,
which is used to step up the angular velocity of the slower
turning rotor shaft. Power electronics are usually employed
to match the frequency of the generated power to that of the
grid by using either synchronous or double-fed asynchronous
machines in combination with current converters.
A hydrostatic transmission represents a type of continuously
variable transmission that uses hydraulic fluid to transmit
power. Hydrostatic transmissions have been employed successfully
for many years, especially in mobile hydraulics.
The implementation of hydrostatic transmissions in the field
of wind energy is not a new concept. Already in 1980, an
early experimental turbine with a hydrostatic transmission
was built. Due to its high hydraulic losses, however, this
attempt turned out to be unsuccessful, see [1] and [2]. Instead,
advances in power electronics led the way for the takeover of
mechanical gear boxes, which are common today. Nowadays,
the application of hydrostatic transmissions for wind turbines
is gathering renewed research interest. This is due to the
fact that a hydrostatic transmission in a wind turbine drive
train offers several benefits over the conventional mechanical
gear box. Among these is the potential to increase the annual
energy production by extending the useful wind speed range
of the turbine, cf. [3]. Moreover, an operation at higher
aerodynamic efficiencies over a wider range of wind speeds becomes possible [4]. The superior damping characteristics
of a hydraulic transmission, cf. [5], also promises a positive
impact on the overall system reliability and lifetime.
The aim of this work is to both reduce the implementation
effort and to extend earlier work presented in [9]. Instead of a
central control approach, a decentralised concept is considered
in this paper: the pitch angle is controlled by a linear control,
whereas a gain-scheduled multi-variable tracking control is designed
for the angular velocities of the rotor and the generator.
The paper is organised as follows: Section II presents the
derivation of a sixth-order simulation model for the wind
turbine with hydrostatic transmission. Section III points out
how the steady-state desired values for the whole range of
wind speeds are computed for the controlled outputs. The
control design – based on a simplified system model with
neglected actuator dynamics – is discussed in Section IV.
Taking advantage of extended linearisation techniques, the PI
state feedback control law is derived and combined with a
feedforward control. In Section V, a reduced-order disturbance
observer is proposed and used for a disturbance compensation.
Corresponding simulation results are presented and discussed
in Section VI. Finally, conclusions and an outlook are given
in Section VII.
II. MATHEMATICAL MODELLING
In this paper, the simplest form of a hydrostatic transmission
is regarded: it consists of a hydraulic pump as well as a
motor connected in a closed circuit, where only the volumetric
displacement of the motor can be varied by a corresponding
displacement unit. Thereby, any desired transmission ratio can
be attained within a certain predefined boundary determined by
the system parameters. Fig. 1 depicts the drive train structure
of a wind turbine with a hydrostatic transmission. For the simulation, a corresponding symbolic system model for the wind turbine is derived from first principles that includes all
dominant dynamic effects, such as the rotor aerodynamics, the
drive train dynamics and the actuator dynamics. The drive train
model has three state variables: the rotor angular velocity ωR,
the difference pressure Δp of the hydrostatic transmission, and
the angular velocity ωG of the generator. The corresponding
model structure is illustrated in Fig. 2. The aerodynamic torque