Grid Power Quality with Variable Speed Wind Turbines.pdf
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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 16, NO. 2, JUNE 2001
Grid Power Quality with Variable Speed
Wind Turbines
Z. Chen
, Senior Member, IEEE
and E. Spooner
, Senior Member, IEEE
Abstract—
Grid connection of renewable energy sources is es-
sential if they are to be effectively exploited, but grid connection
brings problems of voltage fluctuation and harmonic distortion.
In the paper, appropriate modeling and simulation techniques are
discussed for studying the voltage fluctuation and harmonic dis-
tortion in a network to which variable speed wind turbines are
connected. Case studies on a distribution network show that the
voltage fluctuation and harmonic problems can be minimized with
the proposed power electronics interface and control system while
the wind energy conversion system captures the maximum power
from the wind as wind speed varies. The studies have also demon-
strated the ability of the advanced converter to assist the system
voltage regulation.
Index Terms—
Harmonic minimization, maximum power cap-
ture, reactive power control, voltage regulation, wind power.
Fig. 1.
Schematic wind energy conversion system.
II. W
IND
P
OWER
C
ONVERTER
M
ODELING
The wind power conversion system studied has the configu-
ration shown in Fig. 1. The system consists of a wind turbine, a
high pole number modular PM generator [1], a modular rectifier
system [3] and a controllable power electronics inverter [2], [4].
The modeling and simulation of these elements are discussed
below.
I. I
NTRODUCTION
R
ENEWABLE sources often produce power and voltage
varying with natural conditions (wind speed, sun light
etc.,) and grid connection of these sources is essential if they
are ever to realize their potential to significantly alleviate the
present day problems of atmospheric pollution and global
warming. However, electric utility grid systems cannot readily
accept connection of new generation plant without strict condi-
tions placed on voltage regulation due to real power fluctuation
and reactive power generation or absorption, and on voltage
waveform distortion resulting from harmonic currents injected
by nonlinear elements of the plant.
The paper describes a wind farm comprising a number
of turbines housing direct-drive, variable-speed perma-
nent-magnet generators of a novel type proposed in [1] and
whose variable-speed capability is achieved through the use
of an advanced power electronic converter as described in [2].
The modeling of the wind power converter with the network
is addressed using case studies of voltage fluctuation and
harmonics propagation. The studies have demonstrated that the
impacts on voltage fluctuation and harmonic distortion can be
minimized and furthermore, the network voltage control could
also be improved by the advanced power electronic converters
proposed.
A. Wind Modeling
Wind is an intermittent and variable source of energy. Wind
speed varies with many factors and is random in magnitude and
direction. For this study, the wind is simulated with four com-
ponents, namely, base component, ramp component, gust com-
ponent and noisy component [5] as:
(m/s)
(1)
B. Wind Turbine Characteristics
The power in the wind is proportional to the cube of the wind
speed. However, only part of the wind power is extractable. Al-
though a complete aerodynamic model of the wind turbine could
simulate the interaction between the wind and the turbine blades
in detail, the simple expression of (2), which is quite often used
to describe the mechanical power transmitted to the hub shaft,
is sufficient for this study.
(W)
(2)
Where (kg/m ) is the air density and (m ) is the area swept
out by the turbine blades. , a dimensionless power coeffi-
cient, depends on the type and operating condition of the wind
turbine. For a fixed-pitch turbine,
Manuscript received July 20, 1998; revised October 8, 1999.
Z. Chen is with the Department of Electronic and Electrical Engineering, De
Montfort University, The Gateway, Leicester, LEI 9BH, UK.
E. Spooner is with the School of Engineering, University of Durham, South
Road, Durham, DH1 3LE, UK.
Publisher Item Identifier S 0885-8969(01)04330-3.
may be expressed as a
function of
[6], the ratio of blade tip speed to wind speed
(
), with
being the radius (m) of the wind
0885–8969/01$10.00 © 2001 IEEE
CHEN AND SPOONER: GRID POWER QUALITY WITH VARIABLE SPEED WIND TURBINES
149
Fig. 4.
Circuit model of equivalent DC machine.
Fig. 2.
C
–
curve.
Fig. 5.
V
–
I
characteristics (steady state).
Fig. 6.
Variable speed operating curve.
Fig. 3.
Modular connection of stator coil and rectifier.
The parameters ( ) of the equivalent DC machine can
be expressed as functions of frequency and dc current. These
functions can be established by fitting a suitable analytic curve
to data obtained by test or numerical simulation [8].
turbine rotor and (rad/s) being the angular speed. A typical
curve is shown in Fig. 2.
C. PM Generator and Rectifier System Modeling
The circuit configuration of sets of stator and rectifier mod-
ules in a modular PM generator system is shown in Fig. 3. The
multi-phase rectifier system can be seen as an extension of a
three phase parallel bridge rectifier circuit reported in 1970s [7].
A stator coil is represented by an internal resistor ( ), an
inductor ( ) and an electromotive force ( ) which is induced
by the flux produced by multi-pole set of permanent magnets
on the rotor. An ac capacitor is connected in parallel with the ac
input terminals of each rectifier module to enhance the power
output for matching the wind power characteristic [3].
The above circuit model can be simulated in detail, but a
modular PM machine at MW level may have more than a hun-
dred stator modules and associated bridge rectifier units, conse-
quently, the simulation of a circuit model would be very time
consuming. A full simulation would only be used when the
internal behavior is of interest. With such a large number of
phases, the generator-rectifier system produces a smooth dc link
voltage and current, therefore, in the steady state, the electrical
characteristics as viewed from the dc side may be described by
an equivalent DC machine as shown in Fig. 4. The dc system
characteristics within the normal operating region are shown in
Fig. 5. The dc link voltage
D. Modeling of Machine Motion
As shown in Fig. 1, the wind turbine is directly connected
to the generator rotor without a gearbox. The rotational system
may therefore be modeled by a single equation of motion:
(4)
where
rotor speed (rad/s)
mechanical system inertia (kg m )
friction coefficient (N m/rad)
wind turbine input aerodynamic power (W)
generator output power plus electrical loss (W) may
be approximated as
the combined coil resistance (
).
E. Variable Speed Operation
A typical variable speed operating curve is shown in Fig. 6.
Above rated wind speed, power output remains at the rated
value. As the wind speed reaches cut-off speed, the rotor speed
is decreased to induce stall. Below the rated wind speed, the
wind turbine follows the optimal tip speed ratio to extract
maximum power from the wind. One set of optimal operating
and current
are related by (3):
(3)
150
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 16, NO. 2, JUNE 2001
(a)
Fig. 7.
Generator-rectifier optimal power transfer characteristics.
(b)
Fig. 10.
Optimal resistor loading. (a) Circuit diagram. (b) Characteristics.
Fig. 8.
Modular PM generator-rectifier unit.
Fig. 11.
Inverter-grid phase diagram.
ratio, so that the optimum dc voltage profile, as shown in Fig. 7,
is presented at the rectifier terminal for maximum power capture
operation. Meanwhile an appropriate dc voltage is maintained at
the dc bus to enable the voltage source inverters to perform the
optimal real power transfer and reactive power regulation.
It may be observed that the optimum – characteristic in
Fig. 7 can be represented by a variable resistor connected to the
PM generator and rectifier terminal. For the purpose of simu-
lating the generator/rectifier therefore, the DC/DC converter and
its loading can be represented by an adjustable load resistance.
The load resistance value is a function of wind speed as shown
in Fig. 10. In practice, the regulation would be implemented by
means of a varying PWM switching ratio.
Current-Controlled VSI Control:
CC-VSIs can generate an
ac current which follows a desired reference waveform and so
can transfer the captured real power along with controllable re-
active power and with minimal harmonic pollution. The phasor
diagram of relevant variables is shown in Fig. 11.
The real and reactive power supplied to the grid is:
Fig. 9.
Schematic wind farm and grid connection.
curves for the modular generator and rectifier (dc terminal) is
shown in Fig. 7.
F. Controllable Power Electronics
Below rated wind speed, the control objective is to track wind
speed, to capture and transfer the maximum power to the grid.
The generator and rectifier system is uncontrolled and so con-
trol has to be implemented by the power electronics converters.
Several types of power electronics interface have been investi-
gated [2], [4]. One of the options, using a DC/DC converter is
shown in Fig. 8.
In a wind farm, there may be dozens of turbines of the type as
shown in Fig. 8. These units may be connected in parallel at the
dc side to supply power to a common dc bus and current con-
trolled voltage source inverters can then be used to convert the
dc power into ac for connection to the grid. Such an arrange-
ments is shown in Fig. 9.
DC/DC Converter Control:
DC/DC converters regulate the
dc voltages of generator-rectifier units by varying the switching
(pu)
(5)
where is the ac system voltage, is the fundamental com-
ponent of the inverter ac current and is the phase angle be-
tween and .With a given ac line voltage, the real power and
reactive power can be controlled by regulating the magnitude of
and the angle . Equation (5) can be used to represent the
CC-VSI for steady state analysis.
In time domain analysis, the inverter simulation model, de-
veloped on the basis of switching function concept [9] as shown
in Fig. 12, may be used. The desired current and actual current
CHEN AND SPOONER: GRID POWER QUALITY WITH VARIABLE SPEED WIND TURBINES
151
Fig. 13.
Harmonic filter arrangement (single phase).
Fig. 12.
PWM-VSI grid interface simulation model.
are compared and the error signal is compared with a triangle
waveform to generate the inverter firing signals. With this type
of control, the inverter is switched at the frequency of the tri-
angle wave and its output current harmonics are well defined.
In a large wind farm, individual machines could experience
different wind speed and direction, and therefore give different
outputs. However, for the study of the effects of wind power on
the grid, the wind farm may be represented with a single equiv-
alent machine, which has the output power equal to that of the
whole wind farm. For voltage fluctuation studies, the inverter
can then be represented by (5), and for harmonics studies, the
model shown in Fig. 12 can be used.
Fig. 14.
Power system for the case study.
The wind farm may be considered as a PQ bus. The real
power, , injected by the wind farm will be the captured real
power and the reactive power, , can be regulated to meet the
system reactive power or voltage regulation requirements.
B. System Modeling for Harmonics Studies
The time domain simulation method is used for power system
current harmonic studies. The wind farm is represented by an
equivalent PWM current-controlled voltage source inverter as
shown in Fig. 12. The inverter operating point is determined by
a power flow analysis.
The distribution network is represented by its three phase cir-
cuits and the system load is represented by constant resistance
and inductance elements. The values of these elements are also
determined by the analysis of power flow.
The VSI is a voltage harmonic source in the point view of ac
system and a harmonic filter has to be located appropriately to
remove the voltage harmonics it creates [10]. In this study, the
inductor connecting the VSI to the network is split, a damped
second order harmonic filter is placed at the midpoint as shown
in Fig. 13.
III. P
OWER
S
YSTEM
M
ODELING
A. System Modeling for Voltage Fluctuation Studies
The voltage fluctuation problem is closer to a steady state
problem such as load varying, which is well defined by the real
and reactive power distribution. The harmonics effects may be
ignored with PWM switching inverters and appropriately de-
signed filters. Therefore, the conventional power flow equations
are sufficient for voltage fluctuation study. The node voltage and
node injected power are related by
(6)
IV. C
ASE
S
TUDY
A. Power Network Configuration
A radial distribution system [11] has been chosen for the
study. Fig. 14 shows the network configuration.
The slack bus keeps a voltage of 1.053 pu. An equivalent
CC-VSI (which, in practice, would be a number of CC-VSIs) at
bus 13 connects the wind farm to bus 8 of the grid. It is assumed
that the loading at each node is kept constant during the analysis
and the multi-machine wind farm has a total capacity of 32%
system loading.
Where
is the node number of the power network,
is the voltage of bus ,
is the voltage phase angle with respect to the
reference bus,
and
are the real and reactive power injected at bus
,
and
are respectively the real and imaginary parts
of the node admittance.
152
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 16, NO. 2, JUNE 2001
Fig. 15.
Wind speed data for case study.
Fig. 18.
Bus voltage distribution—1.
Fig. 16.
C
traces.
Fig. 19.
Bus voltage distribution—2.
unacceptable for loads connected on some buses even though
the wind power generation is maintained at unity power factor.
However, the bus voltage fluctuation can be reduced if the
wind farm inverters are used to generate reactive power during
system low voltage periods and to absorb reactive power during
system high voltage periods. In this way, the inverters also work
as Var compensators. A simple example of wind power con-
verter operating under such control scheme is shown in Fig. 19.
It can be seen that the bus voltage fluctuation has been greatly
reduced.
Fig. 17.
Output electrical power.
B. Voltage Fluctuation Analysis
The wind speed curve used for the study is shown in Fig. 15.
The trace of the equivalent machine is shown in Fig. 16.
Fig. 17 shows the corresponding electrical power generated by
the wind farm. Inertia smoothing effects are apparent.
A series of power flow analyzes have been carried out using
the generated electrical power shown in Fig. 17 as the real power
input at bus 13.
Fig. 18 shows the bus voltages under the following condi-
tions:
i) wind power not connected,
ii) wind power converter operating at
C. Grid Current Harmonic Distortion
The time domain harmonic analysis has been performed with
the operating points obtained by power flow analysis.
The switching frequency of the grid interface inverter is
3.15 kHz. It is assumed that the system operates in a balanced
condition. The voltage waveform and harmonic spectra of VSI
wind power (bus 13) and bus 8 are shown in Figs. 20 and 21.
Fig. 22 shows the total voltage harmonic distortion at each bus.
These results correspond to the operating condition of
and unity power
factor,
iii) wind power converter operating at
and unity power
as
factor.
and are respectively the minimum and maximum
electrical power shown in Fig. 17.
It can be seen that unity power factor operation of the wind
farm can increase the network voltage level. It is also noted that
the injection of varying power can result in bus voltage fluctua-
tion, although the voltage variation is less than 2% in this case.
If the wind power varied over a wider range and if the load varia-
tion is taken into account, then voltage fluctuations may become
shown in Fig. 17.
It can be seen clearly that the harmonic distortion can be re-
duced sufficiently to meet modern standards for the discussed
type of distribution systems.
V. D
ISCUSSIONS
The estimated overall efficiency of the wind electrical power
system (generator and power electronic converters) is about
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