Modeling Of The Wind Turbine With A Doubly Fed Induction Generator For Grid Integration Studies, 1. ROLNICTWO, OZE ...
[ Pobierz całość w formacie PDF ]
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006
257
Modeling of the Wind Turbine With a Doubly Fed
Induction Generator for Grid Integration Studies
Yazhou Lei, Alan Mullane, Gordon Lightbody, and Robert Yacamini
Abstract—
Due to its many advantages such as the improved
power quality, high energy efficiency and controllability, etc. the
variable speed wind turbine using a doubly fed induction gener-
ator (DFIG) is becoming a popular concept and thus the modeling
of the DFIG based wind turbine becomes an interesting research
topic. Fundamental frequency models have been presented but
these models are often complex with significant numerical over-
head as the power converter block consisting of power control,
rotor side and grid side converter control and DC link are often
simulated in detail. This paper develops a simple DFIG wind
turbine model in which the power converter is simulated as a
controlled voltage source, regulating the rotor current to meet
the command of real and reactive power production. This model
has the form of traditional generator model and hence is easy to
integrate into the power system simulation tool such as PSS/E. As
an example, the interaction between the Arklow Bank Wind Farm
and the Irish National Grid was simulated using the proposed
model. The model performance and accuracy was also compared
with the detailed model developed by DIgSILENT. Considering
the simplification adopted for the model development, the limi-
tation and applicability of the model were also discussed in this
paper.
Index Terms—
Induction generators, power system transient sta-
bility, reactive power control, variable speed drives, wind power
generation.
,
,
Terminal voltage, wind turbine shaft and gener-
ator rotor angle position.
Rotor circuit time constant.
Electromagnetic torque.
Mechanical torque act on the generator rotor.
Low-pass time constant for rotor voltage control.
Wind turbine prime torque from wind.
Voltage.
Wind speed.
, ,
Steady-state, transient, and magnetizing reac-
tance.
Symbols
Integral operator.
Deviation from normal value.
Maximum power tracking logic.
Suffices, Superscripts
,
Direct and quadrature axis components.
,
Maximum and minimum value.
,
Generator’s stator and rotor components.
,
Horizontal and vertical components in the
common reference frame.
Reference value.
Transient state component.
N
OMENCLATURE
Wind turbine blade pitch angle.
Wind turbine blade design constant.
Wind turbine power coefficient.
Voltage behind the transient impedance.
and a possible energy shortage, great efforts have been
taken by the governments around the world to implement re-
newable energy programs, based mainly on wind power, solar
energy, small hydro-electric power, etc. Ever since the first large
grid connected wind farm appeared in California (U.S.) in the
1980s, wind power generation has been undergoing a signifi-
cant development. With improving techniques, reducing costs
and low environmental impact, wind energy seems certain to
play a major part in the world’s energy future. As the wind
power penetration continually increases, power utilities con-
cerns are shifting focus from the power quality issue to the sta-
bility problem caused by the wind power connection [1]–[3]. In
such cases, it becomes important to consider the wind power
impact properly in the power system planning and operation.
Unfortunately, few power system analysis tools have included
wind turbine models such as have been developed for traditional
power generators. Therefore, when carrying out wind power
embedded network planning or operation analysis, engineers
have to put much effort into the modeling of the wind turbines
rather than concentrating on the problem itself. Hence, a wind
turbine model compatible with commercial power system anal-
ysis tools, like PSS/E, is in imminent need.
,
Generator rotor and wind turbine shaft inertia.
Current.
,
Coefficients for the proportional-integral con-
troller.
Shaft stiffness coefficient.
Wind turbine tip-speed ratio.
Inductance,
,
,
Synchronous, wind turbine shaft, and generator
rotor angle speed.
Flux linkage.
,
Active and reactive power.
Air density.
Resistance.
Wind turbine blade radius.
Rotor slip.
Manuscript received November 19, 2003; revised April 15, 2004. This work
was supported by Enterprise Ireland and ESB Ireland. Paper no. TEC-00343-
2003.
The authors are with the Department of Electrical and Electronic Engineering,
University College Cork, Cork, Ireland (e-mail: leiyazhou@yahoo.com).
Digital Object Identifier 10.1109/TEC.2005.847958
0885-8969/$20.00 © 2005 IEEE
I. I
NTRODUCTION
W
ITH growing concerns about environmental pollution
258
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006
Fig. 1. Scheme of a DFIG equipped wind turbine.
In the early stage of wind power development, most wind
farms were equipped with fixed-speed wind turbines and induc-
tion generators. Since such wind generators can only operate
at a constant speed, the power efficiency is fairly low for most
wind speeds. To improve their efficiency, many modern wind
generators adopt a variable speed operation in one of two ways:
direct ac to ac frequency converters, such as the cycloconverters
[4], [5]; or using voltage controlled inverters (ac-dc-ac), which
convert power at varying frequencies at the variable-speed gen-
erator to dc, and then use some form of power electronics to
convert the dc power back to ac at a fixed frequency appropriate
for the grid connection [6], [7].
Amongst many variable speed concepts, the DFIG equipped
wind turbine has many advantages over others [6]. For example,
the power converter in such wind turbines only deals with rotor
power, therefore the converter rating can be kept fairly low, ap-
proximately 20% of the total machine power. This configuration
allows for variable speed operation while remaining more eco-
nomical than a series configuration with a fully rated converter.
Other features such as the controllability of reactive power help
DFIG equipped wind turbines play a similar role to that of syn-
chronous generators.
Whilst the simulation of the DFIG wind turbine has been dealt
with in many publications [7]–[13], most of them were electro-
magnetic models suitable for the detailed study of the power
converter and its control strategy. To meet the demand of power
system simulation, the fundamental frequency DFIG wind tur-
bine model was also proposed in [2], [14], and [15]. The power
converter model in these papers was still complex, consisting
of the power controller, rotor side and grid side converter con-
troller and dc link. However, for power system analysis, the
internal dynamics of power converter are not of interest. As a
small simulation time step is required by the current controller,
such models are time consuming and inappropriate with tradi-
tional power system simulation tools such as PSS/E. This paper
proposes a simplified model, representing the DFIG in terms
of a voltage behind the transient reactance. Assuming an ideal
power converter, a voltage source controlling the rotor current
is applied to the rotor circuit to simulate the effect of the power
converter. In addition, the blade pitch control and a soft cou-
pling shaft system were also modeled to an appropriate extent.
Section II discusses the DFIG transient model and Section III
presents the control scheme and protection scheme model. In
Section IV, the proposed model was applied to analyze the in-
teraction between the Arklow Bank Wind Farm and the Irish
National Grid. The model limitation and applicability were also
discussed by comparison with the fundamental frequency model
presented by DIgSILENT.
II. T
RANSIENT
M
ODEL OF A
DFIG
A typical scheme of a DFIG equipped wind turbine is shown
in Fig. 1. Two voltage fed PWM converters are inserted back-to-
back in the rotor circuit, which connect the slip ring terminals
to the ac supply network. By adjustment of the switching of
the Insulated Gate Bipolar Transistors in both converters, the
power flow between the rotor circuit and the supply can be con-
trolled both in magnitude and in direction [8], [9], [13]. This is
effectively the same as connecting a controllable voltage source
to the rotor circuit [16]. The DFIG can be regarded as a tradi-
tional induction generator with a nonzero rotor voltage. With
the stator transients neglected, the per unit electrical equations
of the DFIG can be written in phasor form as follows [16], [17].
Stator voltage
(1)
(2)
Rotor voltage
(3)
(4)
Flux linkage
(5)
(6)
(7)
(8)
Electromagnetic torque
(9)
LEI
et al.
: MODELLING OF THE WIND TURBINE WITH A DFIG FOR GRID INTEGRATION STUDIES
259
Fig. 2. Steady-state and dynamic equivalent circuits of a DFIG.
In the case of the traditional induction machine, the rotor
voltage in (3) and (4) are zero. To reduce (1) to (8) to a form
suitable for implementation in a transient stability program, it is
necessary to eliminate the rotor currents and rewrite the equa-
tions in terms of a voltage behind a transient reactance. Thus,
by solving (1), (6), and (8), we get
By substituting (10) and (11), the per unit electromagnetic
torque can be written as
(20)
Generally, the power losses associated with the stator resistance
are small enough to be ignored, hence the approximation of elec-
tromagnetic power or torque can be written as
(10)
Similarly, we can also get
(21)
(11)
while the reactive power that the stator absorbs from, or injects
into the power system can be calculated as
where
(22)
(12)
Accordingly, the rotor motion of the DFIG can be written as
(13)
(23)
(14)
By eliminating the rotor currents in (3) and (4), and expressing
the rotor flux linkage in terms of , , the following equations
describing the rotor circuit dynamics can be obtained:
For the case of generators, the value of corresponding to
the direction of current and voltage shown in Fig. 2 is negative.
Similarly, the rotor power (also called slip power) can be cal-
culated as
(15)
(24)
(25)
(16)
When the power losses in the converters are neglected, the total
real power injected into the main network equals to the sum
of the stator power and the rotor power . The reactive
power exchanged with the grid equals to the sum of stator
reactive power
where
and that of grid side converter
. In this
(17)
paper, the value of was fixed to simplify the model.
Additionally, since the wind turbine shaft and generator
rotor are coupled together via a gearbox, the wind turbine shaft
system should not be considered stiff. The interaction between
the windmill and rotor makes the shaft motion more complex
than the lumped-mass system. To account for this effect prop-
erly, an additional equation has been adopted to describe the
motion of the windmill shaft [2]
(18)
Fig. 2 show the steady-state and dynamic equivalent circuit of
the DFIG, respectively.
By eliminating the rotor currents
in the electromag-
netic torque (9), and when
,wefind
(19)
(26)
,
260
IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 1, MARCH 2006
Fig. 3. Simulation scheme for a doubly-fed induction generator equipped wind turbine and interface with PSS/E.
where the mechanical torque can be represented by the twist
angle between the wind turbine shaft and the generator rotor
(27)
III. C
ONTROL
S
CHEME
D
ESCRIPTION
The DFIG wind turbine control usually consists of two parts:
the mechanical control on the wind turbine blade pitch angle
and the electrical control on the power converter. The power
converter usually includes the power control, the rotor side cur-
rent control, dc link dynamics, the grid side current control and
the PWM scheme [2], [14], [15]. In this paper, a controllable
voltage source in the rotor circuit, as shown in Fig. 2 was used
to simulate the power converter. Such simplifications allows for
reduction of the model order whilst retaining the capability of
observing principle features of the converter such as the max-
imum current levels. Such capability is important for assessing
criteria such as fault-ride-through performance.
In power system analysis programs, the state variables for
generator models are usually referred to a common stationary
X-Y axis frame. The angular position of the DFIG terminal
voltage in this reference frame can be determined as
Fig. 4. Power efficiency curves versus tip-speed ratio.
braically in the simulation. A time delay is included in the
rotor voltage control in Fig. 3 to account for the delays associ-
ated with the measurement and voltage vector computation for
a voltage source converter.
To work effectively, the power converter must be controlled
in collaboration with the wind turbine pitch control. As has been
discussed in many published papers, the efficiency is a func-
tion of the tip speed ratio and the pitch angle (in degrees).
Here is the ratio between the linear speed of the blade tip with
respect to the incoming wind speed, . As can be
seen from Fig. 4, the value of can only approach its max-
imum point at some optimal . In other words, given a partic-
ular wind speed, there is a unique rotational speed required to
achieve the goal of Maximum Power Tracking (MPT). At below
the rated wind speed, the wind turbine operates in the variable
speed mode, and the rotational speed is adjusted such that the
maximum value of is achieved. With increasing wind speed,
the rotational speed of wind turbine increases. Once the rotor
speed exceeds its upper limit, the pitch controller will begin to
increase the pitch angle to shed some of the aerodynamic power.
As the pitch angle increases, the value of decreases. The re-
lationship between , and pitch angle can be approximated
by [18]
(28)
Upon aligning the direct axis of the reference frame with the
stator voltage position given by (28), becomes zero, and
is then equal to the amplitude of terminal voltage. Thus ac-
cording to (21) and (22), the real and reactive power are pro-
portional to and respectively. This is the basis of in-
dependent control of torque and reactive power in the DFIG.
According to (5) and (6), the stator currents and are re-
lated to the rotor currents and respectively. By adjusting
rotor voltage appropriately, the desired rotor currents, and hence
the desired stator currents corresponding to the optimal elec-
tromagnetic torque and the desired Var flow/power factor can
be achieved. As the bandwidth of the voltage source converter,
under PWM control, is very large compared with the pitch con-
trol or the shaft motion, the rotor voltage is calculated alge-
(29)
LEI
et al.
: MODELLING OF THE WIND TURBINE WITH A DFIG FOR GRID INTEGRATION STUDIES
261
where is a blade design constant. When the wind speed is
, the wind torque can be calculated as
TABLE I
W
IND
T
URBINE
P
ARAMETERS
(30)
The pitch controller is designed within the working limits of
the pitch actuator, and hence it cannot change the pitch angle
too fast or beyond the limits [19]. This control scheme is also
shown in Fig. 3, in combination with the rotor control system.
According to (21), (23), the desired wind turbine stator power
can be calculated based on the value of , determined by
the Maximum Power Tracking logic. The value of depends
on the chosen reactive power control strategy, i.e., fixed Var flow
or fixed power factor.
Apart from the wind turbine, DFIG and relevant controller
models mentioned above, three protective functions namely;
abnormal voltage, current and speed protection were also im-
plemented in the proposed model. The under/over-voltage unit
monitors the voltage at the high voltage side of the transformer.
If the voltage falls and remains below, for example, to about
0.9 pu, the machine will be disconnected within a minute or
two to protect the power converters. If the supply voltage falls
to an even lower value, they will be cut off instantaneously
[20]. The under/over-speed unit monitors the rotor speed and
triggers the machine in emergency; the over-current protection,
also called Crow-Bar protection in the DFIG, protects the rotor
side converter against over currents. When the rotor current ex-
ceeds a threshold value, the converter is blocked and bypassed
through an additional impedance to avoid the disconnection
of the wind generator [15]. The complete simulation scheme
for a DFIG equipped variable speed wind turbine is shown in
Fig. 3. It should be noted that only the main inputs into some
blocks were indicated on the diagram. Other input variables
that can be easily found in the equations are not given to keep
the diagram clear.
TABLE II
T
EST
S
YSTEM
P
ARAMETERS
IV. S
IMULATION
U
SING
PSS/E
In the following simulation, a simplified model of the Irish
National Grid (ING) and of the planned Arklow Bank offshore
wind park were used to test the performance of the model de-
scribed above. The ING is an isolated power system with the
capacity of 4500 MW, whose backbone is a 220-kV looped net-
work connected with two un-looped 400-kV transmission lines,
which will consume the total power output from the wind park
when commissioned. The example used in this paper was con-
fined to the phase-one project of the wind park, which consists
of seven GE3.6 MW wind turbines (see Table I). A 10-km sub-
marine cable which connects the wind park to the 38-kV dis-
tribution network was included in the model. A total capacity
80 Mvar of switched inductors was also included to absorb the
excessive reactive power generated by the cable (Table II). The
response of the wind turbine to a step increase in the wind speed
and to an electrical bus fault were studied. As no small time con-
stants were included in the proposed wind turbine model, the
simulation was carried out in PSS/E using the normal half cycle
step size.
Fig. 5. Wind turbine pitch angle and captured power versus wind speed.
In the first case, the initial wind speed was assumed to be
12 m/s, and was then ramped to the rated value of 15 m/s in
about 1.5 s. To consider wake effects in wind speeds due to the
spacial siting of wind turbines, the wind change was assumed to
act on the wind turbines one by one with an interval of 0.5 s. As
can be seen from Fig. 5, the captured wind power increased in
response to the incoming wind speed. Once the power exceeded
the rated value, the pitch control system began to regulate the
pitch angle. As the pitch angle increased, the power efficiency of
the wind turbine decreased to reduce wind energy capture. After
several seconds, the wind turbine reached a new stable operating
point. The pitch angle was increased to a quite high value to
shed the excessive wind power at the wind speed of 15 m/s. In
this case, the operation mode of the wind turbine was altered
from the optimal speed tracking to rated power generation. The
overshoot in captured power is accounted for by the fact that the
[ Pobierz całość w formacie PDF ]