PERFORMANCE ANALYSIS OF DOUBLY FED INDUCTION GENERATOR BASED WIND ENERGY CONVERSION SYSTEMS A THESIS Submitted by A. RAMKUMAR (Reg.No. 200809207) In partial fulfillment for the award of the degree of DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING KALASALINGAM UNIVERSITY ANAND NAGAR KRISHNANKOIL–626 126 JUNE 2014
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PERFORMANCE ANALYSIS OF DOUBLY FED
INDUCTION GENERATOR BASED WIND
ENERGY CONVERSION SYSTEMS
A THESIS
Submitted by
A. RAMKUMAR
(Reg.No. 200809207)
In partial fulfillment for the award of the degree
of
DOCTOR OF PHILOSOPHY
DEPARTMENT OF ELECTRICAL AND
ELECTRONICS ENGINEERING
KALASALINGAM UNIVERSITY
ANAND NAGAR
KRISHNANKOIL–626 126
JUNE 2014
1
CHAPTER 1
INTRODUCTION
Electrical power is the most widely used source of energy for the
homes, work places and industries. Population and industrial growth have led
to significant increase in power consumption over the past three decades.
Natural resources like coal, petroleum and gas that have driven the power
plants, industries and vehicles for many decades are becoming depleted at a
very fast rate. This serious issue has motivated nations across the world to
think about alternative forms of energy which utilize inexhaustible natural
resources.
The combustion of conventional fossil fuel across the globe has
caused increased level of environmental pollution. Several international
conventions and forums have been setup to address and resolve the issue of
climate change. These forums have motivated countries to form national
energy policies dedicated to pollution control, energy conservation, energy
efficiency, development of alternative and clean sources of energy. The
“Kyoto Protocol to the Convention on Climate Change” has enforced
international environmental regulations which are more stringent than the
1992 earth summit regulations.
Renewable energy sources like solar, wind, and tidal are
sustainable, inexhaustible, environmentally friendly and clean energy sources.
Due to all these factors, wind power generation has attracted great interest in
recent years. Undoubtedly, wind power is today’s most rapidly growing
renewable energy source. Even though the wind industry is young from a
power systems point of view, significant strides have been made in the past 20
2
years. Increasing reliability has contributed to the cost decline with
availability of modern machines reaching 97-99%. Wind plants have
benefited from steady advances in technology made over past 15 years. Much
of the advancement has been made in the components dealing with grid
integration, electrical machine, power converters and control capability, and
now able to control the real and reactive power of the induction machine,
limit power output, control voltage and speed. There is lot of research going
on around the world in this area and technology is being developed that offers
great deal of capability. It requires an understanding of power systems,
machines and applications of power electronic converters and control
schemes put together on a common platform.
Typically wind generation equipment is categorized in three
general classifications:
1. Utility Scale : Corresponds to large turbines used to generate
bulk power for energy markets.
2. Industrial Scale : Corresponds to medium sized turbines mainly
used by industries for remote grid production to
meet local power requirement.
3. Residential Scale : Corresponds to small sized turbines mainly
utilized for battery charging.
Developments in many other areas of technology are adapted to
wind turbines and have helped to hasten their quick emergence. A few of the
many areas which have contributed to the new generation of wind turbines
include materials science, aerodynamics, power electronics, computer science,
testing and analytical methods. The main options in wind turbine design and
construction include [1-2]:
3
• axis of rotation: horizontal or vertical
• number of blades (commonly two and three)
• rotor orientation: downwind or upwind of tower
• blade material, construction method, and profile
• hub design: rigid, teetering or hinged
• power control via aerodynamic control (stall control) or
variable pitch blades (pitch control)
• orientation by self-align action (free yaw), or direct control
(active yaw)
Today, the most common design of wind turbine is the horizontal
axis and three-bladed design.
1.1 WIND ENERGY CONVERSION
Properties of the wind, which are of interest in this research work,
will be described. First the wind distribution, i.e., the probability of a certain
average wind speed will be presented. The wind distribution can be used to
determine the expected value of certain quantities, e.g. produced power. Then
different methods to control the aerodynamic power will be described.
Finally, the aerodynamic conversion, i.e., the so-called Cp(�, �) curve, will be
presented [1-2].
1.1.1 Wind Distribution
The most commonly used probability density function to describe
the wind speed is the Weibull functions [2]. The Weibull distribution is
described by the probability density function as,
4
( )� �� �� �
k-1
� c- kk �f(�)= e
c c (1.1)
Where k is a shape parameter, c is a scale parameter and � is the
wind speed. Thus, the average wind speed (or the expected wind speed), �
can be calculated from,
( )�ave f� = � � d� (1.2)
� �� �� �
ave
c 1� = �
k k (1.3)
where � is Euler’s gamma function, i.e.,
( ) ��
2-1 -t
0
� z = t e dt (1.4)
If the shape parameter equals 2, the Weibull distribution is known
as the Rayleigh distribution. For the Rayleigh distribution the scale factor c,
given the average wind speed can be found from,
ave
2c = �
� (1.5)
1.1.2 Aerodynamic Power Control
At high wind speeds, it is necessary to limit the input power to the
wind turbine, i.e., aerodynamic power control. There are three major ways of
performing the aerodynamic power control, i.e., by stall, pitch, or active stall
control. Stall control implies that the blades are designed to stall in high wind
speeds and no pitch mechanism is required [1]. Pitch control is the most
common method of controlling the aerodynamic power generated by a turbine
rotor for newer larger wind turbines. Almost all variable speed wind turbines
5
use pitch control. Below rated wind speed, the turbine should produce as
much power as possible, i.e., using a pitch angle that maximizes the energy
capture.
Above rated wind speed the pitch angle is controlled in such a way
that the aerodynamic power. In order to limit the aerodynamic power, at high
wind speeds, the pitch angle is controlled to decrease the angle of attack, i.e.,
the angle between the chord line of the blade and the relative wind direction.
It is also possible to increase the angle of attack towards stall in order to limit
the aerodynamic power. This method can be used to fine tune the power level
at high wind speeds for fixed speed wind turbines. This method is known as
active stall control or combi stall control.
1.1.3 Aerodynamic Conversion
Some of the available power in the wind is converted by the rotor
blades to mechanical power acting on the rotor shaft of the �T. The
mechanical power, Pmech can be determined by the eqn. (1.6)
( ) 3
mech r p
1P = �A C �,� �
2 (1.6)
r r� R
�=�
(1.7)
Where Cp is the power coefficient, � is the pitch angle, � is the tip
speed ratio, � is the wind speed, �r is the rotor speed, Rr is the rotor plane
radius, � is the air density and Ar is the area swept by the rotor.
The rotational speed of a wind turbine is fairly low and must be
adjusted to the electrical frequency. This can be done in two ways: with a
gearbox or with the number of pole pairs of the generator. The number of pole
6
pairs sets the mechanical speed of the generator with respect to electrical
frequency and gearbox adjusts the rotor speed of the turbine to mechanical
speed of the generator.
1.2 TYPES OF WIND TURBINE
The following wind turbine systems are normally used in Wind
Energy Conversion System (WECS).
• Fixed speed wind turbine with an induction generator.
• Variable speed wind turbine equipped with a cage bar
induction generator or synchronous generator or multiple pole
synchronous generator or multiple pole permanent magnet
synchronous generator.
• Variable speed wind turbine equipped with a doubly fed
induction generator (DFIG).
1.2.1 Fixed Speed Wind Turbine
For the fixed speed wind turbine the induction generator (IG) is
directly connected to the electrical grid according to Fig. 1.1. The rotor speed
of the fixed speed wind turbine is in principle determined by a gearbox and
the pole pair of the generator. The fixed speed wind turbine system has often
two fixed speeds. This is accomplished by using two generators with different
ratings and pole pairs, or it can be a generator with two windings having
different ratings and pole pairs. This leads to increased aerodynamic capture
as well as reduced magnetizing losses at low wind speeds [3].
7
Fig.1.1 Fixed speed wind turbine with Induction Generator
1.2.2 Variable Speed Wind Turbine
The system presented in Fig.1.2 consists of wind turbine equipped
with a converter connected to the stator of the generator. The generator could
either be a cage bar induction generator or a synchronous generator. The
gearbox is designed so that maximum rotor speed corresponds to rated speed
of the generator. Synchronous generators or permanent magnet synchronous
generators can be designed with multiple poles which implies that there is no
need for a gearbox, see Fig.1.3. Since this full power converter/generator
system is commonly used for other applications, one advantage with this
system is its well developed and robust control [4-6].
Fig.1.2 Variable speed wind turbine with IG or SG
Grid Gear box Starter
Excitation capacitor
IG
Wind turbine
Wind turbine
Grid
Gear box IG/SG
AC-DC
converter
DC-AC
converter
Converter
8
Fig. 1.3 Variable speed wind turbine with SG
1.2.3 Variable Speed Wind Turbine with DFIG
This system, see Fig. 1.4, consists of a wind turbine with DFIG.
This means that the stator is directly connected to the grid while the rotor
winding is connected via slip rings to a converter. This system has recently
become very popular as generators for variable speed wind turbines. This is
mainly due to the fact that the power electronic converter only has to handle a
fraction (20–30%) of the total power. Therefore, the losses in the power
electronic converter can be reduced. In addition, the cost of the converter
becomes lower.
Fig. 1.4 Variable speed wind turbine with DFIG
Grid
SG
Wind turbine
AC-DC
converter
DC-AC
converter
Converter
Wind turbine
Converter
Grid
Gear box DFIG
G
AC-DC
converter
DC-AC
converter
9
There exists a variant of the DFIG method that uses controllable
external rotor resistances. The main drawback of this method is unnecessarily
energy dissipated in the external rotor resistances [7].
1.3 ENERGY EFFICIENCY OF DFIG
Investigation of energy efficiency of DFIG is discussed in the
following section. The energy efficiency is mainly focusing on:
• Reducing the magnetizing losses of the DFIG system.
• Influence of the converter’s size on the energy production.
• Comparison of the DFIG system to other electrical systems.
In this discussion, aerodynamic losses, gearbox losses, induction
generator losses and converter losses are also taken into account.
1.3.1 Aerodynamic Losses
Fig. 1.5 shows the turbine power as a function of wind speed both
for the fixed speed and variable speed systems. It is seen that the fixed speed
system with only one generator has a lower input power at low wind speeds.
The other systems produce almost identical results [8].
Fig. 1.5 Wind speed versus turbine power
0
20
40
60
80
100
120
0 5 10 15 20 25
Tu
rbin
e p
ow
er (
%)
Wind speed (m/s)
FSIG
DFIG
10
1.3.2 Gearbox Losses
Fig.1.6 shows the gearbox losses of the WECS [9]. The gearbox
losses, Ploss,GB is expressed as follows.
rloss,GB lowspeed nom
r,nom
�P = P +P
� (1.8)
Where is the gear mesh losses constant and is a friction constant.
Fig.1.6 Gearbox losses
1.3.3 Induction Generator Losses
In order to calculate the losses of the generator, the equivalent
circuit of the induction generator with inclusion of magnetizing losses has
been used. For the DFIG system, the voltage drop across the slip rings has
been neglected. Moreover, the stator to rotor turns ratio for the DFIG is
adjusted so that maximum rotor voltage is 75% of the rated grid voltage. This
is done in order to have safety margin, i.e., a dynamic reserve to handle, for
instance, a wind gust. Observe that instead of using a varying turns ratio, the
same effect can also be obtained by using different rated voltages on the rotor
and stator [10]. In Fig.1.7 the induction generator losses of the DFIG system
0
0.5
1
1.5
2
2.5
3
4 6 8 10 12 14 16
% v
alu
e of
gea
rbo
x l
oss
es
Wind speed (m/s)
VSIG
FSIG
11
are shown. The reason that the generator losses are larger for high wind
speeds for VSIG system compared to the DFIG system is that the gearbox
ratio is different between the two systems. This implies that the shaft torque
of the generators will be different for the two systems, given the same input
power. It can also be noted that the losses of the DFIG are higher than those
of the VSIG for low wind speeds. The reason for this is that the flux level of
the VSIG system has been optimized from an efficiency point of view while
for the DFIG system the flux level is almost fixed to the stator voltage. This
means that for the VSIG system a lower flux level is used for low wind
speeds, that is, the magnetizing losses are reduced.
Fig.1.7 Induction generator losses
1.3.4 Converter Losses
In order to feed the IG with a variable voltage and frequency
source, the IG can be connected to a pulse width modulated (PWM)
converter. In Fig.1.8, an equivalent circuit of the converter is drawn, where
each transistor T1 to T6 is equipped with a reverse diode. A PWM circuit
switches the transistors to ON and OFF states. The duty cycle of the transistor
and the diode determines whether the transistor or a diode is conducting in a
transistor leg (e.g., T1 and T4).
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25
% v
alu
e o
f in
du
cti
on
gen
era
tor loss
es
Wind speed (m/s)
DFIG
VSIG
FSIG
12
Fig.1.8 Converter scheme
The losses of the converter can be divided into switching loss and
conducting loss. The switching loss of the transistors is the turn on and turns
off losses. For the diode the switching loss mainly consist of turn off losses
[11], that is, reverse recovery energy. The turn on and turn off losses for the
transistor and the reverse recovery energy loss for a diode can be found from
data sheets. The conducting losses arise from the current through the
transistors and diodes. The transistor and the diode can be modeled as
constant voltage drops, VCE0 and VT0, and a resistance in series, RCE and RT,
see Fig.1.8. The total converter losses are now presented as a function of wind
speed in Fig.1.9. It can, as expected, be noted that the converter losses in the
DFIG system are much lower compared to the full power converter system.
Fig.1.9 Converter losses
0
0.5
1
1.5
2
2.5
0 5 10 15 20 25
% v
alu
e o
f co
nvert
er loss
es
Wind speed (m/s)
DFIG
VSIG
13
1.3.5 Comparison of Wind Turbine Systems
The base assumption made here is that all wind turbine systems
have the same average maximum shaft torque as well as the same mean upper
rotor speed. In Fig.1.10, the produced grid power together with the various
loss components for an average wind speed of 6 m/s are presented for the
various systems. The systems are DFIG system, the full variable speed
system, fixed speed system and a variable speed system equipped with a
permanent magnet synchronous generator (PMSG).
The converter loss of the PMSG system is assumed equal to that of
the VSIG system. It would also be possible to have the PMSG connected to a
diode rectifier with series or shunt compensating capacitors, which may give a
possibility to reduce the converter losses [12]. However, a transistor rectifier
has the potential to utilize the generator best. In Fig.1.10 the produced energy
of the different systems for various average wind speeds are presented.
Fig.1.10 Energy efficiency of Generators
1.3.6 Advantages of the DFIG based Wind Turbine Generator
System
The DFIG is having lot of advantages than the other types such as FSIG,
VSIG and PMSG. Some of the advantages of DFIG are given below.
82
84
86
88
90
92
94
96
5 6 7 8 9 10
% v
alu
e o
f p
rod
uce
d
energ
y
Average wind speed (m/s)
FSIG
PMSG
DFIG
VSIG
14
• It has the ability of decoupling the control of the active and
reactive power by controlling the rotor terminal voltages.
Hence, the power factor control can be implemented in this
system.
• The DFIG is usually a wound rotor induction generator, which
is simple in construction and cheaper than a PMSG.
• In a DFIG based wind turbine generator system, the power
rating of the power converters is typically rated ±30% around
the rated power. This characteristic leads to many merits, such
as reduced converter cost, reduced filter volume and cost, less
switching losses, less harmonic injections into the connected
grid. Improved overall efficiency (approx. 2-3% more than
full-scale frequency converter) if only the generator and power
converters are considered.
• Aerodynamic, gearbox and converter losses of the DFIG are
less.
Because of the above reasons, DFIG is chosen for this research among the
other common types.
1.3.7 Disadvantages of the DFIG based Wind Turbine Generator
System
The major drawbacks of DFIG are specified below:
• Needs slip rings also it requires frequent maintenance.
• Has limited fault ride through capability and needs protection
schemes.
• Have complex control schemes.
15
1.4 PROTECTIVE ARRANGEMENT OF DFIG
For wind power generation systems, the DFIG, with its variable
wind speed tracking performance and relatively low cost compared to fully
rated converter wind power generation system, e.g. PMSG, is a popular wind
generation concept. However, a disadvantage of the DFIG is its vulnerability
to grid disturbances because the stator windings are connected directly to the
grid. So as to protect the wind farm from interruptions due to onshore grid
faults and wind farm faults, crowbar protects the induction generator and
associated power electronics. This is widely used in industrial applications.
1.4.1 Converter Protection Systems
The prevalent DFIG converter protection scheme is crowbar
protection. A crowbar is a set of resistors that are connected in parallel with
the rotor winding on occurrence of an interruption. The crowbar circuit
bypasses the rotor side converter. The active crowbar control scheme
connects the crowbar resistance when necessary and disables it to resume
DFIG control and Fig. 1.11 shows the DFIG with protection scheme.
For active crowbar control schemes, the control signals are
activated by the rotor side converter devices. These have voltage and current
limits that must not be exceeded. Therefore the rotor side converter voltages
and currents are the critical regulation reference. The DC link bus voltage can
increase rapidly under these conditions, so it is also used as a monitored
variable for crowbar triggering.
16
Fig. 1.11 DFIG with protection scheme
A braking resistor (DC chopper) can be connected in parallel with
the DC link capacitor to limit the overcharge during low grid voltage. This
protects the IGBTs from overvoltage and can dissipate energy, but this has no
effect on the rotor current. It is also used as protection for the DC link
capacitor in full rated converter topologies, for example, PMSGs.
In a similar way to the series dynamic braking resistor, which has
been used in the stator side of generators, a dynamic resistor is proposed to be
put in series with the rotor (series dynamic resistor) and this limits the rotor
over current. Being controlled by a power electronic switch, in normal
operation, the switch is on and the resistor is bypassed; during fault
conditions, the switch is off and the resistor is connected in series to the rotor
winding.
The latter are shunt connected and control the voltage while the
series dynamic resistor has the distinct advantage of controlling the current
magnitude directly. Moreover, with the series dynamic resistor, the high
voltage will be shared by the resistance because of the series topology, so the
induced overvoltage may not lead to the loss of converter control. Therefore it
not only controls the rotor overvoltage which could cause the rotor side
converter to lose control, but, more significantly, limits high rotor current. In
addition, the limited current can reduce the charging current to the DC link
Vr
�lr Rr Crow bar DC chopper
Series resistor
RSC
Bypass switch
Rotor
17
capacitor, hence avoiding DC link overvoltage. So, with the series dynamic
resistor, the rotor side converter does not need to be inhibited during the fault.
The crowbar is adequate for protection of the wind turbine system
during grid faults in on-shore developments. The influence of temporarily
losing rotor side control of DFIGs can be neglected, which is not presently the
case for large scale offshore wind farms. The series topology is
straightforward enough to limit the over current and share overvoltage but
there appears to be no literature investigating their use.
1.4.2 Influence of High Crowbar Resistance on Natural Stator Flux
For a DFIG with high total rotor resistance, the stator transient time
constant needs to be expressed in a different way. The natural stator flux,
which is fixed with respect to the stator, generates a voltage in the rotor. Thus
the magnitude and frequency in a rotor reference frame are proportional to the
rotor speed. A current will flow in the rotor, having the same frequency of the
induced voltage and opposite to the rotor speed.
1.4.3 Influence of High Crowbar Resistance on Natural Rotor Flux
The flux in a rotor reference frame is a DC component decaying
with the rotor transient time constant. This fact is no longer true for a DFIG
with high rotor resistance.
1.4.4 Influence of High Crowbar Resistance on Negative Sequence
Fluxes
The rotor negative sequence current can be obtained with a simple
current division between the magnetizing and rotor circuit branches.
18
1.5 OUTLINE OF THE THESIS
Based on the literature survey of mathematical modeling and various
control schemes such as PI, resonant, DTC, DPC and DCC of DFIG, the
thesis is organized in six chapters. The documentation of the research is
accomplished to fulfill the above aims. The chapter organizations of the thesis
are as follows:
Chapter I: Introduction
The background and the motivation for the research have been
presented along with a brief description of the published research work in the
wind energy conversion system.
Chapter II: Literature Survey
The literature review of mathematical modeling of DFIG, PI, resonant,
DTC, DPC and DCC controllers are discussed.
Chapter III: Mathematical Modeling of DFIG
A whole model of a DFIG in grid, equivalent circuits in dq frame,
power flow and back to back PWM converters are discussed.
Chapter IV: Performance of DFIG with Proportional Integral and
Resonant control schemes in Grid
Designing aspects of conventional, proportional integral and resonant
controllers are built using PSCAD simulation software. The effects of those
are DFIG controllers in grid are compared at various cases such as transient
and post transient conditions, wind speed variations, effects of harmonics at
19
unbalanced conditions and load contribution of DFIG with PI and resonant
controllers in grid.
Chapter V: Performance of DFIG with Direct torque and Direct Power
control schemes in Grid
This chapter discusses the expression of torque equation based on sine
and cosine components and mathematical expression of stator power
equations based on dq+ reference frame. Finally, implementing direct torque
and direct power controllers in the rotor circuit of DFIG with grid and
compare its simulation results.
Chapter VI: Control Scheme of Direct current controller in DFIG with
Grid
The transient responses of the control schemes at a short circuit fault in
the external are analyzed in detail. In critical post-fault situations, a control
strategy is proposed to help recovering the terminal voltage and improving the
system transient stability, which is verified by the simulation results.
Chapter VII: Conclusion
The main conclusions and contributions of the research documented in
this thesis are highlighted with suggestions for future work.
Appendices
The DFIG wind turbine model has been developed in the dedicated
power system analysis tool, PSCAD/EMTDC. This appendix describes the
function of the main blocks in the DFIG, e.g. current reference pulse width
modulator (CRPWM), determination of rotating magnetic flux vector,
generation of rotor current in dq axis and Switched Pulse Width Modulation
(SPWM).
20
CHAPTER 2
LITERATURE SURVEY
The performance and controllability of DFIG are excellent in
comparison with FSIG systems; they capture more wind energy, they exhibit
a higher reliability gear system, and high quality power supplied to the grid. It
saves investment on full rated power converters, and soft starter or reactive
power compensation devices (fixed speed systems). Modern wind farms, with
a nominal turbine power up to several MWs, are a typical case of DFIG
application. Besides this, other applications for the DFIG systems are, for
example, flywheel energy storage system, stand alone diesel systems, pumped
storage power plants, or rotating converters feeding a railway grid from a
constant frequency utility grid. In practical applications, the DFIG is
gradually maturing as a technology for variable speed wind energy utilization.
Although topologies of new systems with improved performance are
emerging both in academia and industry, DFIG is the most competitive option
in terms of balance between the technical performance and economic costs.
The following sections discuss about the literature survey of
mathematical modeling, designing of and various controller techniques such
as proportional integral, resonant, direct torque, direct power and direct
current controllers of DFIG.
2.1 MODELING OF DFIG
Lie Xu et al (2007) presented an analysis and control design of a
DFIG based wind generation system operating under unbalanced network
conditions [13]. Variations of stator active, reactive powers and generator
torque are fully defined in the presence of negative sequence voltage and
21
current. A rotor current control strategy based on positive and negative dq
reference frames is used to provide precise control of the rotor positive and
negative sequence currents. The proposed control strategy, the enhanced
system control and operation such as minimizing oscillations in active power,
electromagnetic torque, stator and rotor currents are achieved.
Yi Wang et al (2010) investigated the control and operation of
DFIG and FSIG based wind farms under unbalanced grid conditions [14]. The
behaviors of the DFIG and FSIG systems under unbalanced supplies
described using a mathematical model. The performance of DFIG based wind
farms can be improved by regulating the negative sequence current to
eliminate torque, output power, and DC voltage oscillations. The coordinated
control of the DFIG’s RSC and GSC, for compensating voltage unbalance and
torque ripple are presented. The proposed DFIG control system improved not
only its own performance, but also the stability of the FSIG system with the
same grid connection point during network unbalance.
Alvaro Luna et al (2011) presented the fault ride through (FRT)
capability of DFIG in wind power applications. A simplified model of the
DFIG is extracted from the classical 5th
order model [15]. The mathematical
models of such generators enabled to analyze their response under generic
conditions. However, their mathematical complexity did not contribute to
simplifying the analysis of the system under transient conditions and not help
in finding straightforward solutions for enhancing their FRT. Also, accurately
estimate the behavior of the system while significantly reducing its
complexity is discussed.
2.2 PI AND RESONANT CONTROLLERS OF DFIG
Mansour Mohseni et al (2011) proposed the enhanced hysteresis
based current regulators in the field oriented vector control of DFIG wind
22
turbines [16]. This proposed control scheme is synchronized with the virtual
grid flux space vector, readily extractable by a quadrature phase locked loop
(QPLL) system. Identical equidistant band vector based hysteresis current
regulators (VBHCRs) are used to control the output currents of the rotor and
grid side converters. The proposed current regulator is comprised of two
multilevel hysteresis comparators integrated with a switching table. The main
advantages of this current regulator are the very fast transient response,
simple control structure, and intrinsic robustness to the machine parameters
variations.
Changjin Liu et al (2012) proposed the stator current harmonic
suppression method using a resonant controller to eliminate negative
sequence 5th
and positive sequence 7th
order current harmonics [17]. A stator
current harmonic control loop is added to the conventional rotor current
control loop for harmonic suppression. The overall control scheme is
implemented in dq frame. The proposed resonant controller is provided the
negative sequence 5th
and positive sequence 7th
order harmonics in the stator
current are significantly suppressed and the 6th
order torque pulsations in the
generator are also reduced.
Van-Tung Phan et al (2012) investigated the control of a standalone
DFIG based wind power conversion system with unbalanced and nonlinear
loads. Under these load conditions, the quality of stator voltage and current
waveforms of the DFIG is strongly affected due to the negative and distorted
components, reducing the performance of other normal loads connected to the
DFIG. This problem is tackled by the control strategy is comprehensively
developed in both RSC and GSC of the DFIG. The GSC is used as an active
power filter to compensate for unbalanced and distorted stator currents
whereas the RSC is developed to fully eliminate unbalanced and harmonic
voltages at the point of common coupling (PCC). The proposed compensation
23
method is based on current controllers in either the RSC or the GSC, which
employed a proportional integral plus a resonant controller [18]. Analytical
issues on how to eliminate unbalanced and distorted components in the stator
voltage and current are described.
Jiaqi Liang et al (2013) proposed the feed forward transient
compensation (FFTC) control scheme with proportional integral resonant
current regulators for the low voltage ride through (LVRT) capability of
DFIG during both balanced and unbalanced grid faults. The FFTC current
controller improved the transient rotor current control capability and
minimized the DFIG control interruptions during both balanced and
unbalanced grid faults. The proposed FFTC control introduced minimal
additional complexity to a regular DFIG vector control scheme and promising
enhancements in the LVRT capability of DFIGs [19]. Also the second order
harmonic torque ripple is reduced.
2.3 DIRECT TORQUE CONTROLLER OF DFIG
Slavomir Seman et al (2006) presented a ride through study DFIG
under a short term unsymmetrical network disturbance. DFIG is represented
by an analytical two axis model with constant lumped parameters and by a
finite element method (FEM) based model [20]. The model of the DFIG is
coupled with the model of the active crowbar protected and direct torque
controller (DTC) frequency converter. The results obtained by means of an
analytical model and FEM model of DFIG are compared in order to reveal the
influence of the different modeling approaches on the short term transient
simulation accuracy.
Jihen Arbi et al (2009) presented a grid connection control strategy
of DFIG wind system based on the direct control of both virtual torque and
rotor flux of the generator [21]. This control is achieved with no PI regulator
24
and it is required the measurement of only grid voltages, rotor currents and
rotor position. A field programmable gate array based design of the proposed
control is developed and the experimental results are provided the
effectiveness of the fast and soft grid connection method.
Etienne Tremblay et al (2011) presented the comparison of three of
the most widespread and well performing control approaches which are
implemented in an experimental setup based on a digital signal processor
(DSP), namely, vector control, direct torque control, and direct power control
[22]. Proposed work imposed lower instrumentation constraints and has the
lowest total harmonic distortion (THD), the direct methods are up to four
times faster than vector control in transitory response. The qualitative and
quantitative results are obtained in the field of DFIG based WECS.
2.4 DIRECT POWER CONTROLLER OF DFIG
Peng Zhou et al (2009) proposed an improved coordinate direct
power controller (DPC) strategy for the DFIG and the GSC of a wind power
generation system under unbalanced network conditions [23]. Two improved
DPC schemes for the DFIG and the GSC are presented, respectively. The
torque and stator reactive power pulsations are eliminated by DPC for RSC
and the pulsations of stator active power is compensated by DPC for GSC.
This improved DPC eliminated the torque and power pulsations produced by
the transient unbalanced grid faults. So that the output power of DFIG and
GSC can be directly regulated without any necessity of the positive and
negative sequence decomposition.
Gonzalo Abad et al (2010) analyzed the behavior of a DFIG under
unbalanced grid voltage conditions. This analyze provided the main ideas for
generation of the active and reactive power references for RSC and GSC,
controlled by means of DPC techniques [24]. And also they proposed a new
25
algorithm that generates the RSC power references, without the necessity of a
sequence component extraction, in order to eliminate torque oscillations and
achieve sinusoidal stator currents exchange. Also, the GSC power references
are provided by means of voltage and current sequence extraction. By the
proposed control strategy, the total current exchanged by the wind turbine is
unbalanced; it is not possible to contribute to palliate the grid voltage
unbalance.
Lei Shang and Jiabing Hu (2012) proposed an improved DPC
strategy of grid connected wind turbine driven DFIGs when the grid voltage is
unbalanced. Also it is discussed for directly regulating the instantaneous
active and reactive powers in the stator stationary reference frame without the
requirement of either synchronous coordinate transformation or phase angle
tracking of grid voltage [25]. By this proposed DPC technique, the active and
reactive power compensation method provided without involving the
decomposition of positive sequence grid voltage, negative sequence stator
current and nature of deteriorated performance without considering
unbalanced grid voltage.
Sguarezi Filho A.J et al (2012) proposed a model based predictive
controller for DFIG direct power control. This proposed method derived the
control law objective function that considered the control effort between the
predicted outputs and those outputs calculated using a linearized state space
model [26]. The controller used active and reactive power loop directly for
the generator power control. The generator leakage inductance and resistance
are required for this control method and the influence of the estimation errors
for these parameters is also investigated.
26
2.5 DIRECT CURRENT CONTROLLER OF DFIG
Castilla, M et al (2010) presented a direct rotor current mode
control (CMC) for the RSC of the IGs, which is aimed to improve the
transient response in relation to the dynamic performance achieved with the
conventional (indirect) CMC [27]. These control schemes are compared the
performance and cost with the indirect CMC schemes.
Shuhui Li et al (2012) presented a direct current vector control
method in a DFIG wind turbine based on which an integrated control strategy
is developed for wind energy extraction, reactive power and grid voltage
support controls of the wind turbine [28]. A transient simulation system using
SimPower System is built to validate the effectiveness of the proposed control
method. This control approach is more stable, reliable, has better dynamic
performance, and superior behavior particularly under the ac system bus
voltage control mode. But, for high PCC bus voltage sag, it may be
impossible to boost the PCC voltage to the rated voltage for the converter
linear modulation constraints.
Changjin Liu et al (2013) proposed a novel DC capacitor current
control loop is used to increase the loop gain, is added to the conventional
GSC current control loop [29]. The rejection capability to the unbalanced grid
voltage and the stability of the proposed control system are discussed. But this
proposed system, 2nd
order harmonic current in the dc capacitor as well as dc
voltage fluctuation is eliminated.
2.6 SUMMARY
This chapter discussed about the literature review of modeling of
DFIG, behavior analysis of DFIG with the various controllers. Based on this,
mathematical modeling of DFIG at steady state, dq model of arbitrary and
rotor reference frames are discussed in the next chapter.
27
CHAPTER 3
MATHEMATICAL MODELING OF DFIG
To investigate the performance of grid connected wind turbines and
their interaction with the grid, a proper model of grid connected wind turbines
shall be established first. The grid connected wind turbine model simulates
the dynamics of the system from the turbine rotor where the kinetic wind
energy is converted to mechanical energy to the grid connection point where
the electric power is fed into the grid.
In this chapter, the mathematical modeling of DFIG with grid is
developed. First, a general introduction of the steady state equivalent circuit is
discussed. Next, the dq model in the arbitrary reference frame, dq model in
the rotor fixed reference frame, power flow and PWM voltage source
converters are presented in sequence. Finally, a summary of the models of
different components of DFIG with grid connected wind turbines completes
the chapter.
3.1 OVERALL STRUCTURE OF WIND TURBINE MODEL
The grid connected wind turbine considered here applies a DFIG,
using back to back PWM voltage source converters in the rotor circuit.
Fig.3.1 illustrates the main components of the grid connected wind turbine,
where PDFIG, QDFIG are the DFIG output active and reactive powers. The
complete grid connected wind turbine model includes the wind speed model,
the aerodynamic model of the wind turbine, PWM voltage source converters,
and the control system. Fig. 3.2 shows the overall structure of the grid
connected wind turbine model.
28
Fig.3.1 Block diagram of DFIG
The equivalent wind speed �eq represents the whole field of wind
speeds in the rotor plane of the wind turbine. To include the spatial variations
of the wind speed field in the rotor plane, the wind model uses the turbine
rotor position �R, which is fed back from the mechanical model. The
aerodynamic model uses an equivalent wind speed �eq, the wind turbine rotor
speed �R and the blade pitch angle � as inputs. Its output is the aerodynamic
torque T�.
Fig. 3.2 Overall structure of wind turbine model
The inputs to the mechanical model are the aerodynamic torque T�
and the electromagnetic torque Te. The outputs are �R and the generator speed
�G. The �G is used by the control system for speed control. The electrical
Wind turbine
Grid
Gear box DFIG
AC-DC
converter
DC-AC
converter Crow bar
Rotor side
converter
Grid side
converter
�R
IGRID
QGRID
PGRID
VGRID
�f
�G T�
TG �R �eq
�
Control system
Wind Aero-
dynamic
Mechanical Electrical Grid
29
model provides the generator Te and uses the �G as input. In the other end, the
electrical model interfaces with the grid by the voltage VGRID and current iGRID
on the wind turbine terminal. The electrical model also outputs the active
power PDFIG and reactive power QDFIG representing the measured voltages and
currents of the control system [29]. The control system provides a number of
control signals for the electrical model including the control signals to the
PWM converters. The model of the DFIG with grid connected system is
developed in the dedicated power system analysis tool, PSCAD. It is also
known as PSCAD/EMTDC. EMTDC is the simulation engine, which is the
integral part of PSCAD. It is most suitable for simulating the time domain
instantaneous responses, also popularly known as electromagnetic transients
of electrical systems.The grid model and the electrical components of the
wind turbine are built with standard electrical component models from
PSCAD/EMTDC library. The wind model, the aerodynamic model, and the
mechanical model are built with custom components developed in
PSCAD/EMTDC. The control system of the wind turbine is also built with
custom components developed in PSCAD/EMTDC. The procedure for
developing the DFIG model is discussed in Appendix.
3.2 STEADY STATE EQUIVALENT CIRCUIT
Fig 3.3 shows the diagram of the steady state equivalent circuit of
the DFIG [30], where the quantities on the rotor side are referred to the stator
side. In the equivalent circuit, Vs and Vr are the applied stator phase voltage
and rotor phase voltage to the induction machine respectively [V], Er is the
electro motive force [V], is is the stator current [A], ir is the rotor current [A],
i0 is the no load current [A], Rs is the stator resistance [ � ], Rr is the rotor
resistance [ � ], Xs is the stator leakage reactance [ � ], Xr is the rotor leakage
reactance [ � ], Rm represents the magnetizing losses [ � ], Xm is the
magnetizing reactance [ � ], s is the generator slip.
30
Fig.3.3 Steady state equivalent circuit of DFIG
Applying Kirchhoff’s voltage law to the circuit in Fig. 2.3 we get,
s s s s s rV = R i + jX i - E (3.1)
r rr r r r
V R= i + jX i - E
s s (3.2)
( )r m m oE = - R + jX X (3.3)
0 s ri = i +i (3.4)
This equivalent circuit, based on calculations with rms values of
voltages and currents, can only be applied for steady state analysis of the
DFIG.
3.2.1 Operation Principle
For an ordinary wound rotor induction generator with short
circuited rotor, i.e. the applied voltage to the rotor Vr is zero, the relationship
between the Te and the real current in the rotor circuit can be expressed.
ir
Er io
is
Rm
Rr/s jXr
jXm
jXs Rs
Vs Vr/s
31
e T m raT = C � i (3.5)
Where CT is the torque coefficient, �m is the air gap magnetic flux
per phase [Wb], ira is the real current in the rotor circuit [A].
The real current in the rotor circuit can be calculated using eqn. (3.6).
( ) ( )
r rra 2 222
r rr r
sE Ri =
R + sXR + sX
(3.6)
( )r r
22
r r
sR E=
R + sX (3.7)
The voltage applied to the stator of the induction generator and the
load torque is kept constant, the real current in the rotor circuit will be a
constant value and neglecting the rotor reactance.
rra=
r
sEi = const
R (3.8)
When an external voltage is applied to the rotor circuit,
r rra
r
s'E +Vi =
R (3.9)
Therefore, it is possible to control the speed of the generator as well
as the stator side power factor by modulating the magnitude and phase of the
applied voltage, while keeping the electromagnetic torque constant [30], as
shown in Fig.3.4.
Phasor diagrams of generator are shown in Fig. 3.4. Where B is the
air gap magnetic flux intensity [T], irr is the reactive current in the rotor
circuit [A], �s is the angle between Vs and is [deg]. As Vr is voltage to the rotor
32
in opposite direction of sEr & ira drops, which results in a reduction of the
electromagnetic torque. Assuming the load torque is kept constant, any
reduction in the Te causes the rotor to accelerate. When the generator slip
reaches s�, where Vr + s�E & equals sEr, the ira recovers that leads to a new
balance of the torques. If Vr, sEr have the same direction, the generator slip
arises until the torques are balanced. The generator can even be operated at
sub-synchronous speed provided that the magnitude of Vr is large enough.
Fig. 3.4 Phasor diagrams of the DFIG
For a DFIG driven by a wind turbine, the aerodynamic torque
varies as the wind speed changes. With the interference of the Vr, the Te may
be varied so that the generator operates at the required speeds. Meanwhile,
regulating the rotor voltage may control the stator side power factor.
33
Fig. 3.5 Phasor diagrams of the DFIG in different operation modes