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]:
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• 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].
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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.
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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.
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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.
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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
(a) sub-synchronous mode (b) super-synchronous mode
With the interference of the voltage in the rotor circuit, the DFIG
can be operated in both sub-synchronous and super-synchronous mode. The
corresponding phasor diagrams are shown in Fig. 3.5, where �r is the angle
between Vr and ir [deg]. The rotor subtracts power from the grid when the
generator is operated in sub-synchronous mode. On the contrary, in super-
synchronous mode, the rotor supplies power to the grid.
3.3 dq MODEL IN THE ARBITRARY REFERENCE FRAME
Fig.2.6 shows the equivalent circuit of induction machine with dq
axis in the arbitrary reference frame. By using the dq model, three to two
phase representations are described.
34
(a)
(b)
Fig. 3.6 Equivalent circuit of induction machine in the arbitrary
reference frame (a) d axis equivalent circuit (b) q axis
equivalent circuit
The following assumptions are made for developing the dq model
of induction machine [31]:
• Iron losses are neglected.
• Stator and rotor skin effects are neglected.
• Magnetizing inductance saturation is neglected.
• Constant air gap reluctance.
- -
+ + - + - +
(�-�r)�qr ��qs idr ids
lm
Rr lr
Vds
ls Rs
Vdr
- -
+ + + - + -
(�-�r)�dr ��ds iqr iqs
lm
Rr lr
Vqs
ls Rs
Vqr
35
• Stator and rotor windings of the DFIG are assumed
symmetric.
• Windings are assumed as sinusoidally distributed.
The transformation matrix is expressed in the eqn. (3.10).
[ ]� ��
� �
� �
cos� cos(� - 120 ) cos(�+120 )2P =
3 -sin� -sin(� - 120 ) -sin(�+120 ) (3.10)
Where � is the angle between the abc and dq axis.
Based on the equivalent circuit in Fig. 3.6, stator and rotor voltages
in dq axis are expressed in the following eqns. (3.11)-(3.14).
dsds s ds qs
d�V = R i + -��
dt (3.11)
qs
qs s qs ds
d�V = R i + +��
dt (3.12)
drdr r dr r qr
d�V = R i + -(� -� )�
dt (3.13)
qr
qr r qr r dr
d�V = R i + +(� -� )�
dt (3.14)
Flux linkage of stator and rotor are expressed as:
ds s ds m dr� = l i +l i (3.15)
qs s qs m qr� = l i +l i (3.16)
dr r dr m ds� = l i +l i (3.17)
36
qr r qr m qs� = l i +l i (3.18)
Where
s ls m
l = l +l (3.19)
r lr ml = l +l (3.20)
From the above equations, real and reactive powers of stator and
rotor are expressed in the following eqns. (3.21-3.24).
( )s ds ds qs qs
3P = V i +V i
2 (3.21)
( )r dr dr qr qr
3P = V i +V i
2 (3.22)
( )s qs ds ds qs
3Q = V i -V i
2 (3.23)
( )r qr dr dr qr
3Q = V i -V i
2 (3.24)
Te is calculated by:
( )e m qs dr ds qr
3T = PL i i - i i
2 (3.25)
Where P is the number of pole pairs.
3.4 dq MODEL IN THE ROTOR FIXED REFERENCE FRAME
In general, four types of reference frames are widely used: stator
fixed, rotor fixed, flux vector fixed or synchronous rotating reference frame.
Since an investigation of a rotor phenomenon is to be performed, a rotor fixed
37
reference frame is chosen in this study. The dq model in the rotor fixed
reference frame is expressed as follows [31], where the quantities on the rotor
side are referred to the stator side.
dsds s ds r qs
d�V = R i + -� �
dt (3.26)
qs
qs s qs r ds
d�V = R i + -� �
dt (3.27)
drdr r dr
d�V = R i +
dt (3.28)
qr
qr r qr
d�V = R i +
dt (3.29)
ds s ds m dr� = l i +l i (3.30)
qs s qs m qr� = l i +l i (3.31)
dr s dr m ds� = l i +l i (3.32)
qr s qr m qs� = l i +l i (3.33)
Where
s ls ml = l +l (3.34)
r lr ml = l +l (3.35)
Based on the above discussion, equation of Te is similar for
arbitrary reference frame (3.24). The flux linkages equations are substituted
into the respective voltage equations so that four current equations are derived
to describe the DFIG model.
ds s r m r m ds m
ds r qs dr qr dr
s s r s s s r
di R R l � l V l� = - i +� i + i + i + - V
dt l l l l l l l (3.36)
38
qs qss r m r m mr ds qs dr qr qr
s s s r s s r
di VR � l R l l� =� i - i - i + i + - V
dt l l l l l l l (3.37)
2
dr s m r m r m m drrds qs dr qr ds
s r r r s r s r r
di R l � l � l l VR� = i - i - i - i - V +
dt l l l l l l l l l (3.38)
2qr qrr m s m r m mr
ds qs qr qr qs
r s r s r r s r r
di V� l R l � l lR� = i + i + i - i - V +
dt l l l l l l l L l (3.39)
Where
2
m
s r
l�= 1-
l l (3.40)
3.5 POWER FLOW
In order to investigate the power flow of the DFIG system the
apparent power that is fed to the DFIG via the stator and rotor circuit has to be
determined. The stator apparent power Ps and rotor apparent power Pr can be
found as:
2 2* *
s s s s s 1 s� s 1 m sP = 3V i = 3R i + j3� l i + j3�� i (3.41)
2
2* *
r r r r r 1 s� r 1 m rP = 3V i = 3R i + j3� sl i + j3� s� i (3.42)
This can be rewritten as:
2
2 2 2m *
s s s 1 s� s 1 m rm 1 m r
m
�P = 3R i + j3� l i + j3� + 3R i - j3� � i
l (3.43)
2 2 *
r r r 1 s� r 1 m rP = 3R i + j3� sl i + j3� s� i (3.44)
39
Now the stator and rotor power can be determined as
[ ] � � ≈� � 2 2 * *
rs s s s m r 1 m m r 1 m mP = Real P = 3R i +3R i m +3� i � i 3� i � i (3.45)
[ ] � � ≈� � *
2 *
r s r r 1 m m r 1 m m rP = Real P = 3R i - 3� si � i -3� si � i
(3.46)
The resistive and magnetizing losses have been neglected for the
approximations of stator and rotor powers. Then, by dividing Pmech with
mechanical rotor speed �m = �r/np, the produced electromechanical torque
can be found. Moreover, this means that Ps � Pmech/(1 − s) and
Pr � −sPmech/(1 − s). In Fig. 3.7 the power flow of a lossless DFIG system can
be seen.
Fig. 3.7 Lossless DFIG system
Moreover, the rotor power Pr �−sPs. Therefore, as mentioned
earlier, the rotor converter can be rated as a fraction of the rated power of the
DFIG if the maximum slip is low.
3.6 PWM VOLTAGE SOURCE CONVERTER MODEL
To ensure that the DFIG operates in a wide speed range, the
requirement lies in the configuration of the converter. For most of the
configurations with cyclo converters, naturally or line commutated converters
Pmech
sPmech/(1-s)
Grid
Pmech/(1-s)
Converter
DFIG
40
and low frequency forced commutated thyristor converters, harmonic
distortion and poor power factor are the major shortcomings, along with
limited control flexibility. To realize advanced control and harmonic
reduction, the back to back PWM converter structure is an attractive
candidate. PWM voltage source converters are commonly used in AC motor
drives where the objective is to produce a sinusoidal AC output voltage whose
magnitude and frequency can both be controlled. The control of the
magnitude and frequency of the AC output voltage is achieved by PWM of
the converter switches that is also responsible to shape the AC output voltage
to be as close to a sine wave as possible. The detailed PWM voltage source
converter model has been studied in the literature [31-32].
For a detailed PWM voltage source converter model, the power
electronic components should be switched on and off at a high frequency (few
kHz or higher), which requires a very small simulation time step to well
represent the PWM waveforms. The simulation speed is thus fairly slow.
Therefore, the detailed PWM voltage source converter model is unsuitable for
investigations that require a long simulation time.
Since the study interest is not concentrated on the switches of the
PWM voltage source converter, an average model without switches is used so
that the simulation can be carried out with a larger time step resulting in a
simulation speed improvement [33]. The average model can be built based on
the energy conservation principle. The instantaneous power must be the same
on the DC side and the AC side of the converter (assuming an ideal
converter):
The average model also assumes that the PWM voltage source
converters will ideally reproduce the reference voltages from the control
41
schemes, with the limitation from the DC link voltage value. Thus the
preferred voltages are directly applied to the generator and the grid without
any switches. The average PWM voltage source converter model is shown in
Fig. 3.8.
Fig. 3.8 Block diagram of the average PWM voltage source converter
model
3.7 SUMMARY
Modeling of DFIG with grid is essential for the research work of
DFIG with grid connected system. This chapter discussed about steady state
equivalent circuit, dq model in the arbitrary reference frame, dq model in the
rotor fixed reference frame, power flow of DFIG and the PWM voltage
source converter model.
In the overall structure of the wind turbine model, based on the
aerodynamic, electromagnetic torque inputs and outputs of rotor, generator
speeds the wind turbine is controlled. Also many number of control signals
are controlled the speed of wind turbine.
Output2
Output1
idc
Vabc
iabc
Vdc Input3
Input2
Input1
Vaia+Vbib+Vcic Divider
Vabc_ctrl
42
Operating principle is discussed with the steady state equivalent
circuit of induction machine. Also the wound rotor induction machine model
is built with detailed description of the stator and rotor direct and quadrature
axis currents (or flux linkages) are discussed with arbitrary and rotor reference
frames. The stator and rotor powers of DFIG are derived with the lossless
system.
Switched ON and OFF of the power electronic components with
high frequency and its functions are discussed in detailed PWM voltage
source converter model.
43
CHAPTER 4
PERFORMANCE OF DFIG WITH PROPORTIONAL
INTEGRAL AND RESONANT CONTROL
SCHEMES IN GRID
An advantage of variable speed wind turbine is that the rotor speed
can be adjusted in proportion to the wind speed in low to moderate wind
speeds so that the optimal tip speed ratio is maintained. At this tip speed ratio
the power coefficient is at maximum, which means that the energy conversion
is maximized. For a variable speed wind turbine with a DFIG, it is possible to
control the load torque of the generator directly, so that the speed of the
turbine rotor can be varied within certain limits. Thus, the optimal tip speed
ratio as well as the maximal power coefficient can be obtained.
In general, variable speed wind turbine may have two different
control goals, depending on the wind speed. In low to moderate wind speeds,
the control goal is to maintain a constant optimum tip speed ratio for
maximum energy conversion. In high wind speeds, the control goal is to keep
the rated output power.
This chapter presents the designing procedure of conventional /
vector control, Proportional Integral (PI) controller and Resonant controller
and analyzes the performance characteristics of DFIG in grid. First, the
overall speed control scheme of DFIG is discussed. Then the designing of
vector control scheme is introduced. Next, the designing procedure for PI and
R controllers of DFIG is discussed. Finally, the performances of the DFIG
with those controllers in the grid are described.
44
4.1 SPEED CONTROL SCHEME
Fig. 4.1 Overall control scheme of wind turbine with DFIG
This section is concentrated on description of vector control
techniques, which have been developed for DFIG using back to back PWM
converters [34-36], are applied in the speed control scheme. Fig. 4.1 shows
the speed control scheme is composed of two vector control schemes
designed respectively for the rotor side and grid side PWM voltage source
converter. The objective of the vector control scheme for the grid side PWM
voltage source converter is to keep the DC link voltage constant regardless of
the magnitude and direction of the rotor power as well as keeping sinusoidal
grid currents.
Where Vs and is are the stator voltages [V] and currents [A], ir are
the rotor currents [A], VGRID are the grid voltages [V], iGRID are the grid side
45
converter currents [A], �T is the electrical angular velocity of the generator
rotor [rad/s], Ecap is the DC link voltage [V], PDFIGref, QDFIGref are the
reference values of the stator-side active [W] and reactive power [Var],
QGRIDref is the reference value of the reactive power flow between the grid and
the grid-side converter [Var], Ecapref is the reference value of the DC link
voltage [V], C is the DC link capacitor [F], �ref is the reference value of the
pitch angle [Deg], � is the real value of the pitch angle [Deg].
4.1.1 Vector Control Scheme of Rotor Side Converter
Vector diagram of rotor side converter (RSC) with dq reference
frame [35] is drawn and it is shown in Fig.4.2. From this vector diagram
decoupled control between the stator side active and reactive power is
obtained, which provides the generator with a wide speed range operation.
Fig. 4.2 Vector diagram of the rotor side converter
The stator flux angular position �s is calculated from ��s and ��s.
��s �s s �s� = (V - R i )dt (4.1)
��s �s r �s� = (V - R i )dt (4.2)
� �� � �
� �
�s-1
s s
�s
�� = � dt = tan
� (4.3)
q �s
�s
��s
��s
�s
d
�
�
46
Where ��s, ��s are the stationary stator flux in �� axis, V�s, V�s are
the stator voltages in �� axis, i�s, i�s are the stator current in �� axis.
Since the stator is connected to the grid, and the influence of the
stator resistance is small, the stator flux can be considered constant. With this
consideration, the DFIG model may be written as follows.
Stator and rotor voltages in dq axis are expressed as:
dsV = 0 (4.4)
qs s dsV =� � (4.5)
drdr r dr r sl r qr
diV = R i +�l -� �l i
dt (4.6)
( )qr
qr r qr r s m ms r dr
diV = R i +�l +� l i +�l i
dt (4.7)
The stator fluxes in dq axis are formed by leakage factor �,
inductance of stator and rotor ls, lr are as follows:
s ds m ms s ds m dr� =� = l i = l i +l i (4.8)
s qs m qrl i +l i = 0 (4.9)
2
mdr ms r dr
s
l� = i +�l i
l (4.10)
qr r qr� = �l i (4.11)
47
Let the leakage factor � is written as:
2
m
s r
l� = 1-
l l (4.12)
Assume �s=�e. Where �s is the electrical angular velocity of stator
flux [rad/s], �e is the electrical angular velocity of stator voltage [rad/s].
Finally stator side active PDFIG and reactive QDFIG power flow are written as:
( )DFIG ds ds qs qs
3P = V i +V i
2 (4.13)
( )DFIG qs ds ds qs
2Q = V i -V i
3 (4.14)
4.1.2 Vector Control Scheme of Grid Side Converter
A vector control approach is used with a reference frame oriented
for enabling independent control of the active and reactive power flowing
between the grid and grid side converter (GSC). The d axis current used to
regulate the DC link voltage and the q axis current used to regulate the
reactive power [35].
Fig. 4.3 Grid side converter
48
���
�
�
+
���
�
�
+
���
�
�
=
���
�
�
ccon
bcon
acon
cG
bG
aG
G
cG
bG
aG
G
cGRID
bGRID
aGRID
V
V
V
i
i
i
L
i
i
i
R
V
V
V
_
_
_
_
_
_
_
_
_
_
_
_
Fig. 4.3 shows the diagram of grid side converter. Where VGRID_abc
are the three phase grid voltages [V], Vcon_abc grid side converter voltages
[V], RG and LG are the resistance [�] and inductance [H], iG_a, iG_b, iG_c are the
three phase converter currents [A] and C is the DC link capacitor [F].
The voltage balance across the inductor is:
(4.15)
Using the abc to dq transformation matrix introduced before, the
corresponding equation in the dq reference frame rotating at �e is:
G_d
GRID_d G G_d G e G G_q con_d
diV = R i + L +� L i +V
dt (4.16)
G_q
GRID_q G G_q G e G G_d con_q
diV = R i + L +� L i +V
dt (4.17)
where VGRID_d, VGRID_q are the grid voltages [V] in dq axis, Vcon_d, Vcon_q are the
grid side converter voltages [V] in dq axis, iG_d, iG_q are the grid side converter
currents [A] in d and q axis, �e is the electrical angular velocity of the grid
voltage [rad/s]. The active PGRID and reactive QGRID power flow between the
grid and the grid side converter are:
( )GRID GRID_d G_d GRID_q G_q
3P = V i +V i
2 (4.18)
( )GRID GRID_q G_q GRID_d G_q
3Q = V i -V i
2 (4.19)
49
Fig. 4.4 Vector diagram of the grid side converter
Fig. 4.4 shows vector diagram of the grid side converter. Based on
the Fig. 4.4, active and reactive power flow between the grid and the grid side
converter is written as follows.
GRID GRID_d G_d
3P = V i
2 (4.20)
GRID GRID_d G_q
3Q = - V i
2 (4.21)
4.2 CONVENTIONAL CONTROL TECHNIQUE OF DFIG
Based on the above discussion, the control scheme of conventional
controller of DFIG is discussed and the block diagram of this technique is
shown in Fig. 4.5. Power controller generates the error signal between
reference values of generated powers and stator voltage and current in dq axis.
But the signal is not a steady state [37-38] and it is also pulsating. So, for the
further improvement of conventional controller performance, the decoupling
voltage component CrdqV is added with output signal of P,Q controller.
Mathematical expression for decoupling component is expressed as follows:
q �e
�e
VGRID_�
VGRID_�
VGRID
d
�
�
50
Crdq sl r rdq
= j� �L iV (4.22)
Where �sl is the slip angular frequency, � is the leakage factor.
With σ and sl� , further tuning of real and reactive powers of
fundamental components are achieved. Error signal from fundamental and
decoupling components is transformed into 3-phase quantities and the
transformation output controls the switched pulse width modulation (SPWM)
of RSC.
In GSC, the hysteresis band is used to control the firing angle �
through SPWM of GSC based on the error signal generated between rotor
current ir and rotor reference current irref is shown in Fig. 4.5. This hysteresis
component converts real signal into logic signal. If the input signal of buffer
moves across the input threshold, it provides some noise immunity.
Otherwise, the previous output level is maintained, while the input signal is
within the hysteresis region.
Fig. 4.5 DFIG with Conventional controller
51
4.3 GENERAL DESCRIPTION ABOUT PI CONTROLLER
DESIGN
In vector control scheme of the grid side PWM voltage source
converter, the dq axis line currents are decoupled for controlling the DC link
voltage and the reactive power flow between the grid and the grid side
converter respectively. In rotor side PWM voltage source converter, the dq
axis rotor currents are decoupled for individual stator side active and reactive
power control. The voltage compensation terms are used for decoupling the
current control loops.
It is seen from the transfer functions of the current control loops
that all the plants for the current control loops are stable with only one single
dominant nonzero pole. In this condition, a straightforward approach for
designing a PI controller is to place the zero of the PI controller to cancel the
dominant pole of the plant. This method is called pole placement [39].
Fig. 4.6 shows the current control loop of the generator.
Fig. 4.6 Current control loop of the generator
The open-loop transfer function of the current control loop is:
pc icK K(s+ K )
G(s)=s(s+ p)
(4.23)
-
+
Plant
idq idq*
s
KsK iccp )( + ps
K
+
PI
52
The closed-loop transfer function is written as follows:
pc
pc
K KG(s)=
1+G(s) s+ K K (4.24)
Where Kpc is the proportional gain of current control loop and Kic is
the integral gain of current control loop. The Kpc is determined by:
( )pc
1
ln9K = 1+ m%
Kt (4.25)
icK = p (4.26)
For the first order system, t1 is the rise time, m% is the design
margin. Based on the above transfer functions, the cascade control scheme of
the generator is shown in Fig. 4.7.
Fig. 4.7 Cascade control scheme of the generator
The PI controllers in the power control loops can be designed in a
similar way to the design of the PI controllers in the current control loops.
The proportional gain Kpp and integral gain Kip of power control loops can be
found as:
( )pp
pc 2
ln9K = 1+m%
K KK't (4.27)
- +
-
PDFIG
QDFIG
PDFIGref
QDFIGref idq idq
*
s
KsK icpc )( +
ps
K
+
PI
s
KsK ippp )( + 'K
Plant
+
53
ic pcK = K K (4.28)
In the power control loop, t2 is the rise time, m% is the design margin.
4.3.1 DC Link Voltage Control Loop
Pole placement method is used to design the current control loop
and power control loop of PI controllers. But pole placement is not directly
used in the DC link voltage control loop. Because transfer function of the DC
link voltage control loop that the plant has one single zero pole. Internal
model control is normally used for AC machine control [40-41]. This is
robust control method, controller parameters are expressed directly in the
machine parameter and desired closed loop rise time. This method is used for
designing the DC link voltage control loop.
Fig. 4.8 Internal model control
Fig. 4.8 shows the schematic diagram of internal model control and
closed loop system is expressed as:
( )1
B(s) G(s)C(s)=
A(s) 1+C(s) G(s) - G (s) (4.29)
B1(t)
-
+ -
+
B(t) A(t)
C(s) G(s)
G1(s)
54
If the system is perfect G1(s) is equal to G(s). Then,
B(s)
= G(s)C(s)A(s)
(4.30)
Suppose C(s) = G-1
(s), it is written as:
� �� �� �
n
1
aC(s)= G (s)
s+ a (4.31)
n=1 for the first order system and a is the design parameter which
is used to adjust the desired rise time. With a, the closed loop is expressed as:
B(s) a
= G(s)C(s)=A(s) s+a
(4.32)
Where
ln9
a=t
(4.33)
Classic structure of control system is designed based on the internal
model control is shown in Fig. 4.9.
Fig. 4.9 Classic control system
For the first order system, F(s) is written as:
p iK (s + K )F(s)=
s (4.34)
-
+
B(t) A(t) F(s) G(s)
55
1
a= G (s)
s (4.35)
Where Kp is the proportional gain and Ki is the integral gain.
p
r
ln9K =
Kt (4.36)
i
p r
ln9PK =
KK t (4.37)
4.4 CONTROL SCHEME OF PI CONTROLLER IN DFIG
Based on the general description, PI controller is adopted in the
rotor circuit of DFIG. The traditional Proportional Integral (PI) controller is
usually adopted with either Stator Voltage Orientation (SVO) or stator flux
orientation. In this PI controller, perfect regulation is only achievable for the
DC components, steady state error is zero and a lot of derivatives can be
obtained at high frequency terms. The gain of the PI controller GPI(s)
is
obtained from the proportional gain Kp and integral gain Ki. These gains
reduce the rise time, steady state error and increases overshoot and settling
time.
iPI p
KG (s)= K +
s (4.38)
4.4.1 RSC Control Structure of PI Controller
For avoiding overshoot and settling time problems, the performance
of DFIG is improved by adding the compensations Cd and Cq in the RSC and
the block diagram of PI controller with compensations is shown in Fig. 4.10.
The mathematical expression of Cd and Cq are as follows:
56
� � � �� � � �� � � �
2
m md r r rd r s
s s
l lC = -� l - i -� �
l l (4.39)
� �� �� �
2
mq r r rq
s
lC =� l - i
l (4.40)
By neglecting the stator resistance Rs, PI controller outputs are
tuned by Cd, Cq and it forms the dq component rotor voltage Vdr and Vqr
[42-43] and its values are controlled by real and reactive powers of DFIG
referred in eqns. (4.41) and (4.42). Rotor voltage in dq axis transformed into
three phase quantities by transformation block and these quantities are given
to the input signals of SPWM of RSC. The formula for Vdr and Vqr are
expressed as:
� �� �� �
2
r s m s DFIG r sdr DFIG r
m s s m s m
R l l l dQ R �V = Q + l - -
l V l l l dt l (4.41)
� �� �� �
2
r s m s DFIG
qr DFIG r
m s s m s
R l l -l dPV = P + l -
l l l l l dt (4.42)
By the compensating terms, SPWM controls the RSC is better than
conventional controller. With the PI controller in the rotor circuit, real and
reactive powers PDFIG and QDFIG are expressed in eqns. (4.43) and (4.44).
dr
m
DFIG s 2
s r m
lP =V �
l l - l (4.43)
dr
s r s m
DFIG s2 2
s r m s r m
V l l lQ = � - �
l l - l l l - l (4.44)
57
4.4.2 GSC Control Structure of PI Controller
In GSC, the hysteresis band is used to control the firing angle �
based on the error signal generated between rotor current ir and rotor
reference current irref is shown in Fig. 4.10. This band converts real signal into
logic signal. If the input signal of band moves across the input threshold, it
provides some noise immunity. Otherwise, the previous output level is
maintained while the input signal is within the hysteresis region and its
function is similar to conventional technique.
Fig. 4.10 DFIG with PI controller
58
4.5 CONTROL SCHEME OF RESONANT CONTROLLER
IN DFIG
PI controllers have been widely used in current controllers to
compensate for errors because of their simplicity and effectiveness. However
PI controllers have certain limitations and drawbacks when used to accurate
control of AC reference currents due to limited bandwidth.
To remove these short comings, a resonant controller is introduced
as an improved solution in terms of the AC reference tracking performance in
grid connected converters. Due to the infinite gain at a selected resonant
frequency, this controller is capable of completely eliminating the steady state
control error at that frequency [44-49].
The use of resonant controllers aims to achieve high bandwidth at
certain frequencies and also eliminate current harmonics in the three phase
power converter systems and the DFIG during grid voltage distortion. This
controller is used to keep the current output balanced during a grid voltage
imbalance. In both 5th
and 7th
order harmonics in the stator output voltage are
eliminated by a resonant controller for a standalone DFIG. With the use of
resonant controllers, the steady state errors at the selected resonant
frequencies have been effectively eliminated.
In the resonant controller, the control structure uses an abc to dq
transformation module to transform the control variables from the abc to dq
frame which synchronously rotates with the frequency of grid voltage. As a
consequence, the fundamental components are converted into DC signals,
while both negative sequence 5th
and positive sequence 7th
order harmonics
are converted into sixth order harmonics. A 6th
order harmonic resonant
controller is an option to reduce sixth order harmonic distortions. It is a
double integrator that is active both at the frequencies of −6�s and 6�s;
59
therefore, both the negative sequence 5th
and the positive sequence 7th
order
stator current harmonics can be compensated at the same time.
A higher gain of the PI controller reduces the steady state error and
increases the overshoot. But, the limited bandwidth and gain margin, the
effectiveness of PI controller and appearance of AC voltages/currents
pulsating at twice the grid frequency in the positive synchronous reference
frame. This drawback is avoided by adding the resonant controller with
PI [50].
Fig. 4.11 DFIG with Resonant controller
60
The overall control scheme for the DFIG is illustrated in Fig. 4.11.
Based on the control scheme, transfer function of resonant controller GR(s)
depends upon resonant controller gain Kr, cut-off frequency c� and angular
frequency s� is shown in eqn. (4.45).
( )
r cR 22
c s
2K � sG (s)=
s +2� s+ 6� (4.45)
In the resonant controller technique, rotor voltage in dq component
is calculated by the eqn. (4.46).
* PI R Crdq rdq rdq rdq= - +V V V V (4.46)
Where *rdqV consists of three components. PI
rdqV is the fundamental
components produced by the PI controller, RrdqV is the harmonic component
produced by the resonant controller, and CrdqV is the decoupling voltage
component.
With the harmonic and decoupling voltage components, effective
controlling of RSC is achieved. The minus sign in eqn. (4.46) is due to the
opposite reference directions between the rotor current and the stator current.
The commanded rotor voltage *rdqV is used to control the RSC by an inverse
park transformation and a space vector modulation (SVM). Compared with PI
controllers using multiple dq frames, resonant controllers may be more
sensitive to frequency variations, which may decrease the effect of harmonic
suppression in case of a significant frequency variation. An adaptive resonant
controller that uses the frequency information provided [51] to calculate the
coefficient of �s is proposed to solve the problem of frequency variation.
61
Controlling of GSC is done by hysteresis band which is similar to
previous techniques.
4.6 SIMULATION STUDIES OF DFIG WITH PI AND
RESONANT CONTROLLERS IN GRID
PI and resonant controllers are incorporated in the rotor circuit of
DFIG and analyzed the effectiveness of proposed control schemes such as PI
and resonant controllers of DFIG in grid by PSCAD simulation software
(designing of DFIG model by PSCAD is described in Appendices). The
performance of the system is analyzed by following cases.
Case 1: Characteristics of DFIG at transient and post-transient conditions
Case 2: Characteristics of DFIG with wind speed variations
Case 3: Pulsation of DFIG parameters with PI and resonant control
techniques
Case 4: Effects of 5th
and 7th
harmonics of stator current and grid voltage
Case5: Load contribution of DFIG in grid with the PI and resonant control
schemes
4.6.1 Case 1: Characteristics of DFIG at transient and post-transient
conditions
The behavior of DFIG is analyzed at transient and post-transient
conditions and the test system is shown in Fig. 4.12. At 2 s, the
three phase short circuit fault is applied across the stator terminal and
the length of fault is extended upto 0.15 s. During the transient period, the
speed of the wind turbine is oscillated and it is shown in Fig. 4.13 (a).
62
Fig. 4.12 DFIG with 3 phase short circuit fault
By the c� and
r� , the resonant controller gain GR(s) suppresses the
magnitude of Vs oscillation than other controllers are shown in Fig. 4.13(b)
and the value of voltage oscillation in resonant controller is 13.51% and
8.571% less than conventional and PI controller techniques.
Also, Te oscillation is smaller in resonant controller than others
(that is, its values are 15.385% and 11.538% less than conventional and PI
controllers respectively) based on the impact of resonant components and its
characteristics is shown in Fig. 4.13 (c).
Similarly, pulsation magnitude of real and reactive powers is less in
resonant controller attributable to fundamental and harmonic components.
However in conventional controller, absence of Kp and Ki, the pulsation
rating of these powers are more than PI is shown in Fig. 4.13(d), (e).
Overshoot problem is not reduced by the Kp and Ki of PI. Hence, after the
fault time 2.15 s, the effect of short circuit fault is extended upto 3.2 s is
shown in Fig. 4.13(a-e).
63
(a)
(b)
(c)
(d)
(e)
Fig.4.13 Characteristics of DFIG with conventional, PI and resonant
controllers at faulty conditions. Time (sec) versus (a) Wind
turbine speed (p.u) (b) Vs (p.u) (c) PDFIG (p.u) (d) QDFIG (p.u) and
(e) Te (p.u)
0
0.5
1
1.5
-1 1 3 5
Win
d t
urb
ine
spee
d (
pu)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
-1 1 3 5
Vs(
pu)
Time (sec)
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1 1 3 5
Te(
pu)
Time (sec)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
-1 1 3 5
PD
FIG
(pu)
Time (sec)
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 1 2 3 4 5
QD
FIG
(pu)
Time (sec)
64
At post-transient period, Vs, PDFIG, QDFIG and Te come back to
steady state level. From the above characteristics, pulsation magnitude of
DFIG parameters during the transient period is less in resonant controller
through effective controlling of RSC.
4.6.2 Case 2: Characteristics of DFIG with wind speed variations
Fig. 4.14 DFIG with wind speed variations
The performance of DFIG is analyzed with the 40% of rise in speed
from its rated value and the test system is shown in Fig. 4.14. Upto 2 s, speed
of the generator is maintained at rated value. Fig. 4.15(a) shows that, the
speed is stepped up from 1 to 1.4 p.u at 2 s.
With the stepped up speed, Vs of generator is magnified from its
rated value. However in conventional controller, while not the gains Kp and
Ki, Vs is higher than PI controller and its magnification value is 1.869%
greater than PI controller. By the gains Kp and Ki, the management of Vs is
maintained at lower is shown in Fig. 4.15(b). Simultaneously, in PI controller,
both real and reactive powers are controlled by compensating terms Cd and Cq.
Hence, magnitudes of both the powers are lesser than conventional control
technique (that is real and reactive powers are 8% and 16.667% less than
conventional technique respectively).
65
(a)
(b)
(c) (d)
(e)
Fig. 4.15 Characteristics of DFIG with conventional, PI and resonant
controllers at wind speed variations. Time (sec) versus
(a) speed (p.u) (b) Vs (p.u) (c) Te (p.u) (d) PDFIG (p.u) and
(e) QDFIG (p.u)
In the resonant controller, the magnitude of Vs is magnified higher
than the rated value, however it is less than other controllers such as less than
1.818% and 3.571% compare to PI and conventional controllers respectively
for harmonic and decoupling voltage components is shown in Fig. 4.15(b).
0
0.5
1
1.5
-1 1 3 5
Win
d s
pee
d (
pu
)
Time (sec)
0
0.5
1
1.5
-1 1 3 5
Vs(
pu
)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 1 3 5
Te(
pu)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 1 3 5P
DF
IG(p
u)
Time (sec)
-1.5
-1
-0.5
0
0.5
1
-1 1 3 5
QD
FIG
(pu
)
Time (sec)
66
Also, Te oscillation is smaller in resonant controller for the
resonant components and their characteristic is shown in Fig. 4.15 (c). By the
cut of frequency c� and angular frequency s
� , the pulsation magnitude of
powers is smaller (that is real and reactive powers are 4.762% and 20%
less than the PI controller) at the super synchronous operation shown in
Fig.4.15 (d), (e).
4.6.3 Case 3: Pulsation of DFIG parameters with PI and Resonant
control techniques
Fig. 4.16 DFIG with 3 phase unbalanced load
This analysis is carried out at unbalanced load which is connected
across the proposed system and the test system is shown in Fig. 4.16. By this
unbalanced load, there is an unbalanced stator voltage and current. This is due
to the effect of unbalanced load current drawn by the load.
The fluctuation of DFIG parameters with PI and resonant
controllers are described at unbalanced load condition. The pulsation of
electromagnetic torque Te, PDFIG, QDFIG, % value of total harmonic distortion
67
of stator and rotor currents are only controlled by decoupling voltage
component parameters sl�,� in conventional controller based on eqn. (4.22).
But, with the Kp and Ki, PI controller reduces the rise time and steady state
error at the network disturbance. So, the percentage pulsation of DFIG
parameters and total harmonic distortion of stator and rotor currents are less
than conventional controller.
Table 4.1 Pulsation of DFIG parameters with PI and resonant controllers
DFIG Parameters
DFIG Controllers
Conventional
Controller
PI
Controller
Resonant
Controller
Te Pulsation (%) ± 14.6 ± 12.3 ± 10.2
PDFIG pulsation (%) ±5.02 ± 4.65 ± 4.36
QDFIG Pulsation (%) ±9.23 ± 8.22 ± 7.93
THD value of is (%) 3.87 3.64 3.13
THD value of ir (%) 7.57 7.25 7.17
In the resonant controller, by the fundamental component of PI
controller and harmonic component of resonant controller, the pulsation
ratings of those parameters are minimized. Also total harmonic distortion
values of stator and rotor currents are reduced by resonant controller gain Kr
and cut-off frequency c� based on eqn. (4.45) is shown in Table 4.1.
4.6.4 Case 4: Effects of 5th
and 7th
harmonics of stator current and
grid voltage
In this case, the effects of harmonics distortion are described at
unbalanced load condition and the test system is similar to case 3. By the
resonant controller, the effects of 5th
and 7th
harmonics of stator current is are
68
minimized due to c� and s
� based on eqn. (4.45). However, in PI controller,
without c� , the gains of PI controller controls the harmonic effect. Hence the
harmonic effects are more than resonant controller technique and it is pointed
out in Table 4.2.
Table 4.2 Harmonic Distortion of iS and VGRID with PI and resonant
controllers
Harmonics
(%)
DFIG Controllers
Conventional
Controller
PI
Controller
Resonant
Controller
is VGRID is VGRID is VGRID
5th
12.6 1.3 10.3 1.3 6.42 1.3
7th
5.75 0.7 3.66 0.7 1.17 0.7
Decoupling voltage component is not adequate to reduce the
harmonic effects. Hence, 5th
and 7th
harmonics stator currents are more in the
conventional controller than PI and resonant controllers.
These control techniques are only enforced in the rotor circuit of
DFIG and no impact of those controllers in grid for minimizing the pulsation
of grid voltage VGRID is shown in Table 4.2.
4.6.5 Case 5: Load Contribution of DFIG in grid with the PI and
Resonant control schemes
This case is analyzed at full load condition of the interconnected
system. With this load, contribution of power by DFIG with its controllers and
impact of those controllers in grid are discussed. In the conventional
controller, the rotor decoupling voltage component is added with output of P,
Q controller unit based on eqn. (4.22). Error signal from the controller unit
69
not seem to be controlled by fundamental or harmonic components or gains
except rotor decoupling voltage component shown in Fig. 3.5. Error rating of
P, Q controller unit output signal is more. This signal controls the SPWM
through the dq to 3 phase transformation. Based on this control procedure,
real power PDFIG and reactive power QDFIG delivered by the generator is less
than PI and resonant controllers shown in Table 4.3. At the same time, grid
contributes more load is shown in Table 4.4.
Table 4.3 Contribution of power to the load by DFIG
Time
(sec)
Conventional
Controller
PI
Controller
Resonant
Controller
PDFIG
(MW)
QDFIG
(MVAr)
PDFIG
(MW)
QDFIG
(MVAr)
PDFIG
(MW)
QDFIG
(MVAr)
1 72.07 61.46 74.08 61.77 76.01 61.99
2 72.16 80.16 74.08 80.32 76.08 80.53
3 72.28 80.19 74.43 80.25 76.10 80.55
4 72.31 78.34 74.52 78.56 76.20 78.78
5 72.39 78.79 74.63 78.87 76.26 78.98
6 72.39 78.79 74.63 78.87 76.26 78.98
7 72.39 78.79 74.63 78.87 76.26 78.98
Steady state error and overshoot issues are reduced in the PI
controller by Kp, Ki, Cd and Cq for standardization the output of PI controller.
Rotor voltage in dq axis is calculated based on eqns. (4.41) and (4.42). Hence
� generation of SPWM and controlling of RSC are better than conventional
technique. Also the real and reactive powers generation of DFIG is based on
the inductive components in eqns. (4.43) and (4.44). So the load sharing of
DFIG with PI controller is better than previous technique. Simultaneously,
70
PGRID and QGRID delivered by the grid to load are reduced for higher
contribution of power by DFIG with PI technique shown in Tables 4.3 and 4.4.
Table 4.4 Contribution of power to the load by grid
Time
(sec)
Effects of DFIG Controllers in GRID
Conventional
Controller
PI
Controller
Resonant
Controller
PGRID
(MW)
QGRID
(MVAr)
PGRID
(MW)
QGRID
(MVAr)
PGRID
(MW)
QGRID
(MVAr)
1 497.97 834.38 801.73 899.79 558.81 902.52
2 508.84 756.02 497.61 755.15 497.65 755.02
3 508.09 754.57 507.74 754.43 502.01 754.11
4 508.21 754.22 507.73 754.01 502.96 753.69
5 508.13 755.01 507.62 754.56 502.30 753.76
6 508.13 755.01 507.62 754.56 502.30 753.76
7 508.13 755.01 507.62 754.56 502.30 753.76
By the resonant controller gains Kr and angular frequency s� ,
effective controlling of controller is achieved. Additionally by the
fundamental, harmonic and decoupling voltage components, error value of
rotor voltage on dq axis is minimized than PI controller based on eqn. (4.46).
Hence, effective controlling of RSC is obtained. So, contribution of load by
the DFIG is improved (5.075% and 0.241% values of PDFIG and QDFIG are
improved than conventional controller and 2.137% and 0.139% of PDFIG and
QDFIG are improved than PI controller). Also, power delivered by the grid is
reduced, that is, overloading of grid is avoided than conventional and PI
controller techniques shown in Tables 4.3 and 4.4. From 5 s, steady state
power is delivered to the load by DFIG and grid.
71
4.7 Summary
Overall speed control of a DFIG is achieved by controlling of RSC
and GSC through the voltage, current, real power, reactive power of DFIG
and grid respectively. The conventional, PI and resonant controllers of DFIG
are designed by PSCAD and analyzed its performance in the grid system.
From the simulation results, the following points are observed.
a. At the transient period, the pulsation of Vs, PDFIG, QDFIG and Te
are minimized in resonant controller for the effective
controlling of RSC by Kr, c� , s
� decoupling and harmonic
components. At the super synchronous operation, effects of
DFIG parameters are comparatively less in resonant controller
than others for the gains of PI, fundamental and harmonic
components.
b. Also the pulsation rating of Te, PDFIG, QDFIG, %THD values of
stator and rotor currents and harmonic distortion of is are
suppressed in resonant controller technique by rotor voltage
component.
c. For the higher contribution of load by DFIG with resonant
controller technique, overloading of grid is avoided.
Based on the results, performance of DFIG is improved with the
resonant controller than conventional and PI control techniques in the grid
system.
72
CHAPTER 5
PERFORMANCE OF DFIG WITH DIRECT TORQUE
AND DIRECT POWER CONTROL SCHEMES IN GRID
In this chapter, the designing procedure of direct torque controller
(DTC), direct power controller (DPC) and performance of those controllers in
DFIG are presented. First section of this chapter discusses the general features
of DTC, expression of torque equation based on sine and cosine components
and implementation of torque control scheme in the DFIG. Second section
deals with the control scheme of power control scheme in the DFIG,
mathematical expression of stator power equations based on dq+ reference
frame, and implementation of power control scheme in the RSC and GSC of
DFIG. Finally, the performances of the DFIG with DTC and DPC in the grid
are described.
5.1 CONTROL SCHEME OF DTC IN DFIG
One of the most conventional control methods for DFIG is vector
control in which rotor currents are decoupled into stator active power
(or torque) and reactive power (or flux) and these two currents are controlled
in the reference frame fixed to stator flux (or voltage) [52-53]. In this method,
accurate value of machine parameters such as resistances and inductances are
required and nonlinear operation of converter for tuning current controllers is
not considered. So, performance of vector control method is affected by
changing machine parameters and operation condition.
Normally, sensorless vector control is preferred for achieving a
high dynamic performance of the system due to the reduced hardware
73
complexity, lower cost, better reliability, and reduced maintenance.
Sensorless position and speed estimation methods have been proposed by
several researchers in the recent past [54]. Broadly, these schemes can be
grouped as open loop and closed loop. A few model reference adaptive
scheme (MRAS), which fall under the closed loop category require an ideal
integrator in the reference model.
Commonly, either the current or the flux in the rotor or stator [55]
is considered as the tuning signal for driving the adaptation mechanism and
proportional integral controller is used for the control. A few other closed
loop schemes employing low pass filters with either a fixed or a variable
cutoff frequency, offset compensation along with pure integration, phase
locked loop (PLL) with programmable low pass filter, and a vector rotator are
discussed in [56-57]. Rotor position is obtained through the phase comparison
of actual and estimated rotor currents and processing the error in a closed-
loop resonant controller.
The DTC method is an alternative to vector control and
proportional integral and resonant controllers for DFIG based wind power
generation. Variable switching frequency and high torque ripple are the main
limitations of hysteresis based DTC. To address these limitations, DTC with
space vector modulation based on synchronous reference frame
transformation, predictive control and deadbeat control are reported in
[58-59]. The implementation of DTC using space vector modulation becomes
simple and this method is also capable of independent control of torque and
reactive power. DTC is the scalar control method [60-61]. It directly controls
the flux and torque and indirectly controls the stator voltage and current. This
method is having minimal torque response time, absence of co-ordinate
transformations and absence of separate voltage modulation.
74
When the stator of DFIG is connected to unbalanced grid, the
torque produced by DFIG is pulsating. The torque has periodic pulsations at
twice the grid frequency, which can result in acoustic noise at low levels and
at high levels can damage the rotor shaft, gearbox or blade assembly. Also,
DFIG connected to an unbalanced grid will draw unbalanced current. These
unbalanced current tends to increase the grid voltage unbalance. Methods to
compensate the effects of unbalanced grid voltage based on positive and
negative sequence rotating reference frame theory are well reported in [62].
The stator unbalanced currents and voltages are compensated by
injecting currents into grid by GSC and two synchronously rotating reference
frames are used to determine positive and negative sequence stator currents.
These are controlled to reduce pulsations in any one of the following; torque,
active power, stator current or rotor current. The grid side converter and rotor
side converter control are used to compensate the effects of unbalanced grid.
The positive sequence rotor current is regulated by PI regulator. The
magnitude and angle of rotor voltage vector are controlled independently. The
torque angle is controlled in such a way that torque pulsations are reduced.
The proposed DTC method does not require multiple reference
frame transformation, sequential decomposition and notch filters to remove
second harmonic components. This scheme is simple, complexity in
calculations is significantly reduced and also it controls the 5th
and 7th
order
harmonic at unbalanced condition.
5.1.1 Salient Features of DTC Control Scheme
Some of the features of direct torque control scheme are described below:
1. It is a scalar control.
2. No synchronously rotating reference frame transformation is
required.
75
3. As the controlled rotor voltage is in polar form, it is easy to
apply space vector modulation.
4. Switching frequency of inverter remains constant.
5. It reduces the torque ripple and makes the stator current
almost sinusoidal.
6. As there are no cascaded regulating loops, its structure is
simple and easy to implement.
7. Fast dynamic response of rotor flux and torque.
8. As the angle and magnitude of rotor voltage vector is
controlled independently, decoupled control of torque and
reactive power is possible.
9. By controlling torque angle, the DTC method can be explored
to reduce torque pulsations under unbalanced grid voltage
condition.
5.2 TORQUE EQUATION OF DFIG
The electromechanical torque Te of a DFIG can be described as:
( )� �� �� �
+ +
e m dqs dqs
3 PT = i � i
2 2 (5.1)
Modify Te with the ls and lm
( )� �� �� �
+ + +
e m dqs dqs dqs m
3 PT = i � -� i l
2ls 2 (5.2)
76
Implementing e-j2� te in eqn. (5.2), Te is written as:
( )� �� � � �� � � �� � � �
e e
e e
-j2� t -j2� t+ - + -
dqs dqs dqs dqs
e m -j2� t -j2� t+ - + -
m dqs qds dqr dqr
� +� e (� +� e )3 PT = i
2 2 -l (� +� e ) (i +i e ) (5.3)
Based on the eqn. (5.3), the Te is written as:
( )
� �� �� �� �� �
� �� �� �� �
+ + + + - - - -
qs dr ds qr ds qr qs dr
+ - + - - + - +
e ds qr qs dr ds qr qs dr e
+ - + - - + - +
ds dr qs qr ds dr qs qr e
-� i +� i -� i +� i3lm P
T = - � i +� i -� i +� i cos(2� t)2ls 2
(� i +� i -� i -� i )sin(2� t)
(5.4)
In general, Te is expressed as:
e e_ave e_sin e e_cos eT = T +T sin(2� t)+T cos(2� t) (5.5)
Let Te_ave, Te_sin, and Te_cos are:
� � � � � � � � �
� � � � �� � � � �� � ��
+
dr+ + - -
e_ave qs ds qs ds +
qr+ - + +me_sin ds qs ds qs -
drs - - + +
e_cos ds ds qs ds -
qr
iT -� � � -�
i-3l pT = -� -� � �
i2l 2T � -� � -�
i
(5.6)
At the steady state and neglecting the stator resistance, the eqn.
(5.6) can be rewritten as:
� � � � � � � � �
� � � � �� � � � �� � ��
+
dr+ + - -
e_ave ds qs ds qs +
qr- - + +me_sin qs ds qs ds -
drs - - + +
e_cos ds qs ds qs -
qr
iT -V -V V -V
i-3l pT = V -V V -V
i2l 2T V V -V -V
i
(5.7)
77
Based on the space vector orientation control, Te_sin is expressed as:
� � � � � � � �
- + - + + +me_sin qs dr ds qr ds qr
s e
-3l PT = V i -V i +0 -V i = 0
2l � 2 (5.8)
Similarly Te_cos is written as:
� � � � � � � �
- + - + + +me_cos ds dr qs qr ds dr
s e
-3l PT = V i +V i -V i +0 = 0
2l � 2 (5.9)
Where
( )- - + - +
dr ds dr qs qr+
ds
1i = V i +V i
V (5.10)
( )- - + - +
qr qs dr ds qr+
ds
1i = V i -V i
V (5.11)
5.3 IMPLEMENTATION OF DTC CONTROL SCHEME
IN DFIG
Based on the above discussions, the control scheme of DTC in
DFIG is designed and its schematic diagram is shown in Fig. 5.1. In the DTC
technique, the control is implemented in RSC and hysteresis band is used to
control the GSC.
In the dq+ reference frame, positive sequence components appear
as DC values while the negative sequence components oscillate at 2�e.
Whereas in the dq- reference frame, negative sequence components appear as
DC values while the positive sequence components oscillate at 2�e.
Observing Fig. 5.1, error signal between the actual and reference values of
real and reactive powers of the generator are tuned by dq+ reference frame of
rotor currents. The �sl is obtained to transform the rotor values to the positive
78
and negative sequence rotor reference frames. Further tuned this signals by PI
controllers, dq+ reference frame of rotor voltage and controlled by slj�e .
Those dq+ frame are converted to the abc frame.
Fig. 5.1 Block diagram of DTC in DFIG
Similarly, signal between the actual and reference values of rotor
current in dq- frame are tuned by PI controller and dq- reference frame of
rotor voltage and controlled by j�ee . Those dq- frame are converted to the abc
frame is shown in Fig. 5.1. The positive and negative sequence control
components are regulated independently before being transformed into the
positive sequence reference frame and then summed to form a reference for
the SPWM controller of RSC. Simultaneously the hysteresis band control of
GSC of DFIG is similar to resonant controller.
79
5.4 CONTROL SCHEME OF DPC IN DFIG
DTC of induction machine is based on decoupled torque and flux
control which has very fast and precise dynamic without using inner control
loop. The control of DFIG in which the rotor flux is estimated based on DTC
strategy, direct power control (DPC) is developed to control the DFIG. The
Grid side converter (GSC) is used to maintain DC link voltage at desired
reference level for all operation condition of DFIG.
The conventional voltage oriented control (VOC) is used to control
GSC. In this method, two decoupled current control loops are used to control
DC voltage and reactive power and dependency of system response on system
parameters and operating condition. Due to dependence of rotor active power
on generator speed, it has fast dynamic and in order to have constant DC
voltage the GSC must transmit the active power between rotor and grid with a
fast response.
To improve the power response, to eliminate the torque ripple and
to protect the rotor side converter under grid voltage sags a proportional
control with anti-jamming control is proposed [63]. This control has
satisfactory power response and eliminates the rotor current overshoot in
voltage sags when the loop of torque control is applied, although power and
rotor currents results are shown only in fixed speed operation.
The concept of DPC is applied to DFIG under unbalanced grid
voltage conditions are discussed in [64-65]. Also, the active and reactive
powers are made to track references using hysteresis controllers. These
strategies have satisfactory active and reactive power response under
unbalanced grid voltage.
80
The direct power control is applied to the DFIG power control and
it has been presented in [66-67].This scheme calculates the required rotor
controlling voltage directly based on the estimated stator flux, active and
reactive power and their errors. From the above discussions, the DPC
technique is fast, sensitive and effective method for controlling the DFIG than
DTC.
5.5 STATOR POWER EQUATIONS
DFIG stator apparent power can be expressed in terms of positive
and negative sequence components [68-70]. Using developed equations for
positive and negative sequence voltages and currents, apparent power of a
DFIG can be determined.
The stator power in the positive sequence reference frame is:
DFIG DFIGS = P + jQ (5.12)
+ +
dqs dqs
3= - V +i
2 (5.13)
Stator active and reactive powers can be described as:
( )+ +
DFIG dqs dqs
3P = Real( V i
2 (5.14)
+ +
DFIG dqs dqs
3Q = imaj(V i )
2 (5.15)
Manipulating above eqns. (5.14) and (5.15), we get idqs+
+ + +
dqs dqs dqr m
s
1i = (� - i l )
l (5.16)
81
The eqn.(5.16) is also written as:
( ) ( )s s-2j� t -2j� t+ + - + -m
dqs dqs dqs dqr dqr
s
l1i = � +� e - i +i e
ls l (5.17)
Substituting the above eqn. (5.17) in S, we get
( )
( ) ( )
� �� �� �� �
e e
e e
-j2� t -j2� t+ - + -
dqs dqs dqs dqs
-j2� t -j2� t+ - + -s dqs dqs dqr dqr
(V +V e ) � +(� e3S = -
2l -lm V +V e (i + i e (5.18)
Substitute the real and imaginary components in the eqn. (5.18) and
get the stator power.
DFIG DFIGS = P + jQ
( )= DFIGave DFIG_sin e DFIG_cos eP + P sin(2� t + P cos(2� t))
DFIGave DFIG_sin e DFIG_cos e+j(Q +Q sin(2� t)+Q cos(2� t)) (5.19)
5.6 IMPLEMENTATION OF DPC CONTROL SCHEME
IN DFIG
DPC is based on the instantaneous active and reactive power
control loop. There is no internal current control loop. Based on the theory of
the direct self control and the direct torque control respectively, the goal of
every direct control strategy is to minimize the errors between reference and
actual values. This is done by selecting the appropriate converter output
voltage vector to push the state of the system towards the reference values. In
this case, the controlled values are instantaneous active and reactive power
components of the stator and the grid respectively. The instantaneous active
and reactive power components for a three phase system can be calculated as:
( )DFIG ds ds qs qs
3P = V i +V i
2 (5.20)
82
( )DFIG ds qs qs ds
3Q = V i -V i
2 (5.21)
Fig. 5.2 Block diagram of DPC in DFIG
The power reference values are provided from outer control loops,
like the DC link (voltage or speed) controller and it is able to reach the
maximum dynamic capability of the system. Furthermore, no coordinate
transformations are required. The control loops are based on hysteresis
regulators. In this control technique, the control scheme is implemented in
both RSC and GSC. Fig. 5.2 shows the block diagram of DPC in DFIG and
the instantaneous power of DFIG and grid [71-72] are used to control the
RSC and GSC respectively.
83
5.6.1 Rotor Side Converter Controller
In the DPC scheme, the RSC is controlled by two controllers: one
of them is controlling the stator active power PDFIG and other, the stator
reactive power QDFIG. The output of these comparators for the power errors
are together with the position of the rotor flux vector. The relation between
the rotor flux and the rotor voltage vectors are given in [72-73]:
rr r r
d�V = R i +
dt (5.22)
The rotor flux variation that takes place along the applied rotor voltage vector:
�r r1 r� =� + V dt (5.23)
The rotor flux change (increment) falls opposite to the applied
voltage vector’s direction, as the generator association of signs is adopted.
But, the rotor flux is as follows:
m
r s r r
s
l� = � +l i
l (5.24)
Actual value of real and reactive powers PDFIG and QDFIG are
calculated by power estimator from stator voltage Vs and stator current is are
based on eqns. (5.25) and (5.26).
( )DFIG s r rref
3P = - p� imag � .i
2 (5.25)
( )DFIG s r rref
3Q = - p� Real � .i
2 (5.26)
84
By including the stator flux �s and flux power angle � in the eqns.
(5.25) and (5.26), the PDFIG and QDFIG are written as:
m s rDFIG s
s r
l � �3P = p� sin�
2 l l (5.27)
( )m
DFIG s r s
s r
l3Q = p� � -� cos�
2 l l (5.28)
The improved values of real and reactive powers are obtained and it
is expressed in eqns. (5.29) and (5.30).
DFIG s s r
3P = p� a� � sin�
2 (5.29)
( )DFIG s r s
3Q = p� a � -� cos�
2 (5.30)
Where
m
s r
ia =
i i (5.31)
Real power reference PDFIGref is tuned by error signal between stator
angular velocity and its reference �s and �sref respectively and it is added
with the power estimator output. Similarly, QDFIGref is added with reactive
power of the estimator. By the differentiation of those error signals, dPDFIG
and dQDFIG control the RSC through SPWM and differential powers are
expressed in eqns. (5.32) and (5.33).
rrefs
DFIG sref
s
d� sin�3�dP = - �
2�l dt (5.32)
rrefs
DFIG sref
s
d� cos�3�dQ = �
2�l dt (5.33)
85
Fig. 5.3 Stator and rotor flux vectors in rotor reference frame
By changing the �rrefsin� and �rrefcos�, PDFIG and QDFIG can be
varied based on flux vectors of stator and rotor in rotor reference frame is
shown in Fig. 5.3.
5.6.2 Grid Side Converter Controller
In GSC of DPC, instantaneous active and reactive powers are
controlled by torque and stator flux. The grid side DPC controls the amplitude
of the DC link voltage (active power flow). The voltage equation of GSC is
given by:
GRIDGRID G GRID G con
diV = R i + L +V
dt (5.34)
If, j(K-1)�
3con capV = E e then K = 1,2…..6 Otherwise con
V = 0 , K = 0,7
The change of current can be calculated by neglecting the filter
resistance as follows:
≈ �t
GRIDGRID con
0G
di 1(V -V )dt
dt L (5.35)
�
�rref
�rrefsin�
�rrefcos�
q
�sref
d
86
From the Fig.5.2, the actual value of grid real and reactive powers
PGRID and QGRID are estimated by grid side power estimator from VGRID and
iGRID. The grid real and reactive powers PGRID and QGRID are estimated by grid
side power estimator. Reference value of grid real power PGRIDref is generated
by PI controller from the error signal of Ecap and reference value of DC
capacitor voltage across the converters Ecapref. Error signals of actual and
reference values of grid real and reactive powers are differentiated and these
differential values of dPGRID and dQGRID are expressed in eqns. (5.36) and
(5.37).
≈GRID d GRID d GRID
dP V ×di (5.36)
≈GRID dGRID qGRIDdQ -V × di (5.37)
dPGRID and dQGRID are linear with respect to current.
Fig. 5.4 Grid voltage and current in �� axis
Fig 5.4 shows the VGRID and iGRID in �� axis. From this vector
diagram, dPDFIG and dQDFIG are controlled by grid voltage, current and Vcon
grid side converter output voltage.
Vcon
VGRID-Vcon iGRID
�
�
87
5.7 SIMULATION STUDIES OF DFIG WITH DTC AND DPC
IN GRID
Based on the designing procedure and mathematical description of
DTC and DPC, the performances of DFIG in grid are analyzed using PSCAD
software. In the simulation results, % pulsation of Te, PDFIG, QDFIG and %
THD values of is and ir with DFIG controllers are analyzed at network
disturbance. And also harmonic analysis of is and VGRID are analyzed in the
interconnected grid system. The performance of the system is analyzed by the
following cases.
Case 1: Characteristics of DFIG at transient and post-transient conditions
Case 2: Characteristics of DFIG with speed variations
Case 3: Pulsation of DFIG parameters with the DTC and DPC control
techniques
Case 4: Effects of 5th
and 7th
harmonics of stator current and grid voltage
Case 5: Load contribution of DFIG in grid with DTC and DPC control
techniques
5.7.1 Case 1: Characteristics of DFIG at transient and post-transient
conditions
The performance of DFIG with the DTC and DPC techniques in
grid at transient and post-transient conditions are analyzed. At the time period
of 2 s, the 3 phase short circuit fault is applied across the stator terminal and
the fault is extended upto 0.15 s from the time 2 s which is similar to the
proposed system of case 1 of chapter 4 (Ref. Fig.4.12).
88
(a)
(b)
(c)
(d)
(e)
Fig.5.5 Characteristics of DFIG with DTC and DPC at transient
and post-transient conditions. Time (sec) versus (a) wind
turbine speed (p.u) (b) Vs (p.u) (c) Te (p.u) (d) PDFIG (p.u) and
(e) QDFIG (p.u)
0
0.5
1
1.5
-1 1 3 5
Win
d t
urb
ine
spee
d (
pu)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
-1 1 3 5
Vs
(pu)
Time (sec)
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 1 2 3 4 5
Te
(pu)
Time (sec)
0
0.2
0.4
0.6
0.8
-1 1 3 5
PD
FIG
(pu)
Time (sec)
-0.1
-0.05
0
0.05
0.1
0 1 2 3 4 5QD
FIG
(pu)
Time (sec)
89
DTC: The exponential value of slip angular frequency value depends upon
dq+ frame rotor voltage and current. During the transient period, the short
circuit current of stator is increased. Simultaneously, 3 phase rotor current is
also increased. This increases the magnitude of dq+ frame of rotor current and
this current control the error signals which are given to the PI controller of
RSC.
Similarly, dq- frame of rotor current values are increased and it is
controlled by sj�e by 3 phase rotor current at transient period. This current
controls the error signals for the input of PI controller. Those dq+ and dq-
frames of rotor currents, the oscillation of Vs, Te, PDFIG, QDFIG are 2.17%,
4.55%, 6.98% and 10% less than resonant controller respectively.
After the post-transient period, the magnitude of dq+ and dq-
frames of rotor current and voltage are reduced and it comes to the normal
value. Hence, stator voltage, electromagnetic torque, real and reactive powers
of DFIG is maintained at the stable region shown in Fig. 5.5.
DPC: In this technique, the control techniques are implemented in both rotor
and grid side converters. Leakage factor, stator angular frequency, magnitude
of reference value of rotor flux and flux power angle control the change in
real and reactive powers of DFIG referred in eqns. (5.32) and (5.33). At GSC,
dq frame of grid voltage and current controls the grid side converter.
During the transient period, flux power angle magnitude is
increased with respect to sudden rise in stator current. So the differential value
of real and reactive powers of DFIG is changed and also controls the RSC.
Simultaneously, the magnitude of dq frame of grid current is increased. This
incremental current changes the real and reactive powers of grid and it
controls the GSC.
90
At the post-transient period, flux power angle of RSC and grid
current in dq frame are within the normal range and the system is maintained
at stable region shown in Fig. 5.5 (a-e).
In this control technique, grid voltage and current control the GSC.
But the hysteresis band only controls the GSC in torque controller. The
pulsation magnitudes of Vs, Te, PDFIG, QDFIG are 3.15%, 3.92%, 14.29% and
16.67% less than DTC controller respectively.
5.7.2 Case 2: Characteristics of DFIG with wind speed variations
The performance of DFIG is analyzed with the 40% of rise of speed
from its rated value and the test system is similar to case 2 of chapter 4 (Ref.
Fig. 4.14). At the time of 2 s, the speed is stepped up from 1 to 1.4 p.u shown
in Fig. 5.6.
DTC: With the stepped up speed, Vs is magnified from its rated value. But,
controlling of RSC is achieved by rotor current in dq+ and dq- frames
through sl sj� j�e & e . So, the pulsation of torque Te is 2.54% less than resonant
controller based on sine and cosine components of Te referred in eqns. (5.8)
and (5.9). With the controlling of electromagnetic torque of DFIG, oscillation
of Vs, PDFIG, QDFIG are 0.93%, 7.14% and 8% less than resonant controller
respectively.
DPC: In the DTC control technique, during the stepped up of the wind speed,
the pulsation rating of DFIG parameters are controlled by controlling of Te.
But in DPC, the stator current and voltage, gird voltage and current controls
the converters of DFIG. Hence, the magnitude of pulsation values are 0.89%,
1.79%, 5%, 13.04% of Vs, Te, PDFIG, QDFIG less than DTC technique
respectively.
91
(a) (b)
(c)
(d)
(e)
Fig. 5.6 Characteristics of DFIG with DTC and DPC at wind speed
variations. Time (sec) versus (a) wind speed (p.u) (b) Vs (p.u) (c)
Te (p.u) (d) PDFIG (p.u) and (e) QDFIG (p.u)
0
0.5
1
1.5
-1 1 3 5
Win
d s
pee
d (
p.u
)
Time (sec)
0
0.5
1
1.5
-1 1 3 5
Vs
(p.u
)
Time (sec)
0
0.5
1
1.5
-1 1 3 5
Te
(p.u
)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 1 3 5
PD
FIG
(p.u
)
Time (sec)
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 1 2 3 4 5
QD
FIG
(p.u
)
Time (sec)
92
5.7.3 Case 3: Pulsation of DFIG parameters with the DTC and DPC
control techniques
Table 5.1 Pulsation of DFIG parameters with DTC and DPC techniques
DFIG
Controllers
Te
Pulsation
(%)
PDFIG
Pulsation
(%)
QDFIG
Pulsation
(%)
THD
Value of is
(%)
THD
Value of ir
(%)
DTC ± 6.56 ± 4.18 ± 7.24 2.85 6.84
DPC ± 4.82 ± 3.26 ± 6.56 2.04 5.27
The simulation studies of DFIG parameters are carried out at
unbalanced load which is connected across the DFIG and the proposed system
is similar to case 3 of chapter 4 shown in Fig.4.16.
DTC: With the unbalanced condition, pulsation of real and reactive powers
and THD value of is and ir are controlled by electromagnetic torque. The
oscillation of Te can be controlled by dq+ and dq- frames of rotor current in
RSC and this controlling procedure is already discussed in case 1 and 2.
But in the resonant controller technique, the rise time and steady
state error are reduced by Kp and Ki and overshoot problem is minimized by
Cd and Cq. Also, the fundamental components of PI and harmonic component
of resonant controllers control the RSC. Hence, the pulsation of DFIG
parameters and total harmonic distortion of stator and rotor currents are less
than resonant controller.
DPC: RSC and GSC are controlled by actual value of voltage and current of
DFIG and grid respectively by DPC technique. Separate control scheme is
implemented to control the GSC in DPC, that is, differential value of grid
voltage dVGRID and current diGRID effectively control the GSC.
93
By �s and �, the differential value of real and reactive powers such
as dPDFIG and dQDFIG are controlling the RSC. But �s and � are not considered
in DTC. Hence pulsation of Te, PDFIG, QDFIG, THD of is, VGRID are less than
DTC technique shown in Table 5.1.
5.7.4 Case 4: Effects of 5th
and 7th
harmonics of stator current and
grid voltage
Table 5.2 Harmonic Distortion of iS and VGRID with DTC and DPC
techniques
Harmonics
(%)
DFIG Controllers
DTC DPC
is VGRID is VGRID
5th
4.87 1.3 1.76 1.3
7th
0.86 0.7 0.34 0.7
Effects of 5th
and 7th
harmonic distortion of stator current are
discussed at unbalanced condition of DFIG (Ref. Fig. 4.16).
DTC: In the resonant controller, harmonic distortion of is is controlled by
rotor voltage component. Cd and Cq are only reducing the settling time and
over shoot. But in the DTC technique, for the rotor current and rotor voltage
in dq+ and dq- frames, the controlling of RSC is better than resonant
controller. Also the magnitude of pulsation of torque is minimized based on
eqns. (5.8) and (5.9) and it is discussed in case 3. By the torque controlling,
the 5th
and 7th
harmonic distortion of is is less than resonant controller.
DPC: In the DPC, the differential value of PDFIG, QDFIG, � and �s are
controlling the RSC. With these parameters, controlling of RSC is better than
DTC controller. Simultaneously, the controlling of GSC is achieved by
differentiated value of grid current in dq axis. But only the hysteresis band
94
controls the GSC in DTC controller. Control aspects of RSC and GSC are
achieved effectively in DPC. Hence, effective %THD, 5th
and 7th
harmonics
suppression is possible by DPC than DTC and it is shown in Table 5.2.
DTC and DPC control techniques are only enforced in the rotor
circuit of DFIG. Table 5.2 shows those controllers do not give any impact in
grid for minimizing the pulsation of VGRID.
5.7.5 Case 5: Load contribution of DFIG in grid with DTC and DPC
control techniques
DTC: In this technique, electromagnetic torque Te is resolved into 3
components such as Te_ave, Te_sin and Te_cos in eqn. (5.7). By the space vector
orientation control, the resolving components of Te are calculated from dq+
and dq- frames of rotor voltage and current. Hence, Te pulsation is minimized
and that is already discussed in case 3. So, control of RSC can be done by Te.
But in resonant controller, fundamental, decoupling and harmonic
components are only controlling the RSC. Hence, better control is obtained in
DTC and power delivering by DFIG with DTC control scheme to the load is
improved than resonant controller.
Table 5.3 Power delivered by DFIG to the load
Time
(Sec)
DTC DPC
PDFIG
(MW)
QDFIG
(Mvar)
PDFIG
(MW)
QDFIG
(Mvar)
1 -11.0888 39.5083 -7.8827 42.7405
2 70.9796 43.0673 72.2772 44.2059
3 70.4461 43.7474 72.0417 44.1292
4 70.0843 43.5363 72.1581 44.5224
5 71.2006 43.6229 72.2931 44.2456
6 71.2006 43.6229 72.2931 44.2456
7 71.2006 43.6229 72.2931 44.2456
95
Table 5.4 Power delivered by grid to the load
Time
(Sec)
DTC DPC
PGRID
(MW)
QGRID
(Mvar)
PGRID
(MW)
QGRID
(Mvar)
1 631.4291 727.1206 628.5058 721.5398
2 521.8909 649.8846 519.8081 648.6269
3 521.9481 649.8187 519.7178 648.2622
4 521.9007 649.1962 519.9291 648.3551
5 521.5749 649.1957 519.8726 648.1572
6 521.5749 649.1957 519.8726 648.1572
7 521.5749 649.1957 519.8726 648.1572
DPC: Direct power controller at rotor side, reference value of DFIG real
power PDFIGref is calculated by the PI controller at the inputs of actual and
reference values of stator angular velocity �s and �sref respectively. With Kp
and Ki of PI controllers, steady state error is avoided. So, PDFIGref are obtained
accurately and also error signals of DFIG real and reactive powers are
differentiated in eqns. (5.32) and (5.33). For the � and �, the change in value
of powers dPDFIG and dQDFIG are generated with less error. Hence, better
steady state DC conversion is achieved by RSC.
Simultaneously, in the grid side DPC, reference value of grid real
power PGRIDref is obtained by PI controller based on Ecap. For the proper tuning
of error signals from the grid power estimator and PI controller, better value
of change in real and reactive powers dPGRID and dQGRID are obtained. Based
on the eqn. (5.36), the minimum change of direct axis grid current didGRID is
also reflected in dPGRID and similarly the minor variation of quatrature axis
grid current diqGRID is also considered in dQGRID in eqn. (5.37). From the
values of dPGRID and dQGRID, better controlling of GSC is obtained and the
better load contribution is achieved through the rotor of DFIG than DTC
controller as shown in Tables 5.3 and 5.4. That is, the improved performance
96
is obtained by controlling technique implemented in both RSC and GSC. Also,
contribution of power to the load by DFIG is better (that is, DFIG with DPC
real and reactive powers of DFIG are 1.511% and 1.407% times more than
DTC respectively) and overloading of grid is avoided.
5.8 SUMMARY
This chapter has presented the torque equation of DTC based on
sine and cosine components and mathematical expression of stator power
equation of DPC. Also discussed about the designing of DTC and DPC
control techniques of DFIG and analyzed its performance in the grid system.
From the simulation results, the following points are observed.
a. In the DTC technique, electromagnetic torque Te only controls
the pulsation of DFIG parameters and hysteresis band
technique is adopted in GSC.
b. The separate control schemes are implemented in converters
of DFIG in DPC control technique. Actual value of real and
reactive powers of DFIG and gird controls the RSC and GSC
respectively.
c. So the pulsation magnitude of Vs, Te, PDFIG and QDFIG are
minimized than DTC.
d. Also the impact of 5th
and 7th harmonics values is less than
DTC technique.
e. Simultaneously total harmonic distortion of stator and rotor
currents of the DFIG is comparatively less and load sharing of
DFIG is increased with DPC.
Based on the above discussions, performance of DFIG is improved
with the DPC technique than DTC in the grid.
97
CHAPTER 6
CONTROL SCHEME OF DIRECT CURRENT
CONTROLLER IN DFIG WITH GRID
In the current control scheme, the development of the tuning
current control strategy has adopted typical intelligent control concepts, that
is, a control goal to minimize absolute or root mean square (rms) error
between the desired and actual dq axis currents through an adaptive tuning
mechanism [74-76]. This tuning current is different from the actual measured
or current. For example, for a dq axis current reference, the adaptive tuning
process would continue until the actual d axis current reaches the q axis
reference current. It is necessary to point out that a fast current loop controller
is critical to assure the highest power quality in terms of harmonics and
unbalance for the GSC [77]. Thus, elimination of the current control loop [78]
is not an option for the proposed control design such as direct current
controller.
In this chapter, first section deals the general description of current
control loop and the designing procedure of direct current control with its
control schemes. Second section, the performance of those control schemes
at transient and post-transient periods, high wind speed, effects of 5th
and 7th
harmonics at unbalanced conditions and load contribution of DFIG in grid are
discussed.
98
6.1 GENERAL DESCRIPTION OF CURRENT CONTROL
LOOP
Normally, the inner field oriented current control loop controls the
rotor current. The field orientation could, for example, either be aligned with
the stator flux of the DFIG or the grid flux. For both reference frames the q
component of the rotor current largely determines the produced torque while
the d component can be used to control, for instance, the reactive power at the
stator terminals.
In order to derive the rotor current control law, to eliminate is and �r, we get,
� �� �� �
s ss s r s s
m
d� RV = -R i + + + j� �
dt l (6.1)
( ) srr r r � r � r s
d�diV = R + j� l i +l + + j� �
dt dt (6.2)
rr s r � r �
di= (R + R + j� l )i +l + E
dt (6.3)
� �� �� �
ss r s
m
RE =V - + j� �
l (6.4)
Where E is the back EMF. It is possible to decouple the cross
coupling between d and q components of the rotor current [78-79]. Further, it
is possible to include a feed forward compensating term in the control law
that will compensate for the tracking error caused by variations in the back
EMF. This is done by feed forward of the term and neglecting the derivative
of the flux. Here, an estimate of the whole back EMF E will be used.
99
( )'
r r r � s r EV = V + j� l - R i + K E (6.5)
( )�p i r � s r E= K e+ K edt + j� l - R i + K E (6.6)
Where KE = 0 at without feed forward of E, otherwise KE=1 at feed forward.
By the eqns. (6.5) and (6.6), the rotor current dynamics formed by
the inner loop is given eqn. (6.7).
( )'r� r r s r
dil = V - R + R i
dt (6.7)
In the control law the estimated parameters are assumed as the
correct values. If the back EMF is not compensated for, i.e., KE = 0, it is
treated as a disturbance to the rotor current dynamics. The transfer function is
expressed as:
� r s
1G(P)=
pl + R + R (6.8)
The proportional gain Kp and integral gain Ki are written as:
p c �K = � l (6.9)
i c r sK = � (R + R ) (6.10)
Where �c is closed-loop bandwidth of the current dynamics, giving
cl
c
pG (p)=
p +� (6.11)
100
Fig. 6.1 Block diagram of the current control system
6.2 CONTROL SCHEME OF DIRECT CURRENT
CONTROLLER (DCC)
Based on the general description of current control loop, the direct
current controller technique is implemented in the rotor circuit of DFIG. This
scheme is implemented in both RSC and GSC of DFIG shown in Fig. 6.2.
Fig.6.2 Block diagram of DCC with DFIG
- Vr -
+
-
+ +
+ ir
DFIG
E
E
ref
ri
*
rV p
KK i
p + G(p)
σω ljR rs −
101
6.2.1 RSC Control Structure of DCC
This control structure is implemented by nested loop structure. It is
consisting of inner current loop and outer speed and reactive power. �sref is
generated from the maximum power extraction principle [80-81]. QGRIDref is
generated based on co-ordination of reactive power control with GSC and
wind power reactive power demand. From the Fig. 6.2, by PI controller *
rdi
and *
rqi are obtained from reactive power and speed respectively. The current
controller loop generates Vrd and Vrq based on error signals between reference
and actual rotor currents referred to dq axis. *
rdV and *
rqV are obtained from Vrd
and Vrq plus compensation items. *
rdnewi and *
rqnewi are generated by *
rdV and *
rqV
through current limiter in eqns. (6.12) and (6.13).
( ) ( ) ( )2 2
* * * *
rdnew rq rdqmax rdi = sign i i - i (6.12)
( ) ( ) ( )2 2
* * * *
rqnew rd rdqmax rqi = sign i i - i (6.13)
6.2.2 GSC Control Structure of DCC
Basic DCC of GSC approach using dq axis current for real and
reactive power control is designed based on the eqns. (6.14) and (6.15).
qdqqdd iViViVtP =+−=)( (6.14)
q d d q d qQ(t)= V i -V i = -V i (6.15)
Where P(t) and Q(t) are the instantaneous powers absorbed by GSC
from the grid.
102
From the Fig. 6.2, controller output is a current signal with respect
to dq axis and output current of the controller is a tuning current by the input
error signal. The tuning current is adjusted by the error signal at the dynamic
control process. The tuning current signals *
di and *
qi are transferred to voltage
signals *
dV and *
qV to control the GSC and this is realized from eqns. (6.16)
and (6.17).
* * *
d r d s r q dV = -R i +� l i +V (6.16)
* * *
q r q s r dV = -R i -� l i (6.17)
In GSC control structure, PI controllers operate on a direct target
control principle. The initial values of PI controllers are tuned by fundamental
control principle. So, minimization of rms error is obtained between the
referred and measured values. *
dnewV and *
qnewV are generated by voltage limiter
based on *
dV and *
qV in eqns. (6.18) and (6.19).
( ) ( ) ( )2 2
* * * *
dnew d dqmax qV = sign V V - V (6.18)
( ) ( )� �� �� �
22
* * * *
qnew q dqmax dV = sign V V - V (6.19)
6.3 SIMULATION STUDIES OF DCC OF DFIG
Based on the general description, mathematical discussion and
implementation of DCC in the rotor circuit, the performance of DFIG in grid
are analyzed. In this simulation results, % pulsation of Te, PDFIG, QDFIG and %
THD values of is and ir with DFIG controllers are analyzed at unbalanced
103
condition. And also harmonic analysis of is and VGRID are also analyzed in grid.
The simulation studies of the system are analyzed by following cases.
Case 1: Characteristics of DFIG at transient and post-transient conditions
Case 2: Characteristics of DFIG with wind speed variations
Case 3: Pulsation of DFIG parameters with DCC control technique
Case 4: Effects of 5th
and 7th
harmonics of is and VGRID
Case 5: Load contribution of DFIG in grid with DCC control technique
6.3.1 Case 1: Characteristics of DFIG at transient and post-transient
conditions
Performances of DFIG with DCC in grid at transient and post-
transient conditions are analyzed and the test system is shown in Fig.4.12.
Fault applying time and duration of extension of fault are similar to case 1 of
chapter 4 and 5.
Current controllers are implemented in both RSC and GSC in the
DCC technique. At the RSC, the current controller controls the dq frame of
rotor current *
rdi and *
rqi . At the transient period, PI controllers tuning the input
and output signals of current controller. Current limiter of RSC is controlled
by the rotor angular velocity �r, rotor current in dq frame, magnetizing
reactance lm. With these above parameters of DFIG, RSC is controlled by
*
rdnewi and *
rqnewi through current limiter and it is expressed in eqns. (6.12)
and (6.13).
104
(a)
(b)
(c)
(d)
(e)
Fig.6.3 Characteristics of DFIG with DCC at transient and post-
transient conditions. Time (sec) versus (a) wind turbine speed
(p.u) (b) Vs (p.u) (c) Te (p.u) (d) PDFIG (p.u) and (e) QDFIG (p.u)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-1 1 3 5
Win
d t
urb
ine
spee
d (
p.u
)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
-1 1 3 5
Vs
(p.u
)
Time (sec)
-1.5
-1
-0.5
0
0.5
1
1.5
2
-1 1 3 5
Te
(p.u
)
Time (sec)
0
0.2
0.4
0.6
0.8
-1 1 3 5
PD
FIG
(p.u
)
Time (sec)
-0.1
-0.05
0
0.05
0.1
0 1 2 3 4 5
QD
FIG
(p.u
)
Time (sec)
105
Similarly, in GSC, based on the grid current in dq frame id and iq,
rotor resistance Rr and stator angular velocity �s, the votage in dq frame *
dV
and *
qV are calculated and it is expressed in eqns. (5.16) and (5.17). From this
voltage, GSC controlling is better than DPC technique through voltage limiter
*
dnewV and *
qnewV at transient condition. Because in DPC technique, Vs, is, VGRID
and iGRID only controls the converters. But in DCC technique, by the current
controllers at RSC and GSC, the controlling of converters of DFIG is better
than DPC. Hence, % pulsation values are 4.9%, 4.1%, 6.3% and 8.9% of Vs,
Te, PDFIG and QDFIG less than DPC respectively. Fig. 5.3 shows, after the
transient period the system is maintained at stable region.
6.3.2 Case 2: Characteristics of DFIG with wind speed variations
Performance of DFIG is analyzed with 40% of increase in speed
from its rated value. At the time of 2 s, the speed is stepped up from 1 to
1.4 pu shown in Fig. 6.4 and it is similar to case 2 of chapter 4 and 5.
During the stepped up speed, Vs is magnified from its rated value.
But dq frame of rotor and grid currents control the RSC and GSC respectively.
Simultaneously, the pulsation value of stator voltage, electromagnetic torque,
real and reactive powers are suppressed by stator and rotor angular velocities.
But in DPC rotor angular velocity �r is not considered. Hence, the
% pulsation of values are 1.8%, 10%, 4.6% and 20% of Vs, Te, PDFIG and
QDFIG less than DPC with the wind speed variations respectively.
106
(a) (b)
(c) (d)
(e)
Fig. 6.4 Characteristics of DFIG with DCC at wind speed variations.
Time (sec) versus (a) Wind speed (p.u) (b) Vs (p.u) (c) Te (p.u)
(d) PDFIG (p.u) and (e) QDFIG (p.u)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-1 1 3 5
Win
d s
pee
d (
p.u
)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 1 3 5
Vs
(p.u
)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 1 3 5
Te
(p.u
)
Time (sec)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1 1 3 5
PD
FIG
(p.u
)
Time (sec)
-1
-0.5
0
0.5
1
0 1 2 3 4 5QD
FIG
(p.u
)
Time (sec)
107
6.3.3 Case 3: Pulsation of DFIG parameters with DCC control
technique
Table 6.1 Pulsation of DFIG parameters with DCC technique
DFIG
Controller
Te
Pulsation
(%)
PDFIG
Pulsation
(%)
QDFIG
Pulsation
(%)
THD
Value of is
(%)
THD
Value of ir
(%)
DCC ± 3.56 ± 2.48 ± 5.43 1.56 4.63
From Table 6.1, pulsation of Te is less in DCC than other
controllers with unbalanced condition and the test system is similar to case 3
of chapter 4 and 5. With DCC technique, stator angular velocity �s and rotor
angular velocity �r of the DFIG are controlling the GSC and RSC. By the
consideration of �r, Te pulsation is less in DCC. % values of oscillation of
PDFIG and QDFIG are minimum in DCC due to *
rdnewi and *
rqnewi of RSC in eqns.
(6.12), (6.13) and *
dnewV and *
qnewV of GSC in eqns. (6.18) and (6.19). Other than
the DCC, gain value of PI controller Kp and Ki are tuning the rotor parameters
once in the control structure. But in DCC, PI controllers are added in both
input and output of current controller. So better PDFIG and QDFIG are obtained
and less % value of pulsations of DFIG parameters are occurred.
From the above discussions, % pulsation of DFIG parameters are
controlled by current controllers in converters and better results are obtained
from DCC. With the effective control methodologies of DCC, the total %
value of THD of is and ir is less, that is, better damping is provided by current
controller on both RSC and GSC. In Table 6.1, pulsation of Te, PDFIG and
QDFIG are suppressed in DFIG.
108
6.3.4 Case 4: Effects of 5th
and 7th
harmonics of is and VGRID
In PI controller technique, gain of the Kp and Ki are reducing the
rise time, but increasing the overshoot. So, effective controlling of %THD, 5th
and 7th
harmonics of DFIG stator current is are not obtained from the PI
controller without considering Rs.
Table 6.2 Harmonic distortion of iS and VGRID with DCC technique
Harmonics
(%)
DFIG with DCC
is VGRID
5th
0.65 1.3
7th
0.23 0.7
With the DPC, small change in real and reactive powers of DFIG
and grid are also considered and converters of rotor and grid are controlled
better. Hence the %pulsation values of is are controlled better than resonant
and DTC controllers.
In DCC, the current controller controls the controllable voltages
*
rdV and *
rqV in RSC and *
dV and *
qV in GSC. Based on those controllable
voltages, RSC and GSC are controlled by *
rdnewi and *
rqnewi and *
dnewV and *
qnewV in
eqns. (6.12), (6.13) and (6.18), (6.19). Table 6.2 shows, % pulsation of THD,
5th
and 7th
harmonics of is are minimized in DCC than other controllers. Also
DCC does not perform any impact in grid to minimize the pulsation of VGRID
due to control technique is implemented only in the DFIG and it is same in
all the DFIG controllers is shown in Table 6.2.
109
6.3.5 Case 5: Load contribution of DFIG in grid with DCC control
technique
Table 6.3 Load contribution by DFIG with DCC
Time
(Sec)
DCC
PDFIG
(MW)
QDFIG
(Mvar)
1 -4.8795 43.4589
2 73.2372 45.7212
3 73.3397 45.6388
4 73.6189 45.4197
5 73.5035 45.1113
6 73.5035 45.1113
7 73.5035 45.1113
Direct current controller at rotor side, *
rdi and *
rqi are tuned by PI
controller. By the current controller, *
rdi and *
rqi are further controlled with the
rated and reference values of rotor current. Fig. 6.2 shows the error signals are
generated between the current controller output and actual values of rotor
current with dq component of ird and irq. Those error signals are reduced by Kp
and Ki of the PI controller which is connected after the current controller. By
the controlling parameters such as �rlrird, �rlmims and �rlrird, (shown in Fig. 6.2)
the controlled rotor voltage with dq component *
rdV and *
rqV generates the new
rotor current *
rdnewi and *
rqnewi are obtained from the current limiter in eqns. (6.12)
and (6.13).
110
Table 6.4 Load contribution by grid
Time
(Sec)
DCC
PGRID
(MW)
QGRID
(Mvar)
1 615.5528 713.2706
2 519.1227 646.9674
3 518.9645 646.8207
4 518.7311 646.7763
5 518.8639 646.7772
6 518.8639 646.7772
7 518.8639 646.7772
Similarly, same sequence of operation is implemented in GSC
control of DCC. But, the controlled voltage signals with dq component *
dV
and *
qV are obtained from the controlling parameters Rr, �s and lr. With the
stator angular velocity �s, getting *
dV and *
qV are accurate. Based on this
voltage signals, *
dnewV and *
qnewV of GSC is calculated by voltage limiter in eqns.
(6.18) and (6.19).
By the *
rdnewi and *
rqnewi , *
dnewV and *
qnewV both the converters are
controlled effectively. Also, two sets of PI controllers are placed before and
after current controller in both RSC and GSC. Hence, the controlling of
converters is better than other controllers and better performance is achieved
from the rotor circuit of DFIG. Table 6.3 shows that the power delivered by
the DFIG with DCC technique and it contributes more load than other
controllers (Real and reactive powers of DFIG with DCC are 1.647% and
1.919% times more than DPC technique). Simultaneously, Table 6.4 indicates
the power delivered to the load by grid is reduced in DFIG with DCC.
111
6.4 SUMMARY
The mathematical expression of proportional and integral gains is
found by the current control system. DCC is implemented in the RSC and
GSC of DFIG and simulation analyzes of DFIG in grid is carried out by
PSCAD. With the current controllers and proper selections of Kp and Ki gains
of PI controllers in RSC and GSC, contribution of real and reactive powers by
DCC technique is more than other control techniques such as PI, resonant,
DTC and DPC. So, with the improved performance of DFIG with DCC, the
power delivered by grid is reduced.
Simultaneously, % pulsation of Te, powers, total harmonic
distortion of is and ir of DFIG are minimized with DCC technique. Similarly,
5th
and 7th
harmonic effects at unbalanced condition are minimized in DCC,
that is, damping effect is performed well.
Based on the discussions, DFIG with DCC technique is
contributing more real and reactive powers to the load in the grid than other
techniques. Also, % pulsation of DFIG parameters and harmonic effects are
damped effectively than other control schemes.
112
CHAPTER 7
CONCLUSION
This thesis work mainly focuses on the designing aspects of PI,
Resonant, DTC, DPC and DCC control schemes of DFIG and the
performance of those controllers of DFIG in grid are examined. The specific
goal of the research has been to analyze the characteristics of DFIG in grid at
transient and post-transient conditions, wind speed variations, pulsation of
DFIG parameters and effects of 5th
, 7th
harmonics at unbalanced condition and
load contribution by DFIG. This will benefit in the near future, integrating
more wind power generation into the existing grid in the near future.
As a basis of the research, a model of DFIG with grid was
developed in the dedicated power system analysis tool PSCAD/EMTDC. It
simulates the dynamics of the system from the turbine rotor where the kinetic
wind energy is converted to mechanical energy, where the electric power is
fed into the grid.
The complete system includes the wind speed model, aerodynamic
model of the wind turbine, rotor and grid side PWM voltage source
converters. These models were built with standard electrical component
models from PSCAD/EMTDC library. The wind model, the aerodynamic
model, the mechanical model and the control system were built with custom
components developed in PSCAD/EMTDC. The performances of the control
schemes were designed and illustrated by PSCAD/EMTDC which meets the
design requirements.
113
The simulation results have led to the conclusions along with the
novel aspects of the research. The points observed from the results are listed
below.
Transient and post-transient conditions:
In this case, characteristics of Vs, Te, PDFIG, and QDFIG were
analyzed using various control schemes of DFIG in grid and based on the
simulation results, the following points were obtained.
• Those parameters were controlled byr c s
K ,� ,� , decoupling
and harmonic components in resonant controller. But they
were controlled by Kp and Ki in PI controller.
• In DTC technique, controlling of electromagnetic torque Te
controlled the characteristics of DFIG parameters.
• Actual value of real and reactive powers of DFIG and gird
controlled the RSC and GSC respectively in DPC technique.
• With the current controllers at RSC and GSC controlled the
characteristics of DFIG parameters.
Based on the overall analyze of the transient condition, the effective
controlling of characteristics of DFIG were obtained in DCC than other
techniques. At the post-transient period, the system characteristics came to
stable region.
Wind speed variations:
The performance of DFIG with the various controllers in grid was
analyzed with 40% of increase of speed from its rated value. During the
stepped up speed, Vs was magnified from its rated value in all the controllers,
114
but which was less in DCC and pulsation value of stator voltage,
electromagnetic torque, real and reactive powers of DFIG were suppressed
than other control schemes.
Pulsation of DFIG parameters and effects of 5th
and 7th
harmonics of
is and VGRID:
Fluctuation of Te, PDFIG, QDFIG, total harmonic distortion of stator
current and rotor current of DFIG, effects of 5th
and 7th
harmonics of is with
its controllers in grid were analyzed at unbalanced condition. By the current
controllers in converters and effective control methodologies of DCC, the
total harmonic distortion of is and ir were less and better damping also
provided for the fluctuation of electromagnetic torque, real and reactive
powers, effects of harmonics in stator current than other control schemes. But
those controllers did not perform any impact in grid to minimize the pulsation
of VGRID for control schemes were implemented only in the rotor circuit of
DFIG.
Load contribution of DFIG:
Two sets of PI controllers were placed before and after current
controller in both RSC and GSC in DCC. Hence, the controlling of converters
in the rotor circuit of DFIG was better than other control schemes and DFIG
contributed more load than other controllers. Simultaneously, the power
delivered to the load by grid was less than other control technique for the
better performance was achieved from the DCC technique.
Finally, to conclude, the better performances of DFIG in grid were
obtained with DCC technique than other control schemes.
115
FUTURE WORK
Although many works have been accomplished in this thesis,
several future investigations are interesting. Some subjects for future studies
are listed in the following.
1. Saturation effects should be included in the DFIG.
2. High frequency switches should be implemented in the DFIG.
It might provide more accurate transient responses for grid
connected wind turbines with DFIG.
3. Complete Protection schemes such as under and over voltage,
over current, speed and frequency deviation protection should
be developed for the DFIG.
4. Cost benefit analysis should also be investigated and verified
after an external fault.
5. Development of mathematical models of wind turbines with
voltage sag ride through properties should be analyzed.
116
APPENDICES
DFIG MODEL IN PSCAD/EMTDC
The DFIG wind turbine model has been developed in the dedicated
power system analysis tool, PSCAD/EMTDC. The overview of the DFIG
wind turbine model developed by PSCAD/EMTDC [82-89] is presented.
First, a general introduction about the DFIG wind turbine model and the
functions of main blocks in the DFIG wind turbine model are described. The
major steps involved for designing the converter are given below.
• Current Reference Pulse Width Modulator (CRPWM)
Converter
• Determination of rotating mag. flux vector location
• Generation of dq quantities
• Generation of rotor phase reference currents
• Switched Pulse Width Modulator
A1. MAIN BLOCKS IN THE DFIG WIND TURBINE MODEL
DFIG wind turbines are based on wound rotor induction machines
where the rotor circuit is fed through back to back voltage source converters.
The network shown in Fig. A1, is built in PSCAD software in order to
analyze various aspects of DFIG modeling and operation.
The rotor currents ira, irb, irc of the machine can be resolved into
direct and quadrature components id and iq. The id and iq produces a flux in the
117
airgap which is aligned with the rotating flux vector linking the stator and flux
at right angles to this vector respectively.
Fig. A1 Block diagram of DFIG with wind turbine
The id controls the reactive power entering the machine. The iq
contributes to the machine torque and power. If id and iq can be controlled
precisely, then it is possible to control the stator side real and reactive powers.
The phase reference currents can be obtained by direct and quadrature axis of
the rotor currents.
The crucial step is to obtain the instantaneous position of the
rotating flux vector in space in order to obtain the rotating reference frame.
This can be achieved by realizing that on account of Lenz’s law of
electromagnetism, the stator voltage (after subtracting rotor resistive drop) is
simply the derivative of the stator flux linkage �a as in eqn. (A1) which is
written for phase a.
aa a a
d�V - i R =
dt (A1)
118
A2. CURRENT REFERENCE PULSE WIDTH MODULATOR
(CRPWM) CONVERTER
Fig. A2 CRPWM Converter
Fig. A2 shows the CRPWM. The rotor side VSC converter requires
a DC power supply. The DC voltage is usually generated using another
voltage source converter connected to the AC grid at the generator stator
terminals. A DC capacitor is used in order to remove ripple and keep the DC
bus voltage relatively smooth. This grid side converter is operated so as to
keep the DC voltage on the capacitor at a constant value. In effect, this means
that the grid side converter is supplying the real power demands of the rotor
side converter.
It is possible to operate this converter using a current reference
approach used for the rotor side converter. However, CRPWM has the
119
drawback that the switching frequency, and hence the losses are not
predictable. Therefore, a feedback controller is used in which the error
between the desired and ordered currents is passed through PI controller
which controls the output voltage of a conventional sinusoidal PWM
Converter.
Fig. A3 CRPWM Controller
Fig.A3 shows the function of CRPWM controller with RL load. If
the actual current is below the lower threshold, the upper switch (T1/D1) is
turned on which applies a positive voltage (E/2) to the load. The current in the
source thus rises in response to this voltage. When the current rises above the
upper threshold, the upper switch is turned off and the lower switch (T2/D2) is
turned on. This applies a negative voltage (-E/2) to the load and causes the
current to drop.
Thus, the difference between the desired and actual currents is kept
within the tolerance band. By making the thresholds smaller, the desired
current can be approximated to any degree necessary. However, there is a
limit to which this can be done, because the smaller the threshold, the smaller
the switching periods, that is, the higher the switching frequency and losses.
Using this technique, any given current waveform can be synthesized. A
method that removes all harmonics can be constructed using the approach.
120
A3. DETERMINATION OF ROTATING MAG. FLUX VECTOR
LOCATION
In Fig. A4, the three phase stator voltages after removal of resistive
voltage drop) are converted into the Clarke (� and �) components V� and V�,
which are orthogonal in the balanced steady state. This transformation is
given by:
� � �� � � � � �� �� ��
a
�
b
�
c
1 1V1 - -
V 2 2 2= V
V 3 3 3V0 -
2 2
(A2)
Integrating V� and V�, we obtain �� and ��, the Clarke components
of stator flux, we get,
2 2
a b� = � + � (A3)
� �� �� �
�-1
s
�
�� = tan
� (A4)
The angle �s gives the instantaneous location of stator’s rotating
magnetic field. In practical control circuits, as in Fig. A4, some filtering is
required in order to rid off the quantities �� and �� of any residual DC
component introduced in the integration process.
121
Fig. A4 Rotating Mag. Flux vector location
A4. GENERATION OF dq QUANTITIES
Fig. A5 Generation of dq quantities
The detection of the AC grid voltage reference angle and
generation of dq components of current are done in a straightforward manner
using a dq transformation block as in Fig. A5.
A5. GENERATION OF ROTOR PHASE REFERENCE
CURRENTS
Fig. A6 Generation of rotor phase reference currents
Irc_ref
Irb_ref
Ira_ref
Ird
Irq Ircc
Iraa
Irbb
2 to 3 Transform Rotor to stator
slpang
D alfa
Q beta
alpa
beta
A
B
C
122
The instantaneous values for the desired rotor currents can be
calculated using the inverse dq transformation, with respect to the slip angle,
as shown in Fig. A6. Once the reference currents are determined, they can be
generated using a voltage source converter operated with a technique such as
CRPWM as shown in Fig. A6.
Instantaneous values for the desired rotor currents can be calculated
using the inverse dq transformation and it is expressed in eqns. (A5) and (A6).
� � � � � �� � �
� cos� -sin� d=
� sin� cos� q (A5)
� �
� �� � � � � � � � ��
� ��
1 0a
�1 3b = -
�2 2c
1 3- -
2 2
(A6)
A6. SWITCHED PULSE WIDTH MODULATOR
Fig. A7 SPWM generator
123
Fig. A7 shows a standard sinusoidal PWM controller in which each
of the phase voltages is compared with a high frequency triangle wave to
determine the firing pulse patterns. The advantage of the SPWM controller is
that the number of switchings in a cycle is fixed, and so the losses can be
easily estimated.
A7. DFIG PARAMETERS
Rated voltage (L-L) : 13.8 [KV]
Stator / rotor turns ratio : 2.637687
Base angular velocity : 376.99 [rad/s]
Angular moment of inertia (J=2H) : 0.7267 [s]
Mechanical damping : 0.001 [p.u]
Stator resistance : 0.0054 [p.u]
Wound rotor resistance : 0.00607 [p.u]
Magnetizing inductance : 4.362 [p.u]
Stator leakage inductance : 0.102 [p.u]
Wound rotor leakage inductance : 0.11 [p.u]
A8. TERMINAL DESCRIPTIONS
The terminal description of wound rotor induction machine is
specified below:
A, B, C : 3-phase electrical connection points of the star connected
stator.
W : Speed input [p.u]
S : Switch is selected to either speed control mode (1) or
torque control mode (0).
T : Torque input [p.u].
124
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LIST OF PUBLICATIONS
International Journals
Published
1. A. Ramkumar, S. Durairaj and N. Arun, “PIR Regulator using DTC
for DFIG during Unbalanced Grid Voltage Conditions,” Applied
Mechanics and Materials Vol. 626 (2014), pp. 136-140,
doi:10.4028/www.scientific.net/AMM.626.136.
2. A. Ramkumar, S. Durairaj and K. Dhivya, “Behavior of DFIG with
direct torque controller at unbalanced and distorted grid voltage
conditions,” Applied Mechanics and Materials Vol. 626 (2014),
pp. 150-154, doi:10.4028/www.scientific.net/AMM.626.150.
3. A. Ramkumar and S. Durairaj, “Design and Analysis the Impact of
DFIG Controllers in Interconnected Grid System,” Jokull Journal, vol.
63, No. 10, pp. 98-116, Oct. 2013.
4. A. Ramkumar and S. Durairaj, “Analyzing Load Response of
Interconnected Vector Controlled DFIG with SEIG and Synchronous
Generator,” International Journal of Advances in Engineering &
Technology, vol. 6, issue. 4, pp. 1775-1787, Sep. 2013.
Accepted
1. A. Ramkumar, S. Durairaj and N. Arun, “Comparison of PI and PIR
Regulators for DFIG during Unbalanced Grid Voltage Conditions,”
Lecture Notes in Electrical Engineering (SPRINGER) (Presented in
IEEE International Conference on Power Electronics and Renewable
Energy Systems ICPERES 2014, Rajalakshmi Engineering College,
Chennai, pp. 3, April 25-26, 2014).
2. A. Ramkumar, S. Durairaj and K. Dhivya, “Enhanced Controllers of
DFIG with Unbalanced and Distorted Grid Voltage Conditions,”
Lecture Notes in Electrical Engineering (SPRINGER) (Presented in
IEEE International Conference on Power Electronics and Renewable
Energy Systems ICPERES 2014, Rajalakshmi Engineering College,
Chennai, pp. 2, April 25-26, 2014).
135
In Communication
1. A. Ramkumar and S. Durairaj, “Performance Analysis of DFIG with
PI-R, Direct Power Controllers in Grid System,” Turkish Journal of
Electrical Engineering & Computer Sciences.
2. A. Ramkumar and S. Durairaj, “Transient Analysis of DFIG in Grid
Connected System,” International Journal of Automation and Control
Engineering.
International Conferences
1. A. Ramkumar and S. Durairaj, “Coordinated Control of
Interconnected Hydro Governor Synchronous Generator with SEIG,”
IEEE International Conference on Power, Energy and Control,
PSNA College of Engineering and Technology, Dindigul, pp. 94,
Feb. 6-8, 2013.
2. A. Ramkumar and S. Durairaj, “An Analysis of Transient
Characteristics of Interconnected DFIG with Hydro Governor
Synchronous Generator,” IEEE Sponsored International conference on
Power, Signals, Control and Computations EPSCICON 2012,
Vidya Academy of Science and Technology, Thrissur, pp. 1-10,
Jan 2-6, 2012.
3. A. Ramkumar and S. Durairaj, “Performance Analysis of Doubly fed
Induction Generator during Short Circuit Conditions,” International
Conference on System Dynamics and Control ICSDC-2010, Manipal
Institute of Technology, pp. 83, Aug 19-22, 2010.
National Conference
1. A. Ramkumar and S. Durairaj, “Real and Reactive Power Flows of
DFIG with an External Faulty Condition,” National Power Engineering
Conference NPEC-2010, Thiagarajar College of Engineering, Madurai,
pp. 39-45, Dec 2-3, 2010.
136
CURRICULUM VITAE
A. RAMKUMAR residing at Rajapalayam. His date of birth
is 14-03-1976.
He completed his DEEE degree at PACR Polytechnic College,
Rajapalayam in 1994. He completed his B.E (Electrical and Electronics
Engineering) degree at Thiagarajar College of Engineering, Madurai,
Tamil Nadu affiliated to Madurai Kamarajar University in 1997. And he
completed his M.E (Power Systems) degree at Faculty of Engineering
and Technology (FEAT), Annamalai University, Annamalai Nagar,
Chidambaram, Tamil Nadu in 2002.
He has been working as Assistant Professor (senior) with
Kalasalingam University, Krishnankoil, Virudhunagar District, Tamil
Nadu, since 2003 in the Department of Electrical and Electronics
Engineering. Also previously he worked as a Lecturer at Arulmigu
Kalasalingam Polytechnic College, Krishnankoil for 3 years 7 months.
He organized one international conference, two national
conferences and six short term courses. Under his guidance, 15 M.E /
M.Tech and 20 B.E / B.Tech projects are completed.
His area of interest includes Reactive power compensation,
FACTS, High voltage engineering, Machines, High Voltage DC
transmission systems, Special electrical machines and Power system
control.
