INSTITUTE OF ENERGY TECHONOLOGY
DOUBLY FED INDUCTION GENERATOR FAULT
RIDE THROUGH CONTROL
CONDUCTED BY GROUP WPS3-952
AUTUMN SEMESTER, 2008
INSTITUTE OF ENERGY
TECHNOLOGY AALBORG
UNIVERSITY
Pontoppidanstræde 101 - DK-9220 Aalborg Øst
TITLE
Doubly Fed Induction Generator
Fault Ride Trough control
SEMESTER:
3rd semester, autumn 2008
SEMESTER THEME:
Control of Wind Generator Systems
PROJECT PERIOD
04 September 2008 - 4 January
2009
Project ECTS:
22
PROJECT GROUP
WPS3-952
PARTICIPANTS
Florin Bujac
Piotr Stasiuk
Fernando Valderrey Sanchez
SUPERVISOR
Florin Iov ,
Paul Bach Thøgersen KK-electronic
Telephone +45 96359240
SYNOPSIS
In this project an analysis of different strategies
for Fault Ride Trough protection (crowbars),
control of the rotor side of a DFIG and control for
Fault Ride Trough (FRT) for a Doubly Fed
Induction Generator (DFIG) is presented.
The design of both controls, rotor and FRT, is
done on the basis of simulation of the entire system
in Simulink® environment. The simulation of the
generator, grid, converter and crowbar protection
are performed in PLECS.
For the simulations parameters from [36] are
used. Description to measure parameters of a
machine is presented. For the rotor control a direct
torque strategy is used , and tested for a change in
the wind from 5m/s to 11m/s and a change in the
reactive power of ±0.1*nominal active power.
The crowbar protection for FRT has been design
to be an active crowbar. The control of the crowbar
has been design in order to be able to absorb
overcurrent when a voltage deep occurs keeping the
converter connecting. For this a voltage dip of 15%
grid voltage is simulated and removed after 100ms.
Preface
The present project report entitled “Doubly Fed Induction
Generator Fault Ride Through Control” and it is conducted by the group
WPS3- 952 at the Institute of Energy Technology.
The project theme is proposed by the company KK-electronic and
is covered by the semester theme: Control of Wind Generator Systems.
The project period is: 02.09.2008 - 04.01.2009.
The literature references are mentioned by numbers in square
brackets. Detailed information about the literature used in this project is
presented in Bibliography. Appendices, assigned with letters, are arranged in
alphabetical order. The figures have the format ‘Fig.x.y’, equations are in
format ‘(x.y)’, where ‘x’ is the chapter number and ‘y’ is the item number.
The enclosed CD-ROM contains the project report in Word DOC,
Adobe PDF format, Matlab Simulink and Plecs models.
Authors would like to thank the supervisor Florin Iov and Paul
Bach Thøgersen, for the help and support provided during the project period.
The report is conducted by:
Florin Bujac
_____________
Piotr Stasiuk
_____________
Fernando Valderrey Sanchez
_____________
Table of contents
TABLE OF FIGURES
III
ABBREVIATIONS LIST
V
NOMENCLATURE LIST
VI
CHAPTER 1
INTRODUCTION
1
1.1
Problem Statement
3
1.2
Project goals
4
1.3
Project Limitations
5
CHAPTER 2
DOUBLE FED INDUCTION GENERATOR
6
2.1
Principle of operation and construction
6
2.2
Power Flow in DFIG [28]
6
2.3 Induction Machine Model
2.3.1
General equations in ABC/abc Reference Frame [32]
2.3.2
Complex space Vector representation [32]
2.3.3
General machine equations using space vector [32]
2.3.4
The Clark Transformation ( α , β equivalent frame) [32]
2.3.5
The Park Transformation (d,q equivalent frame) [32]
9
9
12
13
16
17
2.4
19
Aerodynamic conversion
2.5 Control
2.5.1
Pitch Control [32]
2.5.2
Control of DFIG
2.5.2.1
Direct Torque Control [15]
2.5.2.2
Direct Power Control
22
22
23
24
25
2.6 Overview of FRT requirements in Grid Codes
2.6.1
Crowbars
2.6.2
Crowbar topologies
2.6.2.1
Crowbar 1 – Thyristor bridge
2.6.2.2
Crowbar 2 – Diode bridge with GTO thyristor
2.6.2.3
Crowbar 3 – Antiparallel thyristors between phases
2.6.2.4
Crowbar 4 – Diode bridge with thyristor
2.6.2.5
Crowbar 5 - Improved Fault Ride through strategy for DFIG
2.6.3
Crowbar selection
26
28
29
29
30
30
31
32
32
i
CHAPTER 3
SYSTEM DESIGN AND SIMULATIONS
3.1 DFIG simulation Model
3.1.1
Principle of control
3.1.2
Rotor Control
3.1.2.1
Implementation
3.1.2.2
PI-controller design
3.1.2.3
Simulation results
3.1.3
Control of the Crowbar
3.1.3.1
Parameters adjustment
3.1.3.2
Simulation results
CHAPTER 4
34
34
35
37
37
41
42
47
50
51
TESTS
58
4.1 Induction Machine Tests [24] [25] [26]
4.1.1
The transformer
4.1.2
No-load test [24] [25] [26]
4.1.3
Blocked-rotor test [24] [25] [26]
58
58
61
63
CONCLUSIONS
65
FUTURE WORK
65
REFERENCES
66
APPENDIX A: PARAMETERS [36]
70
APPENDIX B: M-FUNCTION CALCULATION OF THE MECHANICAL TORQUE
72
APPENDIX C: CALCULATION OF MAXIMUM POWER POINT (MPP)
73
APPENDIX D: M-FUNCTION CALCULATION OF POWER AND TORQUE
76
APPENDIX E: POWER FLOW
78
APPENDIX F: IGBT & GTO
79
ii
Table of Figures
Fig. 1.1 DFIG topology ............................................................................................................................................. 2
Fig. 1.2 Fault ride through interval .......................................................................................................................... 4
Fig. 1.3 Laboratory setup of DFIG with CB protection ............................................................................................. 5
Fig. 2.1 Distribution of the energy in Doubly Fed Induction Generator for sub-synchronous speed ....................... 7
Fig. 2.2 Distribution of the energy in Doubly Fed Induction Generator for over-synchronous speed ...................... 7
Fig. 2.3 Sub-synchronous speed n<ns ...................................................................................................................... 8
Fig. 2.4 Over-synchronous speed n>ns .................................................................................................................... 8
Fig. 2.5 Concentric stator and rotor windings, currents, voltages and angle dependencies of a three phase
induction machine [32] ............................................................................................................................................ 9
Fig. 2.6 Space vector constructed from a three phase system [32] ....................................................................... 13
Fig. 2.7 Dynamical per phase equivalent diagram for induction machine. ........................................................... 16
Fig. 2.8 Equivalent two-phase machine ................................................................................................................. 16
Fig. 2.9 Park Transformation [32].......................................................................................................................... 18
Fig. 2.10 Cp curve, presented as a relation between rotational speed and wind speed........................................ 19
Fig. 2.11 Cp-Lambda curve for θ=0........................................................................................................................ 20
Fig. 2.12 Maximum Power Point Tracking for Cpmax .............................................................................................. 21
Fig. 2.13 Wind turbine torque vs. rotor speed characteristic ................................................................................ 21
Fig. 2.14 Wind turbine power vs. rotor speed ....................................................................................................... 22
Fig. 2.15 Blade cross section of a WT [32] ............................................................................................................. 23
Fig. 2.16 Torque-speed characteristic of a 2MW DFIG wind turbine [15] ............................................................. 24
Fig. 2.17 Torque control loop of a DFIG ................................................................................................................. 24
Fig. 2.18 Power-speed Characteristic [23] ............................................................................................................. 25
Fig. 2.19 Power control loop of a DFIG .................................................................................................................. 25
Fig. 2.20. International Grid Codes Comparison (IGCC) [12] ................................................................................. 26
Fig. 2.21 Voltage profile regarding fault ride through capability of wind turbines/farms in National Grid Codes
[1] .......................................................................................................................................................................... 27
Fig. 2.22 DFIG topology with attached crowbar protection .................................................................................. 28
Fig. 2.23 DFIG bypass resistors in the rotor circuit with (A) thyristors, (B) GTOs . ................................................. 29
Fig. 2.24 Schematic of Diode Bridge with GTO. ..................................................................................................... 30
Fig. 2.25 Antiparallel (A) thyristors and (B) GTO between rotor phases................................................................ 30
Fig. 2.26 Diode bridge with thyristor crowbar (A). Modificated protection (B) for project purposes. ................... 31
Fig. 2.27 Crowbar topology for improved FRT strategy with static switch S1 and static transfer switch S2. ........ 32
Fig. 2.28 Model of DFIG with attached crowbar nr.2 ............................................................................................ 33
Fig. 3.1 Plecs model of the DFIG wind turbine ....................................................................................................... 34
Fig. 3.2 Simulink blocks for the calculation of the Mechanical Torque.................................................................. 35
Fig. 3.3 Power flow of an ideal DFIG at over synchronous speed and sub synchronous speed [32] ...................... 36
Fig. 3.4 Power flow in the WRIM of 7.5kW ............................................................................................................ 36
Fig. 3.5 Vector diagram of the d,q reference frame aligned to the stator flux, with stator voltage in quadrature
............................................................................................................................................................................... 37
Fig. 3.6 Block diagram for the rotor side control ................................................................................................... 39
Fig. 3.7 Look-up Table for reference Active Power ................................................................................................ 40
Fig. 3.8 PI control in z-domain using backward transform .................................................................................... 41
Fig. 3.9 Step response of the system ..................................................................................................................... 42
Fig. 3.10 Simulink model of the entire system ....................................................................................................... 42
Fig. 3.11 Variation of the wind speed .................................................................................................................... 43
Fig. 3.12 Mechanical and Electrical Torque ........................................................................................................... 44
Fig. 3.13 Rotor speed ............................................................................................................................................. 44
Fig. 3.14 Active Power reference and Active Power measure ............................................................................... 45
Fig. 3.15 Reactive Power reference and Reactive Power measure ........................................................................ 45
Fig. 3.16 D-Rotor current reference and D-rotor current measure ........................................................................ 46
Fig. 3.17 Q-Rotor current reference and Q-rotor current measure ....................................................................... 46
Fig. 3.18 Entire model of DFIG for Fault Ride Trough analysis with crowbar attached ......................................... 47
iii
Fig. 3.19 Generation of duty cycles (∆ - duty cycle, Tsw - switching period, ton – duty cycle reference signal) .... 48
Fig. 3.20 Tuning P controller .................................................................................................................................. 49
Fig. 3.21 First part of crowbar control scheme ...................................................................................................... 49
Fig. 3.22 Second part of crowbar control scheme.................................................................................................. 50
Fig. 3.23 Simulink model of complete system ........................................................................................................ 51
Fig. 3.24Rotor current d-component reference and measured value .................................................................... 52
Fig. 3.25Rotor current q-component reference and measured value .................................................................... 52
Fig. 3.26 Active Power reference and measured value .......................................................................................... 52
Fig. 3.27 Reactive Power reference and measured value ...................................................................................... 53
Fig. 3.28 Mechanical and Electrical Torque ........................................................................................................... 53
Fig. 3.29Rotor speed .............................................................................................................................................. 53
Fig. 3.30 Stator voltage.......................................................................................................................................... 54
Fig. 3.31 Stator current .......................................................................................................................................... 54
Fig. 3.32 Rotor current measured on rotor’s terminals ......................................................................................... 55
Fig. 3.33 Rotor current measured on converter’s terminals .................................................................................. 55
Fig. 3.34 Current in the crowbar’s circuit ............................................................................................................... 55
Fig. 3.35 Rotor current measured on rotor windings ............................................................................................. 56
Fig. 3.36Rotor current on converter terminals....................................................................................................... 56
Fig. 3.37Compared RMS values of rotor current at the rotor’s terminals and converter’s terminals .................... 57
Fig. 3.38 Energy absorbed by crowbar during fault in the grid.............................................................................. 57
Fig. 4.1 Transformer schematic [30] ...................................................................................................................... 59
Fig. 4.2 Transformer windings connections [30] .................................................................................................... 60
Fig. 4.3 Electrical diagram of the no-load test setup [24]...................................................................................... 61
Fig. 4.4 Equivalent induction machine circuit for no-load test [25] ....................................................................... 62
Fig. 4.5 Electrical diagram of the blocked-rotor test setup [24] ............................................................................ 63
Fig. 4.6 Equivalent induction machine circuit for blocked rotor test [25] .............................................................. 63
iv
Abbreviations list
Abbreviation
DFIG
FRT
WTG
PCC
TSO
IGCC
p.u.
IGBT
GTO
WRIM
WRIG
Mmf
Emf
AC
DC
DS
TS
MPP
Description
Doubly Fed Induction Generator
Fault Ride Through
Wind Turbine Generators
Point of Common Coupling
Transmission System Operators
International Grid Codes Comparison
per unit value
Insulated-Gate Bipolar Transistor
Gate Turn-Off Thyristor
Wound Rotor Induction Machine
Wound Rotor Induction Generator
magneto motive force
electromotive force
Alternative Current
Direct Current
Distribution System
Transmission System
Maximum Power Point
v
Nomenclature list
Parameter
Pmshaft
Description
mechanical power delivered to the shaft
Pm
useful mechanical power
Pf
friction losses
Pre
rotor electrical power
Prt
rotor total losses
Pgap
power delivered through air gap
Ps
stator power
Pst
stator total losses
N sξ s
stator effective number of turns
N rξr
θ
ρ
rotor effective number of turns
u
i
electrical angle
the rotor displacement angle
voltage
current
a
Lσ
resistance
flux
stator-rotor ratio
complex vector
leakage flux inductance
Lm
main flux inductance
Te
electromagnetic torque
Tm
mechanical load torque
ωr
ωe
angular rotor speed
J
D
Pn
inertia
damping factor
rotor angle
rotor angle acceleration
nominal power
Pwt
Mechanical power
R
Ψ
n
ρ
ρ&&
electrical angular rotor speed
vi
ρ
R
V
Cp
λ
θ
T
ω
air density
blade radius
wind speed
power coefficient
tip speed ratio
pitch angle
torque
rotational speed
Pe
L
D
P
Q
Ir
electrical power
lift forces
drag forces
active power
reactive power
absolute value of rotor current
Ith
Rcrow
Pmax
s
preset threshold current
crowbar resistance
maximum power
mechanical power through the shaft of the generator
Power through the stator
Power through the stator
rotor angular speed
synchronous speed
slip
kp
ki
u(t)
e(t)
f
Tsw
proportionality constant
integration constant
output signal
error signal
frequency
switching period
N
Pn −l
magneto motive force
input power measured in the no-load test
PCu
copper losses
Prot
rotational losses
R n −l
no-load resistance
Z n −l
no-load impedance
X l ,S
stator leakage reactance
X m1
magnetizing reactance
PM
Ps
Pr
ωr
ωs
vii
Pb − r
input power measured in the blocked rotor test
Rb − r
blocked rotor resistance
Z b− r
ton
U
I
blocked rotor impedance
E
T
pp
electromotive force
time
number of pole pairs
subscript ‘ α ’
subscript ‘ β ’
subscript ’d’
subscript ‘q’
subscript ’s’
component on α axis
component on β axis
component on d axis
component on q axis
stator winding
subscript ‘r’
subscript ’a’
subscript ’b’
subscript ’c’
subscript ‘(s)’
subscript ‘(r)’
rotor winding
winding ‘a’
winding ‘b’
winding ‘c’
referred to the stator
referred to the rotor
subscript ‘(ref)’
reference value
duty cycle reference signal
voltage
current
viii
Chapter 1
Introduction
The prediction of The World Energy Council is that by 2050 the energy mix around
the globe will contain of different energy sources in which renewables will have an important
role. The target of the European Union is that 22% of electricity generation has to be from
renewables by 2010. The wind power will be the principal contributor to this goal, and
according to International Energy Agency it had the highest average annual growth rates
among renewable sources of energy.
Europe is the leader right now at the penetration of the wind power into the electrical
network, where Denmark and Germany have the highest penetration level. The countries that
will install in the near future more wind power are Spain, Great Britain and Ireland. Also
important development of wind power is predicted in Australia, Canada and Japan. [1]
The percentage of renewable energy in total EU countries demand is growing. In some
systems of energy, such as Denmark, wind energy provides up to 20% of all produced energy.
Such large share (part) of the energy used as a key issue involves the stability of the energy
system. [2]
In the last years the wind turbine technology has been continuously developed. The
blade lengths of the wind turbines are becoming larger and the turbines are able to produce
more electricity, fact that make the cost of renewable generation drop.
Today there are two basic types of wind turbine:
• Fixed-speed wind turbines
• Variable-speed wind turbines
Fixed-speed wind turbines are mainly equipped with squirrel-cage induction
generators, and the rotor is connected to the generator shaft using a fixed-ratio gearbox. The
construction and the performances of these wind turbines depend on the characteristics of
mechanical circuits and the time response on some of them. The result is that at a strong rush
of wind can be observed a fast and strong variation of the electrical output power. These load
variations require a stiff power grid for the stable operation and a firmly built mechanical
structure in order to absorb the high mechanical stresses that appear. This solution, applied to
high-rated power leads to expensive mechanical construction. [3]
The specific main advantages of adjustable speed generators compared with the fixedspeed generators are: [3]
• Cost effective and able to provide simple pitch control. The controlling speed of
the generator (frequency) allows the time constants of the pitch control to become
longer. In this way the pitch control complexity and peak power requirements are
reduced. The pitch angle control is performed only to limit the maximum output
power at high wind speed.
• Reducement of the mechanical stresses. The strong rush of wind can be absorbed;
energy is stored in the mechanical inertia of the turbine, creating elasticity that
reduces torque pulsations.
• Dynamic compensation for torque and power pulsations, caused by the back
pressure of the tower.
• Improvement of the power quality, by reducing the torque pulsations due to the
elasticity of the WT system.
1
•
•
Improvement of system efficiency. The turbine is adjusted as a function of wind
speed in order to maximize the output power. The operation at the maximum
power point can be done for a wide power range. As a result is possible an
efficiency improvement of 10%.
Reducement of acoustic noise. Low-speed operation can be made at low wind
power, and therefore low power. [3]
X
Possible implementation schemes of the adjusted-speed generators are: the full scale
power converter system and the DFIG adjusted-speed generator system.
The full scale power converter systems have a couple of disadvantages:
high cost of the power converter rated at 1 p.u. total system power,
the design of the inverter output and electromagnetic interference filters rated at
1 p.u. is difficult and costly
the total system efficiency (over the entire operating range) the converter
efficiency plays an important role.
Most of the modern megawatt wind turbines are variable-speed wind turbines. One
solution is the Doubly Fed Induction Generator (DFIG) that is coupled to the electrical
network via a transformer and supplied to the rotor from a frequency converter [4], as shown
in Fig. 1.1.
Fig. 1.1 DFIG topology
The developments made for the DFIG adjusted-speed generator system avoid the
detriments of the full scale power converter systems, results the following advantages: [3]
cost reduction of the inverter because of handling 25% of the total
system power
inverter output and electromagnetic interference filters are rated at 0.25
p.u. (inverter harmonics represent a smaller fraction of the total system
harmonics)
Improved system efficiency
Power-factor control can be made at lower costs
2
The last advantage can be acknowledged because the DFIG have an operation similar
to a synchronous generator and the converter has to provide only excitation energy.
The DFIG system permit decoupled control of active and reactive power of the
generator.[3]
During large grid disturbances DFIG systems needs a crowbar in order to protect the
converter, short circuiting the rotor circuit. That means that the wind turbine must be
disconnected from the grid, after a large voltage dip. [5]
Some countries have issued dedicated grid codes for connecting the wind turbines or
wind farms to the electrical network. This grid codes are addressed to the transmission and\or
distributed system.
This grid codes are implemented in order to obtain continuity and security of the
supply of wind power into electrical network.[1]
1.1 Problem Statement
An important requirement of the grid codes about wind turbines is the Fault RideTrough (FRT), required for the security of the power system stability. This requirement
dictates that Wind Turbine Generators (WTGs) must remain connected to the grid, even if a
fault occurs and the voltage at the point of common coupling (PCC) drops to low values.
These values are different depending on the country regulations. For manufacturers implies
that the WTG systems must be design to fulfil FRT request. WTGs that use power electronics
are more sensitive to disturbances, the definition of any excessive transient current and
potential over voltages are needed to be determined for their design. [6]
Nowadays DFIG are the most used Wind Turbine Generators; these kinds of
generators are really sensitive to the FRT due to the use of converters in rotor side to control.
When fault occurs, large over currents are induced in stator and rotor windings, this would
produce the destruction of the Back to Back Converter. When the fault occurred, in the range
of operation that grid codes establish and exceeding the maximum current the converter can
hold, rotor circuit is shorted using different protection strategies, and the converter is
disconnected. The boundaries of the operation for FRT are shown in the Fig 1.2. The
requirements for FRT are provided by the Transmission System Operators (TSOs) which
contain certain recovery limitations which DFIG must follow. The main demands are
concerning the maximum voltage dip, time duration and time of full voltage recovery (Fault
ride-through). These specifications differed from the different Local Grid Operators. [2][7]
Specifications, from TSO, about Fault ride-through indicate that wind-turbine
generators (WTGs) must be connected to the grid even at certain low voltage levels. [8]
X
3
100%
Must remain
connected
Voltage levels
estabilished by
TSO
Voltage recovery
Fault interval
Time [s]
Rising time
Fig. 1.2 Fault ride through interval
The design of the DFIG’s converter has to handle the high currents or provide an
alternative path (crowbar) during the fault. As it is said in [6] the use of crowbars to fulfill the
FRT requirement is the most cited solution. The performance of crowbar is essentially the
short circuit of the rotor winding preventing high voltage and current that can destroy the
converter. However, in order to be able to ride through a voltage dip the control of the
crowbars has to remove it when the current transient has decayed to an acceptable level, so
the generator can continue in normal operation. [9]
Crowbars can be differentiated in two groups, active and passive. Essentially, the
passive crowbar is a resistor with variable resistance. Depend of resistance value it is possible
to limit rotor currents, and hence stator currents, after short-circuit fault. For active crowbar,
its structure is more complex than passive crowbar. Active crowbar contains active elements,
such a forced commutated thyristor or transistors. These elements enable to switch on and off
the crowbar with high frequency. Passive crowbars can be easily switch on when needed but
switching off is possible only when current naturally crosses zero. The design of crowbar has
to comply the Grid Code requirements in terms of Fault Ride-Through. [10]
1.2 Project goals
The main goal of this project is the study and the simulation of FRT for a DFIG,
shown in Fig.1.3.
4
To reach this the following aspects will be treated:
•
•
•
•
•
Review, study and analysis of DFIG, FRT and different Crowbars
topologies.
Design of the control of the selected crowbar.
Test of a new rewinded generator in order to obtain all the necessary
parameters.
Control of the generator.
Simulation of the entire system.
Fig. 1.3 Laboratory setup of DFIG with CB protection
1.3 Project Limitations
•
In this setup the generator and the converter will be supplied with the same voltage
level
•
It will not be taken into consideration the entire back-to-back converter, it will be
limited only to one side, only the rotor side converter is considered
•
To face requirements of this project, only active topology must be chosen
•
After comparison, best crowbar topology will be taken into consideration
•
The parameters of the DFIG are taken from [36]
•
The pitch control and stator control are not taken under consideration.
•
The obtained FRT was not compared with any specific grid codes requirements.
5
Chapter 2 Double Fed Induction
Generator
2.1 Principle of operation and construction
This electrical machine, also known as wound rotor induction generator (WRIG), has
the stator windings directly connected to the supply network and the rotor windings are
connected to the grid through a back-to-back converter.
The back-to-back converter consists of a force-commutated rectifier and a forcecommutated inverter connected by a common dc-link capacitor. This converter normally
consists of a machine-side converter and a grid-side converter. The machine-side converter
acts as an inverter, used to control the torque or the speed of the machine as well as the power
factor at the stator terminals. The grid-side converter acts as a rectifier, controlling the DC
voltage of the DC link, while exchanging power with the grid. [13] [32]
The DFIG has a stator mounted on bearings and is separated from the rotor by an air
gap. Alternative current is supplied directly to the stator and by induction to the rotor. The
stator is composed of laminations of high-grade sheet steel and in slots cut on the inner
surface of the stator frame is mounted a three-phase winding. The rotor contains laminated
ferromagnetic material, with the slots cut on the outer surface, and the rotor windings are
connected to three slip rings. The terminals of the rotor can be connected to an external circuit
by using stationary brushes pressing against the slip rings.
When the stator windings are connected to a three-phase supply while the rotor circuit
is closed, the voltages induced in the rotor windings produce rotor currents that will interact
with the air gap field to produce torque.
The rotor will reach a steady-state speed that is less than the synchronous speed at
which the stator rotating field rotates in the air gap. If the steady-state speed will be equal to
the synchronous speed, no voltage and current will be induced in the rotor circuit, so torque
will not be present. The induced currents in the rotor windings will produce a rotating field
and the interaction between this field and the field produced on the stator will generate the
torque.[14]
2.2 Power Flow in DFIG [28]
The power flow in Doubly Fed Induction Generator can have different distribution
which depends on the actual wind speed. In wind plants power in stator flows from generator
to the grid. The DFIG rotor circuit has back to back converter which allows power flow both
ways- to generator or form generator. DFIG is a structure which can work over synchronous
at speed up to 110% with respect to synchronous. It is also possible to operate at sub
synchronous, down to 50% with respect to the synchronous speed.
6
At sub-synchronous speed the power flows to the grid through stator and to the
generator from the grid through converter.
STATOR
ENERGY
INDUCTION
GENERATOR
ROTOR
ENERGY
Fig. 2.1 Distribution of the energy in Doubly Fed Induction Generator for sub-synchronous
speed
When turbine is operating at over synchronous speed the energy flows to the grid
through both stator and rotor.
Fig. 2.2 Distribution of the energy in Doubly Fed Induction Generator for over-synchronous
speed
Power flow in DFIG for different operation speed:
7
Fig. 2.3 Sub-synchronous speed n<ns
Fig. 2.4 Over-synchronous speed n>ns
Pmshaft
- mechanical power delivered to the shaft
Pm
- useful mechanical power
Pf
- friction losses
Pre
- rotor electrical power
Prt
Pgap
- rotor total losses
Ps
Pst
- stator power
- power delivered through air gap
- stator total losses
8
2.3 Induction Machine Model
2.3.1 General equations in ABC/abc Reference Frame [32]
For the mathematical description of the double fed induction machine it will be
assumed that a uniform air gap machine can be modelled as two concentric cylinders with an
air gap of constant radial length. The iron losses and the parameters that change with the
temperature are not considered.
A balanced three phase machine is expressed in Fig.2.5.The subscript‘s’ indicates the
stator windings and ‘r’ the rotor windings with effective number of turns N s ξ s
respectively N r ξ r .
Fig. 2.5 Concentric stator and rotor windings, currents, voltages and angle dependencies of a
three phase induction machine [32]
The coupling between phases is dependent of the electrical angle between the phases
symbolised θ .
The three windings subscripted with ‘a’ ‘b’ and ‘c’ are displaced by ±120°, so the
angle θ is only dependent on the rotor displacement angle symbolised ρ .
9
The equation for stator and rotor voltages can be written as:
s
dΨs
u = Rs ⋅ i +
dt
s
s
s
s
(2.1)
r
d Ψr
u = Rr ⋅ i +
dt
r
r
r
r
(2.2)
Where the voltages u , the currents i and the flux Ψ are vectors exemplified for stator
and rotor values.
 usa 
 
us =  usb 
 u  (2.3)
 sc 
 isa 
 
is =  isb 
 i  (2.4)
 sc 
 Ψsa 


Ψs =  Ψsb 
 Ψ  (2.5)
 sc 
 ura 
 
ur =  urb 
(2.6)
u 
 rc 
 ira 
 
ir =  irb 
(2.7)
i 
 rc 
 Ψra 


Ψr =  Ψrb 
(2.8)
Ψ 
 rc 
The flux in stator of the machine can be defined by the flux created by the stator
phases itself and the flux part that influence the stator originated from the rotor phases. The
flux in the rotor can be expressed the same. The expressions are:
Ψ s = Ψ s(s) + Ψ s(r )
(2.9)
Ψ r = Ψ r (r ) + Ψ r (s)
(2.10)
The flux expressed as a product of an inductance matrix and the current vector
i created from the stator and rotor windings is expressed in the following equations:
Ψ s(s)

 Lσs + Lms

L
=  − ms

2

Lms
 −
2

−
Lms
2
Lσs + Lms
−
Lms
2



⋅is


Lσs + Lms 

Lms
2
Lms
−
2
−
10
(2.11)
Ψ r (r )
2

 L +  N r ξ r  ⋅ L
ms
 σr  N s ξ s 

2
Lms  N r ξ r 


= −
⋅
2  N s ξ s 

2

Lms  N r ξ r 

⋅
 −

2  N s ξ s 

2
N ξ 
⋅  r r 
 N sξ s 
2
 N rξ r 
 ⋅ Lms
Lσs + 
 N sξ s 
L
− ms
2
L
− ms
2
N ξ
⋅  r r
 N sξ s



2





 ⋅is

2

 N rξ r 
 ⋅ Lms 
Lσs + 

 N sξ s 

N ξ
⋅  r r
 N sξ s
L N ξ
− ms ⋅  r r
2  N sξ s
L
− ms
2
2



2



(2.12)
The coupling between the rotor and the stator is dependent on the rotor displacement
angle. The flux initiated in the rotor and penetrating the stator and the stator flux penetrating
the rotor are shown below:
Ψ s(r )
N ξ
=  r r
 N sξ s
cos ρ
cos( ρ + 2π / 3) cos( ρ − 2π / 3) 




 ⋅ Lms ⋅  cos( ρ − 2π / 3)
cos ρ
cos( ρ + 2π / 3)  ⋅ i r

 cos( ρ + 2π / 3) cos( ρ − 2π / 3)

cos ρ


(2.13)
Ψ r (s)
N ξ
=  r r
 N sξ s

 ⋅ Lms

cos ρ
cos( ρ − 2π / 3) cos( ρ + 2π / 3) 



⋅  cos( ρ + 2π / 3)
cos ρ
cos( ρ − 2π / 3)  ⋅ i s
 cos( ρ − 2π / 3) cos( ρ + 2π / 3)

cos ρ


(2.14)
For expression of the stator and rotor system in an equivalent coupled system the
stator-rotor ratio n is introduced.
N ξ
n =  s s
 N rξ r



(2.15)
'
n ⋅Ψr = Ψr
n ⋅ ur = ur
(2.16)
'
(2.17)
n 2 ⋅ Lmr = Lms = n ⋅ Lmsr
(2.18)
With,
Lmsr = Lms ⋅ Lmr
(2.19)
n 2 ⋅ Lσr = L'σr
(2.20)
ir
= i 'r
n
(2.21)
Using the ratio ‘ n ’ the flux equations simplifies to
(2.22) and
(2.23):
11

 Lσs + Lms

L
Ψ s =  − ms

2

Lms
 −
2

−
Lms
2
Lσs + Lms
−
Lms
2



⋅i + L
msr
 s

Lσs + Lms 

Lms
2
Lms
−
2
−
cos ρ
cos( ρ + 2π / 3) cos( ρ − 2π / 3) 



⋅  cos( ρ − 2π / 3)
cos ρ
cos( ρ + 2π / 3)  ⋅ i r
 cos( ρ + 2π / 3) cos( ρ − 2π / 3)

cos ρ


(2.22)
 '
 Lσr + Lmr

L
Ψ r =  − mr

2

Lmr
 −
2

−



⋅i + L
msr
 r

L'σr + Lmr 

Lmr
2
Lmr
2
Lmr
−
2
−
'
Lσr + Lmr
−
Lmr
2
cos ρ
cos( ρ − 2π / 3) cos( ρ + 2π / 3) 



⋅  cos( ρ + 2π / 3)
cos ρ
cos( ρ − 2π / 3)  ⋅ i s
 cos( ρ − 2π / 3) cos( ρ + 2π / 3)

cos ρ


(2.23)
2.3.2 Complex space Vector representation [32]
The Complex space Vector representation is used in machine modelling and machine
control. The phase currents of the machine windings displaced by ± 120 o can be described as
complex vectors.
With the help of the complex vector a
(2.24), the complex vectors can be expressed. The real part of the complex space
vector is aligned to phase ‘a’ of the 3 phase stator system or 3 phase rotor system.
2
j ⋅ ⋅π
1
3
a = 1∠120 o = − +
⋅ j=e 3
2 2
(2.24)
i c = a 2 ic
(2.25)
i a = ia ,
i b = a ⋅ ib ,
Where i a , ib , ic are the absolute values of the current time vector.
By adding the phase current vector defined by equations (2.25), a resulting current
vector is achieved
(2.26).
2
i = i a + i b + i c = i a + a ⋅ ib + a ⋅ ic
(2.26)
A more common definition is achieved multiplying the previous equation by a factor
of 2/3.
is =
2
2
⋅ i as + a ⋅ ibs + a ⋅ ics
3
(
)
(2.27)
12
j⋅β
1
3
a = 1∠120 o = − +
⋅j
2 2
j = 1∠90 o
I b = a ⋅ Ib
120o
−
1
2
−
2
2
I = (I a + a ⋅ I b + a ⋅ I c )
3
Iα = Re{I a } = I a
1
4
2
I c = a ⋅ Ic
−
Ib ⋅ a
Ic ⋅ a
2
α
3
⋅j
2
Fig. 2.6 Space vector constructed from a three phase system [32]
2.3.3 General machine equations using space vector [32]
The voltage equations using the complex space vector for the stator is
(2.28) and for the rotor (2.29)
s
s
u s = Rs ⋅ i s +
r
r
u r = Rr ⋅ i r +
d Ψss
(2.28)
dt
d Ψrr
(2.29)
dt
The flux equations can be written depending on the stator (2.30), (2.32) and rotor
(2.31), (2.33):
3


Ψ s ( s ) =  Lσs + ⋅ Lms  ⋅ i s
2


(2.30)
13
3


Ψ r ( r ) =  Lσr + ⋅ Lmr  ⋅ i r
2


(2.31)
Ψ r (s) =
3
⋅ Lmsr ⋅ i s ⋅ e − jρ
2
(2.32)
Ψ s(r) =
3
⋅ Lmsr ⋅ i r ⋅ e jρ
2
(2.33)
If the mutual inductances and couple inductances are equal, the magnetizing
inductance can be written as in
(2.34):
Lm =
3
3
3
'
⋅ Lms = ⋅ Lmr = ⋅ Lmsr
2
2
2
(2.34)
The equations of the flux become
(2.35)
'
Ψ s = ( Lσs + Lm ) ⋅ i s + Lm ⋅ i r ⋅ e jρ
'
(2.35)
'
Ψ r = ( L'σr + Lm ) ⋅ i r + Lm ⋅ i s ⋅ e − jρ
The equation of the rotor voltage related to the stator become (2.36)
r'
r
'
r
r'
r
u = R ⋅i +
d Ψrr '
(2.36)
dt
The vector representing the rotor current, voltage and flux are related to their own
reference frame and are marked with the upper index ‘r’. The stator vectors that are related to
the stator reference frame are marked with the upper index ‘s’
(2.37). The difference of the two
coordinate systems is expressed with the rotor angle ρ .
s'
i rr ' ⋅ e jρ = i r
(2.37)
s'
− jρ
d ( Ψr ⋅ e j (ϕs − ρ ) ) jp d (Ψr ⋅ e j (ϕs − ρ ) ) jp d (Ψr ⋅ e ) jp dΨrs ' − jp jp
⋅e =
⋅e =
⋅e =
⋅e =
⋅e ⋅e −
dt
dt
dt
dt
dt
s'
dΨr
s'
s'
− jp
jp
− j ⋅ ωr ⋅ Ψ r ⋅ e ⋅ e =
− j ⋅ ωr ⋅ Ψ r
(2.38)
dt
d Ψrr '
jρ
As known
ϕs = ϕr + ρ
ϕr = ϕ s − ρ
(2.39)
, and
s'
s'
s'
(u r ) ⋅ e − jρ = Rr' ⋅ i r ⋅ e − jρ + (
dΨr
s'
− j ⋅ ω r ⋅ Ψ r ) ⋅ e − jρ
dt
14
(2.40)
If we divide the equation
we obtain the rotor voltage equation related to the stator
(2.41)
(2.40) by the factor e − jρ ,
s'
s'
s'
u r = Rr' ⋅ i r +
dΨr
s'
− jω r ⋅ Ψ r
dt
(2.41)
All the equations for modelling an induction machine using space vector representation are:
s
s
s
s'
s'
u s = Rr ⋅ i r +
dΨs
dt
(2.42)
s'
u r = Rr' ⋅ i r +
dΨr
s'
− jω r ⋅ Ψ r
dt
(2.43)
'
Ψ s = ( Lσs + Lm ) ⋅ i s + Lm ⋅ i r ⋅ e jρ
'
(2.44)
'
Ψ r = ( Lσ' r + Lm ) ⋅ i r + Lm ⋅ i s ⋅ e − jρ
Te =
{
ρ&& =
}
(2.46)
dω r
+ Dω r
dt
(2.47)
3
s*
p p ⋅ Im Ψ s ⋅ iss
2
Te − Tm = J
(2.45)
dω e dω r ⋅ p p p p
=
=
⋅ (Te − Tm − Dω r )
dt
dt
J
(2.48)
In the modelling equations the following notations have been used:
Lσ - leakage flux inductance,
Lm - main flux inductance
Te - electromagnetic torque
Tm - mechanical load torque
ωr - angular rotor speed
ω e - electrical angular rotor speed
J - inertia
D - damping factor
ρ - rotor angle
ρ&& - rotor angle acceleration
The dynamical one phase equivalent diagram where the achieved equations and parameters
can be visualised is presented in Fig. 2.7
15
j ⋅ ωs ⋅ Ψ s
Is
L'σr
Lσs
Rs
j ⋅ (ωs − ωr ) ⋅ Ψr
Rr'
'
Ir
'
Is + Ir
Us
d Ψs
dt
Lm
dΨr
dt
'
Ur
Rm
Fig. 2.7 Dynamical per phase equivalent diagram for induction machine.
2.3.4 The Clark Transformation ( α , β equivalent frame) [32]
The α , β components known as Clark Transformation are deduced by separating the
machine complex space vectors into real and imaginary part, and referring them to a
stationary reference system.
With this transformation the three-phase machine is deduced to an equivalent twophase machine (Fig. 2.8).
j⋅β
iβ
i
iα
α
Fig. 2.8 Equivalent two-phase machine
The real and imaginary components are shown in
2

2
iα = Re{i} = Re (ia + a ⋅ ib + a ⋅ ic ) =
3

2

2
i β = Im{i} = Im (i a + a ⋅ ib + a ⋅ ic ) =
3

i +i
2
(ia − b c )
3
2
1
3
(ib − ic )
16
(2.49)
(2.49)
The complex space vector can be written as in
(2.50)
i = iα + j ⋅ i β
(2.50)
The complete transformations, in matrix form, from α , β to a,b,c and from a,b,c to
α , β are presented in
(2.51) and respectively
(2.52).
 iα

i
 β
 ia 
 2  cos(0 o ) cos(120 o ) cos( −120 o )  
= 

 3  sin( 0 o ) sin(120 o ) sin( −120 o )  ib 


 i 
 c


cos(0 o ) sin(0 o )
 ia 
 iα 
i  2 
o
o
 b  = 3  cos(120 ) sin(120 )  i 
i 
 cos(−120 o ) sin(−120 o )  β 
 c


(2.51)
(2.52)
2.3.5 The Park Transformation (d,q equivalent frame) [32]
Similar to the α , β components the d,q components are a separation of the complex
space vector in real and imaginary part
(2.53).
i = id + j ⋅ iq =
2
2
(i a + aib + a ic ) ⋅ e − jγ 2
3
(2.53)
The Clark’s components were referring the space vector to a stationary reference
frame. In the Park Transformation the complex space vector is expressed in the rotating
orthogonal system linked with the rotor of the machine. This method is used to express the
complex space vector in any rotating reference frame and is used for a fast control of
electrical machines.
17
jq
iβs
i
i qr
ωr
ϕS
ϕR
i
d
r
d
γ
iαs
Fig. 2.9 Park Transformation [32]
Fig. 2.9 the Park Transformation in relation to the α , β components are shown. The
transformation between these components and an arbitrary rotating frame is (2.54)
id + j ⋅ iq = (iα + j ⋅ i β ) ⋅ e − j⋅ϕ
(2.54)
For return to the α , β components, expression (2.55) is used.
iα + j ⋅ i β = (id + j ⋅ iq ) ⋅ e j⋅ϕ
(2.55)
If the transformation is expressed in matrices, the matrix
(2.56) is used for forward transformation, and matrix
(2.57) for backward transformation.
 iα   cos(ϕ ) − sin(ϕ )  id 
  = 
 
i 
sin(
ϕ
)
cos(
ϕ
)
β

 iq 
 
(2.56)
 id   cos(ϕ ) sin(ϕ )  iα 
  = 
 
 i  − sin(ϕ ) cos(ϕ )  iβ 
q
 
  
(2.57)
18
2.4 Aerodynamic conversion
Wind blowing on blades cause movement of wind turbine but not all the wind energy
it is transformed into mechanical power by the turbine. Power provided to the shaft of wind
turbine generator depends on wind parameters such as speed and density and wind turbine
model such as blade radius. Total mechanical power extracted from the wind (Fig. 2.10) is
given by equation
(2.58):
[33][34]
1
Pwt = ⋅ ρRV 3Cp(λ ,θ )
2
(2.58)
Pwt - mechanical power
ρ - air density
R - blade radius
V - wind speed
Cp - power coefficient
λ - tip speed ratio
θ - pitch angle
Fig. 2.10 Cp curve, presented as a relation between rotational speed and wind speed.
As it can be seen the mechanical Power is depend in a factor called power coefficient
(Cp). This coefficient is dependent on the tip speed ratio λ and pitch angle of the rotor blades
θ.
First parameter can be developed as a relation between tip of the blade speed and the
wind speed
(2.59)
19
λ=
Ω⋅R
V
(2.59)
In order to calculate the Cp curve, equation
(2.60) is used [34]
c7
 c2
 −
Cp = c1 − c3 ⋅ θ − c 4 ⋅ θ c 5 − c6 e λi
 λi

(2.60)
Where
1
1
c9
=
− 3
λi λ + c8 ⋅ θ θ + 1
(2.61)
For this project values of c1 to c9 have been taken from [34]; c1=0.73, c2=151,
c3=0.58, c4=0.002, c5=2.14, c6=13.2, c7=18.4, c8=-0.02, c9=-0.03
For a certain wind speed, Cp curve can be shown as a function of rotational speed
which is assigned to power efficiency value. The Cp function is limited by maximum value of
59%. The Cp curve is represented in the figure Fig. 2.11 [33]
Fig. 2.11 Cp-Lambda curve for θ=0
The highest effectiveness of the power generation can be obtained by a following
maximum value of Cp curve. It is often an issue to operate with maximum output power and
this can be done by adjusting rotor speed to wind speed (Fig. 2.12), using variable speed
generators, and by pitching the blades (pitch control).[33][34]
20
Fig. 2.12 Maximum Power Point Tracking for Cpmax
It is concerned that output of electrical power given as a product of torque (T) and
rotational speed (ω) is converted from mechanical power on the shaft. The relation between
torque and rotational speed is represented in Fig. 2.13
Fig. 2.13 Wind turbine torque vs. rotor speed characteristic
The torque has small value at the initial speed w=0, it reaches maximum and slightly
falls close to zero line for a high rotational speeds. At that point wind turbine blades turns
almost exactly with the same speed as the wind.
In order to reach maximum wind turbine efficiency tracking of the maximum power
output point is an issue. Maximum power point floats with the wind speed change that is why
rotor speed has to be continuously adjusted [35].
The electrical power generation is given by the equation
(2.62).
21
Pe = T ⋅ w
(2.62)
Fig. 2.14 Wind turbine power vs. rotor speed
2.5 Control
The DFIG combines the advantages of pitch control with efficient power transmission
to the grid and the possibility of dynamic control of active and reactive power. [32]
2.5.1 Pitch Control [32]
Almost all variable wind speed turbines use a pitch control. This is the most used
method in order to control the aerodynamic power generated by a turbine rotor and it is
applied on the high power wind turbines.
The pitch angle should be only at its optimum value in order to produce maximum
power and has to keep the aerodynamic power constant at its rated value.
The pitch control can make possible the power limitations about rated wind speed by
rotating a part or all of each blade about its axis in the direction that reduces the attack angle.
In Fig. 2.15 ϑ is the pitch angle, α is the attack angle and r is the length of the blade.
vw is the wind speed and ωrot r is the tip speed, form the relative wind velocity vrel.
22
The L (lift) and D (drag) are the forces caused when the wind passes through the
blades, causing the blades movement. The interrupted line is the tip chord.
The range of the pitch angle is usually between 0o and 35o.In order to obtain an
effective aerodynamic braking, the blades have to be pitched to 90o.
Fig. 2.15 Blade cross section of a WT [32]
The purpose of changing the pitch angle is to produce maximum power. By this
change, a very effective way of regulating the aerodynamic power and loads produced by the
rotor is done. This control allows keeping the rated values below the mechanical limits.
2.5.2 Control of DFIG
The control of the converter to reach the maximum power in each state of the wind
speed is one of the most important issues in variable speed generators. Two of the common
strategies for this control are the following:
•
•
Direct Torque Control
Direct Power Control
23
2.5.2.1
Direct Torque Control [15]
Wind Turbines just can get a lower amount of the energy deliver by the wind, the
energy obtained is related to the energy available by a factor called ,,Power Coefficient’’
which depends on the tip speed ratio. This tip speed ratio is the ratio between the velocity of
the rotor tip and wind speed. In order to reach the maximum power from the wind the rotor
speed should vary with the wind speed, given that the power coefficient is maximum at a
certain tip speed ratio, as it can be seen at Fig. 2.16
Fig. 2.16 Torque-speed characteristic of a 2MW DFIG wind turbine [15]
Tsp
For this kind of control of DFIG, the generator torque is used for controlling the rotor
speed in order to achieve the highest power possible.
The torque control loop (Fig. 2.17) is based on the dq frame reference; the d
component of the rotor current is used for power factor and/or voltage control, while the q
component is used to control the torque in order to get the maximum power. For this
operation only rotor speed is measured and used to lead the generator through the maximum
power curve shown in Fig. 2.16.
Fig. 2.17 Torque control loop of a DFIG
24
2.5.2.2
Direct Power Control
Direct Power control is based on controlling the instantaneous active and reactive
power (P,Q) in a similar way as torque control. [22]
Fig. 2.18 Power-speed Characteristic [23]
P
The d component of the rotor current is used to control the reactive power (Q)
component in order to complain the demands of the grid, while the q component is used to
control the active power (P) (Fig. 2.19). For this, rotor speed is measured in order to get the
reference power, by using the characteristic curve Fig. 2.18
Fig. 2.19 Power control loop of a DFIG
25
2.6 Overview of FRT requirements in Grid Codes
The development of the big wind farms of large capacity brings a big amount of wind
energy penetration in the network. The possibility of producing a large amount of energy is
high but a limit exists. The network operators will have many technical and economical
problems in order to manage the system, so one of their main concerns is the grid integration
[11]. Therefore, some countries have created dedicated grid codes in order to connect the
wind power plants into the electrical network. These grid codes are referring to the
transmission and/or distributed system. In most of the cases the requirements focus on the
power controllability and quality, fault ride-through capability (Denmark, Germany, and
Ireland). Some grid codes require the support of the grid during the occurrence of the
disturbances in the network (Germany and Spain). Denmark has the most demanding
requirements taking into consideration the controllability of the produced power. All the
existing grid codes require fault ride-through capabilities for wind turbines and the
requirements for the power quality are very strict in respect with flicker emission and
harmonic compatibility. The Transmission Network Operators (TSOs) are giving
specifications of the depth of the voltage dip and the clearance time. In some of the grid codes
the voltage calculation on the duration of all types of unsymmetrical faults is very well
defined (Ireland), while in others it is not defined obviously[1] In order to make a good
International Grid Codes Comparison (IGCC) it is necessary to respect the steps and
procedures presented in Fig. 2.20 [12]
X
X
International Grid Codes Comparison
(IGCC)
Target market definition by the
manufacturer
Relevant Grid Codes search
Evaluation of each Grid Code
and extraction of applicable
connection conditions
Arrangement of connection conditions in
one single table (easy to compare)
Basic IGCC without update service
Information about
proposed changes
in requirements
IGCC with individual
monthly update service
due to revisions and
changes in Grid Codes
Information about new
Grid Code releases
and forthcoming drafts
International Grid Code Comparison
Fig. 2.20. International Grid Codes Comparison (IGCC) [12]
26
The focus is on the basic comparison, without the update service, so a table of ridethrough capability for wind turbines/farms in different national grid codes is established in
Table 1, because all the existing grid codes require fault ride-through capabilities. [1]
X
Fault Ride-Through capability
Voltage
Level
Fault
duration
Voltage
drop level
Recovery
time
Voltage
profile
Ireland
DS
TS
DS/TS
100 msec
100 msec
625 msec
25%Ur
25%Ur
15%Ur
1 sec
1 sec
3 sec
Germany
DS/TS
150 msec
0%Ur
1.5 sec
1, 3-ph
1, 3-ph
1, 3-ph
Positivesequence
Country
Denmark
Reactive
current
injection
No
No
No
Up to 100%
Great
Britain
Spain
Italy
USA
Ontario
DS/TS
140 msec
15%Ur
1.2 sec
Generic
No
TS
>35kV
TS
TS
500 msec
500 msec
625 msec
625 msec
20%Ur
20%Ur
15%Ur
15%Ur
1 sec
0.3 sec
2.3 sec
-
Up to 100%
No
No
No
Quebec
TS
150 msec
0%Ur
0.18 sec
Generic
Generic
Generic
Positivesequence
No
Table 1 Summary of ride-through capability for wind turbines/farms in different national grid
codes.
The voltage profile for the ride-through capability can be summarized as shown in the
next figure [1]
Fig. 2.21 Voltage profile regarding fault ride through capability of wind turbines/farms in
National Grid Codes [1]
27
As it can be seen in Fig. 2.21 each country has its own specifications in terms of
voltage dip, time duration and time of full voltage recovery. These specifications can differ
significant from each country, e.g. Italy is the strictest in recovery time, Denmark in fault
duration etc.
2.6.1 Crowbars
Despite of numerous advantages which give structure of DFIG there are some major
problems concerning to its operation during grid faults. The voltage dip in the grid cause
increase of current in the stator windings and because of the magnetic coupling between stator
and rotor, this current affects power electronics converter at rotor side.
For the safe operating of DFIG during fault ride through the converter must be
protected from high currents. In this chapter various solutions of rotor side converter
protection will be shown. There are numerous different solutions which can solve the problem
of over-current, and some of them will be analyzed for this project. Limiting current by
current-control on rotor side leads to another threat, which is the high voltage. This can lead
to serious damage of the converter.
Short-circuiting the rotor circuit is major used solution. There are plenty of different
short-circuiting strategies and almost all of them are based on a variable resistor and thyristor
called passive crowbar.[16]
In this paper solution based on active elements will be concerned. Topology based on
these active elements such as Insulated-Gate Bipolar Transistor (IGBT) or Gate Turn-Off
Thyristor (GTO) is called an active crowbar. These elements can switch on and what is more
important, switch off circuit. That is why using them in crowbar allows to fully control rotor
bypass during fault.
Nowadays in rotor side circuit crowbar protection is designed, combining resistors,
diode bridge and active elements.[19]
As presented in the Fig. 2.22, the crowbar protection is attached to the rotor windings
between the generator and the AC\DC converter. Further on different crowbar topologies will
be presented.
Fig. 2.22 DFIG topology with attached crowbar protection
28
2.6.2 Crowbar topologies
Figures shown in the next subchapters are crowbar topologies. The ‘A’ topology on
the left is presented in the reference paper. The ‘B’ topology on the right is modified for the
purposes of the project. Passive element like thyristor is replaced by GTO which is an active
element. This modification is done in order to change passive crowbars to fully controllable
active crowbars. In the case of the Diode Bridge with GTO thyristor (Crowbar 2) the
modifications are not necessary, because Crowbar 2 is already an active crowbar.
2.6.2.1
Crowbar 1 – Thyristor bridge
Fig. 2.23 DFIG bypass resistors in the rotor circuit with (A) thyristors, (B) GTOs .
In [17] the resistor bridge with antiparallel thyristors is proposed. Reduced model of
converter can be used in the simulations. Converter stays connected to both rotor and grid
during fault. Resistors exact value is not a must, but should be a compromise between
limitation of current and voltage on converter terminals. Too large voltage can damage
converter.
This protection while voltage dip of 85% reduces the rotor current transient value from
5 times nominal current to approximately 1.5. But in that case current flows through
protection instead of converter. In these conditions both rotor circuit and converter are fully
protected. Calculations of transients are made for the worst case.
Important part is recovery to normal operation of the wind turbine. Soft change to
normal reference of rotational speed is provided by control unit. These way serious transients
can be avoided.
29
2.6.2.2
Crowbar 2 – Diode bridge with GTO thyristor
Fig. 2.24 Schematic of Diode Bridge with GTO.
The issue of this strategy given in [18] is to activate crowbar protection only for short
time. Crowbar is controlled by comparing absolute value of rotor current Ir with preset
threshold Ith. Moreover bypass circuit is open just after current reaches steady state value.
When grid voltage recovers, generator is able back to normal operation without crowbar
reactivation.
For successful use of this crowbar demagnetization needs to be applied. That makes its
control scheme more complicated.
2.6.2.3
Crowbar 3 – Antiparallel thyristors between phases
Fig. 2.25 Antiparallel (A) thyristors and (B) GTO between rotor phases.
The following solution shown at Fig.2.25 is proposed in [19]. Crowbar circuit
contains two pairs of antiparallel connected thyristors set between rotor circuit phases. Bypass
in this topology may have problem to turn-off because of used thyristors. When current has
considerable DC component turning off is not be possible in first case (A). Using a GTO
instead of basic thyristor gives possibility to successful control of the protection. This
structure can have problems with suppressing electrical transients.
30
2.6.2.4
Crowbar 4 – Diode bridge with thyristor
Fig. 2.26 Diode bridge with thyristor crowbar (A). Modificated protection (B) for project
purposes.
Proposed in paper crowbar [19] is based on diode bridge and single thyristor. Diode
Bridge rectifies current in all three phases when bypass is activated. Thyristor in this circuit is
used to control the shorting. Thyristor is able to turn on bypass but not able to turn it off. Until
crowbar won’t be deactivated rotor side converter can’t start normal operation. To fully
control crowbar disconnection a GTO thyristor in this case must be used.
Like in previous paper the crowbar circuit in [20] is based on Diode Bridge with
thyristor and resistor. Switching on the thyristor in the crowbar is controlled by DC link
voltage. When it reaches reference value thyristor starts to conduct. At the same time rotor
circuit bypass rotor side converter by crowbar. To disconnect crowbar from rotor windings
stator circuit breaker has to be used. That will disconnect generator from the grid.
31
2.6.2.5
Crowbar 5 - Improved Fault Ride through strategy for DFIG
T, Ω
Wound rotor
induction generator
3 Windings PCC
Transformer
T, Ω
GRID
Gearbox
Filter
b
a
Crowbar
S1
S2
AC/DC
DC/AC
Fig. 2.27 Crowbar topology for improved FRT strategy with static switch S1 and static
transfer switch S2.
In [21] is proposed control strategy given on Fig.2.27. When the fault in grid occurs
the rotor side converter is bypassed by crowbar. But in this particular strategy rotor side
converter is isolated from rotor circuit. This solution protects it from over-voltage which can
be caused by resistors during short-circuiting large currents.
This control strategy may give some new possibilities to face faults in the grid.
Resistance of resistors in crowbar may be higher than in other crowbar strategies. During the
fault recovery transient mode control is applied to converters.
When terminal voltage reaches its normal level the recovery is recognized and
crowbar can be removed. It is possible to set a delay to smooth current and torque spikes.
2.6.3 Crowbar selection
This project focus on fault ride through of the Doubly Fed Induction Generator during
fault in the grid. To remain connected during fault and to protect converter from over-voltage,
model of the DFIG has a crowbar protection. To get best results during tests model with
active crowbar is used.
Previous chapter shows different crowbar topologies used in various papers. Some of
topologies where specially adapted for this project purposes. Passive crowbars were changed
into active crowbars. Not all presented working schemes are appropriate that is why some
criteria of choice need to be specified.
Main aim is to have a fully controllable crowbar, so it can be activated and deactivated
from rotor circuit whenever operator wants it. All crowbars pointed out above are able to do
this. But the model of the crowbar should stay as simple as possible and preferably have just
32
one controllable element. That is why topology presented in crowbar nr.2 is better than
crowbar nr.1 and nr.3. It has less controllable elements and that makes it easier to control.
Crowbars nr. 2, 4 are based on the similar structure. In first case author proposed
Diode Bridge with GTO as active element, but in crowbar nr.4 topology was adjusted to
become active. Previously was presented in paper with thyristor, but after change it become
same structure as nr.2.
The crowbar nr. 5 shows a new strategy how to do with the over-voltage in rotor
circuit. However it was only mentioned to show that other solutions of converter protection
are available. In this project simple crowbar control is tested and this proposition was rejected
because of advanced control during fault.
Considering the criteria shown above, concept of the crowbar topology nr 2 was
chosen to further examinations.
T, Ω
Wound rotor
induction generator
3 Windings
Transformer
T, Ω
GRID
Gearbox
AC/DC
DC/AC
Crowbar
GTO
Rcrow
Fig. 2.28 Model of DFIG with attached crowbar nr.2
33
PCC
Chapter 3 System
Simulations
Design
and
3.1 DFIG simulation Model
For the simulation, simulink tool Plecs is used. Model of a Wound Rotor Induction
Machine (WRIM), grid, converter and crowbar design, are set in Plecs. Same simplifications
have been considered in this project; The Back to Back converter is represented as the rotor
side converter with a DC voltage source, due to grid side is not necessary to implement for the
purpose of this project, also the transformers are missed in order to simplify the simulation
even though in the implementation have to be taken into consideration. To simulate a three
phase fault in order to study the FRT voltage deep of the grid is simulated by introducing
another three-phase voltage source.
Parameters of the WRIM are taken from the reference [36]; parameters can be seen in
APPENDIX A.
In the next figure (Fig. 3.1) the implemented model of the DFIG generator is shown.
Fig. 3.1 Plecs model of the DFIG wind turbine
The input of the generator is the mechanical Torque (Tm [Nm]) and as outputs are
electrical Torque (Te [Nm]), rotor speed (w [rad/s]) and rotor angle (ρ).
In order to get the Mechanical torque in the rotor of the generator, the equations(2.58),
(2.59), (2.60) and (2.61) are implemented in an m-function (APPENDIX B) and parameters
for the wind speed, pitch angle, blade radius (R), Gear-box ratio, air density (rho), maximum
Power(Pmax), minimum and maximum wind speed are set, and rotor speed from the
generator is measured. In the below figure the simulink blocks are shown.
34
Fig. 3.2 Simulink blocks for the calculation of the Mechanical Torque
3.1.1 Principle of control
A usual WRIG with short-circuit rotor terminals just has a small rotor speed variation,
around 1%, that it is dependent of the frequency at the stator of the generator. Though, DFIG
generators system lets a variation of the rotor speed from -40% to +30% of the synchronous
speed.[28]
The converter attached to the rotor terminals of the DFIG generator makes possible to
provide or get power from the grid through the rotor terminals, obtaining a permanent
injection of power through the stator to the grid. The operation at sub synchronous, as it was
explained before, inject power to the grid from the stator, and some of that power is
consuming in the rotor, and for over synchronous the stator injects power as well as the rotor,
in to the grid. Fig. 3.3
PM = ω r ⋅ Te
(3.1)
PM = Ps + Pr
(3.2)
Ps = − s ⋅ Pr
(3.3)
PM
1− s
(3.4)
ω s − ωr
ωr
(3.5)
Ps =
s=
Where:
PM
Ps
Pr
ωr
Mechanical power through the shaft of the generator
Power through the stator
Power through the stator
rotor angular speed [rad/s]
35
ωs
s
synchronous speed [rad/s]
slip (s>0 sub synchronous operation, s<0 over synchronous
operation)
The ideal power distribution in steady state through the rotor and stator windings is
dependent on the slip of the generator.
Fig. 3.3 Power flow of an ideal DFIG at over synchronous speed and sub synchronous speed
[32]
In the figure below (Fig. 3.4) (obtained using the m-file program in APPENDIX D)
the power flow in the Wound Rotor Induction Machine (WRIM) of 7.5kW working as a
DFIG wind turbine generator from [32], can be seen. It can be observe that the stator terminal
reaches its nominal power (Pn) close to the synchronous speed, in under synchronous speed
the stator is providing power (Ps) and the rotor is subtracting (Pr=-s*Ps), and in over
synchronous speed the stator keeps injecting the nominal power and the rotor injects -s*Pn
(For values of the different Powers in a range of slip from 0.6 to -0.3 see APPENDIX E)
Fig. 3.4 Power flow in the WRIM of 7.5kW
36
3.1.2 Rotor Control
3.1.2.1
Implementation
By controlling the current in the rotor side of the DFIG, active and reactive power of
the wind turbine can be control. A vector-control approach is used, orientating the d-axis
along the stator-flux vector position. In this way the current, voltage and flux of the stator and
rotor become DC values that are easily to control, and also a decoupled control of the active
and reactive power is obtained.[32] [36] [37]
Aligning the d-axis of the reference frame through the stator flux space vector, the q
component of the stator flux is zero (Ψs=Ψqs=0). As it can be seen in the Fig. 3.5 the voltage
and the flux are moving in quadrature, so the d axes of the stator voltage us=uqs=0.[42]
β
ωs
Ψs
us
Ψβs
ϕu
ϕs
Ψαs
α
Fig. 3.5 Vector diagram of the d,q reference frame aligned to the stator flux, with stator
voltage in quadrature
Since the influence of the stator resistance is small, the stator flux can be considered
constant, so uqs can be related to ψds as:
u s = u qs = ω s Ψds
(3.6)
ωs = 2 *π * f
(3.7)
By this assumption the stator flux angular position is calculated as:
 u βs
 uαs
ϕ s = tan −1 
 π
 −
 2
(3.8)
This way of calculation of the stator angle is valid for steady state or to simulate the
three phase fault, for other kind of faults, as two phase or single phase faults, a Phase Lock
Loop (PLL) must be used in order to be able to see variations in the stator angle and
37
frequency, PLL topologies are extended used in grid connected system as it can be seen in
[38],[39]also in [40].
For this project the study of the FRT is done for the worst case, three phase fault, so
equation (3.8) is used to calculate the angle.
Using these considerations the DFIG model is written as:
'
u dr
'
di
'
'
= Rr idr + σLr dr − ω slipσLr iqr
dt
'
'
'
'
'
u qr = Rr i qr + σLr
diqr
dt
'
'
'
+ ω slip ( Lm i ms + σLr i dr )
Ψs = Ψds = L0 ims = Ls ids + L0 i qr
0 = Ls i qs + L0 iqr
(3.9)
'
(3.10)
(3.11)
'
(3.12)
2
L0
'
'
i ms + σLr idr
Ls
Ψdr =
'
Ψqr = σLr i qr
(3.13)
'
(3.14)
ω slip = ω s − ω r
σ =1−
Lm =
(3.15)
L20
Ls Lr
(3.16)
'
L20
Ls
(3.17)
The stator-side active (Ps) and reactive (Qs) power in d,q components are written as
(3.18) and
(3.19).
3
(uds ids + u qsiqs )
2
3
Qs = (u qs ids − u ds iqs )
2
From
Ps =
i qs = −
(3.18)
(3.19)
(3.12) it is obtained:
L0 '
iqr
Ls
(3.20)
Introducing iqs in Ps and knowing that u ds ids = 0 , it results:
38
Ps = −
3 L0
'
u sq iqr
2 Ls
(3.21)
From (3.6) and (3.11) it results:
'
L0 ims − L0 idr L0 u qs
L0 idr
ids =
=
−
Ls
Ls ω s L0
Ls
(3.22)
Introducing ids in Qs and knowing that u ds i qs = 0 , it results:
Qs =
L
3  L0 u qs
3 u qs  u qs
'
'

u qs  ⋅
− 0 idr  =
− L0 i dr 
2  Ls ω s L0 Ls
 2 Ls  ω s

(3.23)
With these equations and due to the constant ‘uqs’ voltage the stator-side active power
is controlled by ‘iqr’ and reactive power by ‘idr’, that the can be controlled using ‘uqr’ and ‘udr’
respectively.
In Fig. 3.6 a schematic block diagram for the rotor side vector control can be seen.
ωr
uqs
d
decoupling
iqr
Qref
d - current idr_ref
calculation
PI
DC-link
udr’
udr_ref
idr
Pref
q - current iqr_ref
calculation
PI
iqr
uqs
uqs
idr
ωr
u(a,b,c)r _ref
DC
PWM
2/3
uqr_ref
ωr
uαr_ref
dq
αβ
uqr’
AC
uβr_ref
q
decoupling
iαr
dq
i(a,b,c)r
2/3
αβ
iβr
ωr
φr
DFIG
uαs
φs
uqs
encoder
rotor angle
calculation
Flux angle
calculation
dq/αβ
2/3
u(a,b,c)s
uβs
Fig. 3.6 Block diagram for the rotor side control
For this system a power-control is implemented. The control is made by a current
control (PI) that provides the rotor voltages to the Pulse-Width Modulator (PWM) that will
provide the input signal for the switches in the converter. By using the decoupling in
equations
(3.9) and
(3.10) the plant for the current control loops is given by
(3.24)
39
'
'
i (s)
idr ( s )
1
= qr *
= '
*
'
u dr ( s ) u qr ( s ) Rr + σLr s
(3.24)
Where
*
'
'
*
'
'
u dr = Rr idr + σLr
u qr = Rr iqr + σLr
didr
dt
'
diqr
'
(3.25)
(3.26)
dt
The idr and iqr currents errors processed by the PI provide the udr’ and uqr’ voltages. In
order to ensure a good tracking of the currents, the decoupling terms are added to these
voltages to obtain the reference voltages udr_ref’ and uqr_ref’. [36]
'
*
'
*
'
u dr _ ref = u dr − ω slipσLr iqr
'
(3.27)
'
'
u qr _ ref = u qr + ω slip ( Lmims + σLr idr )
(3.28)
Introducing in the control the power references (Pref and Qref), the reference currents
introduced in the current control (PI) can be right as in
(3.29) and
(3.30).
'
iqr _ ref = −
'
idr _ ref =
2 Ls Ps _ ref
3 L0 u qs
u qs
ω s L0
−
(3.29)
2 Ls Qs _ ref
3 L0 u qs
(3.30)
For the Pref a look-up table of the Maximum Point of Power for different rotor speeds
is implemented in order to get its instantaneous value. The value of Qref is set to zero.
Fig. 3.7 Look-up Table for reference Active Power
All the equations are referred to the stator side. In the attached CD the control of the
rotor side in simulink is included.
40
3.1.2.2
PI-controller design
The current control show used on the rotor control is based on a PI controller; this
control operates in the rotating d,q reference frame which lets work with DC currents in the
PI. The references currents are getting from equations
(3.29),
(3.30) and compare with the measure rotor current in d,q. The output of the
controller provides the reference voltages for the PWM. The general equation for the PI
control in time domain is [41]:
t
u (t ) ' = k q ⋅ e(t ) + ki ∫ e(t )d (t )
(3.31)
t0
Where u(t) is the output signal, e(t) is the error signal, ‘kp’ the proportionality
constant and ‘ki’ is the integration constant. The PI control in z-domain for a backward
transform previous equation is expressed as:
'
(k p + k i ⋅ Ts ) − k p ⋅ z −1
U ( z)
Ts
= k p + ki
=
E ( z)
1 − z −1
(1 − z −1 )
In
(3.32)
(3.32) Ts is the sampling time.
In Fig. 3.8 is presented the design of the PI in Simulink.
Fig. 3.8 PI control in z-domain using backward transform
For the design of the parameters of the PI the tool from Matlab SISO Design
(command sisotool) is used. The plant use in the design is the one from equation
(3.24).
In order to get a simple control, it has been design to make the system behave as a 1st
order system.
Values for the parameters kp and ki are kp=0.024*ki and ki=2279. By using these
parameters a rising time of 0.00223s is get. In Fig. 3.9, the behaviour of the system for a step
response is shown.
41
Fig. 3.9 Step response of the system
3.1.2.3
Simulation results
The simulation scheme is shown in Fig. 3.10
Fig. 3.10 Simulink model of the entire system
42
It is composed by the following subsystems:
•
Parameters: where the parameter of wind speed, pitch angle, blade radius (R), Gearbox ratio, air density (rho), maximum Power (Pmax), minimum and maximum wind
speed is set.
•
Mechanical Torque calculation: The mechanical Torque for the Generator is calculate
•
Rotor side converter: In this block the rotor-side control is implemented and u_ref
PWM signals are obtained.
•
DFIG model: The entire model of the DFIG and grid is implemented.
•
Measurements: where scopes are placed.
For the simulation of the rotor control parameters for the WRIM and WT are taken
from [36]. Also for the evaluation of the control a change in the wind speed is produced, from
5m/s to 11m/s, this change is produce by a ramp with a slope of 1, and sampling time (Ts) of
0.00001 is used.
In following figures the results compare with the references are presented.
In Fig. 3.11, the change on the wind speed can be seen. This change is introduced in
order to be able to check how the control is working and see how the measure signals follow
the reference ones.
Fig. 3.11 Variation of the wind speed
Fig. 3.12 shows the change in the electrical Torque and mechanical torque, it can be
seen how, when the speed increase, the Mechanical Torque and the Electrical Torque
increase. In this figure, the Torque is shown in per unit.
43
Fig. 3.12 Mechanical and Electrical Torque
In Fig. 3.13, the change of the rotor speed is presented.
Fig. 3.13 Rotor speed
For the active and reactive power the next two figures shown their responses when
the wind speed change. The active power (Fig. 3.14) increases when the wind increases, for
the reactive power (Fig. 3.15) this change does not affect. In the graphic, a change on the
production in the reactive power reference is introduce from 0.1*Nominal Power (7500) to 0.1*Nominal Power (7500). It can be observed how the measured power follows these
changes.
44
Fig. 3.14 Active Power reference and Active Power measure
Fig. 3.15 Reactive Power reference and Reactive Power measure
The following figures (Fig. 3.16) and (Fig. 3.17) show how the reference currents
‘ird’ and ‘irq’ change and how the measure currents follow these changes, proving that the
control is working well.
‘ird’ is changing with the reactive power reference and ‘irq’ changes with the active
power reference, as it was shown in subchapter 3.1.2.1.
45
Fig. 3.16 D-Rotor current reference and D-rotor current measure
Fig. 3.17 Q-Rotor current reference and Q-rotor current measure
In the shown figures it can be seen that the control is working well in the changes of
the wind speed and in the production of reactive power. An error in the measured signals is
caused due to the switching error in the converter.
46
3.1.3 Control of the Crowbar
In the next figure it can be seen the general picture of the DFIG model with fault and
the crowbar attached, . The crowbar used has been explain in subchapter 2.6.3, but instead of
using a GTO an IGBT is used.
Fig. 3.18 Entire model of DFIG for Fault Ride Trough analysis with crowbar attached
Control of the crowbar is simply triggering bypass in rotor circuit. It has to be done
at the time when fault in the grid occurs. After short circuiting rotor DFIG starts to operate
like Squirrel Cage Induction Generator with additional resistance from crowbar circuit. This
will cause over speeding of the rotor during recovery. Moreover this may cause problems with
reactive power control.
There are two ways of triggering the crowbar. First case is based on detecting overcurrent in rotor circuit and the second case is based on detecting over-voltage in DC link
inside back-to-back converter. [18]
Presented control is based on comparison of measured rotor current Ir with rated
rotor current Ir_ref. When fault occur measured rotor current rises over rated value and gives
binary signal 1 on IGBT’s gate. This closes IGBT’s circuit and allows rotor currents to flow
through crowbar. When Ir falls below Ir_ref output from crowbar control is binary 0 at the
IGBT’s gate, IGBT stops conducting and crowbar is disconnected from rotor circuit.
Control scheme of the DFIG protection is divided into two functional main
schematics. In order to get binary signal at IGBT’s gate, duty cycle has to be obtained. First
schematic gives reference signal which is proportional to ton.
Second structure block generates a ramp shape carrier of frequency f=1/Tsw.
Duty cycles are generated by comparing reference signal which corresponds to rotor
overcurrent ton with carrier.
47
Fig. 3.19 Generation of duty cycles (∆ - duty cycle, Tsw - switching period, ton – duty cycle
reference signal)
Input of the first scheme is measured rotor current Ir which is subtracted from
referenced rotor current Ir_ref. To Ir_ref the constant E is added. This value should be big
enough to prevent activation of the IGBT caused by noise or light disturbances in rotor
current, but too big value can deteriorate accuracy. It is assumed that E can vary between 5
and 10% of Ir_ref.
For optimal control ton is calculated from linear function where maximum point is
proportional to 9*Ir_ref which is 90A considered as 0.95 Tsw. This is the highest expected
current which can occur during heavy voltage drop. To prevent conducting of IGBT through
whole cycle period minimal value of duty cycle is set on 0.01 Tsw.
For this assumption, gain kp is calculated from linear function:
y = ax + b
(3.33)
and
(3.34)
kp=1/a
48
Fig. 3.20 Tuning P controller
From previous figure next data is obtained:
x = ∆ (duty cycle) p.u.
x1 = 0.01
x 2 = 0.95
I r _ ref = 11 (A)
E = 1 (A)
I r max = I r _ ref ⋅ 9 = 99 (A)
From basic equation (3.33) and two points, coefficient a of the line is calculated
y1 = ax1 + b
y 2 = ax 2 + b
(3.35)
P1 ( x1 , y1 ) = (0.01, I r _ ref + E )
P2 ( x 2 , y 2 ) = (0.95, I r max − I r _ ref − E )
Using data from Fig. 3.19 equations become (3.36)
I r _ ref + E = a ⋅ 0.01 + b
(3.36)
I r − I r _ ref − E = a ⋅ 0.95 + b
Giving as result,
a=
I r − 2 ⋅ ( I r _ ref + E )
0.94
=
99 − 2 ⋅ (11 + 1)
= 79.787
0.94
(3.37)
And the gain kp: as shown in (3.34) is
kp =
1
1
=
= 0.012533
a 79.787
(3.38)
When measured rotor current is outside linear relationship x value is constant
I r ≤ I r _ ref + E x=0.01
(3.39)
I r ≥ I max
(3.40)
x=0.95
In Fig. 3.21 the first part of the crowbar control scheme is presented.
Fig. 3.21 First part of crowbar control scheme
49
Fig. 3.22 shows how ramp carrier is generated and further compared with obtained
before ton.
Fig. 3.22 Second part of crowbar control scheme
Sampling time T_sampling has significant influence on simulation and setting very
small value can prolong calculation time to several minutes. In this project sampling time of
1e-3/500 to keep high accuracy is proposed. That means every carrier’s ramp step contains
500 sample steps.
Ramp carrier is created by modulus after division (mod) block. Frequency of the
ramp is:
f ramp =
1
1
=
= 1kHz
Tsw 1 × 10 − 3
(3.41)
In last block of the crowbar control carrier is compared with output from previous
control block ton like it was described before in this chapter and is shown on Fig. 3.19
3.1.3.1
Parameters adjustment
In this control strategy some parameters can be modified in case of investigating
different cases.
Calculations and results shown in this chapter and configurations of parameters
assume highest demands of Grid Codes. In many cases fault in the grid can cause voltage dip
to 0V causing rotor current maximum transient value around 100A.
Investigating Grid Codes in other countries voltage drop can be less significant and cause
lower maximum transient value. In this case from equation (3.37) another gain in control
scheme may be calculated. Adjusting gain to certain conditions increases crowbar operation
efficiency. In this project voltage dip down to 15% is simulated that is why gain in the
crowbar control can be modified to different value.
To decrease the time of fault detection constant E can be set to lower value but it is
necessary to follow statements given previously in this chapter.
50
3.1.3.2
Simulation results
The simulation scheme is extended scheme shown in Fig. 3.10. Two new subsystems
were added:
• Fault: The time of fault occurrence and removal is set.
• Crowbar Control: In this block duty cycle of crowbar’s active element is
calculated by comparing measured RMS rotor current with RMS rotor
current rated value.
The complete simulation scheme is shown in Fig. 3.23
Fig. 3.23 Simulink model of complete system
This simulation uses parameters stated in subchapter 3.1.2.3 but used wind speed is
constant and equal nominal value of 10 m/s. Moreover in the Crowbar Control subsystem
gain Kp is set to 0.1, crowbar is activated when measured value of rotor current exceeds 1.05
rated rotor current. Crowbar resistance is Rcb=150Ω.
The fault occurs at the time 0 sec and it’s removed after 100ms. The results are
given in the figures shown below.
51
Fig. 3.24Rotor current d-component reference and measured value
Fig. 3.25Rotor current q-component reference and measured value
Fig. 3.26 Active Power reference and measured value
52
Fig. 3.27 Reactive Power reference and measured value
At the Fig. 3.26 it can be seen that at the time of the fault occurrence Active Power
drops down to 0.4 referenced value. Simultaneously Reactive Power rises to 0.9 p.u. with
negative sign. At the time of fault removal light transients of Active Power 1.2. p.u. are
observed.
Fig. 3.28 Mechanical and Electrical Torque
Fig. 3.29Rotor speed
53
During fault rotor speeds rapidly (Fig. 3.29) to 1.2 p.u. rated speed forced by
oscillating Electrical Torque (Error! Reference source not found.). In steady state rotor
speed sets on 1.22 p.u. that means DFIG works as a generator.
Stator parameters are presented below.
Fig. 3.30 Stator voltage
Fig. 3.31 Stator current
At the figures shown below rotor current and its components are presented. Rotor
current has been measured on rotor’s windings Fig. 3.32 and on converter terminals Fig. 3.33.
Moreover current in the crowbar’s circuit was measured and it is shown at Fig. 3.34.
54
Fig. 3.32 Rotor current measured on rotor’s terminals
Fig. 3.33 Rotor current measured on converter’s terminals
It is crucial to measure currents in proper place in order to get expected results.
Currents in rotor can be measured before crowbar bypass that mean on rotor windings or after
bypass that mean on rotor side converter terminals. For model of DFIG presented in this
project, reference of rotor current used in generator control scheme is measured on converter
terminals. Crowbars control as a reference uses rotor current on rotor windings.
Fig. 3.34 Current in the crowbar’s circuit
55
The Fig. 3.34 shows that crowbar starts operation at the time when the fault occurs.
To see crowbar influence on rotor current two signals needs to be compared:
• rotor current on rotor windings
• rotor current on converter terminals
Rotor current measured on rotor windings does not depend on crowbar operation and can
represent current in rotor without crowbar. It can be seen on Fig. 3.35 and blue colour on Fig.
3.37. Rotor current on converter terminals is given on Fig. 3.36 and in green on Fig. 3.37.
Three phase graphics of rotor currents might be not clear enough. The graphics
of RMS currents might be clearer and give more details.
Fig. 3.35 Rotor current measured on rotor windings
Fig. 3.36Rotor current on converter terminals
56
Fig. 3.37Compared RMS values of rotor current at the rotor’s terminals and converter’s
terminals
Fig. 3.38 Energy absorbed by crowbar during fault in the grid
The figure Fig. 3.37 shows that rotor current measured on inverter terminals is smaller than
current on the rotor windings. It can be seen that crowbar circuit takes part of rotor current. At
the time when fault occurs the first peak is reduced significantly. The same can be said about
transients when the fault is removed. In the state between these transients spikes in rotor
current can be observed. The size of these spikes can be dumped by increasing crowbar’s
resistance, but this worsens damping transients at the fault occurrence and removal. That
mean crowbar resistance value should be set as compromise of both cases. At the Fig. 3.38 it
can be seen total energy absorbed during crowbar operation.
57
Chapter 4
Tests
4.1 Induction Machine Tests [24] [25] [26]
All voltage and current measurements are rms values. The power supply shall
provide balanced phase voltage closely approaching a sinusoidal waveform. The rapid
changes in frequency affects the machine under test and the measuring devices, so during the
tests the variations in frequency shall not exceed 0.33%. The line voltages have to be
measured with the signal leads connected to the machine terminals, and the voltage unbalance
shall not exceed 0.5%. The line currents to each phase of the motor must be measured, and the
arithmetic average value shall be used for calculation. The power input can be measured by
two single phase wattmeters.
On some tests the parameters of the induction machine and the equivalent circuit can
be obtained. There are a lot of factors that we have to consider in order to make these tests.
The winding resistances vary with the temperature, and rotor resistance depends on the
frequency.
The equivalent circuit parameters for an induction machine can be done using
specific tests like: no-load test and blocked-rotor test.
The no-load test corresponds to the open-circuit test on a transformer and the
blocked-rotor test corresponds to a short circuit test of a transformer. Further on the
transformer and the no-load and blocked-rotor test will be presented.
4.1.1 The transformer
A transformer is a device that transfers electrical energy from one circuit to another
by a magnetic coupling without requiring motion between its parts and is one of the most
efficient electrical machines. It has two or more coupled windings and a core to concentrate
the magnetic flux. An alternating voltage applied to one winding creates a time-varying
magnetic flux in the core, which induces a voltage in the other windings. By the variation of
the relative number of turns between primary and secondary windings, the ratio of the input
and output voltages is determinate. The voltage is transformed by stepping it up or down
between circuits. The energy losses are reduced and the economical transmission of power
over long distances is realised by transforming electrical power to a high voltage, low current
form and back again. The losses of the transformer can be differentiated by those that have the
origin in the windings, or in the magnetic circuit named copper loss and iron losses
respectively. The copper losses are related to resistive heating of the conductor during the
current flow in the windings.
The voltage applied to the primary winding causes a current, which produces a
magneto motive force (mmf) in the core. The current that produces the mmf, named the
magnetizing current, is required to drive flux around the magnetic circuit of the core. An
electromotive force (emf) is induced across each winding, an effect called the mutual
58
inductance. The electric circuit quantity of voltage (emf) is analogous to magnetic circuit
quantity of magneto motive force. [29]
I1
I2
U1
E1
N1
N2
E2
Load
U2
Electrical circuit
Magnetic circuit
Electrical circuit
Fig. 4.1 Transformer schematic [30]
An alternating voltage U 1 is applied to the primary terminals. The current I 1 flows
in the primary electrical circuit, establishing an alternating flux in the magnetic circuit which
in turn causes current I 2 to flow in the secondary electrical circuit. The periodic variation of
flux induces an electromotive force (emf) in the windings and it is proportional to the number
of turns. The applied voltage should be equal with the drop in the resistance plus the
electromotive force:
U 1 = R1 I 1 + E1
(4.1)
Where I1 is the current flowing in the primary winding and E1 is the electromotive
force.
Neglecting the voltage drop in the winding, the value of the voltage U1 is equal to the
electromotive force E1:
∂φ
U 1 = E1 = N 1
(4.2)
∂t
The flux links the secondary winding inducing emf and an equal secondary voltage
U 2 , given by:
∂φ
U 2 = E2 = N 2
(4.3)
∂t
Dividing the voltages in (4.2) and
(4.3),
(4.4) is obtained [30].
U 1 N1
=
U2 N2
(4.4)
If is assumed that the leakage flux is zero, the mmf N is equal in both sides of the
transformer:
59
N1 I1 = N 2 I 2
(4.5)
The transformation ratio of the transformer has the following expression:
m=
E1 U 1 N 1 I 2
=
=
=
E2 U 2 N 2 I1
(4.6)
The connection of the primary and secondary windings will be in ∆ or Y
configurations. If the winding sets share a common core assembly or if each winding pair is a
separate transformer, the winding connections are:
primary - secondary
∆
∆
Y
Y
∆
Y
∆
Y
In
Fig. 4.2, the windings connexions are shown.
Fig. 4.2 Transformer windings connections [30]
A 3-phase transformer can have its primary and secondary windings connected in the
same way (∆-∆, Y-Y), or in a different way (∆-Y, Y-∆). When is no phase shift, primary and
secondary windings are connected the same way and the secondary voltage waveforms are in
phase with the primary waveforms. If the primary and secondary windings are connected
differently, a phase shift between the primary and the secondary windings will be introduced
and the secondary voltage waveforms will differ from the corresponding primary voltage
waveforms. The phase shift is clockwise and its values are between 0 and 11.Considering the
difference of the angle between the secondary and the primary voltages, the phase shift is
defined as in (4.7), where α is the lagging angle between the voltage values of the secondary
and primary.
60
P.s. =
α
(4.7)
30
When two transformers are connected in parallel, their phase shifts must be identical,
if not, a short circuit will occur when the transformers are energized. [31]
4.1.2 No-load test [24] [25] [26]
Balanced voltages are applied to the stator terminals at the rated frequency with the
rotor uncoupled from any mechanical load.
The measurement of the current, voltage and power are made at the motor input. The
losses in the no-load test are those due to core losses, winding losses, windage and friction. It
corresponds to the open-circuit test made on a transformer.
Conditions for the test:
In order to reach the thermal steady-state operation, the machine must run with noload 10 to 120 minutes with a power that starts form a value less than 1kW until 1001000 kW.
The fundamental frequency must be constant and the 3-phase voltage system must be
balanced without harmonics and balanced.
The supply voltage is varied in the range of (0.2 − 1.2)U n and the variables measured
are the no-load current, stator active power and the slip.
The electrical diagram of the test setup for the no-load test is shown in Fig. 4.3
Fig. 4.3 Electrical diagram of the no-load test setup [24]
In the no-load test the mechanical load per phase is the internal windage and friction
of the machine. At no load, the slip of the induction machine is very low. The value of the
R'
equivalent resistance represented by r (1 − s ) in the rotor branch of the equivalent circuit is
s
61
very high. The no-load rotor current is then negligible, and it can be neglected the rotor
branch of the equivalent circuit. Then, the approximate equivalent circuit becomes:
Rn −l
U n −l
jX l , S
I n −l
jX m1
Fig. 4.4 Equivalent induction machine circuit for no-load test [25]
In the no-load measurement, the no-load rotational losses (friction, windage and core
losses) will also be seen. For this reason the measurement of the stator winding is required.
The rotor current is negligible at no-load conditions, thus the copper losses are also negligible.
The input power measured in the no-load test ( Pn−l ) is the sum of copper losses and
rotational losses:
Pn − l = PCu + Prot
(4.8)
Where the stator copper losses are given by equation
(4.9).
PCu = 3I n2−l Rs
(4.9)
The value of the no-load resistance ( Rn −l ) is calculated from the no-load
measurement data ( U n −l , I n −l , Pn −l ) and determined from the no-load dissipated power, as
shown in
(4.10)
P
(4.10)
Pn −l = 3I n2−l Rn −l ⇒ Rn −l = n2−l
3I n −l
The no-load impedance (the ratio of the no-load voltage to current) from the no-load
equivalent circuit is:
Z n −l =
U n −l
= Rn2− l + ( X l , S + X m1 ) 2
I n −l
(4.11)
The values of the stator leakage reactance ( X l , S ) and magnetizing reactance ( X m1 )
are not uniquely determined.
The value of X l , S can be determined by the blocked-rotor test. The value of the
magnetizing reactance X m1 can then be determined.
The blocked rotor reactance sum is:
X l , S + X m1 = Z n2−l + Rn2−l
(4.12)
62
4.1.3 Blocked-rotor test [24] [25] [26]
This test involves high mechanical stresses and high rates of heating. It is necessary
to be made safe, to establish the rotational direction and the machine must be at ambient
temperature before the test is started. Since the current is not directly proportional to the
voltage because of the changes in reactance (caused by leakage paths saturation), readings
have to be made at rated voltage and frequency.
R'
The resulting speed-dependent resistance r (1 − s ) goes to zero, and the resistance
s
of the rotor branch of the equivalent circuit becomes very small.
The electrical diagram of the test setup for the blocked rotor case is shown in Fig. 4.5
Fig. 4.5 Electrical diagram of the blocked-rotor test setup [24]
The equivalent circuit for the blocked rotor test is represented in Fig. 4.6:
Rs
U b−r
jX l , S
I b−r
jX l',R
Rr'
Fig. 4.6 Equivalent induction machine circuit for blocked rotor test [25]
The power in the blocked rotor test is:
Pb − r = 3I b2− r ( R s + R r' )
(4.13)
63
From
reflected rotor winding resistance is determined,
Rr' =
Rb −r
− Rs
3I b2−r
(4.13),
the
(4.14).
The blocked-rotor impedance is the ratio of the blocked-rotor voltage to current, and
is:
Z b− r =
U b− r
= ( Rs + Rr' ) 2 + ( X l , S + X l', R ) 2
I b−r
(4.15)
The equation of the reactance sum (stator leakage reactance + stator leakage
reactance) is represented in equation
(4.16).
X b − r = X l , S + X l', R = Z b2− r − ( R s + Rr' )
(4.16)
The blocked rotor test is performed for this reactance. The total leakage reactance
distribution between the stator and the rotor is typically unknown.
Empirical equations for different classes of motors can be used to determine X l , S
and X l',R . For the wound rotor X l , S = 0.5 X b− r and X l', R = 0.5 X b − r .Using this empirical
equations, the values of X l , S and X l',R can be determined calculating X b− r . Given the value
of X l , S , the magnetization reactance is calculated as in
(4.17)
X m1 = Z n −l − Rn2−l − X l , S
(4.17)
64
Conclusions
This project is focused on describing different strategies for Fault Ride Trough
protection, control of the rotor side of a DFIG and the control of the crowbar protection for a
DFIG. For the simulation, Simulink and Simulink tool Plecs are used.
The project is structured in four main chapters:
o The first chapter (Chapter 1) contains introduction, the problem statement, the goals of the
project and the limitations of the project.
o In the Chapter 2 the DFIG is presented with the principle of operation, construction and
the power flow. The induction machine model is presented with the general machine
equations, the Cp curve and the wind turbine torque and power vs. speed characteristics.
Further on a general description of the control is made and the requirements in Grid Codes
of different countries are presented. Then the crowbar and the crowbar topologies are
presented and a selection of a suitable topology for the project is made.
o In Chapter 3, named System Design and Simulations, the DFIG simulation model is
described with the control principles. Then the rotor control is described with the
implementation of the control scheme and the PI-controller design. The simulations
results are then interpreted, showing that the control works for a change in the wind as
well as for a change in the reactive power. Later the crowbar control is presented. Main
model is modified for FRT then crowbar is attached and simulation s are made for voltage
dip down to 15%. Effects of crowbar bypass performance are shown on the figures and
described.
o Chapter 4 is the last part of the project and is focused on describing the transformer and
the no-load and rotor blocked test. These tests are used in order to obtain the necessary
parameters of the induction machine.
Future work
As further work on this project, the following improvements are required:
• Simulation of a more detail DFIG wind turbine, introducing transformers and an entire
Back to Back converter.
• Design and simulation of the stator side converter control
• Improvement of the crowbar control in order to be able to comply with TSOs
requirements.
• Measure of machine parameters of the DFIG machine provided by KK-electronic use
for the implementation of the real setup.
• Simulation of the entire system and control with mention parameters.
• Implementation of the entire control of DFIG and crowbar in dSPACE platform and
compare results with simulation results
65
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Tao Sun “Power Quality of Grid-Connected Wind Turbines with DFIG and
Their Interaction with the Grid”, Institute of Energy Technology Aalborg
University, Denmark, May 2004
68
Kingsley “Electric
[38].
S. Chung, “A phase tracking system for three phase utility interface
inverters”, IEEE Trans. Power Electron., vol. 15, pp. 431-438, May 2000
[39].
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Burgos and Dushan Boroyevich, “Decoupled Double Synchronous
Reference Frame PLL for Power Converters Control”, IEEE Transactions
on Power electronics, vol. 22, no. 2, march 2007
[40].
P. Rodríguez, A. Luna, M. Ciobotaru, R. Teodorescu, and F. Blaabjerg
“Advanced Grid Synchronization System for Power Converters under
Unbalanced and Distorted Operating Conditions”
[41].
Jan Sundvall, Mads Christian Pilgaard Værens, Thordur Ofeigsson,
Maciej Swierczynski “Dynamic Control of an Electrical Truck Motor”,
Institute of Energy Technology, 8. Semester Report, spring 2007
[42].
R. Datta, V.T. Ranganathan, “Decoupled Control of Active and Reactive
Power for a Grid-connected Doubly-fed Wound Rotor Induction Machine
without Positioning Sensors” Department of Electrical Engineering Indian
Institute of Science, Bangalore, India, 1999
69
APPENDIX A: Parameters [36]
Parameters from [36] for the WRIM:
Wind turbine:
Power = 7.5 kW
Radius = 3.24 m
Rated rotational speed = 10 m/s
Rated wind speed = 4 m/s
Maximum speed = 12 m/s
Gear box = 5.065
Wound rotor induction machine (WRIM):
Power = 7.5 kW
Stator voltage = 415 V
Rotor voltage = 440 V
Rated stator current = 19 A
Rated rotor current = 11 A
Rs = 1.06 Ω
Rr = 0.80 Ω
Ls = 0.2065 H
Lo = 0.0664 H (referred to rotor)
Lr = 0.0810 H (refered to rotor)
Pole pairs = 3
Rated speed = 970 rpm
Stator-rotor turns ratio n = 1.7
Stator connection = delta
Rotor connection = star
As for the model of the WRIM in Plecs needs all the parameters refered to the stator, and
leakage inductances are needed, the parameters for this model are:
Rr' = n 2 ⋅ Rr = 2.312
Lo' = n 2 ⋅ Lo = 0.1919
Lr' = n 2 ⋅ Lr = 0.2341
Lm = Lo'2 /Ls = 0.1783
Lσs = Ls - Lm = 0.0282
Lσr' = Lr' - Lm = 0.0558
Parameters for the DFIG wind turbine
R=3.24;
vwind=10;
GearboxRT=5.065;
rho=1.2;
70
Beta=0;
Pmax=9750;
vwind_min=4;
vwind_max=12;
71
APPENDIX B: M-function calculation of
the Mechanical torque
M-function for the calculation of the mechanical torque used in the simulink model desing.
function Torque=Tref(w,vwind,R,GearboxRT,rho,Beta,Pmax,vwind_min,vwind_max)
c1=0.73; %Cp parameters
c2=151;
c3=0.58;
c4=0.002;
c5=2.14;
c6=13.2;
c7=18.4;
c8=-0.02;
c9=-0.003;
if vwind>=vwind_min && vwind<vwind_max
lambda=(w/GearboxRT)*R/vwind;
lambda_i=1/(lambda+c8*Beta)-c9/(Beta^3+1);
cp = c1 * (c2*lambda_i - c3*Beta - c4*Beta^c5 -c6)* exp( -c7 *
lambda_i);
Pref = (0.5*rho*pi*R^2)*vwind^3*cp;
if Pref>Pmax
Pref=Pmax;
end
Torque=-Pref/w;
else
Torque=0;
end
72
APPENDIX C: Calculation of Maximum
Power Point (MPP)
Calculation of the lambda optimum, Cp maximum, Power in the Shaft and Mechanical
Torque for different Wind speeds and lambdas, and also for a range of slip from 0.6 to -0.3
using parameters from [36].
%Calculation of the lambda optimum, Cp maximum, Power in the Shaft and
%Mechanical Torque for different Wind speeds and lambdas, and also for
%a range of slip from 0.6 to -0.3 using parameters from [36]
clc
clear all
c1=0.73; %Cp parameters
c2=151;
c3=0.58;
c4=0.002;
c5=2.14;
c6=13.2;
c7=18.4;
c8=-0.02;
c9=-0.003;
Beta=0; %pitch angle
lambda =[0:0.5:20]; %tip-speed-ratio
vwind=[3.5:0.5:15]; %wind-speed
GearBoxRT=5.065; %Gearbox rate
rho=1.2; %air density
R=3.24; %radius of the rotor
Pn=7500; %nominal Power [W]
omega_n=1000; %nominal speed [rpm]
f=50; %frequency [HZ]
p=3; %pole pairs
ws=(f/p)*2*pi;%stator speed [rpm]
%%
%in the next steps the calculation of the cp curves for different
%tip-speed-ratio is done
lambda_i=1./(lambda+c8*Beta)-c9/(Beta^3+1);
cp = c1 * (c2*lambda_i - c3*Beta - c4*Beta^c5 -c6).* exp( -c7 * lambda_i);
cp=1/2*(cp+abs(cp)); %only positive values of Pref
figure(1)
plot(lambda,cp)
title('Cp-Lambda curves')
xlabel('Lambda')
ylabel('Cp')
hold off
%%
%In the next steps the calculation of the MPPT look up table values is
done,
73
%getting the power in the shaft, stator and rotor, for a range of
%wind speed=[3.5:0.5:15];
%Find the value of the cp max for Beta equal to zero. i is the position
% where cp is max.
[cpmax i]=max(cp);
%lambda(i) is the lambda optimum
lambda_opt=lambda(i);
omega=lambda_opt.*vwind/R;
omega_gen=omega*GearBoxRT;
s=(ws-omega_gen)/ws;
%calculate the value of Pshaft and Torque for optimal landa and max cp,for
% different rotor speed
Pshaft = ((0.5*rho*pi*R^2)*R^3.*(omega).^3/(lambda_opt)^3)*cpmax;
omega_pu=omega_gen*(60/(2*pi));
%Torque calculation
T=Pshaft./omega_gen;
Ps=Pshaft./(1-s); %Stator Power
for u=1:length(Ps)
if Ps(u)>Pn
Ps(u)=Pn;
end
end
Pr=-s.*Ps;%Rotor Power
Pshaft=Ps+Pr; %Total Power
%WP=zeros(length(w),5);
WP(:,1)=vwind;
WP(:,2)=s;
WP(:,3)=omega_gen;
WP(:,4)=Ps; %at w=1 the Pshaft=Power in the stator
WP(:,5)=Pr;
WP(:,6)=Pshaft;
WP(:,7)=T;
figure (2)
plot(omega_pu,Pshaft)
title('Pshaft-Wind speed curve')
xlabel('Rotor speed [pu]')
ylabel('Power [pu]')
hold on
plot(omega_pu,Ps,'color','green')
hold on
plot(omega_pu,Pr,'color','red')
hold off
% hold on
% plot(omega_pu,Ps+Pr,'color','yellow')
%%
%In the next the same as it was done before but setting the range of the
%slip curve for s[0.6 to -0.3]
s1=-0.6:0.01:0.3;
74
omega_gen1=(ws+s1*ws);
omega1=omega_gen1/GearBoxRT;
Pshaft1 = ((0.5*rho*pi*R^2)*R^3.*(omega1).^3/(lambda_opt)^3)*cpmax;
Ps1=Pshaft1./(1+s1);%Stator Power
for u=1:length(Ps1)
if Ps1(u)>Pn
Ps1(u)=Pn;
end
end
Pr1=s1.*Ps1;%Rotor Power
Pshaft2=Ps1+Pr1; %Total Power
T1=Pshaft2./omega_gen1; %Torque
figure(3)
plot(s1,Pshaft2)
title('Pshaft-Wind speed curve')
xlabel('Rotor speed [pu]')
ylabel('Power [pu]')
hold on
plot(s1,Ps1,'color','green')
hold on
plot(s1,Pr1,'color','red')
hold off
WP1(:,1)=s1;
WP1(:,2)=omega_gen1*60/(2*pi);
WP1(:,3)=Ps1;
WP1(:,4)=Pr1;
WP1(:,5)=Pshaft2;
WP1(:,6)=T1;
75
APPENDIX D: M-function calculation of
Power and Torque
Calculation of the Power and Torque in the Shaft for different Wind speeds and Generator
speeds using parameters from [36]
%Calculation of the Power and Torque in the Shaft for different Wind speeds
%and Generator speeds using parameters from [36]
clc
clear all
clc
clear all
c1=0.73; %Cp parameters
c2=151;
c3=0.58;
c4=0.002;
c5=2.14;
c6=13.2;
c7=18.4;
c8=-0.02;
c9=-0.003;
Beta=0; %pitch angle
rho=1.2; %air density
Pn=7500; %nominal Power [W]
wn=1000; %nominal speed [rpm]
GearboxRT=5.065; %Gearbox rate
omega=[1:25:1000*2]; %rotor speed [rpm]
romega=(omega*2*pi/60)/GearboxRT; %calculate the turbine speed [rad/s]
R=3.24;%Blade radius
vwind=[4:1:12]; %wind speed [m/s]
f=50; %grid frequency [Hz]
p=3; %pole pairs
ws=(f/p)*2*pi;%stator speed [rad/s]
%%
for k=1:length(vwind)
%calculation of the tip-speed ratio (lambda)
lambda(k,:)=((omega.*2.*pi./60)./GearboxRT).*R./vwind(k);
%calculation of the Power coefficient
lambda_i(k,:)=1./((lambda(k,:)+1e-5)+c8*Beta)-c9/(Beta^3+1);
cp(k,:) = c1 .* (c2.*lambda_i(k,:) - c3*Beta - c4*Beta^c5 -c6).* exp( c7 .* lambda_i(k,:));
%calculation of the Power in the shaft
Pshaft(k,:) = (0.5*rho*pi*R^2).*vwind(k).^3.*cp(k,:);
T(k,:)=Pshaft(k,:)./romega; %returns the wind turbine torque
end
T=1/2*(Pshaft+abs(Pshaft)); %only positive values of Pref
T=1/2*(T+abs(T))%only positive values of T
Psahft_tr=Pshaft';
76
[w,f]=max(Pshaft_tr); %returns in w the maximum value for each column of
Pshaft_tr
Pshaft_3 = w; %Pshaft_3 is the vector with the maximum values of Pshaft_tr
ome=omega(f); %ome is the vector with the values of omega_ for each
position k in which there is the maximum value of Pshaft_tr
figure(1)
plot(omega/wn,Pshaft/Pn)
title('Pshaft-Omega curves')
xlabel('Omega [pu]')
ylabel('Power [pu]')
hold on
plot(ome/wn,Pshaft_3/Pn,'LineWidth',2,'color','black')
hold off
figure(2)
plot(romega,T)
title('Wind Torque for different Wind speeds')
xlabel('rotor turbine speed [rad/sec]')
ylabel('Torque [Nm]')
hold off
77
APPENDIX E: Power Flow
In the next table a range of the different Powers in a range of slip from 0.6 to -0.3,
with parameter from APPENDIX A is shown
slip
0,6
0,57
0,54
0,51
0,48
0,45
0,42
0,39
0,36
0,33
0,3
0,27
0,24
0,21
0,18
0,15
0,12
0,09
0,06
0,03
0
-0,03
-0,06
-0,09
-0,12
-0,15
-0,18
-0,21
-0,24
-0,27
-0,3
rotor speed
(rpm)
400
430
460
490
520
550
580
610
640
670
700
730
760
790
820
850
880
910
940
970
1000
1030
1060
1090
1120
1150
1180
1210
1240
1270
1300
Stator Power(W)
1220,849096
1410,843736
1614,572929
1832,036674
2063,234972
2308,167822
2566,835224
2839,237178
3125,373685
3425,244744
3738,850356
4066,190519
4407,265235
4762,074504
5130,618325
5512,896698
5908,909623
6318,657101
6742,139131
7179,355713
7500
7500
7500
7500
7500
7500
7500
7500
7500
7500
7500
Rotor Power (W)
-732,509457
-804,18093
-871,869382
-934,338704
-990,352786
-1038,67552
-1078,07079
-1107,3025
-1125,13453
-1130,33077
-1121,65511
-1097,87144
-1057,74366
-1000,03565
-923,511298
-826,934505
-709,069155
-568,679139
-404,528348
-215,380671
0
225
450
675
900
1125
1350
1575
1800
2025
2250
E.1 Powers in a range of slip from 0.6 to -0.3
78
Total Power (W)
488,339638
606,662807
742,703547
897,69797
1072,88219
1269,4923
1488,76443
1731,93468
2000,23916
2294,91398
2617,19525
2968,31908
3349,52158
3762,03886
4207,10703
4685,96219
5199,84047
5749,97796
6337,61078
6963,97504
7500
7725
7950
8175
8400
8625
8850
9075
9300
9525
9750
APPENDIX F: IGBT & GTO
F.1. Insulated-gate bipolar transistor (IGBT)[27]
IGBT is a power semiconductor device. It is a combination of bipolar power transistor and
insolated-gate like in Field Effect Transistor (FET). This unique structure connects
advantages from both components in one structure- IGBT is as easy to control as FET, it’s
switching ability is as fast as bipolar transistors. Moreover it has high break-down voltage
level.
F.1 Symbol and schematic of IGBT [27]
It has three-terminals Collector, Gate and Emitter. If the positive voltage is applied between
the gate and emiter the transistor is on. To turn it off gate signal must be zero or below.
F.2. Gate Turn Off thyristor (GTO)[27]
GTO is a switching device with ablitity to turn on and turn off. It has a gate which is between
Anode and Catode. The gate controls the thyristors by current signal. When pulse of current
will be injected through the gate the GTO will turn on and start to conduct anode-catode
current. To turn it off short reverse pulse of gate current must be applied. Comparing with
typical thyristors, the GTO has highier switching frequency.
F.2 GTO symbol and characteristics [27]
79
Injecting reverse gate current pulse removes free electrons from anode-catode circuit and
there is a lack of carriers which increase anod-chatode voltage and the anode current goes to
zero.
80