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ADVANCED POWER ELECTRONIC FORWIND-POWER GENERATION BUFFERING
By
ALEJANDRO MONTENEGRO LEN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2005
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Copyright 2005
by
Alejandro Montenegro Len
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To my brother
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ACKNOWLEDGMENTS
I would like to first express my gratitude to Charles Edwards, the principle
engineer at S&C Electric Co. (Chicago, IL) for his patience and the knowledge he shared
throughout the project. I would also like to acknowledge Kenneth Mattern (manager at
S&C Electric Co., Power Quality Division) for his constant encouragement and
confidence in my ability. I am grateful to S&C Electric Company in general for all of
their contribution and concern.
Additionally, I would like to thank Alexander Domijan (my supervisory committee
chair) for his funding during my graduate studies. My gratitude also goes to my
supervisory committee (Dr. Ngo, Dr. Arroyo, and Dr. Goswami) for all of their time and
effort.
I would furthermore like to acknowledge my family in Spain, for supporting me
and believing in me throughout my stay in the United States. I would finally like to
express my love and gratitude to my girlfriend, Andrea Victoriano, for her help with the
proofreading and for always being the shoulder I could lean on throughout the project
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ................................................................................................. iv
LIST OF TABLES........................................................................................................... viii
LIST OF FIGURES ........................................................................................................... ix
ABSTRACT.................................................................................................................... xvii
CHAPTER1 INTRODUCTION........................................................................................................ 1
Wind-Energy Outlook .................................................................................................. 1Electrical Issues ............................................................................................................ 3Solutions to Wind-Power Fluctuations.........................................................................9State of the Art.............................................................................................................. 9Objective..................................................................................................................... 11
2 SYSTEM DESIGN.....................................................................................................14
Introduction................................................................................................................. 14Control Scheme .......................................................................................................... 14
Positive Sequence Calculation ............................................................................14Real Power Calculation Using dq Components ..................................................20Phase Locked Loop .............................................................................................21Control Algorithm Design...................................................................................26
Inner regulators ............................................................................................27Outer regulators............................................................................................35
Per-Unit System Model ..............................................................................................56Inverter Output-Filter Design..............................................................................56
Harmonic content .........................................................................................57
Switching frequency.....................................................................................60Passive filter design......................................................................................61Passive filter damping..................................................................................65
Direct-Current Link Capacitor Design ................................................................68Energy Storage Design........................................................................................69Chopper Inductor Design ....................................................................................71Per-Unit System Model Summary.......................................................................72
Simulated Model......................................................................................................... 73
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3 SYSTEM DESCRIPTION..........................................................................................78
System Overview........................................................................................................ 78Electrical Network Model...........................................................................................80
Synchronous Machine .........................................................................................80Voltage regulation ...............................................................................................81Prime Mover ........................................................................................................ 81Synchronous Machine Control Algorithm ..........................................................83
Wind-Farm Model ...................................................................................................... 87Wind-Farm Control Algorithm............................................................................90Wind-Farm Power-Factor Correction..................................................................90Wind-Farm Soft-Start System.............................................................................94
Power Stabilizer.......................................................................................................... 97Power-Stabilizer Hardware Description..............................................................97
Interface board..............................................................................................99Digital signal processor..............................................................................105Field-programmable gate array..................................................................106Intelligent power module ...........................................................................107Isolation interface circuit............................................................................108
Power Stabilizer Software Description .............................................................108Description of DSP program......................................................................109FPGA program description ........................................................................114
4 SYSTEM PERFORMANCE....................................................................................121
System Data .............................................................................................................. 121Power Stabilizer Transient Response .......................................................................121
Direct-Current Link Voltage Control................................................................121
Reactive Current Control...................................................................................123Passive Filter Performance .......................................................................................126Voltage Regulation ...................................................................................................127System Losses........................................................................................................... 128Power Limiter Results ..............................................................................................130
Power Limiter 1 (High Pass Filter) ...................................................................131Power Limiter 1 (Adaptive High Pass Filter)....................................................136Power Limiter 2.................................................................................................138
Power Limiters Comparison Study...........................................................................145
5 SUMMARY.............................................................................................................. 148
Conclusions............................................................................................................... 148Further Work ............................................................................................................ 150
APPENDIX
A MATHEMATICAL TRANSFORMATIONS..........................................................151
B MATLAB CODES ...................................................................................................158
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C POWER STABILIZER CONTROL MODULES ....................................................168
LIST OF REFERENCES.................................................................................................172
BIOGRAPHICAL SKETCH ...........................................................................................176
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LIST OF TABLES
Table page
1-1 Technical specifications of IEC and IEEE................................................................4
1-2 Wind-farm output-power requirements.....................................................................8
1-3 Large-scale wind-power output-leveling projects...................................................10
1-4 Conceptual wind-power filtering projects...............................................................12
1-5 Basic system configurations....................................................................................13
2-1 Outer regulator assignation .....................................................................................35
2-2 Rate-of-change limits or PPA for a 10 MW wind farm ..........................................47
2-3 Generalized Harmonics of line-to-line voltage .......................................................59
2-4 L filter vs. LCL filter...............................................................................................61
2-5 LCL filter design ..................................................................................................... 64
2-6 LCL equivalent impedance with damping resistance .............................................65
2-7 Per-unit system........................................................................................................ 65
2-8 Per-unit system parameters .....................................................................................73
2-9 Designed system results and simulated system results comparison........................76
3-1 Synchronous machine output voltage profile at rated speed...................................82
3-2 Alternatives for the power stabilizer controller.....................................................106
3-3 FPGA code words .................................................................................................120
4-1 System parameters................................................................................................. 122
A-1 Mathematical transformations summary...............................................................157
C-1 Control Modules....................................................................................................168
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LIST OF FIGURES
Figure page
1-1 Wind-power output for two wind farms during one month. .....................................5
1-2 Power fluctuation comparison...................................................................................6
1-3 Typical power curve of a wind turbine. ....................................................................6
1-4 Wind-farm output power vs system frequency. ........................................................7
1-5 Control strategies along the power curve..................................................................8
1-6 Wind-farm generation buffering concept ................................................................13
2-1 Unbalanced system..................................................................................................15
2-2 Space vector trajectory of an unbalanced system in the d-q-o plane ......................16
2-3 Space vector trajectory projection over the d-q plane.............................................16
2-4 Direct and quadrature components of an unbalanced system .................................17
2-5 Representation of an unbalanced system in the frequency domain.........................17
2-6 Positive-sequence extraction algorithm ..................................................................19
2-7 Voltage waveforms for an unbalanced fault event..................................................19
2-8 Response of the positive-sequence extraction algorithm ........................................20
2-9 Distortion of phase angle due to a negative sequence component ..........................22
2-10 PLL diagram............................................................................................................ 23
2-11 PLL simplified model..............................................................................................24
2-12 PLL system step response .......................................................................................25
2-13 Root locus for two different regulator gains ...........................................................25
2-14 PLL system response to an unbalanced system condition ......................................26
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2-15 PLL system response to a frequency excursion ......................................................26
2-16 System description ..................................................................................................27
2-17 Simplified system model .........................................................................................28
2-18 Electrical representation of the dq components ......................................................30
2-19 System model block diagram ..................................................................................30
2-20 Inverter current regulator-system model block diagram .........................................31
2-21 Inverter current regulator-system model simplified block diagram........................32
2-22 Simplified current control diagram .........................................................................32
2-23 Current regulator step response...............................................................................33
2-24 Chopper equivalent system .....................................................................................34
2-25 Chopper current controller ......................................................................................35
2-26 Powers' definition.................................................................................................... 36
2-27 System model .......................................................................................................... 37
2-28 DC link equivalent system block diagram ..............................................................37
2-29 DC link simplified system block diagram...............................................................38
2-30 DC link voltage regulator step response .................................................................38
2-31 Simplified system model .........................................................................................40
2-32 Source impedance voltage drop ..............................................................................41
2-33 Transfer functions of inverters quadrature current component..............................42
2-34 Transfer functions of inverters direct current component......................................42
2-35 Voltage regulator system block diagram.................................................................44
2-36 Positive sequence extraction algorithm equivalent system.....................................44
2- 37 Voltage regulator detailed block diagram ...............................................................45
2- 38 Voltage regulator simplified control diagram .........................................................45
2- 39 System response to a 5% change in voltage reference............................................45
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2-40 Adaptive control scheme.........................................................................................46
2-41 Power Regulator general control scheme................................................................47
2-42 Power limiter 1. Control block diagram..................................................................48
2-43 Power limiter 1. Performance using different cut-off frequencies (unlimitedpower and energy)....................................................................................................49
2-44 Power limiter 1. Performance using different cut-off frequencies (Pinverter=1.0MW and Einverter=8.5 MJ) .......................................................................................49
2-45 Power limiter 2. Limiters details .............................................................................50
2-46 Power limiter 2. Control block diagram..................................................................51
2-47 Power limiter 2. Compensation performance.........................................................51
2-48 Power limiter 2. Inverter response for a sampling time of 2 seconds .....................52
2-49 Power limiter 2. Inverter response for different power ratings. Sampling time 2seconds ..................................................................................................................... 53
2-50 Power limiter 2. Inverter response for different ESS sizes. Sampling time 2seconds ..................................................................................................................... 53
2-51 Power limiter 3. Control block diagram..................................................................54
2-52 Power limiter 3. Compensation performance.........................................................55
2-53 Power limiter 3. Inverter response for a sampling time of 2 seconds .....................55
2-54 Inverter topology ...................................................................................................... 57
2-55 Line-to-line and line-to-neutral voltage of a three phase inverter...........................57
2-56 RMS Line-to-line voltage harmonic spectrum........................................................58
2-57 Static Synchronous Generator diagram...................................................................59
2-58 LCL filter topology .................................................................................................61
2-59 LCL equivalent block diagram................................................................................62
2-60 Single phase equivalent filter model at the fundamental frequency .......................62
2-61 Single phase equivalent filter model at the hth harmonic ........................................63
2-62 LCL equivalent impedance with damping resistance .............................................66
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2-63 Single phase harmonic generator equivalent circuits ..............................................66
2-64 LCL gain frequency response .................................................................................67
2-65 Inverter frequency analysis .....................................................................................67
2-66 Capacitor Voltage vs. Energy Storage ....................................................................70
2-67 ESS-Chopper topology............................................................................................71
2-68 Equivalent circuit for maximum current ripple calculation ....................................72
2-69 System overview ..................................................................................................... 74
2-70 Per-unit electric system model ................................................................................74
2-71 Power Stabilizer Control Scheme ...........................................................................75
3-1 Equivalent system model ........................................................................................79
3-2 DC gen-set............................................................................................................... 83
3-3 Two single quadrant chopper circuit .......................................................................83
3-4 Synchronous generator control system ...................................................................84
3-5 Frequency deviation ................................................................................................85
3-6 DC-GEN set control scheme ...................................................................................85
3-7 System frequency response forf=-1Hz ................................................................86
3-8 Frequency control equivalent system......................................................................87
3-9 Equivalent model frequency response forf= - 0.01666 pu ..................................88
3-10 Dynamic model used for transient studies ..............................................................88
3-11 Static model used for steady-state studies...............................................................88
3-12 Wind-farm model ....................................................................................................89
3-13 Wind-farm controller...............................................................................................90
3-14 Wind-farm power regulator & current regulator step response (P=100%) ..........91
3-15 Induction generator PQ curve .................................................................................92
3-16 Wind-farm PF correction capacitor bank ................................................................93
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3-17 PF correction capacitor bank current waveforms....................................................93
3-18 Capacitor bank impedance frequency scan .............................................................94
3-19 Machine control scheme operating states................................................................95
3-20 Electric power system start-up ................................................................................96
3-21 Detail of the transition from start-up mode to run mode.........................................96
3-22 Power Stabilizer system overview ..........................................................................97
3-23 Interface board overview.......................................................................................100
3-24 AC voltage scaling circuit (input [-1000+1000V], output [0 +3V]) .....................101
3-25 DC voltage scaling circuit (input [0 +1000V], output [0 +3V]) ...........................101
3-26 CT current scaling circuit (input [-5 +5A], output [0 +3V]).................................101
3-27 LEM current scaling circuit (input [-0.36 +0.36A], output [0 +3V])....................101
3-28 Power supplies voltage monitoring......................................................................102
3-29 Systems critical signals during turn on ................................................................103
3-30 Systems critical signals during turn off ...............................................................103
3-31 Darlington drivers .................................................................................................104
3-32 IPM status signals interface circuitry ...................................................................104
3-33 DAC circuit ........................................................................................................... 105
3-34 DSP built-in PWM output performance vs. FPGA...............................................107
3-35 IMP power circuit configuration ...........................................................................108
3-36 Isolated interface board .........................................................................................109
3-38 Power stabilizer control algorithm sampling rates................................................110
3-37 Interconnections between the different sub-systems of the power stabilizer........111
3-39 Power stabilizer control stages..............................................................................113
3- 40 Power stabilizer start-up sequence ........................................................................113
3-41 FPGA system overview.........................................................................................116
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3-42 Up/Down counter. .................................................................................................117
3-43 PWM generator ..................................................................................................... 117
3-44 One phase dead-time generator detailed diagram .................................................119
3-45 Dead-time generators waveforms ........................................................................119
3-46 Watchdog logic .....................................................................................................120
4-1 DC link voltage response for different Kp gains...................................................121
4-2 DC link voltage response for different Ki gains ...................................................122
4-3 Iqrefcommand step change from -0.5 to 0.5 A per unit. Integral gain effect ........123
4-4 Iqrefcommand step change from -0.5 to 0.5 A per unit. Proportional gain
effect....................................................................................................................... 1244-5 Iq current regulator output for different Kp ..........................................................124
4-6 Iqref command step change from -0.5 to 0.5 and back to -0.5 A per unit ............124
4-7 Power stabilizer harmonic injection response for Ki=18 and Kp=1 .....................125
4-8 Current regulator frequency response ...................................................................126
4-9 Front-end inverter current waveform ....................................................................126
4-10 Frequency spectrum of the LCL currents..............................................................1274-11 Simplified system description ...............................................................................127
4-12 Power stabilizer voltage regulation performance..................................................128
4-13 Energy storage charge/discharge cycle .................................................................129
4-14 Control scheme with a losses compensation term.................................................129
4-15 Power stabilizer equivalent system .......................................................................130
4-16 Wind-power conditions under study .....................................................................1304-17 Measured and modeled high pass filter results for Kc=0.0064 W/J,
fcut_off=0.005 Hz......................................................................................................132
4-19 Measured high pass filter performance for different cut-off frequencies. Systemparameters Kc=0.0064 W/J.....................................................................................134
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4-20 Modeled high pass filter performance for different cut-off frequencies. Systemparameters Kc=0.0064 W/J.....................................................................................135
4-21 Measured high pass filter performance for different energy storage sizes.System parameters, Kc=0.0064 W/J, fcut-off=0.005 Hz. ..........................................135
4-22 Cut-off frequency trajectory of the adaptive high pass filter for a given energydeviation................................................................................................................. 136
4-23 Measured adaptive high pass filter performance for different Kfs. Systemparameters, Kc=0.0064 W/J, fcut-off-origin=0.005 Hz.................................................137
4-24 Measured adaptive high pass filter performance for different energy storagesizes........................................................................................................................ 137
4-25 Multiple sampling concept. ...................................................................................139
4-26. Measured and modeled power limiter 2 results for Kc=0.0064, RR=2MW/minute, A=0.3 MW/minute, I=1MW/2 seconds fcut-off=0.005 Hz. ................140
4-27 Measured power indexes activity. System parameters: Kc=0.0064 W/J, RR=2MW/minute, A=0.3 MW/minute, I=1 MW/2 seconds, and fs=10Hz.....................141
4-28 Measured power limiter 2 response to different Kc . System parameters: RR=2MW/minute, A=0.3 MW/minute, I=1MW/2 seconds, and fs=10Hz......................142
4-29 Measured power limiter 2 response to different ramp rate limits. ........................142
4-30 Measured power limiter 2 response to different average power fluctuation
limits....................................................................................................................... 143
4-31 Effect of linear interpolation on the average power fluctuation index activity.The sampling time of the original wind-power data is 2 seconds.... ......................144
4-32 Measured power limiter 2 response to different instantaneous power fluctuationlimits....................................................................................................................... 144
4-33 Measured power limiter 2 response to different sampling frequencies.................145
4-34 Measured synchronous machine output power for the different power limiter
control schemes......................................................................................................1464-35 Measured synchronous machine output power for the different power limiter
control schemes. .....................................................................................................147
4-36 Frequency regulator output for the different power limiters.................................147
A-1 Relationships among ds-qs, and abc axes .............................................................153
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A-2 Stationary ds-qs components in the time domain.....................................................153
A- 3 Relationship among ds-qs and dr-qraxes ...............................................................154
A-4 Direct and quadrature components........................................................................155
A-5 Time domain representation of abc and d-q components .....................................156
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Abstract of Dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy
ADVANCED POWER ELECTRONIC FORWIND-POWER GENERATION BUFFERING
By
Alejandro Montenegro Len
May 2005Chair: Alexander Domijan, JrMajor Department: Electrical and Computer Engineering
As the cost of installing and operating wind generators has dropped, and the cost of
conventional fossil-fuel-based generation has risen, the economics and political
desirability of more wind-based energy production has increased. High wind-power
penetration levels are thus expected to augment in the near future raising the need for
additional spinning reserve to counteract the effects of wind variations. This solution is
technologically viable, but it has high associated costs. Our study presents a different
solution to short-term wind-power variability, using advanced power electronic devices
combined with energy-storage systems. New control schemes (designed to filter power
swings with a minimum of energy) were designed, modeled and verified through
experimental tests. We also determined the procedure to extract the corresponding per-
unit model parameters for simulations and test purposes.
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We first reviewed D-Q transformations with emphasis on modeling of the system
and control algorithm. System components were then designed using criteria similar to
those used to design medium-voltage power products.
We tested a proof-of-concept for performance of the power converter in a scaled-
down isolated system using real wind-power data. Tests were conducted under realistic
system conditions of wind-penetration level and energy-storage levels, to better
characterized the impacts and benefits of the Power Stabilizer. We described the scaled-
down isolated electric power system used in the testing. We also analyzed the
performance of the wind-farm model and the synchronous machines governor to gain aninsight into the model systems limitations.
Simulation results carried out in Mathematical Laboratory (MATLAB) and Power
Systems Computer Aided Design (PSCAD) were compared to experimental data to verify
the performance of the power converter under different system conditions and algorithms.
Power limiters were also contrasted and evaluated for frequency deviations and
attenuated power fluctuations.
In summary we can say that, among all the power limiters considered in our study,
the adaptive high pass filter presented the best performance in terms of system robustness
and effectiveness.
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CHAPTER 1INTRODUCTION
Wind-Energy Outlook
Wind power has been used for at least 3000 years, mainly for milling grain,
pumping water, or driving various types of machines. However, the first attempt to use
wind turbines for producing electricity date back to the 19th century. In 1891, Poul La
Cour in Demark built an experimental wind turbine driving a dynamo. The oil crisis of
the 1970s revived interest in wind turbines. Nowadays, the power is the fastest growing
source of energy in the world and its growth rates have exceeded 30% annually over the
past decade [1]. Cumulative global wind-energy generating capacity approached 40,000
MW by the end of 2003 [2]-[3]. The main drivers for developing of the wind industry in
the United States are
Federal Renewable Energy Policies, particularly the Production Tax Credit (PTC)that provides a 1.5 cent per kilowatt-hour credit for electricity produced from awind farm during the first 10 years of operation. This wind energy PTC expiredDecember 31, 2003 but will be reinstated through 2005 as part of a major taxpackage (H.R. 1308).
State-level renewable energy initiatives, such as the Renewable Portfolio Standard,or green pricing.
The Database of State Incentive for Renewable Energy [4] gives more information
on incentives. These government initiatives, together with technological advances, plus
the need for a new source of energy capable of meeting the worlds growing power
demand and the rising prices of conventional fossil fuel-based generation, make the wind
power one of the most promising industries in the future.
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According to the European Wind Energy Association and Greenpeace, no barriers
exist for wind to provide 12% of the worlds electricity by 2020. The American Wind
Energy Association forecasts that wind power will provide 6% of the USs electricity by
2020 if the wind industry maintains an annual growth rate of 18%.
The positive effects of using such types of renewable resources are well known.
However, wind-power plants, like all other energy technology, have some drawbacks that
should be mentioned. These problems can be divided into major groups: environmental
issues and interconnection issues.
Environmental issues. Most significant among these are the following: Sound from turbines: Some wind turbines built in the early 1980s were very
noisy. However, manufactures have been working on making the turbines quieter.Today, an operating wind farm at a distance of 750 to 1,000 feet is no noisier than amoderately quiet room. Research in aero-acoustics is still being carried out tofurther reduce noise from wind on the blades.
Bird death: Wind turbines are often mentioned as a risk to birds, and severalinternational tests have been performed. The general conclusion is that birds areseldom bothered by wind turbines. Studies show that for example, overhead powerpole lines are far more hazardous for birds than wind turbines [2].
Wind-tower shadow effect: Wind turbines, like other tall structures cast a shadowon the neighboring area when the sun is visible. It may be irritating if the rotorblades chop the sunlight, causing a flickering effect while the rotor is in motion,especially when the sun is low in the sky.
Interconnection issues. Connecting wind turbine to operate in parallel with the
electric power system influences the system operating point (load flow, nodal voltages,
power losses, etc). These changes in the electric power system state bring up new system-
integration issues that system operators and power quality engineers must take into
account. These interconnection issues can be divided into operational issues and electrical
issues.
Operational Issues: These include unit commitment and spinning reserve.
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The unit commitment problem is to schedule specific or availablegenerators (on or off) on the utility system to meet the required loads at aminimum cost, subject to system constraints. The most conservativeapproach to unit commitment and economic dispatch is to discount anycontribution from interconnected wind resources because of wind
variability. Operating reserve is further defined to be a spinning or non- spinning
reserve. Any probable load or generation variations that cannot beforecasted, such as wind power, have to be considered when determiningthe amount of operating reserve to carry out.
Electrical issues: These factors are considered in the next section.
Electrical Issues
Wind-turbine generator-system operation has some negative influence on power
systems. This influence on the electric power system depends on wind variations and on
wind-turbine technology. Impacts on the electric power system can be grouped as
follows:
Power quality: Voltage variations, flicker, harmonics, power-flow variations Voltage and angle stability Protection and control
The IEEE 1547 [5] and the IEC 61400-21 [6] standards are the bases to evaluating
the impact of such wind-turbine generation systems on the electric power system.
According to the IEEE 1547 [5, page 2] abstract,
This standard focuses on the technical specifications for, and testing of, theinterconnection itself. It provides requirements relevant to the performance,operation, testing, safety considerations, and maintenance of the interconnection. Itincludes general requirements, response to abnormal conditions, power quality,islanding, and test specifications and requirements for design, production,
installation evaluation, commissioning, and periodic tests. The stated requirementsare universally needed for interconnection of distributed resources (DR), includingsynchronous machines, induction machines, or power inverters/converters and willbe sufficient for most installations. The criteria and requirements are applicable toall DR technologies, with aggregate capacity of 10 MVA or less at the point ofcommon coupling, interconnected to electric power systems at typical primaryand/or secondary distribution voltages.
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According to the IEC 61400-21 [6, page 9] abstract,
The purpose of this part of IEC 61400 is to provide a uniform methodology thatwill ensure consistency and accuracy in the measurement and assessment of powerquality characteristics of grid connected wind turbines (WTs). In this respect the
term power quality includes those electric characteristics of the WT that influencethe voltage quality of the grid to which the WT is connected.
This standard provides recommendations for preparing the measurements andassessment of power quality characteristics of grid connected WTs.
Table 1-1 shows technical specifications for interconnection and power assessment
covered in both standards.
Table 1-1. Technical specifications of IEC and IEEEInterconnection systemresponse to excursions Power quality assessment
IEEE VoltageFrequency
IEC VoltageFrequency
Voltage fluctuations:Continuous operationSwitching operation
Harmonics
As shown in Table 1-1, both standards overlooked one of the most significant
characteristics of wind farms: its variability (i.e., power fluctuations) [7], the mostimportant ones being
Gusty wind variations having a spectrum of frequencies from 1-10 Hz.
Shadow effect having a spectrum of frequencies from 1-2 Hz and producing torquevariations up to 30%.
Complex oscillations of the turbine tower, rotor shaft, gear box, and blades withspectrum frequencies from 2-100 Hz, and creating torque variations up to 10%.
Figure 1-1 shows actual output power data collected by NREL from two large
wind-power plants in the United States. The small wind farm has a capacity of about 35
MW, and the large one has a capacity of 150 MW.
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0 0.5 1 1.5 2 2.5 3
x 106
0
10
20
30
40
Power(MW)
Time (s)
0 0.5 1 1.5 2 2.5 3
x 106
0
50
100
150
Trent Mesa Project. Wind power output May 2003
Power(MW)
Time (s)
Figure 1-1. Wind-power output for two wind farms during one month (May 2003). A)
Nominal capacity 35 MW. B) Nominal capacity 150 MW.
Even though the technology used in constructing the small wind farm is more than
a decade older than the large one, power fluctuations keep being an issue. Figure 1-2 is a
close-up ofFigure 1-1 and shows the magnitude of these power fluctuations.
Wind turbine manufactures usually provide power curves (Figure 1-3) to
developers to determine the amount of power that will be transferred into the grid for a
single turbine, given the wind speed. However, those figures represent only the mean
values, since a series of stochastic values cannot be controlled, and create additional
power fluctuations.
Wind-output power fluctuations can have different effects on the electric power
system, but the most significant ones are voltage variation and frequency variation in
small or isolated systems.
A
B
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0 1 2 3 4 5 6 7 8
x 104
0
10
20
30
40
.
Power(MW)
Time (s)
0 1 2 3 4 5 6 7 80
50
100
150
Trent Mesa Project. Wind power output May 2003
Power(MW)
0 1 2 3 4 5 6 7 8
x 104
0
10
20
30
40
Power(MW)
Time (s)
0 1 2 3 4 5 6 7 8
x 104
40
50
60
70
80Trent Mesa Project. Wind power output May 2003
Power(MW)
Time (s)
Figure 1-2. Power fluctuation comparison. A) Nominal capacity 35 MW. B) Nominalcapacity 150 MW.
Figure 1-3. Typical power curve of a wind turbine.
As the power fluctuates, the reactive power required by the turbines changes as
well, and therefore voltage variations are expected, especially when the wind farm is
A
B
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7
located at weak points in the system. To compensate for such voltage variations and keep
the voltage close to its rated value, several solutions are available: simple capacitor
banks, static voltage compensator (SVC), or static compensators (STATCOM).
A different approach must be taken for frequency variations due to power
fluctuations. Normally, wind farms connected to big systems do not present a major
problem in terms of frequency variations, because of the stiffness of the system.
However, with small or isolated systems that contain slow or no automatic generation
controls, a mismatch between generated and absorbed power can significantly affect
system frequency unless spinning reserves are significant. Figure 1-4 shows the effect ofwind-power fluctuation on an isolated system with a wind penetration level of 1%.
To counter these negative effects, countries and small isolated systems with high
wind-penetration factors developed special purchase power agreement (PPA)
requirements or indexes for wind-farm developers (Table 1-2).
Figure 1-4. Wind-farm output power vs system frequency.
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Table 1-2. Wind-farm output-power requirements
Ramp Rate dP/dt InstantaneousAverage (maxvariation)
Netherlands
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Solutions to Wind-Power Fluctuations
To reduce the effects of wind-power variations and meet the PPA requirements for
electric utilities, two solutions can be considered:
Higher spinning reserves Wind farm buffer
Increasing spinning reserves is a costly solution. A better approach would be to use
an energy-storage system that could deliver the required power when needed.
Work has been done in developing large-scale energy storage systems that have
overcome these issues by absorbing undesirable power fluctuations and providing firm,
dependable peaking capacity [8]. However, a less costly solution should be explored
based exclusively on power-fluctuation indexes (such as ramp rate indexes or
instantaneous fluctuation indexes).
State of the Art
Storing wind power is not a new concept; in fact, back in 1900, the father of the
modern wind turbine, Poul La Cour, tackled for the first time the problem of energy
storage. He used the electricity from the wind turbines for electrolysis and to store energy
in the form of hydrogen. However, with time, system requirements, energy storage
systems, and wind turbine ratings have changed.
Nowadays, the average wind turbine installed is around 1 MW, according to the
European Wind Energy Association, and wind-power farms usually consists of ten to
several tens of wind-turbine generators of rated power up to 2 MW. Thus, the amount of
energy storage needed to stabilize the power output change in the short term has
increased. Table 1-3 shows some recent projects dealing with output leveling of wind-
energy conversion.
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Table 1-3. Large-scale wind-power output-leveling projects
Project name Wind farm size Energy storage systemActive power refercontrol scheme
Subaru Project [9].Tomamae wind-powerstation.
1.65 MW *16(Vestas).1.5 MW * 5(Enercon).
Total Capacity30.6 MW
VanadiumRedox Flow Battery
PVRB nominal =4.000kWEVRB=6.000kWhS inverter=6.000kVA
Moving Average odetermined as
Pbattery=Pwind average ((fort=8 seconds t
King Island [10]. Energy-storage system providedby Pinnacle VRB
250 kW*3850 kW*2
Total Capacity2.45 MW
VanadiumRedox Flow Battery
PVRB nominal=200kWPVRB short-term ( 5 minutes)=300kWPVRB short-term (10 seconds)=400kWEVRB =1100kWh
Isochronous frequepower range.
Speed droop characand short-term loa
Oki project by FujiElectric
600 kW *3
Total Capacity1.8 MW
Flywheel
E flywheel = 100 kW - 90 secP inverter flywheel side= 110kVAP inverter power system side= 150kVA
Power ramp rate lim
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However, small-scale concepts and technical/economic feasibility studies have
been proposed (Table 1-4). Each of these projects has a different objective (frequency
control, power smoothing, load leveling, etc.). However, they all end up using one of the
topologies and energy-storage systems shown in Table 1-5, where the flywheel or
capacitors may be replaced by some other energy-storage medium. Tables 1-3 and 1-4
show that the amount of energy needed for wind-power balancing using current
technology and current pricing is so significant, that a more flexible and integrated
approach is needed.
Our study focused on developing new power smoothing control algorithms. Thenew integrated approach used a shunt-connected voltage-source converter with added
storage included on the DC link bus. The system can
Exchange active power with the system. Regulate voltage at the point of common coupling Increase power quality and system stability
Objective
Our purpose was to develop, simulate, and implement a proof-of-concept prototype
advanced-power electronic device capable of controlling and smoothing the power
fluctuations of a wind farm using an optimal amount of energy. The wind-power
generation buffering concept is shown in Figure 1-6. The Power Stabilizer was designed
to store excess power during periods of increased wind-power generation and release
stored energy during periods of decreased generation due to wind fluctuations.
We tested the performance of the advanced electronic device on
DC-synchronous machine set Passive load DC-asynchronous machine set Wind-farm buffer or also called Power Stabilizer
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Table 1-4. Conceptual wind-power filtering projectsWind farm size Energy storage system Active power reference control scheme 20 MW Zinc-bromide battery
PZBB nominal (charge) =-750kWPZBB nominal (discharge)=1500kWEZBB =1500 kWh
Limiting instantaneous power fluctuations basedon a 2 seconds intervalPinstantaneous (t=2 seconds) = 1.3 MWAverage power levels over a 2 hour windowPaverage(t- t=2hours)= 200 kW
Maximum poweroscillation 2.5 MW
Super-conducting magneticenergy storage (SMES)
Active power reference is chosen to controlsystem frequency
300kW Electric double layercapacitorP ECS =100 kWE ECS =1.1 kWh
ESS active power reference is determined bydetection power oscillation components using ahigh pass filter
6GW Redox-flow battery(Regenesys )E=62004 MWhP=255MW
Power balancing
45KW FlywheelE flywheel= 12MJP drive=45kW
The active power demand is extracted via a 2ndorder Butterworth high pass filter, with a 5mHzbandwidth
55kW Lead Acid BatteryE battery=35kWhP converter=50kVA
Power smoothing
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A
B
C
A
B
C 0.69
#2 #1
12.47
?L1
L2
L3
Vestas
VRCCV47
VnaS
NAS
VnbS
NBS
VncS
NCS
A
B
C
A
B
C0.48
#2#1
12.47
?
g1
g2
g3
g4
g5
g6
2
1
300.0
2
3
2
5
2
4
2
6
2
2
dcCur
gc12
5
gc22
5
1.0
ChopperReactor
1.0
EnergyStorageCapacitor
A
B
C
A
B
C 12.47
#2 #1
69.0
?
INVERTER
WIND FARM
0 20 40 60 80 100 1208800
9000
9200
9400
9600
9800
10000
10200
10400
10600
10800Wind Power Output
Power(W)
Time (s)
0 20 40 60 80 100 120-1000
-800
-600
-400
-200
0
200
400
600Power Stabilier Power Output
Power(W)
Time (s)
0 20 40 60 80 100 1208800
9000
9200
9400
9600
9800
10000
10200
10400
10600
10800Wind Power Output
Power(W)
Time (s)
Wind power + Wind farm buffer Power
Figure 1-6. Wind-farm generation buffering concept
Table 1-5. Basic system configurations
System configuration
Voltage source inverterESS connected at the DC link side [19]-[21]-[24]
SynchronousMachine
Voltage Source
Inverter
ESS (flywheel)
Electric SystemWind Turbine
DClink
ESS connected at the AC side [18]-[20]-[22]-[23]-[25]
InductionMachine
Voltage Source
Inverter ESS (flywheel)
Electric SystemWind Turbine
DClink
Current source inverter (shunt connected) [13]
InductionMachine
Current Source
Inverter ESS (capacitors)
Electric SystemWind Turbine
Chopper(DC/DCconverter)
ECS
Energy storage system
Available options [26] Compressed air energy storage Battery storage Electro-chemical flow cell systems Fuel cell/electrolyser/hydrogen systems Kinetic energy (flywheel) storage Pumping water
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=
=
=
240
120
0
0.1
0.1
5.0
c
b
a
V
V
V
(2-1)
Figure 2-1 shows the time domain representation of this three-phase unbalanced system.
Figure 2-1. Unbalanced system
If we now calculate the symmetrical components of this unbalanced system, we obtain
=
=
=
1800
1802
01
167.0
167.0
833.0
V
V
V
(2-2)
The symmetrical components transformation is a good tool to determine the type of
distortion or asymmetry the system has. However, it has the drawback of having to use
phasors as input instead of time domain signals. Therefore a different transformation was
needed in order to extract the positive sequence component out of the rotating space
vector.Figure 2-2 shows the trajectory followed by the rotating space vector of the
unbalanced system in the d-q-o plane using Clarkes transformation. This trajectory is
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clearly distorted from the ideal one, and the space vector no longer follows a circular path
(Figure 2-3).
Figure 2-2. Space vector trajectory of an unbalanced system in the d-q-o plane
Figure 2-3. Space vector trajectory projection over the d-q plane
Figure 2-4 shows the Vdrand Vqrcomponents (Parks transformation) of the
unbalanced system in the time domain for= 0.
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Figure 2-4. Direct and quadrature components of an unbalanced system
It is clear that the Vdrcomponent is not constant any more, and it contains a 2nd
harmonic due to the negative sequence. This effect can also be explained in the frequency
domain as shown in Figure 2-5. The rotating reference frame aligns with the fundamental
frequency, w=2f, and therefore
a negative sequence (-w) appears as a 2nd harmonic a dc component appears as a 1st harmonic a positive sequence (w) has a constant value.
abcaxis
drq
raxis
0.167
0.833
-w wdcw
dc-w-2w
Figure 2-5. Representation of an unbalanced system in the frequency domain
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Thus, it can be concluded that Clarkes and Parks transformations do not provide
suitable components that can be used in a voltage regulation control algorithm. It is
therefore necessary then to redefine the transformations in order to extract the desired
components.
Assuming the three-phase electric system has positive and negative sequence
components
)34
cos()34
cos(
)3
2cos()
3
2cos(
)cos()cos(
++=
++=
+=
wtVwtVV
wtVwtVV
wtVwtVV
npc
npb
npa
(2-3)
Clarkes transformation can be used to obtain
+
+
+==
+=+=
qsqsnpqs
dsdsnpds
VVwtVwtVV
VVwtVwtVV
)sin()sin(
)cos()cos((2-4)
where+ds
V and+qs
V are the d-q components of the positive sequence, whileds
V andqs
V
are the d-q components of the negative sequence.If we now assume that the symmetrical components remained constant for at least a
quarter of cycle, the equations can be rewritten as
( ) ( )
( ) ( )
( ) ( )
( ) ( )
=
+=
+
=
=
+
+
ttt
ttt
ttt
ttt
qsdsqs
qsdsds
qsdsqs
qsdsds
V2
V2
1V
2VV
21V
V2
V2
1V
2VV
2
1V
(2-5)
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These components can now be transformed using the rotating reference frame in
order to obtain the positive sequence component. Figure 2-6 shows the block diagram of
the algorithm used to extract the positive-sequence component. The same concept could
be used if the negative sequence magnitude is needed.
abd
dsq
s
Vds
Vqs
Delay (1/f/4)
+
+
0.5
Delay (1/f/4)
_
+
0.5
Vds+
Vqs+
dsqs
drq
r
x+
+
+
Vdr+
Vqr+
x Vmagnitudepositive sequence
Vdr
Vqr
VaVbV
c
dsq
s
drqr
Filter
Sliding windowfilter
Figure 2-6. Positive-sequence extraction algorithm
Figure 2-8 shows the algorithm performance when an unbalanced fault condition
takes place at t=0.02 sec (Figure 2-7). The data used for this example is given by
Equation 2-2.
Figure 2-7. Voltage waveforms for an unbalanced fault event
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Figure 2-8. Response of the positive-sequence extraction algorithm. A) Positive sequenceusing and 1 cycle filters. B) Positive sequence using Vdrwith 1 cycle filter
The meaning of the different plotted variables is the following:
Vpositive-sequence magnitude is the output of the positive-sequence extraction algorithm. Asexpected, its time response is only one quarter of a cycle. However, the transientresponse is very abrupt an uneven.
Vpositive-sequence magnitude (1/2 cycle filter) is the filtered signal of Vpositive-sequence magnitude usinga half cycle sliding window filter.
Vpositive-sequence magnitude (1 cycle filter) is the filtered signal of Vpositive-sequence magnitude using aone-cycle sliding window filter. Its transient response is the slowest but at the sametime the smoothest among the three signals.
Vdr filtered is the filtered signal of Vdr . The one cycle sliding window filter (alsocalled moving average) rejects all harmonics. Therefore there is no need to use theVds+ and Vqs+ calculator to extract the positive sequence. However its transientresponse is not as smooth as the Vpositive-sequence magnitude (1 cycle filter) one.
Real Power Calculation Using dq Components
As shown in Appendix A Parks transformation matrix is not unitary
( [ ] [ ] 1 dqot
dqo TT ) and therefore is not power invariant.
The total instantaneous power in abc quantities can be transformed into q-d-o
quantities as shown in Equation 2-6.
A B
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This relationship between dqo quantities and the instantaneous power is later used
in the control system to determine the amount of direct-current component ( drI ) needed
to meet the power fluctuation requirements.
[ ] [ ]
[ ] [ ][ ] [ ]
[ ]
( )ooqrqrdrdr
o
qr
dr
oqrdr
o
qr
dr
dqo
t
dqooqrdr
o
qr
dr
dqo
t
o
qr
dr
dqo
c
b
a
t
c
b
a
ccbbaaabc
IVIVIV
I
I
I
VVV
II
I
TTVVV
I
I
I
T
V
V
V
T
I
I
I
V
V
V
IVIVIVP
++=
=
=
=
=++=
3
1
2
3
3
100
02
30
002
3
11
11
(2-6)
Phase Locked Loop
The phase angle of the utility voltage () is of vital importance for the operation of
most of the advanced power electronic devices connected to the electric utility, since it
has a direct effect on their control algorithms.
A simple and fast method to obtain the phase angle of the utility voltage is to use
Clarkes transformation as shown in Equation 2-7.
=
=
ds
qs
c
b
a
qs
ds
X
X
X
X
X
X
Xarctan
2
3
2
30
2
1
2
11
3
2 (2-7)
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However, this approach is not robust since it is very sensitive to system
disturbances. The phase angle distorts as the utilitys voltage becomes affected by
different power quality events, such as voltage unbalance, voltage sags, frequency
variations, etc.
Figure 2-9 shows the voltages phase angle under unbalanced conditions using
Equation 2-7. The angle distortion is due to the negative sequence component of the
unbalanced three-phase system.
Figure 2-9. Distortion of phase angle due to a negative sequence component
In order to lock the phase angle of the utility voltage in a robust way, a phase
locked loop (PLL) was used.
Assuming a balanced three phase system, the control model of the PLL was
obtained using Parks transformation as shown in Equation 2-8.
=
=
=
)240cos(
)120cos(
)cos(
21
21
21
)240sin()120sin()sin(
)240cos()120cos()cos(
3
2
21
21
21
)240sin()120sin()sin(
)240cos()120cos()cos(
32
***
***
***
***
wtV
wtV
wtV
V
V
V
V
V
V
c
b
a
o
qr
dr
(2-8)
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Where * is the PLL phase angle output, is the utilitys phase angle, anddt
dw = .
Thus, if(t=0)=0, we can substitute wt for(t) and obtain
=
)240cos(
)120cos()cos(
21
21
21
)240sin()120sin()sin()240cos()120cos()cos(
3
2 ***
***
V
VV
V
VV
o
qr
dr
(2-9)
Using trigonometric identities, Equation 2-9 results in
=
=
0
)sin(
)cos(
0
)sin(
)cos(*
*
VV
V
V
V
o
qr
dr
(2-10)
Where is the error between the utility angle and the PLL output. If the is set to
zero, Vdr=V and Vqr=0. Therefore, it is possible to lock the utility angle by regulating Vqr
to zero without needing any information regarding the magnitude of the utility voltage.
Figure 2-10 shows the details of the PLL algorithm used in our study. The limits of
the controller integrator and the limiter were 30 rad/sec. Thus, the PLL was able to track
the system frequency as long as this was within 26030 rad/sec or 55 to 65 Hz range.
To use linear control techniques for the design and tuning of PLL controller, it was
assumed that:
For small values of, the term sin () behaved linearly, i.e., sin() . Wref was assumed to be a constant perturbation. Limiters behave linearly for small control actions, and therefore can be removed.
abd
dsq
s
Vds
Vqs
dsq
s
drq
r
Vdr
Vqr
Va
Vb
Vc
Ki
Kp +
+
30
-30
s
1
30
-30
+
+
Wref
=2f
s
1
Figure 2-10. PLL diagram
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Figure 2-11 shows the PLL control loop after eliminating the non-lineal terms.
Ki
Kp +
+
s1
s
1
-
+
PLL controller Plant transfer
Function
Control
action
Figure 2-11. PLL simplified model
The closed loop transfer function ofFigure 2-11 determines the dynamic
characteristics and stability of the system, and can be expressed as
Ip
Ip
KsKsKsKH++
+==2
*
(2-11)
The control system (Kp and Ki) was designed to satisfy two performance
objectives
< 10% overshoot Settling time inside the 2% band error lower than 2 secs
The criterion to select the settling time was a tradeoff between high distortion
rejection and tracking of normal system frequency variations.
The PLL closed loop transfer function was compared to a standard second order
transfer function to determine the regulators gains. The obtained values were
485.27.022
1.827.0
44
sec2t
)overshoot5%for(7.0
22
2
s
===
=
=
==
=
=
np
s
nI
K
tK
Figure 2-12 shows the systems closed-loop step response for two different PI
regulators.
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The originally designed regulator did not meet the system requirements due to the
effect of the zero introduced by the PLL regulator. This additional zero increased the
overshoot, but it had very little influence on the settling time. Thus, it was necessary to
tune the original regulator gains in order to meet the system requirements.
Figure 2-12. PLL system step response
Figure 2-13 shows the root locus of the single-input single output PLL system for
the two regulators.
Figure 2-13. Root locus for two different regulator gains
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Figures 2-14 and 2-15 show the PLL system response to a negative sequence
condition (V2=16.6%) and a system frequency excursion (w=260+30 rad/sec).
Figure 2-14. PLL system response to an unbalanced system condition
Figure 2-15. PLL system response to a frequency excursion. A) Angle. B) PLL error.
Control Algorithm Design
Parks transformation was used to model the systems equations to facilitate the
design of the control system. The usage of a rotating reference frame had the following
advantages:
Improvement of the steady-state performance of the current controllers:Sinusoidal signals were transformed into dc components, and accordingly it ispossible to achieve small signal errors.
High bandwidth current controllers: Feedback signals and reference signalswere not sinusoidal, but dc.
A B
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Decoupling of active and reactive power: This was very useful when trying tocontrol voltage at the point of coupling while meeting the system requirements interms of power fluctuations.
Figure 2-16 shows the overall system topology as well as the sign notation that was
used in the control system design. In general, power flowing out of the inverter will be
considered to be positive. The objective was to smooth out wind-power fluctuations using
the power stabilizer as a buffer. The energy-storage voltage was expected to change in
order to accommodate for those changes in wind power.
Iwind
Vpcc
Vf
Iinv Vinv
VdcVchopper Vstorage
IchopperCdcLfLxfrm
Cf
WIND
FARM
UTILITY
SYSTEM
Xsource
Transformer
equivalent impedance
Filter
Inverter DC link bus Chopper
ESS
P + Figure 2-16. System description
Inner regulators
Inverter system model. For the following set of equations, it was assumed that the
inverter behaved as an ideal controllable voltage source, neglecting the effects of the
current harmonics. Systems non-linearities, such as saturation or dead-time effects were
taken into consideration later on in the design.
The capacitor filter was neglected in the analysis, since the filter current
represented a small portion of the inverters current.
The system can then be represented as shown in Figure 2-17.
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Vpcc a R L Vinv a
VDC LINKC
Vpcc b R L Vinv b
Vpcc c R L Vinv c
Iinv a
Iinv b
Iinv c
Figure 2-17. Simplified system model
The system equations for the simplified model are
+
+
=
pcca
pcca
pcca
invc
invb
inva
invc
invb
inva
invc
invb
inva
V
V
V
I
I
I
dtdL
I
I
I
R
V
V
V
(2-12)
Applying Parks transformation we get
[ ] [ ] [ ] [ ]
+
+
=
opcc
qrpcc
drpcc
dqo
oinv
qrinv
drinv
dqo
oinv
qrinv
drinv
dqo
oinv
qrinv
drinv
dqo
V
V
V
T
I
I
I
Tdt
dL
I
I
I
TR
V
V
V
T1111 (2-13)
[ ] [ ] [ ] [ ] [ ] [ ]
+
+
=
opcc
qrpcc
drpcc
dqodqo
oinv
qrinv
drinv
dqodqo
oinv
qrinv
drinv
dqodqo
oinv
qrinv
drinv
V
V
V
TT
I
I
I
Tdt
dLT
I
I
I
TRT
V
V
V111 (2-14)
[ ][ ]
[ ]
+
+
+
=
opcc
qrpcc
drpcc
oinv
qrinv
drinv
dqo
oinv
qrinv
drinv
dqo
dqo
oinv
qrinv
drinv
oinv
qrinv
drinv
V
V
V
I
I
I
dt
dT
I
I
I
dt
TdTL
I
I
I
R
V
V
V1
1
(2-15)
[ ][ ]
[ ] [ ]
+
+
+
=
opcc
qrpcc
drpcc
oinv
qrinv
drinv
dqodqo
oinv
qrinv
drinv
dqo
dqo
oinv
qrinv
drinv
oinv
qrinv
drinv
V
V
V
I
I
I
dt
dTTL
I
I
I
dt
TdTL
I
I
I
R
V
V
V1
1
(2-16)
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[ ][ ]
+
+
+
=
opcc
qrpcc
drpcc
oinv
qrinv
drinv
oinv
qrinv
drinv
dqo
dqo
oinv
qrinv
drinv
oinv
qrinv
drinv
V
V
V
I
I
I
dt
dL
I
I
I
dt
TdTL
I
I
I
R
V
V
V 1
(2-17)
Where
[ ]
dt
d
dt
d
dt
d
dt
Td dqo
=
=
=
0)240cos()240sin(
0)120cos()120sin(
0)cos()sin(
1)240sin()240cos(
1)120sin()120cos(
1)sin()cos(1
(2-18)
It can be shown that
[ ] [ ]
=
=
=
=
000
00
00
000
001
010
0)240cos()240sin(
0)120cos()120sin(
0)cos()sin(
21
21
21
)240sin()120sin()sin(
)240cos()120cos()cos(
3
2 ***
***
1
dt
TdT
dqo
dqo
(2-19)
Thus, the equations for the simplified model in the d-q plane are
+
+
+
=
opcc
qrpcc
drpcc
oinv
qrinv
drinv
oinv
qrinv
drinv
oinv
qrinv
drinv
oinv
qrinv
drinv
V
V
V
I
I
I
dt
dL
I
I
I
L
I
I
I
R
V
V
V
000
00
00
(2-20)
The zero-sequence component can be removed, since the system is a three-phase
three-wire inverter with the DC link bus isolated from the AC side (the DC link mid-
point will not be tapped to neutral). Removing the zero sequence we obtain
drinvqrpcc
qrinv
qrinvqrinv
qrinvdrpcc
drinv
drinvdrinv
ILVdt
dILIRV
ILVdt
dILIRV
+++=
++=
(2-21)
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Equation 2-21 can be represented as a coupled electrical system as shown in Figure
2-18.
R LV
pcc drV
inv dr
Iinv dr
LIinv qr
R L
Vpcc qr
Vinv qr
Iinv qr
LIinv dr
Figure 2-18. Electrical representation of the dq components. A) Direct circuit. B)Quadrature circuit.
Using Laplaces transformation we can re-write the equations as Equation 2-22.
( )
( ) )()()()(
)()()()(
sILsVsILsRsV
sILsVsILsRsV
drinvqrpccqrinvqrinv
qrinvdrpccdrinvdrinv
+++=
++=
(2-22)
Thus, the block diagram of the system is represented in Figure 2-19.
Vpcc dr
Vinv dr
Iinv dr
LsR +
1+
-
L
L
Vinv qr
Iinv qr
LsR +
1+
-
Vpcc qr
+
-
Figure 2-19. System model block diagram
A
B
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The inverters critical control variable was the inverters current. This was due to
the fact the outer control loops, such voltage regulators, power regulators, etc, were based
on the inner current regulators. That was why the current controllers were designed to
meet two basic requirements, which were high accuracy and high bandwidth.
The inverters terminal-voltage needed to generate the desired inverter current can
be determined as
drinvqrpccdropdrinvqrpcc
qrinv
qrinvqrinv
qrinvdrpccdropqrinvdrpcc
drinv
drinvdrinv
ILVVILVdt
dILIRV
ILVVILVdt
dILIRV
qr
dr
++=+++=
+=++=
(2-23)
The voltage drop due to the filter inductance was compensated using a PI
controller. Figure 2-20 shows the inveters current controller implementation for the
system given in Equation 2-23.
Vpcc dr
Vinv dr
Iinv dr
LsR +
1+
-
L
L
Vinv qr
Iinv qr
LsR +
1+
-
Vpcc qr
+
-
SYSTEM MODEL
+
-+
Vdrop dr
++
+
Vdrop qr
Ki
Kp +
+
s1
+
-
Ki
Kp +
+
s
1
+
-
Iinv dr
Iinv qr
Iinv dr ref
Iinv qr ref
L
L
CURRENT REGULATORS
drpccV
qrpccV
Figure 2-20. Inverter current regulator-system model block diagram
The character ^ over a constant or variable indicates that the quantity is estimated,
and therefore subject to measurement errors.
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To design the current regulator gains, cross-coupling factors were assumed to
cancel each other out. Under these conditions, the simplified current regulator block
diagram is shown in Figure 2-21.
Iinv dr
LsR +
1
Iinv qr
LsR +
1
SYSTEM MODEL
Ki
Kp +
+
s
1
+
-
Ki
Kp +
+
s
1
+
-
Iinv dr
Iinv qr
Iinv dr ref
Iinv qr ref
CURRENT REGULATORS
Figure 2-21. Inverter current regulator-system model simplified block diagram
Figure 2-21 shows that:
The system behaves linearly, and therefore linear control techniques can be used to
determine the regulators gains. Both regulators are identical.
Only an estimation of L and R (filter inductance + transformer equivalentimpedance) are needed to design the current regulator.
Given the filter/transformer characteristics in p.u., the closed-loop transfer function
ofFigure 2-22 is shown in Equation 2-24.
Ki
Kp +
+
s
1
+
-
Iref
LsR +
1 IControl Action
Figure 2-22. Simplified current control diagram
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( )Ip
Ip
ref KsKRLs
KsK
I
IsH
+++
+==
2)( (2-24)
Using the following system data, the transfer function is given in Equation 2-25.
X=Xtransfomer+Xfilter=5%+10% = 0.15 L= 400 H X/R=10 R=0.015 Note: More on the system parameters can be found in the per-unit mode section.
( )Ip
Ip
KsKs
KsKsH
+++
+=
015.00004.0)(
2(2-25)
The Figure 2-23 shows the system step response for two different current regulator
gains.
Figure 2-23. Current regulator step response
Even though the current regulator with the highest gains had a faster settling time,
the control action required to obtain such a response doubled the regulator with the
lowest gains. To avoid possible system saturations the control action was kept below 1
pu.
The best PI controller performance was achieved when the plants dominant pole
was cancelled by the controller (Equation 2-26). Thus, the zero at -p
I
K
K was assigned to
the time constant of the plant, which was,L
R
K
K
p
I = .
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s
K
KsK
s
KKPI
p
Ip
Ip
+
=+= (2-26)
The synthesis was done by selecting the integral time constant of the PI equal tothat of the load. For our study the selected values were
1
5.37
=
==
p
I
K
L
RK
Chopper system model. The analysis of the chopper system was less complex than
the inverter one, since no transformations were involved. Again, it was assumed that the
chopper behaved as an ideal controllable voltage source and therefore the effects of the
current harmonics were neglected.
Vchopper Vstorage
Ichopper
Figure 2-24. Chopper equivalent system
The system equations for the chopper equivalent circuit (Figure 2-24) are given in
Equaion 2-27.
dt
dILVV
Vdt
dILV
chopper
storagechopper
chopper
chopper
storage
=
+=
(2-27)
The choppers terminals voltage needed to generate the desired chopper current
can be determined as
dropstoragechopper VVV = (2-28)
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The voltage drop due to the chopper inductance was compensated using a simple P
controller. The gain of the controller was found by converting the continuous system into
discrete time system as shown in Equation 2-29.
t
LKIKVV
dt
IILV
dt
ILVV
LchopperLstoragechopper
chopperchopper
storage
chopper
storagechopper
ref
==
=
=
where
)(
(2-29)
Where KL is the regulators gain and t is half of the sampling time period.
Figure 2-25 shows the implementation of the choppers current regulator.
Ichopper
+-
KL
Vstorage
-+
Ichopper ref
Vchopper
Figure 2-25. Chopper current controller
Outer regulators
There were a total ofthree controllable currents, which consisted of Ichopper_ref,
Iinvdr_ref, and Iinvqr_ref.. However, there werefourvariables that needed to be controlled,
which were voltage at the dc link bus, voltage at the point of common coupling, voltage
at the energy storage system, and wind farm power fluctuation. Table 2-1 shows how
these variables were assigned to the respective current regulators.
Table 2-1. Outer regulator assignationInner current
regulator
Variable to be
controlled CommentsIinv dr ref Vstorage, Pwind The direct current component will be responsible
for controlling the state of charge of the ESSand for smoothing the wind farm output power
Iinv qr ref Vpcc The quadrature current component will bedeployed for voltage regulation purposes
Ichopper ref Vdc link The chopper current will regulate the DC link busvoltage.
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DC link Voltage regulator. The DC link bus was the bridge between the energy
storage system (chopper) and the inverter. Therefore, it was a critical variable in the
overall system. Poor DC voltage regulation could bring the system down, since the
inverter and chopper would not be able to meet their respective voltage requirements.
The DC link system can be mode