UFDC Home  myUFDC Home  Help 



Full Text  
ADVANCED POWER ELECTRONIC FOR WINDPOWER GENERATION BUFFERING By ALEJANDRO MONTENEGRO LEON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005 Copyright 2005 by Alej andro Montenegro Le6n To my brother ACKNOWLEDGMENTS I would like to Birst express my gratitude to Charles Edwards, the principle engineer at S&C Electric Co. (Chicago, 1L) for his patience and the knowledge he shared throughout the proj ect. 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 Domij an (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 Einally 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 proj ect TABLE OF CONTENTS page ACKNOWLEDGMENT S .............. .................... iv LI ST OF T ABLE S ................. ................. viii............ LIST OF FIGURES .............. .................... ix AB STRAC T ................ .............. xvii CHAPTER 1 INTRODUCTION ................. ...............1.......... ...... WindEner gy Outlook .............. ...............1..... Electrical Issues .............. .... ........ .............. Solutions to WindPower Fluctuations ................. ...............9................ State of the Art. ................ .......... .................. .........................9 Obj ective ................. ...............11................. 2 SY STEM DESIGN ................. ...............14........... .... Introducti on ................. ...............14................. Control Scheme ................ ...... ...............1 Positive Sequence Calculation .............. .... ...............14. Real Power Calculation Using dq Components .............. .....................2 Phase Locked Loop .............. ...............21.... Control Al gorithm Design ................. ...............26........... .... Inner regulators .............. ...............27.... Outer regulators ................. ...............35................. PerUnit System Model .............. ...............56.... Inverter OutputFilter Design ................. ...............56........... .... Harmonic content ................. ...............57.......... ..... Switching frequency ................. ...............60................. Passive filter design............... ...............61. Passive filter damping .............. ...............65.... DirectCurrent Link Capacitor Design .............. ...............68.... Energy Storage Design ................. ...............69........... .... Chopper Inductor Design .............. ...............71.... PerUnit System Model Summary............... ...............72 Simulated Model ................. ...............73................. 3 SY STEM DESCRIPTION ................. ...............78........... .... Sy stem Overview............... ...............78 Electrical Network Model ................. ...............80........... .... Synchronous Machine .............. ...............80.... Voltage regulation .............. ...............8 1.... Prim e M over ................... ........ ....... .... ...............8 1. Synchronous Machine Control Algorithm .............. ...............83.... WindFarm Model .............. .... ...............87.. WindFarm Control Al gorithm............... ...............9 WindFarm PowerFactor Correction............... ...............9 WindFarm SoftStart System .............. ...............94.... Power Stabilizer................... ... .. .........9 PowerStabilizer Hardware Description............... ..............9 Interface board............... ...............99. Digital signal processor .....__.....___ ..........._ ............10 Fieldprogrammable gate array .............. ...............106.... Intelligent power module .............. ...............107.... Isolation interface circuit............... ...............108 Power Stabilizer Software Description .............. ...............108.... Description of DSP program ............_.. ....__.....__ ...........10 FPGA program description ................. ...............114................ 4 SY STEM PERFORMANCE ................. ......... ...............121 ..... System D ata ............... .. .......... ...............121...... Power Stabilizer Transient Response .............. ...............121.... DirectCurrent Link Voltage Control .............. ...............121.... Reactive Current Control ................. ...............123................ Passive Filter Performance .............. ...............126.... Voltage Regulation ................ ...............127................ System Losses................. ...............12 Power Limiter Results .............. ........... ..............13 Power Limiter 1 (High Pass Filter) ............... ...............131... Power Limiter 1 (Adaptive High Pass Filter) ................. .........................136 Power Limiter 2 ................... .......... ...............138...... Power Limiters Comparison Study ................. ...............145............... 5 SUMMARY ................. ...............148................ Conclusions............... ..............14 Further W ork .............. ...............150.... APPENDIX A MATHEMATICAL TRANSFORMATIONS ................. .............................151 B MATLAB CODES .............. ...............158.... C POWER STABILIZER CONTROL MODULES .............. ...............168.... LIST OF REFERENCES ................. ...............172................ BIOGRAPHICAL SKETCH ................. ...............176......... ...... LIST OF TABLES Table pg 11 Technical specifications oflIEC and IEEE ......____ ..... ... .__ ........_........ 12 Windfarm outputpower requirements .....__.....___ ..........._ ............. 13 Largescale windpower outputleveling proj ects ...._ ................ .. .............10 14 Conceptual windpower filtering proj ects ................. ........._ ...... 12___ ... 15 Basic system configurations ............ .....___ ...............13.. 21 Outer regulator assignation .............. ...............35.... 22 Rateofchange limits or PPA for a 10 MW wind farm ................... ...............4 23 Generalized Harmonics of linetoline voltage .............. ...............59.... 24 L filter vs. LCL filter............... ...............61. 25 LC L filter design .............. ...............64.... 26 LCL equivalent impedance with damping resistance .............. ....................6 27 Perunit sy stem ............ ..... .._ ...............65... 28 Perunit system parameters .............. ...............73.... 29 Designed system results and simulated system results comparison ......................76 31 Synchronous machine output voltage profile at rated speed ............... .........._....82 32 Alternatives for the power stabilizer controller............... ..............10 33 FPGA code words .............. ...............120.... 41 System parameters............... ..............12 A1 Mathematical transformations summary ................. ...............................157 C1 Control Modules............... ...............168 LIST OF FIGURES Figure pg 11 Windpower output for two wind farms during one month. .................. ...............5 12 Power fluctuation comparison............... ............... 13 Typical power curve of a wind turbine. ............. ...............6..... 14 Windfarm output power vs system frequency. ............. ...............7..... 15 Control strategies along the power curve ................. ...............8......._._. .. 16 Windfarm generation buffering concept .................._...... .........._. .......1 21 Unbalanced system............... ...............15. 22 Space vector trajectory of an unbalanced system in the dqo plane ...................... 16 23 Space vector traj ectory proj section over the dq plane ........._._ ...... .._............16 24 Direct and quadrature components of an unbalanced system .............. ..................17 25 Representation of an unbalanced system in the frequency domain......................... 17 26 Positivesequence extraction algorithm .............. ...............19.... 27 Voltage waveforms for an unbalanced fault event ................. ....._._ ............19 28 Response of the positivesequence extraction algorithm ................. ................. .20 29 Distortion of phase angle due to a negative sequence component ................... .......22 210 PLL diagram............... ...............23 211 PLL simplified model ................. ...............24................ 212 PLL system step response .............. ...............25.... 213 Root locus for two different regulator gains .............. ...............25.... 214 PLL system response to an unbalanced system condition ................... ...............26 215 PLL system response to a frequency excursion .............. ..... ............... 2 216 System description .............. ...............27.... 217 Simplified system model ........._.._.. ...._... ...............28... 218 Electrical representation of the dq components ........._.._.. ......._ ........._.....30 219 System model block diagram .............. ...............30.... 220 Inverter current regulatorsystem model block diagram ................ ................ ...31 221 Inverter current regulatorsystem model simplified block diagram ................... .....32 222 Simplified current control diagram .............. ...............32.... 223 Current regulator step response ......... ........_____ ..... ........ .......33 224 Chopper equivalent system .............. ...............34.... 225 Chopper current controller .............. ...............35.... 226 Powers' definition ............ __.. ......... ...............36.... 227 System model .............. ...............37.... 228 DC link equivalent system block diagram .............. ...............37.... 229 DC link simplified system block diagram ................. ....___ .............. .....3 230 DC link voltage regulator step response .............. ...............38.... 231 Simplified system model ................. ...............40.____..... 232 Source impedance voltage drop .............. ...............41.... 233 Transfer functions of inverter' s quadrature current component. ................... ..........42 234 Transfer functions of inverter' s direct current component ................. ................ .42 235 Voltage regulator system block diagram ................. ...............44........... .. 236 Positive sequence extraction algorithm equivalent system ................ ................ .44 2 37 Voltage regulator detailed block diagram .............. ...............45.... 2 38 Voltage regulator simplified control diagram .............. ..... ............... 4 2 39 System response to a 5% change in voltage reference ................. .....................45 240 Adaptive control scheme .........__.._ ....._... ...............46..... 241 Power Regulator general control scheme ........._..._.. ....._.._ ......._._. .......4 242 Power limiter 1. Control block diagram ........._..._.. ....._.._ ..................4 243 Power limiter 1. Performance using different cutoff frequencies (unlimited power and energy) ........._..._. ....._... ...............49..... 244 Power limiter 1. Performance using different cutoff frequencies (Pinverter=1.0O MW and Einverter=+8.5 MJ) .............. ...............49.... 245 Power limiter 2. Limiters details ....__. ...._.._.._ ......._.... ..........5 246 Power limiter 2. Control block diagram ........._.._.. ....._.. ......._.._........5 247 Power limiter 2. Compensation performance............... ..............5 248 Power limiter 2. Inverter response for a sampling time of 2 seconds .....................52 249 Power limiter 2. Inverter response for different power ratings. Sampling time 2 second s .............. ...............53.... 250 Power limiter 2. Inverter response for different ESS sizes. Sampling time 2 second s .............. ...............53.... 251 Power limiter 3. Control block diagram ........._.._.. ....._.. .......__. .......5 252 Power limiter 3. Compensation performance............... ..............5 253 Power limiter 3. Inverter response for a sampling time of 2 seconds............._.._. ...55 254 Inverter topology .............. ...............57.... 255 Linetoline and linetoneutral voltage of a three phase inverter...........................57 256 RMS Linetoline voltage harmonic spectrum ................. .......... ................5 8 257 Static Synchronous Generator diagram ................. ...............59........... ... 258 LC L filter topology .............. ...............61.... 259 LCL equivalent block diagram ................. ...............62........... ... 260 Single phase equivalent filter model at the fundamental frequency .......................62 261 Single phase equivalent filter model at the hth harmonic .............. ....................63 262 LCL equivalent impedance with damping resistance .............. .....................6 263 Single phase harmonic generator equivalent circuits ................. ......................66 264 LCL gain frequency response .............. ...............67.... 265 Inverter frequency analysis .............. ...............67.... 266 Capacitor Voltage vs. Energy Storage .............. ...............70.... 267 ES SChopper topology ................. ...............71................ 268 Equivalent circuit for maximum current ripple calculation .................. ...............72 269 System overview .............. ...............74.... 270 Perunit electric system model .............. ...............74.... 271 Power Stabilizer Control Scheme .............. ...............75.... 31 Equivalent system model .............. ...............79.... 32 DC genset............... ...............83 33 Two single quadrant chopper circuit ................. ...............83............... 34 Synchronous generator control system .............. ...............84.... 35 Frequency deviation .............. ...............85.... 36 DCGEN set control scheme ................ ...............85........... ... 37 System frequency response for Af=1Hz ................. ...............86........... .. 38 Frequency control equivalent system ................. ...............87........... ... 39 Equivalent model frequency response for Af= 0.01666 pu ................. ...............88 310 Dynamic model used for transient studies .............. ...............88.... 311 Static model used for steadystate studies............... ...............88 312 Windfarm model .............. ...............89.... 313 Windfarm controller ................. ...............90........... .... 314 Windfarm power regulator & current regulator step response (AP=100%) ..........91 315 Induction generator PQ curve .............. ...............92.... 316 Windfarm PF correction capacitor bank ................. ...............93............... 317 PF correction capacitor bank current waveforms ................. ................ ...._.93 318 Capacitor bank impedance frequency scan .............. ...............94.... 319 Machine control scheme operating states ................. ...............................95 320 Electric power system startup .............. ...............96.... 321 Detail of the transition from startup mode to run mode ................. ................ ..96 322 Power Stabilizer system overview .............. ...............97.... 323 Interface board overview............... ...............10 3 24 AC voltage scaling circuit (input [1000+1000V], output [0 +3V]) ................... ..101 325 DC voltage scaling circuit (input [0 +1000V], output [0 +3V]) ................... ........101 326 CT current scaling circuit (input [5 +5A], output [0 +3V]) ................. ...............101 327 LEM current scaling circuit (input [0.36 +0.36A], output [0 +3V])....................101 328 Power supplies' voltage monitoring ................. ...............102............ 329 System' s critical signals during turn on ......___ ..... .._.. ....._._........10 330 System' s critical signals during turn off ........._._ ...... .__ .. ...._._.......10 331 Darlington drivers .............. ...............104.... 332 IPM status signals interface circuitry ..............._ ......... ........... .........0 333 DAC circuit ................. ...............105............... 334 DSP builtin PWM output performance vs. FPGA ................. ............ .........107 335 IMP power circuit configuration .....__.....___ ..........._ ...........10 336 Isolated interface board ............ ..... .__ ...............109.. 338 Power stabilizer control algorithm sampling rates ......____ ..... ...___...........110 337 Interconnections between the different subsystems of the power stabilizer........ 111 339 Power stabilizer control stages ................. ...............113........... ... 3 40 Power stabilizer startup sequence ................. ...............113.............. 341 FPGA system overview ................. ...............116............... 3 42 Up/Down counter ................. ...............117............... 343 PWM generator ................. ...............117............... 3 44 One phase deadtime generator detailed diagram ................. .......................119 345 Deadtime generator' s waveforms ................. ...............119........... ... 346 W watchdog logic .............. ...............120.... 41 DC link voltage response for different Kp gains............... ...............121. 42 DC link voltage response for different Ki gains .............. .....................2 43 Iqrer command step change from 0.5 to 0.5 A per unit. Integral gain effect ........123 44 Iqrer command step change from 0.5 to 0.5 A per unit. Proportional gain effect ................. ...............124................ 45 Iq current regulator output for different Kp .............. ...............124.... 46 Iqref command step change from 0.5 to 0.5 and back to 0.5 A per unit ............124 47 Power stabilizer harmonic inj section response for Ki=18 and Kp=1 ................... ..125 48 Current regulator frequency response .............. ...............126.... 49 Frontend inverter current waveform ................. ...............126........... ... 410 Frequency spectrum of the LCL currents ........._.._.. ....._.. ........._.._.......2 411 Simplified system description ...._.._.._ ..... .._._. ...._.._ ...........2 412 Power stabilizer voltage regulation performance ........._._. .........._._............128 413 Energy storage charge/discharge cycle .............. ...............129.... 414 Control scheme with a losses compensation term ................. ........... ...........129 415 Power stabilizer equivalent system .............. ...............130.... 416 Windpower conditions under study .............. ...............130.... 417 Measured and modeled high pass filter results for Ke=0.0064 W/J, fat off0.005 Hz ............ ..... .._ ...............132.. 419 Measured high pass filter performance for different cutoff frequencies. System parameters Ke=0.0064 W/J............... ...............134.. 420 Modeled high pass filter performance for different cutoff frequencies. System parameters Ke=0.0064 W/J............... ...............135.. 421 Measured high pass filter performance for different energy storage sizes. System parameters, Ke=0.0064 W/J, fcutoff0.005 Hz. ............. .....................13 422 Cutoff frequency traj ectory of the adaptive high pass filter for a given energy deviation ................. ...............136................ 423 Measured adaptive high pass filter performance for different Kf' s. System parameters, Ke=0.0064 W/J, fcutofforigin=0.005 Hz..........._.._.. .......__. ..........137 424 Measured adaptive high pass filter performance for different energy storage sizes. ............. ...............137.... 425 Multiple sampling concept. .............. ...............139.... 426. Measured and modeled power limiter 2 results for Ke=0.0064, RR=2 MW/minute, A=0.3 MW/minute, I=1MW/2 seconds fcuton0.005 Hz. ................140 427 Measured power indexes activity. System parameters: Ke=0.0064 W/J, RR=2 MW/minute, A=0.3 MW/minute, I=1 MW/2 seconds, and fs=10Hz. ................... .141 428 Measured power limiter 2 response to different K, System parameters: RR=2 MW/minute, A=0.3 MW/minute, I=1MW/2 seconds, and fs=10Hz ................... ...142 429 Measured power limiter 2 response to different ramp rate limits. ........................142 430 Measured power limiter 2 response to different average power fluctuation lim its. ........... ........... ...............143.... 431 Effect of linear interpolation on the average power fluctuation index activity. The sampling time of the original windpower data is 2 seconds ................... .......144 432 Measured power limiter 2 response to different instantaneous power fluctuation lim its ................. ...............144................ 433 Measured power limiter 2 response to different sampling frequencies.................145 434 Measured synchronous machine output power for the different power limiter control schemes ................. ...............146......... ...... 435 Measured synchronous machine output power for the different power limiter control schemes. ............. ...............147.... 436 Frequency regulator output for the different power limiters. .............. .... ...........147 A1 Relationships among dsqs, and abc axes .............. ...............153.... A2 Stationary dsqs components in the time domain ........................... ...............153 A 3 Relationship among dsqs and d,gr axes .............. ...............154.... A4 Direct and quadrature components ................. ...............155........... ... A5 Time domain representation of abc and dq components .............. ................... 156 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ADVANCED POWER ELECTRONIC FOR WINDPOWER GENERATION BUFFERING By Alej andro Montenegro Le6n May 2005 Chair: Alexander Domijan, Jr Major Department: Electrical and Computer Engineering As the cost of installing and operating wind generators has dropped, and the cost of conventional fossilfuelbased generation has risen, the economics and political desirability of more windbased energy production has increased. High windpower 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 shortterm windpower variability, using advanced power electronic devices combined with energystorage 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. We first reviewed DQ transformations with emphasis on modeling of the system and control algorithm. System components were then designed using criteria similar to those used to design mediumvoltage power products. We tested a proofofconcept for performance of the power converter in a scaled down isolated system using real windpower data. Tests were conducted under realistic system conditions of windpenetration level and energystorage 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 windfarm model and the synchronous machine' s governor to gain an insight into the model system's 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. XV111 CHAPTER 1 INTTRODUCTION WindEnergy 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 windenergy 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 kilowatthour credit for electricity produced from a wind farm during the first 10 years of operation. This wind energy PTC expired December 3 1, 2003 but will be reinstated through 2005 as part of a maj or tax package (H.R. 1308). * Statelevel renewable energy initiatives, such as the Renewable Portfolio Standard, or green pncmig. 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 world' s growing power demand and the rising prices of conventional fossil fuelbased generation, make the wind power one of the most promising industries in the future. According to the European Wind Energy Association and Greenpeace, no barriers exist for wind to provide 12% of the world' s electricity by 2020. The American Wind Energy Association forecasts that wind power will provide 6% of the US's 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, windpower plants, like all other energy technology, have some drawbacks that should be mentioned. These problems can be divided into maj or 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 a moderately quiet room. Research in aeroacoustics is still being carried out to further reduce noise from wind on the blades. * Bird death: Wind turbines are often mentioned as a risk to birds, and several international tests have been performed. The general conclusion is that birds are seldom bothered by wind turbines. Studies show that for example, overhead power pole lines are far more hazardous for birds than wind turbines [2]. * Windtower shadow effect: Wind turbines, like other tall structures cast a shadow on the neighboring area when the sun is visible. It may be irritating if the rotor blades 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. The unit commitment problem is to schedule specific or available generators (on or off) on the utility system to meet the required loads at a minimum cost, subj ect to system constraints. The most conservative approach to unit commitment and economic dispatch is to discount any contribution 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 be forecasted, such as wind power, have to be considered when determining the amount of operating reserve to carry out. * Electrical issues: These factors are considered in the next section. Electrical Issues Windturbine generatorsystem operation has some negative influence on power systems. This influence on the electric power system depends on wind variations and on windturbine technology. Impacts on the electric power system can be grouped as follows: * Power quality: Voltage variations, flicker, harmonics, powerflow variations * Voltage and angle stability * Protection and control The IEEE 1547 [5] and the IEC 6140021 [6] standards are the bases to evaluating the impact of such windturbine 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, the interconnection itself. It provides requirements relevant to the performance, operation, testing, safety considerations, and maintenance of the interconnection. It includes 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 requirements are universally needed for interconnection of distributed resources (DR), including synchronous machines, induction machines, or power inverters/converters and will be sufficient for most installations. The criteria and requirements are applicable to all DR technologies, with aggregate capacity of 10 MVA or less at the point of common coupling, interconnected to electric power systems at typical primary and/or secondary distribution voltages. MW, and the large one has a capacity of 150 MW. Switching operation Harmonics According to the IEC 6140021 [6, page 9] abstract, The purpose of this part of IEC 61400 is to provide a uniform methodology that will ensure consistency and accuracy in the measurement and assessment of power quality characteristics of grid connected wind turbines (WTs). In this respect the term power quality includes those electric characteristics of the WT that influence the voltage quality of the grid to which the WT is connected. This standard provides recommendations for preparing the measurements and assessment of power quality characteristics of grid connected WTs. Table 11 shows technical specifications for interconnection and power assessment covered in both standards. Table 11. Tec chnical specifications of IEC and IEEE Interconnection system respnseoexursonsPower quality assessment IEEE Voltage Frequency IEC Voltage Voltage fluctuations: Frequency Continuous operation As shown in Table 11, both standards overlooked one of the most significant characteristics of wind farms: its variability (i.e., power fluctuations) [7], the most important ones being * Gusty wind variations having a spectrum of frequencies from 110 Hz. * Shadow effect having a spectrum of frequencies from 12 Hz and producing torque variations up to 30%. * Complex oscillations of the turbine tower, rotor shaft, gear box, and blades with spectrum frequencies from 2100 Hz, and creating torque variations up to 10%. Figure 11 shows actual output power data collected by NREL from two large windpower plants in the United States. The small wind farm has a capacity of about 35 0 0.5 1 1.5 2 2.53 Time (s) x 10 Fiue150 idpwrotu o w idfam uigoemnh(a 03.A coeu Figure 11. Wi ndoe soututfo two wginud ofarm es drn poner month (ay200).A Wind turbine manufactures usually provide power curves (Figure 13) 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. Windoutput 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. 0 A 0 1 2 3 4 5 6 7 8 Tim (s) Xl 44 0 1 2 3 4 5 6 7 8 Tim (s) x 104 Figure 12. Power fluctuation comparison. A) Nominal capacity 35 MW. B) Nominal capacity 150 MW. 600 0+ 10 in, avraevaue Mea vau sre n 4 1 2 4 16 1 v (mis Fiue13 yia oe creo idtrie As the owrfutaeteratvpoereurdbthtubnscngss well,~~~ an terfre olag vritln.ion r xetd seill hntewn ami 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 maj or 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 14 shows the effect of windpower fluctuation on an isolated system with a wind penetration level of 1%. To counter these negative effects, countries and small isolated systems with high windpenetration factors developed special purchase power agreement (PPA) requirements or indexes for windfarm developers (Table 12). 4.10 1 MA; .Lnr'rd Poweri~ D ~ D i 020 250 secnc Fiue .I Windfr oupu poesssemfeuny Table 12. Windfarm outputpower requirements Average (max Ramp Rate dP/dt Instantaneous variation) Netherlands <12 MW per min Denmark <0.1Pnom per min <0.05 Pnom per 60 sec period Hawaii <2 MW per min 1 MW change <0.3MW per 60 per 2 sec sec period scan Germany <0.1Pnom per mi Scotland No limit for Pnom<15 MW/min Pnom/15 for Pnom= [15150] MW/min 10 MW for Pnom>150 MW per min These power requirements guarantee minimum impact on system voltage and frequency control. However, today's wind farms have limited capacity to reduce the rate of change of power, especially the down ramp rate. At high wind speeds (above the rated wind speed), active and stalled pitch controls, among other strategies, can help keep the output power under control. However, modern wind turbines are designed to obtain as much power as possible at low wind speeds (Figure 15), making them very vulnerable to wind variations. Figure 15. Control strategies along the power curve Solutions to WindPower Fluctuations To reduce the effects of windpower 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 energystorage system that could deliver the required power when needed. Work has been done in developing largescale 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 powerfluctuation 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 windpower farms usually consists of ten to several tens of windturbine 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 13 shows some recent projects dealing with output leveling of wind energy conversion. Table 13. Largescale windpower outputleveling proj ects Prj c nm Wn fr. sz Active power reference Project ame md arm ize Energy storage system control scheme Moving Average of wind farm output determined as Subaru Proj ect [9]. Tomamae windpower station. King Island [10]. Energy storage system provided by Pinnacle VRB Oki proj ect by Fuji Electric 1.65 MW *16 (Vestas). 1.5 MW 5 (Enercon) . Total Capacity 30.6 MW 250 kW*3 850 kW*2 Total Capacity 2.45 MW 600 kW *3 Total Capacity 1.8 MW VanadiumRedox Flow Battery PVRB nominal =4.000kW EVRB6.000kWh S inverter=6.000kVA VanadiumRedox Flow Battery PVRB nominal=200kW PVRB shortterm ( 5 minutes)=300~kW PVRB shortterm (10 seconds)=400kW EVRB =1100kWh Flywheel E flywheel = 100 kW 90 sec P inverter flywheel side 1 10kVA P inverter nower system side 150~kVA Pbattery=Pwind average (tAt)Pwind(t) (for At=8 seconds to 8 hours) Isochronous frequency mode over the VRB power range. Speed droop characteristic during instantaneous and shortterm load (>+ 200 kW). Power ramp rate limiting However, smallscale concepts and technical/economic feasibility studies have been proposed (Table 14). Each of these proj ects has a different obj ective (frequency control, power smoothing, load leveling, etc.). However, they all end up using one of the topologies and energystorage systems shown in Table 15, where the flywheel or capacitors may be replaced by some other energystorage medium. Tables 13 and 14 show that the amount of energy needed for windpower 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. The new integrated approach used a shuntconnected voltagesource 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 proofofconcept prototype advancedpower electronic device capable of controlling and smoothing the power fluctuations of a wind farm using an optimal amount of energy. The windpower generation buffering concept is shown in Figure 16. The Power Stabilizer was designed to store excess power during periods of increased windpower generation and release stored energy during periods of decreased generation due to wind fluctuations. We tested the performance of the advanced electronic device on * DCsynchronous machine set * Passive load * DCasynchronous machine set * Windfarm buffer or also called Power Stabilizer Table 14. Conceptual windpower filtering projects Wind farm size Energy storage system 20 MW Zincbromide battery PZBB nominal (charge) =750kW PZBB nominal (discharge)=1500kW EZBB=1500 kWh Maximum power Superconducting magnetic oscillation 2.5 MW energy storage (SMES) 300kW Electric double layer capacitor P ECs =100 kW E Ecs =1.1 kWh Active power reference control scheme Limiting instantaneous power fluctuations based on a 2 seconds interval APinstantaneou (At=2 seconds) 11.3 MW Average power levels over a 2 hour window Paverage(t At=2hours)= 200 kW Active power reference is chosen to control system frequency ESS active power reference is determined by detection power oscillation components using a high pass filter Comments Technical and economical feasibility evaluation [l l] Simulation study [12] Simulation study [13] 6GW 45KW 55kW Redoxflow battery (Regenesys ) E=62004 MWh P=255MW Flywheel E flywheel 12MJ P drive=45kW Lead Acid Battery E battery=35SkWh P converter50kVA Power balancing Feasibility study [14] The active power demand is extracted via a 2nd order Butterworth high pass filter, with a 5mHz bandwidth Power smoothing Practical results [15][16] Practical results [17] Wind% powbr+ Win farm buffer Power Figure 16. Windfarm generation buffering concept Table 15. Basic system configurations Voltage source inverter ESS connected at the DC link side [19][21][24] ESS (flywuheel) ESS connected at the AC side [18][20][22][23][25] Wind Turbine Electric System System configuration 6i Voltage Surce ESS (flywuheel) Current source inverter (shunt connected) [13] Wind TrbineElectric System Current Source Inetr ESS (capacitors) Available options [26] *Compressed air energy storage *Battery storage Energy storage system Electrochemical flow cell systems *Fuel cell/electrolyser/hydrogen systems *Kinetic energy (flywheel) storage *Pumping water CHAPTER 2 SYSTEM DESIGN Introduction One of the most difficult tasks when designing a control algorithm for a power electronic converter is to calculate the regulators' gains. Determination of the controllers' parameters is based on the electric power system they are connected to, and also on the power electronic converter topology. This chapter details the design of the different regulators involved in the control of the Power Stabilizer and also the design of the different components that define its topology. The system design was carried out per unit, so results can be extrapolated to any system size, to facilitate implementation of the control scheme in a Eixedpoint digital signal processor. The system design was also compared to simulation results to assure the correctness of the design methodology used Control Scheme Positive Sequence Calculation Threephase systems are not always balanced, especially during fault conditions, and it is expected to have positive, negative and even zero sequence components. However, for voltage regulation purposes, only the positive sequence component is of importance. Before going into detail on the positive extraction algorithm description, we will explain first where the transformations given in Appendix A fail in coupling the different symmetrical components. Consider the following set of phasors Va = 0.5 0 V, = 1.0 1200 (21) V =1.0 2400 Figure 21 shows the time domain representation of this threephase unbalanced system. 0 08 U 0 002 0.004 0 006 0 008 0 01 0 012 0 014 0.016 0 018 0.02 Time (sec) Figure 21. Unbalanced system If we now calculate the symmetrical components of this unbalanced system, we obtain V, = 0.833,o V2 L0= 0.167/1o (22) Vo = 0. 167,,so 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 22 shows the traj ectory followed by the rotating space vector of the unbalanced system in the dqo plane using Clarke's transformation. This traj ectory is 16 clearly distorted from the ideal one, and the space vector no longer follows a circular path (Figure 23). 0.1  0.1 1::; ~ .:::: 0.2 1 0 1 1 Vds Vqs Figure 22. Space vector traj ectory of an unbalanced system in the dqo plane /1 0ji.5 0.5 0.5 Vds Vqs Figure 23. Space vector traj ectory proj section over the dq plane Figure 24 shows the Vd, and Vqr components (Park' s transformation) of the unbalanced system in the time domain for 6 = 00. ,w dc w_ 2w 4v dc 06  Vqr 0.20' 0 002 0 004 0.006 0 008 0.01 0.012 0 014 0 016 0.018 0 02 Time (sec) Figure 24. Direct and quadrature components of an unbalanced system It is clear that the Vd, component 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 25. The rotating reference frame aligns with the fundamental frequency, w=2xnf, 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. acaxis 0.833 0.167 Figure 25. Representation of an unbalanced system in the frequency domain Thus, it can be concluded that Clarke's and Park' s 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 threephase electric system has positive and negative sequence components Va = Vp cos(wt)+V , cos(wt) 2xi 2xi Vb =~ Vcos(wt )+V ,cos(wt + (23) hp3 3 4xi 4xi Vc = Vp cos(wt )+V ,cos(wt + 3 3 Clarke's transformation can be used to obtain Vds = Vp cos(wt) +V , cos(wt) = Vds +Vyds (24) V=~ V sin(wt)V nsin(wt) = V +V where Vds and V,,z are the dq components of the positive sequence, while V, and V, are the dq 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 Es. (t) = Vd t) Vat (25) V ,s(t)= dst Vqjt 19 These components can now be transformed using the rotating reference frame in order to obtain the positive sequence component. Figure 26 shows the block diagram of the algorithm used to extract the positivesequence component. The same concept could be used if the negative sequence magnitude is needed. dq d~q, V Figure 26. Positivesequence extraction algorithm Figure 28 shows the algorithm performance when an unbalanced fault condition takes place at t=0.02 sec (Figure 27). The data used for this example is given by Equation 22. 0. / /ik, i 0 03 0.035 0.04 06 0.8 0 0 005 0.01 0 015 0 02 0.025 Time (sec) Figure 27. Voltage waveforms for an unbalanced fault event nR~ 1 08 3 4 U) 06 a, n, a 0 04 1,,3 ..: 1 ****: ***)6 Time (sec) 111. Time (sec) Figure 28. Response of the positivesequence extraction algorithm. A) Positive sequence using V/2 and 1 cycle filters. B) Positive sequence using Vdr With 1 cycle filter The meaning of the different plotted variables is the following: * Vpositivesequence magnitude is the output of the positivesequence extraction algorithm. As expected, its time response is only one quarter of a cycle. However, the transient response is very abrupt an uneven. * Vpositivesequence magnitude (1/2 cycle filter) is the filtered signal of Vpositivesequence magnitude USing a half cycle sliding window filter. * Vpositivesequence magnitude (1 cycle filter) iS the filtered signal of Vpositivesequence magnitude USing a onecycle sliding window filter. Its transient response is the slowest but at the same time the smoothest among the three signals. * Vdr filtered is the filtered signal of Vdr The one cycle sliding window filter (also called moving average) rej ects all harmonics. Therefore there is no need to use the Vds+ and Vqs+ calculator to extract the positive sequence. However its transient response is not as smooth as the Vpositivesequence magnitude (1 cycle filter) One. Real Power Calculation Using dq Components As shown in Appendix A Park' s transformation matrix is not unitary (~, t [ dqo ) and therefore is not power invariant. The total instantaneous power in abc quantities can be transformed into qdo quantities as shown in Equation 26. This relationship between dqo quantities and the instantaneous power is later used in the control system to determine the amount of directcurrent component (Idr ) needed to meet the power fluctuation requirements. Pabc = Va la +Vyb .b +V e Ic = V bI b~,I Vd I, V I Vdr V, V, Tdqo 13 q 1 q 2 Idr 01 I 3 / 1 I,+C+1 (26) =2 dr dr+3 7,+ V l Phase Locked Loop The phase angle of the utility voltage (6) 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 Clarke's transformation as shown in Equation 27. 1X 1 1 artnX 27 Xds 2 2 a X rX, 3 X:11 X X, However, this approach is not robust since it is very sensitive to system disturbances. The phase angle 6 distorts as the utility's voltage becomes affected by different power quality events, such as voltage unbalance, voltage sags, frequency variations, etc. Figure 29 shows the voltage's phase angle under unbalanced conditions using Equation 27. The angle distortion is due to the negative sequence component of the unbalanced threephase system. Phase Alng e idea" 0 0005 0.01 0.015 0 02 0.025 0.03 O 035 0.04 Time (sec) Figure 29. 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 Park' s transformation as shown in Equation 28. 6, cos(8*) cos(8* 1200) cos(6* 2400)  V,= sin(8*) sin(8* 1200) sin(6* 2400) yay Irb (28) cos(6 ) cos(6* 1200) cos(6* 2400) V cos(wt) sin(8 ) sin(8* 1200) sin(6* 2400) V co(wt 12400) V co(wt 2400) Where 8* is the PLL phase angle output, 6 is the utility' s phase angle, and w = dBO Thus, if 8(t=0)=0, we can substitute wt for 8(t) and obtain V,.cos(6 ) cos(6* 1200) cos(6* 2400) . Vcos(0) V,,. sin(8 ) sin(8* 1200) sin(6* 2400) V cos(6 12400)(29 V, _Vcos(8 240") 2 Using trigonometric identities, Equation 29 results in V,. cos(8* 8) cos(AO) V,=V in06 V si(O) (210) Where AO is the error between the utility angle and the PLL output. If the AO is set to zero, Vdr=V and Vq,=0. Therefore, it is possible to lock the utility angle by regulating Vq, to zero without needing any information regarding the magnitude of the utility voltage. Figure 210 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 22n60130 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 AO, the term sin (AO) behaved linearly, i.e., sin(AO) A O. *Wrer was assumed to be a constant perturbation. *Limiters behave linearly for small control actions, and therefore can be removed. v v v Wref=271f Figure 210. PLL diagram Figure 211 shows the PLL control loop after eliminating the nonlineal terms. PLL controller Plant transfer Function Figure 211. PLL simplified model The closed loop transfer function of Figure 211 determines the dynamic characteristics and stability of the system, and can be expressed as *K~s +K H : (211) B s2 +Kps +K, The control system (Kp and Ki) was designed to satisfy two performance obj ectives * < 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 rej section 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 regulator' s gains. The obtained values were r = 0.7(for 5% overshoot) ts = 2 sec 4 4 K, =i,, m.72 8. 1 K, =2(m~ = 20.72.85 =4 Figure 212 shows the system's closedloop step response for two different PI regulators. 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 212. PLL system step response Figure 213 shows the root locus of the singleinput single output PLL system for the two regulators. Figure 213. Root locus for two different regulator gains Figures 214 and 215 show the PLL system response to a negative sequence condition (V2=16.6%) and a system frequency excursion (w=2xn60+30 rad/sec). PLL response PLL response 000 ooos ob 15 002 0025 003 0035 Time(sec) Figure 214. PLL system response to an unbalanced system condition Ae (phase angle error) 002 004 006 008 01 012 014 016 018 02 Time(sec) 0 01 02 03 04 05 OB 07 08 09 1 Time (sec) Figure 215. PLL system response to a frequency excursion. A) Angle. B) PLL error. Control Algorithm Design Park' s transformation was used to model the system's equations to facilitate the design of the control system. The usage of a rotating reference frame had the following advantages: * Improvement of the steadystate performance of the current controllers: Sinusoidal signals were transformed into dc components, and accordingly it is possible to achieve small signal errors. * High bandwidth current controllers: Feedback signals and reference signals were not sinusoidal, but dc. *Decoupling of active and reactive power: This was very useful when trying to control voltage at the point of coupling while meeting the system requirements in terms of power fluctuations. Figure 216 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 obj ective was to smooth out windpower fluctuations using the power stabilizer as a buffer. The energystorage voltage was expected to change in order to accommodate for those changes in wind power. WIND UTILITY FARM SYSTEM Transformer Inverter DC link bus equivalent impedance Chopper LnnVr L Cde ~ ~ chopper c, 1,ny vn Vchopper 5Vstorage Filter ESS P+ Figure 216. 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. System's nonlinearities, such as saturation or deadtime 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 inverter' s current. The system can then be represented as shown in Figure 217. Vpoc0 li aP Cr ,, Viny c DC LINK Figure 217. Simplified system model The system equations for the simplified model are ylv =.I IbIL In Vcc Ia Jla ro pccaI (2 Applying Park' s transformation we get RT I I + Ld dq 1Td (213) dqo d Inqr do tq dt o invqr pccqr nvdr invdr tvdr Ypccdr ]bo I II V 214 lr,, 1I,, +Il r 1 I I1 V ~nvdr twvdr 1nvdr twvdr pccdr RI +L Tdq d TdqoTdq 1 dl + V (215) ~,,I,, I,, I,, Vc Invov invov twovd invo pccov Ivdr twdr~vq Snvdr twdrv + pccdr vq tqro dt nvr dt q pcr I ~ I. I V 26 vo two two, twopcc Vny 1 a imdr tw~dr dE.p~ 1 Invdr invdr pccdr l: R R I'P +L Tdq dTdqo + dl + (27) wqr tqr odt In""" dt Invqr pccqr Io, invo o twno pcco Where 1 1 cos(8 ") sin(B 1 0) 1 sin(B 10)snB20) cos(B40) 0 d d[Tdqo d d6H)sn~ cs(8 100) sn(8 100) 1 = sn(8 100) cos(8 1200) 0 dt dt dt cos( 2400) sin( 2400) 1 si(24)co(20)0 (218) dB It can be shown that [dq dq  cos(6 ) cos(6* 1200) cos(6* 2400) _ sin(8) cos(8) 0(9 = msin(8 ) sin(8 1200) sin(8 2400)1 _sin( 1200) cos( 1200) 0 3 sin(8 2400) cos( 2400) 0 0 1 00 m 0 =m I1 0 OO = 00 00 00 Thus, the equations for the simplified model in the dq plane are Invdr twvdr invdr invdr pccdr ylvvIRlIln +Lm~i 0 0I + I +V 20 nvqrtwqrinvqr dt invqr pccqr nvo, Invo, inv tw ,,,J o pcco The zerosequence component can be removed, since the system is a threephase threewire 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 dl~nd yn =RIlvd +L + La (221) dllnq ynq R Iln +L "' +V +La~I nvqrtwqrdt pccqr twvdr Equation 221 can be represented as a coupled electrical system as shown in Figure 218. d iny qr Vpoo Vpcc Viny dr V iny qr B Figure 218. Electrical representation of the dq components. A) Direct circuit. B) Quadrature circuit. Using Laplace's transformation we can rewrite the equations as Equation 222. Vnvd rr (S.) = (R + Ls) Invdr ~j(S) +Vpccdr (S.) L m Invqr y(S.) (222) V,,,, (s) = (R + Ls) I'"nvqr (S)+ +VpCCqr (S) +L m, Invdr (S) Thus, the block diagram of the system is represented in Figure 219. I iny dr Figure 219. System model block diagram L liny dr The inverter' s critical control variable was the inverter' s 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 inverter' s terminalvoltage needed to generate the desired inverter current can be determined as dl nVd =R Iv +L +V LaI AV+VLa nvdrtwdrdt pccdr invqr dropd, pccdr invqr (223) dl V RI +L """' +V +La~I = AV +V +LaIl Inv qr tvqr dt pccqr twvdr drope pccqr twvdr The voltage drop due to the filter inductance was compensated using a PI controller. Figure 220 shows the inveter' s current controller implementation for the system given in Equation 223. Ipd Oj III my,,,t dr re/ AtVdrop dr +~ / Vlnyd t u d I I~ny dr I I wt IK I II IV"et II mL t~doq t t I I I I. II Ipeq I; I II CURRENT REGULATORS SYSTEM MODEL Figure 220. Inverter current regulatorsystem model block diagram The character ^` over a constant or variable indicates that the quantity is estimated, and therefore subj ect to measurement errors. 32 To design the current regulator gains, crosscoupling factors were assumed to cancel each other out. Under these conditions, the simplified current regulator block diagram is shown in Figure 221. II II I II III II II R sII II II I II II II II II II I II (______________31 Fiur 221 shw ht Th sytmbhvs liealy an hrfr iercnrl ehiuscnb sdt dtrine the reuaos'gis *I Bot reuaor rdetcl Fimpdacere n1 I reeddt esg h current regulator.sse oe ipife lc iga ofFigure 222 i shown inEqatio 4 Figure 222. Simplified current control diagram I Kp s+ K H(s) = (224) Ie Ls2 +(R+Ks+K Using the following system data, the transfer function is given in Equation 225. *X=Xtransfomer+Xfilter5%+10% = 0.15 R 0 L= 400 CIH *X/R=10 R=0.015 R Note: More on the system parameters can be found in the perunit mode section. H(s) = 000s +(05Ky:K (225) The Figure 223 shows the system step response for two different current regulator gamns. O, Sytern closed loop output Kp=1 Ki=36 Kp=1 Ki=36 Figure 223. 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 plant' s dominant pole was cancelled by the controller (Equation 226). Thus, the zero at KI was assigned to K, the time constant of the plant, which was, K( =R K, L K s+ KK PI =K, + ; (226) s s The synthesis was done by selecting the integral time constant of the PI equal to that of the load. For our study the selected values were K, 37.5 K, = 1 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. Chopper Vchppe Vto rag e Figure 224. Chopper equivalent system The system equations for the chopper equivalent circuit (Figure 224) are given in Equaion 227. dl V = L chopper +V storage dt chopper (227) dl V =~ V L chopper chopper storage dt The chopper's terminals voltage needed to generate the desired chopper current can be determined as chopper = storage drop AV (228) 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 229. MJhpe (Ichpe~ Ichpe ) V, = V L chopper = L chper copr chope storage dt soaedt (229) Ychopper storage L .chopper LhreK Where KL is the regulator' s gain and At is half of the sampling time period. Figure 225 shows the implementation of the chopper' s current regulator. Chopper ref + _V hpe Chopper Vstorage Figure 225. Chopper current controller Outer regulators There were a total of three controllable currents, which consisted of Ichopper ref, linvdr~ref, and linvrrf~.. However, there were four variables that needed to be controlled, which were voltage at the de link bus, voltage at the point of common coupling, voltage at the energy storage system, and wind farm power fluctuation. Table 21 shows how these variables were assigned to the respective current regulators. Table 21. Outer regullator assignation Inner current Variable to be Comments regulator controlled liny dr ref Vstorage, Pawind The direct current component will be responsible for controlling the state of charge of the ESS and for smoothing the wind farm output power liny qr ref Vec The quadrature current component will be deployed for voltage regulation purposes Ichopper ref Vdc link The chopper current will regulate the DC link bus voltage. 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 modeled as shown in Figure 226. choppe dchn losse zpou Pdcnk cope Vstrag out osse DCLN "p Asu ing ise 0 we hav (Vtoag I We can rerie heeqatona Vdu link,, PS) =n 2Clstorag choppe (S) Figure 2227 Poeshow dnthebockdarmo h ytmmdl out + 7 Ichopper .. storage Figure 227. System model Considering 4%,~ as a disturbance, the transfer function of the system is 1 d(V ) 1 2 dc dt chopper storage 2 dc( s chopperS)Vstrg V (s) 2 soae(23 3) Ichopper (S) Cdc S The system model and the DC link voltage regulator can be represented in the form of a block diagram as shown in Figure 228. PStoragetog Yd Imkref + ~chopper 2 storaged n Cdchnk *S DC LINK VOLTAGE REGULATOR SYSTEM MODEL Figure 228. DC link equivalent system block diagram Pou Under ideal conditions the terms o cancel each other out, resulting in a storage simplified block diagram (Figure 229). K DC LINK VOLTAGE REGULATOR SYSTEM MODEL Figure 229. DC link simplified system block diagram The closedloop transfer function of the simplified DC link system is: 2V ,, (K.s+K,) H(s)=strg (234) dchlnk S storage Ks+I2Vtrg Figure 230 shows the system step response for two different regulator gains, using the following system data: *Cdc link =15700C1F *Vstorage nominal =1.533 p.u. 18} 1.6 14 System closed loop output slmcoe opotu Kp=2l Ki=22 a, 1.2 ~K= i2 1 0.6C Q System closed loop control action Kp=2 Ki=22 0 4 ::\. System closed loop control action \ Kp=1 KIl=11 0.2 U 0 005 a 01 .015 0 02 0 025 0 03 0 035 0 04 0 045 0 05 Time (sec) Figure 230. DC link voltage regulator step response To avoid a possible saturation of the DC link voltage regulator, the controller with lower gains was chosen. In this case, the control action was the chopper current, and it was designed to always be below 1.pu. Point of common coupling voltage regulator. The voltage support capability of the inverter depended on the available line impedance back to the utility source voltage, and its dynamics response was directly affected by the line parameters. The regulation of the voltage at the point of common coupling was accomplished by changing the amount of reactive current generated / absorbed (lin q) by the inverter. It was also possible to improve the voltage regulation controlling the real current component. However, as it will be shown, the voltage regulation range was significantly reduced. The system model used in our study (Figure 23 1) was a simplified version of the actual system. It consisted of the source (modeled as an infinite bus with a series impedance), and the inverter (modeled as a controllable current source). System non liberalities, such as switching of the semiconductor devices, transformer saturation, etc, were neglected. The system of the equations for Figure 23 1 is V~:pc II' dtI V,"Y,,b( 5 pcca inva r oa orce dl y =Rouc I + L I 4 + yoVcq ,,, (235)Ilvd pcccv invv inc ure EQUIVALENT SYSTEM MODEL 'LRL V 0 ce lInva Vpocab V as L, ce Inyb Vpcc b I pee lInv a V nv a Vpee Inyb Vlnyb I Vpee lIny c VIny c Figure 231. Simplified system model Using Laplace's transformation and reorganizing the terms, we obtain the transfer functions shown in Equation 237 R Itd 1 sIl~d (s) = R oreI (s) w Il q (s) + V s () source source (s + 1;r, ,,,, V s) s) invdr v(S) = SUe sourceVdYS) souvcesource (s 1V s V (s)+ invdr Lpcqouer twqr v(S) = source S+ source r (S)=source Defining the voltage drop, AV, as the voltage across the source impedance (Figure 232), it was possible to find the amount of current needed to obtain the desired voltage drop (Equation 23 8). AVL Figur 232. Sourc imeac volag dro 'LL Iznvdr~ ~ ~ ~ ~ ~ ~~~n bS = o V, s ore 2 bd S Lsourr R~~crce LSOourcline s +Rsorc 'LL Figur 23. Sorce mpedace vsourcero w 1. /L /L Iznvqr R (S) = SOYC sou e yd (S) + source V, s s + Rsorc 2 auc Lsource,, ) Lsorc s + Rsour /L /L The Bode plots of the Equation 239 for a system with a source impedance of 10%, and X/R=10 are shown in Figure 233 and Figure 234. Even thought the Bode plots of I iny dr and I iny, qr 0k very similar, the effect on the amount of voltage drop for a given source impedance were significantly different. There are two ways of controlling the amount of voltage drop at the source impedance; regulating AV, (s) and/orB Ad(S). However, in order to increase system stability and gain robustness, the phase shift between the utility voltage and the voltage at 42 the point of common coupling must be as small as possible. Therefore, it was preferable to regulate Vec by controlling AT1,, (s) exclusively. Bode Diagram Frequency (Hz) Figure 233. Transfer functions of inverter' s quadrature current component Bode Diagram Frequency (Hz) Figure 234. Transfer functions of inverter' s direct current component Comparing Figure 233 to Figure 234, it is clear that, in the low frequency range, the cross coupling between I,,,q z, nd AT is much greater than the direct gain between Irwdr and Aydr This means that the voltage can be regulated by controlling only the quadrature current. Thus, for instance, the steadystate bus voltage of a system with a source impedance of 10%, and X/R=10 in terms of Iznvdr and I,,,,, is R I td 1 (, r,,.(, 0= SOUrCe I (s)+wII q (s)+ V (sV s) L 2nd wr L pcd ouer soure sorce(240) R I t 1," ,,, S) L Invqrrd L pcr ucq source source Forllnvdr = 0, V a= V 2 V~i 2 = V iadw I~r~al )2 + Vrar +R uI e)2 (241) FrIznvqr = 0, Vyc = IVpcdr Vpccdr Vsourcer +Rsorcezd) sucqr+~orzd (242) If Iraqr = 1pu (capacitive),Vsourcedr = 1pu, Vsourceqr = 0 pu, Xsource = 0.102, and source w The amount of Irwdr needed to obtained the same voltage would be V =1.1 (V +R )2+ V +wL I ) >InV = 3.67pu This proves that for a system where the ratio X/R>1, the PCC bus voltage can be regulated in an efficient way by inj ecting only quadrature current. The design of the voltage regulator requires the knowledge of the source impedance. However, this impedance varies with time and on online estimation can be very complex if transient situations are present in the system. For steadystate conditions the transfer function between AV and I inyqrca b reduced to just the source impedance of value XsourcewLsource Therefore, the control block diagram of the voltage regulator can be interpreted as shown in Figure 23 5. I I ource dr CON IO~pERIMPEDANCE POSITIVE  SEQUENCE EXTRACTION L________________________,L_______________I___ VOLTAGE REGULATOR SYSTEM MODEL Figure 235. Voltage regulator system block diagram The current controller is represented as a second order transfer function in Equation 243. K s+K H (s) = ~pcurrent regulator I current regulator 23 current regulator 0.004s + (.05 K + pcurrent regulator I current regulator For Kp=1 and Ki=36 the current controller transfer function is I s+36 H,,, euao (s) = /M curet eglaor I 0.0004s2 +1.015s + 36 invref The positive sequence extraction transfer function can be modeled in continuous time as shown in Figure 236. Integrator Td Transport delay Figure 236. Positive sequence extraction algorithm equivalent system sore1%Xsource=20% Xgurce 5 6 // Xsource 1%b For the simplified voltage regulator system, there was not need for any transformation. Only the modeling of the positive sequence 1 cycle sliding window filter (Td=16.666msec) was required (Figure 2 37). VOLTAGE REGULATOR SYSTEM MODEL Figure 2 37. Voltage regulator detailed block diagram The system was further simplified assuming that the current regulator time response was much faster than voltage regulator time response (Figure 2 38). VOLTAGE REGULATOR SYSTEM MODEL Figure 2 38. Voltage regulator simplified control diagram Figure 2 39 shows the system step response for a given voltage regulator under different system conditions. Xur=1%Xsource=20% /Xo urce 59 Tine(sec) A ,,m., B Figure 2 39. System response to a 5% change in voltage reference for Kp=2 Ki=250. A) With saturation. B) Without saturation The settling time was a function of the system impedance, and therefore it was not possible to predict the system response without knowing the source impedance. One solution was to use an adaptive parameter tuner capable of adjusting the regulator gains according to the identified plant dynamics. The block diagram of the adaptive control scheme is shown in Figure 240. Adaptive Parameter Tuner VPccre; poserve seqe~ zn rr LN /d + Figure 240. Adaptive control scheme However, due to the difficulty in distinguishing between changes in the system impedance, load variations, and utility voltage, a simpler but robust solution was adopted. It consisted of a classic PI regulator, with gains that were tuned in the field. The drawback was a slower response that could occur for any given condition. Power regulator. The power regulator required to control the power fluctuations of a wind farm was the most complicated control scheme among all the described so far. It involved nonlinear algorithms which made the system very sensitive to instabilities due to non forecasted conditions. The basic idea behind the power regulator was to determine the amount of the real power required by the inverter in order to meet the utility's power fluctuation limits. A generic power regulator control scheme is shown in Figure 241. Iwinda Vo X Rampnat vae Is Vstorage Iwindb Vn Vpccb X Pur+Limiters I toret r Iwindc Vpccc X+ ESArequired  power Allowedccentenngpower Powerlnverter Reference Figure 241. Power Regulator general control scheme First the wind farm power was calculated and the compared to rateof change limits (Table 22). If limits were exceeded, the difference would be compensated by the inverter. The centering algorithm was a control scheme used to hold the energy storage near its nominal value, to be ready for the next supply or absorption cycle. If the wind farm power was causing the limiters to activate, this centering action would not take place. That way a higher priority was given to the power limiters. Table 22. Rateofchange limits or PPA for a 10 MW wind farm Parameter Value Instantaneous 1 MW change per 2 second scan Sub minute average average of 0.3MW change per 2 second scan for any 60 second period Ramp rate 2 MW per minute up, and down when operationally possible The first proposed control scheme of the power limiter consisted of a high pass (HP) filter which canceled the high frequency power fluctuations independently of the rateofchange limits. Figure 242 shows the HP filter control block diagram. A small bias power was added to assure the charging of the energy storage system. This approach had three maj or drawbacks: * Rateofchange limits might not meet unless inverter' s power and energy requirements were increased. * Optimal cutoff frequency design was unknown. * Inverter duty cycle was higher than the next approaches. Wind Farm Output HI igh Pass Filter Storage Nominal State of Charge Centering Storage I, Charge/ +_ Inverter (Integrator) I V~D discharge Centering ~V I Power Constant Figure 242. Power limiter 1. Control block diagram Wind farm power data records were used to test the power limiter control scheme under different system conditions. Figure 243 and Figure 244 show the inverter requirements as well as the system performance for different cutoff frequencies. Note: Inverter size requirements cannot be extrapolated from the 15 minutes simulation. A more detailed study must be performed using long windpower data records (perhaps years). It was also not cost effective to correct every possible scenario. Therefore, the number of times and/or amount that the wind farm may exceed the power index limits, with a Power Stabilizer installed, needs to be determined, when traded off against inverter and storage ratings. The main advantages of the HP power limiter were its simplicity and its stability under unexpected power fluctuations. The control scheme was implemented in MATLAB in order to test the power limiter performance under different system conditions. Appendix B gives more information on the MATLAB code. 10F 06 1=0 005Hz ~1 .2 O 20 60 _ 0 Time secss) f =0 oos~iz , 0' 100 200 300 400 500 Time secss) 600 700 800 900 1000 Sf=0 005Hz 100 200 300 400 500 Time secss) 600 700 800 900 1000 Figure 243. Power limiter 1. Performance using different cutoff frequencies (unlimited power and energy). A) Power to utility. B) Powerstabilizer output power. C) Power stabilizer's energy storage. 10r 5 O ~1 12 O i 20  S10 c 1 d farrr power 'A 100 200 300 400 500 Time secss) 600 700 800 900 B I I I I 100 200 300 400 500 Time secss) 600 700 800 900  =0 005Hz 100 200 300 400 500 Time secss) 600 700 800 900 Figure 244. Power limiter 1. Performance using different cutoff frequencies (Pinverter MW and Einverter=+8.5 MJ). A) Power to utility. B) Powerstabilizer output power. C) Power stabilizer's energy storage. The second proposed control scheme of the power limiter consisted of a power limiter with the three rateofchange limiters in cascade (Figure 245). The ramp limit was first applied, followed by the sub minute limit, and finally the scantoscan limit. Input+R +s Scanto Output a ~Scan R sJ ~ Limiter R S Subminute Limit Calculator Figure 245. Power limiter 2. Limiters details As mentioned earlier, the "centering" of the energy storage energy was needed so that it could supply or absorb power from its nominal state. Therefore this energy must be taken into account when calculating the rateofchange limits, since it was real power being interchanged with the system. Thus, the power limiter control scheme had two limiters in parallel (Figure 246); one limiter acted upon the wind farm output only, another limiter acted on the wind farm power plus the desired centering power. If the inverter were big enough to supply or absorb the excess power and energy from the wind farm, the power limiter would keep the power within that allowed by the rateof change limits. The problem occurred when the power or energy storage is beyond the rating of the inverter, since the history of what is actually delivered to the utility could be wrong. Thus, a saturation limiter was needed in order to adjust the buffer input data. The control scheme was implemented in MATLAB in order to test the power limiter performance under different system conditions. Appendix B gives mode information on the MATLAB code. 51 Desired Power (Wind+Storage Centering) Lmte Last thing to be updatedlevaluated r~;i=1+ Previous scansI (BUFFER) Wind r~~ Output aLimiter Storage Nominal Centering State of Centering Charge/ Charge ES eurdPower DiscargeSupply/Absorb Allowed Constant SInverter Power Limiter Figure 246. Power limiter 2. Control block diagram Wind farm power data stored on a 2 second basis was used to test and size the power limiter control scheme under different scenarios. The following figure shows the system performance for a period of 15 minutes. a VT\ Wind farm power 5.0 100 200 300 400 500 600 700 800 Times secss) , Zoom in Figure 247. Power limiter 2. Compensation performance ' Wind farrn power 450 500 550 Times secss) 52 The inverter power and energy required to meet the rateofchange limits for the 15 minute simulation is shown in Figure 248. L O C 4 5 UJ  100 200 300 400 500 600 700 800 900 Time secss) n~tn inrl 0O 100 200 300 400 500 600 Time secss) 700 800 900 1000 Figure 248. Power limiter 2. Inverter response for a sampling time of 2 seconds. A) Powerstabilizer output power. B) Power stabilizer's energy storage. To test the stability of the control algorithm, saturation effects were taken into account. Figure 249 and 250 show the system performance for different underrated inverters. Rateofchange limits were not met, but the system was stable. It is very difficult anticipate all of the types of misbehavior that might occur in the system, and that there could be unusual power fluctuations from the wind farm could get the inverter into a mode where it would continue to swing the power around in an undesirable manner. Therefore it was recommended to include some type of "misbehavior detector" in the power limiter control scheme to protect the inverter and the sy stem. 0 100 200 300 400 500 600 700 800 900 1000 Time secss) u. 4 R 5 0 100 200 300 400 500 600 Time secss) 700 800 900 1000 Figure 249. Power limiter 2. Inverter response for different power ratings. Sampling time 2 seconds .A) Powerstabilizer output power. B) Power stabilizer's energy storage. Zoom in F r o a, 5 00.5 a II I I I I 100 200 300 400 500 Time (sec 600 700 800 900 1000 \, : :' r~5ld;itia;=i I13'i 'i I;li;r nd*= i 4 :d'," 1. Ziirei nir= uriii:~d r' B 100 200 300 400 500 600 Time secss) 700 800 900 1000 Figure 250. Power limiter 2. Inverter response for different ESS sizes. Sampling time 2 seconds. A) Powerstabilizer output power. B) Power stabilizer' s energy storage. The third control scheme considered for the power limiter consisted of a power limiter with the three rateofchange limiters in parallel (Figure 251). The limiter' s input was the power out to the utility instead of the wind power, plus the centering power, for a more accurate control of the power fluctuations seen by the utility. Each limiter determined the maximum and minimum amount of power allowed changing per scan. Then the absolute maximum and minimum were calculated in order to establish the centering power limits and the required power from the inverter. Figure 251. Power limiter 3. Control block diagram Figure 252 shows the response of the power limiter 2 using the same windpower data records used previously. It can be concluded from Figure 247 and Figure 252 that both power limiters have the same response under normal conditions. 9.5 9 O~ 7 5 .5 c1 07 O .5 0 100 200 300 400 500 600 700 800 900 1000 Time secss) C 0. 0 100 200 300 400 500 600 700 800 900 1000 Time secss) Fiue25.Pwrlmtr3 netrrspnefrasmln ieo eod.A Poetaiie oupu poer B)Poer stabilizrseegysoae PerUnit System Model The reasons why to convert system variables into per unit are: *System easily scalable *Facilitate fixed point operations *Power system components can be treated uniformly no matter what voltage level The two variables selected as based values are Vbase = Va neta p V Ibase = max line = 1pu (A) Thus, the rest of variables can be calculated as VRSlne neutral V Base Impedance: Zbas I/S ae ase2 I I RM/S line base *Base Power (3 phase): Phse= inererraepower = RM/S line neutral RM/S line = JZ 3 = .5 Inverter OutputFilter Design The purpose of inverter filter was to attenuate the high frequency switching harmonics produced by the inverter in order to avoid disturbing other EMI sensitive equipment on the grid. Its optimal design is very complex and it involves coupled design constraints and nonlinear equations. The inverter topology for which the filter would be designed was a 6pulse 3wire inverter, without DC bus midpoint tapped to neutral (Figure 254), where power semiconductors were considered as ideal switches. Iny a Vlny a Iny b Vlny b myv c Vlny a Figure 254.Inverter topology Harmonic content The typical linetoneutral and linetoline voltage of a three phase inverter using a PWM strategy is shown in Figure 255. Time secss) Time secss) Figure 255. Linetoline and linetoneutral voltage of a three phase inverter Figure 256 shows the harmonic spectrum of the linetoline voltage under the following conditions: *fsw = 4860 Hz *fi=60 Hz switching fr~equency f,, *Frequency Modulation, mf *81 Sfundamentaldd~~~dd~~~ddd~~ frequency f, *Vdc = 2.04 pu *Vsource max linetoneutral= 1 pu Y.a ele Peak amplitude of the control signal = a eie *Amplitude of the triangular signal = 1 58 peak amplitud'e of the control signal Amplitude modulation, m =1 aamplitude of the triangular signal 1.4 mf81 h= 1 1.2 V=1i.24 I 0 00 40 00 80 00 20 Freqenc(Hz Fiue25.RSLietievlae amncsetu Th anhroi opnnt ftelnoln upu otg eecluae (SSG)r capabl ofS producing et vofg adusablei volctags hc myb opldt na power sytm texhamnge independently o t lnetrollabe realu and ractie pwer. This wase acomlihe b the usulte age of 28 a synhoosidco hc ikdteivreuptt th a sauppl sid e (Figuren 257).cn efon n ale23 Table 23. Generalized Harmonics of linetoline voltage for a large and odd mf that is a multiple of 3 K (Generalized Harmonics of Vrms 11) ma h 0.2 0.4 0.6 0.8 1 1 0. 122 0.245 0.367 0.490 0.612 mfd 2 0.010 0.037 0.080 0. 135 0. 195 mfd 4 0.005 0.011 2mfd 1 0. 116 0.200 0.227 0. 192 0. 111 2mfd 5 0.008 0. 020 3mfd 2 0. 027 0.085 0. 124 0. 108 0.038 3mfd 4 0.007 0. 029 0. 064 0.096 4med 1 0. 100 0.096 0. 005 0.064 0. 042 4mfd 5 0. 021 0.051 0.073 4mfd 7 0.010 0.030 synchronous  Inductor Ivre SSG Figure 257. Static Synchronous Generator diagram Thus, the inverter voltage harmonics would generate current harmonics, which amplitude would not only be a function of the inverter' s mf and ma, but the synchronous inductor as well. The inverter current harmonics can be calculated as: *For h=1 (fundamental frequency): ~netv m 1Vs,, Ys1 1 I (h = vers re:2 ourc re:2(245) res~24 h L *For h>1 (assuming no harmonics are present in the utility bus voltage): nvrerrs2() 1 Vdc K 1 I nl(h)= I~~re res 24 hL 24c h L (246) Where fl is the fundamental frequency. The inverter current harmonics must be attenuated in order to avoid interference with communication circuits and other types of equipment, the increase of system losses, resonance conditions, and malfunction of power electronic devices. The IEEE 519 Standard [29] is a recommended practice to be used for guidance in the design of power systems with nonlinear loads and therefore should be taken into account on the design of the switching ripple filter. The worst case scenario is for general distribution systems (120V through 69000V) with a TDD < 5% for current harmonics below the 50th. TDD is the total demand distortion and is defined as TDD(%) = h=2 100 (247) The maximum demand load, which is IL, can be estimated from data used to size the inverter isolation transformer. Switching frequency The selection of the switching frequency was based on the recommendations given by [28], which stated that: * Because of the relative ease in filtering harmonic voltages at high frequencies, it is always desirable to use as high a switching frequency as possible. * In most applications, the switching frequency is selected to be either less than 6 k * In order to avoid subharmonics, synchronous PWM must be used. Synchronous PWM requires that me be an integer. * In the 3wire threephase inverters, only the harmonics in the linetoline voltage are of concern, and only the odd harmonics exit as sidebands, centered around mf and its multiples, provided mf is odd. * If mf is chosen to be an odd multiple of 3 the most dominant harmonics in the line toline voltage (even harmonics of mf) will be cancelled out. Characteri sti cs L filter LCL filter Control method Hysteresis controllers Fixed switching frequency control methods Attenuation above 20dB 60 dB resonance frequency ( first order system) (third order system) Igrzdte (S> Total line filter inductance High line inductance, and Low line inductance, and for a given grid current therefore poor transient fast transient performance ripple magnitude performance *For high power applications (kVA) where switching losses play a maj or role in the overall system design, the switching frequency is usually selected between 3 k Taking all these elements into consideration, the optimal switching frequency selected for the inverter and for the chopper was f,, = J; mf = 60 81 = 4860H: Passive filter design The switching ripple filter topology selected for the inverter filter was based on a LCL network as shown in Figure 258. Isolation transformer Filter or synchronous equivalent impedance Inductor I~ . Inverter sorc I LCL switching ripple filter Figure 258. LCL filter topology The main advantages of the LCL filter compare to the L filter are summarized in Table 24. Table 24. L filter vs. LCL filter I S Invre Filter capacitor The LCL inverter filter equations are the following: dl dl V V = L, grid (248) in e te ri d t Applying Laplace's transform, the LCL inverter filter can be modeled as shown in Figure 259. Irx Figure 259. LCL equivalent block diagram The inverter filter was divided into two different equivalent filter models based on the frequency under study. Thus, we have: Equivalent filter circuit configuration at fundamental frequency. Under these conditions the inverter was considered as an ideal sinusoidal voltage source. This was the lineal inverter model valid for the design of the system controllers. Figure 260 shows the filter equivalent system at fundamental frequency. r Vsou~rce(l Lt L, ~ y(i Figure 260. Single phase equivalent filter model at the fundamental frequency Equivalent filter circuit configuration for the h harmonic (for h>1). At high frequencies the converter was considered to be a harmonic generator, while the grid can be considered shortcircuited. Vsourc (hfl)= 0fYT Sgrld(hfl) I nverter (hfl) Figure 261. Single phase equivalent filter model at the hth harmonic Thus, the current ripple attenuation, passing from the inverter side to the grid side can be calculated as Igrzd rms(S) 1 nverter, msIn(s) s3 Lt CfLf + s (Lt + Lf) 5,,nvter res(s) s42 Ci Lr +1 (9 nveterms ns)3 L, Cr ,L + s (L, + Lr) Igrzd rms(S) 1 Iznverteru re(s) s2 C, Lt +1 There are different ways of designing the LCL inverter filter, as well as different specifications or constrains. Table 25 is a summary of the most common parameter used to design the inverter filter. It can be inferred from Table 25 that there is no a unique approach or limit when designing the LCL filter. The LCL parameters selected for the inverter filter design are X,, = 10% > L, = 265.25 pH Xof = 3333.33% > C, = 79.577pFF X,, = 5% > L, = 132.62plI (typical transformer equivalent impedance) Table 25. LCL filter design Parameter Description Eauations Limits Current Maximum Peak to Peak For ma < 1 Peak to Peak value: ripple value m, yd 15%25% of rated current [35] nr =Msi m2 37 31% of rated current [32] Note: Maximum r',,te ma 4 L, f, 4 L, f, current ripple at Vsource(t)=0 differs For ma = from Vsource(t)= Vmax Vdc ernveter repple max 7 Li fSn Most significant For ma =1 Most significant harmonic component harmonic components Islefrmph=m 2"Vde0 1 (mf+t2) '" 27rf h Lf 10% of rated current [30] *1.6% of rated current [31] Attenuation Laplace domain Igradrms(S) 1 0.2 attenuation [30] of I,;,, ,(s) s2 Cf L+ 0.5 attenuation [32] harmonic content Frequency domain Igrrd rms h = mf 2) Zc,~ (A h) I~mterem h= y ) IZc, (A;h)+ Z, Cf; h) Voltage drop across the filter during AllmaxL IlnverterI ma1x 21f, Lf Total value of inductance should be normal operation lower than 10% to limit the voltage drop and the de link voltage[30],[33] *1.7% on the inverter kVA base [34] Filter resonant frequency 1 Resonance frequency between 10 times 2reso I =2x C (L, //L, the line frequency and half of the switching frequency[30][33] Filter capacitor reactive power 1 Lc,i (%) Pinveter ratedi power Qf C, = 2 *<5%[30][33][34] 100 32z f,suc V, I ourc res" *15% [35] The electrical characteristics of the LCL filter for the system parameters given Table 27 in are summarized in Table 26. Table 26. LCL equivalent impedance with damping resistance Parameter Equation Stiff system Current ripple At twerter current ripple max i 0.2264 pu (App) (peak to peak) rwLf , Current ripple (most i,,,~ i(fiM 2) p Vdc 0.2 1 0.00003 pu significant J5 21(fsw 2 fl). Lf (Arms) harmonic) Harmonic Igrzd rms fsw 2 f) ZC(, /w 2 fl) attenuation r,,nverter rm(fs 2 flzc ZC/s 2 fl)+ ZLt (sw 2 fl)85d Max Voltage 0 p Vls Amax L Inverter max 2x fl LI. u Vls drop Filter resonant 1 fresonant = 1897 Hz frequency 2.2 C (Lt//L ) Filter capacitor c,32rf V 3.0% VAr reactive power COc, (%) = Pnveter rated on ev ms: lo (Icf, = 0.03 pu ) Table 27. Perunit system Variable Per unit M4nX lineneutra 1.0 V 1.22474 RM/S linelne YRM/S lneneutral .07 I 1.0 M4X Inverter nommnal Im wrernma 0.70711 Zbase1. nverter 1.5 V, 2.0412 Passive filter damping To determine the system stability, the LCL inverter filter damping resistances must be taken into account when calculating the system attenuation at resonance frequency. The system resistors are given in Figure 262. VInveter Vsource Figure 262. LCL equivalent impedance with damping resistance Using a X/R=10 for all inductors, the damping resistances of the LCL filter are X X, = 10% > = 10 > R, = 0.0 la X '= 10 > R, = 0.0050 R, X,, = 5% > The LCL inverter filter could resonate due to harmonics generated either from the source or from the inverter. The two equivalent circuits are vorc Rt Vpacltr __L^ Rf Vlne Figure 263. Single phase harmonic generator equivalent circuits. A) Inverter as a harmonic generator. B) Source as a harmonic generator Thus, the apa o transfer functions are given in Equations 250 and 251: (250) caa~cro, (2 51) capacrto, 1 ~nverter 1 1 ~ 1+Z, + 67 The Bode frequency response of both models is given in Figure 264. Bode Diagram Vaa ol ule Frequency (Hz) Figure 264. LCL gain frequency response It can be deduced from Figure 264 that there is a significant gain at the resonance frequency (small system damping resistance), and therefore harmonics close to this frequency could be amplified by the LCL filter. From the inverter point of view there are two sources of disturbances: 1. Voltage harmonics due to the PWM 2. Disturbances amplified by the current regulator LCL (Vcapacitor/Vinverter) 40 Current regulator Vlnvelter In harmonics 102 103 104 Frequency Figure 265. Inverter frequency analysis Figure 265 shows the current regulator frequency response, the filter frequency response, and the inverter linetoneutral harmonic spectrum. It can be inferred from Figure 265 that the current regulator attenuates any signal with a frequency > 400Hz (cutoff frequency), and the inverter voltage harmonics do not make the LCL filter resonate. From the point of view of the voltage source there are two sources of disturbances: * Large infrequent transient, such as capacitor bank switching. This type of disturbance may ring the filter, but it will damp out in a few cycles. * System harmonics. A detail study of the system it is required to determine if it is likely . DirectCurrent Link Capacitor Design The DC link bus voltage had the following constrains: * IPM Max voltage 1200V. * Line to line voltage 480 V. This would allow the use standard isolation transformers * Minimum DC link voltage = 1.1 Vmax rlne ro ane = 1.1 .480 J = 750 V Minimnum voltage to guarantee system controllability. * IPM trip level = 900V. Capacitor switching voltage transients tend to raise the DC link voltage and could damage the IGBT's. A trip level of 900 V allows riding through the maj ority of the capacitor switching transients. * Low DClink voltage was desirable in order to reduce the switching losses. Given these system restrictions the selected DClink voltage was 800V. In per unit 800 Vdclnk =J2 2.0412 pu The dimensioning of the DC link capacitor was determined by the following constramns: * Maximum permissible current stress for a required working life (current ripple) * Existence of any zero sequence component * System controllability ( avoid large gains) * Max ripple voltage 10% For a traditional STATCOM configuration, the DClink capacitor is necessary for an unbalanced system operation and harmonic absorption. For a configuration with energy storage, the DC link capacitor main function is to reduce the DC current ripple from/into the ESS and therefore a smaller DClink capacitor could be used. DC link Energy The time constant selected for our study was = 21.5 msec Thus, InverterPower the DClink capacitor in perunit model is DC link Energy = 2msc=DC link Energy,, Inverter Power n'erter pu DClink Energy, DClink Energy ,, = 0.033J 1.5W DC link Energy, = t Cdchnk 1 hnk, d chnk 15700 p F Energy Storage Design The Energy Storage System (ESS) design parameters were * The voltage at the energy storage system (ESS) was designed to vary from 95% to 0.95*"50% of the DC link voltage. Total Energy in the ESS=204se Inverter Power Note: More on the design and size of the Power Stabilizer energy storage system can be found in [36]. The center voltage of the ESS can be calculated as 1 (1 1 1 (1 2 2 storage storage max storage cetr 2 storage storage center storage m (252) V,, 1 V2+V Thus, for a system with a Vdcnominal = 2.0412pu the ESS nominal voltage was storage max0.95 2.0412 = 1.9391nu ysyg m=0.95 0.50 2.0412 = 0.9695 pu Figure 266 shows the relationship between the capacitor voltage and the energy storage. The capacitance of the ESS in perunit can be calculated from the time constant Total Energy in the ESS as Inverter Power Max Energy Max Energyp S20.45 sec > Max Energy, = 30.67J Power nverter pu Max~~ Enrg, storage storage ma storage =1. Figure 266. Capacitor Voltage vs. Energy Storage Chopper Inductor Design The purpose of chopper inductor was to reduce the current ripple produced by the chopper in order to guarantee the ESS working life (Figure 267). The current ripple current selected for this application was 30%. Under this condition the chopper inductance in per unit is calculated as shown in Equation 253. A chopper = Lhopper dchtye ,w eeA chopper = e Vdnk storage (3 dclink Ichopper Lehopper d clink V I ~~storage trg Figure 267. ESSChopper topology In the worst case scenario the DClink voltage is at its nominal value, while the voltage at the ESS is at its minimum. Thus, the maximum voltage drop across the chopper inductor is chopper max = dcknk nommal storage mm r .42099 .77p Discretization of the chopper inductor voltage drop differential equation yields the Equation 254. AI AV = L chopper (254) chopper chopper a 1 1 Where Alhope is the ripple current, and At = as shown in Figure 268. chopper 2 fr T, Triangular waveform I chopper t l Time Vdclink=2.0412 pu Time Figure 268. Equivalent circuit for maximum current ripple calculation Thus, the chopper inductor in per unit is: 1 1.0717 246 chopper A chopper max At chopper L chopper chope = 0.03 Icopr ae (30% ripple) SLehoppe = 500plI Pinveternomal I chopper rated V dchnk 1.5W 2.0412 0.73 52 pu (A) PerUnit System Model Summary Table 28 is a summary of the perunit system parameters used in the control and modeling of the system. Al chopper ( ,,,,V,,=.65p Lehopper Specs Table 28. Perunit system parameters Variable Perunit Model yM4X kneneutral 1O YRM/S knehne1.22474V RM/S kneneutral 0.70677V I 1.0A M4X Inverter nommnal IIms Inverter nommnal 0771 Base 10 ~nverter 1. 5W V 2.0412V dc nommnal V 1.533V storage center Cdc knk 15700 IF Cstrg 16.31F Lehopper 500.01H Rchpe 0.0188490 L, 265.251H R, 0.010 C, 79.57 IF L, 132.631H R, 0.050 21.5 msec time constant 20.45 sec time constant (at maximum ESS voltage) 30% current ripple X/R=10 10% Impedance X/R=10 3% VArs (3333.3% Impedance) 5% Impedance X/R=10 Simulated Model Power Systems Computer Aided Design (PSCAD) was used for the modeling and simulation of the power stabilizer. The PSCAD model was based on the perunit system, so that the system performance could be compared to any given unit size. Figure 269 shows the main components of the system. The PSCAD model can be divided into two main subsystems; the electric system (Figure 270) and the control algorithm (Figure 271). The maj ority of components used in the modeling were part of the PSCAD library. Only the power limiter 2 had to be implemented in FORTRAN and linked to PSCAD given the complexity of its design. UTILITY SYSTEM XsourceChopper WIND FARM LCL INVERTER ESS Figure 269. System overview I I t t II I I I I~ II I I II LCL filter Inverter DC link bus Chopper Figure 270. Perunit electric system model Table 29 shows the model performance as well as the designed specifications for comparison. It can be observed that designed and simulated system closely agree. I In e',~;~;~,~,d"' Sve Irt rl" In IIt I~Vr,,, Irr I III I I I I Currentregulator Limiters & Transformations IT~t" Frame transformation & positive seq uence calculation Flattop I CarKV1 PLL aarK 1 ParK 1 L k ~~~~ abe / .,,,,,,,,, 4v. 4 me, I ~,... ParKV1 L /d,q, 'eguafor V. rorurrent 41. R snonDtar ,onnotar u. ;rl~c~,, 'eguafor ,r I "'"' ,, ,.,...~..,..... ""'' ,,,,,,,...~..,..... ,~~~~~~~~~~~~ rg "'"'" "'"' g snrtnDtar rosonDtar r~ P"o""'"' v, ~ ~'t~,3~0 Y^". ~~~~;3~0 '. n f  ,, ,,..,,,.,.  ~ L______________________________r Chopper Control Scheme Figure 271. Power Stabilizer Control Scheme Rotating Reference Power Limiter 76 Table 29. Designed system results and simulated system results comparison. System conditions: V de link =2.04 pu, V source, ma=1 pu, stiff system Parameter Inverter current ripple Model response Design system/Comments 4L,f~ 2 4  "= Marnwessy tem_= Marx(0 198, O 2241)= 0 2241 pu (App) Isvr or res _(h =m + 2)4 V 0 2 1 1 2nf h L, Isaver,res_(h =mi &2)4 002986 pu(A rms) Frequency(Hz) Harmonic attenuati OH I nnn(frw I,,,,.(f, Ignd rs(fr Isanrd nr (f m 2.f) Zc,12f  2 ) Z ,(s ) z /w2 2,) = 18 5bB 2 ) 2 )=0O11880O02986= 00035pu(Arms) 0 005 3500 4000 4500 5000 5500 6000 6500 Frequency(Hz) Current regulator step response Iqref step change[ 1 (from capacitive to inductive) No PCC voltage regulator Stiff system Limiters: Vmax=1.15, Vflat=1 05 0 002 0 004 0 006 0 008 0 01 0 012 0 014 0 016 0 018 0 02 Time(sec) Dc link step response Vdc ref Step change [2.0412 2.3] Stiff system 20L 0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 Time secss) SI4loit nllnilodi i :o lio :a 1 :n a: ia: n Table 29. Continued Parameter Model response Voltage ls, , regulation xsource20% Design system/Comments Vpecrerstep change [1.0 1.05] Variable line impedance: [1% 2% 4% 5% 10% 20% ] Current regulator bandwidth I,,er =0.2sin (wt) Idref Iess+0.2cos (wt) f= [120 300 420 540 660 Vdclink=2.0412pu (V) Vsouce max 1n= 1 pu (V) Stiff system Theortic current regulator frequency response PSCAO model current regulator frequency response Frequency (Hz) Cutoff frequency 400 Hz Power filtering Power limiter 2 simulation results for a sampling time of 2 seconds CHAPTER 3 SYSTEM DESCRIPTION System Overview The performance of the power advanced electronic device was tested in a test bench based on: * DC motor synchronous machine set * Passive load * DC motor asynchronous machine set * Wind farm buffer The basic idea was to reproduce the basic electrical components of a small isolated system in order to asses the benefits of smoothing windpower fluctuations. Figure 31 shows this main idea. Bulk generation. The system model's bulk generation was represented with a single synchronous machine, which the main function was to control the system frequency and voltage. Load. The power system's load composition was strongly dependent on the time of day, month, and season, but also on weather. A typical load profile was studied in [37], and can have the following approximate composition: * Induction motors, 60 per cent * Synchronous motors, 20 per cent * Other ingredients (passive load, electronics...), 20 per cent Wind Farm model OCMotor I\rynohronour Lne 1 .~c ~t~t L: Electric Network Model Figure 31. Equivalent system model Dynamic loads usually consume between 60 to 70 % of the total power system energy. However, their dynamics are of special importance for voltage stability studies due to their reactive power requirements. Thus, since only real power fluctuations were of interest in our study, the system' s load was reduced to a one threephase passive load. Renewable Resources. Renewable resources are growing faster than traditional energy sources, with the fastest growth being in wind and solar energy. It is expected that in the near future, they will play a significant role in the generation mix. The system's renewable resources were modeled using a single induction generator that would represent 15% of the system capacity. This number was very conservative compared to other grids such as Western Denmark with a penetration level of 63% of peak load and the Island of Crete, where wind power has a penetration level close to 40%. Pil SLW ~sunohronou ~ ..,,,.. I II.1LL t'"~i ":"~" Power Stabilizer Power Quality Devices. Because of wind power' s high penetration factor in the near future, new advanced power electronic devices as well as grid operation procedures have to emerge to minimize the impact of nondispatchable wind power. In modeling the system, only a proof of concept wind farm buffer was considered to study different control schemes that could reduce windpower fluctuations. Electrical Network Model Synchronous Machine The first requirement of a reliable service is to have the synchronous generators with adequate capacity to meet the load demand. Any unbalance between the generation and load initiates a transient that causes the synchronous machine to accelerate or decelerate due to the appearance of net torques on the rotor. It can be shown that the interconnection ofj finite machines with inertia constants Mj can be reduced to a single finite machine with inertia H, where H can be calculated as shown in Equation 31. H = (31) 11 1 ++...+ H, H2 H~ The synchronous machine selected for modeling the electrical system is a three phase, brushless, self excited, externally regulated, AC generator. The ratings of the synchronous machine were * Rated Power 7.0 kW intermittent, 5.4 kW Continuous * Rated Voltage 240/480 3ph 60 Hz * Rated Speed 1800 rpm The system voltage selected for the model is 480V; therefore the synchronous machine's coils were connected in a high series Y configuration. Voltage regulation Load voltage regulation was mainly carried out by the generator's exciter using an external voltage regulator. The automatic voltage regulator received both its input power and voltage sensing from the generator' s output terminals. The DC output voltage of the exciter field required to maintain constant the generator' s terminal voltage was automatically changed by the voltage regulator, which had a voltage regulation accuracy of 1%. The voltage regulator set point was 480V, line to line. Due to synchronous machine imperfections and asymmetries, output voltage was not an ideal sinusoidal waveform, as shown in Table 31. The most significant distortions were the second, third, fourth, and fifth harmonics, with an unbalance of approximately 1%. Such types of distortions were not very common in electric systems and may have an impact on the control system. Simple sliding windows were used to filter/reduce their impact. Prime Mover The prime movers of large generators are principally hydraulic turbines, steam turbines, and combustion turbines. In our model the prime mover that was used to produce the mechanical torque was a DC machine with the following specs: * Rated Power: 7.5 HP * Armature Voltage 240 V dc * Field Voltage 150 V dc * Rated Speed 1750 rpm Both machines were connected in cascade through their shaft, so power could be transferred from one machine to another. Figure 32 shows the system configuration as well as the variables used in the control. Table 31. Synchronous machine output voltage profie at rated speed Synchronous Machine Voltage Synchronous Machine Voltage Features profie for unloaded condition profie for unloaded condition Waveform so FFT Frequency(Hz) Unbalance A single quadrant chopper was used for speed control of the DC machine. Chopper circuit specs are shown in Figure 33. Note: Figure 33 shows that the DC power supply was used by the two choppers required in the model. One was for the prime mover of the synchronous machine, and the other one a different DC machine that would represent wind speed variations. 