Real-Time Power Quality Waveform Recognition with a Programmable Digital Signal Processor

Transcription

1 Real-Tme Power Qualty Waveform Recognton wth a Programmable Dgtal Sgnal Processor M. Wang, Student Member, IEEE, G. I. Rowe, Student Member, IEEE, and A. V. Mamshev, Member, IEEE Abstract--Power qualty (PQ) montorng s an mportant ssue to electrc utltes and many ndustral power customers. Ths paper presents a DSP-based hardware montorng system based on a recently proposed PQ classfcaton algorthm. The algorthm s mplemented wth a Texas Instruments (TI) TMS30VC5416 dgtal sgnal processor (DSP) wth the TI THS106 1-bt 6 MSPS analog to dgtal converter. A TI TMS30VC5416 DSP Starter Kt (DSK) s used as the host board wth the THS106 mounted on a daughter card. The mplemented PQ classfcaton algorthm s composed of two processes: feature extracton and classfcaton. The feature exacton projects a PQ sgnal onto a tme-frequency representaton (TFR), whch s desgned for maxmzng the separablty between classes. The classfers nclude a Heavsdefuncton lnear classfer and neural networks wth feedforward structures. The algorthm s optmzed accordng to the archtecture of the DSP to meet the hard real-tme constrants of classfyng a 5-cycle segment of the 60 Hz snusodal voltage/current sgnals n power systems. The classfcaton output can be transmtted serally to an operator nterface or control mechansm for loggng and ssue resoluton. Index Terms Dgtal Sgnal Processor (DSP), Power Qualty (PQ) Montorng, Event Classfcaton, Classfcaton-Optmal TFR, Artfcal Neural Networks. T I. INTRODUCTION he ncreasng popularty of power electroncs has led to recent focus on power qualty (PQ) related dsturbances n power systems by electrc utltes and ndustral power customers. Software and hardware for automatc classfcaton of voltage and current dsturbances are hghly desred. Exstng recognton methods need much mprovement n terms of ther capablty, relablty, and accuracy. Today, power qualty has become a very nterestng cross-dscplnary topc, couplng power engneerng and power electroncs wth other research areas, such as dgtal sgnal processng, software engneerng, networkng, and VLSI. Voltage related PQ dsturbances are the major causes of dsrupton n ndustral and commercal power supply systems, Ths work s supported by the Advanced Power Technologes (APT) Center at the Unversty of Washngton. The APT Center s supported by ALSTOM ESCA, LG Industral Systems, and Mtsubsh Electrc Corp. Ths work s also partally supported by the Natonal Scence Foundaton Career Award Grant # and Amercan Publc Power Assocaton. All authors are wth the SEAL (Sensors, Energy, and Automaton Laboratory), Department of Electrcal Engneerng, Box 35500, Unversty of Washngton, Seattle, WA (E-mals: mwang@ee.washngton.edu; gaber@ee.washngton.edu; mamshev@ee.washngton.edu) sgnfcantly affectng e-commerce and many manufacturng ndustres, such as semconductors, automobles, and paper. A report by CEIDS (Consortum for Electrc Infrastructure to Support a Dgtal Socety) shows that the U.S. economy s losng between $104 bllon and $164 bllon each year due to outages and another $15 bllon to $4 bllon due to PQ phenomena [1]. Tradtonal montorng methods are based on RMS measurements and constraned by ther accuraces. Recently proposed approaches for automated detecton and classfcaton of PQ dsturbances are based on wavelet analyss, artfcal neural networks, hdden Markov models, and bspectra [-6]. Real-tme PQ montorng hardware should be capable of acqurng voltage or current waveforms, dentfyng the event type based on the waveform pattern, understandng the cause of the dsturbance, and makng system protecton and preventon decsons. Dgtal sgnal processors (DSP) are dstnct from generalpurpose mcroprocessor, manly due to ther capacty for realtme computng. Wth more optmzed archtectures towards faster multplcatons and accumulatons than general-purpose mcroprocessors, DSPs have wde applcatons n speech, dgtal audo, mage, and vdeo processng, and telecommuncatons. Ths paper presents a dgtal sgnal processor-based hardware system for PQ classfcaton based on a recently proposed PQ classfcaton algorthm by the authors [7]. The algorthm s mplemented wth a Texas Instruments (TI) TMS30VC5416 dgtal sgnal processor (DSP) wth the TI THS106 1-bt 6 MSPS analog to dgtal converter. A TI TMS30VC5416 DSP Starter Kt s used as the host board wth the THS106 mounted on a daughter card. Ths paper demonstrates the feasblty of mplementng the proposed PQ classfcaton algorthm n real-tme wth a DSPbased system and s one of the frst case studes of usng DSP technologes n the area of power qualty montorng [8,9]. II. THE PQ CLASSIFICATION ALGORITHM PQ dsturbances cover a broad frequency range and sgnfcantly dfferent magntude varatons. In ths paper, a new PQ classfcaton algorthm s presented wth an example applcaton of dscrmnatng fve major power system waveform events: harmoncs, voltage sags, capactor hgh frequency swtchng, capactor low frequency swtchng, and normal voltage varatons, as shown n Fg. 1. The complete

2 mplementaton algorthm presented n ths paper s shown n Fg.. The two sequental processes: feature extracton and classfcaton are explaned n detals n the followng two subsectons. of the classfcaton-optmal TFRc. Fsher s dscrmnant functon (FDF), whch was developed by R. A. Fsher n 1930s, s a method that projects hghdmensonal data onto low-dmensonal space for classfcaton. A. Feature extracton A.1. Theoretcal background There s an nfnte number of possble tme-frequency representatons (TFRs) correspondng to a sgnal [10]. For waveform recognton problems, features need to be selected from a TFR that maxmzes the separablty of sgnals n dfferent classes and mnmzes the smlarty of sgnals n the same class. Therefore, t s desrable to desgn a classfcatonoptmal representaton TFR c that specfcally emphaszes the dfferences between classes, but not necessarly descrbes the tme-frequency nformaton accurately [11,1]. Tme-frequency ambguty plane has been an mportant tool n the radar feld, n analyzng and constructng radar sgnals, formulatng the performance characterstcs of a waveform, and relatng range and velocty resoluton [13]. It has also been used extensvely n the felds of sonar, rado astronomy, communcatons, and optcs [14]. Gllespe and Atlas have recently proposed feature extracton methods based on desgnng class-dependant TFRs from tme-frequency ambguty plane. Ths class of new technques has been successfully appled for tool-wear montorng and radar transmtter dentfcaton [1,15,16]. The connecton between the ambguty plane and tmefrequency representatons has been recognzed for a long tme. Any blnear (Cohen class) TFR P(, t f ) can be expressed as the two-dmensonal Fourer transform of the product of the ambguty plane A( ητ, ) of the sgnal and a kernel functon ϕητ (, ) [10]: jπηt j π fτ P(, t f) A( ητ, ) ϕητ (, ) e e d d = η τ (1) where t represents tme, f represents frequency, η represents contnuous frequency shft, and τ represents contnuous tme lag. Equaton (1) shows that the kernel functons determne the TFRs and ther propertes. A kernel functon s a generatng functon that operates upon the sgnal to produce the TFR. The characterstc functon for each TFR P(, t f ) s A( ητ, ) ϕητ (, ). The classfcaton-optmal representaton TF can be obtaned through smoothng the ambguty plane wth an approprate kernel ϕ, whch s a classfcaton-optmal kernel. The problem of desgnng the TFRc becomes equvalent to desgnng the classfcaton-optmal kernel ϕ ( η, τ). Features can also extracted drectly from the A( ητ, )ϕ( ητ, ), nstead R c Tme [ms] Fg. 1. Fve classes of PQ sgnals for classfcaton: (a) harmoncs; (b) voltage sag; (c) normal voltage varatons; (d) capactor hgh frequency swtchng; (e) capactor low frequency swtchng. Wth the Fsher s crtera, locatons on the ambguty plane are ranked accordng to ther mportance for ths classfcaton task. For example, when desgnng kernel, a Fsher s dscrmnant score s calculated for each locaton ( ητ), on the ambguty plane, J F ( m[ ητ, ] m [ ητ, ]) ( ητ, ) = D [, ] [ ητ, ] reman ητ+ D reman where m [ and represent mean values ητ, ] m [, ] reman ητ correspondng to class and the remanng classes at locaton ( ητ, ), and [ ητ, ] and D [ ητ, ] represent varance values. D reman A.. Detaled tranng and mplementaton methods Accordng to the Fsher s dscrmnant functon, four classfcaton-optmal kernels are desgned for four classes/class-groups: harmoncs, voltage sags, capactor swtchng class-group, and capactor hgh-frequency swtchng, respectvely. The dscrete verson of equatons (1) s [1], TFR n k 1 [, ] = Fη n{ Fτ k{ A[ ητϕητ, ] [, ]}} N 1 N 1 1 j( π/ N) τk j( π/ N) ηn = A[ ητϕητ, ] [, ] e e N η= 0 τ= 0 () (3)

3 wth A[ ητ, ] = F { R[ n, τ]} n η N 1 = Rn [, τ] e n= 0 j( π/ N) ηn where n represents sample, k represents dscrete frequency, η represents dscrete frequency shft, and τ represents dscrete tme lag. The nstantaneous autocorrelaton functon Rn [,τ] s defned as (4) sgmod transfer functon as the transfer functon for the hdden layer, the lnear transfer functon as the transfer functon for the output layer, the Levenberg-Marquardt backpropagaton as the network tranng functon, the gradent descent learnng functon as the weght learnng functon, and the mean squared error functon as the performance evaluaton functon. A PQ event sgnal * R[ n, τ ] = x [ n] x[mod( n+τ, N)] (5) where the functon mod( p1, p) represents modulus after p. In ths applcaton, the kernel ϕ η s defned as a bnary dvdng the frst parameter p 1 by the second parameter [, τ] matrx (each matrx element s ether 0 or 1), therefore, A[ ητ, ], f ϕ[ ητ, ] = 1 A[ ητϕ, ] [ ητ, ] = 0, f ϕ[ η, τ] = 0 Feature ponts are ambguty plane ponts of locatons ( ητ), where ϕ η. Therefore, the process of feature extracton [, τ ] = 1 s to select ponts that are optmal for the classfcaton task from the ambguty plane. The feature rankng mechansm s shown n Equaton (). Locatons that receve hgher dscrmnant scores are selected as feature locatons. B. Classfcaton (6) Harmoncs kernel Heavsde classfer Sag kernel NN 1 (-1-) Capactor swtchng kernel Harmoncs event Sag event Multple classfers are adopted n the presented method. Each classfcaton node conssts of a kernel functon and a classfer. Dependng on the nature of the kernel, classfcaton node s to ether dscrmnate sgnals that belong to class from sgnals that belong to class {+1,, n}, or dscrmnate sgnals n class {,, +m} from sgnals n class {+m+1,, n}. Four classfers are employed n ths classfcaton applcaton for fve types of PQ events. They are a Heavsde lnear classfer (for the class of harmoncs) and three feedforward neural network classfers (for the other three classes) wth smple structures. For a two-class classfcaton problem and an nput f, the Heavsde lnear classfer s defned as 1( f belongs to class1), f f t 0 H( f t) = 0( f belongs to class ), f f t < 0 where t s a real threshold value. Tranng ths classfer s to determne the threshold parameter t. Three feedforward neural network (FNN) classfers adopted n ths algorthm all have three layers. The structure of the FNN for dscrmnatng sags s -1- (nput layer node number-hdden layer node number-output layer node number); the one for capactor swtchng s 3-10-; the one for capactor hgh-frequency swtchng s The transfer and tranng functons adopted for the FNN nclude: the hyperbolc tangent (7) NN (3-10-) Normal varaton event Capactor lowfrequency swtchng event Capactor hgh-frequency swtchng kernel NN 3 (3-10-) Capactor hghfrequency swtchng event Fg.. The proposed PQ classfcaton algorthm (mplementaton phase). III. DATA FLOW AND DSP FEATURES A global block dagram for the montorng system s shown n Fg. 3. The nput sgnal s frst passed through a potental transformer and sampled usng a 1-bt analog to dgtal converter (ADC) daughter card. The 1-bt ADC collects sgned nteger values wth a range from -047 to 047. Ths data s then placed nto a 3-word FIFO buffer. Upon fllng the buffer, a data avalable sgnal actvates an external nterrupt on the C5416 processor External Perpheral Interface bus. Wthn the nterrupt servce routne, the FIFO s read

4 through an nput/output (IO) port va the External Memory Interface bus on the C5416 processor. Ths data s moved nto a 640-element array for nput to the feature extracton and classfcaton algorthm. Whle n fle mode, text fles are sent from a host computer va the USB port to the C5416 usng the C standard IO functons convenently modfed for bdrectonal transmsson along the USB port. Whle n standalone mode, the resultng classfcaton of a sampled sgnal would be relayed to a control devce va the general purpose IO port on the Host Port Interface as a bnary number from 1 to 5 ( ). The TMS30VC5416 s a fxed-pont DSP processor wth 18 KB of on-chp memory and a 160 MHz clock speed, whch can perform 160 MIPS. Ths processor has a 17x17 parallel multply accumulator unt whch allows sngle cycle multply accumulate operatons. Ths allows for fast executon of nteger multplcatons. Whle floatng pont multplers on other processors may allow drect multplcaton of floatng pont values, ths DSP processor executes sngle clock cycle nteger multplcatons. Optmzaton to use all ntegers s therefore necessary. However, f a loss of precson s allowable, ths processor wll actually execute an nteger multplcaton faster than a floatng-pont processor of a smlar clock speed due to the parallel multpler and accumulaton unts n the place of a ppelned multpler. The ppelned multpler on the TMS30VC6711, a 3-bt DSP, requres 4 cycles to complete a 3-bt multplcaton. Whle the ppelne may theoretcally allow for faster sequental multplcatons, n practce a sngle multplcaton s carred out and stalls the ppelne whle t fnshes and stores the result to the accumulator or a memory locaton. IV. OPTIMIZATION FOR REAL-TIME COMPUTING Because the major task of the presented PQ montor s to classfy dsturbances n real-tme, sgnfcant optmzaton efforts have been taken when programmng the DSP, n order to reduce the algorthm computaton tme. A. Reduce the quanttes to be calculated The results of kernel and classfer tranng show that only nne kernel ponts from seven columns of ambguty plane are needed for mplementng the classfcaton process. Accordng to equatons (5) and (4), t s enough to just calculate seven kernel-related columns from the matrx Rnτ [, ] and nne kernel ponts from the matrx A[ ητ, ]. If the process wndow sze s N, the computaton cost for calculatng the entre autocorrelaton matrx Rnτ [, ] s ON ( ) multplcatons, and the cost for calculatng the entre 3 ambguty plane matrx A[ ητ, ] s ON ( ) multplcatons and 3 ON ( ) addtons. After reducng the number of quanttes to be calculated as stated n the prevous paragraph, the worstcase computaton cost for the autocorrelaton step s reduced to ON ( ) multplcatons, and the worst-case cost for the ambguty plane step s reduced to ON ( ) multplcatons and ON ( ) addtons. Snce N s equal to 640 n ths applcaton, the optmzaton approxmately reduces the computaton tme 640 tmes n the autocorrelaton step and =409,600 tmes n the ambguty plane step. B. Use fxed-pont nteger multplcaton as much as possble Due to the 16-bt fxed-pont nature of the processor used n ths paper, optmzaton was requred to ensure floatng-pont values were avoded. The analog to dgtal converter convenently produces nteger values rangng from -047 to 047 to allow a smooth transton nto the algorthm executon wthout converson. Whle these values could be stored as 16- bt ntegers, the subsequent steps requred the use of long (3- bt) ntegers. The dscrete Fourer transform (DFT) requres multply accumulatons whch would easly exceed 3-bts qute quckly. The long nteger values were broken nto seven bt ntegers to allow for use of the sngle cycle multplyaccumulate (MAC) functon. Each accumulaton represents a porton of the fnal summaton after beng multpled by 7 and s then normalzed for storage nto a floatng-pont value. For each DFT operaton, ths normalzaton and addton step would occur once for the real part and once for the magnary part. Ths all-nteger optmzaton cut the algorthm executon tme n half. C. Use hard-coded sn table and cos table The dscrete Fourer transform (DFT) s mplemented wth cos and sn functons nstead of the exponental functon, accordng to the Euler s Equaton. Due to the focus on accuracy n the standard C math header fle, the sn and cos are qute costly n processor tme. Because the on-chp memory had not been completely consumed by other operatons of the algorthm, the use of a lookup table for these functons was chosen. The values were stored as sgned ntegers rangng from to Due to the 1-bt ADC resoluton, ths range was adequate. V. RESULTS AND DISCUSSIONS A. Real-tme montorng capablty The classfcaton process of an ms wndow takes 10.9 ms when the ADC s not runnng on the same board, whch satsfes the real-tme constrants n most power qualty montorng tasks. Wthn the 10.9 ms, 1.7 ms are used for the autocorrelaton step, 8.5 ms for the DFT step, and 0.70 ms for classfer step. In Fg. 4, the classfcaton process of the same fve-cycle wndow takes 11. ms, whch s measured when the ADC s runnng on the same board and nterruptng 960 tmes per second. Ths requres a real-tme constrant of movng the data from the FIFO buffer nto program memory wthn a 1/960 sec wndow.

5 80 THS106 1-bt ADC daugher card USB port nterface PC workstaton Voltage/current sgnals under montorng Potental/current transformers External memory nterface External perpheral 80 nterface 80 On-board IO nterface TMS30VC5416 DSK 80 TMS30VC MHz DSP Host port nterface Other decson modules Fg. 3. Block dagram of the hardware PQ montorng system. B. Classfcaton performance In ths study, the classfcaton experment s conducted wth fve-class examples, as shown n Fg. 1, under fle mode va USB port. A total of 860 real world voltage sgnals were collected from ndustral databases for system testng. A sngle text fle represents a voltage sgnal to be dentfed. It conssts of fve cycles of voltage waveform sampled 18 tmes per cycle, and has a length of 640 samplng ponts. A wndow sze of 83.3 ms (fve snusodal waveform cycles n a 60 Hz system) was adopted due to the followng two reasons. Frst, a fve-cycle wndow s long enough to capture the characterstcs of all types of PQ events under our study. Second, a fve-cycle wndow s short enough for generatng real-tme montorng outputs for many PQ-related applcatons. The 83.3 ms wndow sze used n ths paper for demonstraton of the algorthm, can be adjusted approprately for specfc applcatons. For example, when ths method s appled for the dscrmnaton of dfferent types of hgh frequency power system transents, the wndow sze can be reduced to one or two cycles. The classfcaton results from Matlab smulatons and from the DSP system (both 1-bt and 14-bt) are presented n Table 1. Matlab uses 64-bt for the double calculatons, but the presented system uses 1-bt precson. C. Dscussons The ADC daughter card allows for rapd evaluaton of dfferent ADCs wth a host DSK. However, lmtatons due to processor context changes for nterrupt servce routnes occur and typcally lmt these ADCs to 1MSPS (wthout Drect Memory Access ports). For the purposes of ths paper, ths was not an ssue. However, ths DSK may not be adequate for the hgh samplng rates assocated wth power protecton applcatons. A custom prnted crcut board would be requred for ths applcaton and the use of non-nterrupt based technques, such as pollng, would most lkely be requred to manage context swtchng delays. TABLE 1. RESULTS OF A CLASSIFICATION EXPERIMENT WITH REAL WORLD POWER QUALITY DATA Classes Testng events Matlab DSP wth 1-bt ADC DSP wth 14-bt ADC Harmoncs % 100% 100% Sags % 100% 100% Cap. slow swtchng Cap. fast swtchng Normal varatons % 9.% 93.3% % 9.8% 9.8% % 90.4% 96.5% Total % 95.0% 96.5% Programmatcally, the optmzatons enacted to yeld faster algorthm performance could be carred further wth the use of all assembly language routnes and ntrnsc functons. Average calculaton tmes could also be decreased by performng only the porton of the algorthm requred for each classfcaton step and checkng the neural network output mmedately. Whle ths would yeld faster average computaton tmes, ths would ncrease the executon tme length for the worst case as the functon calls to perform these short queres would slow the DFT step even further. The assumpton that only one power qualty class wll occur wthn a fve-cycle wndow ntroduces the possblty of naccurate classfcaton. VI. CONCLUSIONS A DSP-based hardware montorng system for power qualty event dentfcaton s presented n ths paper. The algorthm s mplemented wth a Texas Instruments (TI) TMS30VC5416 dgtal sgnal processor (DSP) wth the TI THS106 1-bt 6 MSPS analog to dgtal converter. In the algorthm, by desgnng classfcaton-optmal TFRs, features are selected from the tme-frequency ambguty plane based on the Fsher s prncple. Four lnear and neural network classfers are used as classfers. The algorthm s optmzed accordng to the archtecture of the DSP to meet the real-tme constrants of classfyng a fve-cycle segment of the 60 Hz snusodal voltage/current sgnals n power systems. The proposed system s successfully tested wth a fve-class PQ classfcaton experment. A waveform wndow of 83 ms (640 sample ponts) can be classfed n 10.9 ms. Recognton rate of 96.5% wth 14-bt ADC and 95.0% wth

6 1-bt ADC are acheved on 860 testng PQ waveforms. The real-tme power qualty montorng system has potental applcatons of enhancng power system protectons and accumulatng PQ event statstcs for power qualty assessment. Fg. 4. Real-tme montorng duty cycle. VII. ACKNOWLEDGMENTS Specal thanks go to UW EE undergraduate students Cheuk-Wa Mak and Jeff Chen for ther work on sgnal processng algorthms and DSP programmng respectvely. The authors also would lke to acknowledge the help on power qualty data collectons from Joe Wlson (Eugene Water and Electrc Board) and James Harrs (Bonnevlle Power Admnstraton). The authors would also lke to thank scholarshp sponsorshps from the EEIC (Electrcal Energy Industral Consortum) and Granger Foundaton undergraduate research programs at the Unversty of Washngton. VIII. REFERENCES [1] CEIDS (Consortum for Electrc Infrastructure to Support a Dgtal Socety), "The Cost of Power Dsturbances to Industral and Dgtal Economy Companes Executve Summary," July 001. [] J. Chung, E. J. Powers, W. M. Grady, and S. C. Bhatt, "Electrc Power Transent Dsturbance Classfcaton Usng Wavelet-Based Hdden Markov Models," Proceedngs of 000 IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol. 6, 000, pp [3] A. M. Gaouda, M. A. Salama, M. R. Sultan, and A. Y. Chkhan, "Power Qualty Detecton and Classfcaton Usng Wavelet- Multresoluton Sgnal Decomposton," IEEE Transactons on Power Delvery, vol. 14, no. 4, pp , Oct [4] J. S. Lee, C. H. Lee, J. O. Km, and S. W. Nam, "Classfcaton of Power Qualty Dsturbances Usng Orthogonal Polynomal Approxmaton and Bspectra," Electroncs Letters, vol. 33, no. 18, pp , Aug [5] B. Peruncc, M. Malln, Z. Wang, Y. Lu, and G. T. Heydt, "Power Qualty Dsturbance Detecton and Classfcaton Usng Wavelets and Artfcal Neural Networks," The 8th Internatonal Conference on Harmoncs and Qualty of Power, 1998, pp [6] S. Santoso, E. J. Powers, W. M. Grady, and A. C. Parsons, "Power Qualty Dsturbance Waveform Recognton Usng Wavelet-Based Neural Classfer. I. Theoretcal Foundaton," IEEE Transactons on Power Delvery, vol. 15, no. 1, pp. -8, Jan [7] M. Wang, P. Ochenkowsk, and A. V. Mamshev, "Classfcaton of Power Qualty Dsturbances Usng Tme-Frequency Ambguty Plane and Neural Networks," IEEE Power Engneerng Socety Summer Meetng, 001, vol., 001, pp [8] G. Bucc and C. Land, "On-Lne Dgtal Measurement for the Qualty Analyss of Power Systems Under Nonsnusodal Condtons," IEEE Transactons on Instrumentaton and Measurements, vol. 49, pp , Aug [9] A. Lakshmkanth and M. M. Morcos, "A Power Qualty Montorng System: a Case Study n DSP-Based Solutons for Power Electroncs," IEEE Transactons on Instrumentaton and Measurements, vol. 50, pp , June 003. [10] L. Cohen, Tme-Frequency Analyss, Prentce-Hall, [11] M. Davy and C. Doncarl, "Optmal Kernels of Tme-Frequency Representatons for Sgnal Classfcaton," Proceedngs of the IEEE-SP Internatonal Symposum on Tme-Frequency and Tme-Scale Analyss, 1998, pp [1] B. W. Gllespe and L. Atlas, "Optmzng Tme-Frequency Kernels for Classfcaton," IEEE Transactons on Sgnal Processng, vol. 49, no. 3, pp , Mar [13] L. Cohen, "Tme-Frequency Dstrbutons - A Revew," Proceedngs of the IEEE, vol. 77, no. 7, pp , July [14] F. Hlawatsch and G. F. Boudreaux-Bartels, "Lnear and Quadratc Tme-Frequency Sgnal Representatons," IEEE Sgnal Processng Magazne, vol. 9, no., pp. 1-67, Apr [15] B. W. Gllespe and L. Atlas, "Optmzaton of Tme and Frequency Resoluton for Radar Transmtter Identfcaton," Proceedngs of 1999 IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol. 3, 1999, pp [16] B. W. Gllespe and L. Atlas, "Data-Drven Tme-Frequency Classfcaton Technques Appled to Tool-Wear Montorng," Proceedngs of 000 IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol., 000, pp IX. BIOGRAPHIES Mn Wang receved a Bachelor s degree from Tsnghua Unversty, Bejng, Chna, n 1999, and a M.S.E.E. degree from the Unversty of Washngton, Seattle, n 001. Currently he s a Ph.D. student and research assstant at the Department of Electrcal Engneerng, Unversty of Washngton. Hs research nterests nclude pattern recognton, tme-frequency analyss, dgtal sgnal processng, and power qualty montorng. He s a recpent of the Frst Prze Award n the Student Paper-Poster Competton n the 00 IEEE Power Engneerng Socety Summer Meetng n Chcago. Gabrel I. Rowe s an undergraduate student n the Department of Electrcal Engneerng at the Unversty of Washngton, Seattle. He wll receve hs BSEE n June 003. Hs research nterests nclude sensors and DSP for applcatons n power qualty montorng and the bomedcal feld. He s a recpent of the EEIC Scholarshp n 00. Alexander V. Mamshev receved an equvalent of B.S. degree from the Kev Polytechnc Insttute, Ukrane, n 199, M.S. degree from Texas A&M Unversty n 1994, and a Ph.D. degree from MIT n 1999, all n electrcal engneerng. Currently he s an assstant professor and drector of SEAL (Sensors, Energy, and Automaton Laboratory) n the Department of Electrcal Engneerng, Unversty of Washngton, Seattle. Prof. Mamshev s an author of about 50 journal and conference papers, and one book chapter. Hs research nterests nclude PQ montorng, sensor desgn and ntegraton, delectrometry, and electrcal nsulaton dagnostcs. He serves as an Assocate Edtor for the IEEE

7 Transactons on Delectrcs and Electrcal Insulaton and a revewer for the IEEE Transactons on Power Delvery. He s a recent recpent of the NSF CAREER Award and the IEEE Outstandng Branch Advsor Award.