A Novel Impedance Measurement Technique for Power Electronic Systems

Transcription

1 A Novel mpeance Measurement Technque or Power Electronc Systems Peng Xao, Stuent Member, EEE, Ganesh enayagamoorthy, Senor Member, EEE, an Keth Corzne, Senor Member, EEE Real-Tme Power an ntellgent Systems Laboratory Electrcal an Computer Engneerng Department Unversty o Mssour-Rolla, Rolla, MO 65401, USA Abstract - When esgnng an bulng power systems that contan power electronc swtchng sources an loas, system ntegrators must conser the requency-epenent mpeance characterstcs at an nterace to ensure system stablty. Stablty crtera have been evelope n terms o source an loa mpeance or both c an ac systems an t s oten necessary to measure system mpeance through experments. Tratonal njecton-base mpeance measurement technques requre multple onlne tests whch lea to many savantages. The mpeance entcaton metho propose n ths paper greatly reuces onlne test tme by moelng the system wth recurrent neural networs. The recurrent networs are trane wth measure sgnals rom the system wth only one njecton. The measurement an entcaton processes or c an three-phase ac nteraces are evelope. Smulaton tests emonstrate the eectveness o ths new technque.. NTRODUCTON Stablty analyss n power electroncs base strbute power systems s a more crucal tas than n conventonal power systems ue to the nearly eal control capablty o many moern power converters. The excellent loa regulaton capablty o a converter s a esrable eature n many applcatons, but t also maes the converter a constant-power loa evce, whch s a potental cause o negatve mpeance nstablty [1]. For small-sgnal stablty analyss, most research ocuses on the mpeance/amttance metho that nvolves examnng the Nyqust contour o the prouct o the source mpeance an loa amttance n a c system [2]. n recent years, base on the mpeance/amttance metho, a varety o stablty crtera an esgn approaches or both c an ac systems have been propose [3-4]. n the esgn, ntegraton an analyss o strbute power systems, t s oten necessary to obtan the small-sgnal mpeance/amttance characterstcs o an exstng power electronc component or subsystem at a gven operatng pont. To get the requency-epenent characterstcs by experment, peroc voltage or current perturbatons are usually njecte to the system whle t s uner operatonal power. Measurements o the perturbe system are then taen an processe to etermne the mpeance at a specc requency. Several methos have been propose or mpeance measurement n hgh-power ac systems, nclung utlzaton o three-phase brge converters, woun-rotor nucton machnes an three-phase chopper crcut [5-6]. An mpeance measurement technque utlzng a lne-to-lne current njecton chopper crcut was recently propose [7], whch has a smple structure an s much easer to mplement compare wth other methos. A common problem o these mpeance measurement technques s that they requre njecton o perturbaton sgnals to the system one requency at a tme. To obtan the mpeance characterstcs over a we requency range or stablty analyss, multple tests must be repeately perorme. Durng each test, a perturbaton sgnal o a specc requency s njecte nto the system, an the voltages an currents are measure an recore. When tests or all requences are nshe, the recore ata s processe to calculate the mpeance value at each requency. The man savantages o ths proceure nclue: () t taes a long onlne tme to complete the njectons or all requences; () The operatng pont o the system may vary urng the prolonge test proceure, whch can lea to nconsstency n the measure system mpeance characterstcs; () the mpeances at atonal requences are neee, new tests must be perorme on the system, whch may cause nterrupton to the normal operaton o the system. n ths paper, a erent approach s taen to enty the mpeance characterstcs o a c or three-phase ac system. nstea o measurng system mpeance at one specc requency each tme, the propose metho requres only one njecton an measurement process. The recore ata s use not to rectly calculate mpeances, but to bul a moel o the system at the spece operatng pont by tranng a recurrent neural networ (RNN). The trane neural networ s then use to obtan the mpeance characterstcs. Smulaton results show that the propose metho s capable o accurately entyng mpeances o both c an threephase ac systems.. MPEDANCE MEASUREMENT FOR STABLTY ANALYSS The analyss o small-sgnal stablty aroun steay states o a power electronc system s mportant or both control esgn an component ntegraton. n the esgn stage, the mathematcal moel o the system s nown, t can be use to extract the mpeance characterstcs o the system. n /07/$ EEE 955

2 aton, moels o erent system components can be connecte together to smulate ther behavors uner erent operatng contons, an lnearzaton tools are usually avalable to etermne the state-space matrces o the system. The stuaton s erent n the component ntegraton stage, when the harware components are connecte together to orm a system. n ths case, the etale moels o the components are oten not avalable, especally when the components are esgne an manuacture by erent venors. To evaluate the stablty o the ntegrate system, measurements an tests are necessary to obtan the mpeance normaton o each component. The njecton-base mpeance measurement technques utlze small voltage or current sgnals to perturb the system uner stuy, whle t s operatng n steay state. arous njecton evces have been propose. For low-power systems, power amplers can be use. For hgh-power systems, erent conguratons o chopper crcuts are oten use, n whch swtchng evces are turne on an o to prove a varyng mpeance branch that creates the perturbatons. The mpeance measurement test or three-phase ac systems s more complcate. As shown n Fg. 2, the shunt njecton requres a three-phase current source an measurement o nne sgnals. Also, the mpeance normaton or the source an loa s represente by a 3 by 3 matrx. For three-phase balance systems wthout neutral wre, reerence rame transormaton theory proves a convenent way to stuy the mpeance characterstcs. n the synchronous reerence rame, the mpeance an amttance tae matrx orms q q q q Y (2) where qq q Y qq Y 1 q Y (3) q Yq Y To etermne the our mpeance entres n the matrx, two sets o njecton sgnals are neee at each requency. Ths actually oubles the number o tests neee to enty the system mpeance characterstcs over a we requency range. Fg. 1. mpeance Measurement n c systems. Fg. 1 shows the shunt njecton agram or c systems. The system s ve nto two parts, esgnate as source an loa, although the actual power low can be ether rom the loa to the source or rom the source to the loa. The njecton evce s connecte at ther common nterace. n the shunt njecton system, a current sgnal o a specc requency s njecte nto the system at a steay-state operatng pont. The c voltage at the nterace, together wth the loa an source currents, are measure. The waveorms o these sgnals are recore. Fourer transorm s then use to process these sgnals an etermne the magntues an phase angles o the components at the njecton requency. The small sgnal mpeances o the loa an source can then be calculate wth s l (1) s l where s the njecton requency,, s an l are complex numbers obtane rom Fourer transorm o the c voltage, source current, an loa current sgnals. Ths sngle njecton test gves the mpeance normaton o the system at a sngle requency. To obtan mpeances at other requences, the same test proceure s be repeate, each tme wth a erent njecton requency. Fg. 2. mpeance Measurement n three-phase ac systems.. RNN-BASED MPEDANCE DENTFCATON METHOD The ey pont o the propose metho s the moelng o a ynamc system uner stuy. a moel can be bult to accurately prouce the small-sgnal tme-oman responses o the system to all ns o nputs, then t also has the ablty to prouce the requency-oman characterstcs o the system. For an exstng harware system, the nternal evce parameters are oten unavalable, thus t s mpractcal to bul the moel base on nowlege o the evce s nternal structure an control algorthms. nstea, the moelng process has to rely on measurement o ts nput an output sgnals. A. Recurrent Neural Networ as a Moelng Tool For ynamc systems, recurrent neural networ has been emonstrate to be an eectve moelng tool n many applcatons. Unle the wely-use multlayer eeorwar neural networs that can only establsh statc mappng relatonshp between nputs an outputs, RNNs contan nternal eebac loops an states. The outputs o RNNs are unctons o nternal states as well as the nputs, just as they are n ynamc systems. The eebac mechansm proves a 956

3 memory to the recurrent networs so that they are capable o moelng systems wth nternal ynamcs. n ths stuy, the Elman RNN topology s chosen as the moelng tool. Fg. 3 shows a smple agram o a two-layer Elman recurrent networ structure. For a networ wth l nputs, m hen neurons, an n outputs, the hen layer equatons are s l (1) (2) t w x t w j j t 1 m j1 where t sgms 1 (4) (5) x(t) s the nput vector, w (1) s the weght matrx assocate wth the nputs an hen neurons, an w (2) s the weght matrx assocate wth the states an hen neurons. The outputs o the networ are etermne by y t m 1 w (3) t where w (3) s the weght matrx assocate wth the hen neurons an the outputs. (6) RNN. Durng the tranng process, nput ata are e to the networ to calculate the output, an the nternal weght parameters o the RNN are ajuste base on the output error. Several RNN tranng algorthms are avalable. Both bacpropagaton an partcle swarm optmzaton algorthms [12] are use n ths stuy. C. Ranom PWM Sgnal njecton Tranng o the RNN requres measurement ata o a perturbe system, thus njecton o perturbaton sgnals s stll necessary n the propose metho. For the shunt njecton, chopper crcuts propose n [7] are use to hanle the hgh voltage an power o the teste system. Fg. 4 shows the crcut as beng use or lne-to-lne current njecton n a three-phase ac system. The crcut contans a b-rectonal swtch that controls the branch s mpeance, whch n turn causes varatons n the branch current. A properly esgne swtchng pattern can thus ntrouce a perturbaton current sgnal nto the system. A xe-requency xe-uty-cycle PWM swtchng scheme was use n [7] to generate a perturbaton sgnal o a specc requency. Fg. 3. Topology o the Elman recurrent networ. Past research has emonstrate the ablty o the RNN to learn process ynamcs an prove ecent orecasts, an t has oun applcaton n many areas such as wn spee an power orecastng [8], esgn o a power system stablzer [9], nucton motor spee estmaton[10], an precton o elephant mgraton [11]. B. Moelng wth RNN To moel a ynamc system wth RNN, the networ must be trane wth measure ata so that t learns the behavors o the system. t shoul be note that the purpose o the tranng s not to obtan a complete moel o the complex nonlnear power electronc system. nstea, throughout the test, the system s runnng at a specc steay-state operatng pont. Small varatons o voltage or current are ae to the system to create perturbatons. The neural networ s then use to moel the behavor o the system responng to small sgnal nputs. The measure sgnals are voltage an current waveorms at the nterace o the source an loa. These waveorms are use as tranng ata or the nput an target output o the Fg. 4. Chopper crcut shown n three-phase system njecton. Fg. 5. Spectrum o a ranom PWM sgnal. 957

4 For the RNN to learn the ynamc behavor o the system, the spectrum o the perturbaton sgnal must cover a we requency range. A ranom PWM sgnal wth lmte banwth s use n ths stuy, whch can be generate by a PWM swtchng scheme wth ranom uty cycle an ranom swtchng requency. n each PWM cycle, the swtchng requency s ranomly chosen between two bouns, mn an max, whch are etermne accorng to the requency range o nterest. Fg. 5 shows the spectrum o such a swtchng sgnal, wth mn = 1 Hz an max = 5 Hz. t can be seen that the sgnal has a relatvely even magntue at requences below 3 Hz. At requences above 3 Hz, the magntue ecreases wth a slope between 20 B/ecae an 40 B/ecae. Durng the pero when the system s beng perturbe by a ranom PWM swtchng crcut, the voltage an current sgnals o the source an loa are measure, ltere an recore. For a c system, the recore ata s normalze an use rectly to tran the RNN. Ether the voltage or the current sgnal can be use as the nput, an the other sgnal s use as the target output. For a three-phase ac system, the measure sgnals are rst transorme nto the synchronous reerence rame so that the unamental components become c sgnals. Ater normalzaton, the ata s then use or RNN tranng. The tranng process o the RNN nvolves repeately eeng the networ wth the nput ata, calculatng the outputs, an comparng the calculate outputs wth the target outputs. The networ weghts are moe n each epoch to mnmze the error. The tranng stops when the error s below a certan threshol value. A well-trane RNN can prouce correct outputs even when the nputs are erent rom ts tranng ata. t s ths generalzaton capablty o RNNs that maes them sutable or mpeance characterstcs extracton. The trane RNN can be seen as an accurate small-sgnal moel o the system, an tests can be perorme on the RNN nstea o on the real system to obtan the mpeance normaton. D. entcaton Process or c Systems For a c system, to etermne the mpeance value at a requency, a snusoal sgnal o requency s e to the trane RNN to prouce the output. The nput an output sgnals are then processe wth Fourer transorm to etermne ther magntues an phase angles. The mpeance/amttance o the system at can be calculate wth (1). E. entcaton Process or Three-Phase ac Systems For a three-phase ac system, the RNN s trane wth currents as nputs an voltages as outputs, then t s relatvely easer to calculate the mpeance matrx. For each requency, there are our mpeance values to be etermne an two steps are neee. n the rst step, a snusoal sgnal o requency s e to the trane RNN as q, whle the nput sgnal s set to a zero vector. The RNN output voltages v q an v are then calculate wth (4)-(6). Accorng to (2), two mpeance entres can be etermne by qq q q (7) q q where q, an q are the complex results rom Fourer transorm o v q, v an q, respectvely. The secon step s smlar to the rst one except that the snusoal sgnal s e to the RNN as, whle q s set to zero. The other two mpeance entres can be etermne by q q (8) Fg. 6 shows a lowchart o the propose mpeance measurement proceure or three-phase ac systems. t can be seen that the onlne part o the proceure only nclues the njecton o the ranom PWM sgnal an ata measurement, an the rest o the process only requres olne tranng an calculatons. Fg. 6. Flow chart o the propose mpeance measurement proceure or three-phase ac systems.. 958

5 Fg. 7. Test system or c mpeance measurement.. SMULATON RESULTS The propose mpeance measurement technque was vere wth smulaton results o both c an three-phase ac systems. A. Test Results n c Systems A 3.7 W varable-spee motor rve system s use or the c test, an ts agram s shown n Fg. 7. The example system conssts o a three-phase actve recter, 300 c ln, a three-phase nverter, an a 5 hp nucton motor. nput an output lters are use to reuce the PWM swtchng noses. The c ln nterace o a recter-nverter-nucton motor system s use or the c sgnal njecton. The locaton o the njecton evce s shown n Fg. 7, where the current source on the c ln represents the chopper crcut as shown n Fg. 4. To measure the mpeance o the subsystem to the rght o the njecton evce, both v c an loa are measure an save. The requency range o nterest s rom 10 Hz to 1 Hz, an the requency bouns o the ranom PWM sgnal s set to be 400 Hz an 1 Hz. The measure sgnals are ltere to avo alasng, an sample at a requency o 10 Hz. The ata s then normalze to be wthn the range rom -1 to 1. An Elman recurrent neural networ s trane wth the voltage ata as nput an current ata as output. The extracte mpeance characterstcs are shown n Fg. 8. The actual mpeance curves are obtane base on the lnearze state-space matrx n a smulaton moel o the system. As can be seen, a very close match between the measure an actual values s acheve. B. Test Results n ac Systems The ac test system nclues a salent-pole synchronous generator eeng an R-L loa (R = 27.29, L = 19.9 mh). The chopper crcut s connecte to the b an c phases o the generator termnals. The njecton an ata processng contons are smlar to those n the c test, except that the abc sgnals are transorme nto the synchronous reerence rame beore normalzaton. An Elman RNN s use or the tranng, where the nputs are the currents an the outputs are the voltages. Fg. 8. Actual an measure mpeances o the c subsystem.. For a symmetrc three-phase R-L loa, ts mpeance matrx n the synchronous reerence rame can be expresse as R jl el RL (9) el R jl where e s the spee o the synchronous reerence rame. Fgs. 9 an 10 clearly show the agreement between (9) an the measure mpeance characterstcs. Fg. 11 shows the measure magntue curves o qq an o the synchronous generator. The mpeances ente wth the propose metho are very close to the actual values. The q- an -axs mpeances are erent because o rotor salency o the generator. C. Evaluaton o mpeance Accuracy The accuracy o the propose mpeance entcaton metho epens on several actors. Frstly, sgnal measurement errors have a large mpact on the RNN tranng ata because the small perturbaton sgnals are usually ae to very large steay-state currents an voltages. Seconly, the RNNs also contrbute to mpeance naccuraces. The number o hen neurons s rectly relate to the moelng capabltes o a networ. Generally more neurons are neee 959

6 or the RNN to accurately moel systems wth complex ynamcs. Fnally, snce recurrent networs contan nternal states, ther ntal values also aect the accuracy o the moel. Ther eects can be reuce by scarng the rst porton o the nput an output ata n the entcaton process.. CONCLUSONS By moelng the small-sgnal ynamcs o a power electronc system wth recurrent neural networs, the propose mpeance entcaton metho sgncantly reuces the onlne test tme to extract the requency-epenent mpeance characterstcs, whch prove vtal normaton or stablty analyss. Ranom PWM sgnals an resstve chopper crcuts are use to nject perturbaton sgnals nto the system uner test, whch prouces voltage an current sgnals or RNN tranng. A laboratory test platorm has been bult to urther very the eectveness o the propose metho. REFERENCES Fg. 9. qq an q o a three-phase RL loa Fg. 10. an q o a three-phase RL loa. [1] Ema, A., Khalgh, A., Rvetta, C.H., et. al., Constant power loas an negatve mpeance nstablty n automotve systems: enton, moelng, stablty, an control o power electronc converters an motor rves, EEE Transactons on ehcular Technology, olume 55, ssue 4, Pages: , July [2] Mlebroo, R. D., nput lter conseratons n esgn an applcaton o swtchng regulators, EEE Proceengs o ASAM, October [3] Wlrc, C.M., Lee, F.C., Cho, B.H., et. al., A metho o enng the loa mpeance speccaton or a stable strbute power system, EEE Transactons on Power Electroncs, olume 10, ssue 3, Pages: , May [4] Suho, S.D., Glover, S.F., Lamm, P.T., et. al., Amttance space stablty analyss o power electronc systems, EEE Transactons on Aerospace an Electronc Systems, olume 36, ssue 3, Part 1, Pages: , July [5] Famlant, Y.L.; Corzne, K.A.; Huang, J., et. al., AC mpeance Measurement Technques, EEE nternatonal Conerence on Electrc Machnes an Drves, Pages: , May 2005 [6] M. Belhayat an M.L. Wllams, mpeance Extracton Technques or Dc an Ac Systems, Proceengs o the Naval Symposum on Electrc Machnes, Phlaelpha PA, December [7] J. Huang an K. A. Corzne, AC mpeance Measurement by Lne-to- Lne njecte Current, Proceengs o EEE AS Annual Conerence, October [8] Barbouns, T.G., Theochars, J.B., et al., Long-term wn spee an power orecastng usng local recurrent neural networ moels, EEE Transactons on Energy Converson, volume 21, ssue 1, Pages , March [9] Chun-Jung Chen an Ten-Ch Chen, Desgn o a Power System Stablzer Usng a new Recurrent Neural Networ, nnovatve Computng, normaton an Control, CCC '06., volume 1, Pages 39-43, Aug [10] Goetel, A., aslva,.n., an Amaral Sern, P.J., Recurrent Neural Networ or nucton Motor Spee Estmaton n nustry Applcatons, EEE MELECON 2006., Pages , August [11] Palangpour, P., enayagamoorthy, G.K. an Duy, K., Recurrent Neural Networ Base Prectons o Elephant Mgraton n a South Arcan Game Reserve, nternatonal Jont Conerence on Neural Networs, Pages , July [12] el alle Y, enayagamoorthy GK, Mohaghegh S, Hernanez JC, Harley RG, Partcle Swarm Optmzaton: Basc Concepts, arants an Applcatons n Power Systems, EEE Transactons on Evolutonary Computaton, n press. Fg. 11. qq an o a three-phase synchronous generator. 960