Online school frequency and time service of high precision clock based on the generalized regression model of GPS

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1 COMPUER MODELLING & NEW ECHNOLOGIES (12C) Oli school frqucy ad tim srvic of high prcisio cloc basd o th gralizd rgrssio modl of GPS Abstract Jiazhu Zhg, Yhmi Gao Najig Forstry Uivrsity, Najig, , Chia Rcivd 1 vmbr 2014, I ordr to improv accuracy ad stability of GPS wid ara tim srvic, this papr stablishd gralizd rgrssio modl of cloc basd o th diffrt charactristics of GPS cloc ad crystal cloc, ad stimatd crystal frqucy by gralizd last squars (GLS) mthod. Algorithm corrctd th rror causd by masurmt valu frqucy driftig i th xistig rgrssio modl, thrby ralizig accurat stimatio wh crystal frqucy driftig is larg or itrval of masurmt valu is log. Basd o that, tim srvic of scod that is sychroous with coordiatd uivrsal tim (UC) was gratd. hrough phras compsatio algorithm, th phras diffrc btw th gratd scod ad scod GPS was corrctd to raliz accurat tim srvic, thrby providig accurat tim scal for wid ara masurmt ad fault locatio ad mtig th oli wid ara tim srvic rquirmts of powr systm moitorig systm. Kywords: GPS, gralizd rgrssio modl, high prcisio; last squar mthod 1 Itroductio o a larg xtt, th dvlopmt of tchologis, li wid ara masurmt ad fault locatio of powr systm, dpds o th iovatio of wid ara tim srvic tchology. It is quit importat to labl accurat wid ara tim labl for sampld data usig wid ara tim srvic tchology [1]. GPS ca provid all-whthr tim srvic all ovr th world, with biggst covrag ara ad highst accuracy. Morovr, it is ot limitd by gography ad climat ad covit to rciv. I th lctrical powr systm sychroizatio phasor critria publishd i 1998, IEEE powr systm rlay protctio rcommdd th implmtatio modl of GPS i th sychroizatio phasor masurmt. Aftr that, a icrasig umbr of xprts pay atttio to ad study th wid ara tim srvic i th powr systm suprvisio fild basd o GPS. I articl Ky chology i Bidou/GPS High- Prcisio im Srvic Schm for Smart Grid Costructio [2], Zhao Dogya, Yua Yidog, Shi Li ad Zhag Haifg put forward th thr-mod dual chal ad high-prcisio tim srvic which ca b usd for smart powr grid costructio basd o Bidou first gratio systm, Bidou scod gratio systm ad GPS systm. h schm has ffctivly guaratd th accuracy of smart powr grid cut tim bchmar. I articl Dvlopmt of a Cloc Sychroizatio Dvic Basd o GPS ad IEEE-1588 Protocol [3], Zhuag Yufi, Huag Qi ad Jig Shi dvlopd a id of cloc sychroizatio dvic usig FPGA tchology. h dvic ca simultaously xpric IEEE-1588 ad rciv th scod sychroous sigal st by GPD ad IRIG-B cod, which guarats th accuracy ad rliability of sychroous cloc ad mt th rquirmt of powr systm wid ara masurmt to sychroous cloc. I articl A Nw im Providr for Wid-ara Powr Systm Stabilizr Cotrol Egirig [4], Liu Zhixiog, t al discussd th rquirmts of tim sychroizatio i wid ara PSS cotrol systm. Aimig at th tim sychroizatio applicatio of PM U Srvr ad cotrol d, thy put forward th cloc grator which combis UPS tim srvic ad CPU tim stamp coutr (SC), which is asy, rliabl ad of high accuracy. Exprimt showd that this mthod could ffctivly provid th ral tim cloc that mts th applicatio of wid ara PSS cotrol gir. his papr coctratd o th oli frqucy corrctio ad tim srvic schm of gralizd rgrssio modl basd o GPS. h xistig rsarch also showd that th tim srvic schm basd o GPS ad crystal oscillator ca hac GPS tim accuracy, which also guaratd th tim srvic accuracy of GPS. Howvr, all of schms mtiod abov glctd th frqucy chags amog masurmt valus. I othr word, th coutd valu of crystal oscillator withi crtai priod of tim was srvd as th tim valu dirctly, which glctd th tim dviatio causd by crystal oscillator frqucy drift durig this priod of tim, ad th modl vracity also dcrasd. hrfor, this papr rcostructd th complmtary cloc rgrssio modl, ad providd th schm of high-accurat cloc oli frqucy corrctio ad tim srvic. 2 Pla dsig for oli frqucy adjustmt ad tim srvic of high prcisio cloc Structur of oli frqucy ad tim srvic of high prcisio cloc dsigd is show i figur 1: Corrspodig author s -mail: 710

2 COMPUER MODELLING & NEW ECHNOLOGIES (12C) crystal oscillator GPS modul crystal cloc GPS- PPS phaslocd loop GEN- ERR high frqucy cloc high accuracy frqucy adjustmt of GPS gratio of scod phas discrimiator GEN PPS phas discrimiatio valu frqucy adjustd valu frqucy adjustd valu GEN- PPS phras stimatd valu phras stimatio frqucy doublig FPGA microscod tim iformatio microscod cloc FIGURE 1 Structur diagram of oli frqucy adjustmt ad tim srvic of high prcisio cloc I figur 1, oli frqucy adjustmt ad tim srvic fuctio of high prcisio cloc is ralizd o FPGA platform. Crystal cloc (50 MHz) is trasformd ito high frqucy cloc (250 MHz) through digital phas locd loop frqucy doublig. Spcific cott of stps ar as follows: (1) Frqucy adjustmt. High accuracy frqucy adjustmt modul stimats th accurat frqucy of th currt high frqucy cloc ad ralizs frqucy adjustmt through masurig high frqucy cloc cout valu of scod GPS_ PPS wh GPS is ffctiv. (2) im srvic. Puls pr scod gratio modul grats w scod GEN_PPS accordig to frqucy adjustd valu ad phras stimatio diffrc to raliz tim srvic fuctio; phras discrimiator tracs th phras diffrc of GPS_PPS ad GEN_PPS, ad phras stimatio modul stimats tim diffrc btw GEN_PPS ad coordiatd uivrsal tim (UC) ad th fdbac to scod gratio modul for adjustmt. (3) Frqucy doublig. Frqucy doublig modul prforms frqucy doublig o GEN_PPS to 1 MHz accordig to frqucy adjustd valu to raliz microscod lvl cloc output. 3 Oli frqucy adjustmt of high accuracy cloc 3.1 GPS AND CRYSAL CLOCK MODEL Assssmt of cloc frqucy grally icluds accuracy ad stability. Accuracy rfrs to th dviatio dgr of practical frqucy ad omial valu ad stability rfrs to th firc dgr of radom chag of output frqucy. Crystal cloc will b affctd by compot bur-i, viromtal tmpratur ad short-trm disturbac. Amog thm, compot bur-i is th irrvrsibl tdcy chag ad tmpratur driftig is rvrsibl priodic chag. Grally, radom disturbac of crystal oscillator ca b igord sic it is small. hrfor, crystal cloc has high stability ad accuracy ca b affctd by tim ad viromt. GPS tim output is affctd by phmris chag, satllit cloc rror, coductio rror ad rcivr rror. h amout of satllit mt th rquirmt ad cloc rror basically mt ormal distributio. I additio, GPS has o accumulatd rror i log trm opratio; thrfor, it has high accuracy. hus it ca b s that GPS cloc ad crystal cloc has complmtary frqucy charactristics. Adjustig crystal cloc by GPS cloc ca improv accuracy ad stability. Frqucy masurmt of complmtary cloc is show i figur 2. scod 0 scod 1 scod 2 scod -1 scod UC scod ; CPS-PPS FIGURE 2 Frqucy masurmt of complmtary cloc 711

3 COMPUER MODELLING & NEW ECHNOLOGIES (12C) GLS ESIMAION OF COMPLEMENARY CLOCK MODEL Last squars stimatio, put forward by Gaussia i 1975, is th most widly usd optimizatio algorithm at prst. Its algorithm is simpl without owig th statistical iformatio of th stimatd subjct ad masurmt valu [5]. I gralizd rgrssio modl, bcaus ois squc has o charactristics of whit ois, although ordiary last squar stimatio algorithm has ubiasdss ad cosistcy i spcific coditio, th rsult is o logr ffctiv stimatio. I ordr to solv th problm, GLS stimatio basd o rlaxatio itratio algorithm is itroducd ito whitig filtr. Aftr maig prprocssig o data, rlatd ois is trasformd ito whit ois, ad th ordiary last squar mthod is adoptd for obtaiig modl paramtr. Stps for applyig GLS o complmtary cloc modl ar as follows: Suppos modl ordr is. Us N+ to iput x ad output y. GLS stimatio is prformd accordig to th followig modl. 1 1 a( z ) y b( z ) x v (1) 1 [ aˆ, aˆ,..., aˆ, bˆ, bˆ,..., bˆ ] ( y (2) ) y y1 x x1 y 1 y2 x 1x2 (3) yn 1 yn xn 1 xn y y, y,..., y ] (4) [ 1 2 N Calculat rsidual squc {}. aˆ( z ) y bˆ( z ) x Suppos thr is whit ois squc maig th quatio tru c { } (5) (6) 1 N 1, 1 2 1,..., N 2 N [ cm, cm1,..., c1 [ 1, 2,..., N ] m1 m2 N m (7) (8) c ] (9) (10) Last squar stimatio of that modl ca b obtaid, as follows. 1 (11) c ( ) Updat iput ad output valu. yˆ y cm y 1... c1 ym (12) xˆ x cmx 1... c1x m (13) Substitut formula (16)- (18) ito updat data xˆ ad ŷ, thus to stimat modl paramtr ˆ agai st whthr paramtr ˆ mt th rquirmt. If ot, th rtur to stp 2); if it is, th us ˆ to stimat dtrmiistic trd ŷ ad frqucy stimatd valu. 1 a z ) ~ 1 ( y b( z ) x (14) ~ y fˆ (15) I formula, fˆ is crystal frqucy stimatd valu. Oli frqucy adjustmt procdur of high accuracy cloc ca b dsigd usig complmtary cloc modl ad GLS stimatio algorithm mtiod abov, as show i figur 3: start collct masurmt valu N updat complmtary cloc modl calculat frqucy stimatd valu +1 whthr masurmt valu is ffctiv? Ys collct masurmt valu N frqucy stimatd valu -1 = N whthr is th o. N+ masurmt valu? Ys whthr masurmt valu is ffctiv? Ys updat N+ masurmt valu apply GLS stimatio FIGURE 3 Flow chart of oli frqucy adjustmt of high prcisio cloc 712

4 COMPUER MODELLING & NEW ECHNOLOGIES (12C) Accurat adjustmt dsig of scod phras of tim srvic Aftr obtaiig th accurat frqucy of crystal cloc by cloc frqucy adjustmt basd o GPS, crystal cloc ca grat puls sigal GEN_PPS that is sychroous with scod UC. At that momt, tim squc of scod UC, GPS_PPS ad GEN_PPS ar show i figur 4. Suppos stimatd valu of crystal frqucy is idal valu, th th gratd puls pr scod GEN_PPS ad scod UC ar compltly sychroous. Sic scod UC is ivisibl, GEN_PPS is boud to hav phras diffrc with scod UC durig gratio. I ordr to limiat that phras diffrc, phras discrimiator is usd to rcord phras diffrc squc {q}. h w ca obtai th followig rlatioship: q q... q a ( ) 1 2 (16) scod 0 scod 1 UC scod scod 2 GEN-PPS scod -1 CPS-PPS scod It is ow that GPS cloc rror squc { } is 2 whit ois that mt ormal distributio N (0, ). hrfor, wh is big ough, th formula (16) ca b trasformd ito q1 q2... q a a ( q1 q2... q ) / (17) Valu of phras rror a ca b obtaid via formula (17). I th idal coditio, iitial phras rror oly ds o tim of adjustmt. I practic, tiy frqucy stimatio rror ca accumulat to larg phras rror i log-trm opratio, sic crystal frqucy stimatd valu ca ot b compltly accurat. hrfor, phras rror adjustmt oly prforms at itrvals, i ordr to dur th tim srvic accuracy of gratd scod. h implmtatio flow is show i figur 5: start phras discrimiatio valu coutr =0 phras stimatio a= 0 collct phras discrimiatio valu q =+1 Whthr =? Ys updat phas stimats a =0 FIGURE 4 im squc figur of 3 ids of scod 5 Coclusio At prst, som importat filds such as powr systm, commuicatio systm, ad idustrial automatio systm all dpd o sychroous cloc to prform ral tim schdulig ad cotrol. hs applicatios rquirs highr o th cosistcy ad accuracy of cloc i distributio systm [6-7]. Aimig at th problms abov, may scholars prform a larg amout of rsarchs, ad also propos svral valuabl solutios [8-10]. Wid ara tim srvic pla implmtd o FPGA platform was dsigd i this papr. his papr aalyzd th accurat adjustmt of scod phras of oli frqucy adjustmt ad tim srvic of cloc ad dsigd accurat complmtary cloc modl through aalysis of charactristics of GPS cloc ad crystal cloc. I additio, th rquirmt of that modl coformig to gralizd rgrssio modl was dducd, ad frqucy stimatio rcursiv flow basd o GLS was giv. Aimig at accurat adjustmt algorithm of scod phras, oli implmtatio flow basd o phras adjustmt algorithm was giv. Exprimtal rsult provd that, frqucy stimatd valu obtaid by that algorithm has high accuracy of GPS cloc, ad its stability is also suprior tha GPS cloc. h gratd scod ad scod UC hav good sychroism. Aftr procssig by phras adjustmt algorithm, phras rror btw thm was ffctivly limiatd, which mt th rqust of accurat wid ara tim srvic of powr systm? adjust GEN_PPS phras FIGURE 5 Flow chart of phras rror stimatio 713

5 COMPUER MODELLING & NEW ECHNOLOGIES (12C) Rfrcs [1] Ma Jig, Li Jilog, Wag Zgpig, t al 2010 Wid-ara Bac-up Protctio Basd o Fault Corrlatio Factor. Procdigs of th CSEE, 30(31) p [2] Zhao Dogya, Yua Yidog, Shi Li, Zhag Haifg 2013 Ky chology i Bidou/GPS High-Prcisio im Srvic Schm for Smart Grid Costructio [J]. Powr Systm chology, 9, 37(9) p [3] Zhuag Yufi, Huag Qi, Jig Shi 2011 Dvlopmt of a Cloc Sychroizatio Dvic Basd o GPS ad IEEE-1588 Protocol. Powr Systm Protctio ad Cotrol, 7, 39(13) p [4] Liu Zhixiog, Su Yuazhag, Li Xiog, Zhag Fag, Zhao Wixig, Liu Zhshg 2013 A Nw im Providr for Wid-ara Powr Systm Stabilizr Cotrol Egirig. Automatio of Elctric Powr Systms, 3, 37(6) p [5] Dog Yulog, H You, Wag Guohog, t al 2006 Gralizd Last Squars Rgistratio Algorithm with Earth-ctrd Earth-fixd (ECEF) Coordiat Systm. Acta Aroautica Et Astroautica Siica, 27(3) p [6] Huag Xiag, Jiag Daozhuo 2010 A High Accuracy im Kpig Schm Basd o GPS. Automatio of Elctric Powr Systms, 34(18) p [7] Gog Wizhg, Fag Xiya 2011 A O-li Voltag Stability Idx Basd o Wid Ara Masurmt Systm. Powr Systm chology, 35(4) p [8] Jiag Lupig, Zg Xiagju, Li Zw, t al 2011 Ralizatio of High Accuracy Sychroous Cloc for Powr Systm Basd o GPS. Powr Systm chology, 35(2) p [9] Xu Zhiqiag, Li Yutia, Zhag Kr, t al 2011 A Approach of im Masurmt for Itlligt Compots i Smart Substatios. Powr Systm chology, 35(12) p [10] Luo Ya, Dua Xiogyig, Zhag Migzhi, t al 2012 Rsarch o im Sychroizatio for IEC Procss Bus. Powr Systm chology, 36(11) p Autors Jiazhu Zhg, bor 1971, Jiagsu Provic of Chia Currt positio, grads: associat profssor Uivrsity studis: PHD dgr was ard i major of survyig ad mappig, Najig Forstry Uivrsity i Scitific itrst: GPS pricipl ad its applicatio i forstry girig, th applicatio of civil girig, prcis girig survy Yhmi Gao, bor 1992, Ahui Provic of Chia Currt positio, grads: studt Uivrsity studis: Postgraduat studis i major of survyig ad mappig girig, Najig Forstry Uivrsity. Scitific itrst: GPS pricipl ad its applicatio i forstry girig, th applicatio of civil girig, prcis girig survy 714

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