Local detection of PMU measurement errors using dynamic state

1 downloads 0 Views 532KB Size Report
Abstract—This paper proposes the use of a couple of local PMUs ... The proposed approach is implemented using a two-axis model of a synchronous generator ...


/RFDO'HWHFWLRQRI3080HDVXUHPHQW(UURUV 8VLQJ'\QDPLF6WDWH(VWLPDWRUV $OLUH]D5RXKDQLIEEE Student Member

$OL$EXU IEEE, Fellow

'HSDUWPHQWRI(OHFWULFDODQG&RPSXWHU(QJLQHHULQJ 1RUWKHDVWHUQ8QLYHUVLW\ %RVWRQ0$86$ DURXKDQL#HFHQHXHGX

'HSDUWPHQWRI(OHFWULFDODQG&RPSXWHU(QJLQHHULQJ 1RUWKHDVWHUQ8QLYHUVLW\ %RVWRQ0$86$ DEXU#HFHQHXHGX

Abstract²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ndex Terms6\QFKURQRXV *HQHUDWRU 3RZHU 6\VWHPV '\QDPLFV '\QDPLFVWDWHHVWLPDWLRQ.DOPDQ)LOWHU5REXVW6WDWH(VWLPDWLRQ

,

,1752'8&7,21

3

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

‹,(((

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



,,

6@>@ D

YHFWRU WKDW LQFOXGHV WKH G\QDPLFV RI ERWK WZRD[LV PRGHO RI D V\QFKURQRXVJHQHUDWRUDQGWKH,(((W\SH H[FLWHU +HQFHWKH VWDWHDQGLQSXWYHFWRUVDUHJLYHQDVIROORZV x

>G  Z  Eqc  Edc  E fd  V f  VR @T 

u

> PM

$ EULHIGHVFULSWLRQRIWKH8.)DOJRULWKPLVJLYHQEHORZ

'\QDPLFHTXDWLRQVRIDWZRD[LVV\QFKURQRXVJHQHUDWRU

G

Z  Z 

T @T  

V

A. Unscented Kalman Filter:

H Z Sf  T c E c

PM  Pe  D Z  Z  Z

$VVXPH WKDW WKH GLVFUHWL]HG QRQOLQHDU VWDWH G\QDPLFV DQG PHDVXUHPHQWHTXDWLRQVDUHJLYHQE\WKHIROORZLQJHTXDWLRQV

 Eqc  X d  X dc I d  E fd

xk 

c E dc Tqo

 Edc  X q  X qc I q  

do

q

ZKHUH ªVd º «V » ¬ q¼ Id

ª VLQ G  FRV G º ªV FRV T º «FRV G VLQ G »¼ «¬V VLQ T »¼ ¬ Eqc  Vq  Vd  Edc  Iq X dc X qc

Vd I d  Vq I q  Qe

Pe

Vd I q  Vq I d  

f xk  k  wk 

 

zk h xk  k  vk   ZKHUH f xk  k LV WKH QRLVH IUHH V\VWHP G\QDPLFV HYDOXDWHG DW WLPH

VWHS k  h xk  k LV WKH QRLVH IUHH PHDVXUHPHQW HTXDWLRQV HYDOXDWHG DW WLPHVWHS k  xk  ƒ n LVDGLVFUHWHVWDWHYHFWRUDWWLPHVWHS k  z k  ƒ m LVDGLVFUHWHPHDVXUHPHQWYHFWRUDWWLPHVWHS k  wk a N  Qk *DXVVLDQSURFHVVQRLVHDWWLPHVWHS k vk a N  Rk *DXVVLDQPHDVXUHPHQWQRLVHDWWLPHVWHS k

ZKHUH 

Qk DQG Rk DUHFRYDULDQFHPDWULFHVRI wk DQG vk UHVSHFWLYHO\

G LVWKHURWRUDQJOH Z LVWKHURWRUVSHHG PM LVWKHPHFKDQLFDOLQSXWSRZHU Eqc DQG Edc DUHGD[LVDQGTD[LVWUDQVLHQWYROWDJHV

V DQG T DUHJHQHUDWRUWHUPLQDOEXVYROWDJHPDJQLWXGHDQGSKDVH

,PSOHPHQWDWLRQVWHSVRI8.)EDVHGRQ n VLJPDSRLQWV>@ DUH GHVFULEHG EHORZ 7KHDOJRULWKPLVLQLWLDOL]HGE\FKRRVLQJ

xÖ

E x  P

E> x  xÖ  x  xÖ  T @  

DQJOHUHVSHFWLYHO\   Pe DQG Qe DUHWKHDFWLYHDQGWKHUHDFWLYHSRZHUGHOLYHUHGE\WKH ZKHUH xÖ k Pk DUHWKHSRVWHULRULHVWLPDWHDQGSRVWHULRUL FRYDULDQFHDWWLPHVWHS k UHVSHFWLYHO\7KHQWKHIROORZLQJ JHQHUDWRU VWHSVDUHFDUULHGRXW E '\QDPLFHTXDWLRQVRIWKH,(((7\SHH[FLWHU

Te E fd

VR  K e E fd

T f V f

V f 

TaVR

Kf Te

VR 

VR  K a Vref

Ke K f Te

E fd

 V  V f  

Step 1 : Calculation of sigma points:

xÖk i  i

x

n i

x

i xÖk  x  i

n

 T k  i

nP

 i  k 

 nP

 n

 i T i

 n  

ZKHUH Efd, Vf, DQG VR DUH ILHOG YROWDJH VFDOHG RXWSXW RI WKH VWDELOL]LQJ WUDQVIRUPHU DQG VFDOHG RXWSXW RI WKH DPSOLILHU RU 3OHDVHQRWHWKDW nP i LVWKH i WKURZRI Step 2: SLORWH[FLWHU UHVSHFWLYHO\>@>@

,,,

352326('$3352$&+)25 7+(52%867'@,WKDVEHHQVKRZQWKDW DW HDFKWLPHVWHS WKH FDOFXODWHGSGIRIWKHUHVLGXDOVFDQEHXVHGDV DQLQGLFDWRUWRTXDQWLI\WKHSHUIRUPDQFHRID'6( 6DPHLGHDLV H[WHQGHGWRWKH'6(HYDOXDWLRQLQWKLVSDSHU $W HDFKWLPHVWHS WKHSGIRIWKHPHDVXUHPHQWUHVLGXDOV LV XSGDWHGDV IROORZV

pdf rk

¦ pdf r

j

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

i 

¦ xÖ

N

j 

Step 4:

h xÖk i  k  zÖk

pdf rkj k

,QRUGHUWRVDYHFRPSXWDWLRQDOHIIRUW VWHS  FDQEHRPLWWHG >@ZLWKDVOLJKWGHJUDGDWLRQLQILOWHUSHUIRUPDQFH

zÖk i

zk  zÖk DQG m LV WKH

WRWDO QXPEHURIWKHPHDVXUHPHQWV 1RWH WKDW D VHSDUDWH '6( ZLOO EH LPSOHPHQWHG IRU HDFK 308 7KHQ WKH IROORZLQJ PHWULF ZLOO EH FDOFXODWHG DW HDFK WLPH VWHS IRUHDFK'6(

H[S rkT Pzrk     S m   _ Pz _  

0HDVXUHPHQWVSURYLGHGE\ 308

'6(

xÖ r '6(VSHUIRUPDQFH HYDOXDWLRQWHFKQLTXH

0HDVXUHPHQWVSURYLGHGE\ 308

'6(

xÖ  r

)LJ %ORFNGLDJUDPRIWKHSURSRVHGDSSURDFKIRUWKHUREXVWG\QDPLFVWDWHHVWLPDWLRQ

‹,(((





,9

6,08/$7,215(68/76



7KHSURSRVHGDSSURDFKZLOOEHXVHGWRSHUIRUPWKHG\QDPLFVWDWH HVWLPDWLRQ RI D WZRD[LV PRGHO RI V\QFKURQRXV JHQHUDWRU ZLWK DVVRFLDWHG ,(((7\SH  H[FLWHU ZLWKLQ WKH :(&& WHVW V\VWHP 7KLV WHVW V\VWHP LQFOXGHV  EXVHV DQG  V\QFKURQRXV JHQHUDWRUV 7KH IROORZLQJ DVVXPSWLRQV DUH PDGH IRU WKH VLPXODWLRQV x 'XUDWLRQRIWKHVLPXODWLRQLVVHF x 6LPXODWLRQWLPHVWHSLVVHF x 6WDUWLQJDWW VHFVHYHUDOOLQHVZLWFKLQJHYHQWVDUH VLPXODWHG x 'HOLYHUHGDFWLYHDQGUHDFWLYHSRZHUE\WKHJHQHUDWRUVDUH FRQVLGHUHGDVPHDVXUHPHQWVIRUWKHG\QDPLFVWDWH HVWLPDWLRQ x :KLWH*DXVVLDQQRLVHZLWKVWG DUHDGGHGWRWKHQRLVH IUHHPHDVXUHPHQWVSURYLGHGE\DVLPXODWRUWRREWDLQWKH HUURQHRXVPHDVXUHPHQWVDQGLQSXWVIRUWKHG\QDPLFVWDWH HVWLPDWLRQSURFHVV

5RWRUDQJOH>'HJ@











 









7LPH>6HF@

)LJ(VWLPDWHGDQG WUXHWUDMHFWRULHVRIWKHURWRUDQJOH FRPSXWHGXVLQJWKH SURSRVHGDSSURDFK 



5RWRUDQJOH>'HJ@

,Q RUGHU WR HYDOXDWH WKH SHUIRUPDQFH RI WKH SURSRVHG G\QDPLF VWDWH HVWLPDWLRQ DSSURDFK XQGHU EDGGDWD WZR GLIIHUHQW FDVH VWXGLHVZLOOEHLQYHVWLJDWHG A. Case study 1 ,QWKLVFDVHVWXG\LWZLOOEHDVVXPHGWKDWEDGGDWDZLOORFFXULQ WKH PHDVXUHG YROWDJH SKDVRU SURYLGHG E\ WKH PDLQ 308 7KH GHWDLOVRIWKLV VLPXODWLRQDUHJLYHQEHORZ









 









7LPH>6HF@

x

6WDUWLQJ DW W  VHF WKH PHDVXUHG YROWDJH PDJQLWXGH SURYLGHG E\ WKH PDLQ 308 LV UHSODFHG E\  WLPHV RI LWV )LJ(VWLPDWHGDQGWUXHWUDMHFWRULHVRIWKHURWRUDQJOHFRPSXWHGXVLQJWKH WUXHYDOXH VLPXODWLQJDVFDOLQJHUURU IRUD GXUDWLRQRIVHF FRQYHQWLRQDODSSURDFK x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

B. Case Study 2

0 PDLQ'6(



&RQVLGHU D VLWXDWLRQ ZKHUH WKH GHOLYHUHG DFWLYH SRZHU E\ WKH JHQHUDWRU FDUULHV D ODUJH DGGLWLYH ZKLWH *DXVVLDQ QRLVH ,Q DGGLWLRQ WKH IROORZLQJ DVVXPSWLRQV DUH PDGH LQ VLPXODWLQJ WKLV FDVH







x

 









7LPH>6HF@ )LJ&DOFXODWHGSHUIRUPDQFHHYDOXDWLRQPHWULFDVVRFLDWHGZLWKWKHPDLQ'6( &DVHVWXG\

‹,(((

x x

6WDUWLQJDWW VHFRQGVIRUD GXUDWLRQRIVHFRQGV ZKLWH *DXVVLDQ QRLVH ZLWK VWG  LV DGGHG WR WKH YDOXHV RI GHOLYHUHGDFWLYHSRZHUE\WKHJHQHUDWRU $OO RWKHU PHDVXUHPHQWV DUH PRGLILHG E\ DGGLWLYH ZKLWH *DXVVLDQQRLVHZLWKVWG  7KH WKUHVKROG IRU WKH PHWULF RI SHUIRUPDQFH HYDOXDWLRQ RI WKHPDLQ'6(LV VHWDV 



VWLOO WKH SURSRVHG DSSURDFK FDQ VXFFHVVIXOO\ LGHQWLI\ WKH 308 ZLWK OHVV WKDQ DFFHSWDEOH DFFXUDF\ DQG HQVXUH GHOLYHULQJ UREXVW HVWLPDWHVRIWKHVWDWHYDULDEOHRILQWHUHVW



0 PDLQ'6(





9

&21&/86,216



7KLV SDSHU¶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

9,

5()(5(1&(6



5RWRUDQJOH>'HJ@

>@ 

>@





>@



>@  









>@

7LPH>6HF@

)LJ(VWLPDWHGDQGWUXHWUDMHFWRULHVRIWKHURWRUDQJOHXVLQJWKHSURSRVHG G\QDPLFVWDWHHVWLPDWLRQDSSURDFK

>@

5RWRUDQJOH>'HJ@

>@ 

>@



>@









 









7LPH>6HF@

)LJ(VWLPDWHGDQGWUXHWUDMHFWRULHVRIWKHURWRUDQJOH8VLQJWKHFRQYHQWLRQDO DSSURDFK

$V HYLGHQW IURP )LJXUHV   DQG  WKH HIIHFW RI WKH ODUJHU DGGLWLYH ZKLWH *DXVVLDQ QRLVH DVVRFLDWHG ZLWK WKH GHOLYHUHG DFWLYH SRZHU E\ WKH JHQHUDWRU RQ WKH DFFXUDF\ RI WKH G\QDPLF VWDWH HVWLPDWLRQ LV OHVV WKDQ WKH SUHYLRXV FDVH VWXG\ +RZHYHU

‹,(((

6:DQJ:*DRDQG$30HOLRSRXORV$QDOWHUQDWLYHPHWKRGIRUSRZHU V\VWHP G\QDPLF VWDWH HVWLPDWLRQ EDVHG RQ XQVFHQWHG WUDQVIRUP IEEE Trans. Power Syst., YROQRSS0D\ =+XDQJ.6FKQHLGHUDQG-1LHSORFKD)HDVLELOLW\VWXGLHVRIDSSO\LQJ .DOPDQ ILOWHU WHFKQLTXHV WR SRZHU V\VWHP G\QDPLF VWDWH HVWLPDWLRQ LQ Proc. International Power Engineering Conf  ( *KDKUHPDQL DQG , .DPZD 2QOLQH VWDWH HVWLPDWLRQ RI D V\QFKURQRXV JHQHUDWRUXVLQJXQVFHQWHG.DOPDQILOWHUIURPSKDVRUPHDVXUHPHQWVXQLWV IEEE Trans. Energy Con., YROQRSS'HF 1 =KRX ' 0HQJ DQG 6 /X (VWLPDWLRQ RI WKH G\QDPLF VWDWHV RI V\QFKURQRXV PDFKLQHV XVLQJ DQ H[WHQGHG SDUWLFOH ILOWHU IEEE Trans. Power Syst., YROQRSS1RY $ 6LQJK DQG % 3DO 'HFHQWUDOL]HG G\QDPLF VWDWH HVWLPDWLRQ LQ SRZHU V\VWHPVXVLQJXQVFHQWHGWUDQVIRUPDWLRQIEEE Trans. Power Syst., YRO QRSS0DUFK $ 5RXKDQL DQG $ $EXU /LQHDU SKDVRU HVWLPDWRU DVVLVWHG G\QDPLF VWDWH HVWLPDWLRQIEEE Trans. Smart Grid., (DUO\DFFHVV ' 6LPRQ 2SWLPDO 6WDWH (VWLPDWLRQ .DOPDQ + ,QILQLW\ DQG 1RQOLQHDU $SSURDFKHV1HZ-HUVH\-RKQ:LOH\ 6RQV -*ORYHU06DUPDDQG72YHUE\HPower Systems Analysis and Design. 7KRPVRQ. 36DXHUDQG03DLPower System Dynamics and Stability. 3UHQWLFH+DOO .

Suggest Documents