<%BANNER%>

A Novel Index to Analyze Power Quality Phenomena Using Discrete Wavelet Packet Transform

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E20110112_AAAABE INGEST_TIME 2011-01-12T23:48:13Z PACKAGE UFE0002760_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES
FILE SIZE 35946 DFID F20110112_AAAIAJ ORIGIN DEPOSITOR PATH hari_a_Page_50thm.jpg GLOBAL false PRESERVATION BIT MESSAGE_DIGEST ALGORITHM MD5
0cf8e0e35c402126dab4c5678e7278dc
SHA-1
389401fb77e5ca0262b8dc04fb5a07e391a76e4c
51235 F20110112_AAAHJR hari_a_Page_40.jp2
c2f9f1da085b590c7cd6b7e4ca1becc8
6c9fb399523972809796a3acb92adef46d711e55
11241336 F20110112_AAAHTM hari_a_Page_55.tif
ccca7617c95fff41de271588a38221f0
9949f61a792939c5f9b1957e34804764e13532db
72029 F20110112_AAAHOO hari_a_Page_01.jpg
7e52347f4f9b0701df2c8940ac950acd
6398cd3b20ad47aea21f0e0b42d84879e09bfd2a
97117 F20110112_AAAHYJ UFE0002760_00001.xml FULL
867ba2eac5c6b6e246922803b6f35198
a93cbe0ff5816c25c4255ed0041a5a16b3a0db71
65962 F20110112_AAAIAK hari_a_Page_50.QC.jpg
dfb09a5a3f234d6eb202635aa26fc275
af27761f3539734acd34cb6211ced0d68c8770f1
492592 F20110112_AAAHJS hari_a_Page_22.tif
04dae59c42dbb50388919dc55f5ad17f
ec2ba5a7a1955f719ba7719842ac8298e01699e0
11241796 F20110112_AAAHTN hari_a_Page_56.tif
750862a1c5c52f61e8e4af110372d781
e1cf04869e8ba8c2a90ccaf380a8c6a91689361f
32308 F20110112_AAAHOP hari_a_Page_02.jpg
bd69f2761b94746a817e86429961027c
c609b242ef4c2ffcdf6b8cfe97a637e669c70eb0
23304 F20110112_AAAHYK hari_a_Page_02.QC.jpg
c4b1548ecda525fbda2235a1d888e584
9df79f89e649be4cdc177320239cb3cf4a8af4a6
81122 F20110112_AAAIAL hari_a_Page_51.QC.jpg
7acbb97f15f66892430f4a472142e9e6
35d7403153b43283d520b209ccd06c6f30d64a18
1445 F20110112_AAAHJT hari_a_Page_59.txt
9b680b45814e065607b4b92c58994649
2cad2f42b8721753a30d00de6b39f2ecd5ab897d
491616 F20110112_AAAHTO hari_a_Page_57.tif
4941ea27eed38358613c446546d4935a
d46a522275dad93c7b8a14781a6e81a3e42cdda9
31977 F20110112_AAAHOQ hari_a_Page_03.jpg
5bc3929833d3430213ace129c94acab9
45f35d39e202272831ed64fcfd96e3f0db47d77f
22668 F20110112_AAAHYL hari_a_Page_03.QC.jpg
56fbc51facf0652ac7ed67641e3910a5
1a8ab8d8596e1e52ff54bfc544225451a090acb2
73711 F20110112_AAAIAM hari_a_Page_53.QC.jpg
d7b18ad106387c539ec27a16716ed500
4bc94ef2109fe202ee021ce7d4475ce6e8623314
1223 F20110112_AAAHJU hari_a_Page_02.pro
7ce527ddae2dc8d5b3dad310e7173d0e
530fffa42d194614d98c8dfeaebaaf7909523a38
493292 F20110112_AAAHTP hari_a_Page_58.tif
60b96c2e5644de16150ed5c5726065da
44cadb62f5bfde7c53a9c75b5d11eb2bd1803769
136195 F20110112_AAAHOR hari_a_Page_04.jpg
21a6b93651e4c2603c7e7c588260614d
bc0a065d6572e79fbfba208c3fc4825a8ab84f06
35727 F20110112_AAAHYM hari_a_Page_04thm.jpg
ac0360d5b229ceb525d35912955700ce
16093c40d91b417a47c63aec5dbab0d410d7da1e
37923 F20110112_AAAIAN hari_a_Page_54thm.jpg
7c67c61093c4c5585804b6214b684915
f082e76718b2fb24e5b369bcdc2a43ae2cf34328
185066 F20110112_AAAHJV hari_a_Page_36.jpg
f498537d8d6394bb702e5c977ad73b42
1b97f984c617d8869724672747ac8ed0731b9c49
491992 F20110112_AAAHTQ hari_a_Page_59.tif
36aa1c2838162bd964095e2e057fd1ad
11074bc88cec2bf1e94511f1dc54dba089eb6f02
320327 F20110112_AAAHOS hari_a_Page_06.jpg
371e87c80d082409aed99be81ab50572
1f5a348028023fbeec985bf852f4768cdc0d7c40
64974 F20110112_AAAHYN hari_a_Page_04.QC.jpg
a1b41817e0ae5fe6d86a6bb69dabd4d9
0c1b16be531b8d5dbbfaebe3ba6669286761393c
73789 F20110112_AAAIAO hari_a_Page_54.QC.jpg
297abfdf6f600b2da3aa28a1ff4c5c3f
1570f56d5fc56227a790fba0d5d24c37ff550acf
50542 F20110112_AAAHJW hari_a_Page_63.QC.jpg
0385b8b97e29f6d25adebf34bd9147ec
5d0f2c1f5e9d4370c03b6135ed9f550db105f155
493144 F20110112_AAAHTR hari_a_Page_60.tif
08d7e5931f8fb3221d2dd5dc14ccf4ab
457120dd84bb1748744c37dd846c9caa3703ab45
155792 F20110112_AAAHOT hari_a_Page_08.jpg
1b7eea2317e69143e431bb049f68853a
bfe43ad9f2bdb2f7846c515c39551f986a77db4b
111870 F20110112_AAAHYO hari_a_Page_06.QC.jpg
b7b415cb2d92255dde058eb356c8b827
f78f3498dcf06d31ac589635ec63cdd4ef282773
71463 F20110112_AAAIAP hari_a_Page_55.QC.jpg
fc266700ad818a10e6be88461c74ade1
3b360b3416c280d761c4d502a6fad95caffacdfc
174542 F20110112_AAAHJX hari_a_Page_35.jpg
01504d023ea9d6197ff208933d0a9346
316fb31a7ab6b15c1aeabb103c31eee3df400a42
491284 F20110112_AAAHTS hari_a_Page_61.tif
72cd61c97f65da751d6d31558e67546f
03f8f9d264755f281ff9d69b7733a666cca0732c
236138 F20110112_AAAHOU hari_a_Page_09.jpg
efb2aa61cfa0078da3816c2180445eba
ce3968c31f2931a39840331cd7343e45e4a86c02
68411 F20110112_AAAHYP hari_a_Page_08.QC.jpg
3358d8fc71bb7dbba18da20db1bed3c7
26d5c27c96222ab143db50c0d00a1d16bfca6df5
40005 F20110112_AAAIAQ hari_a_Page_56thm.jpg
8169c236e85b006ccb4f6e34b836543c
8a48dfee45529397ba29adf0e368bb89c5823659
38871 F20110112_AAAHJY hari_a_Page_36.pro
18e50810a2924bdd39ef7bce0ec336e6
d55a584111e5eb3562073fe374b38989ad041d20
194992 F20110112_AAAHOV hari_a_Page_13.jpg
3595d27170ca2003c37aa1a7d8dbb036
58465325ab2ccaeffef6349099b5b07f756197f4
42098 F20110112_AAAHYQ hari_a_Page_10thm.jpg
421fcfdb0b52eeb836a3c28f54bdc1b9
47becb58289496c9fb4ff7ff06f5dc5da4a0e4a6
76479 F20110112_AAAIAR hari_a_Page_56.QC.jpg
736561c0287691fda59e60ab2c085885
3f99a1a6cd575cbda6d483352b3573deee0f0dd8
2422 F20110112_AAAHJZ hari_a_Page_56.txt
d129be4ffad0b160d472965224d21eff
df93e1b99390f733146f1771b189b3cac3050628
493696 F20110112_AAAHTT hari_a_Page_62.tif
f2c7cd688d5e702192e63a44468773cb
59739c8157022436ec1680854586a422f65277d8
151210 F20110112_AAAHOW hari_a_Page_14.jpg
104efac466a6b608383fab621907955f
12bc6902e9a21e38700f6fb7d8c61888730b1eeb
29959 F20110112_AAAHYR hari_a_Page_11.QC.jpg
dc58064122bd8154c409ad1f753bc40c
d7e882674d4023521568c68031544cc88d7025b8
58366 F20110112_AAAIAS hari_a_Page_57.QC.jpg
b05f73ef9e73d8edcccaa834ba0ea408
e0ac14a6dbbfa63c52b97e3fa9329e32c10b798e
489912 F20110112_AAAHTU hari_a_Page_64.tif
2efd1233990f4fe236ed33d74ff26231
7a7480d3c2c661e9982e9606c40a3e3eee5da651
158052 F20110112_AAAHOX hari_a_Page_15.jpg
da9b044f6f3ba335cf9baef39384dc27
4108637b95837d1ebccbce620c06a631d2b32463
43337 F20110112_AAAHYS hari_a_Page_12thm.jpg
937cf3d45dc99ba2d84523eef64df9ee
4904b51fc91ebeb2d2297752f2c373fd55f8294b
75716 F20110112_AAAIAT hari_a_Page_59.QC.jpg
90c724883a69ea0d6716d179b822f234
2d98f3e8cef464799a58c8820c97d84c73887a06
8112 F20110112_AAAHTV hari_a_Page_01.pro
a55557638c29498e2c0c9e6f216a6121
d2687e857ef238a905b3ac9a143a4b0cc3d5f992
162730 F20110112_AAAHMA hari_a_Page_17.jpg
6be597fa6cbbb78cbdea25b1628636a7
f868fc4b4bb5878ae2de8a8d7b129c6c4985a0e1
199118 F20110112_AAAHOY hari_a_Page_19.jpg
40e1207687ffc78ecb28c584c0d083eb
9e759d1a7020646d190f826866106fb9f9408172
87664 F20110112_AAAHYT hari_a_Page_12.QC.jpg
f82b198acc43c354692f1d8c7f965332
a08be291fadaedf5bcd8e68d6fe2d0b150e0c8dd
44592 F20110112_AAAIAU hari_a_Page_60thm.jpg
30ce5d224595dd1245b8f149923a70ce
8c4469c90f07578b7360eb8c0e9515c713cad26f
1011 F20110112_AAAHTW hari_a_Page_03.pro
768d164c921cfe5ec88cfe50c2eb0675
5a6ebd13ff48db9f8ab5715b94e16728f99bd92a
45349 F20110112_AAAHMB hari_a_Page_39.pro
e8eac9c5f456f2b32a269838b064e191
09549a9175329b902a0c23d2534791b0a249e627
199517 F20110112_AAAHOZ hari_a_Page_20.jpg
ec430332096776c4713f88dfb62ac61f
b1f15469dd4a298171f9099a2643ef41b8253dce
86550 F20110112_AAAHYU hari_a_Page_13.QC.jpg
9aadfb853d122f1f380bba754a7bf733
0d14dba8e98882973d1acb69443163d9663bf5b2
87838 F20110112_AAAIAV hari_a_Page_60.QC.jpg
e701cc68b4beaea25c596d8e5843bf5d
1c31c9b58574cc362238397aac719c9e46860ab8
26000 F20110112_AAAHTX hari_a_Page_04.pro
35bc58444a1a267f6e356510695620d3
daa18caee44ac80f01f24e89130513c5bd38a67d
37372 F20110112_AAAHMC hari_a_Page_24thm.jpg
c8f0c8e3196967df235e1fff4468cd96
9bdb0be147ad011ff6ee47eb69739eeb23347267
37468 F20110112_AAAHYV hari_a_Page_14thm.jpg
993d6838fb0546df4991caecbe35d487
12bc620b1450d35c8337d5e980fe84e41f42337f
67170 F20110112_AAAIAW hari_a_Page_61.QC.jpg
dbaf3937c6c6091d512d7b148cb07317
74000800973970afe8f464cddc59285eaa72a6f8
73948 F20110112_AAAHTY hari_a_Page_05.pro
eb9bba7395938b9a2a2a47bb1d7bd712
3ad21cb9a9d6516363320eae80c4a3707b00233f
450544 F20110112_AAAHMD hari_a_Page_54.jp2
2319fa8818168cf89657135e1d81d02d
521722018603f1e1179bc8f8940b89d1ac248091
70657 F20110112_AAAHYW hari_a_Page_14.QC.jpg
2c958b97fa83c2d33d6edd722c23403b
11ea363ed73c904b739f1140ac9661b4e6072d07
48507 F20110112_AAAHRA hari_a_Page_33.jp2
c764f9752950880b210ffe53520f6da0
50f24044da3543834ef4213af9f9062b77e53f82
44826 F20110112_AAAIAX hari_a_Page_62thm.jpg
46748ad107bff4f9b88ea2403132a089
1e9e0dc63669ec0874da25b01f4fe17b5b905720
96188 F20110112_AAAHTZ hari_a_Page_06.pro
0e2df11c1cffb54e32da1c674d2e2f1a
7a7dd58c76e7d3cffad1fe298a74ed236ef5c47f
43607 F20110112_AAAHME hari_a_Page_09thm.jpg
7efe53e329456aaf5a566d4fd2700d3e
ef8aec1cdb2381a82ff90c8522d66953e0c6e01d
37767 F20110112_AAAHYX hari_a_Page_15thm.jpg
78f9529b9bb980165ba86e022dafe0e2
c27ac1570997b70ae102f830b8343f3a52aced5b
47775 F20110112_AAAHRB hari_a_Page_35.jp2
1fc042a68857f72cfefcde2c3cc74ded
c413440d596177de78b30bac2f017274220581eb
29434 F20110112_AAAIAY hari_a_Page_63thm.jpg
265b513c0b080f0e18e59d78295c146e
fe523d7d7f7c35c44e669c57b1c03c7746bdb1bb
493408 F20110112_AAAHMF hari_a_Page_41.tif
fa0b5d49a070e725f31343b5f47aa568
f54007ad2dd7ed8999a699ab6cafeb9302046a6d
51857 F20110112_AAAHRC hari_a_Page_36.jp2
7dc27c8f23d658f570a8776d6e057518
ed36f3116414e7d3da4b945ec6be8a14ad214e98
30675 F20110112_AAAIAZ hari_a_Page_64thm.jpg
ec4b7f1baf0560265cf53b783f13e05a
ff33433ff646c01f80315ec805b891f13fee853d
22451 F20110112_AAAHMG hari_a_Page_07thm.jpg
4cebb7002e637b92f5574b57605c8047
18ef0fa0f4497c65ee1b5135a334863ad7419c1a
3940 F20110112_AAAHWA hari_a_Page_06.txt
225d6120753f14c4937f5279ee941bdf
a96f1f9f68c490bc68ce6de2e5d948a6c0e65335
72313 F20110112_AAAHYY hari_a_Page_15.QC.jpg
6d7835d83cb21f829c73f49dcc6e3847
07e16a1f077878b80014837ff2469493d29e7251
40719 F20110112_AAAHRD hari_a_Page_37.jp2
61f36a67831883bdaa53b51c1bb655a7
bfebbf7877022f2874c5e86c66d6f844b4ebbf00
781 F20110112_AAAHMH hari_a_Page_44.txt
5e25e88a19985323bc893e062275afc4
5eeb2bf265a7192de54f977a649e35bccd714f89
258 F20110112_AAAHWB hari_a_Page_07.txt
16cefa6eafb3ddd4d3c84ad1ba1fb444
d2a08f90029d9ad18be0300d40f1098ed1c063c3
73750 F20110112_AAAHYZ hari_a_Page_16.QC.jpg
964b9e3dc71baf08358d42385a5d199a
567559e3a1e5f5fdefe9a26304886ebb238c1867
57362 F20110112_AAAHRE hari_a_Page_38.jp2
516018ef6e6cbd9556c43930e8204434
f981fe1521d85b79ce24f45505d076f12514557d
72747 F20110112_AAAHMI hari_a_Page_28.QC.jpg
d5a74c4e6383d13bfb1c3476f1d03130
9b5799d27740a39987af33b28b330a4909777db7
1294 F20110112_AAAHWC hari_a_Page_08.txt
29f88f65635bf4af4e02710bbd5cd89b
d2b0c899ce3823004d88d73b021421d7d861e251
56353 F20110112_AAAHRF hari_a_Page_41.jp2
563cfe58bb8a2992aafee48300fd488c
d4ee78e1f9944f0ef7df28dcc4b79cacd612aca0
54457 F20110112_AAAHMJ hari_a_Page_20.jp2
55e8f0aff1abc41ee2af626a3f5e56c4
29e2ecd471c163b467c2f663c23b560e723cfcd8
190 F20110112_AAAHWD hari_a_Page_11.txt
bc8ff81df8a90c441f21b6b0719276ae
ba43cca37d88bbb46e489964e1ce59804e3a4c1f
53529 F20110112_AAAHRG hari_a_Page_43.jp2
f61bb64807be63df24cec1cad4bf1190
feb0a03ba45ecdb843df9d019f302a7fc4cac242
39104 F20110112_AAAHMK hari_a_Page_53thm.jpg
c9877d5817ef277812c0be9ea00ab7f6
f4fe1f7896ca82cee526f05f26fbc280f5183c3c
1800 F20110112_AAAHWE hari_a_Page_12.txt
6bec87d3cf33d4013582a573ca7e0498
a395c7e6b3ae0b6566e8eb5845355d925e5e363a
24506 F20110112_AAAHRH hari_a_Page_44.jp2
34b5e685c08d37c284e812538206d6b2
9143438d2d8c3c3d94153b1fe10b30a1b79d7491
1632 F20110112_AAAHML hari_a_Page_49.txt
570999d3df54ceeed21029d54c856add
231dabdb232d32669a9580a60006b3309e26be76
1676 F20110112_AAAHWF hari_a_Page_13.txt
d70cfe044b29c5eba5538cedbc8f055b
2c6fe7b5b94392a5d1b8019bd581c37e8c567447
49391 F20110112_AAAHRI hari_a_Page_45.jp2
b910a56f327e88d78ec59ef8ab30c9f3
5a9ca2d57f9958144b28a36615f1477b14cb201d
1628 F20110112_AAAHWG hari_a_Page_14.txt
2ff3050b2766429a69176bd07c60e0f0
88401622d32f8dbf785eef28ed011c5cd5878d4c
30982 F20110112_AAAHRJ hari_a_Page_46.jp2
acb671bb97bd6d20bf83fe74280caf9f
0cba382ab0c3bd192ccc957831928a2491f5c5d5
67572 F20110112_AAAHMM hari_a_Page_25.QC.jpg
76ca7ddcdc0ebcc6f31aba6d9c1339a6
35ab71c1d7c7b21fc647c423b5add5a1ed2b1fbc
1328 F20110112_AAAHWH hari_a_Page_15.txt
43331bd52c4b8097af0c4d9db2c9398d
0c88ad4313ce652d0c7d9c929e9c8b4707c13582
63745 F20110112_AAAHRK hari_a_Page_47.jp2
e565304d69bba4484344d4a3c2154b2d
4fbd64129851699919202dbbcc49e75529aed782
97 F20110112_AAAHMN hari_a_Page_03.txt
f257277654fdde68c4ee5879611bccc7
a51f337c330c7de2e9f9ea9da981f0f89da8820b
1759 F20110112_AAAHWI hari_a_Page_16.txt
0dc9faf36e0bda358aab7d866bcdb67e
9c2e8af5be8d416a27d26eaaf72de7c30b2901ea
411398 F20110112_AAAHRL hari_a_Page_48.jp2
37cb2aec36696fdc467f398aacf4949f
f47b49cf99cffca2338c1f973deeb6534457bd38
196267 F20110112_AAAHMO hari_a_Page_12.jpg
b391fa3e9f1ff670f975c8d70e26e66f
f2016398179a0375f1debad42a36c90e1968098e
1385 F20110112_AAAHWJ hari_a_Page_17.txt
6e2dc8e382a00a6298af28bd50c01871
461c0031bdf3b9d32cabe6358d677d3b042b7977
48971 F20110112_AAAHRM hari_a_Page_49.jp2
67ed1578248c9893d742ab408af3e70e
e8b8b2ac67f9b2848fd89d995b60ca7fef91b34c
209514 F20110112_AAAHMP hari_a_Page_39.jpg
57e40cc43d051ce7d21945e39943d4b9
75150488d5bf70aec76181d174de2f0b2d8fe1e0
1741 F20110112_AAAHWK hari_a_Page_19.txt
a585200ccb39a01820a94a6213a1f9ab
9f0f23d8c37ed64996a36b1e22c69802b2683b50
37618 F20110112_AAAHRN hari_a_Page_50.jp2
6c8f83e125692860e0eb533de1c92d42
69a429a563e3a4723b670ff9259f7f85985fd39e
230371 F20110112_AAAHMQ hari_a_Page_47.jpg
652fa9e4edd1fea320fa049ec0d28407
854e39def4b07fc115c2f82deccc1bf40be7fd60
1702 F20110112_AAAHWL hari_a_Page_20.txt
4bf114f3ec8633ebde84883980a73464
d5d850e6d5eb671f1cf9a3c8aab3a3f807b16b0e
40365 F20110112_AAAHRO hari_a_Page_52.jp2
8db9f9b6d10df89d08f8a915847a0b50
ead1b55501c8b3a41470db7e72804aa5f1dba940
162351 F20110112_AAAHMR hari_a_Page_59.jpg
2876cf69ec72ec86b13da205257c4f46
7de9d6e647835ffdae1985ad33c4ec980f1f550f
2025 F20110112_AAAHWM hari_a_Page_21.txt
9b3c1feadc9e9ba025d2e4f7bc14da22
948e8c41d5c8709a4f007e54b70e515f12827a40
442684 F20110112_AAAHRP hari_a_Page_53.jp2
b5229c953b10660bba9caaab0b6be67f
64266ff05a8a346e4cf5b368dd3197daef7c330a
86029 F20110112_AAAHMS hari_a_Page_10.QC.jpg
cf5a7d1c28db85a94c13e6286be7eaef
3c8edb21dc511b7069b4a36011271c8d9885a5f0
1569 F20110112_AAAHWN hari_a_Page_22.txt
746240ce9314843d299d02c1513512eb
c5c0ea56cf1ed4b25e7e94098ec0b9ebe51ab96b
420123 F20110112_AAAHRQ hari_a_Page_55.jp2
da1d7a269b1344b2f71f1e73e0d49b22
c5fd978a6657dff0986c5e154735f984ca48fb18
41738 F20110112_AAAHMT hari_a_Page_29.pro
d467f6047ad1362493d0b05a2a99a477
cddb80a95d1dda43431700da29f9241344bbfb86
1032 F20110112_AAAHWO hari_a_Page_25.txt
ac5e6f4f1956721f00a4890f774d1eba
c6b6b9361fa5a27bc5967473abb2da91da2e889d
94650 F20110112_AAAHMU hari_a_Page_39.QC.jpg
0017c3d82b53500ef093905e36ab507e
64d2901d7afd1918939cb3f38e7e03651df30c02
1516 F20110112_AAAHWP hari_a_Page_26.txt
7c68f5f7b341d5a2e05757b8d320db2e
5a66f24c0989da26bd29041b6a65239acaec0022
29286 F20110112_AAAHRR hari_a_Page_57.jp2
555ed954465b791628c4b65e8fa167a6
cf0bdfc397df15f085e0ea81fdb27239ff7dc6c8
491228 F20110112_AAAHMV hari_a_Page_24.tif
7ca265ccb10dc84dd43a5ee36731101d
4984c2f4d5b236e9bfbc73a6a580bb6a911f9ea7
272 F20110112_AAAHWQ hari_a_Page_27.txt
fb4cee07756c75cef45d5d892c5f2b3a
ab1fdd43e620c7d3bb1e1fd815ad9d608b8c966b
45059 F20110112_AAAHRS hari_a_Page_59.jp2
f8b3f303f9bbe9cad4f9e3d259bfd38b
4847848ea913ef488883a25d009e275d6e7e0d5b
492580 F20110112_AAAHMW hari_a_Page_51.tif
f66d1cbc07607b8e63ff980a4fad8e58
9fcf0c266b3c480c50bc0a8adba0d7b1f7e4ec38
1413 F20110112_AAAHWR hari_a_Page_28.txt
7ef2dccbe73c5f1ac1ac4652897ff271
85bc3f3b0bd009b46cda42adbd4b67fe40090a47
55246 F20110112_AAAHRT hari_a_Page_60.jp2
9fba9e154ac68b1622a8021cf51805eb
06bd6b00f9623e491c65f59a244edcef08f3c974
43903 F20110112_AAAHMX hari_a_Page_20thm.jpg
1391eac01bd6752b6906c1315f3407a1
3cc40f8e9c8ef692cb93a5282a18b15e1daf65cc
1685 F20110112_AAAHWS hari_a_Page_29.txt
62737419328a1a67d06c25602fe62ecd
a2da2b2a308923f368e9e91b83713f0320ba1727
39478 F20110112_AAAHRU hari_a_Page_61.jp2
3c2dd14ab122267ce4b42c913e319ac6
aa4ddbd0c04f479f2196a9f56ea64627a0d06bd1
1404 F20110112_AAAHWT hari_a_Page_30.txt
483458b415423ce51cbb42ae08301b96
c2e345cffee2aef139fa9bdb1be3c27cd2a639f6
65312 F20110112_AAAHRV hari_a_Page_62.jp2
f4b56de87a5bf59947ae7591a94fc92d
ce95a52e3ae1422f2dea2f37c6f787e6348a184a
52779 F20110112_AAAHKA hari_a_Page_56.pro
f1f26379ea096bae139d50799b82e14a
e1487c999a25f1cd0ccbd65b29ba6e6e40c7ac12
103349 F20110112_AAAHMY hari_a_Page_64.jpg
0bf30c0b83de91cca2aa42465cbf96be
89281452ba41278aedefdc5f2b25f8b288ea830d
1453 F20110112_AAAHWU hari_a_Page_31.txt
514112525e1544838a9f5b5cd037cd64
f5b0e3e5663b5ff9a3386d2f051c695e4b5b4c92
27922 F20110112_AAAHRW hari_a_Page_63.jp2
fbf46bb626a7fa01ceabe6ac00c2daca
369e1fd198598e333c921ca6f3e62003d4649250
45135 F20110112_AAAHKB hari_a_Page_06thm.jpg
fa17d0e6db322b6a23899fe828405e7e
a2345c260f5efcb00a64cdf98038cb457813b18c
41617 F20110112_AAAHMZ hari_a_Page_51thm.jpg
1fc97389227e9e7e52dba684da559cb2
64c906d2940fa5f5093d99a5042acb7d7b2ef2de
1532 F20110112_AAAHWV hari_a_Page_33.txt
21bff612c97bc014ee7caa0fa741006c
96a5a5a851c0130ecc89691723359e74c7c30851
487416 F20110112_AAAHRX hari_a_Page_02.tif
fc39b21b59fe67b7ed033ad25e733f8c
81fee66a8d49755e0b3d2d60e55e8731c003c28c
492532 F20110112_AAAHKC hari_a_Page_52.tif
57dbabd35f468d1db426bc269daaac3e
09def3b8ea01a61656c1e93fad858633a2272126
202302 F20110112_AAAHPA hari_a_Page_23.jpg
7a165b32603d985c8d46ae7de5729462
a1148113f03a89990700068d38e1a43515cffd18
487364 F20110112_AAAHRY hari_a_Page_03.tif
e4323a2f05ac3a97d51a4af30899e543
0780f9b9e8e8ed3bb2b2d5887c00049078bf87ff
467511 F20110112_AAAHKD hari_a_Page_56.jp2
72bbdcdd584bdc942507a6551c11ee8f
e62a76ceadb10fb99ae375f26be76174e631758d
F20110112_AAAHWW hari_a_Page_35.txt
fd9cf2ca64e99b65bf03ca2b36510228
4d4fc12f081220b049f49b1974e24a5e3daba913
142558 F20110112_AAAHPB hari_a_Page_24.jpg
a7d05264f5d833c569c4720d35ffcd8d
915c9bcec4640b41e8338c95134b0eb6bb26c06e
491072 F20110112_AAAHRZ hari_a_Page_04.tif
183fdc85aa6278e417eb31775638d94b
76a0b71b7831af1d274033142720f054ea7a1757
58076 F20110112_AAAHKE hari_a_Page_39.jp2
1ea8077388afc10927a5a6fb8996c47f
0f51655b4f28209c6e4aa2795400e2654559b0ff
1670 F20110112_AAAHWX hari_a_Page_36.txt
faecaa51a6989a5a99fc86e54b7f2e83
60328821ce7a0d77496feaec6c1e14f04d25cf80
138138 F20110112_AAAHPC hari_a_Page_25.jpg
9fb72409ed3fe2be490034c74b954de7
95f060097ed6c946194966e06845764f93f946d9
492664 F20110112_AAAHKF hari_a_Page_43.tif
54eb07cf4b7883aa78059a62e0e8d0cf
3f058b93be89cb0c39d7a6d43dba4b260800493e
1450 F20110112_AAAHWY hari_a_Page_37.txt
d50c2591fafc4d9a146e71538a0506c7
c88167672cdee513bf835f914b84ee0e6e33b931
182079 F20110112_AAAHPD hari_a_Page_26.jpg
c960221c7d14cd0bf4ae91aeb848f741
0e434e213e64aef51f7f8c1c415230e9ea9369c4
1764 F20110112_AAAHKG hari_a_Page_45.txt
691c3bdfc9fa159a101c17841985c324
df87f9377c14b2739f174eebb726ba183d7a589f
6388 F20110112_AAAHUA hari_a_Page_07.pro
314c2e71b61f1f4df5adf404bcefcb39
6291b2b55de523f8447de0e50d1b0563d31e3525
1831 F20110112_AAAHWZ hari_a_Page_39.txt
a4ed23dc37805e8e10a3dc0e50a66110
09e2d87af782dc1c98096cf2a8bbb3456ec0681f
76936 F20110112_AAAHPE hari_a_Page_27.jpg
bf20e72c0d6f63bba041fa915246f1c0
dcf969593255b41e54d3fdf2d5a0d8af076281c4
178165 F20110112_AAAHKH hari_a_Page_56.jpg
1661e9086556a6e4bb055736615da4df
73d1f8af4515675484774986f94cf46af13ea0bf
31532 F20110112_AAAHUB hari_a_Page_08.pro
14306c632a30568e9109dbd2883d8e9d
8c2a7c3277507e71ea4ddd6c86c566415e86f7f3
158757 F20110112_AAAHPF hari_a_Page_28.jpg
42e676605983fbc8772b3eff1af18be3
c529f571ed58c70d1dcd992955ada3be62c47bde
44619 F20110112_AAAHKI hari_a_Page_17.jp2
4411e44adad13dd2a7c90d324b3ce2c3
4a2fecce0f50c76a3066e2e690e02c0bbede7255
54966 F20110112_AAAHUC hari_a_Page_09.pro
0c128117636096b8fc3e8dd1d2c0095a
e8723d80435e412a13c99bab44eb553d7e46e799
197562 F20110112_AAAHPG hari_a_Page_29.jpg
541d91498373b16a553c6b0ee98969d3
882a61fa3e7dcb4925c1e7cfdea644eb84ca22f3
38335 F20110112_AAAHZA hari_a_Page_01.QC.jpg
c57b1f5dee90636c6b15d333dbb857c9
436e8fa1081d579ccde0618af1cee148e5a7bfa6
164843 F20110112_AAAHKJ hari_a_Page_54.jpg
9131e65925f13dcc026bd17e952375f5
b7d371dcb3c4a8a578a7a15744d04cd89c466b20
40607 F20110112_AAAHUD hari_a_Page_10.pro
08443f49814e90b902f6dcacd35dbfa5
f18b4c14cf50c6a4a21c231543bb727e8454b037
73890 F20110112_AAAHZB hari_a_Page_17.QC.jpg
8254b6be4d7c4bd9a8f979c3fca81603
27281719c7b8e756b5a485f7003861ce42ca8aa8
121956 F20110112_AAAHPH hari_a_Page_30.jpg
30877a8b1cd232281fe2c276eee2037d
4755ee4749bc322422ece11a6687a6cef7ffbe47
4718 F20110112_AAAHUE hari_a_Page_11.pro
9fd01cda8f9669595949cfe4aef78749
46ef50fd6f39b9892ef46d44880ef4a18a476c61
38227 F20110112_AAAHZC hari_a_Page_18thm.jpg
bb1c5c702de9c41085e61406fd67293a
064738b64e9a3219f2ff7c0789819ee721805f70
145321 F20110112_AAAHPI hari_a_Page_32.jpg
7f9329613e26959c3051c6aa5d98cc90
62b343e4af05061e8e594b1cc4ccc6fdbe47618e
155340 F20110112_AAAHKK hari_a_Page_18.jpg
8420c0fcf034a150207e553d46c47c97
2ce4ded566637ce14e33751e742aaf3edcb08f71
42545 F20110112_AAAHUF hari_a_Page_12.pro
7edeac55df92dc0cee589ebbfd8cc90d
b6c4fedb7a5155154d935cee08389b7543962075
72436 F20110112_AAAHZD hari_a_Page_18.QC.jpg
94fc6b6e22085943a015425dabf5c8ed
6e6ddad7cb6d49ece4c6356060234a75f91fd259
177606 F20110112_AAAHPJ hari_a_Page_33.jpg
5acb0c789deb2dab329c4dc819e7b112
7fa6e4efb658dce846f745a15736fc73110baefb
27993 F20110112_AAAHKL hari_a_Page_07.QC.jpg
51d5d8784a2d84a07c76dfaacfca54ad
b9c8eb3cab1acdcca3df01b5b24e25bc9e65b2f2
41280 F20110112_AAAHUG hari_a_Page_13.pro
06a30ce53c9ad383395439069551290d
a8870d6b3ca40230bf02988f10e22d4e723d4cda
43693 F20110112_AAAHZE hari_a_Page_19thm.jpg
e0ddc8996ea91998da244bbfb083380b
0fa502a3a0a37e406be98a816c3aca2176b34c64
171773 F20110112_AAAHPK hari_a_Page_34.jpg
6f938feee28cfa95052ca6e2e74103d5
9588f2b39fb6ac043913a709f7471ec8329afcab
95482 F20110112_AAAHKM hari_a_Page_62.QC.jpg
7bbee29e1d59e4066fd740c30ef44e3d
95dd8f84533c841a7be3198e0423a8f350dfc032
31969 F20110112_AAAHUH hari_a_Page_15.pro
3ba2e182492356236e67f64f2658ff77
9745a06f9f393aa45f6c4c14a699e5d3cbecb328
87448 F20110112_AAAHZF hari_a_Page_19.QC.jpg
de5d2a52a8775d27d22f25a0ffa54ab4
a0e814cd094a9ef4a760e6365b0cf328e7506b14
162413 F20110112_AAAHPL hari_a_Page_37.jpg
72bd95a441b077cd725cb6c24db473a7
d0135ee03cfd24eecfed59e6e206a1316d4cae85
22473 F20110112_AAAHKN hari_a_Page_11thm.jpg
8aa654f0237c38a5ddbe600570587590
df6b8cc2ba44a5e42f167f58ca98d2a46118256b
31602 F20110112_AAAHUI hari_a_Page_16.pro
e71a634fac3f010b8449294c69130191
a26d2c2dc062c658ddb92425e095182c26b33573
88582 F20110112_AAAHZG hari_a_Page_20.QC.jpg
7ad2a8f3ea3ae994934b1ede5b73670a
5b224b2a79e86a4785fee004d16b7789a48d4a88
205572 F20110112_AAAHPM hari_a_Page_38.jpg
f21cf14050581caa2bac04f360ce9d4e
c177e651335d066bfda16b632cf1cda77698662c
467603 F20110112_AAAHKO hari_a_Page_06.jp2
b3c571677393dd0915fd3c181a166c5d
6413b230a3814eebd67534695d54374114a837e0
34001 F20110112_AAAHUJ hari_a_Page_17.pro
709238dc516193afc5b783321bdaa58b
5a8517e80074e6d7d609d44a28ab1cd6916ff513
48286 F20110112_AAAHZH hari_a_Page_21thm.jpg
cfa54595a53a183180afa9c80498b6aa
9b4f2378486313f07115e967ba4342db83e09083
193871 F20110112_AAAHPN hari_a_Page_40.jpg
03bf169f55de6c966a8672e3a8700b98
91500419de9845ad096cd3bb16183475de6ed3f2
66141 F20110112_AAAHKP hari_a_Page_42.QC.jpg
e2dd576dfc8378f972106c7e0d542f69
e4a26895b12f66e37d66aca4349e7bcf64c376d5
31237 F20110112_AAAHUK hari_a_Page_18.pro
57d5c9970183a3a56556bc7005c72c3a
fe3602d3af9f8746f5c7b98b8184ee61674d2f55
98825 F20110112_AAAHZI hari_a_Page_21.QC.jpg
72755a8380ec6f5614fac7629d3d3005
53a222529e90527382c1c07f4376eb2ee2af9eb7
197602 F20110112_AAAHPO hari_a_Page_41.jpg
dc4bc0193e63e79d726404971183e011
7f2d0db8c9e23b349d05be7eab529ade2213c572
20615 F20110112_AAAHKQ hari_a_Page_02thm.jpg
a802a0c1143102d38ec47ade00b93d32
1d49df655a857cf24f96a5d6093665906b9c06ae
41555 F20110112_AAAHUL hari_a_Page_19.pro
f9fe307a743bc98cb047e8122e8219af
b72190724b2300379c3142a161396d62bdac6edc
41825 F20110112_AAAHZJ hari_a_Page_22thm.jpg
e72d252c666eeb12350884482bf631b9
e391579769cf0239be9c5ed4dd1319dcca349578
25108 F20110112_AAAHKR hari_a_Page_30.pro
60325b1711b19124ec76b27de4138a27
66dd313442cc8c42da01cbf6ec842030279b3c4b
42580 F20110112_AAAHUM hari_a_Page_20.pro
421a8036fde7a1070d1115de12ea436b
21cc1fbf0e92b047e48158e2a755666fba4ff557
46421 F20110112_AAAHZK hari_a_Page_23thm.jpg
2621ba4acfa7394dbf5e9a7ebeca96bb
9972ea9bf87858fcae2be42db87c7abbe57933e4
130307 F20110112_AAAHPP hari_a_Page_42.jpg
54d8661ef5799b929be25bd1a4154f48
2fc7b9babf4146900ae3720baaf5cd4ce87087ad
95793 F20110112_AAAHKS hari_a_Page_09.QC.jpg
6ab9efcac0061b44aab18692e5748d34
173fe17f4b06410b2e6f3dbc6654940fdbec85c1
49058 F20110112_AAAHUN hari_a_Page_21.pro
dbc62a344e3ac0072a1b33c9589ec9b5
4f7ed36ae7d63d1c147a8e4fb2baf41eff75289e
90790 F20110112_AAAHZL hari_a_Page_23.QC.jpg
0e98e3dfd39c3231a43d77ea89d84f3a
71b0b2187a2986886a5ab823f2f5b81925dc2d9d
191121 F20110112_AAAHPQ hari_a_Page_43.jpg
9d0ee72935b3ffb28c246b0e572a71b4
62a3135090e17b1d1e028c9b19f3ca0fc9dde2d7
196687 F20110112_AAAHKT hari_a_Page_10.jpg
caba8d009a0a8e9d20cead7f5d4adf60
04c8167b45543c6026d1869a74de29870c89b30f
37650 F20110112_AAAHUO hari_a_Page_22.pro
974fe6832e4f89a2b326c0543f50c8bf
ef35b52fc235cee9244f1c8929b107f2eaa74350
41846 F20110112_AAAHZM hari_a_Page_26thm.jpg
6eb0edd371504259000ef32fefd955fb
f8300f731254b28df5306ad2dce9d9bbc938ed36
103433 F20110112_AAAHPR hari_a_Page_44.jpg
1ff4d2a5fe4a9b204216409a4ce40e80
10dd239e7d7b1a01c0b84c5273a5422beebfe580
3537 F20110112_AAAHKU hari_a_Page_02.jp2
f89dde8a0568443714f240e8555f2df0
656862e5089efe35e25acc9b336194ba4d5e0e19
44787 F20110112_AAAHUP hari_a_Page_23.pro
c0284f1d221b5326bac41cbf0dad354f
9e5cc11807d9f3e3f7b7f5be07244e08c9f84253
29515 F20110112_AAAHZN hari_a_Page_27thm.jpg
a17c6a2344840bb977921d68f41ed741
757cc72379717a609138c9d80a64f666b2ff41c5
180684 F20110112_AAAHPS hari_a_Page_45.jpg
f4c82b680fdbfc0e25d44ab7f806fd29
58f34ac81530a867b096640091c2504a9ca14f0d
488768 F20110112_AAAHKV hari_a_Page_01.tif
511dba74b691fb6b127b446702419204
19b55d6c3f943b0be8e4b23156fcc05b983c2ea5
23113 F20110112_AAAHUQ hari_a_Page_25.pro
df9ced992f6ca662531d04dbca71b3bd
0e461c5a51677958b14904f0117d60b1b61f792c
89589 F20110112_AAAHZO hari_a_Page_29.QC.jpg
f248c918d1b6d27ecc16c2c6450f2470
457f64f78126bed3114dc169c4afe9afb9c41e4b
159480 F20110112_AAAHPT hari_a_Page_48.jpg
7208d8cbba86c0c52f847342cc759199
0327d0befe562665e5978e99ff5426bcd2595f1f
56049 F20110112_AAAHKW hari_a_Page_30.QC.jpg
d980fb4d7846896c4665801d0b9a16ce
f4c5ce6675a57a627a53018ff33def356f0fa674
37880 F20110112_AAAHUR hari_a_Page_26.pro
f9f32e96d41257adbaab22f2918f8696
6f22d2c457398a6db6e04e225412ce2df1c1a8dd
40840 F20110112_AAAHZP hari_a_Page_31thm.jpg
f803d0952fadf9514192ebd6ca65083a
03b513a81cdd85f589edf22dd313a6b4ce2e28c0
36291 F20110112_AAAHKX hari_a_Page_25.jp2
fa01bba8b9f3c116ace9c894dd698812
0cb9622fcdba3a9af630fe4b10b246051d4b27b7
5123 F20110112_AAAHUS hari_a_Page_27.pro
ebf3b93bf8cbfa7d1b3bbeddf839009f
305acfc68d7a7d7acd1386b0a3b2cd71e8c77cf6
178819 F20110112_AAAHPU hari_a_Page_49.jpg
a8ae542545e9416b97efb8c74c748484
1ba4e20c4c09a29d6d1847160e6796a66c3b5dbe
84293 F20110112_AAAHZQ hari_a_Page_31.QC.jpg
66dab8f2fed0a4d45f9acfd72f5a157f
5f734c178394e73a7602bc6f5a2648524cd4a67f
492952 F20110112_AAAHKY hari_a_Page_29.tif
931c19b3cd987f29d0d2cb9a6220a5ec
da73749e8551c7fe1dc72b68b24646f27123be38
31917 F20110112_AAAHUT hari_a_Page_28.pro
f4ff459bc5c87c7976b1821c13405418
99e41ca27ab60056ec9271c4a894eecdc9b8aab7
140003 F20110112_AAAHPV hari_a_Page_50.jpg
8f9be734b44d42500564d37893a02b77
14047ccd9cb71ddeab45d49d0269afa283bab001
34102 F20110112_AAAHZR hari_a_Page_32thm.jpg
5880378e3aab5ba516cf8fe5631c1fbd
8e6cfb6f761e88dec7fa1b42cfb0db41ae756234
1805 F20110112_AAAHKZ hari_a_Page_40.txt
cda748e74f1b0a831aeafac6cba3c6e1
41e18080c2ac4bd8784dec6e17a454b4e99f2063
187577 F20110112_AAAHPW hari_a_Page_51.jpg
26412337169567bef50a724f958af51c
8ecad3c884d9579cb577f86e1029273be111ef0d
81976 F20110112_AAAHZS hari_a_Page_33.QC.jpg
f08e9e8d173ea26dcf9a7eda249f85e6
36a41b8eb684bdb9e18cd53ba4060d40be268b9d
32222 F20110112_AAAHUU hari_a_Page_31.pro
d64b1d9280833342c856d215465269be
2531a17207ae027488ef6eb253f01c241f3860a8
161133 F20110112_AAAHPX hari_a_Page_52.jpg
96917afb3e45c86d7f7b549492f2d20e
114bcde08dbe73c6b3deeec797b41299ebff2157
74122 F20110112_AAAHZT hari_a_Page_34.QC.jpg
d3425d12ac236e0e893dd2ea50e318d2
833d50c96047f3a7a272a86f9567233b802afa01
25089 F20110112_AAAHUV hari_a_Page_32.pro
c2fc7c333e0670f7475f0f69152dc9c7
0b0b82e07569936ec85fb97e7530f2f234d7de6b
37708 F20110112_AAAHNA hari_a_Page_25thm.jpg
4b91d1002a4c482169b300ea5b374c20
c12cddd0957ecb8e73d6f6dc3b0e8bc4349b3031
167016 F20110112_AAAHPY hari_a_Page_53.jpg
0160020e9fa307d7ed8ad3ce2729fb7f
bf5f2c13b54448e263cfa9e1b1886562cc7cf2fb
39536 F20110112_AAAHZU hari_a_Page_35thm.jpg
1331eb52d69caab1072a95b637eca4a7
1f8c667623bed2be9dc7162bf5bdf63f561e3316
36797 F20110112_AAAHUW hari_a_Page_33.pro
d0d0983935de383b7514d7a974b1b046
e47a795225cee615bded5bd860fbecc6e4eebe1d
24272 F20110112_AAAHNB hari_a_Page_24.pro
8266d2df336b5969e2cedfdc433ddf8a
5ee7295259cbe99b606332550a75d0bbce0e04ea
160546 F20110112_AAAHPZ hari_a_Page_55.jpg
0123b4e395765a496d855a12568d7db3
dfba5a3f20ba2e639146940a245004dccec5e129
41622 F20110112_AAAHZV hari_a_Page_36thm.jpg
81edacf1c721c7bb7d240116a03b1438
1e14d78bd460ca2adc65b2c92a4538f5d63e12d4
29882 F20110112_AAAHUX hari_a_Page_34.pro
9198ca014bacf1564882159aaa10f4d8
0c2c599b0377ecce7f6d9416f8c2c3422e1427ae
39228 F20110112_AAAHNC hari_a_Page_34thm.jpg
0362ff5bd014fc101b8c9a9e2def279e
ad7f9b64a508d5db84f760d3c6ad4a78e30c8b07
82267 F20110112_AAAHZW hari_a_Page_36.QC.jpg
95820932cfba5d472a5fd235538296fe
00ba5b5759ce5d27c8787ca50146e6a4cccf1c40
11241484 F20110112_AAAHSA hari_a_Page_05.tif
41ccdaa251c0d7eb502154670c281377
4b0bef60e5ebf2e34e506ffeef8eaaaec0ea3b92
35045 F20110112_AAAHUY hari_a_Page_35.pro
e009247410576a1ce401e803590f4780
4dae6b40746d96ba1742d2e06f821943e3f766e4
236919 F20110112_AAAHND hari_a_Page_62.jpg
d1b92ca1a5420b1379674d9c60028378
179c950da8cd46130251fa5787254bb83fee50f4
75637 F20110112_AAAHZX hari_a_Page_37.QC.jpg
d0547ef59303be804cf4668624cb2222
a5c75567429f34aed462cd57174e92d0b0698812
11241864 F20110112_AAAHSB hari_a_Page_06.tif
fe1d7387efc2655d7df794dac10a466e
1ca0816874e8b68ad0bbcfec5c1b4a6804a53604
30401 F20110112_AAAHUZ hari_a_Page_37.pro
00dbd0b34170ae186a864e43a11a195c
532c6bdb7006067b820de4bf31cf8d5368ae5ccb
84523 F20110112_AAAHNE hari_a_Page_40.QC.jpg
893611e16b2e4c0eae631106aaa24883
4a59175b01af42844789a9540806bf2c17657c27
46419 F20110112_AAAHZY hari_a_Page_38thm.jpg
a4b20e36b65439ee636f5e5e0b030f96
c846f6ac3e9199c30d5bd78dbdf8920684cbd3a7
11240820 F20110112_AAAHSC hari_a_Page_08.tif
bfb12e28a6563ec8c7fe0d6bf4b2c49c
f04f597518753a2ebd91bcebf2c3460e0e9b7cc9
54627 F20110112_AAAHNF hari_a_Page_13.jp2
7676e96034c4accf1eccb08eead7658f
b7994baad065d2593eca2f3e1da1d9647e0d746b
11241768 F20110112_AAAHSD hari_a_Page_09.tif
15f1480330821ce514955505ce9de189
483f65e0aab18f826a781cbdb1156f0e67ca4623
1617 F20110112_AAAHNG hari_a_Page_52.txt
a61b7d5c1b792175b72d6bbfd924137d
55cc3277ed566f206b8e36977979e0065dca557e
1815 F20110112_AAAHXA hari_a_Page_43.txt
7ff2b5b3208160584927c9ad1bd240ea
bdeb2f7369d618bc3356e26dafd829288418578d
46304 F20110112_AAAHZZ hari_a_Page_39thm.jpg
dc2d9e5766c7690138d4d9c8b1947134
1103d0bd8c1983cc88ddd070897ed9c2fc5a0a1d
492712 F20110112_AAAHSE hari_a_Page_10.tif
fda65f9ca9ef89003c9d2c4ccf78f40e
7a0e28e039eb4b08570fbcaf840be6d30c177a39
60755 F20110112_AAAHNH hari_a_Page_46.QC.jpg
651047b83e4eb4a3826d0c883886de18
3bf3ba5beecd8215e82caed1a4ccd13363aeb19f
904 F20110112_AAAHXB hari_a_Page_46.txt
deaced6bdf7ac27555b64bfa5db7b4b0
50bebe094aa36df83f5e2c9c08f4d9fd0f052086
487712 F20110112_AAAHSF hari_a_Page_11.tif
fd4e5e7153c1fbadcc71a7d497c06e2e
ac1131beef95649a0ad701ef1cf11f0da3a81954
38746 F20110112_AAAHNI hari_a_Page_28thm.jpg
1d4d3d53ae5693aee9b3e43f9193dca3
7a061eb00ee1b5717d4da30264ff17821facc915
1062 F20110112_AAAHXC hari_a_Page_48.txt
f5c0ea81756291bb410f1d57edb11e3d
ad1a82f91734e0ad8157524878d61d49efa13b3a
492932 F20110112_AAAHSG hari_a_Page_12.tif
39e1af93f7700b6e732e59901502997f
26a91156050216a57d23df00d98f127a3ef205f9
1891 F20110112_AAAHNJ hari_a_Page_23.txt
af471ecb24dc6d12f4069ed83a12cdb0
74cb4953cae2fb43b9dcc30c003084c93cb28d52
1150 F20110112_AAAHXD hari_a_Page_50.txt
b702b0a6e3c8ddf0d6f516c2eec751cc
c8f9f5098d8480150bee7bbe21bd6e6868542750
11241848 F20110112_AAAHSH hari_a_Page_14.tif
82e7a250c4dc33a5cc39affcd26bc837
6e30772e2ce1a2b6a853489c52c3e909241877e7
52269 F20110112_AAAHNK hari_a_Page_64.QC.jpg
42c87ff0ac435ed7a930b14408bee130
1caa293ad3ce4d3a30d382e47e777440c7d7120d
1677 F20110112_AAAHXE hari_a_Page_51.txt
17707fd3055fb0da56a579e0810856b9
4cb7df04380c5690d015f3f46674a0dcd10c49f5
491516 F20110112_AAAHSI hari_a_Page_15.tif
e3ca1ada8b198f49db029c17e8a2c610
64dfc2767d799c48a968d5bd02fd557505d15863
2067 F20110112_AAAHNL hari_a_Page_58.txt
a44497a3727e84d41bd65af8f42083c9
34d4c9c1b3164a3cda0b81c68394f679fa25a2fe
1083 F20110112_AAAHXF hari_a_Page_53.txt
2623c5b08df2f1f389ad182c0a477999
cb4724a40195ad197bb407dae8b2d52fb5c6ede3
11242116 F20110112_AAAHSJ hari_a_Page_16.tif
2e75508addae04b0e337a9c10d29cd3f
59b407a1da11f15aa9f6bd6fb434a3c14a7ed0d2
F20110112_AAAHNM hari_a_Page_45.tif
ad049f6989dcb478c58408fe88e623c9
664561d311674cee49e299833aca2c47c621bb46
2137 F20110112_AAAHXG hari_a_Page_54.txt
6b832138d52bda8b27f4768b53005c07
01520f5ea7ad919931014533b95cf0fbeb6e9307
492056 F20110112_AAAHSK hari_a_Page_17.tif
0839530d3389e94fa100badc573f1c24
5e56811c2f29ad6f1092afda0f58320aa8debb13
1530 F20110112_AAAHXH hari_a_Page_55.txt
5f4523bed77ea400f9a513b66b80be5d
b331d5942239809c3245a8cce0bc859ea9759d43
491988 F20110112_AAAHSL hari_a_Page_18.tif
f6005aa0888fa45b9aa2811ece0a25da
891dba02d7ab1898b74b0c1f4b2e2939aeac5c48
45813 F20110112_AAAHNN hari_a_Page_11.jpg
6c2e4b64f0bf0bb7e08aeb0205d75a62
e2ec834828c03648fa78dcc5a350f98b07ec1d82
1046 F20110112_AAAHXI hari_a_Page_57.txt
3ad9830bf8e860f303ba11a1319b2a17
0e628a9ff51a488c95b99683aea3ac7332e5330f
492992 F20110112_AAAHSM hari_a_Page_19.tif
533a71ab7c8122d35cd850581c97c04e
a30314d3c542fabd32b3bde2f54bff97f6b93dbe
30460 F20110112_AAAHNO hari_a_Page_14.pro
2deeaa0ba3184ff7eca1533f81c17482
f58aac3ba483c61beb506b40a3a0b99ba34a3133
1749 F20110112_AAAHXJ hari_a_Page_60.txt
c58e7c63577c622523d9977b7627e7e9
3e643a5a954b18dbc158d8ed920a70aa3d9fd992
492996 F20110112_AAAHSN hari_a_Page_20.tif
a13140612de32b406090a6b0cbca034c
0cf7cf0a56a5b5fff263b02aad2cc0b8c6d3558f
40107 F20110112_AAAHNP hari_a_Page_05thm.jpg
d9d5c6cbc153d472eb86d03738cb239a
bba06e5f0eee6defe6c978d454c9cb86afb1dd0a
1247 F20110112_AAAHXK hari_a_Page_61.txt
81cfd25f9a18548233307bee04a46779
f1aa60b65ced73c56624633bfc6f56bc58d9230e
493980 F20110112_AAAHSO hari_a_Page_21.tif
82a13befe3ad78fbb34e8e6ed82fcd0b
3c690bf5ce93fe94a2a87ef9190328a3682341ac
162317 F20110112_AAAHNQ hari_a_Page_58.jpg
a75f4f9e4888e82e3d6cef7cc3e75bf9
cfcaba098d1ba947842fb584b6abce9bc58e4631
2110 F20110112_AAAHXL hari_a_Page_62.txt
e0e41e13cba687dd44ea76b32ee08668
5e85beb56661a48628c9f782997562e4d9038e21
493372 F20110112_AAAHSP hari_a_Page_23.tif
f48e53e9959cadf23917792cd57bc054
4dee27feae64196574e120ee6ce4b8127d3e3b08
467575 F20110112_AAAHNR hari_a_Page_34.jp2
a190cdbf0b281874acc27eba48d3e9d8
318edbc4d06810ed4a9ce10a5d5179bfd38d0137
937 F20110112_AAAHXM hari_a_Page_63.txt
37a9b6e6f5d97deaf39fe9bc1e84b64a
afbe95a0d6e52b163a2e39049b5627d62a6d39af
491632 F20110112_AAAHSQ hari_a_Page_25.tif
a4eb362132ef387e1f60f129871e2415
08e434773ae08de6940205cf937f1bd003f7b67a
56700 F20110112_AAAHNS hari_a_Page_23.jp2
2f5092d4c6df783545246d149ac6a0d8
bba1d36528bbbf0181cfc6918dad5d6a382086f4
773 F20110112_AAAHXN hari_a_Page_64.txt
01cd558804a1a6c2ff4db92ca2bacffd
22c033f96eac8939da6eead4a3b41eace29cfc81
76789 F20110112_AAAHNT hari_a_Page_35.QC.jpg
4cee5a50c081809d2123d1b394a9a585
01d931390ee4dd8d01c5d50eee8d1831410599eb
26040 F20110112_AAAHXO hari_a_Page_01thm.jpg
9a894c2d1f571232f8d1b7facb289a24
eff06cddd790ebdc9a6eae53bd6ac54e9b55d4ac
492440 F20110112_AAAHSR hari_a_Page_26.tif
5c2a6686410be1455bfe1b48df05b2a1
ac06d7c53af0e6e5cc507b937a183438c267dc6d
26362 F20110112_AAAHNU hari_a_Page_64.jp2
1da4598d821dcee77510400175bd9fc9
6394c19b7c051ae3afba0e067d16b464c986679d
867287 F20110112_AAAHXP hari_a.pdf
5d78111c9a72b59dff6655d515a704bb
cb2de138beb608e879e9d83ecc0f89971b12ace5
2047 F20110112_AAAHNV hari_a_Page_47.txt
b333e76a5f607c85fe5d5d8f55455924
a635a453274feb062811e8a6b15cd61f9c037e31
40973 F20110112_AAAHXQ hari_a_Page_59thm.jpg
424b48ce8afa440e8eab4a4238a9dbf2
ffeeb55f89f8d1028e3c553f9a92e6100eb3dcde
489816 F20110112_AAAHSS hari_a_Page_27.tif
3a981f01086638dc3a9d0f420d075041
edce6bf5983a7add7343e5c7c35ad2a8afc41391
82878 F20110112_AAAHNW hari_a_Page_26.QC.jpg
34eb89b7601ea4e654644393ead156ef
16599ed69b67ba2a254358e015eded04893401e9
42817 F20110112_AAAHXR hari_a_Page_27.QC.jpg
6a2861028549d4349c4af8986e90d85e
586d2a1e99a20da4de8ec092508d760a61e37f7b
491864 F20110112_AAAHST hari_a_Page_28.tif
8994f6e2707a69cee00f9a19dbb9c871
2e394186fc213e284d03bf934a9f80a3a9720e98
38904 F20110112_AAAHNX hari_a_Page_16thm.jpg
1ced7d781c56c2fc3215557bc3a56f99
70b783926d85a93f5514a38c6565f3554323ce96
69586 F20110112_AAAHXS hari_a_Page_48.QC.jpg
d29b24754ae24985f5c030b07c794269
fbeca8e7e79db6366761c0f2cc4e2e42d82183f8
11240504 F20110112_AAAHSU hari_a_Page_30.tif
37af26099b08de495c01d56a18799c37
1ceb236fd2cdd8406663147afa879e6e64d161ba
157056 F20110112_AAAHLA hari_a_Page_16.jpg
3d2b38c81cc4ffae2069d5bdd0dbc5a1
bf1011c58d3c3d9d61e3aac67fa08440268f038c
74094 F20110112_AAAHNY hari_a_Page_52.QC.jpg
3dea4419e689a6916e28ead9032344da
65fdb23f44ee82b138af0623169f1ca0ae6e6350
90033 F20110112_AAAHXT hari_a_Page_41.QC.jpg
4f98deb01531c4619f3ddbcde939697c
0433337852f8c1b0a5b400be9b6f18386b835994
11241988 F20110112_AAAHSV hari_a_Page_31.tif
d1f31e0cc1aa66ca70cc1467aa239e44
268ca2c801e469c8c79ad73ba4d7e95f4b682c92
49935 F20110112_AAAHLB hari_a_Page_22.jp2
db81588dd35296c2f60e006b1593f042
5ed3eec448244ad0b4ba8c90dd2e96604ae82f75
39276 F20110112_AAAHNZ hari_a_Page_17thm.jpg
3364dacb1c82b6f2f1bf6f1891a5301d
03dc8bccf21e1d9d73f60d16227e8e4e88eb0fe1
44182 F20110112_AAAHXU hari_a_Page_40thm.jpg
30bf8aa7eb7dafe708c281f72c333e9e
31cb28889bc0e642e5137b2515cf3b3c5a009b25
11241068 F20110112_AAAHSW hari_a_Page_32.tif
3df483c5defef860aa577d47947fcdd3
b6bf9b0f40c9d686a254b209897f7acd5bcc9c78
107796 F20110112_AAAHLC hari_a_Page_42.jp2
d9201966abacf77f1fc4d0cc184683d5
9a59d034a98725d6cf71d5d7bdada209a4c8165c
97362 F20110112_AAAHXV hari_a_Page_47.QC.jpg
5bd1325cf22123254ca8bac3b08479f7
aec25d18cb051228d7bcfe82bd12d2dceb4bc6fc
493012 F20110112_AAAHSX hari_a_Page_33.tif
f6564a114b513e701b86000394818b02
54050ea986b100a10d4581f9b6e539b403162139
45262 F20110112_AAAHLD hari_a_Page_38.pro
d0457887f1853ae8abf87a0a3dd59b93
21ebb192a1877121fd4dac92ddd2d83c1aa5c546
67397 F20110112_AAAHXW hari_a_Page_24.QC.jpg
566a4b2e2f4207fdd9fa8796bfe9c7b8
856f8b90ec1b7c725c12009033007c983e62c18a
125119 F20110112_AAAHQA hari_a_Page_57.jpg
22705d36cc78e37677920abbd39f8aaa
9cb640a6de49c66db85ec0322bf533ab3f89bf42
F20110112_AAAHSY hari_a_Page_34.tif
acfb03fbbac1021b73499dc10616d906
90debc357a8c663ad4deea5d3847f7bb2a1585fe
197289 F20110112_AAAHQB hari_a_Page_60.jpg
1216b814242220e29cdf181b5f02ee6c
8dfc9eab89354a9a767689745f1350e47d247f1d
492184 F20110112_AAAHSZ hari_a_Page_35.tif
a564161c77126a03267aec12664fbaab
bc79169ea975ae5941f5a10fb041a3fe2914dd7a
2606632 F20110112_AAAHLE hari_a_Page_42.tif
6cd0e61d000416c021131fc5e625e98d
511d41f258f7fb3cd50e166741c0d860cbe4e1d2
98406 F20110112_AAAHXX hari_a_Page_05.QC.jpg
f006cb9c3052a48a8043c2c7b21bf9b9
646779db2d118decee440743be1eb851fa52a3f4
143315 F20110112_AAAHQC hari_a_Page_61.jpg
a73849f8c14a7b91f04ee3de2f225a53
7697e850cf043ccec5f9c35dd643f15e05c9a269
42516 F20110112_AAAHLF hari_a_Page_28.jp2
5d64241572565a00a6bbddc6f5449477
0406b0cee7b0215157ff453e4aa5c61fb2807da3
39144 F20110112_AAAHVA hari_a_Page_40.pro
db3f2159577c394bbba1fdebbbaf2cdc
f6dd519663e8b8aba421adce04b90b8b3aa628e3
34899 F20110112_AAAHXY hari_a_Page_57thm.jpg
9a689bd8e1df311aea00083d80b02ed4
79829f74a2d1411a29107d0791f59e13505d2db7
114531 F20110112_AAAHQD hari_a_Page_63.jpg
5f724535cfec3717043cf618ae9113fa
6369b3a83e706d0ee2d60dd57f0e37f534b47bae
25593 F20110112_AAAHLG hari_a_Page_48.pro
f32ed8fd220cf512268e01074e157f6e
52354a8f1a3d656db235810719e159a877abcc80
42965 F20110112_AAAHVB hari_a_Page_41.pro
a240bb1e64ed42bfbe4033b67247f37d
71e3c19ccb33ac005587c9d091598a7c17fb6495
40240 F20110112_AAAHXZ hari_a_Page_58thm.jpg
45ad24a6ae55a3ae6487ac93458c6d25
f0daa76c10633f4576b1a4f0fd475b2b293b3671
15613 F20110112_AAAHQE hari_a_Page_01.jp2
93e473b31f1df439840c89d11339ca91
96e0b9c848022971f44f83bcfa7409c925a0429e
489664 F20110112_AAAHLH hari_a_Page_63.tif
3f4954284b1ba82f920e90331b592715
80837d9a2cf0530c17f57fe4995e8b90a9b96ad5
21893 F20110112_AAAHVC hari_a_Page_42.pro
aeb2fc1cb01b0a38e4f0fdc5a187cf17
a635af9053b7eb9f2eda28b128c04aa7190c6da2
3644 F20110112_AAAHQF hari_a_Page_03.jp2
c9a9972e3db9961a9c2d34c54cb259b3
8d37fe8f4458b8744ebb58f3b9b67442b498d942
37578 F20110112_AAAHLI hari_a_Page_49.pro
31ea3219285017fd57d9af739a994966
14c66efcb8d28ef112cbf30e86ae40d5ce9a090d
41009 F20110112_AAAHVD hari_a_Page_43.pro
2d2e18e140f204a2c25988876fb3d280
cb5158e618796535cf9b43829ac3ce6245ab1fdf
35779 F20110112_AAAHQG hari_a_Page_04.jp2
4b8d2b9ddc79efe6fe2a890927977cee
8af1f40fb2f960b06ddc89178abce58e8cb7bbe6
34206 F20110112_AAAHLJ hari_a_Page_55thm.jpg
b6a72d120da43600b4ebf95a4021c839
065db19a067eec80c774ca39096fbed38f728c0d
15361 F20110112_AAAHVE hari_a_Page_44.pro
af6f73443877e96bea4e6dce2eaff82b
a05eb6a7839c441487cfcae3b38186c2ef4b5ed9
467602 F20110112_AAAHQH hari_a_Page_05.jp2
bcc58513259d729bb0fa37ff6aa48fec
d871b62e6e10c4e1ffa35e51e1b626ae4def37e6
974 F20110112_AAAHLK hari_a_Page_42.txt
1906bfaf604831f6f4b42e7672e67885
372d034ee7367d71086a94ace12abbc865787584
38513 F20110112_AAAHVF hari_a_Page_45.pro
76bc3e696b7a0ef0cba48db8ec101cad
6289b29f9bcecc4623031cd47463d35f57337a14
94185 F20110112_AAAHQI hari_a_Page_07.jp2
78776344f8409040f83815b2da2626f0
c3ea6d7f06d0c88fce65b189dc0c3c052cd5f134
20728 F20110112_AAAHVG hari_a_Page_46.pro
efcc15c4624777943ee4352eae97b352
d4e7783a70ba5db206b70fe5d0534d78669d0bee
467599 F20110112_AAAHQJ hari_a_Page_08.jp2
afa765beb0effa97c8aac85c08e00c58
269aa8f0d77d302a50052830e461b782cdd92271
1785 F20110112_AAAHLL hari_a_Page_10.txt
ff55e7cd392e4845e9691927ac2d1192
59434976bc2398f081edd25af097272316140db7
49693 F20110112_AAAHVH hari_a_Page_47.pro
3705576f2b3b83f5a52a75c1ae0107d6
47aff0a276d82f58765f344433cb1127e43a7859
467597 F20110112_AAAHQK hari_a_Page_09.jp2
fcfc0a0b643acbd6f00da44a7a557117
3864170844f70689aec18b1eb57006c7d16c8ce6
2200 F20110112_AAAHLM hari_a_Page_09.txt
eef8cc334eba4e2bfb7b28173a671d7c
d22506eee1d49a894d7ccb310470ca62704cea73
28261 F20110112_AAAHVI hari_a_Page_50.pro
a24eb0ba9508abf868d9bc80222a62c0
24b2058c673a7e8ed7ea77d33a88fafcbf72fd9c
53982 F20110112_AAAHQL hari_a_Page_10.jp2
b8c963aff916ead5d50ab6f3448b7742
a02333c7bf2e32d4401cc6ef1d4e080271a54f3e
263745 F20110112_AAAHLN hari_a_Page_05.jpg
0b8d7dcc63a41302db0480bfbaf2424c
aed0c45a55253c97cf801f771dbfd236673421bf
38443 F20110112_AAAHVJ hari_a_Page_51.pro
9f5c4b7a2498bc530cee81c8efd1438f
df0919458a665bf1c72d8f09dd7db84e78252901
8752 F20110112_AAAHQM hari_a_Page_11.jp2
c0bb7940f672e6da3e7589f2459bd3ff
d7ebc1e326927becec2b0fdc2bb9460e3e1d1850
1411 F20110112_AAAHLO hari_a_Page_18.txt
57e2217388f7002d6b39724ef045e73d
7f597b3c0a4f05800829f819e2f3f6c3c424f97c
30937 F20110112_AAAHVK hari_a_Page_52.pro
b421ef93830f5cbf24de72c14dc763d7
2547acb67df4c9e39ef7016cfa9cf3d18525c578
385059 F20110112_AAAHQN hari_a_Page_14.jp2
472db37e3e7e9a0a633b44239e502c44
237381d719eb8dbe704a9d3f4364c3899fab9039
42035 F20110112_AAAHLP hari_a_Page_49thm.jpg
07a4b04783c3d91cd66a678fc470fb30
417396d8db6b6c2134d6a6bf6f621545f5bbbd09
19672 F20110112_AAAHVL hari_a_Page_53.pro
1cbbe680902f378ac1328f4c13b12e9e
5abf33539dd1eba9c9d8437a8ec602028e8374eb
42818 F20110112_AAAHQO hari_a_Page_15.jp2
e074f98972d748b90f014539c6326de8
7d97ad40c6f400091d7cd5b33b6d104d4877af16
43654 F20110112_AAAHLQ hari_a_Page_33thm.jpg
a24eb57130d9889a04b78c45494ecb91
63ecff247a5fbc456d6ed930d5ed78fdadb4e747
42432 F20110112_AAAHVM hari_a_Page_54.pro
35f7090c82a9100981fc0f7aac1b42a7
e12ffc722cc5a06040f108806caa872476695bd8
405496 F20110112_AAAHQP hari_a_Page_16.jp2
c5982e18ff51bdcb8046c5c648d2cb89
7567e7d0bbab49c92fd534fddd4569080ee5a491
1024 F20110112_AAAHLR hari_a_Page_24.txt
cb8bce1ba03c46fb66153c37d6376c02
655329478078508a3d7374563003873d1e9d7fce
20404 F20110112_AAAHLS hari_a_Page_03thm.jpg
f7e3eaf705c57f6c09dc128df0e8bd64
1a5a6bb2eac0e0ee12056620a2244f92c86332a4
31251 F20110112_AAAHVN hari_a_Page_55.pro
74fe3002aadb5f77b6fc0079669324fc
f57ebc588eb2b750cfe74f3809bb79874627d6e1
43053 F20110112_AAAHQQ hari_a_Page_18.jp2
dd9594b0f2676b618e425406a638a9ba
3eeb249165b6ec93ebadf72e218df2ea85cef2e3
178475 F20110112_AAAHLT hari_a_Page_22.jpg
725c30c863beaa7667d0206ce4e84e09
676dabbfe3e3ec5c8852d697db2b527bcdfa858f
21725 F20110112_AAAHVO hari_a_Page_57.pro
fe1814b4f1a4486205f72d1f00e6c729
2439cdc28270a2c361a0fc9c64343f6bd270b443
55352 F20110112_AAAHQR hari_a_Page_19.jp2
d5075b9f6bc1a9b89941906d0c39afbd
9a0a1797184b23590daf9c4a5086a4598ec72ba0
1134 F20110112_AAAHLU hari_a_Page_32.txt
e441166852e86e8a5acf0f30e3f7b997
2caf93e808cc73bbcee8c56d723b7bd23ea917bf
33598 F20110112_AAAHVP hari_a_Page_58.pro
924091068cdc5a2cb19f07bf6b35a3bb
48c5a56f6b60bfcd3386a5ed532c4b6c5f448bf5
63610 F20110112_AAAHQS hari_a_Page_21.jp2
58b2ab12b32e108225c87b2ad1248c2a
432d55dee337d643061619fd400280b06377a62a
1269 F20110112_AAAHLV hari_a_Page_34.txt
e69d139336605fa2c366e2711947e39a
ce3f1ff46b2043c9f1f465ee9754f612edd2551a
32904 F20110112_AAAHVQ hari_a_Page_59.pro
7a4c9a4dd239f5f2f47c2f819759bb43
f4422ca4698ac6f841ea73af8aba4ae2a1e7a85a
36957 F20110112_AAAHQT hari_a_Page_24.jp2
bb4181dd0c6209fb6c51433df43f6a39
58f5ddd03a251b3578b17882362ca4cce06b4a37
1790 F20110112_AAAHLW hari_a_Page_41.txt
257fb78ec1344d7f5a359ed6a6728571
d96ab926fed64c7146c1e298a04b5f694a85c440
42419 F20110112_AAAHVR hari_a_Page_60.pro
2adc7289904b893858847dd614387cfb
8304f94c059443a4663089f1a90226fd9d767446
49812 F20110112_AAAHQU hari_a_Page_26.jp2
3f080dcb63e009fe4f07bf1b3e25dccc
55966232088ac20338d606d5ed73c850182d9816
72374 F20110112_AAAHLX hari_a_Page_58.QC.jpg
e885b245606379776533d76cdf9331c1
707568c3e80a6ace1b998c91d81b0c4c59d4d529
29655 F20110112_AAAHVS hari_a_Page_61.pro
65e019675495cde4d6af888f161a2a65
4518307b1b9d2e8eaff53e73375eeb5c4bff4fd4
15234 F20110112_AAAHQV hari_a_Page_27.jp2
7400c9e2ac172be20747779243e805a6
bbf3f9a6bb8348cd2f06b48cc6a4e183660f6bce
124000 F20110112_AAAHLY hari_a_Page_46.jpg
ffc31afbc1af124a48b6169a4083d385
6db7cdb4bb622b85ec689afe50ce903bdcd7756a
50887 F20110112_AAAHVT hari_a_Page_62.pro
6e84ecb14d5174601bb7816c621b1dba
63a9ca2d673914a473e85e8e6c553ed4c9623592
54863 F20110112_AAAHQW hari_a_Page_29.jp2
84cc15425cf328d10304cc96d1498480
56d6d29956724fe942d3eb7e9eb82395101bdb5c
11239168 F20110112_AAAHLZ hari_a_Page_07.tif
2a64c336a6625ecbf7f131f4b7f06393
1f6566ff1f888e6358a9a97361b83025e0e40aca
21213 F20110112_AAAHVU hari_a_Page_63.pro
3456c31587e2c60d4091ee726f13d431
3d68c584ed2d7daadfb26224db993c0d77b2aeb4
321367 F20110112_AAAHQX hari_a_Page_30.jp2
7a467e67fb859bf3aef9169ad4f26402
bcc8028156f08fd0a46b6a668d57e54aa2dae1ce
467593 F20110112_AAAHQY hari_a_Page_31.jp2
6ebe883488cfa5c0bb67dd3cfc02bdd7
eb0c016147b6a3526dc4c7788f4bb37320dfeaf1
18187 F20110112_AAAHVV hari_a_Page_64.pro
ae90a3de2b1f5c98fc37a4c0b7ae21ea
3cb1104d4b09ec1634d3999676f3558e8a32c5b9
193716 F20110112_AAAHOA hari_a_Page_31.jpg
d9c4fb40603df48b4d05e15ee9abbf04
cf1a35dfab196bab93db4dd676a8f7616c10a4f3
418661 F20110112_AAAHQZ hari_a_Page_32.jp2
d82c36e7199d15a594e4fcb54e4ea7f1
cbafa08eebb6a18e4608c364660b9270c9d95461
459 F20110112_AAAHVW hari_a_Page_01.txt
73214f50aab2de77dc818715851ede2d
eb5504275e6b6094ff08c0fa4466a4baf86441e5
1816 F20110112_AAAHOB hari_a_Page_38.txt
bf70d332ff67e89709a805afa2db92ab
032b31fa7dd6bc3ad9804d8bd44520243debdd3c
115 F20110112_AAAHVX hari_a_Page_02.txt
2da748a6835f74ba5fbaa77b1af25da7
c57b0daa474758537e805b99e98452cecc6dd530
52448 F20110112_AAAHOC hari_a_Page_51.jp2
035428954ef9f9168f149b17a746485e
3c1a87b3329d6bf15368e6abd187535c0dd94e34
492540 F20110112_AAAHTA hari_a_Page_36.tif
e7f35d86a14170d563fe58afd3d91db8
b9e8c5b3b830d7b3cbdf0b697308a31a3a887467
1107 F20110112_AAAHVY hari_a_Page_04.txt
82db2fffe8b06d334524104cf9d12613
634d2e701f1c0174ba0aa4b4bd70aa5cdcddacf9
492772 F20110112_AAAHOD hari_a_Page_13.tif
9589df5d9321102d8f4971a42777a66c
7dfac09444684d7d68dc1c00508efce5b203bc3c
493576 F20110112_AAAHTB hari_a_Page_38.tif
589f277d8e64c10b9daf9a9acf84eb39
6535fb35315fee1683a71a6e76af6181d037cfd8
3051 F20110112_AAAHVZ hari_a_Page_05.txt
19014a87c5a6019634de7928f4fd93b9
d012791f339c31bdea1edb3ff7139e21aa0f60fc
45357 F20110112_AAAHOE hari_a_Page_07.jpg
cf8c2ad4e485d6e2c874115f33d36bab
1585bb06a90f37261f374e91729ee7c8ae332129
493440 F20110112_AAAHTC hari_a_Page_39.tif
aba0fed70b791a4903288d39be737b49
47af957842e1143940ff2132bd59fb90845c0dd5
42130 F20110112_AAAHOF hari_a_Page_37thm.jpg
007500d8da5e7312829c6c938c3cc1c3
5b5e5f25f0d3461d94a0b1c8825a8207c3a5bd93
34982 F20110112_AAAIAA hari_a_Page_42thm.jpg
70308a9775dc15f4614792b5fe346595
730d6508bd30d2ec507ef0bd7977a7ace7e85b91
38549 F20110112_AAAHYA hari_a_Page_52thm.jpg
25760e3f5783d3e868e3e5d7b360bdc5
abdf7c9a844ba7ca0e8af5bc8106ffc46ed2847d
494064 F20110112_AAAHTD hari_a_Page_40.tif
c15cdeba9e3bb62328d27df18bde2bb2
4f47206913a7893ef6a1de6b8c1738961e699720
44498 F20110112_AAAHOG hari_a_Page_41thm.jpg
db0d68014316a5584e5b36c050cbdfde
c954d78b7e0bd47c9002361299048ad506c92128
43766 F20110112_AAAIAB hari_a_Page_43thm.jpg
78d8410ec03c3c3c6f35bfa9a154d2d3
3b89542246dcda711c08114705af089596015e4e
80633 F20110112_AAAHYB hari_a_Page_22.QC.jpg
54c8b16d0b2ceafee9d8748c5b7ad698
ee82274e1d3362b9f8ad726f0bf51a469429fba6
491128 F20110112_AAAHTE hari_a_Page_44.tif
074c17c4658a55355b2009af35ed2008
c3a4d8c5f7a2f31a2f8abc0d5f6e96af5e4350e1
90793 F20110112_AAAHOH hari_a_Page_38.QC.jpg
5f940de2c3f37a4d7376d5b1201b0697
3d0a49b408246cbd5cc0d7e2e3e7ebc5c1847318
84993 F20110112_AAAIAC hari_a_Page_43.QC.jpg
5eb02132ad3d754154f6c301157deedb
da995158163c20f0603793209d83c40a2034d3c8
34266 F20110112_AAAHYC hari_a_Page_08thm.jpg
77149de4d17aefa726639e7246894277
b8893703b82da0b5bdf0f66b5a1d14c3f8ad720f
491312 F20110112_AAAHTF hari_a_Page_46.tif
8311278b1d89ba443c85629e739dded0
faf8fa148fafa88d4116bd4eda76b11192791e69
494172 F20110112_AAAHOI hari_a_Page_37.tif
0abf09730861d4ea05631ca9ff8d7aec
5f8173a698bbb238eb62f5322daadb627689ada3
53511 F20110112_AAAIAD hari_a_Page_44.QC.jpg
64ffde5e87a06384fd7803b6b6187abe
13a09df30441193de1f10565115e039e8215702c
33048 F20110112_AAAHYD hari_a_Page_44thm.jpg
23331e3a5e903e78d61515b98e62a105
311435f91c273f1c4781c4437b00271612bd12e7
493480 F20110112_AAAHTG hari_a_Page_47.tif
304766b9cc1bd4ccd38c580d8b2256e9
7b09482333fbf7ace9375c51e81b5cada022a3f4
228040 F20110112_AAAHOJ hari_a_Page_21.jpg
352a0a4604f8059303e1612b3fb93c17
1a84b0890d04a5a4a9de088cd99342f2cf660452
41914 F20110112_AAAIAE hari_a_Page_45thm.jpg
dd0010f79fd32cf681c690702665c507
508be971be760bc1491347083f89d0ed8db16020
68934 F20110112_AAAHYE hari_a_Page_32.QC.jpg
e88f34069e77ff419461e38e1ea628e0
b2a1057bd83accb69945d14b415e9beea1461ec0
11241548 F20110112_AAAHTH hari_a_Page_48.tif
93ee49c68fa624b5783de7764227873f
af85b0fd4d8795a6003afa6b6477fc5903a41e64
40249 F20110112_AAAHOK hari_a_Page_58.jp2
9f778b5e903688573a038329387e5f46
3ccd0be91a7cc2579b8753bedefed905f500039f
82393 F20110112_AAAIAF hari_a_Page_45.QC.jpg
3f929810c02058594950ba5152fb0a5c
f906e1bb2a2d2bca7d6c98476a773822bc4e1b25
43677 F20110112_AAAHYF hari_a_Page_29thm.jpg
930b6990c3a2973bafb0d76d2cc151d6
c32cb63a3a2897f9253e8fa1ebb0b9db9a2c9805
492660 F20110112_AAAHTI hari_a_Page_49.tif
196a213949a6cb612e56821090fc979a
2e26a4640e61d20647966def2937515b2c9ad584
75334 F20110112_AAAHOL UFE0002760_00001.mets
ac353ec700e2df814212f534407f446a
38759d804356181cb5fcea5fbb6d54742c4171ee
34930 F20110112_AAAIAG hari_a_Page_46thm.jpg
04ff55b6d23e5a3f6479e8ae04f4cfd1
8e530a8542565dcf1874ebaab533689db5fa7afc
42804 F20110112_AAAHYG hari_a_Page_13thm.jpg
5a693ab176dbbd77c5f11fc8d3b6db0b
12ea82d029f26a964aebd3be30f384b787d2bd3b
491004 F20110112_AAAHTJ hari_a_Page_50.tif
981d48580e3c4aaa3058ddebcf2bcce4
46aee26a215daeb0517dcfa9e227af3085cd1ba0
46038 F20110112_AAAIAH hari_a_Page_47thm.jpg
49c9a53f6d6ae93f89762bd04a2658c8
1b1b3b65e2cd46c746b125325aefd7a4f0cf05cc
36780 F20110112_AAAHYH hari_a_Page_61thm.jpg
c47914ad11b1e3fa1d4b04d3aa73ca3c
d61bcc8e028eedb708525866d1d0ebf0a9de187f
55938 F20110112_AAAHJP hari_a_Page_12.jp2
ca2add6c45b2d1ec0773c08229bbf2f9
73f2bda611c2ab49888050ce77183ad115c1056e
11241716 F20110112_AAAHTK hari_a_Page_53.tif
e504effc9f0c84c5f0365581a6e5c08f
71082a311f89999d13af9a85938f966a733061b9
36894 F20110112_AAAIAI hari_a_Page_48thm.jpg
efb5e14002fed91f9ede7e6d038c008b
e35b32fe148ee58418ba6992d11f441b55aa325e
33837 F20110112_AAAHYI hari_a_Page_30thm.jpg
3c2ff94605ba3b16d7c74f982fc9f605
ad91706921d4d0a83415e3e8ae76a4cb9423b1a7
77891 F20110112_AAAHJQ hari_a_Page_49.QC.jpg
502cade27c5887a801c4c7d8a8db942d
6e30916e8e212f45f74664d06a5e818add750d87
11241652 F20110112_AAAHTL hari_a_Page_54.tif
5c149467de73b657545a23a629cefa9c
37d433f9010161e3b16d61c4ec7dc7f2a28bf505



PAGE 1

A NOVEL INDEX TO ANALYZE POWE R QUALITY PHENOMENA USING DISCRETE WAVELET PACKET TRANSFORM By AJAY KARTHIK HARI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2003

PAGE 2

Copyright 2003 by Ajay Karthik Hari

PAGE 3

To AMMA, AJAPPA and SANDEEP.

PAGE 4

ACKNOWLEDGMENTS I would like express my sincere thanks to Dr. Alexander Domijan for giving me an opportunity to work on this project. I am indebted to him for offering me a research position in his group and for his gentle and friendly attitude. I would also like to thank Dr. Khai D.T. Ngo and Dr. A. Antonio Arroyo for serving on my thesis committee. I express my sincere gratitude to Dr. Tao Lin for introducing me to the wavelets and for his constant support during the entire thesis work. I would also like to thank my colleague and friend Alejandro Montenegro for helping me in understanding power quality and EMTP. I thank my fellow colleague and friend Roop Kishore for patiently reading my thesis and critiquing its grammar. I also extend my thanks to Hemanth for patiently listening to my endless lectures on my thesis. I also thank all my wonderful friends and lab mates. Last but not least, I would like to thank my parents for their constant support and encouragement. iv

PAGE 5

TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iv LIST OF TABLES........................................................................................................... viii LIST OF FIGURES ........................................................................................................... ix ABSTRACT.........................................................................................................................x CHAPTER 1 PROLOGUE.................................................................................................................1 1.1 Definition of Power Quality ...................................................................................1 1.2 Importance of Power Quality..................................................................................2 1.3 Review of Various PQ Problems............................................................................3 1.4 Scope of the Thesis.................................................................................................4 1.5 Organization of Thesis............................................................................................5 2 INTRODUCTION TO WAVELET TRANSFORMS..................................................7 2.1 Definition of Wavelet Transform ...........................................................................7 2.2 Why Wavelets for Power Quality...........................................................................8 2.3 Disadvantages of Traditional Signal Processing Tools ..........................................8 2.3.1 Fourier Transforms.......................................................................................8 2.3.2 Short-time Fourier transforms .....................................................................9 2.4 Advantages of Wavelet Transforms .....................................................................10 2.5 Discrete Wavelet Transform ................................................................................11 2.6 Wavelet Packets and Multi Resolution Algorithm...............................................12 3 SELECTION OF APPROPRIATE WAVELET ........................................................17 3.1 Introduction...........................................................................................................17 3.2 Introduction to Wavelet Families .........................................................................17 3.3 Analysis of Harmonics in Time-Frequency Plane................................................18 3.3.1 Frequency Characteristics of Daubechies Wavelets...................................18 3.3.2 Comparison of Best Frequency Res ponses from the Wavelet Families .....20 3.4 Complexity of Computation .................................................................................21 v

PAGE 6

3.5 Quantification of the Selected Wavelet ................................................................22 3.5.1 Spectrum Leakage ......................................................................................22 3.5.2 Scaling Property .........................................................................................24 4 PROPOSAL OF A NOVEL POWER QUALITY INDEX........................................25 4.1 Introduction...........................................................................................................25 4.2 Power Quality Indices...........................................................................................25 4.3 Drawbacks Associated with Harmonics...............................................................27 4.3.1 Total Harmonic Distortion .........................................................................27 4.3.2 Power Factor...........28 4.3.3 Other Indices ..............................................................................................29 4.4 Criterion for New Index.......................................................................................30 4.5 Wavelet Energy ....................................................................................................31 4.5.1 Wavelet Energy in Frequency Domain ......................................................31 4.5.2 Wavelet Energy in Time Domain...............................................................34 4.6 Wavelet Energy Based Harmonic Detection and Classification ..........................35 4.7 Signal Energy Distortion ......................................................................................38 5 CRITICAL EVALUATION OF THE PROPOSED METHOD ................................40 5.1 Test Cases.............................................................................................................40 5.2 Detection and Classification of Harmonics ..........................................................40 5.2.1. Periodic Test Cases....................................................................................41 5.2.1.1 Waveform with regular harmonics i.e. odd and even harmonics.....41 5.2.1.2 Explanation.......................................................................................42 5.2.2. Harmonics with additional PQ Events: .....................................................42 5.2.2.1 Harmonics with sags and swells.......................................................42 5.2.2.2 Explanation.......................................................................................43 5.2.2.3 Amplitude varying harmonics..........................................................43 5.2.2.4 Explanation.......................................................................................44 5.2.2.5 Frequency varying harmonics with respect to time.. .......................44 5.2.2.6 Explanation.......................................................................................45 5.3 Signal Energy Distortion ......................................................................................45 5.3.1. Periodic Test Cases....................................................................................45 5.3.2. Harmonics with additional PQ Events ......................................................46 6 EPILOGUE.................................................................................................................48 6.1 Conclusions...........................................................................................................48 6.2 Further Work ........................................................................................................49 6.3 Afterpiece .............................................................................................................50 vi

PAGE 7

LIST OF REFERENCES...................................................................................................51 BIOGRAPHICAL SKETCH .............................................................................................53 vii

PAGE 8

LIST OF TABLES Table page 3-1 Complexities of various wavelets under investigation ..........................................22 3.2 Frequency ranges of various nodes in level 3 DWPT decomposition with sampling frequency of 1920 Hz ............................................23 3.3 Peak voltages at 8 nodes of DWPT decomposition using coif5............................24 4-1 Summary of power quality indices ........................................................................26 4-2 Drawbacks of THD in terms of numbers...............................................................29 4-3 RWE in each frequency band ................................................................................33 4-4 RWE in various time divisions ..............................................................................35 5-1 Frequency bands corresponding to DWPT nodes at level 3 decomposition .........41 5-2 Time ranges corresponding to the time windows of each node decomposed........41 5-3 Comparison between THD and SED for various waveforms................................46 5-4 Performance of SED for harmonics with additional PQ events ............................47 viii

PAGE 9

LIST OF FIGURES Figure page 1-1 Average loss per industry due to particular PQ event..............................................3 1-2 Main aspects of electric power quality. Shaded boxes show the areas addressed in this thesis.............................................................................................5 2-1 MRA using LP and HP ..........................................................................................13 2-2 DWPT filter bank implementation of a signal.......................................................14 2-3 Frequency bands in Hz of a level 3 DWPT decomposition with a sampling frequency 1920Hz..................................................................................................16 3-1 Low pass and high pass decomposition filters of db5.........................................19 3.2 Frequency response of low pass (red) and high pass (blue) decomposition filters of db10 ......................................................................................................19 3-3 Frequency responses of all the wavelets in Daubechies families. .........................20 3-4 Low pass and High pass frequency characteristics of db10 (black), Coif5 (green) and Sym8 (red)................................................................................21 3-5 Spectrum leakage of Daubechies filters. X-axis denotes nodes in Level 3 decomposition of dwpt..............................................................................23 4-1 Level 3 decomposition of a signal using DWPT ...................................................31 4-2 Identification of harmonics using frequency scalogram........................................37 5-1 Deviation in frequency domain for regular harmonics..........................................42 5-2 Deviation in frequency domain for harmonics with swell.....................................43 5-3 Time varying harmonics ........................................................................................44 5-4 Frequency varying harmonics................................................................................45 ix

PAGE 10

Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science A NOVEL INDEX TO ANALYZE POWER QUALITY PHENOMENA USING DISCRETE WAVELET PACKET TRANSFORM By Ajay Karthik, Hari December 2003 Chair: Dr. Alexander Domijan, Jr. Major Department: Electrical and Computer Engineering A novel index to analyze harmonics is proposed in this thesis. Also, a new method to identify and classify harmonics present in a power system is presented. The main goal of the thesis is to identify pitfalls in current power quality indices and to present a new index based on Discrete Wavelet Packet Transform. Wavelets with its unique ability to give good time and frequency localizations simultaneously are best suited for power quality applications. Wavelets can be used to identify, classify and quantify power quality disturbances. This approach is extremely useful for power quality instrumentation purposes as it proposes a very fast and robust algorithm to detect and quantify harmonics. Furthermore, the algorithm developed also has the unique ability to identify additional power quality events occurring along with harmonics. The ability of this algorithm to identify and measure harmonic disturbances in both time and frequency domains will aid in exact disturbance localization and detection. Thereby, it assists in designing of proper mitigation techniques to eliminate power quality disturbances. The primary idea of this x

PAGE 11

thesis is to develop a power quality index based on energy content of the signal which is suitable to analyze amplitude, frequency varying harmonics and aperiodic signals. xi

PAGE 12

CHAPTER 1 PROLOGUE Power quality (PQ) is cynosure of all eyes not only in the electric power industry but also in the eyes of various sensitive power customers, like semiconductor industry, where poor power quality combined with down time can cause huge monetary losses. The attention it has captured is also because of an integrated approach used by researchers and engineers throughout the world to solve the problem instead of tackling them individually. It is a multi-disciplinary field encompassing power electronics, signal processing, and hardware design among a host of other fields. 1.1 Definition of Power Quality Power quality definition is often twisted by different agencies to suit their needs. Utilities often equate it to reliability because doing so will give them better statistics. An equipment manufacturer may define PQ as characteristics of power supply that enables the equipment to work properly. These characteristics may vary from one manufacturer to another. Ultimately, it is a customer driven issue and customers satisfaction and point of reference occupies the front seat. The following is the widely accepted definition of power quality. Power quality can be defined as being any problem manifested in voltage, current, or frequency deviations that result in disoperation or failure of customer equipment. (1) Thus, it is very important to supply a 60HZ clean sinusoidal waveform without any deviations to the customers. PQ is difficult to quantify. The ultimate measure of PQ is measured by the performance and productivity of the customers equipment. 1

PAGE 13

2 1.2 Importance of Power Quality The proliferation of nonlinear loads in the modern power systems has triggered a growing concern for PQ related issues. The proliferation of power semiconductor devices in power systems along with electronic loads, including personal computers and information technology devices have resulted in waveform distortion in the power systems. The nonlinear elements present in these electronic devices such as diodes, transistors, thyristors etc contribute harmonics to the power system resulting in poor PQ and at the same time they are the most sensitive ones to perilous effects of the poor PQ. The importance of PQ is augmented by the fact that many things are now interconnected in a network/grid. Failure of any electrical equipment has much more serious consequences in the present day power systems than in the past. The recent New York blackout, though not exactly because of power quality, underscores how interconnected the network is and the impact of the failure of a network can have on our day to day lives. Safe and reliable operation of electric equipment can be ensured with good power quality Also, as the sophistication of electronic equipment increases, there is a need for good power quality and the utilities will leave a bad impression on customers, otherwise. The importance of PQ is more thoroughly understood when its economic value is emphasized. It has a direct impact on all most all the types of customers. The following figure shows the direct economic impact of a particular PQ event on various industries.

PAGE 14

3 Textile Industry $1K$10K$100K$1M$10M$Plastic IndustryGlass IndustrySpecializedProcess IndustrySemiconductorIndustryIndustries$0 Average loss per sag for different indutriesSource: "Power Electronics Applications in Energy Systems". NarainG. Hingorani Figure 1-1: Average loss per industry due to particular PQ event. Apart from obvious financial reasons, there are numerous indirect and intangible costs which are associated with PQ problems. Customer satisfaction is a key factor. Even though, small residential customers do not suffer direct financial loss due to PQ problems but their dissatisfaction can work as propaganda against utilities. Especially when utilities are facing tough competition among each other 1.3 Review of Various PQ Problems The PQ problems can be categorized briefly as follows: Transients Impulsive transient and Oscillatory transient. Short duration voltage variations Voltage Sag and Voltage Swell Long duration voltage variations Under Voltage and Over Voltage Interruptions Momentary, Temporary and Long term Interruptions. Waveform distortions Harmonics, Notching and Noise.

PAGE 15

4 Voltage fluctuation Frequency variation Other Miscellaneous problems Voltage unbalance, DC offsets Reactive power consumption. 1.4 Scope of the Thesis A. Domijan, G.T. Heydt et al. in the paper titled Directions of Research on Electric Power Quality (2) showed various fields of research in the electric power quality area. Which include: Modeling and Analysis, Instrumentation, Sources, Solutions, Fundamental concepts and effects. The present thesis encompasses parts of Time domain, Transfer domain and waveform analysis part of research in the electric power quality area. It is more clearly depicted in Figure 1.2. The present thesis presents new techniques that can be used to analyze PQ waveforms in both time and frequency domain simultaneously. It also proposes a new criterion that can be used to select a Wavelet (defined in the Chapter 2) appropriate for PQ monitoring. It also critically evaluates various PQ Indices widely used and proposes a novel PQ Index. The proposed Index is based on energy content present in a signal. This thesis also forms as a basis for further research for a proposed PQ monitoring device to be developed in PQ&PE Laboratory at the University of Florida.

PAGE 16

5 Electric Power Quality Modeling and Analysis Solutions Sources Fundamental Concepts Instrumentation Effects Harmonics Models Stochastic models Voltage support Software Analysis Time domain Transform domain Network Methods Metering Measurement Waveform Analysis Converters Pulse Modulated Methods Grounding FACTS Adaptive Compensators Filters SWCS SVCS Definitions Standards Procedure User Issues Figure 1-2 Main aspects of electric power quality. Shaded boxes show the areas addressed in this thesis In other words, the goal of the present thesis is to use wavelet transform (WT), an advanced signal processing tool, to analyze the time-frequency-energy properties of PQ signals and use it as a basis to classify the PQ events and to develop a PQ Index exploiting the unique time-frequency properties of the Wavelet transform. 1.5 Organization of Thesis The present thesis is divided into five chapters. It can be further split into two parts: the first part deals with introduction to wavelet transform theory (chapter 2) and selection of appropriate wavelet (chapter 3); while, the second part deals with introduction to PQ

PAGE 17

6 indices and proposal of a new index( chapter 4) ,Furthermore, a discussion on results ( chapter 5) obtained is presented More detail explanation of the organization follows: Chapter 2: This chapter starts out with historical background of wavelet transform theory and explains basic theory of wavelet transforms. It also justifies the selection of WT for PQ applications. Furthermore, it compares and contrasts various other signal processing techniques with respect to WT. Chapter 3: This chapter deals with selection of appropriate wavelet filter bank for PQ applications. It starts out with a brief description of various wavelet families present in literature and explains the criterion behind the selection of a particular wavelet family for PQ application. The chapter ends by justifying the selection by using various signal processing techniques. Chapter 4: In this chapter, a close look is taken at various PQ indices present in the literature. The problems with existing Indices are explained. Then a novel index is proposed. Chapter 5: Results obtained are presented in this chapter, followed by a discussion on the results obtained. The Index proposed is critically evaluated. Chapter 6: Conclusions from the results and scope for further work is presented in this chapter.

PAGE 18

CHAPTER 2 INTRODUCTION TO WAVELET TRANSFORMS Wavelet transforms have been in existence for a long time. It was first mentioned by Alfred Haar in his doctoral dissertation in 1909 and it was mentioned in its present theoretical form by Jean Morlet in 1975 while working for Elf Aquitaine under Alex Grossmann. Other important contributors include Dr. Ingrid Daubechies, Stephane Mallat and Yves Meyer. The wavelet transform has been found to be particularly useful for analyzing noisy, aperiodic, transient and intermittent signals. It has a very different ability to examine the signal simultaneously in both time and frequency. 2.1 Definition of Wavelet Transform Wavelets, little wave like functions, are used to transform the signal under investigation into another representation which presents the signal information in a more useful form. This transformation of the signal is known as the wavelet transform (WT). Mathematically, WT (3) is defined as the inner product of wavelet function ),(ba and real signal s (t): T (a, b) = )(*),(),(ttSba where )(),(tba = )(1abta The parameters a and b are called dilation and translation parameters respectively. 7

PAGE 19

8 2.2 Why Wavelets for Power Quality The occurrence of power quality events should be detected and located in time, the content of these events should also be monitored accurately so as to classify the events and carry out appropriate mitigations techniques to alleviate PQ problems. There is a need for a powerful tool that can be used to classify the PQ events both in time and frequency domain. Wavelets satisfy this need and scores over other Time-Frequency methods such as Short Time Fourier Transform (STFT). These advantages are explained in more detail in the following sections of this chapter. Also, Wavelet basis functions have compact support, which means that basis functions are non-zero over a finite interval, unlike sinusoidal Fourier basis functions which extend infinitely. This property along with unique property of wavelet basis to be squeezed (dilation) and movement along axis (translation) gives greater flexibility in analyzing localized features of analyzing signal. Furthermore, recent advances in PQ mitigation techniques are based on extraction of harmonic components instead of traditional fundamental component. Thus, time-frequency domain based techniques come into picture as they give a distinct advantage of eliminating selected harmonics, subject to availability of accurate information on individual harmonic components. 2.3 Disadvantages of Traditional Signal Processing Tools 2.3.1 Fourier Transforms The Fourier transform (FT) of a finite energy function of a real variable t is given by )()(2RLtf .)exp()()(dttjtff

PAGE 20

9 It is evident from the above definition that FT cannot be carried out until the entire waveform in the whole axis ( ), is known. The above equation can be evaluated at only one frequency at a particular time. (4) This causes great difficulties while processing non stationary signals. Even though, faster algorithms exist to carry out this computation they cannot be implemented for real time signals. This is undesirable from PQ monitoring point of view. As explained before FT fails to give time domain information of the signal and is thus a serious handicap for PQ analysis and Instrumentation techniques based on it. Fast Fourier transform (FFT) and its variants are generally used in spectral analyzers and also other PQ monitoring instruments. It suffers from all the disadvantages mentioned above and also due to its spectral leakage component; it does not accurately show the spectrum. This will in turn lead to imprecisely calculated signal parameters such as magnitude, phase and frequency. Furthermore, it is very difficult to distinguish between the harmonics and transients in an FFT spectrum. 2.3.2 Short-time Fourier transforms Short-time Fourier transforms (4) are very intuitive. In order to achieve time-frequency localization, it obtains the frequency content of a signal at any instant t by windowing the signal using an appropriate window function and then FT the remaining portion of it. More crudely, it is removing the desired part of the signal and then performs FT on it. Thus, it is some times referred as windowed Fourier transform or running window Fourier transforms.

PAGE 21

10 Mathematically, if f (t) is the signal under consideration and )(t is the window function used to obtain a windowed function, say, )'tt (*)()('tftf then STFT evaluated at location ( ),' t in the time-frequency plane is given by RtjdtetttftfG)()'()(:),'( STFT needs to know the signal information only in the interval of the window function used. This is a major improvement from FT, where it needs to know the signal information over the entire time axis. The major disadvantage of STFT comes from uncertainty principle. Low frequencies can hardly be depicted using short windows and short pulses are poorly located in time with long windows. From the above two sections, it can be safely concluded that traditional FT poses a serious handicap for PQ monitoring. Also, other variants of FT such as STFT also have serious drawbacks. 2.4 Advantages of Wavelet Transforms As presented in the previous section, traditional signal processing tools have some serious drawbacks for PQ applications. A more viable alternative is the use of wavelet transform. The wavelet transform has good localization in both frequency and time domain. This makes it an attractive option for PQ applications. WT is apt for studying non-stationary power waveforms. Unlike, the sinusoidal function used in FT, wavelets are oscillating waveforms of short duration with amplitude decaying quickly zero at both ends and thus are more suitable for short duration disturbances. The wavelets dilation and translation property gives time and frequency information accurately. Apart from it this process of shifting enables the analysis of waveforms containing nonstationary disturbance events. To enhance the electric power quality, sources of disturbances must be detected and then appropriate mitigation techniques have to be applied. In order to

PAGE 22

11 achieve this, a real-time PQ analyzer with an ability to do time-frequency analysis is required. Hence wavelets transforms with its ability to give good Time-Frequency resolution is suitable for PQ applications. Another important application in PQ is data compression. (5) A single captured event recorded for several seconds using monitoring instruments can produce megabytes of data. This increases the cost of storing and transmitting data. Again, WT comes into picture. Its ability to concentrate a large percentage of total signal energy in a few coefficients helps in data compression. Thus, it reduces the need to store huge voluminous of data and reduces costs associated with it. In this research project, discrete wavelet packet transform, popularly called DWPT, an enhancement of multi resolution algorithm (MRA) using discrete wavelet transform (DWT) has been used as a tool for PQ analysis. DWPT has many inherent advantages over DWT (3) which are explained in more detail after a formal introduction to discrete wavelets in the following sections. 2.5 Discrete Wavelet Transform In the previous section, wavelet transform was defined as the inner product of wavelet function ),(ba and real signal s (t): T (a, b) = )(*),(),(ttSba where )(),(tba = )(1abta and the parameters a and b are called dilation and translation parameters respectively. This is called continuous wavelet transform (CWT).

PAGE 23

12 Discrete wavelet transform (3) is defined for a continuous time signal, s(t) where discrete values of a and b are used. The DWT is thus the discretized counter part of CWT, which is defined as T (a, b) = nooommaanbktSam[)(1 ] where The integers m and n control the wavelet dilation and translation respectively; a o is a specified fixed dilation step parameter set at a value greater than 1; And, b o is the location parameter which must be greater than zero. But, common choices for discrete wavelet parameters a o and b o are 2 and 1 respectively. This type of scaling is popularly called dyadic grid arrangement. When certain criteria are met it is possible to completely reconstruct the original signal using infinite summations of discrete wavelet coefficients rather than continuous integrals. This leads to a fast wavelet transform for the rapid computation of the discrete wavelet transform and its inverse. DWPT, which is used in this research project is based upon discrete wavelet transform. It allows for adaptive partitioning of the time-frequency plane. It is a generalization of multi resolution algorithm explained in the following section. 2.6 Wavelet Packets and Multi Resolution Algorithm MRA was initially developed to decompose the signal into various resolution levels to facilitate a very fast time-frequency analysis. A multi-stage filter bank is used to decompose the signal into various levels using a Low Pass(LP) filter and a High Pass(HP) filter as shown in the figure 2.1. (6) The LP filter will result in approximate coefficients of the original signal and the HP filter in detailed coefficients of the signal.

PAGE 24

13 S (t) LP HP 2 2 LP HP 2 2 LP HP 2 2 Figure 2-1: MRA using LP and HP DWPT, as stated earlier, is a generalization of the DWT. The difference is that in the WP signal decomposition, both the approximation and detailed coefficients are further decomposed at each level. This leads to a decomposition tree which is shown in Figure 2.2. This will lead to an array of wavelet packet coefficients with M levels and each containing N coefficients. A total of N coefficients from this M*N array can be selected to represent the signal. The main advantage of DWPT is better signal representation than decomposition using MRA. The DWT technique is not suitable for harmonic analysis because the resulting frequency bands are not uniform. In DWPT, with clever manipulation of sampling frequency, the important harmonics such as odd harmonics can be made center frequency of the resulting frequency bands. Furthermore, DWPT gives uniform bands is

PAGE 25

14 important for harmonic identification purposes. A level 2 decomposition using DWPT filter bank can be depicted as follows S (t) LP HP 2 2 LP HP 2 2 LP HP 2 2 Figure 2-2: Depicting DWPT filter bank implementation of a signal Similar to DWT, LP filter gives approximation coefficients and HP filter gives detailed coefficients. The coefficients are given by the following equations: Let be the scaling equation (or dilation equation) associated with the mother wavelet. Then, the scaling function can be convolved with the signal to produce approximation coefficients given by )(t A m, n = dtttsnm)()(, The function of mother wavelet can be convolved with the signal to produce detail coefficients given by D m, n = dtttsnm)()(, The following explanation forms the basis of the next chapter and much of the research done for this thesis. As explained earlier DWPT can be used to separate

PAGE 26

15 harmonics. It can be best illustrated as follows. Let us assume a signal with fundamental frequency 60HZ and 3rd, 5th, 7th and 9th Harmonics. Let the sampling frequency be 1920 Hz. Then the maximum measurable frequency is 960Hz (Sampling theorem). The figure depicted in the next page shows the decomposition and how the harmonics are separated using DWPT. Frequency ordering after DWPT is very important and it has to be understood. (7) The decomposition resulting from a high pass filter is always a mirror image. Thus, before doing any further analysis, it is of great importance to sort out the frequency in desired order. The example illustrated in the following page (8) shows level three DWPT decomposition and the first frequency band is 0-120Hz thus, its center frequency is 60Hz. Hence selection of sampling frequency is very important and it should be done in an intelligent manner such that the important frequencies one is dealing with are usually the center frequency of the band. The maximum level of decomposition one has to go for decomposition varies from application to application. Usually, for power system applications it is 60Hz/50 Hz. But, due to the presence of sub-harmonics present in the power systems it is advisable to go further down. At the same time, as the number of nodes increase with increase in decomposition levels, it makes analysis more complicated or in other words, it reduces the readability.

PAGE 27

16 LP 960 Hz 480-960 0-480 480-720 720-960 240-480 0-240 240-360 360-480 120-240 0-120 720-840 840-960 HP LP HP LP HP 600-720 480-600 Figure 2-3 Frequency bands in Hz of a level 3 DWPT decomposition with a sampling frequency 1920Hz Note that the center frequency in each of the nodes is exactly odd harmonics of 60 Hz.

PAGE 28

CHAPTER 3 SELECTION OF APPROPRIATE WAVELET 3.1 Introduction More often than not power researchers tend to neglect the choice of appropriate wavelet filter for their application. The selection of wavelet assumes more importance if one wants to implement their algorithm in DSP and develop an instrument out of it. It is a general trend among researchers to take db10 (more appropriately higher order db coefficients) to study harmonics and db4 or db3 to study transient related phenomena. In this paper, we have made an effort to study various wavelet families, which exist in the literature, suitable to study PQ problems and to suggest a suitable wavelet filter that can be used to study harmonics in particular. 3.2 Introduction to Wavelet Families Today, there are a number of wavelet families which exist. Each one of them has a particular application. In fact, one can develop a wavelet family to suit ones particular needs. But to study PQ phenomena there are some wavelet families like Daubechies etc which already exist in the literature. Some of the widely used wavelet families that can be used to study the PQ phenomena are 1. Daubechies 2. Symlets 3. Coiflets 4. Biorthogonal Wavelets. 17

PAGE 29

18 3.3 Analysis of Harmonics in Time-Frequency Plane In the analysis of harmonics in time-frequency plane, it is very important to exactly localize the harmonics in the frequency plane. The DWPT algorithm (as explained in the previous chapter) partitions the time-frequency plane, one partition for every decomposition. It allocates the lower interval to low pass filtered part and higher frequency interval to the high pass filtered part. Thus, it is very important to select an appropriate wavelet filter appropriate whose frequency is close to an ideal filter. 3.3.1 Frequency Characteristics of Daubechies Wavelets: Ingrid Daubechies has proposed 10 wavelets often represented as db1, db2db10 or some times db2, db4..db20. Where, db stands for Daubechies and the numbers 1, 2 stand for number of zero moments in the former representation and numbers 2, 4,..20 stand for number of non-zero scaling coefficients in the latter representation. In this thesis the former approach is being used as it is used by the MATLAB wavelet tool box and makes programming and interpretation easier. To facilitate this, Daubechies wavelets were decomposed into low pass and high pass filters. The frequency characteristics of both the low pass and high pass filters have to decrease faster near the filter band edges. This will give good frequency separation and there by localization in the time-frequency plane will be lot easier. Another advantage is that it will reduce frequency leakage into neighboring bands. For example decomposition of Daubechies wavelet db5 is shown in fig 3.1

PAGE 30

19 1 2 3 4 5 6 7 8 9 10 -0.5 0 0.5 1 Low Pass Decomposition filter of db5 1 2 3 4 5 6 7 8 9 10 -1 -0.5 0 0.5 1 High Pass Decomposition filter of db5 Figure 3-1: Low pass and high pass decomposition filters of db5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.5 1 1.5 Frequency response of Low pass and High pass filters of db10 High PassLow Pass Figure 3-2: Frequency response of low pass (red) and high pass (blue) decomposition filters of db10 To make this study more effective frequency responses of all the families were individually and taking the best out of each one of it, a comparison was made. The following figures will make this explanation more clear.

PAGE 31

20 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.5 1 1.5 db2db3db4db5db6db7db8db9db10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 0.5 1 1.5 db1db2db3db4db5db6db7db8db9db10 3-3 (a) 3-3(b) Figure 3-3: Frequency responses of all the wavelets in Daubechies families. (a) High pass decomposition filter. (b) Low pass decomposition filter In a similar fashion, the frequency responses of all the wavelets in Symlets, Coiflets and biorthogonal families were calculated and plotted. All the relevant graphs are attached in the appendix. From fig 3.3, it is clear that db10 has the best frequency response suited to our application i.e. the frequency characteristics decrease faster near the filter band edges. Following the same rule of thumb we can say that coif5 and sym8 have good frequency characteristics. Frequency response of biorthogonal wavelets are not in the same league of the other 3 families. 3.3.2 Comparison of Best Frequency Responses from the Wavelet Families As explained in the previous paragraph, the best frequency responses from the 3 families under investigation are Daubechies 10 (db10), Symlets 8(sym8), Coiflets 5(coif5). To find out the better among them for our application, all the 3 were plotted out in a same graph as shown below

PAGE 32

21 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.5 1 1.5 Figure 3-4: Low pass and high Pass frequency characteristics of db10 (black), Coif5 (green) and Sym8 (red) It can be seen from the graph that all the three have similar frequency responses and coif 5 has the best response among them. The selection now depends upon the accuracy range required for the application. For PQ applications more the accuracy, the better it is. Since, all the 3 have almost similar Frequency Responses it would be a good idea to see the complexity of computation of them. 3.4 Complexity of Computation Complexity of computation using the above filters becomes a very cardinal issue while implementing them on a DSP board. The low pass and high pass wavelet filters are discrete in nature. For an N point filter to process it requires N 2 multiplications and N 2 -1 additions.

PAGE 33

22 Table 3-1: Shows the complexities of various wavelets under investigation S. No Name of the Wavelets Complexity 1 db10 160399 2 Sym8 65791 3 Coif5 810899 From the above table, it is clear that coif5 has the highest complexity but again it has the best frequency and phase response. When sampling frequency is around 1930Hz (Typical value for PQ applications), it is more sensible to opt for a wavelet with better frequency response. Furthermore, the benchmarks of the latest DSP processors released by companies like TI and Analog Devices for Data Acquisition, Test and Measurement applications can do complex multiplications in 19ns. Thus, it is better and more realistic to choose coif5 because its complexity is not too high, when compared to db10, and will not burden the DSP. 3.5 Quantification of the Selected Wavelet A scientific approach was adopted to select the wavelet for this particular application. To ascertain this selection the selected wavelet i.e. coif 5 was tested for various characteristics that are suited for this application, especially, the behavior of wavelet, when it is used in the DSP board for real time monitoring. 3.5.1 Spectrum Leakage As explained in the previous section the frequency response of coif5 is sharper at the edge of the band. Hence, it should show less frequency leakage when compared to

PAGE 34

23 other wavelets. To quantify this theory, a sine wave was decomposed using coif1 and coif5 wavelet filters and by applying DWPT. The equation of the sine wave tested is: X=0.1*sin(2*pi*60*t)+0.1*sin(2*pi*180*t)+2*sin(2*pi*300*t)+0.1*sin(2*pi*420*t) With t=0:5.2083e-004:1 (a sampling period of 1920Hz.).The graph depicted in the next page has Nodes of level 3 decomposition on x-axis and magnitude (Peak voltage) on the Y-axis. As explained in the previous chapter. Each node corresponds to a frequency band. The number of nodes is given 2 power(level). The frequency band for a level three decomposition with sampling frequency 1920Hz is given as follows: Table 3.2 Depicts frequency ranges of various nodes in Level 3 DWPT decomposition with sampling frequency of 1920 Hz Nodes 1 2 3 4 5 6 7 8 Frequency Range (Hertz) 0-120 120-240 240-360 360-480 480600 600-720 720840 840960 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 Coif1 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 Coif1 Figure 3-5: spectrum leakage of Daubechies filters. X-axis denotes nodes in Level 3 decomposition of DWPT.

PAGE 35

24 It is clear from figure 3.5 that coif1 has more leakage than coif5. 3.5.2 Scaling Property It is very important to check this property for any digital filter. It basically checks if the output is proportional to the input. This property ensures that the filter does not have any inconsistencies and with the including of appropriate scaling/correction factor, it can be used for real time measurements. To check the scaling property of coif5, two signals; one with double the amplitude of other was processed using coif5 wavelet filter and its scalability was tested. It was found that the ratio between the resultant coefficients of the two filters is exactly two. This makes the selected filter more suitable for data acquisition. The following table depicts the scaling property more clearly. Table 3.3: Peak voltages at 8 nodes of DWPT decomposition using coif5 X=1*sin(2*pi*60*t) X=2*sin(2*pi*60*t) V1peak = 1.0444 V2peak =0.0684 V3peak =0.0155 V4peak =0.0053 V5peak =0.0037 V6peak =0.0022 V7peak =9.2321e-004 V8peak =3.7354e-004 V1peak =2.0888 V2peak =0.1369 V3peak =0.0310 V4peak =0.0107 V5peak =0.0073 V6peak =0.0045 V7peak =0.0018 V8peak =7.4708e-004 The above steps ensure that when implemented in a DSP, the selected wavelet coif5 is suitable for data acquisition and measurement purpose.

PAGE 36

CHAPTER 4 PROPOSAL OF A NOVEL POWER QUALITY INDEX 4.1 Introduction The system operators have the responsibility to deliver electric power in accordance with the standards set by their clients. With ever increasing number of sensitive power customers, reporting about quality of power back and forth between customers and system operators has increased. In order to characterize quality of power being supplied and received by customers, there is a need to develop standards, preferably common one which is accepted world wide. The development of such an index will remove any differences that may arise between the supplier and customer. An ideal power quality index should be able to summarize the degree of distortion present in a system Also, to avoid ambiguity the number of indices should be kept at minimum. (9) It should be as simple as possible and easily interpretable by layman. Representative of the actual distortion and its impact Readily implementable in practical equipment. Valid for all topologies and conditions. Allow comparisons of performance in time-domain. 4.2 Power Quality Indices Most of the PQ indices are proposed long back and some of them have been developed for other applications. With increasing importance given to PQ and huge distortions found in present day power systems some of them do not exactly characterize the distortion. Furthermore, they are not applicable to many cases and violate electric 25

PAGE 37

26 engineering principles in some of the cases. A list of power quality indices is provided in the following table (10) Table 4-1: Summary of power quality indices Index Definition/Formula Application Total Harmonic Distortion iiiII/2 General purpose Power Factor P tot /(|V rms |*|I rms |) General purpose; Revenue metering Telephone Influence Factor rmsiiiIIW/2 Audio circuit interference C message Index rmsiiiIIC/2 Communications interference IT product 1)(iiiWI 2 Audio circuit interference; Shunt capacitor stress VT product 1)(iiiWV 2 Voltage distortion index K factor 1h h 2 I h 2 /I 1h h 2 Transformer derating Crest factor V peak /V rms Dielectric stress Many of the indices presented in the table 4.1 have evolved over a period of time and have been proposed after many years of practical observations. It is not easy to discard them from usage. Some of them are applicable to some specific purposes, while others are for general purposes. But, they fail to characterize PQ phenomena and thus

PAGE 38

27 there is a need for new indices to suit the present day needs. The present thesis is a step in that direction. 4.3 Drawbacks Associated with Harmonics 4.3.1 Total Harmonic Distortion The most popular PQ index used is total harmonic distortion (THD). (11) It is probably the most popular way of characterizing distortion due to harmonics. It is widely used not only in the field of power systems but also in the field of Electronic circuits to characterize non linearity present in a circuit/system. Unfortunately, it has some serious drawbacks. Basically, THD is the ratio of energy content in harmonics to that of fundamental component. The term harmonics and the index associated with it i.e. THD is often used to describe perturbations present in the waveform. But, this has some serious problems if one closely examines the definition of harmonics. The term harmonics means multiples and is originated from the musical tones whose frequency is integral multiples i.e. harmonics of a fundamental tone. Similarly, in power systems, harmonics refer to frequencies that are integral multiples of fundamental frequency (60Hz/50Hz). Thus, THD becomes problematic when non-integer harmonics are present and also if the signal is aperiodic. The other significant pitfall of THD is that all frequencies are weighed equally. The value of THD obtained is same for a signal with 5th harmonic which has the same value of a signal with 3rd harmonic. But, it is a known fact that they have different effect on power systems. THD fails to capture this information. It also fails to convey any information about phase angles of the harmonics. (12) The index is not affected by the presence of phase angles.

PAGE 39

28 The other significant drawbacks include the fact that THD is not applicable when the fundamental frequency is absent. If a 60 Hz voltage is switched as in a PWM drive for an I.M. the resulting induction motor stator voltage is around 60+/-0.2 Hz. Furthermore, another serious pitfall is that it is possible to have THD excess of 100% i.e. it is theoretically possible to have THD of 140% (13) This is not a good figure of merit because it does not make sense to say 140% THD distortion and the amount of distortion at 140% is not twice as that of 70%. Another pitfall of THD which has some important consequences is that it does not give time domain information. For example, if a power system has time varying harmonics, THD or as a matter any other PQ index fails to capture this information. Also, it can not distinguish between harmonics with sag or swells. 4.3.2 Power Factor The traditional definition is suitable only for fundamental component i.e. 60 Hz. Although there are some modifications of PF which exist in literature such as PF= cos ()/ ( (1+THD 2 ) This modification is extremely handy but when the application of THD in the field of power quality is questioned, there is a need to suggest a new change for PF definition. Also, PF fails to address the time-varying loads. In some extreme cases, PF changes from 0.5 to 0.85 lagging in 3-4 seconds. Any improvement in the definition of power factor or development of any index in this area would definitely benefit power electronic engineers who design the Power Factor Correction (PFC) devices. The importance of PFC in power quality need not be further underscored. Apart from this, it can also help to improve the revenue metering.

PAGE 40

29 The following table shows some of the drawbacks of THD in terms of numbers and makes the above claims more clear. Table 4-2: Drawbacks of THD in terms of numbers Waveform under consideration THD Reason 110sin(60)+10sin(180) 9.0909% 110sin(60)+10sin(660) 9.0909% Equal weightage to higher frequency components 110sin(60)+10sin(660+80 o ) 9.0909% Can not characterize phase angles 110sin(60)+10sin(180)+2sin(220) 9.0909% (actually Not Applicable) Can not quantify Inter harmonics For t=0 to 0.6 seconds 110sin(60) For t=0.6 to 0.8 seconds 110sin(60)+10sin(180) for t=0.8 to 10 seconds 110sin(60)+10sin(300) 12.86% (Not Applicable) The answer shown is not correct as THD is not applicable to this frequency varying harmonics case. Also, the signal is aperiodic 4.3.3 Other Indices Other factors such as VT product can also be improved. They also suffer from the same defects mentioned above. Also, K-factor summarizes the harmonic distortion into one number. The stray losses which occur due to harmonics are a small portion of the total losses for the low-order harmonics. The stray losses are so small that the increase in net loss due to it can be negligible. It means that effect of heating for a distorted current is nearly the same as the heating for a sinusoidal current with same value. There is a need for an index that can measure the heating effect of various loads.

PAGE 41

30 4.4 Criterion for New Index The above sections make it clear that there is a need for a new index for PQ applications. In order to propose a new index suitable for PQ applications we need an index which can address in both time and frequency domain. All the indices present in the literature are suitable for periodic case which possesses Fourier components. In this proposal, Wavelet Transforms are utilized to propose a novel index. In signal processing the energy content of a particular signal is given by E= f 2 (t) dt It is nothing but the area under the squared signal. Parsevals theorem states that energy content of a signal in time domain is equal to energy of the signal in frequency domain. It is given by E= f 2 (t) dt =1/ (2) f 2 (f) dt. where f (t) is the equation in frequency domain. This property is very handy and can be used to develop an index which gives both time domain and frequency domain information. The energy content of a signal is chosen because it is very handy when we are dealing with aperiodic waveforms and very useful as it can characterize subharmonics, inter-harmonics, etc. present in the system. This idea of using energy content for PQ applications was proposed by A. Domijan et al. This formed a basis for research on PQ indices. Many other variants of THD were proposed based on this idea but they all suffer from THD mindset and other inherent problems associated with THD. In the present thesis, the energy of the signal is found out using wavelet transforms. Wavelets as mentioned before give both time and frequency domain information and thus can be used

PAGE 42

31 to find out an index which can be analyzed in both the domains. The following section explains in detail the approach used to find out the energy of the signal 4.5 Wavelet Energy In this thesis, the signal under investigation is decomposed using DWPT (explained in Chapter 2). The coefficients of the signal are then used to find out the energy. This process is more clearly explained with the following figure Figure 4-1 Level 3 decomposition of a signal using DWPT The decomposition is done using the DWT. The coefficients are given by C j = where S (t) is the signal under consideration. j, k is the wavelet filter used for analysis; j denotes the level of decomposition and j gives the node in the decomposition level k. 4.5.1 Wavelet Energy in Frequency Domain The energy of the signal (14) in each band is given by E j = kjKC|)(| 2 The total energy of the signal is thus given by

PAGE 43

32 E tot = jkjkC|)(| 2 = jjE It is always better to represent any index in normalized values, in other words, it is desirable to remove any units associated when developing any index. In this case, the present PQ index under development needs to quantify the deviation of a signal under consideration with a perfect 60Hz sinusoidal wave. Thus, normalizing the energy in each band with total energy makes sense. The normalized energy or relative wavelet energy (RWE) in each band is given by P j = EtotjE)( If the analyzed signal is a pure sine wave with 60 Hz then the relative wavelet energy in the band containing 60 Hz should be exactly equal to one. In other words, there should be no leakage of energy in other bands and it should be exactly concentrated in the 60Hz band. An intuitive theory based on the above discussion can be proposed. It can be stated that if the relative energy in a frequency band containing fundamental frequency component is equal to one, then harmonics are absent in the system. This statement assumes that the frequency band is as narrow as possible. As explained, the wavelet filter selected for our application coif5 is close to ideal filter but not exactly ideal. Infact, realization of a causal ideal digital filter is not possible. The RWE for a pure 60 Hz sine wave is found out to be 0.9957 i.e. an error of 0.0043 is present. This error can be either removed by a scaling factor or it can be cleverly used in the index such that its effect is negated. The latter approach has been used here.

PAGE 44

33 The following example shows the RWE for an impure sine wave i.e. sine wave with harmonics. The sine wave under consideration is 100*sin60+10*sin180+10*sin300+5*sin420 This waveform is decomposed using DWPT up to level 3. The sampling frequency is 1920 Hz. The decomposition exactly follows the Table 3.1 and Fig 3.5. Table 4-3 RWE in each various frequency bands Frequency band Hz Relative Wavelet Energy 0-120 0.9745 120-240 0.0157 240-360 0.0070 360-480 0.0022 480-600 0.0006 600-720 0.0001 720-840 0.0000 840-960 0.0000

PAGE 45

34 4.5.2 Wavelet Energy in Time Domain In order to define useful quantifiers it is very important to study the temporal evolution of the signal. The analyzed signal is divided into non overlapping windows of length L. Thus, the number of time windows for the signal is give by (14) Number of time windows, N t = (Total length of the analyzed signal)/ L. The mean wavelet energy at resolution level j for time window i is given by: E j (i) = |2 )(|1.1)1(kCNLiLikjj Where N j represents the number of wavelet coefficients at the resolution j in the time interval i. Then the total mean energy at this time window is given by E tot = jjE (i) The relative energy in time domain is given by P j (i) = i)(EtotjEi The following table shows the RWE in time domain for a pure 60 Hz sine wave which is analyzed from 0 to 1 second. The sine wave is decomposed to level 3 using DWPT with coif 5 filter bank. The total number of coefficients after decomposition at level 3 is 265, which in fact gives us the length of the signal under consideration. The window length, L is taken to be 33 and thus N t= 8 (rounded off to nearest integer). The energy for a pure sine wave is evenly distributed throughout in its time domain. But, this will definitely change when there is a sine wave with harmonics and swell or time varying harmonics. The energy will be concentrated at the time instant where swell/sag occurs and thus it can be easily distinguished.

PAGE 46

35 Table 4-4 RWE in various time divisions Time Interval (sec) Relative Wavelet Energy 0-0.1245 0.1129 0.12450.2490 0.1288 0.24900.3735 0.1233 0.3735-0.4980 0.1288 0.4980-0.6225 0.1233 0.6225-0.7470 0.1288 0.7470-0.8715 0.1233 0.8715-0.99610 0.1308 4.6 Wavelet Energy Based Harmonic Detection and Classification The following section proposes a new methodology to detect and classify the presence of harmonics in a power system. Various types of harmonics are usually found in power systems. They could be broadly classified as 1. Regular harmonics: periodic-odd, even, inter-harmonics. 2. Amplitude varying harmonics with respect to time 3. Frequency varying harmonics with respect to time. 4. Sub-harmonics 5. Harmonics with sags and swells.

PAGE 47

36 There is a need to detect harmonics which occur with additional PQ events. This can help engineers in designing appropriate mitigation techniques for PQ. This can be achieved using scalograms. Scalogram is a plot of time-frequency-energy. It is analogous to spectrogram, which is a plot of energy density surface of the short time Fourier transforms. To put, in simpler terms, scalogram is a plot of squared magnitude of the wavelet transform values. The scalogram surface highlights the location and scale of dominant energetic features within the signal. Using DWPT, the signal under consideration is decomposed into coefficients at various bands. The energy of the signal at each band can be found out by squaring and summing all the coefficients as explained in section 4.5. The following is the procedure to be followed when plotting scalograms. 1) Using DWPT, decompose the signal under consideration into different resolutions (levels). The energy in each node can be calculated using the procedure described in section 4.4. The maximum level a signal can be decomposed is given by 2 log (M). Where, M is the discretized length of the signal under consideration. Let the Energy in each band is given by E (i) 2) Using DWPT, decompose an ideal 60Hz pure sine wave into the same number of levels as for the above mentioned signal. Let the Energy in each band is given by E1 (i) 3) The deviation of the signal from ideal behavior is found out by taking the squared difference of the energies of the above two signals as shown below:Deviation in Energy = (E (i)-E1 (i)) 2 4) A plot between nodes in a particular decomposition level with the Deviation in Energy is a scalogram in frequency domain. The plot obtained from the above procedure exactly identifies the additional frequencies present in the system. Consider a sine wave with the following equation. For

PAGE 48

37 t=0 to 1 seconds with sampling frequency 1920Hz. Each band has a width of 120 Hz Therefore; the maximum frequency in the 8th band is 860. 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14 16x 1010 Frequency bandsSquared Deviation in Energy Figure 4-2: Identification of 3 rd harmonic and its deviation from ideal behavior using frequency scalogram. To detect and classify the presence of additional PQ events along with harmonics there is a need to draw a scalogram in time domain. This will aid in detecting any other PQ events occurring with harmonics or even if the harmonics are amplitude changing or frequency changing with time. This is extremely useful in detecting harmonics with sags/swells, amplitude varying harmonics and frequency varying harmonics. Advantages: 1) This is very handy in PQ instrumentation as it has the capabilities of classifying the PQ events. 2) The squared deviation of energy gives how much the wave is distorted and the deviation from ideal behavior.

PAGE 49

38 3) While implementing in a Digital Signal Processor (DSP), automatic detection can be done using simple pattern recognition algorithm (15) 4) This can be used for both PQ classification and detection. 5) In fact, the above energy deviation can also be called an index. Though an unconventional index that is measured/calculated using graphs. 4.7 Signal Energy Distortion A more conventional index based on the above principle is presented in this section. This index, which we call, signal energy distortion (SED) tries to condense the information of a signal under analysis into a single number. The signal energy distortion is given by SED= (P (i)-P1 (i)) where i is the number of nodes in decomposition level j. or, Max number of harmonics present P=RWE in each node for a signal under consideration. P1=RWE in each node for a pure 60Hz sinusoidal wave. The above index gives the deviation in frequency domain of a sine wave from a pure 60Hz sine wave. To capture time domain information, the following formulae are very helpful: DEV time (i) = P (i)-P (i+1) If DEV time (i) = 0 for all i, then harmonics not varying with time else, SED time (i) = P (i) P1 (i), gives the deviation due to additional PQ events occur. While, SED gives the distortion in the waveform under consideration, SED time gives the time instant or time range where additional PQ events along with harmonics took place.

PAGE 50

39 In other words, SED time is extremely helpful to capture the PQ events which occur along with harmonics. There are instances where it has been observed that 2 or more PQ events take place simultaneously. PQ monitoring for over 6 months of time at the Dairy Research Unit (DRU) for a period of 6 months by the Power Quality Laboratory at the University of Florida reinforces the same fact. It is very common to see: Harmonics along with sags and swells. Frequency changing harmonics with time Time varying harmonics. Advantages: 1. It is applicable for aperiodic waveforms. 2. It accelerates with frequency i.e. it gives weightage according to effect of a particular frequency component on frequency component. 3. It gives time domain information regarding additional PQ events occurring with Harmonics. 4. Obtaining a value more than 100% distortion is not possible unlike, THD. 5. A fresh look at the problem instead of traditional THD and its variants. This index is critically evaluated and tested on all permutations of test cases in next section.

PAGE 51

CHAPTER 5 CRITICAL EVALUATION OF THE PROPOSED METHOD A detailed theoretical idea to the methodology proposed to classify and detect harmonics was presented in the last chapter. Furthermore, a novel index based on the same methodology was also proposed. The index proposed in this thesis is critically evaluated in this chapter. It is an undeniable fact that the veracity of any theory proposed in an engineering field has to be proven by extensive testing under various conditions. The methodology proposed in this thesis is tested under simulated conditions. Using MATLAB a variety of cases are generated and tested on the various algorithms developed. 5.1 Test Cases To evaluate the indices proposed, various test cases were generated using MATLAB. The following are the test cases: 1. Periodic cases Odd and even harmonics, inter-harmonics, sub-harmonics. 2. Aperodic cases Harmonics with additional PQ events such as sags/swells Time varying harmonics (amplitudes of harmonics that change with time) Frequency varying harmonics (harmonics with different frequencies at different instances of time) All these test cases were generated in MATLAB. The algorithms were developed using Wavelet Tool Box in MATLAB. 5.2 Detection and Classification of Harmonics Wavelet Energy based detection and classification was introduced formally in section 4.6. Also, a systematic procedure required to draw scalograms was explained. 40

PAGE 52

41 Furthermore, scalogram based detection and classification was also demonstrated with examples. In the present chapter, this methodology is thoroughly investigated with the following test cases. In all the test cases the following frequency ranges were used: Table 5-1: Frequency bands corresponding to DWPT nodes at level 3 decomposition Node Frequency Range Hz. Center Frequency Hz. 1 0-120 60 2 120-240 180 3 240-360 300 4 360-480 420 5 480-600 540 6 600-720 660 7 720-840 780 8 840-960 900 In all the test cases the following time windows were used Table 5-2: Time ranges corresponding to the time windows of each node decomposed Time Window Time Range Seconds Time instant (average) Seconds. 1 0-0.1 0.05 2 0.1-0.2 0.15 3 0.2-0.3 0.25 4 0.3-0.4 0.35 5 0.4-0.5 0.45 6 0.5-0.6 0.55 7 0.6-0.7 0.65 8 0.7-0.8 0.75 9 0.8-0.9 0.85 10 0.9-1.0 0.95 5.2.1. Periodic Test Cases 5.2.1.1 Waveform with regular harmonics i.e. odd and even harmonics Test conditions: Waveform: 110sin60+11sin180+11sin300

PAGE 53

42 Sampling frequency=1920Hz Decomposition level=3 Number of nodes =2 3 =8. Frequency in each band= 0-120 Hz in first band and so on till 860Hz in 8 th band. 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14 16x 104 1 2 3 4 5 6 7 8 9 10 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Fig 5.1 (a) Fig 5.1 (b) Figure 5-1 (a) X-axis Frequency bands (1-8) Y-axis Squared Energy Deviation, 5.1 (b) X-axis: Time intervals (1-10) Y-axis Squared Energy deviation 5.2.1.2 Explanation In the frequency-energy deviation scalogram, the deviation in 2 nd and 3 rd bands can be clearly seen. The centre frequencies of 2 nd and 3 rd bands correspond to 180 and 300Hz respectively. Furthermore, there is no deviation in time domain. This indicates that, there are no additional PQ events along with harmonics. 5.2.2. Harmonics with Additional PQ events 5.2.2.1 Harmonics with sags and swells Test conditions are the same as above i.e. 5.2.1.a1The following is the equation of the waveform t=0 to 0.6 seconds; X= 110sin60+10sin180 t=0.6 to 0.8 seconds; X=140sin60+10sin180

PAGE 54

43 t=0.8 to 1 seconds; X=110sin60+10sin180. 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9x 105 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3x 104 Fig 5.2 (a) Fig 5.2 (b) Figure 5-2 (a) X-axis Frequency bands (1-8) Y-axis Squared Energy Deviation 5.2 (b) X-axis: Time intervals (1-10) Y-axis Squared Energy deviation 5.2.2.2 Explanation In the frequency-energy deviation scalogram, the deviation in 2 nd band can be clearly seen. The central frequency of 2 nd band is 180Hz. But this does not show that there is a swell. Time-Energy scalogram is useful here. There is a deviation in time domain at 7 th 8 th interval i.e. from 0.6 seconds to 0.8 seconds and the energy is also positive. This indicates that there is a swell from 0.6 to 0.8 seconds. Thus, by using a very simple pattern recognition algorithm one can classify harmonics. 5.2.2.3 Amplitude varying harmonics Test conditions are the same as above. The waveform under consideration is as follows: Time, t1=0 to 0.6 seconds; x1=110sin60 t2=0.6 to 0.8 seconds; x2=110sin60+30sin180 t3=0.8 to 1.0 seconds; x3=110sin60+60sin180.

PAGE 55

44 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10x 105 1 2 3 4 5 6 7 8 9 10 0 50 100 150 200 250 300 350 400 450 500 Fig 5.3 (a) Fig 5.3 (b) Figure 5-3 (a) X-axis Frequency bands (1-8) Y-axis Squared Energy Deviation 5.3 (b) X-axis: Time intervals (1-10) Y-axis Squared Energy deviation 5.2.2.4 Explanation In the frequency-energy deviation scalogram, the deviation in 2 nd band can be clearly seen. The central frequency of 2 nd band is 180Hz. Furthermore, there is a deviation in time domain at 6 th 7 th 8 th 9 th interval i.e. from 0.6 seconds to 0.8 seconds and the energy is also increases with increasing harmonic amplitude. This indicates that amplitude varying harmonics are present. 5.2.2.5 Frequency Harmonics with respect to time. Test conditions are the same as above i.e. 5.2.1.a1 The following is the equation of the waveform t=0 to 0.5 seconds; X= 110sin60+30sin420 t=0.5 to 0.8 seconds; X=110sin60+30sin300 t=0.8 to 1 seconds; X=110sin60+30sin300.

PAGE 56

45 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 105 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5x 10-3 Figure 5-4 (a) X-axis frequency bands (1-8) Y-axis squared energy deviation 5.4 (b) X-axis: time intervals (1-10) Y-axis squared energy deviation 5.2.2.6 Explanation In the frequency-energy deviation scalogram, the deviation in 3 rd and 4 th bands can be clearly seen. The central frequencies of 3 rd and 4 th band are 300Hz and 420 Hz. respectively. Furthermore, there is a deviation in time domain at 6 th and 9 th interval i.e. at 0.6 seconds and 0.8 seconds. This indicates that frequency varying harmonics are present and the time instant at which it takes place can also be captured. 5.3 Signal Energy Distortion Signal energy distortion (SED) condenses the information of a waveform under analysis into one number. This idea behind the index and its advantages were mentioned in the previous chapter. In the current chapter it is tested under various test conditions mentioned in section 4.1. 5.3.1. Periodic Test Cases 5.3.1.1 Waveform with regular harmonics i.e. odd and even harmonics Test conditions: Sampling Frequency=1920Hz

PAGE 57

46 Decomposition Level=3 Number of nodes =2 3 =8. Frequency in each band= 0-120 Hz in first band and so on till 860Hz in 8 th band. Table 5-3: Comparison between THD and SED for various waveforms Waveform THD % SED % DEV time SED (time) % Comments t=0 to 1 seconds 110sin60+11sin740+11sin420 14.14 1.91 Not Required No Additional PQ events t=0 to 1 seconds 110sin60+11sin300+11sin420 14.14 1.87 -doNo change in THD t=0 to 1 seconds 110sin60+11sin433+11sin515 N.A 1.90 -doTHD not applicable for interhamronics 5.3.2. Harmonics with additional PQ events Test conditions: Sampling Frequency=1920Hz Decomposition Level=3 Number of nodes =2 3 =8. Frequency in each band= 0-120 Hz in first band and so on till 860Hz in 8 th band.

PAGE 58

47 Table 5-4: Performance of SED for harmonics with additional PQ events Waveform SED % DEV time SED (time) % Comments t=0 to 0.6 seconds X= 110sin60+10sin180 t=0.6 to 0.8 seconds X=140sin60+10sin180 t=0.8 to 1 seconds X=110sin60+10sin180. 6.22 7 th and 8 th time window SED 7 =4.11 SED 8=4.08 Additional PQ events found in 6 th and 7 th time window The deviation of signal from ideal behavior is given by SED (time) t=0 to 0.6 seconds X= 110sin60 t=0.6 to 0.8 seconds X=110sin60+30sin180 t=0.8 to 1 seconds X=110sin60+60sin180. 7.32 7 th and 9 th time window i.e. it tracks time instant where the change energy takes place SED 7 =1.36 SED 9=3.12 Additional PQ events found in 7 th and 9 th time window Amplitude varying harmonics is found t=0 to 0.6 seconds X= 110sin60+30sin420 t=0.6 to 0.8 seconds; X=110sin60+30sin300 t=0.8 to 1 seconds X=110sin60+30sin300. 6.83 6 th and 7 th time window. SED 6 =0.22 SED 7 =0.33 Frequency varying harmonics were found. Their deviation in time domain is found to be less. As harmonics change form 420 to 300.

PAGE 59

CHAPTER 6 EPILOGUE 6.1 Conclusions The energy deviation based index and harmonic classification methodology proposed is extremely handy for PQ instrumentation. The proposed index has been shown in chapter 5 to be far better than THD. It overcomes the limitations posed by THD and it is more apt for PQ than THD. Furthermore, the unique ability of SED to give time domain information and knowledge about additional PQ disturbances, present along with harmonics, is extremely helpful for developing appropriate PQ mitigation techniques. Also, the algorithm proposed for this approach is extremely robust and fast. This algorithm can be programmed on a Digital Signal Processor (DSP) and can be used for real time monitoring of PQ. The proposed index has many advantages over traditional variations of THD suggested by various researchers. One achievement of the proposed index is that it does not suffer from THD mindset. The index proposed satisfies all the basic electrical engineering principles and quantifies the harmonic distortion using the energy content of the signal. In summary, the advantages of the new index and classification methodology proposed are as follows: It gives deviation in both frequency and time domain. 48

PAGE 60

49 A single algorithm detects, classifies and quantifies harmonics present in a power system. The proposed algorithm is fast, robust and easy to implement in a DSP. It is suitable for real-time monitoring. It is suitable for aperiodic signals and gives weightage to higher frequency components depending upon the signal deviation it causes. 6.2 Further Work Signal Energy Distortion (SED) as a measure of harmonics present in a system has been proposed and supported in this thesis through simulations. This idea (methodology) can to be implemented in a DSP. It requires any where between 3-4 months to implement this idea in a DSP board. The suggested pattern recognition algorithm has to be developed. This has to be developed prior to implementation of the proposed methodology in a DSP. Furthermore, empirical testing should be done for a long period of time so as to find out what value of SED is bad for the distribution system or transmission system. THD is used as a linearity indicator in microelectronic circuits, it posses several problems in electronic circuits as well. A study about its drawbacks and the possible application of SED to it should be studied in detail. Shannons Entropy gives a measure of order/disorder of the signal (14) This can give us the deviation of an analyzed signal from a pure 60Hz sine wave. This has to be further investigated and studied in detail as it gives a number for distortion. This is used as a distortion indicator in the field of communications and signal processing. Its application for power quality has to be exploited in detail.

PAGE 61

50 6.3 Afterpiece This thesis is an attempt towards achieving better PQ indices or possibly one index which can sum up all the information in a single number. There is a tradeoff here: More the preciseness of information we are looking for, lesser the clarity. In other words, the ambiguity of the index increases with increasing information one is seeking to get. There is an urgent need among the researchers and engineers throughout the world to debate the pros and cons of the existing indices. Although, a need for new PQ indices has been identified by A. Domijan, G.T. Heydt and others back in 1993. There has been little work in this direction and even the debate started by them is abating slowly. Joseph Joubert said "It is better to debate a question without settling it than to settle a question without debating it." I am in full agreement with him. It is better to have a debate on PQ indices even without settling to one. It is often difficult to come up with an index in a short period of time yet, a debate in this direction would make engineers more aware of the pitfalls of the indices while applying them.

PAGE 62

LIST OF REFERENCES 1. Dugan R.C., McGranaghan M.F., Beaty H.W., Electric Power Quality, McGraw-Hill, New York, 1996. 2. Domijan A., Heydt G.T., Meliopoulos A.P.S., Venkata S.S., West S., Directions of research on power quality, IEEE Transactions on Power Delivery 8(1), 1993, 429-436. 3. Addison P.S., The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance, IOP Publishing, Ltd, Bristol, 2002. 4. Goswami J.C., Chan A.K., Fundamentals of Wavelets: Theory, Algorithms and Applications, John Wiley & Sons & Inc, New York, 1999. 5. Hamid E.Y., Mardiana R., Kawasaki Z.I., Wavelet-based compression of power disturbances using the minimum description length criterion, IEEE Power Engineering Society Summer Meeting 2002, Volume 3, 2001, 1772-1777. 6. El-Saadany E.F., Abdel-Galil T.K., Salama M.M.A., Application of wavelet transform for assessing power quality in medium voltage distribution system, Transmission and Distribution Conference and Exposition, 2001 IEEE/PES, Volume 1, 2001, 7. Pham V.L., Wong K.P, Antidistortion method for wavelet transform filter banks and nonstationary power system waveform harmonic analysis, IEE proceedings Generation, Transmission and Distribution, 148 (2), 2001, 8. Jensen A, La-Cour Harbo A, Ripples in MathematicsThe Discrete Wavelet Transform, Springler Verlag, Berlin, 2001. 9. Heydt G.T, Jewell W.T, Pitfalls of electric power quality indices, IEEE Transactions on Power Delivery, 13 (2), 1998, 570-578. 10. Beaulieu G, Bollen M.H.J, Malgarotti S, Ball R and other CIGRE working group 36-07 members, Power quality indices and objectives ongoing activities in CIGRE WG 36-07, IEEE Power Engineering Society Summer Meeting 2002, 2( 21-25),789-794. 11. Heydt G.T., Problematic power quality indices, IEEE Power Engineering Society Winter Meeting, 4, 2000, 2838-2842. 51

PAGE 63

52 12. Domijan A., Shaiq M., A new criterion based on the wavelet transform for power quality studies and waveform feature localization, ASHREA Transaction, 104, 1998, 3-16. 13. Gruzs T.M., Uncertainties in compliance with harmonic current distortion limits in electric power systems, IEEE Transactions on Industrial Applications, 27(4), 1991, 680-685. 14. Rosso O.A., Blanco S., Yordanova J., Kolev V., Figlioa A., Schurman M., Basar E., Wavelet entropy: A new tool for analysis of short duration brain electrical signals, Journal of Neuroscience Methods, 105, 2001, pp-65-75. 15. Gaouda A.M., Salama M.M.A., Sultan M.R., Chikhani A.Y., Power quality detection and classification using wavelet multi-resolution signal decomposition, IEEE Transactions on Power Delivery, 14(4), 1999, 1469-1475.

PAGE 64

BIOGRAPHICAL SKETCH Ajay Karthik Hari obtained his Bachelor of Technology degree in electrical and electronics engineering from Jawaharlal Nehru Technological University (JNTU), India, in June 2001. While working on his bachelors degree, he was secretary of Electrical Technical Association (ETA). Starting from fall 2001, he is pursuing the Master of Science degree in electrical and computer engineering at the University of Florida. His research interests include advanced signal processing, power quality and power ICs. His other interests include politics, current affairs and quizzing. He was a member of Youth Parliament team in India, which won first prize for the year 1994. 53


Permanent Link: http://ufdc.ufl.edu/UFE0002760/00001

Material Information

Title: A Novel Index to Analyze Power Quality Phenomena Using Discrete Wavelet Packet Transform
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0002760:00001

Permanent Link: http://ufdc.ufl.edu/UFE0002760/00001

Material Information

Title: A Novel Index to Analyze Power Quality Phenomena Using Discrete Wavelet Packet Transform
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0002760:00001


This item has the following downloads:


Full Text












A NOVEL INDEX TO ANALYZE POWER QUALITY PHENOMENA USING
DISCRETE WAVELET PACKET TRANSFORM















By

AJAY KARTHIK HARI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2003


































Copyright 2003

by

Ajay Karthik Hari



































To AMMA, AJAPPA and SANDEEP.
















ACKNOWLEDGMENTS

I would like express my sincere thanks to Dr. Alexander Domijan for giving me an

opportunity to work on this project. I am indebted to him for offering me a research

position in his group and for his gentle and friendly attitude. I would also like to thank

Dr. Khai D.T. Ngo and Dr. A. Antonio Arroyo for serving on my thesis committee.

I express my sincere gratitude to Dr. Tao Lin for introducing me to the wavelets

and for his constant support during the entire thesis work. I would also like to thank my

colleague and friend Alejandro Montenegro for helping me in understanding power

quality and EMTP.

I thank my fellow colleague and friend Roop Kishore for patiently reading

my thesis and critiquing its grammar. I also extend my thanks to Hemanth for patiently

listening to my endless lectures on my thesis. I also thank all my wonderful friends and

lab mates.

Last but not least, I would like to thank my parents for their constant support and

encouragement.
















TABLE OF CONTENTS
page

A CK N O W LED G M EN TS ................................................................... .................... iv

L IS T O F T A B L E S ............................................................................ .......................... viii

LIST OF FIGURES .............................................................................. ix

A B ST R A C T ........................ ................................. ...... .................x

CHAPTER

1 PR O LO G U E ......... ..... ............................... .... ...... ..... ....... ........... .....

1.1 D definition of Pow er Quality ................................. .........................................1
1.2 Importance of Power Quality.............. .......................... ....................2
1.3 Review of Various PQ Problem s ...................................... .......... ....................3
1.4 S cop e of th e T h esis ...................................................................... .. ... .. .........
1.5 O organization of T hesis................................................................... .................... 5

2 INTRODUCTION TO WAVELET TRANSFORMS...............................................7

2.1 Definition of W avelet Transform ............................................. .................... 7
2.2 Why Wavelets for Power Quality..........................................8
2.3 Disadvantages of Traditional Signal Processing Tools ........................................8
2.3.1 Fourier T ransform s .............................................................. .................... 8
2.3.2 Short-tim e Fourier transform s ........................................ ...................9
2.4 Advantages of Wavelet Transforms ........................... .............................10
2.5 D iscrete W avelet Transform ........................................................................... 11
2.6 Wavelet Packets and Multi Resolution Algorithm.............................................12

3 SELECTION OF APPROPRIATE WAVELET................................ ..................... 17

3.1 Introduction...................... ................................ ... .......... ......... ..... ..... 17
3.2 Introduction to W avelet Fam ilies ...................................................................... 17
3.3 Analysis of Harmonics in Time-Frequency Plane..............................................18
3.3.1 Frequency Characteristics of Daubechies Wavelets...................................18
3.3.2 Comparison of Best Frequency Responses from the Wavelet Families .....20
3.4 Com plexity of Computation ........................... ... ........................................... 21










3.5 Quantification of the Selected Wavelet............................................................22
3.5.1 Spectrum Leakage ........................................................ ....................22
3.5.2 Scaling Property ........................................................... .................... 24

4 PROPOSAL OF A NOVEL POWER QUALITY INDEX ........................................25

4.1 Introduction ........................... ............... .......................................................... 25
4.2 Power Quality Indices.................... ..........................25
4.3 Drawbacks Associated with Harmonics .....................................................27
4.3.1 Total Harmonic Distortion .................................. ..... ..................27
4.3.2 Power Factor............................................................28
4 .3 .3 O th er In dices .............. ....... .................................................................... 29
4.4 Criterion for N ew Index..............................................................30
4 .5 W av elet E energy .............................. ............... ............................... ............... ..3 1
4.5.1 Wavelet Energy in Frequency Domain ....................................................31
4.5.2 Wavelet Energy in Time Domain......................... .........................34
4.6 Wavelet Energy Based Harmonic Detection and Classification .........................35
4.7 Signal Energy D istortion ........................................................ .................... 38

5 CRITICAL EVALUATION OF THE PROPOSED METHOD ..............................40

5 .1 T e st C a se s .......... .. ............... .. ................. ....... ..................... .................... ... 4 0
5.2 Detection and Classification of Harmonics .......................................................40
5.2.1. Periodic Test Cases................... .... .. .....................41
5.2.1.1 Waveform with regular harmonics i.e. odd and even harmonics.....41
5.2.1.2 Explanation ................................... ......... .. ......................42
5.2.2. Harmonics with additional PQ Events: ........................................ ....42
5.2.2.1 Harmonics with sags and swells........................... .................... 42
5.2.2.2 Explanation ............. ....... ................................... ........ ......43
5.2.2.3 Amplitude varying harmonics.........................................................43
5.2.2.4 E explanation ........................................................... .................... ... 44
5.2.2.5 Frequency varying harmonics with respect to time.. .......................44
5.2.2.6 Explanation ..................... ............ .................. ...... ....................45
5.3 Signal Energy D istortion ........................................................ .................... 45
5.3.1. Periodic Test Cases................................... .................... 45
5.3.2. Harmonics with additional PQ Events ....................... ......... ....46

6 EPILO G U E ........... ....................................... ............... ......... 48

6 .1 C on clusion s........... ................................................................... ....................48
6 .2 Further W ork .................. ................................................................................. 49
6 .3 A fterp iece .............. ........... ................................................... .............. ......... 50










LIST O F REFEREN CES ......................................... ....................... ........................51

BIO G RA PH ICA L SK ETCH ............................................................... ....................53
















LIST OF TABLES


Table Page

3-1 Complexities of various wavelets under investigation ........................................ 22

3.2 Frequency ranges of various nodes in level 3 DWPT
decomposition with sampling frequency of 1920 Hz .........................................23

3.3 Peak voltages at 8 nodes of DWPT decomposition using coif5............................24

4-1 Summ ary of power quality indices ........................................ ..... ............... 26

4-2 Drawbacks of THD in terms of numbers...........................................................29

4-3 RW E in each frequency band ............................. ...... ..........................33

4-4 RW E in various time divisions ............................. ...... ..........................35

5-1 Frequency bands corresponding to DWPT nodes at level 3 decomposition .........41

5-2 Time ranges corresponding to the time windows of each node decomposed........41

5-3 Comparison between THD and SED for various waveforms................................46

5-4 Performance of SED for harmonics with additional PQ events .........................47
















LIST OF FIGURES


Figure

1-1 Average loss per industry due to particular PQ event ...........................................3

1-2 Main aspects of electric power quality. Shaded boxes show the area's
addressed in this thesis ............... ................................................ ... .................. 5

2-1 M RA using LP and H P .......................................................... ....................13

2-2 DWPT filter bank implementation of a signal.....................................................14

2-3 Frequency band's in Hz of a level 3 DWPT decomposition with a sampling
frequency 1920H z .................... ............... ................. ..... .. ... ... ................. 16

3-1 Low pass and high pass decomposition filters of 'db5'......................................19

3.2 Frequency response of low pass (red) and high pass (blue) decomposition
filters of 'db l0' ............................................................... ...... .............. 19

3-3 Frequency responses of all the wavelets in Daubechies families. .........................20

3-4 Low pass and High pass frequency characteristics of dblO (black),
Coif5 (green) and Sym 8 (red)................................................ ........ ............ 21

3-5 Spectrum leakage of Daubechies filters. X-axis denotes nodes in
Level 3 decom position of dwpt ................................... ........... ....................... 23

4-1 Level 3 decomposition of a signal using DWPT ............................................31

4-2 Identification of harmonics using frequency scalogram........................................37

5-1 Deviation in frequency domain for regular harmonics........................................42

5-2 Deviation in frequency domain for harmonics with swell...................................43

5-3 Time varying harmonics .................. ..................................... 44

5-4 Frequency varying harmonics ................................................... ........ ......... 45
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

A NOVEL INDEX TO ANALYZE POWER QUALITY PHENOMENA USING
DISCRETE WAVELET PACKET TRANSFORM

By

Ajay Karthik, Hari

December 2003

Chair: Dr. Alexander Domijan, Jr.
Major Department: Electrical and Computer Engineering

A novel index to analyze harmonics is proposed in this thesis. Also, a new method

to identify and classify harmonics present in a power system is presented. The main goal

of the thesis is to identify pitfalls in current power quality indices and to present a new

index based on Discrete Wavelet Packet Transform. Wavelets with its unique ability to

give good time and frequency localizations simultaneously are best suited for power

quality applications. Wavelets can be used to identify, classify and quantify power quality

disturbances. This approach is extremely useful for power quality instrumentation

purposes as it proposes a very fast and robust algorithm to detect and quantify harmonics.

Furthermore, the algorithm developed also has the unique ability to identify additional

power quality events occurring along with harmonics. The ability of this algorithm to

identify and measure harmonic disturbances in both time and frequency domains will aid

in exact disturbance localization and detection. Thereby, it assists in designing of proper

mitigation techniques to eliminate power quality disturbances. The primary idea of this









thesis is to develop a power quality index based on energy content of the signal which is

suitable to analyze amplitude, frequency varying harmonics and periodic signals.















CHAPTER 1
PROLOGUE

Power quality (PQ) is cynosure of all eyes not only in the electric power industry

but also in the eyes of various sensitive power customers, like semiconductor industry,

where poor power quality combined with down time can cause huge monetary losses.

The attention it has captured is also because of an integrated approach used by

researchers and engineers throughout the world to solve the problem instead of tackling

them individually. It is a multi-disciplinary field encompassing power electronics, signal

processing, and hardware design among a host of other fields.

1.1 Definition of Power Quality

Power quality definition is often twisted by different agencies to suit their needs.

Utilities often equate it to reliability because doing so will give them better statistics. An

equipment manufacturer may define PQ as characteristics of power supply that enables

the equipment to work properly. These characteristics may vary from one manufacturer

to another. Ultimately, it is a customer driven issue and customer's satisfaction and point

of reference occupies the front seat. The following is the widely accepted definition of

power quality.

"Power quality can be defined as being any problem manifested in voltage, current,

or frequency deviations that result in disoperation or failure of customer equipment." (1)

Thus, it is very important to supply a 60HZ clean sinusoidal waveform without any

deviations to the customers. PQ is difficult to quantify. The ultimate measure of PQ is

measured by the performance and productivity of the customer's equipment.









1.2 Importance of Power Quality

The proliferation of nonlinear loads in the modem power systems has triggered a

growing concern for PQ related issues. The proliferation of power semiconductor devices

in power systems along with electronic loads, including personal computers and

information technology devices have resulted in waveform distortion in the power

systems. The nonlinear elements present in these electronic devices such as diodes,

transistors, thyristors etc contribute harmonics to the power system resulting in poor PQ

and at the same time they are the most sensitive ones to perilous effects of the poor PQ.

The importance of PQ is augmented by the fact that many things are now

interconnected in a network/grid. Failure of any electrical equipment has much more

serious consequences in the present day power systems than in the past. The recent New

York blackout, though not exactly because of power quality, underscores how

interconnected the network is and the impact of the failure of a network can have on our

day to day lives. Safe and reliable operation of electric equipment can be ensured with

good power quality Also, as the sophistication of electronic equipment increases, there is

a need for good power quality and the utilities will leave a bad impression on customers,

otherwise. The importance of PQ is more thoroughly understood when its economic

value is emphasized. It has a direct impact on all most all the types of customers. The

following figure shows the direct economic impact of a particular PQ event on various

industries.











$
Average loss per sag for different indutries
Source Power Electronics Applications in Energy System s Narain
$10M G H ngoran I


$1M


$100K



$10K -
$1K


$0 0



I- [_ (I Q. =
N I ~Industries






Figure 1-1: Average loss per industry due to particular PQ event.

Apart from obvious financial reasons, there are numerous indirect and intangible

costs which are associated with PQ problems. Customer satisfaction is a key factor. Even

though, small residential customers do not suffer direct financial loss due to PQ problems

but their dissatisfaction can work as propaganda against utilities. Especially when utilities

are facing tough competition among each other

1.3 Review of Various PQ Problems

The PQ problems can be categorized briefly as follows:

* Transients
Impulsive transient and Oscillatory transient.
* Short duration voltage variations
Voltage Sag and Voltage Swell
* Long duration voltage variations
Under Voltage and Over Voltage
* Interruptions
Momentary, Temporary and Long term Interruptions.
* Waveform distortions
Harmonics, Notching and Noise.









* Voltage fluctuation
* Frequency variation
* Other Miscellaneous problems
Voltage unbalance, DC offsets Reactive power consumption.

1.4 Scope of the Thesis

A. Domijan, G.T. Heydt et al. in the paper titled "Directions of Research on

Electric Power Quality" (2) showed various fields of research in the electric power quality

area. Which include: Modeling and Analysis, Instrumentation, Sources, Solutions,

Fundamental concepts and effects. The present thesis encompasses parts of Time domain,

Transfer domain and waveform analysis part of research in the electric power quality

area. It is more clearly depicted in Figure 1.2. The present thesis presents new techniques

that can be used to analyze PQ waveforms in both time and frequency domain

simultaneously. It also proposes a new criterion that can be used to select a Wavelet

(defined in the Chapter 2) appropriate for PQ monitoring. It also critically evaluates

various PQ Indices widely used and proposes a novel PQ Index. The proposed Index is

based on energy content present in a signal. This thesis also forms as a basis for further

research for a proposed PQ monitoring device to be developed in PQ&PE Laboratory at

the University of Florida.







5




Electric Power Quality





Mode g d nsumentation Sources Solutions Fundamental Effects
Analysts ste he So Concepts (Ta

CoHarmonics LMetering C
s-igna els ands i as s Pulse Modulated


Stoch aslc ] Groundmg
models Methods SVC'S

UserIssues
FACTS
Voltage Adaptive
support Compensators Procedure

Software









Network Methods




Figure 1-2 Main aspects of electric power quality. Shaded boxes show the areas
addressed in this thesis

In other words, the goal of the present thesis is to use wavelet transform (WT), an


advanced signal processing tool, to analyze the time-frequency-energy properties of PQ


signals and use it as a basis to classify the PQ events and to develop a PQ Index


exploiting the unique time-frequency properties of the Wavelet transform.


1.5 Organization of Thesis

The present thesis is divided into five chapters. It can be further split into two parts:


the first part deals with introduction to wavelet transform theory (chapter 2) and selection


of appropriate wavelet (chapter 3); while, the second part deals with introduction to PQ









indices and proposal of a new index( chapter 4) ,Furthermore, a discussion on results (

chapter 5) obtained is presented More detail explanation of the organization follows:

Chapter 2: This chapter starts out with historical background of wavelet transform

theory and explains basic theory of wavelet transforms. It also justifies the selection of

WT for PQ applications. Furthermore, it compares and contrasts various other signal

processing techniques with respect to WT.

Chapter 3: This chapter deals with selection of appropriate wavelet filter bank for

PQ applications. It starts out with a brief description of various wavelet families present

in literature and explains the criterion behind the selection of a particular wavelet family

for PQ application. The chapter ends by justifying the selection by using various signal

processing techniques.

Chapter 4: In this chapter, a close look is taken at various PQ indices present in the

literature. The problems with existing Indices are explained. Then a novel index is

proposed.

Chapter 5: Results obtained are presented in this chapter, followed by a discussion

on the results obtained. The Index proposed is critically evaluated.

Chapter 6: Conclusions from the results and scope for further work is presented in

this chapter.














CHAPTER 2
INTRODUCTION TO WAVELET TRANSFORMS

Wavelet transforms have been in existence for a long time. It was first mentioned

by Alfred Haar in his doctoral dissertation in 1909 and it was mentioned in its present

theoretical form by Jean Morlet in 1975 while working for Elf Aquitaine under Alex

Grossmann. Other important contributors include Dr. Ingrid Daubechies, Stephane Mallat

and Yves Meyer. The wavelet transform has been found to be particularly useful for

analyzing noisy, periodic, transient and intermittent signals. It has a very different

ability to examine the signal simultaneously in both time and frequency.

2.1 Definition of Wavelet Transform

Wavelets, little wave like functions, are used to transform the signal under

investigation into another representation which presents the signal information in a more

useful form. This transformation of the signal is known as the wavelet transform (WT).

Mathematically, WT (3) is defined as the inner product of wavelet function y(a, b) and

real signal s (t):


T (a, b) = S(t), q1* ,,a(t)

where

S)( t t t t t-)

The parameters a and b are called dilation and translation parameters respectively.









2.2 Why Wavelets for Power Quality

The occurrence of power quality events should be detected and located in time,

the content of these events should also be monitored accurately so as to classify the

events and carry out appropriate mitigations techniques to alleviate PQ problems. There

is a need for a powerful tool that can be used to classify the PQ events both in time and

frequency domain. Wavelets satisfy this need and scores over other Time-Frequency

methods such as Short Time Fourier Transform (STFT). These advantages are explained

in more detail in the following sections of this chapter.

Also, Wavelet basis functions have compact support, which means that basis

functions are non-zero over a finite interval, unlike sinusoidal Fourier basis functions

which extend infinitely. This property along with unique property of wavelet basis to be

squeezed (dilation) and movement along axis (translation) gives greater flexibility in

analyzing localized features of analyzing signal.

Furthermore, recent advances in PQ mitigation techniques are based on extraction

of harmonic components instead of traditional fundamental component. Thus, time-

frequency domain based techniques come into picture as they give a distinct advantage of

eliminating selected harmonics, subject to availability of accurate information on

individual harmonic components.

2.3 Disadvantages of Traditional Signal Processing Tools

2.3.1 Fourier Transforms

The Fourier transform (FT) of a finite energy function f(t) e L2 (R) of a real

variable t is given by


f() = Jf(t)exp(-jt)dt.









It is evident from the above definition that FT cannot be carried out until the entire

waveform in the whole axis (- oc, oc) is known. The above equation can be evaluated at

only one frequency at a particular time. (4) This causes great difficulties while processing

non stationary signals. Even though, faster algorithms exist to carry out this computation

they cannot be implemented for real time signals. This is undesirable from PQ monitoring

point of view.

As explained before FT fails to give time domain information of the signal and is

thus a serious handicap for PQ analysis and Instrumentation techniques based on it.

Fast Fourier transform (FFT) and its variants are generally used in spectral

analyzers and also other PQ monitoring instruments. It suffers from all the disadvantages

mentioned above and also due to its spectral leakage component; it does not accurately

show the spectrum. This will in turn lead to imprecisely calculated signal parameters such

as magnitude, phase and frequency. Furthermore, it is very difficult to distinguish

between the harmonics and transients in an FFT spectrum.

2.3.2 Short-time Fourier transforms

Short-time Fourier transforms (4) are very intuitive. In order to achieve time-

frequency localization, it obtains the frequency content of a signal at any instant 't' by

windowing the signal using an appropriate window function and then FT the remaining

portion of it. More crudely, it is removing the desired part of the signal and then performs

FT on it. Thus, it is some times referred as windowed Fourier transform or running

window Fourier transforms.










Mathematically, if f (t) is the signal under consideration and 0(t) is the window

function used to obtain a windowed function, say, f'(t) = f(t) (t t'), then STFT

evaluated at location (t', c) in the time-frequency plane is given by

G/(t', c) := f(t)O(t t')e"o dt
R
STFT needs to know the signal information only in the interval of the window

function used. This is a major improvement from FT, where it needs to know the signal

information over the entire time axis. The major disadvantage of STFT comes from

uncertainty principle. Low frequencies can hardly be depicted using short windows and

short pulses are poorly located in time with long windows. From the above two sections,

it can be safely concluded that traditional FT poses a serious handicap for PQ monitoring.

Also, other variants of FT such as STFT also have serious drawbacks.

2.4 Advantages of Wavelet Transforms

As presented in the previous section, traditional signal processing tools have some

serious drawbacks for PQ applications. A more viable alternative is the use of wavelet

transform. The wavelet transform has good localization in both frequency and time

domain. This makes it an attractive option for PQ applications. WT is apt for studying

non-stationary power waveforms. Unlike, the sinusoidal function used in FT, wavelets

are oscillating waveforms of short duration with amplitude decaying quickly zero at both

ends and thus are more suitable for short duration disturbances. The wavelet's dilation

and translation property gives time and frequency information accurately. Apart from it

this process of shifting enables the analysis of waveforms containing nonstationary

disturbance events. To enhance the electric power quality, sources of disturbances must

be detected and then appropriate mitigation techniques have to be applied. In order to









achieve this, a real-time PQ analyzer with an ability to do time-frequency analysis is

required. Hence wavelets transforms with its ability to give good Time-Frequency

resolution is suitable for PQ applications.

Another important application in PQ is data compression. (5) A single captured

event recorded for several seconds using monitoring instruments can produce megabytes

of data. This increases the cost of storing and transmitting data. Again, WT comes into

picture. Its ability to concentrate a large percentage of total signal energy in a few

coefficients helps in data compression. Thus, it reduces the need to store huge

voluminous of data and reduces costs associated with it.

In this research project, discrete wavelet packet transform, popularly called DWPT,

an enhancement of multi resolution algorithm (MRA) using discrete wavelet transform

(DWT) has been used as a tool for PQ analysis. DWPT has many inherent advantages

over DWT (3), which are explained in more detail after a formal introduction to discrete

wavelets in the following sections.

2.5 Discrete Wavelet Transform

In the previous section, wavelet transform was defined as the inner product of

wavelet function y/(a, b) and real signal s (t):


T (a, b) = S(t),q1* ,,,(t)

where

y (a, b)(t) = -y(-) and the parameters a and b are called dilation and translation


parameters respectively. This is called continuous wavelet transform (CWT).









Discrete wavelet transform (3) is defined for a continuous time signal, s(t) where

discrete values of a and b are used. The DWT is thus the discretized counter part of

CWT, which is defined as

T(a,b) ~ k-nboao
T (a, b) S(t)T[ ]
Jamn a
where

The integer's m and n control the wavelet dilation and translation respectively;

a o is a specified fixed dilation step parameter set at a value greater than 1;

And, b o is the location parameter which must be greater than zero.

But, common choices for discrete wavelet parameters a o and b o are 2 and 1

respectively. This type of scaling is popularly called dyadicc grid' arrangement.

When certain criteria are met it is possible to completely reconstruct the original

signal using infinite summations of discrete wavelet coefficients rather than continuous

integrals. This leads to a fast wavelet transform for the rapid computation of the discrete

wavelet transform and its inverse. DWPT, which is used in this research project is based

upon discrete wavelet transform. It allows for adaptive partitioning of the time-frequency

plane. It is a generalization of multi resolution algorithm explained in the following

section.

2.6 Wavelet Packets and Multi Resolution Algorithm

MRA was initially developed to decompose the signal into various resolution levels

to facilitate a very fast time-frequency analysis. A multi-stage filter bank is used to

decompose the signal into various levels using a Low Pass(LP) filter and a High

Pass(HP) filter as shown in the figure 2.1. (6) The LP filter will result in approximate

coefficients of the original signal and the HP filter in detailed coefficients of the signal.
































Figure 2-1: MRA using LP and HP

DWPT, as stated earlier, is a generalization of the DWT. The difference is that in the WP

signal decomposition, both the approximation and detailed coefficients are further

decomposed at each level. This leads to a decomposition tree which is shown in Figure

2.2. This will lead to an array of wavelet packet coefficients with M levels and each

containing N coefficients. A total of N coefficients from this M*N array can be selected

to represent the signal.

The main advantage of DWPT is better signal representation than decomposition

using MRA. The DWT technique is not suitable for harmonic analysis because the

resulting frequency bands are not uniform. In DWPT, with clever manipulation of

sampling frequency, the important harmonics such as odd harmonics can be made center

frequency of the resulting frequency bands. Furthermore, DWPT gives uniform bands is






14


important for harmonic identification purposes. A level 2 decomposition using DWPT

filter bank can be depicted as follows


Figure 2-2: Depicting DWPT filter bank implementation of a signal

Similar to DWT, LP filter gives approximation coefficients and HP filter gives detailed

coefficients. The coefficients are given by the following equations:

Let ()(t)be the scaling equation (or dilation equation) associated with the mother

wavelet. Then, the scaling function can be convolved with the signal to produce

approximation coefficients given by

A m,n= s(t)+,n(t)dt
The function of mother wavelet can be convolved with the signal to produce detail

coefficients given by


Dm,n = s(t)q,,n(t)dt

The following explanation forms the basis of the next chapter and much of the

research done for this thesis. As explained earlier DWPT can be used to separate









harmonics. It can be best illustrated as follows. Let us assume a signal with fundamental

frequency 60HZ and 3rd, 5th, 7th and 9th Harmonics. Let the sampling frequency be

1920 Hz. Then the maximum measurable frequency is 960Hz (Sampling theorem). The

figure depicted in the next page shows the decomposition and how the harmonics are

separated using DWPT.

Frequency ordering after DWPT is very important and it has to be understood. (7)

The decomposition resulting from a high pass filter is always a mirror image. Thus,

before doing any further analysis, it is of great importance to sort out the frequency in

desired order. The example illustrated in the following page (8) shows level three DWPT

decomposition and the first frequency band is 0-120Hz thus, its center frequency is 60Hz.

Hence selection of sampling frequency is very important and it should be done in an

intelligent manner such that the important frequencies one is dealing with are usually the

center frequency of the band. The maximum level of decomposition one has to go for

decomposition varies from application to application. Usually, for power system

applications it is 60Hz/50 Hz. But, due to the presence of sub-harmonics present in the

power systems it is advisable to go further down.

At the same time, as the number of nodes increase with increase in decomposition

levels, it makes analysis more complicated or in other words, it reduces the readability.





































Figure 2-3 Frequency band's in Hz of a level 3 DWPT decomposition with a sampling
frequency 1920Hz

Note that the center frequency in each of the nodes is exactly odd harmonics of 60 Hz.















CHAPTER 3
SELECTION OF APPROPRIATE WAVELET

3.1 Introduction

More often than not power researchers tend to neglect the choice of appropriate

wavelet filter for their application. The selection of wavelet assumes more importance if

one wants to implement their algorithm in DSP and develop an instrument out of it. It is a

general trend among researchers to take dblO (more appropriately higher order db

coefficients) to study harmonics and db4 or db3 to study transient related phenomena. In

this paper, we have made an effort to study various wavelet families, which exist in the

literature, suitable to study PQ problems and to suggest a suitable wavelet filter that can

be used to study harmonics in particular.

3.2 Introduction to Wavelet Families

Today, there are a number of wavelet families which exist. Each one of them has a

particular application. In fact, one can develop a wavelet family to suit ones particular

needs. But to study PQ phenomena there are some wavelet families like Daubechies etc

which already exist in the literature. Some of the widely used wavelet families that can be

used to study the PQ phenomena are

1. Daubechies
2. Symlets
3. Coiflets
4. Biorthogonal Wavelets.









3.3 Analysis of Harmonics in Time-Frequency Plane

In the analysis of harmonics in time-frequency plane, it is very important to exactly

localize the harmonics in the frequency plane. The DWPT algorithm (as explained in the

previous chapter) partitions the time-frequency plane, one partition for every

decomposition. It allocates the lower interval to low pass filtered part and higher

frequency interval to the high pass filtered part. Thus, it is very important to select an

appropriate wavelet filter appropriate whose frequency is close to an ideal filter.

3.3.1 Frequency Characteristics of Daubechies Wavelets:

Ingrid Daubechies has proposed 10 wavelets often represented as dbl, db2...dbl0

or some times db2, db4.....db20. Where, db stands for Daubechies and the numbers 1,

2... 10 stand for number of zero moments in the former representation and numbers 2,

4,..20 stand for number of non-zero scaling coefficients in the latter representation. In this

thesis the former approach is being used as it is used by the MATLAB wavelet tool box

and makes programming and interpretation easier. To facilitate this, Daubechies wavelets

were decomposed into low pass and high pass filters. The frequency characteristics of

both the low pass and high pass filters have to decrease faster near the filter band edges.

This will give good frequency separation and there by localization in the time-frequency

plane will be lot easier. Another advantage is that it will reduce frequency leakage into

neighboring bands. For example decomposition of Daubechies wavelet db5 is shown in

fig 3.1








19



Lows Pass Decorrposition filter of db5



0 5






2 3 4 5 6 7I 8 9 10

High Pass Decomposition filter of db5









2 3 4 5 6 7 8 9 10


Figure 3-1: Low pass and high pass decomposition filters of 'db5'
high Pass Decomposition filter f db5


0 5 ( - L - - - --k












Figure 3-1: Low pass and high pass decomposition filters of'db5'


Frequency response of Low pass and High pass filters ofdblO
High Pass
S-- L w Pass


-I -_ __ -
I I I I I I I


I I I I I I I


0 005 01 015 02


025 03 035 04 045


Figure 3-2: Frequency response of low pass (red) and high pass (blue) decomposition
filters of 'dbl0'


To make this study more effective frequency response's of all the families were


individually and taking the best out of each one of it, a comparison was made. The


following figures will make this explanation more clear.







20


S-- ---------------- -------------
I Ii



006 01 01I 02 024 04 04













3-3 (a) 3-3(b)

Figure 3-3: Frequency responses of all the wavelets in Daubechies families. (a) High pass
decomposition filter. (b) Low pass decomposition filter

In a similar fashion, the frequency response's of all the wavelets in Symlets,

Coiflets and biorthogonal families were calculated and plotted. All the relevant graphs

are attached in the appendix. From fig 3.3, it is clear that dblO has the best frequency


response suited to our application i.e. the frequency characteristics decrease faster near

the filter band edges.

Following the same rule of thumb we can say that coif5 and sym8 have good

frequency characteristics. Frequency response of biorthogonal wavelets are not in the

same league of the other 3 families.

3.3.2 Comparison of Best Frequency Responses from the Wavelet Families

As explained in the previous paragraph, the best frequency responses from the 3

families under investigation are Daubechies 10 (dblO), Symlets 8(sym8), Coiflets

5(coif5). To find out the better among them for our application, all the 3 were plotted out

in a same graph as shown below





















05------------


0 5 --- - -- - -I -- - - - -






0 005 0 1 0 15 02 025 03 035 04 045 05



Figure 3-4: Low pass and high Pass frequency characteristics of dblO (black), Coif5
(green) and Sym8 (red)

It can be seen from the graph that all the three have similar frequency responses

and coif 5 has the best response among them. The selection now depends upon the

accuracy range required for the application. For PQ applications more the accuracy, the

better it is. Since, all the 3 have almost similar Frequency Responses it would be a good

idea to see the complexity of computation of them.

3.4 Complexity of Computation

Complexity of computation using the above filters becomes a very cardinal issue

while implementing them on a DSP board. The low pass and high pass wavelet filters are

discrete in nature. For an N point filter to process it requires N multiplications and N2 -1

addition's.









Table 3-1: Shows the complexities of various wavelets under investigation


From the above table, it is clear that coif5 has the highest complexity but again it

has the best frequency and phase response. When sampling frequency is around 1930Hz

(Typical value for PQ applications), it is more sensible to opt for a wavelet with better

frequency response. Furthermore, the benchmarks of the latest DSP processors released

by companies like TI and Analog Devices for Data Acquisition, Test and Measurement

applications can do complex multiplications in 19ns. Thus, it is better and more realistic

to choose coif5 because its complexity is not too high, when compared to dblO, and will

not burden the DSP.

3.5 Quantification of the Selected Wavelet

A scientific approach was adopted to select the wavelet for this particular

application. To ascertain this selection the selected wavelet i.e. coif 5 was tested for

various characteristics that are suited for this application, especially, the behavior of

wavelet, when it is used in the DSP board for real time monitoring.

3.5.1 Spectrum Leakage

As explained in the previous section the frequency response of coif5 is sharper at

the edge of the band. Hence, it should show less frequency leakage when compared to


S. No Name of the Wavelets Complexity


1 dblO 160399


2 Sym8 65791


3 Coif5 810899










other wavelets. To quantify this theory, a sine wave was decomposed using coifl and

coif5 wavelet filters and by applying DWPT. The equation of the sine wave tested is:

X=0.1*sin(2*pi*60*t)+0.1*sin(2*pi* 180*t)+2*sin(2*pi*300*t)+0. 1*sin(2*pi*420*t)

With t=0:5.2083e-004:1 (a sampling period of 1920Hz.).The graph depicted in the

next page has Nodes of level 3 decomposition on x-axis and magnitude (Peak voltage) on

the Y-axis. As explained in the previous chapter. Each node corresponds to a frequency

band. The number of nodes is given 2 power(level). The frequency band for a level three

decomposition with sampling frequency 1920Hz is given as follows:

Table 3.2 Depicts frequency ranges of various nodes in Level 3 DWPT decomposition
with sampling frequency of 1920 Hz

Nodes 1 2 3 4 5 6 7 8

Frequency 0-120 120-240 240-360 360-480 480- 600-720 720- 840-
Range 600 840 960
(Hertz)


Zr --
15r -


2 3


4 5 6 7 8


Figure 3-5: spectrum leakage of Daubechies
decomposition of DWPT.


filters. X-axis denotes nodes in Level 3









It is clear from figure 3.5 that coifl has more leakage than coif5.

3.5.2 Scaling Property

It is very important to check this property for any digital filter. It basically checks if

the output is 'proportional' to the input. This property ensures that the filter does not have

any inconsistencies and with the including of appropriate scaling/correction factor, it can

be used for real time measurements.

To check the scaling property of coif5, two signals; one with double the amplitude

of other was processed using coif5 wavelet filter and its scalability was tested. It was

found that the ratio between the resultant coefficients of the two filters is exactly two.

This makes the selected filter more suitable for data acquisition. The following table

depicts the scaling property more clearly.

Table 3.3: Peak voltages at 8 nodes of DWPT decomposition using coif5

X=l*sin(2*pi*60*t) X=2*sin(2*pi*60*t)

Vlpeak 1.0444 Vlpeak 2.0888
V2peak =0.0684 V2peak =0.1369
V3peak =0.0155 V3peak =0.0310
V4peak =0.0053 V4peak =0.0107
V5peak =0.0037 V5peak =0.0073
V6peak =0.0022 V6peak =0.0045
V7peak 9.2321e-004 V7peak =0.0018
V8peak =3.7354e-004 V8peak =7.4708e-004


The above steps ensure that when implemented in a DSP, the selected wavelet

'coif5' is suitable for data acquisition and measurement purpose.















CHAPTER 4
PROPOSAL OF A NOVEL POWER QUALITY INDEX

4.1 Introduction

The system operators have the responsibility to deliver electric power in

accordance with the standards set by their clients. With ever increasing number of

sensitive power customers, reporting about quality of power back and forth between

customers and system operators has increased. In order to characterize quality of power

being supplied and received by customers, there is a need to develop standards,

preferably common one which is accepted world wide. The development of such an index

will remove any differences that may arise between the supplier and customer.

An ideal power quality index should be able to summarize the degree of distortion

present in a system Also, to avoid ambiguity the number of indices should be kept at

minimum. (9) It should

* be as simple as possible and easily interpretable by layman.
* Representative of the actual distortion and its impact
* Readily implementable in practical equipment.
* Valid for all topologies and conditions.
* Allow comparisons of performance in time-domain.

4.2 Power Quality Indices

Most of the PQ indices are proposed long back and some of them have been

developed for other applications. With increasing importance given to PQ and huge

distortions found in present day power systems some of them do not exactly characterize

the distortion. Furthermore, they are not applicable to many cases and violate electric









engineering principles in some of the cases. A list of power quality indices is provided in

the following table (10)

Table 4-1: Summary of power quality indices

Index Definition/Formula Application

Total Harmonic General purpose
Distortion 2 / L


Power Factor Ptot/( Vrms Irms) General purpose; Revenue metering


Telephone Influence Audio circuit interference
Factor W L//r


C message Index Communications interference
C1 / In


IT product Audio circuit interference; Shunt
I (IW) 2 capacitor stress


VT product ( 2 Voltage distortion index



K factor h2I2/ Ih Transformer derating
h=1 h=1


Crest factor Vpeak/Vrms Dielectric stress


Many of the indices presented in the table 4.1 have evolved over a period of time

and have been proposed after many years of practical observations. It is not easy to

discard them from usage. Some of them are applicable to some specific purposes, while

others are for general purposes. But, they fail to characterize PQ phenomena and thus









there is a need for new indices to suit the present day needs. The present thesis is a step in

that direction.

4.3 Drawbacks Associated with Harmonics

4.3.1 Total Harmonic Distortion

The most popular PQ index used is total harmonic distortion (THD). (") It is

probably the most popular way of characterizing distortion due to harmonics. It is widely

used not only in the field of power systems but also in the field of Electronic circuits to

characterize non linearity present in a circuit/system. Unfortunately, it has some serious

drawbacks.

Basically, THD is the ratio of energy content in harmonics to that of fundamental

component. The term harmonics and the index associated with it i.e. THD is often used to

describe perturbations present in the waveform. But, this has some serious problems if

one closely examines the definition of harmonics. The term harmonics means multiples

and is originated from the musical tones whose frequency is integral multiples i.e.

harmonics of a fundamental tone. Similarly, in power systems, harmonics refer to

frequencies that are integral multiples of fundamental frequency (60Hz/50Hz). Thus,

THD becomes problematic when non-integer harmonics are present and also if the signal

is periodic.

The other significant pitfall of THD is that all frequencies are weighed equally. The

value of THD obtained is same for a signal with 5th harmonic which has the same value

of a signal with 3rd harmonic. But, it is a known fact that they have different effect on

power systems. THD fails to capture this information. It also fails to convey any

information about phase angles of the harmonics. (12) The index is not affected by the

presence of phase angles.









The other significant drawbacks include the fact that THD is not applicable when

the fundamental frequency is absent. If a 60 Hz voltage is switched as in a PWM drive

for an I.M. the resulting induction motor stator voltage is around 60+/-0.2 Hz.

Furthermore, another serious pitfall is that it is possible to have THD excess of 100% i.e.

it is theoretically possible to have THD of 140% (13). This is not a good figure of merit

because it does not make sense to say 140% THD distortion and the amount of distortion

at 140% is not twice as that of 70%.

Another pitfall of THD which has some important consequences is that it does not

give time domain information. For example, if a power system has time varying

harmonics, THD or as a matter any other PQ index fails to capture this information. Also,

it can not distinguish between harmonics with sag or swells.

4.3.2 Power Factor

The traditional definition is suitable only for fundamental component i.e. 60 Hz.

Although there are some modifications of PF which exist in literature such as

PF= cos (0)/ (( (1+THD2)

This modification is extremely handy but when the application of THD in the field of

power quality is questioned, there is a need to suggest a new change for PF definition.

Also, PF fails to address the time-varying loads. In some extreme cases, PF changes from

0.5 to 0.85 lagging in 3-4 seconds. Any improvement in the definition of power factor or

development of any index in this area would definitely benefit power electronic engineers

who design the Power Factor Correction (PFC) devices. The importance of PFC in power

quality need not be further underscored. Apart from this, it can also help to improve the

revenue metering.









The following table shows some of the drawbacks

makes the above claims more clear.

Table 4-2: Drawbacks of THD


of THD in terms of numbers and



in terms of numbers


Waveform under consideration THD Reason

110sin(60)+10sin(180) 9.0909%
Equal weightage to higher
frequency components
110sin(60)+10sin(660) 9.0909%


110sin(60)+10sin(660+800) 9.0909% Can not characterize phase angles


110sin(60)+10sin(180)+2sin(220) 9.0909% Can not quantify Inter harmonics
(actually Not
Applicable)


For t=0 to 0.6 seconds The answer shown is not correct as
110sin(60) 12.86% THD is not applicable to this
For t=0.6 to 0.8 seconds (Not frequency varying harmonics case.
110sin(60)+10sin(180) Applicable) Also, the signal is periodic
fort=0.8 to 10 seconds
110sin(60)+10sin(300)


4.3.3 Other Indices

Other factors such as VT product can also be improved. They also suffer from the

same defects mentioned above. Also, K-factor summarizes the harmonic distortion into

one number. The stray losses which occur due to harmonics are a small portion of the

total losses for the low-order harmonics. The stray losses are so small that the increase in

net loss due to it can be negligible. It means that effect of heating for a distorted current is

nearly the same as the heating for a sinusoidal current with same value. There is a need

for an index that can measure the heating effect of various loads.









4.4 Criterion for New Index

The above sections make it clear that there is a need for a new index for PQ

applications. In order to propose a new index suitable for PQ applications we need an

index which can address in both time and frequency domain. All the indices present in

the literature are suitable for periodic case which possesses Fourier components. In this

proposal, Wavelet Transforms are utilized to propose a novel index.

In signal processing the energy content of a particular signal is given by

E= fJ (t) dt

It is nothing but the area under the squared signal. Parseval's theorem states that energy

content of a signal in time domain is equal to energy of the signal in frequency domain.

It is given by

E=J f2 (t) dt =1/ (211) f2 (f) dt.

where f(t) is the equation in frequency domain. This property is very handy and can be

used to develop an index which gives both time domain and frequency domain

information.

The energy content of a signal is chosen because it is very handy when we are

dealing with periodic waveforms and very useful as it can characterize subharmonics,

inter-harmonics, etc. present in the system. This idea of using energy content for PQ

applications was proposed by A. Domijan et al. This formed a basis for research on PQ

indices. Many other variants of THD were proposed based on this idea but they all suffer

from THD mindset and other inherent problems associated with THD. In the present

thesis, the energy of the signal is found out using wavelet transforms. Wavelets as

mentioned before give both time and frequency domain information and thus can be used









to find out an index which can be analyzed in both the domains The following section

explains in detail the approach used to find out the energy of the signal

4 5 Wavelet Energy

In this thesis, the signal under investigation is decomposed using DWT (explained

m Chapter 2) The coefficients of the signal are then used to find out the energy This

process is more clearly explained with the foll owing figure


Figure 4-1 Level 3 decomposition of a signal using DWPT

The decomposition is done using the DWT The coefficients are given by

C1=


where

S (t) is the signal under consideration


Wf,k is the wavelet filter used for analysis, J denotes the level of decomposition andJ

gives the node in the decomposition level k

4 5 1 Wavelet Energy m Frequency Domain

The energy of the signal 14) in each band is given by










Etot= J Cj(k) 2- EJ.
j k

It is always better to represent any index in normalized values, in other words, it is

desirable to remove any units associated when developing any index. In this case, the

present PQ index under development needs to quantify the deviation of a signal under

consideration with a perfect 60Hz sinusoidal wave. Thus, normalizing the energy in each

band with total energy makes sense.

The normalized energy or 'relative wavelet energy' (RWE) in each band is given by

E(j)
P
Etot

If the analyzed signal is a pure sine wave with 60 Hz then the relative wavelet energy in

the band containing 60 Hz should be exactly equal to one. In other words, there should be

no leakage of energy in other bands and it should be exactly concentrated in the 60Hz

band.

An intuitive theory based on the above discussion can be proposed. It can be stated

that if the 'relative energy' in a frequency band containing fundamental frequency

component is equal to one, then harmonics are absent in the system. This statement

assumes that the frequency band is as narrow as possible.

As explained, the wavelet filter selected for our application coif5 is close to ideal

filter but not exactly ideal. Infact, realization of a causal ideal digital filter is not possible.

The RWE for a pure 60 Hz sine wave is found out to be 0.9957 i.e. an error of 0.0043 is

present. This error can be either removed by a scaling factor or it can be cleverly used in

the index such that its effect is negated. The latter approach has been used here.









The following example shows the RWE for an 'impure' sine wave i.e. sine wave

with harmonics. The sine wave under consideration is

100*sin60+10*sinl80+10*sin300+5*sin420

This waveform is decomposed using DWPT up to level 3. The sampling frequency is

1920 Hz. The decomposition exactly follows the Table 3.1 and Fig 3.5.

Table 4-3 RWE in each various frequency bands


Frequency band Relative Wavelet Energy
Hz


0-120 0.9745


120-240 0.0157


240-360 0.0070


360-480 0.0022


480-600 0.0006


600-720 0.0001


720-840 0.0000


840-960 0.0000









4.5.2 Wavelet Energy in Time Domain

In order to define useful quantifiers it is very important to study the temporal

evolution of the signal. The analyzed signal is divided into non overlapping windows of

length L. Thus, the number of time windows for the signal is give by (14)

Number of time windows, N t= (Total length of the analyzed signal)/ L.

The mean wavelet energy at resolution level j for time window i is given by:

1 L
E 1 | C,(k) 2
/ k=(I 1)L+1

Where N represents the number of wavelet coefficients at the resolution j in the time

interval i. Then the total mean energy at this time window is given by

E tot= L (')


The relative energy in time domain is given by


Pj t) E(j)'
Etot'

The following table shows the RWE in time domain for a pure 60 Hz sine wave

which is analyzed from 0 to 1 second. The sine wave is decomposed to level 3 using

DWPT with coif 5 filter bank. The total number of coefficients after decomposition at

level 3 is 265, which in fact gives us the length of the signal under consideration. The

window length, L is taken to be 33 and thus N t= 8 (rounded off to nearest integer). The

energy for a pure sine wave is evenly distributed throughout in its time domain. But, this

will definitely change when there is a sine wave with harmonics and swell or time

varying harmonics. The energy will be concentrated at the time instant where swell/sag

occurs and thus it can be easily distinguished.









Table 4-4 RWE in various time divisions


Time Interval Relative
sec) Wavelet Energy


0-0.1245 0.1129


0.1245- 0.2490 0.1288


0.2490- 0.3735 0.1233


0.3735-0.4980 0.1288


0.4980-0.6225 0.1233


0.6225-0.7470 0.1288


0.7470-0.8715 0.1233


0.8715-0.9961 0.1308


4.6 Wavelet Energy Based Harmonic Detection and Classification

The following section proposes a new methodology to detect and classify the

presence of harmonics in a power system. Various types of harmonics are usually found

in power systems. They could be broadly classified as

1. Regular harmonics: periodic-odd, even, inter-harmonics.
2. Amplitude varying harmonics with respect to time
3. Frequency varying harmonics with respect to time.
4. Sub-harmonics
5. Harmonics with sags and swells.









There is a need to detect harmonics which occur with additional PQ events. This

can help engineers in designing appropriate mitigation techniques for PQ. This can be

achieved using scalograms.

Scalogram is a plot of time-frequency-energy. It is analogous to spectrogram,

which is a plot of energy density surface of the short time Fourier transforms. To put, in

simpler terms, scalogram is a plot of squared magnitude of the wavelet transform values.

The scalogram surface highlights the location and scale of dominant energetic features

within the signal.

Using DWPT, the signal under consideration is decomposed into coefficients at

various bands. The energy of the signal at each band can be found out by squaring and

summing all the coefficients as explained in section 4.5. The following is the procedure

to be followed when plotting scalograms.

1) Using DWPT, decompose the signal under consideration into different resolutions
(levels). The energy in each node can be calculated using the procedure described
in section 4.4. The maximum level a signal can be decomposed is given by 2 log
(M). Where, M is the discretized length of the signal under consideration. Let the
Energy in each band is given by E (i)

2) Using DWPT, decompose an ideal 60Hz pure sine wave into the same number of
levels as for the above mentioned signal. Let the Energy in each band is given by
El (i)

3) The deviation of the signal from ideal behavior is found out by taking the squared
difference of the energies of the above two signals as shown below:Deviation in
Energy= (E (i)-E1 (i)) 2

4) A plot between nodes in a particular decomposition level with the 'Deviation in
Energy' is a scalogram in frequency domain.

The plot obtained from the above procedure exactly identifies the additional

frequencies present in the system. Consider a sine wave with the following equation. For










t=0 to 1 seconds with sampling frequency 1920Hz. Each band has a width of 120 Hz

Therefore; the maximum frequency in the 8th band is 860.


2 3 4 5 6 7
Frequency bands


Figure 4-2: Identification of 3rd harmonic and its deviation from ideal behavior using
frequency scalogram.

To detect and classify the presence of additional PQ events along with harmonics

there is a need to draw a scalogram in time domain. This will aid in detecting any other

PQ events occurring with harmonics or even if the harmonics are amplitude changing or

frequency changing with time. This is extremely useful in detecting harmonics with

sags/swells, amplitude varying harmonics and frequency varying harmonics.

Advantages:

1) This is very handy in PQ instrumentation as it has the capabilities of classifying
the PQ events.

2) The squared deviation of energy gives how much the wave is distorted and the
deviation from ideal behavior.









3) While implementing in a Digital Signal Processor (DSP), automatic detection can
be done using simple pattern recognition algorithm (1".

4) This can be used for both PQ classification and detection.

5) In fact, the above energy deviation can also be called an 'index'. Though an
unconventional index that is measured/calculated using graphs.

4.7 Signal Energy Distortion

A more conventional index based on the above principle is presented in this

section. This index, which we call, signal energy distortion (SED) tries to condense the

information of a signal under analysis into a single number.

The signal energy distortion is given by

SED=_ (P (i)-P1 (i))

where

i is the number of nodes in decomposition level j.

or, Max number of harmonics present

P=RWE in each node for a signal under consideration.

P1=RWE in each node for a pure 60Hz sinusoidal wave.

The above index gives the deviation in frequency domain of a sine wave from a pure

60Hz sine wave.

To capture time domain information, the following formulae are very helpful:

DEV time (i) P (i)-P (i+l)

If DEV time (i) = 0 for all i, then harmonics not varying with time

else,

SED time (i) = P (i) P1 (i), gives the deviation due to additional PQ events occur.

While, SED gives the distortion in the waveform under consideration, SED time gives the

time instant or time range where additional PQ events along with harmonics took place.









In other words, SED time is extremely helpful to capture the PQ events which occur along

with harmonics. There are instances where it has been observed that 2 or more PQ events

take place simultaneously. PQ monitoring for over 6 months of time at the Dairy

Research Unit (DRU) for a period of 6 months by the Power Quality Laboratory at the

University of Florida reinforces the same fact. It is very common to see:

* Harmonics along with sags and swells.
* Frequency changing harmonics with time
* Time varying harmonics.

Advantages:

1. It is applicable for periodic waveforms.

2. It accelerates with frequency i.e. it gives weightage according to effect of a
particular frequency component on frequency component.

3. It gives time domain information regarding additional PQ events occurring with
Harmonics.

4. Obtaining a value more than 100% distortion is not possible unlike, THD.

5. A fresh look at the problem instead of traditional THD and its variants.

This index is critically evaluated and tested on all permutations of test cases in next

section.















CHAPTER 5
CRITICAL EVALUATION OF THE PROPOSED METHOD

A detailed theoretical idea to the methodology proposed to classify and detect

harmonics was presented in the last chapter. Furthermore, a novel index based on the

same methodology was also proposed. The index proposed in this thesis is critically

evaluated in this chapter. It is an undeniable fact that the veracity of any theory proposed

in an engineering field has to be proven by extensive testing under various conditions.

The methodology proposed in this thesis is tested under simulated conditions. Using

MATLAB a variety of cases are generated and tested on the various algorithms

developed.

5.1 Test Cases

To evaluate the indices proposed, various test cases were generated using

MATLAB. The following are the test cases:

1. Periodic cases
Odd and even harmonics, inter-harmonics, sub-harmonics.
2. Aperodic cases
Harmonics with additional PQ events such as sags/swells
Time varying harmonics amplitudess of harmonics that change with time)
Frequency varying harmonics (harmonics with different frequencies at
different instances of time)

All these test cases were generated in MATLAB. The algorithms were developed using

'Wavelet Tool Box' in MATLAB.

5.2 Detection and Classification of Harmonics

Wavelet Energy based detection and classification was introduced formally in

section 4.6. Also, a systematic procedure required to draw scalograms was explained.










Furthermore, scalogram based detection and classification was also demonstrated with

examples. In the present chapter, this methodology is thoroughly investigated with the

following test cases. In all the test cases the following frequency ranges were used:

Table 5-1: Frequency bands corresponding to DWPT nodes at level 3 decomposition


Node Frequency Range Center Frequency
Hz. Hz.
1 0-120 60
2 120-240 180
3 240-360 300
4 360-480 420
5 480-600 540
6 600-720 660
7 720-840 780
8 840-960 900

In all the test cases the following time windows were used

Table 5-2: Time ranges corresponding to the time windows of each node decomposed


Time Window Time Range Time instant
Seconds (average) Seconds.
1 0-0.1 0.05
2 0.1-0.2 0.15
3 0.2-0.3 0.25
4 0.3-0.4 0.35
5 0.4-0.5 0.45
6 0.5-0.6 0.55
7 0.6-0.7 0.65
8 0.7-0.8 0.75
9 0.8-0.9 0.85
10 0.9-1.0 0.95


5.2.1. Periodic Test Cases

5.2.1.1 Waveform with regular harmonics i.e.

Test conditions:

Waveform: 110sin60+ lsinl80+1 lsin300


odd and even harmonics











Sampling frequency=1920Hz

Decomposition level=3

Number of nodes =2 -8.


Frequency in each band= 0-120 Hz in first band and so on till 860Hz in 8t band.


x10'



















Figure 5-1 (a) X-axis Frequency bands (1-8) Y-axis Squared Energy Deviation, 5.1 (b)
X-axis: Time intervals (1-10) Y-axis Squared Energy deviation
5.2.1.2 Explanation
SI042 I _
10 - --- I I -






5.2.2.1 Har nics with sags and



























Test conditions are the same as above i.e. 5.2.1.alThe following is the equation of
t= to 0.6 seconds; X= 110sin60+10sin-- --80








t= 1 0.6 to 0.8 seconds X=140sin60+10sin80 1 2 3 4 5 1
5.2.1.2 Explanation




















the waveform

t0 to 0.6 seconds; X- 110sin60+10sinl80


t-0.6 to 0.8 seconds; X=140sin60+10sinl80












t=0.8 to 1 seconds; X=110sin60+10sinl80.


x 10 x 10







III









Fig 5.2 (a) Fig 5.2 (b)
9 2 3 4 5 6 7 182 3 4 5 6 719 10





Figure 5-2 (a) X-axis Frequency bands (1-8) Y-axis Squared Energy Deviation 5.2 (b) X-
axis: Time intervals (1-10) Y-axis Squared Energy deviation


5.2.2.2 Explanation


In the 'frequency-energy deviation' scalogram, the deviation in 2nd band can be


clearly seen. The central frequency of 2nd band is 180Hz. But this does not show that


there is a swell. Time-Energy scalogram is useful here. There is a deviation in time


domain at 7h 8th interval i.e. from 0.6 seconds to 0.8 seconds and the energy is also


positive. This indicates that there is a swell from 0.6 to 0.8 seconds. Thus, by using a very


simple pattern recognition algorithm one can classify harmonics.


5.2.2.3 Amplitude varying harmonics


Test conditions are the same as above. The waveform under consideration is as


follows:


Time, tl=0 to 0.6 seconds; xl1=110sin60


t2=0.6 to 0.8 seconds; x2=1 10sin60+30sin180


t3=0.8 to 1.0 seconds; x3=110sin60+60sinl80.
a _ -i- _ _ _ i _
35 | -- | 4 | _
7 _ _ _ _ _
6 __ _ _ _ _ 3 _ ._ __ _ _ _ _
5 _ _ _ _ _ _
15 | + |- | -
4 _ _ _ _ _
3 I_ _ _ 1 _ _ _ _



















































t3=0.8 to 1.0 seconds; x3=110sin60+60sinl80.







44



10'_600 - - - - -0- --- - - -
S100

4-0-- I I I 4- -1
L5.2 4 EI I I 3 4 4
6 0-0 I I I - -_- -

4 2 I I I 1
42 -_ -_ i i-- I I I 0 v i 1










Fig 5.3 (a) Fig 5.3 (b)
Figure 5-3 (a) X-axis Frequency bands (1-8) Y-axis Squared Energy Deviation 5.3 (b) X-
axis: Time intervals (1-10) Y-axis Squared Energy deviation

5.2.2.4 Explanation

In the 'frequency-energy deviation' scalogram, the deviation in 2nd band can be


clearly seen. The central frequency of 2"d band is 180Hz. Furthermore, there is a


deviation in time domain at 6 7h 8 9th interval i.e. from 0.6 seconds to 0.8 seconds


and the energy is also increases with increasing harmonic amplitude. This indicates that


amplitude varying harmonics are present.


5.2.2.5 Frequency Harmonics with respect to time.

Test conditions are the same as above i.e. 5.2.1.al


The following is the equation of the waveform


t=0 to 0.5 seconds; X= 110sin60+30sin420


t=0.5 to 0.8 seconds; X=110sin60+30sin300


t=0.8 to 1 seconds; X=110sin60+30sin300.











x 10s 3x 1

I I I5 I
35 I 7 - -






5--------- ---- --- --
7 I I I I I3 4 5 I 710














axis: time intervals (1-10) Y-axis squared energy deviation

5.2.2.6 Explanation

In the 'frequency-energy deviation' scalogram, the deviation in 3rd and 4th bands

can be clearly seen. The central frequencies of 3rd and 4tb band are 300Hz and 420 Hz.


respectively. Furthermore, there is a deviation in time domain at 6thand 9b interval i.e. at

0.6 seconds and 0.8 seconds. This indicates that frequency varying harmonics are present

and the time instant at which it takes place can also be captured.












mentioned in section 4.1.

5.3.1. Periodic Test Cases

5.3.1.1 Waveform with regular harmonics i.e. odd and even harmonics

Test conditions:


Sampling Frequency=1920Hz
3 V I _
5 I I I _ _ _I__ _






I II I I II




Figure 5-4 (a) X-axis frequency bands (1-8) Y-axis squared energy deviation 5.4 (b) X-
axis: time intervals (1-10) Y-axis squared energy deviation

5.2.2.6 Explanation

In the 'frequency-energy deviation' scalogram, the deviation in 3rd and 4h bands

can be clearly seen. The central frequencies of 3rd and 4h band are 300Hz and 420 Hz.

respectively. Furthermore, there is a deviation in time domain at 6t and 9 interval i.e. at

0.6 seconds and 0.8 seconds. This indicates that frequency varying harmonics are present

and the time instant at which it takes place can also be captured.

5.3 Signal Energy Distortion

Signal energy distortion (SED) condenses the information of a waveform under

analysis into one number. This idea behind the index and its advantages were mentioned

in the previous chapter. In the current chapter it is tested under various test conditions

mentioned in section 4.1.

5.3.1. Periodic Test Cases

5.3.1.1 Waveform with regular harmonics i.e. odd and even harmonics

Test conditions:

Sampling Frequency=1920Hz









Decomposition Level=3

Number of nodes =2 3


Frequency in each band= 0-120 Hz in first band and so on till 860Hz in 8' band.

Table 5-3: Comparison between THD and SED for various waveforms

Waveform THD SED DEV SED (time) Comments
% % time %

t=0 to 1 seconds 14.14 1.91 Not No Additional PQ
110sin60+1 lsin740+1 lsin420 Required events


t=0 to 1 seconds 14.14 1.87 -do- No change in THD
110sin60+1 lsin300+1 lsin420

THD not applicable
t=0 to 1 seconds N.A 1.90 -do- for interhamronics
110sin60+1 lsin433+1 lsin515


5.3.2. Harmonics with additional PQ events

Test conditions:


Sampling Frequency


1920Hz


Decomposition Level=3


Number of nodes


2 3 8.


Frequency in each band= 0-120 Hz in first band and so on till 860Hz in 8t band.









Table 5-4: Performance of SED for harmonics with additional PQ events


Waveform SED DEV time SED(time) Comments


Additional PQ events
t=0 to 0.6 seconds found in 6th and 7th
X= 110sin60+10sinl80 time window

t=0.6 to 0.8 seconds 7h and 8h time SED7=4.11 The deviation of
X=140sin60+10sinl80 6.22 window signal from ideal
SED behavior is given by
t=0.8 to 1 seconds 8=4.08 SED(time)
X=110sin60+10sinl80.



Additional PQ events
t=0 to 0.6 seconds found in 7th and 9th
X= 110sin60 time window

t=0.6 to 0.8 seconds 7th and 9th time SED7=1.36 Amplitude varying
X=110sin60+30sinl80 7.32 window harmonics is found
SED
t=0.8 to 1 seconds i.e. it tracks 9=3.12
X=l10sin60+60sinl80. time instant
where the
change energy
takes place

t=0 to 0.6 seconds
X= 110sin60+30sin420 6th and 7th time SED6=0.22 Frequency varying
window. SED7=0.33 harmonics were
t=0.6 to 0.8 seconds; found.
X=110sin60+30sin300 6.83 Their deviation in
time domain is found
t=0.8 to 1 seconds to be less. As
X=l 10sin60+30sin300. harmonics change
form 420 to 300.















CHAPTER 6
EPILOGUE

6.1 Conclusions

The energy deviation based index and harmonic classification methodology

proposed is extremely handy for PQ instrumentation. The proposed index has been

shown in chapter 5 to be far better than THD. It overcomes the limitations posed by THD

and it is more apt for PQ than THD.

Furthermore, the unique ability of SED to give time domain information and

knowledge about additional PQ disturbances, present along with harmonics, is extremely

helpful for developing appropriate PQ mitigation techniques. Also, the algorithm

proposed for this approach is extremely robust and fast. This algorithm can be

programmed on a Digital Signal Processor (DSP) and can be used for real time

monitoring of PQ.

The proposed index has many advantages over traditional variations of THD

suggested by various researchers. One achievement of the proposed index is that it does

not suffer from THD mindset. The index proposed satisfies all the basic electrical

engineering principles and quantifies the harmonic distortion using the energy content of

the signal.

In summary, the advantages of the new index and classification methodology

proposed are as follows:

* It gives deviation in both frequency and time domain.









* A single algorithm detects, classifies and quantifies harmonics present in a power
system.

* The proposed algorithm is fast, robust and easy to implement in a DSP.

* It is suitable for real-time monitoring.

* It is suitable for periodic signals and gives weightage to higher frequency
components depending upon the signal deviation it causes.

6.2 Further Work

Signal Energy Distortion (SED) as a measure of harmonics present in a system has

been proposed and supported in this thesis through simulations. This idea (methodology)

can to be implemented in a DSP. It requires any where between 3-4 months to implement

this idea in a DSP board.

The suggested pattern recognition algorithm has to be developed. This has to be

developed prior to implementation of the proposed methodology in a DSP.

Furthermore, empirical testing should be done for a long period of time so as to

find out what value of SED is bad for the distribution system or transmission system.

THD is used as a linearity indicator in microelectronic circuits, it posses several

problems in electronic circuits as well. A study about its drawbacks and the possible

application of SED to it should be studied in detail.

Shannon's Entropy gives a measure of order/disorder of the signal (14). This can

give us the deviation of an analyzed signal from a pure 60Hz sine wave. This has to be

further investigated and studied in detail as it gives a number for distortion. This is used

as a distortion indicator in the field of communications and signal processing. Its

application for power quality has to be exploited in detail.









6.3 Afterpiece

This thesis is an attempt towards achieving better PQ indices or possibly one index

which can sum up all the information in a single number. There is a tradeoff here: More

the preciseness of information we are looking for, lesser the clarity. In other words, the

ambiguity of the index increases with increasing information one is seeking to get.

There is an urgent need among the researchers and engineers throughout the world

to debate the pros and cons of the existing indices. Although, a need for new PQ indices

has been identified by A. Domijan, G.T. Heydt and others back in 1993. There has been

little work in this direction and even the debate started by them is abating slowly. Joseph

Joubert said

"It is better to debate a question without settling it than to settle a question without
debating it."

I am in full agreement with him. It is better to have a debate on PQ indices even

without settling to one. It is often difficult to come up with an index in a short period of

time yet, a debate in this direction would make engineers more aware of the pitfalls of the

indices while applying them.
















LIST OF REFERENCES


1. Dugan R.C., McGranaghan M.F., Beaty H.W., Electric Power Quality, McGraw-
Hill, New York, 1996.

2. Domijan A., Heydt G.T., Meliopoulos A.P.S., Venkata S.S., West S., Directions of
research on power quality, IEEE Transactions on Power Delivery 8(1), 1993, 429-
436.

3. Addison P.S., The Illustrated Wavelet Transform Handbook: Introductory Theory
and Applications in Science, Engineering, Medicine and Finance, IOP Publishing,
Ltd, Bristol, 2002.

4. Goswami J.C., Chan A.K., Fundamentals of Wavelets: Theory, Algorithms and
Applications, John Wiley & Sons & Inc, New York, 1999.

5. Hamid E.Y., Mardiana R., Kawasaki Z.I., Wavelet-based compression of power
disturbances using the minimum description length criterion, IEEE Power
Engineering Society Summer Meeting 2002, Volume 3, 2001, 1772-1777.

6. El-Saadany E.F., Abdel-Galil T.K., Salama M.M.A., Application of wavelet
transform for assessing power quality in medium voltage distribution system,
Transmission and Distribution Conference and Exposition, 2001 IEEE/PES,
Volume 1, 2001,

7. Pham V.L., Wong K.P, Antidistortion method for wavelet transform filter banks
and nonstationary power system waveform harmonic analysis, IEE proceedings
Generation, Transmission and Distribution, 148 (2), 2001,

8. Jensen A, La-Cour Harbo A, Ripples in Mathematics- The Discrete Wavelet
Transform, Springier Verlag, Berlin, 2001.

9. Heydt G.T, Jewell W.T, Pitfalls of electric power quality indices, IEEE
Transactions on Power Delivery, 13 (2), 1998, 570-578.

10. Beaulieu G, Bollen M.H.J, Malgarotti S, Ball R and other CIGRE working group
36-07 members, Power quality indices and objectives ongoing activities in CIGRE
WG 36-07, IEEE Power Engineering Society Summer Meeting 2002, 2(21-
25),789-794.

11. Heydt G.T., Problematic power quality indices, IEEE Power Engineering Society
Winter Meeting, 4, 2000, 2838-2842.






52


12. Domijan A., Shaiq M., A new criterion based on the wavelet transform for power
quality studies and waveform feature localization, ASHREA Transaction, 104,
1998, 3-16.

13. Gruzs T.M., Uncertainties in compliance with harmonic current distortion limits in
electric power systems, IEEE Transactions on Industrial Applications, 27(4), 1991,
680-685.

14. Rosso O.A., Blanco S., Yordanova J., Kolev V., Figlioa A., Schurman M., Basar
E., Wavelet entropy: A new tool for analysis of short duration brain electrical
signals, Journal of Neuroscience Methods, 105, 2001, pp-65-75.

15. Gaouda A.M., Salama M.M.A., Sultan M.R., Chikhani A.Y., Power quality
detection and classification using wavelet multi-resolution signal decomposition,
IEEE Transactions on Power Delivery, 14(4), 1999, 1469-1475.
















BIOGRAPHICAL SKETCH

Ajay Karthik Hari obtained his Bachelor of Technology degree in electrical and

electronics engineering from Jawaharlal Nehru Technological University (JNTU), India,

in June 2001. While working on his bachelor's degree, he was secretary of Electrical

Technical Association (ETA). Starting from fall 2001, he is pursuing the Master of

Science degree in electrical and computer engineering at the University of Florida. His

research interests include advanced signal processing, power quality and power ICs. His

other interests include politics, current affairs and quizzing. He was a member of Youth

Parliament team in India, which won first prize for the year 1994.