Journal of Electrical Engineering & Technology, ol., No. 3,. 4~47, 4 Uncertainty Analyi in Potential Tranformer Caliration Uing a High oltage Caacitance Bridge Jae Ka Jung, Sang Hwa Lee*, Jeon Hong Kang*, Sung Won Kwon* and Myungoo Kim* Atract Precie aolute meaurement of the error in a otential tranformer (PT) can e achieved uing high voltage caacitance ridge (HCB) and caacitive divider. The uncertainty in a PT meaurement uing the HCB ytem wa evaluated y conidering the overall factor affecting during the caliration of a PT. The exanded uncertaintie are found to e not more than 3-6 for ratio and 3 μrad for hae u to the rimary voltage of = k. For ame PT, the meaured error in KRISS (Korea Reearch Intitute of Standard and Science) uing our ridge are well coincide with thoe in NMIA (National Meaurement Intitute of Autralia) and PTB (Phyikalich-Techniche Bundeantalt) within the correonding uncertaintie. Keyword: High oltage Caacitance Bridge, Potential Tranformer, Ratio Error, Phae Dilacement, Uncertainty, PT Comarator, Caacitor. Introduction Potential tranformer (PT) are normally ued in the ower indutry for high voltage and ower lo meaurement [ 3]. The mot widely ued method for calirating PT in the caliration laoratory i one in which the PT under tet i comared to a tandard PT having the ame nominal ratio [4-5]. The error of the PT under tet are meaured uing a PT comarator y comaring it value with thoe of a tandard tranformer of higher accuracy. The aolute error of PT under tet i otained y adding the aolute error of a tandard PT to the error meaured y a PT comarator. One of effective method for meauring aolute error of a tandard PT utilize the high voltage caacitance ridge (HCB). Thi method can e oile to etalih the traceaility chain to the national tandard. Thu, national metrology intitute (NMI) have erformed the PT caliration uing HCB u to now [6-]. A caliration ytem of a tandard PT in KRISS ha een et u recently. The ytem conit mainly of HCB, high voltage (H) caacitor and low voltage (L) caacitor. The uncertainty in a tandard PT meaurement uing HCB i analyzed y conidering the whole oile effect during the caliration of PT. Eecially, the uncertainty contriution due to the linearity of HCB dial and the error of the PT urden are etimated y the analyi of a PT equivalent circuit. For the validity check of the PT caliration ytem uing the HCB ytem, exerimental Correonding Author: Korea Reearch Intitute of Standard Science, Korea (jkjung@kri.re.kr) * Korea Reearch Intitute of Standard Science, Korea Received 7 Novemer, 6 ; Acceted Feruary, reult of the PT meaured in KRISS uing our ytem are comared with thoe meaured in NMI.. Analyi of Pt Equivalent Circuit An equivalent circuit for a PT with a zero urden i hown in Fig. [6, ]. in Fig. i the leakage outut imedance of the econdary of the PT, written a = R + j. The comlex ratio of the rimary voltage vector ( ) to the econdary voltage vector ( ) of the PT i given y [6, ] = N α ) e ( where N i the rated tranformation ratio. α and β are ratio error and hae dilacement, reectively, at a zero urden. Fig.. An equivalent circuit for a PT with a zero urden. ()
4 Uncertainty Analyi in Potential Tranformer Caliration uing a High oltage Caacitance Bridge We now conider the effect of the external urden on the ratio error and hae dilacement of the PT. An equivalent circuit for the PT with an external urden,, i hown in Fig. [6, ]. The PT urden conit of a erial connection of the reitance and the inductor, exreed a. = R + j The comlex ratio of the rimary voltage vector ( ) to the econdary voltage vector ( ) of a PT with an external urden i given y By taking the real art of eq. (6), we can otain the ratio error with the external urden a follow. R α = α + ( α ) R + R ( α ) β R (7) = N( α ) e () We otain the hae dilacement having the external urden y taking the imaginary art of eq. (6), a follow. where α β i ratio error and hae dilacement, reectively, with the external urden. Equating the current aing through and, a hown in Fig., we otain a follow. β = kβ k R R + kβ R, R α. (8) k = α = (3) Thi can e rewritten in the following form: = + + (4) Eq. (4) can e changed into eq. (5) uing eq. () and (), a: = j β + α ) e ( α ) e (5) ( 3. Caliration Method of Pt in Hvc Sytem The caliration of the PT uing the HCB comrie two te rocee []. The ridge i the firt ued to etalih the ratio etween L caacitor (C L ) and H caacitor (C H ) under a few hundred voltage. In the firt te, C L and C H were connected to N x and N winding of ridge, reectively. The econd te of the roce i to exchange the connection of the two caacitor to the ridge winding and aly the two voltage whoe ratio i to e determined to the aroriate caacitor. The detail of the rocee and meaurement rincile are well decried in the reviou aer [6, 8, 9]. In the caliration of the PT y the HCB, the comlex ratio of the actual rimary voltage for actual econdary voltage of the PT in two te rocee i given y CL N = ( ) ( ) ( jd) C N (9) H x = N RCF( ) = N( α)( ) Fig.. An equivalent circuit for a PT with a urden,. In the cae of the normal PT within. cla, the oth value of β and β were le than.5 crad. Thu the quadratic and higher order term in the exonential erie of eq. (5) were neglected. Eq. (5) can then e converted into eq. (6) a: ( α)( ) = ( α j )( β) + R + + j j (6) D i the diiation dial etting value of caacitor under tet correonding to the hae dilacement ( β ) of a PT under tet. (C L /C H ) and (N /N x ) are ratio dial etting value otained from the firt and the econd te of meaurement, reectively. (C L /C H ) (N /N x ) correond the actual meaured tranformation ratio, N a, of tranformer under tet. The RCF i the ratio correction factor defined a the actual tranformation ratio divided y the rated tranformation ratio. Therefore ratio error and hae dilacement of the PT under tet are otained from the two te meaurement in the HCB.
Jae Ka Jung, Sang Hwa Lee, Jeon Hong Kang, Sung Won Kwon and Myungoo Kim 43 4. Uncertainty Evaluation The individual contriution of the uncertainty factor affecting in the meaurement of the error of the PT uing the HCB ytem are calculated a follow. 4. Reeated Meaurement The A-tye uncertainty due the reeated meaurement i given ( δ i δ ) where δ i i the meaured ratio u = A n( n ), error or hae dilacement, δ i the average value, and n i the meaurement numer. 4. Linearity of HCB Dial A linearity of the HCB dial can e checked y emloying the non-reactive PT urden. We ue the nonreactive urden with the negligile AC-DC difference le than -5 ( =). The value of β in PT under tet i.74 mrad and then lat term in eq. (7) and (8) are neglected. Thu, the eq. (7) and (8) can e written, reectively, a follow. α α + ( α ) R ( ) () R β β ( ) () R where the value of α, β, R and are contant at a fixed voltage. Both the ratio error and hae dilacement with the external urden are then roortional to recirocal of the reitance of the nonreactive urden, (/R ). Conequently, y lotting α and β a a function of /R, we can evaluate the linearity of ratio error and hae dilacement meaured in the HCB dial. The exerimental reult of urden effect on ratio error i hown in Fig. 3. Fig. 3 i meaured reult for the rated tranformation ratio of 33 : at the econdary voltage of 85. The inet of Fig. 3 i meaured reult for the rated tranformation ratio of 55 : at the econdary voltage of 3. The two olid line fitted y eq. () in Fig. 3 how good conitency with the meaurement reult within -6 for the ratio error range of -39-6 -66-6 and 334-6 888-6. Ratio Error in m 5 5 Ratio Error in m - - -3 / : 55 / = 3... /R (Ω) / : 33 / = 85...4.6.8. /R (Ω) Fig. 3. A change of ratio error a a function of reitance of non-reactive urden. The external urden effect on hae dilacement are rereented in Fig. 4. Fig. 4 i meaured reult for the rated tranformation ratio of 33 : at the econdary voltage of 85. The olid line fitted y eq. () in Fig. 4 how good conitency with meaurement reult within μrad for the hae dilacement range of -8 μrad 6 μrad. Therefore, the uncertainty due to a linearity of HCB dial i written a u = ( ) / 3 = 5.8. B Phae dilacement (μrad) - - / : 33 / = 85-3...4.6.8. /R (Ω) Fig. 4. A change of hae dilacement a a function of reitance of non-reactive urden. 4.3 Change of the PT Burden A hown in eq. (7) and (8), oth the ratio error and the hae dilacement of the PT deend directly on the conductance and the ucetance of the PT urden. Thu, an error of % in the meaurement of the PT urden caue the uncertainty of % in oth ratio and hae. Thi mean the uncertainty (u B ) of the PT due to the urden error i given a ub = ( ) / 3 =.6 in the cae of. % cla PT.
44 Uncertainty Analyi in Potential Tranformer Caliration uing a High oltage Caacitance Bridge 4.4 HCB Caliration The ratio dial etting in the HCB were calirated y comarion with a cale of lo-le ga dielectric caacitor which were trimmed to exact ratio uing a elfvalidating uild-u technique []. The diiation dial etting were checked y injecting a calirated quadrature current into the ridge in arallel with that from a F caacitor at / ratio. The uncertainty (u B3, r ) in the ratio dial meaurement wa le than 5-6 u to ratio. The uncertainty (u B3, ) in the diiation factor dial meaurement wa not more than ±.5 % of the dial indication. 4.5 oltage Coefficient (C) of H Caacitor High voltage caacitor of comreed ga tye have a voltage deendence of it caacitance due to the dilacement of the electrode and the reure-veel effect [3]. We have meaured a C of F caacitor of 3 k rated voltage againt a reference F caacitor of k rated voltage having a negligile C. Fig. 5 how the voltage deendence for F caacitor. The change in the caacitance of comreed ga caacitor increae exonentially with the alied voltage. The olid line in Fig. 5 i fitted a Δ with a =.77 - C = a C x x and =.63. The tandard uncertainty (u B4 ) due to the C of high voltage caacitor i then given a.63 = (.77 ) / 3. u B 4 ΔC/C in art er million 3 5 5 Alied oltage () Fig. 5. Relative caacitance variation with the change of the alied voltage. 4.6 Reolution of HCB Dial The reolution of the HCB i -6 in oth ratio and hae meaurement. The uncertainty (u B5 ) due to the reolution i then written a u B5 = / 3 =.9 y conidering roaly a rectangular ditriution., 4.7 Change of Secondary oltage of PT Under Tet The uncertainty (u B6 ) due to an error of % of the rated econdary voltage can e written a δ δ, where δ ub6 = i the ratio error or 3 hae dilacement at firt econdary voltage, δ i the ratio error or hae dilacement at econd econdary voltage, i the firt econdary voltage, i the econd econdary voltage, and i the rated econdary voltage. 4.8 Change of Alied Frequency at 6 Hz The uncertainty (u B7 ) due to an error of % at 6 Hz can e given a δ δ 6 u 7 =, where δ B i the f f 3 ratio error or hae dilacement at firt frequency, δ i the ratio error or hae dilacement at econd frequency, f i the firt frequency, and f i the econd frequency. 4.9 Change of Temerature of Caacitor The temerature coefficient of the two caacitor wa not more than 3-6 / according to the manufacturer ecification. We aume the change of the temerature during the meaurement i within ±.5 and the uncertainty (u B8 ) due to the change of temerature i then otained y conidering roaly a rectangular ditriution a u B8 = (5 ) / 3 = 8.7. The individual uncertainty contriution otained from the uncertainty analyi for the cae of / = 66 / Tale. Summary of ignificant factor contriuting to the uncertainty in the PT caliration for the cae of / = 66 /. Source of uncertainty α (art in -6 ) β (μrad) Reeated meaurement, u A Linearity of HCB dial, u B Change of PT urden, u B HCB caliration, u B3 C of H caacitor, u B4 Reolution of HCB, u B5 Change of econdary voltage, u B6 Change of alied frequency, u B7 Change of tem. of caacitor, u B8 3. 5.8.6 5..8.3.3.4 8.7 3. 5.8.6 5..8.3..4 8.7 Comined tandard uncertainty, u c Exanded uncertainty (k =) 4 4
Jae Ka Jung, Sang Hwa Lee, Jeon Hong Kang, Sung Won Kwon and Myungoo Kim 45 are ummarized in Tale. The comined tandard uncertainty (u c ) i rereented a a root um of quare of the individual uncertainty. The exanded uncertaintie were otained y auming a normal ditriution and multilying the comined tandard uncertainty y a coverage factor of k =. The exanded uncertainty u to the rimary voltage of = k i etimated to e not more than 3-6 for ratio and 3 μrad for hae. 5. Intercomarion etween NMI To check the validity in HCB ytem, the meaured reult of the PT in our ytem are comared thoe in two NMI for ame PT. Tale i rereented the comarion of meaured reult for ame PT etween KRISS and NMIA. According to NMIA caliration certificate, the uncertaintie of the PT are not more than 3-6 for ratio μrad for hae. Meanwhile tale 3 i rereented the comarion of meaured reult for ame PT etween KRISS and PTB. The uncertaintie of the PT in PTB are 3-6 for ratio and 3 μrad for hae. Conequently, the two intercomarion reult for KRISS-NMIA and KRISS- PTB how the conitency with each other within the correonding uncertaintie. Tale. Comarion of meaurement reult for ame PT etween KRISS and NMIA ( A, 6 Hz) Rated Tranformation ratio : 44 : 55 : : : 33 : 66 : : 3 : : Secondary Ratio error (%) Phae dilacement (crad) oltage (%) KRISS NMIA KRISS-NMIA KRISS NMIA KRISS-NMIA -.6 -.6 -.3 -.4 -.3 -.3 +.3 +.9 +.3 +.7 +.3 +.7 +. +.4 +. +.3 +.3 +.3 +.5 +.9 -.5 -.5 -.5 -.4 -.5 -.4 +.5 +. +. +.6 +.3 +.6 +.8 +.3 +.3 +.4 +. +.3 +.3 +.9 +. +. +. -. +. +. +. +. +. +. +. +. +. +. +.8 +.4 +. -.3 -.4 -.3 -.5 +. -.3 -.5 -.5 -.5 +.4 +. +.3 +. +.3 +. +.6 +.3 -. -.4 -.4 -.4 -.4 +.4 -. +. -.4 -.3 -.3 -.3 -. -.3 +. +. +. +. +. +. -. -. -. 6. Concluion Two ytem for calirating the PT u to k have een uccefully et u recently in KRISS. One i comoed a the HCB and caacitive divider, a tudied already in reent aer. The other i a commercial emiautomatic ytem, which i comoed a a tandard PT and a tranformer comarator. The commercial ytem i mainly ued for calirating the PT elonging to indutry. In order to etalih the traceaility chain to the national tandard, the aolute error of the tandard PT in the commercial ytem are otained y emloying the HCB ytem. The meaurement uncertainty in the HCB ytem wa evaluated y conidering the overall factor affecting during the caliration of PT under tet. The exanded uncertaintie are found to e not more than 3-6 for ratio error and 3 μrad for hae dilacement. The meaured value for a PT uing the ridge are well coincide with thoe in NMI within the correonding uncertaintie for ame PT. Reference [] W. J. M. Moore and P. N. Miljanic, The current comarator, Peter Peregrinu Ltd., London, United Kingdom, 988.
46 Uncertainty Analyi in Potential Tranformer Caliration uing a High oltage Caacitance Bridge Tale 3. Comarion of meaurement reult for ame PT etween KRISS and PTB(5 A, coβ =, 6 Hz) Rated tranformation ratio : : 38 : 44 : 55 : : : 33 : Secondary oltage (%) 8 8 8 8 8 8 8 8 Ratio error (%) Phae dilacement (crad) KRISS PTB KRISS-PTB KRISS PTB KRISS-PTB -.3 -. -. +. -.4 -.3 -. -. +. +. +. +. +. -.9 -. -.7 -.8 -.7 -.7 -.6 -.7 -.6 -.6 -.5 -.6 -.5 -.5 -.4 -.4 -.9 -.9 -.9 -.9 -.6 -.9 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.3 -.3 +. +. +. +. +. +. [] E. B. Shim, J. W. Woo and S. O. Han, Digital Time- Domain Simulation of Ferroreonance of Potential Tranformer in the 54 k GAS Inulated Sutation KIEE International Tranaction on PE, vol. A-4,. 9-4,. [3] G. S. Choi, S. Y. Yoon, S. H. Baek and K. Yong, Power Lo Calculation of High Frequency Tranformer J. Electrical Engineering & Technology, vol., no. 3,. 338-34, 6. [4] Tettex Intrument, High Quality Meauring Intrument General Catalog,. 4-4, 999. [5] ERA GmH, Tet equiment of intrument tranformer Intruction Manual,., 4. [6] W. E. Anderon A Caliration Service for oltage Tranformer and High-oltage Caacitor" NBS Meaurement Service Secial Pulication,. 5 33, June 988. [7] G. Jone, The Traceale Caliration of oltage Tranformer NPL Secial Pulication, 994. [8] N. L. Kuter and O. Peteron, A Tranformer Ratio Arm Bridge for High oltage Caacitance Meaurement IEEE Tran. Communication and Electronic, vol. 8,. 66-6, 963. [9] Eddy So, A Microroceor-Controlled High oltage Current Comarator Baed Caacitance Bridge IEEE Tran. on Power Delivery, vol. 5, no.,. 533-537, Aril 99. [] Eddy So, Han-Georg Latzel, NRC-PTB Intercomarion of oltage tranformer Caliration Sytem for High oltage at 6 Hz, 5 Hz, and 6.66 Hz IEEE Tran. on Intrumentation and Meaurement, vol. 5, no.,. 49-4, Aril. [] J. K, Jung, S. W. Kwon, K. T. Kim, and M. Kim, A Study on Ratio Error and Phae Angle Error Caued y an External Burden in oltage Tranformer Tran. KIEE. vol. 53C, no. 3, 37 4, March 4. [] W. J. M. Moore and P. N. Miljanic, The current comarator, IEE Electrical Meaurement Serie, ol. 4, London, United Kingdom, Peter Peregrinu Ltd., 988. [3] G. Gao and D. u, Exerimental Study of the oltage Coefficient of Precie Comreed-Ga Caacitor IEEE Tran. on Intrumentation and Meaurement, vol. 4, no.,. 64-68, Feruary 993. Jae Ka Jung He received hi B. S., M. S. and h. D. degree in hyic from Korea Univerity in 99, 99 and 998, reectively. Since, he ha een worked for Korea Reearch Intitute of Standard and Science. Hi reearch interet include AC high voltage and current meaurement technique.
Jae Ka Jung, Sang Hwa Lee, Jeon Hong Kang, Sung Won Kwon and Myungoo Kim 47 Sang Hwa Lee He received hi B. S. degree in Electronic from Hanat Univerity in 994. Since 986, he ha een worked for Korea Reearch Intitute of Standard and Science. Hi reearch interet include high voltage and current caliration. Jeon Hong Kang He received hi B. S. and M. S. degree in Electrical Engineering from Hanat Univerity in 988 and 998, reectively. Since 988, he ha een worked for Korea Reearch Intitute of Standard and Science. Hi reearch interet include reitance meaurement. Sung Won Kwon He received hi B. E. degree in Electronic from Han-Gug Aviation Univerity in 974, reectively. Since 978, he ha een worked for Korea Reearch Intitute of Standard and Science. Hi reearch interet include AC voltage and current tandard. Myungoo Kim He received hi B. S. degree in Chemical Engineering from Seoul National Univerity in 977. He received hi M. S. and h. D. degree in Chemical Engineering from Miouri Univerity of USA in 983 and 986, reectively. Since 987, he ha een worked for Korea Reearch Intitute of Standard and Science. Hi current field include diemination of national tandard.