1 Chapter 10 Dgtal Dfferental Protecton of Power Transformer Usng Matlab Adel Aktab and M. Azzur Rahman Addtonal nformaton s avalable at the end of the chapter 1. Introducton Power system development s reflected n the development of all the power system devces generators, transformers wth dfferent szes, transmsson lnes and the protecton equpment. Modern power transformer s one of the most vtal devces of the electrc power system and ts protecton s crtcal. For ths reason, the protecton of power transformers has taken an mportant consderaton by the researchers. One of the most effectve transformer protecton methods s the dfferental protecton algorthm. Typcally, transformer protecton s focused on dscrmnatng the nternal faults from the magnetzng nrush currents n the power transformers and overcomng the CTs related ssues [1 5]. 2. Conventonal dfferental protecton scheme Ths scheme s based on the prncple that the nput power to the power transformer under normal condtons s equal to the output power. Under normal condtons, no current wll flow nto the dfferental relay current col. Whenever a fault occurs, wthn the protected zone, the current balance wll no longer exst, and relay contacts wll close and release a trp sgnal to cause the certan crcut breakers (CBs) to operate n order to dsconnect the faulty equpment/part. The dfferental relay compares the prmary and secondary sde currents of the power transformer. Current transformers (CTs) are used to reduce the amount of currents n such a way ther secondary sde currents are equal. Fg. 1 shows the dfferental relay n ts smplest form. The polarty of CTs s such as to make the current crculate normally wthout gong through the relay, durng normal load condtons and external faults. Current transformers ratngs are selected carefully to be matched wth the power transformer current ratngs to whch they are connected so as the CTs secondary sde currents are equal. However, the problem s that the CTs ratos avalable n the market have standard ratngs. They are not avalable exactly as the desred ratngs. Therefore, the 2012 Aktab and Rahman, lcensee InTech. Ths s an open access chapter dstrbuted under the terms of the Creatve Commons Attrbuton Lcense ( whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted.
2 220 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 prmary ratngs of the CTs are usually lmted to those of the avalable standard rato CTs. Commonly the prmary sde of the current transformer has only one turn (1) and the secondary sde has many turns dependng on the transformaton rato (N) of the CT, whch s selected to match the ratngs of the power transformer. Snce the transformaton rato of transformers s the rato between the number of turns n the prmary sde to the number of the turns n the secondary sde. Therefore, the turn rato of the prmary current transformer s and the turn rato of the secondary sde current transformer s. The secondary current of the CT located n the prmary sde of the power transformer s , ; Where: = (1) : the prmary sde current of the power transformer, : the secondary sde current of. : the number of turns n the secondary sde of In the same manner for the CT located at the secondary sde of the power transformer, the CT secondary current s: Where: : secondary sde current of the power transformer, : secondary sde current of. : number of turns n the secondary sde of = (2) SnglePhase Power Transformer N p :N s CT 1 CT Dfferental Relay = 1 2 Fgure 1. Dfferental protecton for sngle phase two wndng transformer
3 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 221 Snce the dfferental current s: =, then, from equaton (1) and equaton (2) the dfferental current flowng n the relay operatng col current can be calculated as; = (3) If there s no nternal fault occurrng wthn the power transformer protected zone, the currents are assumed equal n magntude and opposte n drecton. That means the dfferental current =0 as shown n fgure 2. The prmary and secondary sde current of the power transformer are related to each other by equaton (4); Where: = (4) and : prmary and secondary sde turns of the power transformer, respectvely : power transformer transformaton rato o 1 Fgure 2. Output currents of the CTs are equal n magntude and opposte n drecton If there s any fault n the power transformer protected zone, the currents are no longer equal n magntude and opposte n drecton. That means the dfferental current = has a sgnfcant value as shown n fgure Fgure 3. Output currents of the CTs are not equal n magntude and not opposte n drecton The amount of current = nduces the relay operatng col to operate n order to send a trp sgnal to the crcut breakers to solate the transformer. From equaton (4) the secondary current wth respect to the prmary current of the power transformer s , ; = (5) Therefore, by manpulatng equatons (3) and (5),
4 222 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 =. = 1 =1 (6) From equaton (6) t s obvous that the term must be equal to zero n order to make =0 ( 1 = (7) Equaton (7) gves the condton for the securty of the dfferental relay, whch means the recprocal of the rato of the secondary sde turns of the CTs must equal to the turns rato of the power transformer. In power transformers, the nput power s equal to the output power. However, the voltage and the current n both the prmary and secondary sdes are dfferent dependng on whether the transformer s step up or step down. For nstance, f the transformer s step up that means; the nput voltage of the power transformer s low and the current s hgh, meantme the voltage n the secondary sde s hgh and the current s low. Ths acton makes both the nput and output power equal. Due to ths nature the CTs n the prmary and the secondary sdes of the power transformer do not have same turn rato. However, they are carefully selected, n terms of turn rato and magnetzng characterstcs, so that they have the same output current at normal condtons of operatons. If dentcal CTs are not avalable, the closer ones are chosen and then the msmatch between them s compensated by usng the nterposng CTs. The nterposng CTs can fx the msmatch n the CTs; however they add ther own burden to the output of the man CTs. The same argument s appled for three phase (3) transformers, except some extra ssues may appear n polyphase transformers. Fgure 4 shows the schematc dagram of the 3 dfferental protecton. In some cases, of 3 power transformer connectons as shown n fgure 5, a 30 phase shft between prmary and secondary currents s takng place. Ths phase shft occurs n the Y or Y connected transformers due to the transformaton of the current from Y or Y as llustrated n the fgure 4. Ths phase shft can be corrected easly by connectng the CTs secondary crcuts n opposte way to the way that the power transformer phases are connected. I.e. f the transformer wndngs are connected n Y the CTs secondary wndngs should be connected n Y and vce versa . As shown n fgure 4 the relaton between the lnetolne voltage ( ) to the phase voltage ( ) can explan the phase shft between the Y transformer connecton. The followng equaton gves the relatonshp between the lnetolne voltage ( ) to the phase voltage ( ) , , , :. ) = 0
5 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 223 =. = (8) = 3 Y Fgure 4. Connecton of dfferental protecton of 3phase Y transformer c n a 30 o ½ b Fgure 5. The relatonshp between lne to lne voltage and the phase to neutral voltage and the phase shft between them whch reflects the phase shft n Y or Y connected transformers
6 224 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 3. Dfferental protecton dffcultes Generally, three man dffcultes handcap the conventonal dfferental protecton. They nduce the dfferental relay to release a false trp sgnal wthout the exstng of any fault. These complcatons must be overcome n order to make the dfferental relay workng properly , : Magnetzng nrush current durng ntal energzaton, CTs Msmatch and saturaton, Transformaton rato changes due to Tap changer Magnetzng nrush current Ths phenomenon, the transent magnetzng nrush or the exctng current, occurs n the prmary sde of the transformer whenever the transformer s swtched on (energzed) and the nstantaneous value of the voltage s not at 90. At ths tme, the frst peak of the flux wave s hgher than the peak of the flux at the steady state condton. Ths current appears as an nternal fault, and t s sensed as a dfferental current by the dfferental relay. The value of the frst peak of the magnetzng current may be as hgh as several tmes the peak of the full load current. The magntude and duraton of the magnetzng nrush current s nfluenced by many factors, some of these factors are , , ; The nstantaneous value of the voltage waveform at the moment of closng CB, The value of the resdual (remnant) magnetzng flux, The sgn of the resdual magnetzng flux, The type of the ron lamnatons used n the transformer core, The saturaton flux densty of the transformer core, The total mpedance of the supply crcut, The physcal sze of the transformer, The maxmum fluxcarryng capablty of the ron core lamnatons, The nput supply voltage level, The effect of the nrush current on the dfferental relay s false trppng the transformer wthout of any exstng type of faults. From the prncple of operaton of the dfferental relay, the relay compares the currents comng from both sdes of the power transformer as explaned above. However, the nrush current s flowng only n the prmary sde of the power transformer. So that, the dfferental current wll have a sgnfcant value due to the exstence of current n only one sde. Therefore, the relay has to be desgned to recognze that ths current s a normal phenomenon and to not trp due to ths current False trp due to C.T characterstcs The performance of the dfferental relays depends on the accuracy of the CTs n reproducng ther prmary currents n ther secondary sde. In many cases, the prmary
7 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 225 ratngs of the CTs, located n the hgh voltage and low voltage sdes of the power transformer, does not exactly match the power transformer rated currents. Due to ths dscrepancy, a CTs msmatch takes place, whch n turn creates a small false dfferental current, dependng on the amount of ths msmatch. Sometmes, ths amount of the dfferental current s enough to operate the dfferental relay. Therefore, CTs rato correcton has to be done to overcome ths CTs msmatch by usng nterposng CTs of mult taps . Another problem that may face the perfect operaton of the CTs s the saturaton problem. When saturaton happens to one or all CTs at dfferent levels, false dfferental current appears n the dfferental relay. Ths dfferental current could cause maloperaton of the dfferental relay. The dc component of the prmary sde current could produce the worst case of CT saturaton. In whch, the secondary current contans dc offset and extra harmoncs ,  False trp due to tap changer OnLoad TapChanger (OLTC) s nstalled on the power transformer to control automatcally the transformer output voltage. Ths devce s requred wherever there are heavy fluctuatons n the power system voltage. The transformaton rato of the CTs can be matched wth only one pont of the tapchangng range. Therefore, f the OLTC s changed, unbalance current flows n the dfferental relay operatng col. Ths acton causes CTs msmatches. Ths current wll be consdered as a fault current whch makes the relay to release a trp sgnal , . 4. Dgtal dfferental protecton Many dgtal algorthms have been used so far after the nventon of the computer. These algorthms do the same job wth dfferent accuracy and speed. The acceptable speed accordng to IEEE standard for transformer protecton s 100 msec. All modern algorthms are faster than ths IEEE standard. Nowadays, there are some algorthms performs ther functon n less than 10 msec. In ths chapter, a fast algorthm s ntroduced. Its speed s n the range of 1 to 15 msec. Ths algorthm s based on the Fast Fourer algorthm (FFT). Ths algorthm s not new, however, sgnfcant changes has been ntroduced to make t much faster. The proposed dgtal dfferental relay s desgned usng a smulaton technque n Matlab Smulnk envronment. The desgn s mplemented to protect the power transformer aganst nternal faults and prevent nterrupton due to nrush currents. Ths algorthm s bult on the prncple of harmonccurrent restrant, where the magnetzngnrush current s characterzed by large harmonc components content that are not notceably present n fault currents. Due to the saturated condton of the transformer ron, the waveform of the nrush current s hghly dstorted. The
8 226 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 ampltude of the harmoncs, compared wth the fundamental s somewhere between 30% to 60% and the thrd harmonc 10% to 30%. The other harmoncs are progressvely less  , . Fast Fourer Transform () s used to mplement ths approach. In general, any perodc sgnal () can be decomposed to ts sne and cosne components as follows: f(t) = a 2 C cos(kwt) S sn(kwt) Where: s the DC component of the f (t), and, are the cosne and sne coeffcents of the frequences present n (), respectvely. The dscrete forms of the coeffcents, are expressed n the followng equatons: C = 2 x(n) cos 2kwt N N S = 2 x(n) sn 2kwt N N The Fourer harmonc coeffcents can be expressed as : F = S C Where: s the harmonc coeffcent for k = 1, 2,...,N and () s the sgnal () n ts dscrete form. The produces exactly the same results as the ; however, the s much faster than DFT, where the speed of calculaton s the man factor n ths process . Fg 6 llustrates the flow chart of the desgned dgtal Fourer Transform based logc technque algorthm. In ths algorthm the output currents of the undergo over two analyss processes, ampltude comparson process and harmonc content calculaton process. The ampltude comparson between the values of the output currents ( ) s n the left hand sde of the flowchart, and the harmonc calculaton s n the rght hand sde of the flowchart. The software s mplemented accordng to the followng steps : Step 1. Readng data from the. Step 2. Data calculaton, whch s gven as follows; For the ampltude calculaton, f the absolute dfference ( ) between the output currents s greater than zero the logc (1) takes place, whch ndcates the case of an nrush current or an nternal fault. Otherwse, the logc (0) takes place, whch ndcates a detecton of an external fault.
9 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 227 START Data entry comng from C.Ts = > Id1 Id2 : 0 Calculaton of 1st & 2nd Harmoncs Detecton of external fault or ncrease of load (0) Detecton of nrush or nternal fault (1) Yes 0.3F1<F2<0.7F1 No Detecton of nrush (0) Detecton of Internal, external fault or ncrease of load (1) No Both logcs are (1) Yes Detecton of nrush or external fault Detecton of Internal fault No Trp Trp sgnal released Return to Process The next sample Stop smulaton Fgure 6. Flow chart of the proposed Dgtal Dfferental Relay Scheme
10 228 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 In the meantme, the harmonc calculaton s performed. If the percentage value of the second harmonc ampltude s n the range of (0.3 to 0.6) of the fundamental component ampltude, then the logc (0) occurs, that means recognton of nrush current. Otherwse, the logc (1) takes place, whch ndcates a detecton of an nternal or external fault. Step 3. Takng the fnal decson: If the logc cases receved from both cases (a & b) n step two are both (1), that ndcates a detecton of an nternal fault. Then a trp sgnal s released to stop the smulaton. For the other logc optons of (0,1) means an external fault, (1,0) means an nrush current, or (0,0) ndcate an occurrence of an nrush current or an external fault, and the smulaton goes back to step two to start the calculaton agan for the next sample. 5. Implementaton of the dgtal dfferental protecton usng matlab Ths mplementaton s done usng Matlab/Smulnk envronment. Fgure 7 shows the smulated power system bult n Matlab/Smulnk envronment. In whch a three phase, 250MVA, 60Hz, (735/315) kv, Y/ power transformer s used n ths system. The contents of each desgned block are llustrated n separate fgs. 8 to 12. There are some coeffcents are kept hdden for the reader to fnd them. These coeffcents can change the behavor of the desgn. Dscrete, Ts = 5e005 s. scope 1 A N B C Iabc_B2 A a B b C c CB1 A B C a b c scope 4 CTs A B C a b c Power Transformer A B C CTs A a B b C c CB2 scope 3 Iabc_B3 I1 I2 I3 I4 I5 I6 a A a1 A1 a A a1 A1 a A a1 A1 A B C fault a A a1 A1 a A a1 A1 a A a1 A1 a b c A B C 45 kw scope 5 Trp Dff. Relay scope 2 Fgure 7. Matlab/Smulnk Model of the proposed system
11 Dgtal Dfferental Protecton of Power Transformer Usng Matlab I1 2 I2 3 I3 4 I4 5 I5 6 I6 In2 In2 In2 Out1 Out1 Out1 In1 In1 In1 comparator comparator comparator 1 Trp Fgure 8. The dfferental relay block contents 2 In1 ampltude comparator IA Ia y AND 1 Out1 1 In2 Id1 Id2 y2 Harmonc Calculaton Fgure 9. The comparator block contents
12 230 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 1 IA sgnal rms u In1 Out2 Out1 Flter <= 1 y 2 Ia sgnal rms Fgure 10. The ampltude comparator block contents h1 Id1 1 magntude sgnal angle h2 z1 z2 y rato 1 y magntude sgnal angle C Fgure 11. The harmonc comparator block contents C C < 2 z2 1 z1 2 rato < y 1 < C Fgure 12. The rato block contents
13 Dgtal Dfferental Protecton of Power Transformer Usng Matlab The results and dscussons The results wll be gven for dfferent cases: Case 1: magnetzng nrush current, Case 2: magnetzng nrush wth addng load, Case 3: Three phase to ground fault at loaded transformer, Case 4: Phase A to ground external fault at loaded transformer, Other cases of dfferent types of faults and nrush currents such as sngle lne to ground fault, lnetolne fault, lne to lne to ground fault and three phase fault n both cases loaded and unloaded transformer are llustrated. Case 1: Magnetzng nrush current: In ths secton of smulaton, when the prmary sde CB1 s closed at 0.1 sec, only the nrush current flows n the prmary crcut of the power transformer and no current passes through the power transformer to the secondary sde as shown n Fg. 13. The harmonc comparator shows n Fg. 14 that the value of the 2nd harmonc s hgher than 0.3 of the fundamental component. Fgure 13. Inrush currents waveforms of the three phases at the prmary sde of the power transformer.
14 232 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 Fgure 14. Harmonc comparator result: the 2nd harmonc and the fundamental component for the 1 st case. Fgure 15. Ampltude comparator results for the 1 st case. In ths case the harmonc calculaton part released logc (0) but the ampltude comparator showed n Fg. 15 that the dfferental current s equal to the nrush current, where both curves are drown over each other, then the ampltude comparator release logc (1). For ths logc coordnaton (0,1) no trp sgnal s released.
15 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 233 Case 2: Magnetzng nrush wth addng load: Ths test s carred out after the energzaton of the power transformer by swtchng ON the CB1 at 0.1sec and CB2 at 0.3 sec from the begnnng of the smulaton to see the effect of load excurson on the accuracy of the desgned approach. Therefore, a 500W resstve load s added to the system at 0.3 sec. Consequently, the nrush current dsappeared and load current started to flow n the prmary and secondary crcuts of the transformer accordng to the transformaton rato of the power transformer as shown n Fg. 16. However, the ampltude of the output currents of the prmary and secondary CTs are equal due to the proper selecton of the transformaton rato of the prmary and secondary CTs, whch can obvously notced n Fg. 18. Where, before the tme 0.3 sec the dfferental current was equal to the nrush current, but after the swathng ON of the load the dfferental current went to zero and the prmary and secondary currants became equal. Fgure 16. Normal load current starts flowng at 0.3sec. As shown n Fg. 17, after the swtchng of CB2, the value of the 2nd harmonc become lower than 0.3 of the fundamental component. Accordngly, the harmonc calculaton part released logc (1) but the ampltude comparator released logc (0). Consequently, for ths logc coordnaton (1,0) no trp sgnal s released. Fgure 18 shows the ampltude comparator results.
16 234 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 Fgure 17. 2nd harmonc and the fundamental component for the 2 nd case. Fgure 18. Ampltude comparator results for the 2 nd case. Case 3: Three phase to ground fault at loaded transformer: In ths secton, a three phase to ground fault s created to test the securty of the algorthm. After the swtchng of CB1 at 0.1sec, an nternal fault s created at 0.5 sec at the secondary sde of the power transformer by connectng the three phases A, B and C of the secondary sde of the power transformer to the ground. In ths case, a sgnfcant ncrease of the
17 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 235 prmary current takes place due to the fault occurrence nsde the protected zone at 0.5 sec as shown n Fg. 19. The relay detected ths ncrease usng the harmonc and ampltude comparators and realzed t as an nternal fault. Consequently the transformer s solated from the grd. Also t s obvous from Fg. 20 that the relay has released a trp sgnal after 0.57 msec after the occurrence of the fault, whch can be consdered as a very good speed to solate the transformer. As shown n Fg. 21, after the occurrence of the fault at tme 0.5 sec, the value of the 2nd harmonc ncreased durng the transent tme and then decreased rapdly to a value lower than 0.3 of the fundamental component once the steady state s acheved. Accordngly, the harmonc calculaton part released logc (1). Also from Fg. 22 whch shows the result of the ampltude comparator the value of the dfferental current s no longer equal to zero. Accordngly the ampltude comparator released logc (1). Therefore, for ths logc coordnaton (1,1) a trp sgnal s released n order to solate the power transformer from the grd. Fgure 19. Increase of phase A, B & C currents due to the occurrence of the fault at 0.5 sec for loaded transformer Fgure 20. Zoomed trp sgnal, trp tme s around 0.57 msec
18 236 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 Fgure 21. 2nd harmonc and the fundamental component for the case of three phase to ground fault at loaded transformer. Fgure 22. Ampltude comparator result for the 3 rd case. Case 4: Phase A to ground external fault at loaded transformer. Ths case s smlar to case 2, where the occurrence of the fault current outsde the protected zone leaded to the ncrease of fault currents n both sdes of the power transformer. Therefore the relay consdered ths case as a sever ncrease n load currents. Fg. 23 shows the ncrease n phase A currant and no trp sgnal s released
19 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 237 Fgure 23. Increase of phase A current due to the occurrence of the fault at 0.5 sec for loaded transformer Fgure 24. 2nd harmonc and the fundamental component for the Case for the 4 th case. As llustrated n Fg. 24, after the occurrence of the external fault at 0.5 sec, the value of the 2nd harmonc decreased to a value less than 0.3 of the fundamental component. Accordngly, the harmonc calculaton part released logc (1) but the ampltude comparator released logc (0) because the dfferental current s almost zero as t can be seen from Fg. 25. Consequently, for ths logc coordnaton (1,0) no trp sgnal s released.
20 238 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 Fgure 25. Ampltude comparator result for the 4 th case. Smlarly, the relay s tested for all other cases of dfferent types of faults such as sngle lne to ground, lne to lne, lne to lne to ground and three phase faults n both cases loaded and unloaded transformer. In all cases the relay has successfully released a trp sgnal n each case. The results of some of these dfferent types of faults are shown n Fgs (26 30). Fgure 26. Increase of phase A & B currents due to the occurrence of the fault at 0.5 sec, for unloaded transformer
21 Dgtal Dfferental Protecton of Power Transformer Usng Matlab 239 Fgure 27. Increase of phase A, B & C currents due to the occurrence of the fault at 0.5 sec, for unloaded transformer Fgure 28. Increase of phase A current due to the occurrence of the fault at 0.5 sec for loaded transformer
22 240 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 Fgure 29. Increase of phase B & C currents due to the occurrence of the fault at 0.5 sec for loaded transformer Fgure 30. Increase of phase A current due to the occurrence of the fault at 0.5 sec, for unloaded transformer
23 Dgtal Dfferental Protecton of Power Transformer Usng Matlab Summary of all tested cases case type Relay response Trp sgnal release tme (m sec) Loaded unloaded Phase A to ground Trp Phase B to ground Trp Phase C to ground Trp Phase A to phase B Trp Phase B to phase C Trp Phase A to phase C Trp Phase A to phase B to ground Trp Phase B to phase C to ground Trp Phase A to phase C to ground trp Three phase to ground Trp Three phase Trp Inrush current Restran No trp sgnal Load current Restran No trp sgnal External fault Restran No trp sgnal Table 1. Summary of the performance of the desgned dfferental relay at dfferent types of dsturbances that may occur to the power transformer 8. Conclusons Ths chapter s talkng about the mplementaton and smulaton of a small power system wth a dfferental protecton for the power transformer. The mplementaton s shown n step by step. Ths smulaton s tested for varous cases and for all cases t gave satsfactory results. All the tests gave satsfactory results. There are some dffcultes are faced n the mplantaton of ths system such as the lack of some toolbox n the Smpowersystem. For example, there s no current transformer n the toolbox. In ths case, there are two choces to solve ths problem. The frst one s to use a regular sngle phase and make some changes n ts specfcaton to ft the current transformer specfcatons. The second one s to use a current measurement, but ths one wll not smulate the problems of the CTs. Author detals Adel Aktab and M. Azzur Rahman Memoral Unversty of Newfoundland, Canada
24 242 MATLAB A Fundamental Tool for Scentfc Computng and Engneerng Applcatons Volume 1 9. References  M. A. Rahman and B. Jeyasurya, A stateoftheart revew of transformer protecton algorthms, IEEE Trans. Power Delvery, vol. 3, pp , Apr  P. M. Anderson, Power System Protecton, Pscataway, NJ: IEEE Press,  C. D. Hayward, HarmoncCurrent Restraned Relays for Transformer Dfferental Protecton, AIEE trans., vol. 60, pp 276,  M. S. Sachdev, T. S. Sdhu, H. C. Wood, A Dgtal Relayng Algorthm for Detectng Transformer Wndng Faults, IEEE Transactons on Power Delver, vol. 4, No. 3. July  K. Yabe, Power Dfferental Method for Dscrmnaton between Fault and Magnetzng Inrush Current n Transformers, IEEE Transactons on Power Delvery, Vol. 12, No. 3, July  A. R. Van C. Warrngton, Protectve Relays Ther Theory and Practce, vol. 1, Chapman Hall Press, 3rd edton,  J. Duncan Glover and Mulukutla Sarma, power system analyss and desgn, PWS publshng company, 2 nd ed.,  AREVA, KBCH 120, 130, 140 Transformer Dfferental Protecton Relays Servce Manual, KBCH/EN M/G11, France,  W. Rebzant, T. Hayder, L. Schel, Predcton of C.T Saturaton Perod for Dfferental Relay Adaptaton Purposes, web ste,  A. G. Zocholl, G. Benmouyal and H. J. Altuve, Performance Analyss of Tradtonal and Improved Transformer Dfferental Protectve Relays, web ste,  Y. Marty, W. Smolnsk, and S. Svakumar, Desgn of a dgtal protecton scheme for power transformer usng optmal state observers, IEE Proceedngs Vol. 135,pt. C, No.3 May  ABB relays, Power transformer protecton applcaton gude, AG035005E,  M. A. Rahman, Y.V.V.S. Murthy and Iv Hermanto, "Dgtal Protectve Relay for Power Transformers", U.S. Patent No. 5,172,329, December  P.K. Dash and M.A. Rahman, "A New Algorthm for Dgtal Protecton of Power Transformer", Canadan Electrcal Assocaton Transactons, Vol. 26, Part 4, 1987, pp. 1 8, (87SP169),  A. Gangopadhay, M.A. Rahman, B. Jeyasurya, "Smulaton of Magnetzng Inrush Currents n Sngle Phase Transformers", Internatonal Journal of Energy Systems, Vol. 7, No. 1, 1987, pp  M.A. Rahman and A. Gangopadhay, "Dgtal Smulaton of Magnetzng Inrushes Currents n ThreePhase Transformers", IEEE Transactons on Power Delvery, Vol. PWRD1, No. 4, October 1986, pp (Over 100 ctatons)  Adel Aktab and M. A. Rahman, A Software Desgn Technque for Dfferental Protecton of Power Transformers, Internatonal Electrc Machnes & Drves Conference (IEMDC 2011), IEEE, 1518 May 2011, Page(s):