a new algorithm for three-phase power transformer di erential...

Scientia Iranica D (2014) 21(3), 904{923

Sharif University of TechnologyScientia Iranica

Transactions D: Computer Science & Engineering and Electrical Engineeringwww.scientiairanica.com

A new algorithm for three-phase power transformerdi�erential protection considering e�ect ofultra-saturation phenomenon

B. Noshad�, M. Razaz, S.Gh. Seifossadat

Department of Electrical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Received 27 February 2013; received in revised form 27 May 2013; accepted 18 June 2013

KEYWORDSThree-phasepower transformerdi�erential protection;Ultra-saturationphenomenon;Magnetic inrushcurrent;Internal faults;External faults;False trip;Harmoniccomponents;Di�erential current.

Abstract. A transient phenomenon that leads to the false trip of the power transformerdi�erential protection during the energization of a loaded power transformer is theultra-saturation phenomenon. In this paper, at �rst, a new algorithm for three-phasepower transformer di�erential protection, considering the e�ect of the ultra-saturationphenomenon, is presented. To model the ultra-saturation phenomenon, the nonlinearcharacteristic of the transformer core and the e�ect of saturation of the current transformersare taken into account. It is assumed that the load of the transformer is resistive andinductive. In this algorithm, the ultra-saturation phenomenon, external and internal faultsof the power transformer and magnetic inrush current are simulated, and appropriatecriteria using the signal harmonic components of the di�erential current will be presentedfor the Discrete Fourier Transform (DFT) algorithm to distinguish between. In this paper,simulation is done by PSCAD and MATLAB programs.

c 2014 Sharif University of Technology. All rights reserved.

1. Introduction

The di�erential relay of power transformers is the mostimportant part of power systems [1]. Magnetizinginrush current in the power transformer is a transientphenomenon that can cause the false trip of thetransformer di�erential protection, as when a powertransformer is switched on, it can be much higherthan its nominal value and, hence, may cause the falsetrip of the di�erential protections [1-2]. Normally, inorder to distinguish between external faults, internalfaults and magnetizing inrush current, an algorithm

*. Corresponding author. Tel: +98 611 3330015;Fax: +98 611 3330016E-mail addresses: [email protected] (B. Noshad);razaz [email protected] (M. Razaz); [email protected](S.Gh. Seifossadat)

is used in which the di�erential protection operateswhen the amplitude of the basic component of thedi�erential current is �xed higher than 0.25 p.u andthe level of the second harmonic to the basic harmonicof the di�erential current �xes lower than 15% [3-7]. However, it has been shown that under certainconditions, the false trip of di�erential protection undermagnetizing inrush current has lead to the trippingof healthy transformers [3-5]. When a loaded powertransformer is switched on, it may cause a status calledthe nominated ultra-saturation phenomenon. In thiscase, the DC ux in the magnetic core of the powertransformer at the primary stage of the process in-creases rather than decreases [3]. Hence, the amplitudeof the basic component of the di�erential current getshigher and the level of the second harmonic decreaseslower than the level of the relay restrain [3-5]. Foranalytical study of the ultra-saturation phenomenon,

B. Noshad et al./Scientia Iranica, Transactions D: Computer Science & ... 21 (2014) 904{923 905

an initial loaded power transformer energization modelwas suggested and the false trip of the di�erentialprotection has been described using this model, [3-5]. In [3], many simpli�cations during the simulationsare carried out, which take the magnetizing reactanceof the time-variant characteristic as an equivalentinductance, neglecting the core model of the powertransformer, without considering the transferring e�ectof the current transformer to the primary inrush, andonly considering the resistive load, which does notcoincide with real situations. Weng et al. revisedtheir previous model in 2007. According to them,the previous model cannot be used to study the ultra-saturation phenomenon. So, a new model for studyingthe ultra-saturation phenomenon during loaded powertransformer energization is proposed with the currenttransformer model, including the e�ect of the magnetichysteresis and the nonlinear magnetizing reactance,not only the resistive load [4]. But in [4], the corelosses of the power transformer are neglected anda di�cult model for the current transformer in theprimary side is considered whose main di�culty incurrent transformer modeling is the hysteresis loop sim-ulation. Wiszniewski et al. illustrated the conditionswhich must be discovered to make ultra-saturation andexcessive ultra-saturation possible in 2008 [5]. TheATP-EMTP program is used for simulation. Fordetermining the conditions that discovered the ultra-saturation and excessive ultra-saturation phenomenonin [5], the core model of the power transformer andthe magnetizing reactance are ignored, which doesnot correspond with the real status. In all previousstudies of ultra-saturation phenomenon, the model ofa loaded power transformer was considered as single-phase and an appropriate protection algorithm hadnot been described for preventing the false trip ofdi�erential protection due to the ultra-saturation phe-nomenon [3-5]. Several studies have been done todistinguish internal faults from external faults andmagnetic inrush current using various algorithms, suchas wavelet transform [8,9], the fuzzy technique [10,11],the neural network [12,13], combined wavelet trans-form and neural network [14], harmonic restraint [15]and park transform [16]. Also, some work has usedspecial algorithms, such as short-time correction trans-form [17], the support vector machine-based protectionscheme [18], self adaptive transformer di�erential pro-tection [19], time-domain analysis of the di�erentialpower signal [20], an inner bridge connection [21],standard 87T di�erential protection for a power trans-former and a special power transformer [22,23] andintelligent hybrid systems [24] to distinguish betweenthe transient phenomena. But, in all these studies,the ultra-saturation phenomenon was not taken intoaccount.

In this paper, at �rst, a new model for investigat-

ing the ultra-saturation phenomenon during the ener-gization of a loaded three-phase power transformer ispresented. To model the ultra-saturation phenomenon,the nonlinear characteristic of the transformer coreand the saturation e�ect of current transformers aretaken into account. It is assumed that the load ofthe transformer is a resistive and inductive load. Also,a new model is presented for the current transformerwhich is very simple and e�ective. In addition to anew model for the power transformer and the currenttransformer, in this paper, a new algorithm for three-phase power transformer di�erential protection, con-sidering the e�ect of the ultra-saturation phenomenon,is presented. In this algorithm, the ultra-saturationphenomenon, power transformer external faults (in-cluding three-phase fault, three-phase-to-ground fault,phase-to-ground fault, phase-to-phase fault, and phase-to-phase-to-ground fault), power transformer internalfaults (including turn-to-ground fault, turn-to-turnfault, and phase-to-phase fault), and magnetic inrushcurrent are simulated, and appropriate criteria usingsignal harmonic components of the di�erential currentto distinguish between these phenomenon using theDFT algorithm will be presented. The di�erentialprotection of the power transformer must be fast andaccurate, so the description and control of the ultra-saturation phenomenon are necessary for preventingthe false trip of the di�erential protection. In thispaper, simulation is done by PSCAD and MATLABprograms.

2. Ultra-saturation modeling

2.1. Modeling of loaded three-phasetransformer energization

The modeling of power transformers is always doneusing both magnetic and electrical circuits. Thebasic structure of a three-phase, two-winding, three-legged power transformer is shown in Figure 1(a);Figure 1(b) shows the magnetic equivalent circuit ofthe transformer shown in Figure 1(a). According to

Figure 1a. The basic structure of a three-phase,two-winding, three-legged power transformer.

906 B. Noshad et al./Scientia Iranica, Transactions D: Computer Science & ... 21 (2014) 904{923

Figure 1b. The magnetic equivalent circuit ofthree-phase transformer.

Figure 1(b):

�Npipea + fa �<d�d = 0; (1)

�Npipeb + fb �<d�d = 0; (2)

�Npipec + fc �<d�d = 0; (3)

�a + �b + �c + �d = 0: (4)

By considering the saturation curve, reluctances a,b, and c in Figure 1(b) are nonlinear and de�ned asfollows [25]:

<a(fa)�1 =k1a�

1 +� jfajf0a

�pa� 1pa

+ k2a; (5)

<b(fb)�1 =k1b�

1 +� jfbjf0b

�pb� 1pb

+ k2b; (6)

<c(fc)�1 =k1c�

1 +� jfcjf0c

�pc� 1pc

+ k2c: (7)

According to Figure 1(b):

fa = <a(fa):�a; (8)

fb = <b(fb):�b; (9)

fc = <c(fc):�c: (10)

Due to Eqs. (5)-(10):

�a =

0BB@ k1a�1 +

� jfajf0a

�pa� 1pa

+ k2a

1CCA :fa; (11)

�b =

0BB@ k1b�1 +

� jfbjf0b

�pb� 1pb

+ k2b

1CCA :fb; (12)

�c =

0BB@ k1c�1 +

� jfcjf0c

�pc� 1pc

+ k2c

1CCA :fc: (13)

According to the fact that most three-phase powertransformers are connected as a YN/d connection, theelectric equivalent circuit can be shown in Figure 2.According to Figure 2, the following equations arepresented:

upa = Rpipa + Ldpdipadt

+Npd�adt

; (14)

Figure 2. The electric equivalent circuit of a Wye to ground-delta transformer.


upb = Rpipb + Ldpdipbdt

+Npd�bdt

; (15)

upc = Rpipc + Ldpdipcdt

+Npd�cdt

; (16)

usab = �Rsisa � Lds disadt +Nsd�adt

; (17)

usbc = �Rsisb � Lds disbdt +Nsd�bdt

; (18)

usca = �Rsisc � Lds discdt +Nsd�cdt

: (19)

For simulating the ultra-saturation phenomenon, thethree-phase power transformer is loaded and it is as-sumed that the balanced three-phase load of the powertransformer is resistive and inductive. By connectingthe complex load (Rb � Lb) in Wye form to theequivalent circuit of the three-phase power transformerin Figure 2, and based on Kirchho� voltage and currentlaws in the secondary side, the following equations canbe written:

usab = Rbia + Lbdiadt�Rbib � Lb dibdt ; (20)

usbc = Rbib + Lbdibdt�Rbic � Lb dicdt ; (21)

usca = Rbic + Lbdicdt�Rbia � Lb diadt ; (22)

ia = isa � isc; (23)

ib = isb � isa; (24)

ic = isc � isb: (25)

Due to Eqs. (17)-(25):

�Rsisa � Lds disadt +Nsd�adt

= Rb(isa � isc)

+ Lbd(isa � isc)

dt�Rb(isb � isa)

� Lb d(isb � isa)dt

; (26)

�Rsisb � Lds disbdt +Nsd�bdt

= Rb(isb � isa)

+ Lbd(isb � isa)

dt�Rb(isc � isb)

� Lb d(isc � isb)dt

; (27)

�Rsisc � Lds discdt +Nsd�cdt

= Rb(isc � isb)

+ Lbd(isc � isb)

dt�Rb(isa � isc)

� Lb d(isa � isc)dt

: (28)

Also, according to Figure 2:

ipa = ipea + (Ns=Np)isa;

ipb = ipeb + (Ns=Np)isb;

ipc = ipec + (Ns=Np)isc: (29)

In Eqs. (1)-(29) and Figures 1-3, upa, upb, upc, usab,usbc, usca, ipa, ipb, ipc, ia, ib and ic are the voltages andcurrents of the primary and secondary windings. Rp,Rs, Ldp and Lds are the resistance and inductance ofthe primary and secondary windings. �a, �b, �c and �dare the ux of the core magnetic through the windinglegs and air branch. Np and Ns are the primary andsecondary windings turn. epa, epb, epc, esa, esb and

Figure 3a. The current transformer model.

Figure 3b. The current transformer model referred to assecondary side.

Figure 3c. The magnetizing characteristic of transformercore.


esc are the inducted primary and secondary voltagesof winding legs. fa, fb, fc and fd are the magneticpotential through the three-legged and air branch. pa,pb, pc, k1a, k1b, k1c, k2a, k2b, k2c, f0a, f0b and f0c arerelated to the transformer saturation curve, and Rband Lb are resistive and inductive load of the powertransformer.

2.2. Current transformer modelingIn this paper, a new simple and e�ective model ispresented for the current transformer. The currenttransformer equivalent circuit and the current trans-former equivalent circuit referred to in the secondaryside are shown in Figures 3(a) and 3(b). In thesecircuits, R1 and L1 are the resistive and inductivecomponents of the equivalent impedance, comprisedof the system impedance and leakage impedance ofthe transformer primary winding; R2 and L2 are theresistive and inductive winding of the secondary sideof the current transformer; and Rb and Lb are theresistive and inductive burden of the current trans-former. To explain the current transformer modelin this paper, an appropriate model is developed topredict the transient behavior of a current transformerwith a burden consisting of inductance and resistance,taking saturation into account. To model the currenttransformer, Figures 3(a) and 3(b) are considered.Since the core loss does not a�ect the behavior ofthe current transformer saturation, it is neglected [26].Although the hysteresis e�ect is not taken into accountin this proposed model, but is considered by theIEEE Power System Relaying Committee (IPSR), bothresults are in good agreement. The main advantages ofthis proposed model are as follows:

1. Information concerning the B-H curve for the mag-netic branch is not required.

2. The hysteresis e�ect is not taken into account andthe results of the proposed model can be comparedwith the IEEE model considering the hysteresise�ect.

3. It involves proper computing speed and accuracy.

If fault occurs in the primary winding of the currenttransformer and the fault current passes through theprimary winding, the core ux increases due to theasymmetrical component. So, the current transformercore approaches the saturation region and this leads toa secondary current distortion. Therefore, an e�ectivecurrent transformer model for protection systems isrequired, and, in this paper, a very simple and e�ectivemodel for a current transformer is presented. The ac-curate curve of the magnetizing curve should be shownas multi-valued if taking hysteresis into account. Forthe convenience of solving the di�erential equations,the magnetization curve can be simpli�ed, as shown in

Figure 3(c). We suppose that the saturation point is(i�0 ; s). The inductance inside and outside the satu-ration regions are Ls and L�, respectively. It shouldbe emphasized that the inductance of the magnetizingbranch of the transformer is still nonlinear, even ifthe above-mentioned simpli�cation is used. In mostpapers, in the linear region of the approximate curve,the magnetization current is considered zero, but,in this model, the magnetization curve is consideredaccurately. Thus, the magnetization curve illustratedin Figure 3(c) is used for the current transformer core.This single-valued magnetization curve is used for thecurrent transformer. Since the hysteresis characteristicdoes not considerably a�ect the current transformertransient behavior [27], the single-valued curve is anappropriate curve for transient analysis of the currenttransformer and can be used instead of a multi-valuedcurve. According to Figure 3(c):

i� =

8>>>>>><>>>>>>: �� sLs + i�0 � > s

�+ sLs � i�0 � < � s

i�0 � s j �j � s

(30)

In this equation, � represents the ux linkages, srepresents the ux linkages at the saturation kneepoint of the magnetization curve, i�0 represents themagnetization current at the saturation knee pointof the magnetization curve, and Ls represents theslope of the saturation zone. To model the currenttransformer, the equivalent circuit shown in Figure 3(b)is considered. In this circuit, we de�ned:

R = R2 +Rb; L = L2 + Lb: (31)

According to the equivalent circuit shown in Fig-ure 3(b):

ips = i� + is; (32)

es = Ris + Ldisdt; (33)

ips =NpNs

ip: (34)

In these equations, ips represents the primary currentthat refers to the secondary side, i� is the magnetizingcurrent, is is the secondary current, Np is the numberof primary turns, Ns is the number of secondary turns,and es represents the induced voltage in the secondarywinding. According to Eq. (32):

is = ips � i�: (35)

According to Figure 3(c), the magnetization curve of


the current transformer has three regions.

For region 1, � > s:

i� =( � � s)

Ls+ i�0 : (36)

According to Eqs. (35) and (36):

is = ips � 1Ls

( � � s)� i�0 : (37)

Di�erentiate from Eq. (37):

disdt

=dipsdt� 1Ls

d �dt

: (38)

Due to d �dt = es, from Eqs. (33), (37) and (38):

d �dt

=RLsLs + L

�ips � ( � � s)

Ls� i�0

�+

LLsLs + L

�dipsdt

�: (39)

For region 2, � < � S :

i� =1Ls

( � + s)� i�0 : (40)


is = ips � 1Ls

( � + s) + i�0 : (41)


disdt

=dipsdt� 1Ls

d �dt

: (42)


d �dt

=RLsLs + L

�ips � ( � + s)

Ls+ i�0

�+

LLsLs + L

�dipsdt

�: (43)

For region 3, j �j � s:i� = i�0

� s: (44)


is = ips � i�0

� s: (45)


disdt

=dipsdt� i�0

sd �dt

: (46)


d �dt

=R s

s+Li�0

�ips�i�0

� s

�+

L s s+Li�0

�dipsdt

�:

(47)

3. Proposed algorithm for the di�erentialprotection

The di�erential protection should be able to distinguishbetween internal and external faults, the magnetizinginrush current and the ultra-saturation phenomenon,and it should only operate under internal faults.Several studies have been done to distinguish inter-nal faults from external faults and magnetic inrushcurrent by various algorithms, but, in all studies,the ultra-saturation phenomenon was not taken intoaccount. In this paper, at �rst, a new model forinvestigating the ultra-saturation phenomenon duringthe energization of a loaded three-phase power trans-former is presented. For modeling the ultra-saturationphenomenon, modeling of the power transformer andthe current transformer on the primary and secondarysides of the power transformer is required. So, byusing Eqs. (1)-(29), the power transformer is modeled,as described in Section 2.1. By using Eqs. (1)-(29), the magnetic linkage of the transformer coreand the primary and secondary currents of the three-phase power transformer are calculated. The primarycurrents of the power transformer are the primarycurrents of the current transformers on the primary sideof the power transformer, and the secondary currents ofthe power transformer are the primary currents of thecurrent transformers on the secondary side of the powertransformer. The di�erential currents are calculated bysubtraction between secondary currents of the currenttransformers on the primary and secondary sides of thepower transformer, and they will reach the di�erentialrelay. Therefore, to calculate the di�erential currents,modeling of the current transformer is required usingEqs. (30)-(47) in Section 2.2. On the other hand, usingEqs. (1)-(47) for the power transformer and the cur-rent transformers, the ultra-saturation phenomenon ismodeled and the unusually false trip of the di�erentialprotection due to the ultra-saturation phenomenon ispresented using the DFT algorithm of the di�erentialcurrents. In this algorithm, the PSACAD programis also used for simulating the inrush current, andinternal and external faults. Normally, in order todistinguish between external faults, internal faults andmagnetizing inrush current, an algorithm is used inwhich the di�erential protection operates when theamplitude of the basic component of the di�erentialcurrent �xes higher than 0.25 p.u, and the level ofthe second harmonic to the basic harmonic of thedi�erential current �xes lower than 15%. However,it has been shown that under certain conditions, thefalse trip of the di�erential protection under the ultra-saturation phenomenon has lead to the tripping ofhealthy transformers. In this algorithm, to distinguishinternal from external faults, the magnetizing inrushcurrent and the ultra-saturation phenomenon, �rst


the di�erential currents of phases are obtained fromsubtraction of the secondary currents of the currenttransformers from the primary and secondary sides ofthe power transformers. Then, to distinguish betweentransient phenomena, appropriate criteria using signalharmonic components of di�erential currents will bepresented by the DFT algorithm. Finally, the followingsteps are performed to distinguish transient phenom-ena:

a) At �rst, the ratio of the second harmonic to thebasic harmonic ( H2

Hbase) of the di�erential currents is

calculated by the use of the DFT algorithm. If theratio �xes higher than 15%, the inrush current willoccur. Otherwise, the other transient phenomenamay occur.

b) In the next step, the steady state amplitudes of thebasic component of the di�erential currents (idss)are calculated using the DFT algorithm. If thesteady state amplitudes �x lower than 0.25 p.u.,external faults will occur. Otherwise, the ultra-saturation phenomenon or internal faults may oc-cur.

c) In the last step, to distinguish between the ultra-saturation phenomenon and the internal faults, theratio of the seventh harmonic to the �fth harmonic(H7H5

) of the di�erential currents is calculated usingthe DFT algorithm. If this ratio stabilizes below20%, an internal fault occurs and the di�erentialprotection must operate.

On the other hand, if the amplitudes of the di�erentialcurrents stabilize higher than 0.25 p.u., the ratiochange of the second harmonic to the basic harmonicstabilizes lower than 15% and the seventh harmonicto the �fth harmonic stabilizes lower than 20%, aninternal fault occurs and a di�erential relay should beoperated. Otherwise, the other transient phenomenamay occur and the di�erential relay will not operate.To prove the results in the next section, the proposedalgorithm is investigated for various cases of transientphenomena. The owchart of the proposed algorithmis shown in Figure 4.

4. Simulation results

4.1. Simulation of the ultra-saturationphenomenon

It is supposed that the three-phase power transformeris load connected and is switched on from the high-voltage side at t = 0. The source and three-phasepower transformer parameters are:

upa = Um sin(!t+ �);

upb = Um sin(!t+ � � 120�);

Figure 4. The owchart of the proposed algorithm.

upc = Um sin(!t+ � � 240�);

Um = 400 kV; ! = 100� rad; � = 80�;

k = 400=230 kV; Rp = 0:9 ;

Ldp = 0:1019 H; Rs = 0:5 ;

Lds = 0:0337 H; Np = 610;

Ns = 352; Rb = 5 ; Lb = 0:3029 H;


S = 500 MVA; <d = 2500 A.t/Wb;

f0a = 10:05 A.t; pa = 5;

k1a = 28 Wb/A.t; k2a = 0:995 Wb/A.t;

f0b = 10:03 A.t; pb = 5;

k1b = 45 Wb/A.t; k2a = 0:9152 Wb/A.t;

f0c = 10:05 A.t; pc = 5;

k1c = 28 Wb/A.t; k2c = 0:9134 Wb/A.t:

�a(0) = 1:5878 e�3wb; �b(0) = 4:7619 e�3 wb;

�a(0) = �6:3518 e�3wb:

Parameters for the current transformer on the high-voltage side of the power transformer are:

k = 600=5; Bs = 1:8 T; Ls = 0:7 mH;

A = 3:472 e�3m2; s = 0:75 (wb*turns);

i�0 = 0:05 mA; R = 0:05 :

Parameters for the current transformer on the low-voltage side of the power transformer are:

k = 1000=5; Bs = 1:9 T; Ls = 0:7 mH;

A = 3:53 e�3m2; s = 1:34 (wb*turns);

i�0 = 0:03 mA; R = 0:15 :

For modeling of the ultra-saturation phenomenon, ipa,ipb, ipc, ia, ib, ic, �a, �b and �c can be solved fromEqs. (1)-(4), (11), (16) and (23)-(29). ipa, ipb, ipc,ia, ib and ic are the primary and secondary currentsof the three-phase power transformer. ipa, ipb andipc are the primary currents of current transformerson the primary side of the power transformer, andia, ib and ic are the primary currents of currenttransformers on the secondary side of the power trans-former. Now, the secondary currents of the currenttransformers on the primary and secondary sides ofthe power transformer should be calculated. � isrelated to the current transformers on the primaryand secondary sides of the power transformer, andcan be solved from Eqs. (39), (43) and (47) usingthe fourth-order Runge-Kutta method with a 10�stime step. The magnetic current, i�, according toEq. (30), and the secondary current of the currenttransformers, according to given Eqs. (37), (41) and(45), have been calculated using the computed �. Inthese relations, ips is the primary current of the powertransformer. The wave forms of the magnetic linkageof the transformer core, and the primary and secondarycurrents of the three-phase power transformer due toultra-saturation are shown in Figures 5(a), 5(b) and5(c), respectively. The di�erential currents (id) due tothe ultra-saturation phenomenon that are calculatedby subtraction between the secondary currents of thecurrent transformers on the primary and secondarysides of the power transformer is shown in Figure 5(d).Figure 6(a) displays the changes of the amplitudesof the basic component of the di�erential currents inFigure 5(d), obtained with the DFT algorithm. Inthis �gure, the amplitudes of the basic component of

Figure 5a. Wave shapes of the magnetic linkage of transformer core due to the ultra-saturation phenomenon.


Figure 5b. Wave shapes of the primary currents of transformer due to the ultra-saturation phenomenon.

Figure 5c. Wave shapes of the secondary currents of transformer due to the ultra-saturation phenomenon.

Figure 5d. Wave shapes of di�erential currents due to the ultra-saturation phenomenon.


Figure 6a. The normalized amplitudes of the basic component of the di�erential currents with DFT algorithm due to theultra-saturation phenomenon.

Figure 6b. The ratio of the second harmonic to basic harmonic of the di�erential currents with DFT algorithm due tothe ultra-saturation phenomenon.

the di�erential current are normalized according to thesecondary current of the current transformers (5A).Figure 6(b) displays the ratio change of the secondharmonic to the basic harmonic of the di�erentialcurrents, which is obtained with the DFT algorithm.As illustrated in Figure 6(a), the basic component ofthe di�erential currents is above 0.25 p.u. From thebeginning of energization and after, approximately, 6cycles, it is stabilized above 0.25 p.u. Also, according toFigure 6(b), as the energization time exceeds 0.1344 s,0.1463 s and 0.1537 s for A, B, and C phases, respec-tively, the ratio of the second harmonic to the basicharmonic stabilizes lower than 15%. So, according toFigures 6(a) and 6(b), if the di�erential protection uses0.25 p.u. as the operating threshold for the amplitudes

of the basic component of di�erential currents, and 15%as the second harmonic restraint ratio, the false tripoccurs at 0.1344s.

4.2. Simulation of the inrush currentIf the amplitude and polarity of the residual ux arenot in agreement with the amplitude and polarity ofthe instantaneous value of the steady state ux, inrushcurrent happens. So, when a transformer is switchedon, inrush currents are caused by saturation e�ects inthe magnetic core. One of the important characteristicsof inrush current in the di�erential relay is the secondharmonic. The level of the second harmonic in inrushcurrent is high, and the value of the second harmonicis a function of the degree of saturation. Hence, to


Figure 7a. The di�erential currents and the ratio of the second harmonic to basic harmonic of the di�erential currentsdue to inrush current by the change of the residual ux.

Figure 7b. The di�erential currents and the ratio of the second harmonic to basic harmonic of the di�erential currentsdue to inrush current by the change of the switching time.

determine the degree of saturation caused by transientinrush currents from steady state currents, the contentof the second harmonic is used. So, in the proposedalgorithm, the second harmonic is used for distinguish-ing inrush current from steady state currents and othertransient phenomena. For simulation of the inrush cur-rent, the unloading transformer is switched on at 0.1 s.Showing the accuracy of the proposed algorithm underall conditions, various test signals by changing someparameters are simulated. Some important parameterssuch as residual ux, switching time and inceptionangle have a direct impact on magnetic inrush currents.So, to prove the results of the proposed algorithm, some

di�erent signals due to inrush current are generatedby the change of residual ux, switching time andinception angle. At various transient inrush currentsin the power transformer, 60 test signals for di�erentcondition of the inrush current are simulated. Dueto limitation of paper length, some cases of inrushcurrent are shown in Figures 7(a), 7(b) and 7(c). Inthese �gures, the di�erential currents and the ratioof the second harmonic to the basic harmonic of thedi�erential currents due to inrush current, by changesin residual ux, switching time and inception angle, areshown. According to these �gures, the ratio changeof the second harmonic to the basic harmonic of the


Figure 7c. The di�erential currents and the ratio of the second harmonic to basic harmonic of the di�erential currentsdue to inrush current by the change of the inception angle.

Figure 8a. The di�erential currents and the normalized amplitudes of the basic component of the di�erential currents dueto the three-phase external fault by the change of the residual ux.

di�erential currents due to the inrush current alwaysstabilizes higher than 15%. Therefore, the di�erentialprotection under the inrush current condition will notoperate. The obtained results for inrush current showthe accuracy of the proposed algorithm.

4.3. Simulation of the external faultsFor simulation of the external faults, PSCAD andMATLAB programs are used. Fault is occurred onthe outside of the protective zone of the di�erentialrelay on the load side. The simulated fault typesare the three-phase fault, the three-phase-to-groundfault, the phase-to-ground fault, the phase-to-phase

fault and the phase-to-phase-to-ground fault. In theexternal faults, di�erent signals are generated by thechange of the residual ux, load level, fault resistance,inception angle and fault occurrence time. At varioustransient external faults in the power transformer, 500test signals for di�erent conditions of external faultsare simulated. Due to the limitation of paper length,some cases of external faults by changes in residual ux, load level, fault resistance, inception angle andfault occurrence time are shown in Figures 8(a) to8(e). For simulation of the external faults, the timeof fault occurrence is considered 0.2 s. In these �gures,the di�erential currents and the steady state ampli-


Figure 8b. The di�erential currents and the normalized amplitudes of the basic component of the di�erential currentsdue to the three-phase-to-ground external fault by the change of the load level.

Figure 8c. The di�erential currents and the normalized amplitudes of the basic component of the di�erential currents dueto the phase-to-phase external fault by the change of the occurrence time.

Figure 8d. The di�erential currents and the normalized amplitudes of the basic component of the di�erential currentsdue to the phase-to-phase-to-ground external fault by the change of the inception angle.


Figure 8e. The di�erential currents and the normalized amplitudes of the basic component of the di�erential currents dueto the phase-to-ground external fault by the change of the fault resistance.

Figure 9a. The di�erential currents, the normalized amplitudes of the basic component of the di�erential currents andthe ratio of the second harmonic to basic harmonic of the di�erential currents due to the turn-to-ground internal fault bythe change of the residual ux.

tudes of the di�erential currents due to the externalfaults by changes in residual ux, load level, faultresistance, inception angle and fault occurrence timeare shown. According to these �gures, the amplitudesof the di�erential currents due to the external faultsstabilize lower than 0.25 p.u. Therefore, the di�erentialprotection under the external faults condition will notoperate.

4.4. Simulation of the internal faultsFor simulating the internal faults of the power trans-former which involve turn-to-ground, turn-to-turn andphase-to-phase, PSCAD and MATLAB programs arealso used. In the turn-to-ground fault, the fault is

occurred on the secondary winding of phase A at the25% position of winding, and in the turn-to-turn fault,the fault is occurred on the secondary winding of phaseA in which 10 percent of the turns are short circuited.In the phase-to-phase fault, the fault is occurred onthe secondary windings of phases A and B at the 25%position of windings. In the internal faults, di�erentsignals are generated by the changes in residual ux,load level, fault resistance, inception angle and faultoccurrence time. At various transient internal faultsin the power transformer, 300 test signals for di�erentconditions of internal faults are simulated. Due to thelimitation of paper length, some cases of internal faultsare shown in Figures 9(a), 9(b) and 9(c). For simu-


Figure 9b. The di�erential currents, the normalized amplitudes of the basic component of the di�erential currents andthe ratio of the second harmonic to basic harmonic of the di�erential currents due to the turn-to-turn internal fault by thechange of the load level.

Figure 9c. The di�erential currents, the normalized amplitudes of the basic component of the di�erential currents andthe ratio of the second harmonic to basic harmonic of the di�erential currents due to the phase-to-phase internal fault bythe change of the inception angle.

lation of internal faults, the time of fault occurrenceis considered 0.2 s. In these �gures, the di�erentialcurrents, the steady state amplitudes of the di�erentialcurrents and the ratio of the second harmonic to basicharmonic of the di�erential currents, due to internalfaults, by changes in residual ux, load level andinception angle, are shown. According to these �gures,the amplitudes of the basic component and the ratiochange of the second harmonic to the basic harmonic ofthe di�erential currents, due to internal faults, exceedthreshold values and the di�erential protection willoperate.

4.5. Distinguish between the ultra-saturationphenomenon and the internal faults

According to simulations, if the di�erential protec-tion uses 0.25 p.u. as the operating threshold foramplitudes of di�erential currents, and 15% as thesecond harmonic restraint ratio, the di�erential re-lay, due to the ultra-saturation phenomenon and theinternal faults, will operate. The di�erential relayis used for protecting transformers against internalfaults, but it should not operate under the ultra-saturation phenomenon. Therefore, to distinguish theinternal faults from the ultra-saturation phenomenon,


Figure 10a. The ratio of the seventh harmonic to the �fth harmonic of the di�erential currents due to the turn-to-groundinternal fault by the change of the residual ux.

Figure 10b. The ratio of the seventh harmonic to the �fth harmonic of the di�erential currents due to the turn-to-turninternal fault by the change of the load level.

the ratio of the seventh harmonic to the �fth harmonicis another criterion that is necessary for preventingthe false trip of the di�erential protection due to theultra-saturation phenomenon. At various transientphenomena in the power transformer, 380 test sig-nals involving internal faults and the ultra-saturationphenomenon are simulated. In the ultra-saturationphenomenon, di�erent signals are generated by thechanges in residual ux, load level, inception angle anddi�erent state of current transformer saturation. Inthe internal faults, as mentioned, di�erent signals aregenerated by the changes in residual ux, load level,fault resistance, inception angle and fault occurrencetime. Figures 10(a), 10(b) and 10(c) show the ratiochange of the seventh harmonic to the �fth harmonicof the di�erential currents, due to internal faults, and

Figures 11(a) to 11(d) show the di�erential currentsand the ratio change of the seventh harmonic to the�fth harmonic of the di�erential currents, due to theultra-saturation phenomenon, which are obtained withthe DFT algorithm. According to these �gures, ifthe ratio change of the seventh harmonic to the �fthharmonic of the di�erential currents stabilizes lowerthan 20%, an internal fault occurs and the di�erentialprotection should operate. On the other hand, if theamplitudes of the di�erential currents stabilize higherthan 0.25 p.u., the ratio change of the second harmonicto the basic harmonic stabilizes lower than 15% and theseventh harmonic to the �fth harmonic stabilizes higherthan 20%, the ultra-saturation phenomenon occursand the di�erential relay, due to the ultra-saturationphenomenon, will not operate. As mentioned, this


Figure 10c. The ratio of the seventh harmonic to the �fth harmonic of the di�erential currents due to the phase-to-phaseinternal fault by the change of the inception angle.

Figure 11a. The di�erential currents and the ratio of the seventh harmonic to the �fth harmonic of the di�erentialcurrents due to the ultra-saturation phenomenon by the change of the residual ux.

Figure 11b. The di�erential currents and the ratio of the seventh harmonic to the �fth harmonic of the di�erentialcurrents due to the ultra-saturation phenomenon by the change of the load level.


Figure 11c. The di�erential currents and the ratio of the seventh harmonic to the �fth harmonic of the di�erentialcurrents due to the ultra-saturation phenomenon by the change of the inception angle.

Figure 11d. The di�erential currents and the ratio of the seventh harmonic to the �fth harmonic of the di�erentialcurrents due to the ultra-saturation phenomenon under very heavy current transformer saturation.

proposed algorithm, under di�erent conditions, suchas di�erent loads (various percentages of nominalload), various inception angles, fault resistance, var-ious residual ux and current transformer saturation(if the resistance component increases in the burdenimpedance of the current transformer, the distortionwill increase in the secondary current of the currenttransformer and the current transformer is subjectedto a high saturation) has been investigated, and un-der all conditions, the ratio of the seventh harmonicto the �fth harmonic of the di�erential currents isalways higher than 20%, due to the ultra-saturationphenomenon. Furthermore, in the current transformersaturation conditions under inrush current and external

faults, the seventh harmonic to the �fth harmonic ishigher than threshold value (20%). So, using theproposed algorithm, internal from external faults, theinrush current and the ultra-saturation phenomenonare distinguished and, hence, will prevent the false tripof the di�erential protection of power transformers.

5. Conclusion

In this paper, at �rst, a new model for investigating theultra-saturation phenomenon during the energizationof a loaded three-phase power transformer was pre-sented. To model the ultra-saturation phenomenon,the nonlinear characteristics of the transformer core


and the saturation e�ect of the current transformerswere taken into account. It was assumed that the loadof the transformer is a resistive and inductive load.Also, a new simple and e�ective model was presentedfor the current transformer. In this paper, in additionto a new model for the power transformer and thecurrent transformer, a new algorithm for three-phasepower transformer di�erential protection, consideringthe e�ect of the ultra-saturation phenomenon, waspresented. In this algorithm, the ultra-saturationphenomenon, and the external and internal faults ofthe power transformer and inrush current were sim-ulated and appropriate criteria using signal harmoniccomponents of the di�erential current were presentedto distinguish between these phenomena using the DFTalgorithm. The di�erential protection of the powertransformer must be fast and accurate, so, the descrip-tion and control of the ultra-saturation phenomenon isnecessary for preventing the false trip of the di�erentialprotection.

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Biographies

Bahram Noshad was born, in 1980, in Marvdasht,Iran. He received a BS degree in Electrical Engineeringfrom Shiraz, Iran, in 2002, an MS degree from the

University of Tarbiat Modares, Tehran, Iran, in 2004,and is currently pursuing a PhD degree at ShahidChamran University (SCU), Tehran, Iran. His areasof interest include operations, power electronics andpower system protection.

Morteza Razaz was born in Dezful, Iran, in 1948. Hereceived BS and MS degrees in Electrical Engineeringand Applied Mathematics from Texas University, USA,in 1977 and 1979, respectively, and a PhD degreefrom Sharob University, UK, in 1993. Currently, heis with the Department of Electrical Engineering atShahid Chamran University, Ahvaz, Iran. His researchinterests include power electronics, protection relay,and electric machinery.

Seyed Ghodratollah Seifossadat was born in Ah-vaz, Iran, in 1963. He received a BS degree inElectrical Engineering from Iran University of Scienceand Technology (IUST), Tehran, Iran, in 1989, anMS degree in Electrical Engineering from FerdowsiUniversity of Mashhad, Iran, in 1992, and a PhDdegree from IUST, Tehran, Iran, in 2006. Currently,he is in the Department of Electrical Engineering atShahid Chamran University, Ahvaz, Iran. His researchinterests are power electronics, protection relay, andelectric machinery.

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