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Abstract—A novel scheme based on generalized leakage
inductance (GLI) to distinguish the inrush current from the internal fault current in the power transformer is proposed. By eliminating the mutual flux linkage in the transformer loop equation and adopting the trapezoid principle, the GLI is calculated in the real time. According to the difference between the GLI and the leakage inductance obtained from transformer manufacturer, the criterion to identify the internal fault is developed. A total of 162 experimental cases have been tested and the proposed method is able to reliably and accurately discriminate internal faults from inrush currents with easy implementation. Also, the method is suitable if it is not possible to measure the currents in the delta winding. Furthermore, the method is independent of the B-H curve and iron losses.
Index Terms—generalized leakage inductance, inrush current, internal fault current, power transformer.
I. INTRODUCTION ISCRIMINAION between an internal fault and a magnetizing inrush current has long been recognized as a
challenging power transformer protection problem. Since a magnetizing inrush current generally contains a larger 2nd order harmonic component than that of internal fault, conventional transformer protection systems are designed to restrain during inrush transient phenomenon by sensing this large 2nd order harmonic [1]. However, the 2nd order harmonic component may also be generated during internal faults in the power transformer. In certain cases, the magnitude of the 2nd order harmonic in an internal fault current can be close to or greater than that present in the magnetizing inrush current [2].
This work is supported in part by the National Science Foundation of China (No. 50907021, 50777016, 50837002), in part by the Chinese University Scientific Fund Project (09QX64), and in part by the “111” project (B08013).
Jing Ma is with the School of Electrical and Electronic Engineering, North China Electric Power University, and also with the Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University. (e-mail: [email protected]).
Tong Wang is with the Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education, North China Electric Power University, 102206, Beijing, China.
Jie Wu is with the State Nuclear Electric Power Planning Design and Research Institute, 100094, Beijing, China.
Zengping Wang is with the Key Laboratory of Power System Protection and Dynamic Security Monitoring and Control under Ministry of Education, North China Electric Power University, 102206, Beijing, China.
Moreover, 2nd order harmonic components in the magnetizing inrush currents tend to be relatively small in modern large power transformers because of improvements in the power transformer core material [3]. Consequently, the commonly employed conventional differential protection technique based on the second harmonic restraint differential protection will thus have difficulty in distinguishing between an internal fault and an inrush current. Alternatively, improved protection techniques for accurately and efficiently discriminating between internal faults and inrush currents have thus to be found. These techniques include waveform correlation [4], artificial neutral networks [5-8], fuzzy logic [9-11], and wavelet analysis [12-16]. To enhance the reliability of the differential protection, several other techniques have utilized voltage signals as well as current signals. An equivalent instantaneous inductance-based technique has been developed in [17] to distinguish the internal fault from the inrush current. In [18], the differential active power method has been proposed to perform the relaying operation. The proposed method in [19] is based on the transformer model and loop equations to identify the internal fault. These techniques provide alternatives or improvements to the existing protective relaying functions.
By combining the current and voltage information, this paper presents a technique for discrimination between an internal fault and an inrush current using generalized leakage inductance (GLI). The technique is suitable for the situation in which it is possible to measure the delta winding currents. Also, the technique does not make use of the presence of harmonic currents to restrain the relay during magnetizing inrush. Furthermore, the technique does not require data on the B-H curve or knowledge of iron losses.
At first, the basic theory and calculation method about the GLI are developed. Then, the GLI and the leakage inductance obtained from the transformer manufacturer are compared and then are employed to develop the criteria. Finally, the proposed method is verified by the experimental results.
II. BASIC PRINCIPLE
A. The GLI of Single-Phase Transformer A two-winding single-phase transformer is shown in Fig. 1.
A Generalized Leakage Inductance-Based Method for Discrimination of Internal Faults
from Inrush Currents
Jing Ma, Member, IEEE, Tong Wang, Student Member, IEEE, Jie Wu, Zengping Wang, Member, IEEE
D
978-1-4577-1002-5/11/$26.00 ©2011 IEEE
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The primary and secondary voltages can be expressed as:
dtψd
dtdi
Lriu mff ++= 1
11 (1)
dtψd
dtdi
Lriu mgg ++= 2
22 (2)
where u1 and u2 are the voltages of primary and secondary windings, respectively. i1 and i2 are the currents of primary and secondary windings, respectively. rf and rg are the resistances of primary and secondary windings, respectively. Lf and Lg are the leakage inductances of primary and secondary windings, respectively. ψm is the mutual flux linkage.
Fig. 1. A two-winding single-phase transformer.
The mutual flux linkage of the primary and secondary
windings is equal and can be eliminated by using (1) and (2) as follows
dtdi
Lriu dffdd += (3)
with
dtdix
riuuu kkd
2221 ω
++−= (4)
21 iiid += (5)
gfk rrr += (6)
)( gfk LLωx += (7) where rk and xk are the winding resistance and the short-circuit reactance, respectively.
The trapezoid principle is adopted in (3) to transform the continuous differential equation into a discrete difference equation. At kT instant, its digital realization is given by
TkikiLrkiku dd
ffdd 2)1()1()()( −−++= (8)
where T is the sampling cycle. The samples of the ud at kT and (k+1)T instants, and the
samples of the id at (k-1)T, kT, (k+1)T, and (k+2)T instants are utilized to eliminate rf of the (3) and the calculated GLI at kT instant is written as
))2()()1()1()1()(())()1()1()((2
22 +−+−−+++−+=
kikikikikikikikukikuTL
dddddd
ddddf (9)
kfl LLL −= (10)
where Lk is the leakage inductance of the secondary winding obtained from the transformer manufacturer. Ll is the absolute
difference of leakage inductance (ADOLI) between Lf and Lk. During normal conditions of the power transformer, Lf is
equal to Lk. However, when an internal fault occurs, Lf and Lk are not equal owing to the variation of the physical dimension in the power transformer. If ADOLI is less than a threshold, the relay judges that there is an inrush current and rejects the tripping. Otherwise, the relay judges that an internal fault occurs. In theory, the threshold is close to zero.
B. The ADOLIs of Two-Winding Three-Phase Transformer Fig. 2 shows the connections of the primary and secondary
windings of a Δ/Y transformer. The following equations express the Δ and Y connected windings as the functions of the mutual flux linkages and the currents of the windings.
dtd
dtdi
Lriu maaaaa
ψ++= (11)
dtd
dtdi
Lriu mbbbbb
ψ++= (12)
dtd
dtdi
Lriu mccccc
ψ++= (13)
dtd
dtdi
LRiu maAAAA
ψ++= (14)
dtd
dtdi
LRiu mbBBBB
ψ++= (15)
dtd
dtdi
LRiu mcCCCC
ψ++= (16)
where the parameters of the secondary winding have been converted to the primary winding by the transformer ratio. ua, ub, uc, ia, ib, ic, La, Lb, Lc and r are the voltages, currents, leakage inductances and resistance of the primary winding, respectively. uA, uB, uC , iA, iB, iC, LA, LB, LC and R are the voltages, currents, leakage inductances, and resistance of the secondary winding, respectively. ψma, ψmb, and ψmc are the mutual flux linkages.
Fig. 2. A two-winding three-phase Δ/Y transformer.
The line currents in the Δ connected winding are obtained as
follows baLa iii −= (17)
cbLb iii −= (18)
acLc iii −= (19) Consider the leakage inductances to be constant and equal in
the normal operation state and during the inrush current period. La=Lb=Lc=L11, LA=LB=LC=L22. The equations of the primary and secondary sides can be written as
3
dtψψd
dtdi
Lriuu mbmaLaLaba
)(11
−++=− (20)
dtψψd
dtdi
Lriuu mcmbLbbLcb
)(11
−++=− (21)
dtψψd
dtdi
Lriuu mamcLccLac
)(11
−++=− (22)
dtψψd
dtiid
LRiiuu mbmaBABABA
)()()( 22
−+
−+−=− (23)
dtψψd
dtiid
LRiiuu mcmbCBCBCB
)()()( 22
−+
−+−=− (24)
dtψψd
dtiid
LRiiuu mamcACACAC
)()()( 22
−+
−+−=− (25)
The flux linkages mutual to the primary and secondary windings of each phase are equal and can be eliminated by using (20)-(25) as follows
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
+=
+=
+=
dtdiLRiu
dtdiLRiu
dtdiLRiu
dcdcd
dbdbd
dadad
223
222
221
(26)
with
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−−+−−=
−−+−−=
−−+−−=
dtdi
ωx
riuuuuu
dtdi
ωx
riuuuuu
dtdi
ωx
riuuuuu
cLkkkkcLACacd
bLkkkkbLCBcbd
LakkkkLaBAbad
3
2
1
(27)
⎪⎩
⎪⎨
⎧
−+−=−+−=−+−=
)()()(
ACcLdc
CBbLdb
BALada
iiiiiiiiiiii
(28)
⎩⎨⎧
+=+=
)( 2211 LLωxRrr
kk
kk (29)
The trapezoid principle is adopted in (26) and a procedure similar to the single-phase transformer provides Lo, Lp, and Lq at kT instant, which are all defined as the ADOLIs.
1 12 2
2 22 2
3
2 ( ( ) ( 1) ( 1) ( ))( ( ) ( 1) ( 1) ( 1) ( ) ( 2))
2 ( ( ) ( 1) ( 1) ( ))( ( ) ( 1) ( 1) ( 1) ( ) ( 2))
2 ( ( ) (
d da d dao kk
da da da da da da
d db d dbp kk
db db db db db db
d dcq
T u k i k u k i kL L
i k i k i k i k i k i k
T u k i k u k i kL L
i k i k i k i k i k i k
T u k i kL
+ − += −
+ + − − + − +
+ − += −
+ + − − + − +
+= 3
2 2
1) ( 1) ( ))( ( ) ( 1) ( 1) ( 1) ( ) ( 2))
d dckk
dc dc dc dc dc dc
u k i kL
i k i k i k i k i k i k
⎧⎪⎪⎪⎪⎨⎪⎪ − +⎪ −⎪ + + − − + − +⎩
(30)
where Lkk is the leakage inductance of the secondary winding obtained from the transformer manufacturer.
If the ADOLIs of three phases are all less than the threshold, the relay judges there is an inrush current and rejects the tripping. Otherwise, the relay judges that there is an internal fault.
C. The ADOLIs of Three-Winding Three-Phase Transformer A three-winding three-phase transformer with Δ/Y/Y0
connection is shown in Fig. 3. The following equations express the voltages of the windings as functions of the mutual flux linkages and the currents of the windings.
Fig. 3. A three-winding three-phase Δ/Y/Y0 transformer.
dtd
dtdi
mdt
dim
dtdi
Lriu maaaaaa
ψ++++= 3
312
211
1111 (31)
dtd
dtdi
mdt
dim
dtdi
Lriu mbbbbbb
ψ++++= 3
312
211
1111 (32)
dtd
dtdi
mdt
dim
dtdi
Lriu mcccccc
ψ++++= 3
312
211
1111 (33)
dtd
dtdi
mdt
dim
dtdi
Lriu maaaaaa
ψ++++= 3
321
122
2222 (34)
dtd
dtdi
mdt
dim
dtdi
Lriu mbbbbbb
ψ++++= 3
321
122
2222 (35)
dtd
dtdi
mdt
dim
dtdi
Lriu mcccccc
ψ++++= 3
321
122
2222 (36)
dtd
dtdi
mdt
dim
dtdi
Lriu maaaaaa
ψ++++= 2
231
133
3333 (37)
dtd
dtdi
mdt
dim
dtdi
Lriu mbbbbbb
ψ++++= 2
231
133
3333 (38)
dtd
dtdi
mdt
dim
dtdi
Lriu mcccccc
ψ++++= 2
231
133
3333 (39)
where the parameters of the secondary and the tertiary windings have been converted to the primary winding by the transformer ratio. ua1, ub1, uc1, ia1, ib1, ic1, r1, and L1 are the voltages, currents, resistance and self-leakage inductance of the primary winding, respectively. ua2, ub2, uc2, ia2, ib2, ic2, r2, and L2
are the voltages, currents, resistance and self-leakage inductance of the secondary winding, respectively. ua3, ub3, uc3, ia3, ib3, ic3, r3, and L3 are the voltages, currents, resistance and self-leakage inductance of the tertiary winding, respectively. m12 and m21 are the mutual leakage inductances between the primary and secondary windings. m31 and m13 are the mutual leakage inductances between the primary and tertiary windings. m32 and m23 are the mutual leakage inductances between the secondary and tertiary windings. Assume the mutual leakage
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inductances to be constant and equal during normal operation conditions and the inrush currents: m12=m21, m13=m31, m23=m32. ψma, ψmb, and ψmc are the mutual flux linkages.
The flux linkages mutual to the primary, secondary, and tertiary windings of each phase are equal and can be eliminated by using (31)-(39) as follows
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−+=
−+=
−+=
dtdimLriu
dtdimLriu
dtdimLriu
ddca
ddbc
ddab
31211312
21211212
11211112
)(
)(
)(
(40)
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−+=
−+=
−+=
dtdimLriu
dtdimLriu
dtdimLriu
ddca
ddbc
ddab
32322323
22322223
12322123
)(
)(
)(
(41)
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−+=
−+=
−+=
dtdimLriu
dtdimLriu
dtdimLriu
ddca
ddbc
ddab
33133323
23133223
13133131
)(
)(
)(
(42)
with
⎪⎩
⎪⎨
⎧
−+−+=−+−+=−+−+=
332213
332212
332211
acacLcd
cbcbLbd
babaLad
iiiiiiiiiiiiiiiiii
(43)
12 2 2 1 1 2 2 1 2
2 2 3 31 2 13 3 1
12 2 2 1 1 2 2 1 2
2 2 3 31 2 13 3 1
12
( )( ) ...( ) ( )
( )
( )( ) ...( ) ( )
( )
ab b a a b a b
a b a ba b
bc c b b c b c
b c b cb c
ca
u u u u u i i r rd i i d i ix x x
i i rdt dt
u u u u u i i r rd i i d i ix x x
i i rdt dt
u
ω ω
ω ω
= − + − + − + +− −+
+ − +
= − + − + − + +− −+
+ − +
= 2 2 1 1 2 2 1 2
2 2 3 31 2 13 3 1
( )( ) ...( ) ( )
( )
a c c a c a
c a c ac a
u u u u i i r rd i i d i ix x x
i i rdt dtω ω
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪
− + − + − + +⎪⎪ − −+⎪ + − +⎪⎩
(44)
23 3 3 2 2 3 3 2 3
2 3 3 3 121 2
23 3 3 2 2 3 3 2 3
2 3 3 3 121 2
23 3 3 2 2 3
( )( ) ...( )
( )( ) ...( )
(
ab b a a b a b
a b LaLa
bc c b b c b c
b c LbLb
ca a c c a c
u u u u u i i r rx x d i i dix
i rdt dt
u u u u u i i r rx x d i i dix
i rdt dt
u u u u u i
ω ω
ω ω
= − + − + − + ++ −
+ +
= − + − + − + ++ −
+ +
= − + − + 3 2 3
2 3 3 3 121 2
)( ) ...( )
a
c a LcLc
i r rx x d i i dix
i rdt dtω ω
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪
− + +⎪⎪ + −⎪ + +⎪⎩
(45)
31 1 1 3 3 1 1 3
1 3 1 3 2 22 2 3
31 1 1 3 3 1 1 3
1 3 1 3 2 22 2 3
31 1 1 3 3 1
( ) ...( )
( )
( ) ...( )
( )
ab b a a b La
La a ba b
bc c b b c Lb
Lb b cb c
ca a c c a Lc
u u u u u i r rx x di x d i i
i i rdt dt
u u u u u i r rx x di x d i i
i i rdt dt
u u u u u i
ω ω
ω ω
= − + − + + ++ −
+ − +
= − + − + + ++ −
+ − +
= − + − + 1 3
1 3 1 3 2 22 2 3
( ) ...( )
( )Lc c ac a
r rx x di x d i i
i i rdt dtω ω
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪
+ +⎪⎪ + −⎪ + − +⎪⎩
(46)
where iLa1, iLb1, and iLc1 are the line currents of the primary winding.
A procedure similar to the two-winding transformer provides three groups of the ADOLIs Lr, Ls, Lt, Lu, Lv, Lw, Lx, Ly, and Lz at kT instant.
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
−+−+−−++
+−+=
−+−+−−++
+−+=
−+−+−−++
+−+=
13333
23
23
312312
12222
22
22
212212
11111
21
21
112112
))2()()1()1()1()(())()1()1()((2
))2()()1()1()1()(())()1()1()((2
))2()()1()1()1()(())()1()1()((2
kdddddd
dcadcat
kdddddd
dbcdbcs
kdddddd
dabdabr
Lkikikikikiki
kikukikuTL
Lkikikikikiki
kikukikuTL
Lkikikikikiki
kikukikuTL
(47)
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
−+−+−−++
+−+=
−+−+−−++
+−+=
−+−+−−++
+−+=
23333
23
23
323323
22222
22
22
223223
21111
21
21
123123
))2()()1()1()1()(())()1()1()((2
))2()()1()1()1()(())()1()1()((2
))2()()1()1()1()(())()1()1()((2
kdddddd
dcadcaw
kdddddd
dbcdbcv
kdddddd
dabdabu
Lkikikikikiki
kikukikuTL
Lkikikikikiki
kikukikuTL
Lkikikikikiki
kikukikuTL
(48)
⎪⎪⎪⎪
⎩
⎪⎪⎪⎪
⎨
⎧
−+−+−−++
+−+=
−+−+−−++
+−+=
−+−+−−++
+−+=
33333
23
23
331331
32222
22
22
231231
31111
21
21
131131
))2()()1()1()1()(())()1()1()((2
))2()()1()1()1()(())()1()1()((2
))2()()1()1()1()(())()1()1()((2
kdddddd
dcadcaz
kdddddd
dbcdbcy
kdddddd
dabdabx
Lkikikikikiki
kikukikuTL
Lkikikikikiki
kikukikuTL
Lkikikikikiki
kikukikuTL
(49
) where Lk1, Lk2, and Lk3 are self-leakage inductances of the primary, secondary, and tertiary windings, respectively. x1, x2, and x3 are the short-circuit reactances of primary, secondary and tertiary windings, respectively. All of these values can be obtained from the transformer manufacturer.
⎪⎩
⎪⎨
⎧
+−−=+−−=
+−−=
)()()(
12231333
13231222
23131211
mmmLxmmmLx
mmmLx
ωωω
(50)
If three groups of the ADOLIs are all less than a preset threshold, the relay determines that there is an inrush current and rejects the tripping. Otherwise, the relay determines that an internal fault occurs.
III. EXPERIMENTAL SYSTEM To verify the effectiveness of the proposed method, the
5
experimental tests [20] have been carried out at the Electrical Power Dynamic Laboratory (EPDL). The experimental transformer is a three-phase, two-winding transformer bank with Y0/Δ-11 connection, which is fed by a large power system grid, as shown in Fig. 4. The parameters of the two-winding transformers are given in Table I. Three identical current transformers (CTs) are connected in Δ on the primary winding, and another three identical CTs are connected in Y on the secondary winding of the power transformer. The sampling rate is one sample per millisecond.
Fig. 4. Experimental system.
TABLE I PARAMETERS OF THE TRANSFORMER USED IN THE TEST
Rated capacity 30kVA
Rated voltage ratio 1732.05/380V Rated current ratio 10/45.58A Rated frequency 50Hz No load current 1.45% No load loss 1% Short circuit voltage 9.0~15.0% Short circuit loss 0.35%
The experiments provide samples of three phase differential
currents when the transformer is energized or when a fault occurs or when both occur simultaneously. In order to test various features of the algorithm, a total of 162 cases have been divided into three main categories: 56 cases for switching the transformer with no load, 52 cases for simultaneous internal fault and inrush conditions, and 54 cases for faulty conditions only. Different switching and clearing instants for inrush currents, as well as different faults and short circuit turn ratios for internal faults are considered in the tests. These cases are used to identify the response of the developed algorithm.
Figs. 5-9 show some examples of the experimental test results: the differential currents and the resulting analysis
IV. TESTING RESULTS ANA ANALYSIS
A. Responses to Different Inrush Conditions A total of 56 test cases were carried out in this situation. The
inrush current waveform is a function of the different core residual magnetization and the switching instant, so the waveforms of the inrush current are different from each other. However, the ADOLIs calculated by using (30) present identical results due to eliminating flux linkages. An example taken from these cases is given in Fig. 5, where the differential currents of three phases and their ADOLIs are shown in Figs. 5(a) and (b), respectively. We can find that the calculated ADOLIs of three phases are negligible and only have little
variation resulting from the measurement and calculation errors as shown in Fig. 5(b). According to the criterion of the two-winding three-phase transformer, the protection will be blocked.
Fig. 5. Differential currents and experimental results when the transformer is energized. (a) Differential currents. (b) ADOLIs.
B. Responses to Simultaneous Fault and Inrush Conditions When the transformer is energized with an internal fault, the
inrush current may occur and would affect the differential current waveforms of fault phases. This has been verified by a total of 52 cases with simultaneous inrush currents and internal fault currents.
Fig. 6(a) as an example shows this condition, which is obtained by switching in the transformer bank with no load and a turn-to-ground fault in the phase B. Nonfault phase C presents the magnetizing current and fault phases A and B show little distortion. The differential currents of three phases are all larger than the nominal magnetizing current. Therefore, the ADOLIs of three phases are calculated by using (30). Fig. 6(b) shows that the ADOLI of phase C is close to zero, whereas the ADOLIs of phases A and B are very noticeable.
To justify the reliability and sensitivity of the technique, Fig. 7(a) shows differential currents with more severe distortion compared with Fig. 6(a), where the transformer bank is energized with no load and a 2.4% turn-to-turn fault occurs in the phase A.
After analysis in the frequency domain, we can find that the magnitudes of the second harmonic in fault phases A and C are greater than that of some magnetizing inrush currents. Consequently, the commonly employed conventional differential protection technique based on the second harmonic will thus have difficulty in distinguishing between an internal fault and an inrush current. However, the ADOLIs of fault
6
phases show high amplitudes in Fig. 7(b), which makes the relay judge there is an internal fault and trip the relay.
Fig. 6. Differential currents and experimental results when the transformer is switched with no load and a turn-to-ground fault in the phase B. (a) Differential currents. (b) ADOLIs.
Fig. 7. Differential currents and experimental results when the transformer is energized with a 2.4% turn-to-turn fault in the phase A. (a) Differential currents. (b) ADOLIs.
These results are in accordance with the practical state of the transformer bank. In the total of the 52 cases, the identical results verify that the proposed technique can be used to discriminate internal faults from inrush currents when the
simultaneous inrush currents and faults occur in the transformer.
C. Responses to Internal Fault Conditions Only Data from a total of 54 cases are used to calculate the
ADOLIs based on (30). In all of the 54 cases, the calculated ADOLIs are noticeable, which show the internal fault feature of the transformer. Two examples are shown in Figs. 8 and 9.
Fig. 8. Differential currents and experimental results when a turn-to-ground internal fault occurs in the phase B. (a) Differential currents. (b) ADOLIs.
Fig. 9. Differential currents and experimental results when a 2.4% turn-to-turn fault occurs in the phase A. (a) Differential currents. (b) ADOLIs.
7
One is a turn-to-ground fault in the phase B (the same fault location as the example shown in Fig. 6, and the other one is a 2.4% turn-to-turn internal fault in the phase A (the same fault location as the example shown in Fig. 7. It can be seen from Figs. 8 (a) and 9 (a) that the differential currents of nonfault phases are within the range of nominal magnetizing currents but the differential currents of fault phases are larger than the nominal value. Therefore, the ADOLIs of faulted phases need to be calculated. In Figs. 8(b) and 9(b), the ADOLIs of all fault phases show very high amplitudes. Moreover, the ADOLIs of fault phases in Figs. 8(b) and 9(b) present similar results with those in Figs. 6(b) and 7(b), respectively. These results prove the accuracy of the calculated ADOLIs and the effectiveness of the method to identify the internal faults.
V. CONCLUSION Application of the generalized leakage inductance to
discriminate between inrush current and the internal fault current of a transformer is proposed. The basic theory of the generalized leakage inductance is first derived. Then, the criteria of the single-phase transformer, the two-winding three-phase transformer, and the three-winding three-phase transformer are developed in detail. A large number of experiments were carried out to test the proposed techniques. In all of the 162 cases, the ADOLIs of phases with the inrush currents are close to zero. On the other hand, the ADOLIs of fault phases are noticeable. The method is suitable whether it is possible to measure the winding currents. Also, the method does not require the presence of harmonic currents to restrain the protection system during magnetizing inrush. Furthermore, the proposed method is independent of the B-H curve and iron losses. The experimental results verify the reliability, sensitivity and the computational simplicity of the method.
VI. ACKNOWLEDGEMENTS Many faculties and students contribute greatly to this
research. The authors would like to thank Dr. James S. Thorp, Dr. Arun G. Phadke, and Mr. Andrew J. Arana.
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VIII. BIOGRAPHIES
Jing Ma is (S’06-M’08) was born in Hebei Province, China on February 25, 1981. He received his B.S. and Ph.D. degree from North China Electric Power University, China, in 2003 and 2008, respectively. He has been a visiting research scholar in the Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University from 2008 to 2009. He is currently a lecturer in the
School of Electrical and Electronic Engineering, North China Electric Power University, China. His major interests include power system protection and small signal analysis and control. (e-mail: [email protected]).
Tong Wang is currently a Ph.D. candidate in the School of Electrical and Electronic Engineering, North China Electric Power University, China. She received her B.S degree from North China Electric Power University in 2007. Her interests mainly include wide area measurements, and small signal analysis and control. (e-mail: [email protected]).
8
Jie Wu was born in Fujian Province, China, on September 30, 1985. She received her B. S. degree from North China Electric Power University, China, in 2007. She is currently an assistant engineer working in the State Nuclear Electric Power Planning Design and Research Institute, Beijing, China. Her current research interests are power system analysis, power system equipment modeling and substation automation.
Zengping Wang was born in Hebei, China, on November 3, 1964. He received the B.S. and M.S. degree in Electric Engineering from North China Eletric Power University, China, in 1985 and 1988, respectively. He received the Ph. D. degree from Harbin Institute of Technology, China, in 1997. He is a professor and the dean of the School of Electrical and Electronic Engineering at North China Eletric Power University. His special fields of interest include relay protection, accident analysis and system
security protection.
