Energy and Power Engineering, 2013, 5, 1425-1428
doi:10.4236/epe.2013.54B270 Published Online July 2013 (http://www.scirp.org/journal/epe)
The Discrimination of Inrush Current from Internal
Fault of Power Transformer based on EMD
Fanyuan Zeng, Qianjin Liu, Chao Shi
School of Electric Power, South China University of Technology,Guangzhou, China
Received March, 2013
ABSTRACT
The method is based on that the waveform of the inrush distorts seriously, while the fault current nearly keeps sinusoid.
The complicated signal can be decomposed into a finite intrinsic mode functions (IMF) by the EMD, then define and
compute the projection area on X-axis of each IMF—, the specific gravity of SIMF—
ci
Sci
K
, and the maximum of
ci
K
—max
K
. We can get a new scheme of transformer-protection based on comparing the difference between inrush and
fault current. Theoretical analysis show that the method can precisely discriminate inrush and fault current, fault clear-
ance time is about 20ms. Moreover, it is convenient to achieve and hardly be affect by not-periodic component.
Keywords: Inrush Current; Transformer Protection; HHT; EMD; IMF
1. Introduction
At present, the domestic transformer primary protection
in power system configuration mainly uses second har-
monic restraint principle and longitudinal differential
protection based on current discontinuous corner braking
principle. The long-term operating experience shows that
the differential protection can not accurately distinguish
the difference between the transformer internal faults and
external faults, so the main contradiction is still focused
on the identification of magnetizing inrush and internal
fault.
2. Empirical Mode Decomposition
Empirical Mode Decomposition (EMD) can effectively
identify magnetizing inrush and internal fault. EMD is
suitable for the analysis of non-linear, non-stationary
signal sequence with a high signal-to-noise ratio. The
center of this technology is empirical mode decomposi-
tion, which can decompose complex signals into a finite
number of intrinsic mode functions (IMF).The decom-
posed IMF component contains the local features signal
of the different time scales of the original signal. The
empirical mode decomposition method can make the
non- stationary data become smooth and get the Hilbert
transform spectrogram and the frequency of physical
significance. Compared with the short-time Fourier
transform and wavelet decomposition methods, this
method is intuitive, direct, posterior and adaptive.
Basic principles of empirical mode decomposition:
In order to obtain th e intrinsic mode fun ction s , the d ata
signal must be decomposed with EMD. So it is necessary
to introduce the definition of the basic concepts of EMD
decomposition process: IMF. This is the basis of the
master of EMD method.
The intrinsic mode function must satisfy the following
two conditions:
1) In the entire time range, the number of lo cal extreme
points and zero-crossing points of the function must be
equal to, or up to a diffe rence of one;
2) At any time, the average of the local maximum of
the envelope (upper envelope) and the local minimum of
the envelope (the envelope line) must be zero.
The first condition obviously has the similar require-
ments with traditional narrowband stationary Gaussian
signal. For the second condition, it is a new concept
which is the classic global requirements modifies local-
ized requirements, so that the instantaneous frequency is
no longer subject to the asymmetric waveform with un-
necessary fluctuations. In fact, this condition should be
“the local mean of the data is zero”. However, for non-
stationary data calculating the local mean involves the
concept of the local time scale, which is difficult to de-
fine. Therefore, in the second condition, the envelope
flocal maxima and local minimum values of the average
envelope are instead of zero, which make the wave form
of a signal locally symmetric. Huang et al study shows
that, under normal circumstances, to use this instead of
the physical significance of the instantaneous frequency
is in line with the system studied. Intrinsic mode func-

F. Y. ZENG ET AL.
1426
tions show the inherent vibration mode of data. Because
of the intrinsic mode functions defined by the ze-
ro-crossing point of each vibration cycle, there is only
one vibration mode with no other complex riding waves.
3. Decomposition Process of EMD Method
The EMD decompositio n method is based on the follo w-
ing as assumptions:
1) Data must include at least two extreme values, a
maximum value and minimum value; 2) Local time
domain characteristics of the data is uniquely deter
mined by the time scalebetweentheextreme points; 3) If
data has an inflection point instead of extreme point, the
decomposition results can be obtained by differentiating
the data once or more times and integrating the
extremum. The essence of this approach ge ts the intrinsic
fluctuations mode by the characteristic time scale of the
data, and then break down the data. This decomposition
process can be vividly called “selecting” process.
Decomposition process: Find out all the maxima of the
original data sequence ()
x
t and cubic saline interpolat-
tion function fitting form of th e original data on envelope;
Similarly, find out all the minimum point, and all of the
minimum point formed by cubic spline interpolation
function fitting the data under the envelope, the upper
envelope and lower envelope means recorded as 1
m,
The original data sequence ()
x
t by subtracting the av-
erage envelope obtain a new data sequence .
1
m1 h
1
()hxtm
1
(2-1)
4. Hilbert Spectra and Marginal Spectrum
Huang et al proposed a new method for analysis of a
signal systematically on the basis of the IMF and EMD,
which called Hilbert—Huang Transform (HHT). It in-
cludes EMD and Hilbert spectral analysis methods cor-
responding to EMD.
First arbitrary signal s (t) is broken down into a finite
number of IMF with EMD.
 
1
n
j
j
s
tctr


t
1
(3-1)
Then each IMF component is analyzed by Hilbert
transform, and finally get the homeopathic frequency
signal
 



1
11
Re Re
nn
j
tj
ii
ii
sta tea te





tdt 
(3-2)
Here omitted the residual function , Re represent
the real part. We call the right side of the above formula
for the Hilbert spectrum, referred to as the Hilbert spec-
trum.

n
rt
 

1
,Re
j
tdt
i
Ht ate



 (3-3)
Omitting the residual function since it is a con-
stant, or a monotonic function. Although

n
rt


n
rt can be
seen as a part of a long period wave, taking into account
the long period of uncertainty, and signal the information
contained in the high-frequency component, so we
should do the omission processing. In the expansion of
each component, the amplitude and phase is time vari-
able, and the same signal s (t) of the Fourier transform
expansions is

1
1
it
i
i
s
tae



 (3-4)
This clearly shows that: Generalizing the Fourier ex-
pansion can not only increase the frequency of the signal,
but also represents a variable frequency. New ways break
the shackles of the Fourier transform.
 
,
H
Htd 


t
(3-5)
5. Transformer Protection Based on EMD
5.1. Fundamental
Under condition of no-load closing of a transformer, due
to core saturation nonlinear magnetic properties, it may
produce the magnetizing inrush comparable short-circuit
current. In Figure 4-1(a), the line OABP is basic mag-
netizing curve of the transformer .The line OABP is re-
placed by a two-stage approximate magnetization of pol-
yline OC and CP, and when closing power supply volt-
age is set : sin( )
m
uU ta


, without considering the
transformer leakage reactance.
While transformer is no-load closing (t = 0), we can
get the magnetizing inrush approximate expression as
(4-1) show.
cos cos()
cos cos()
mr
oc m
c
mr
c
cp m
c
Uata
L
iUata
L

















c
i

 





(4-1)
In Equation (4-1),

is core flux of the transformer;
r

is remanence of transformer; m

is amplitude of the
steady-state flux，rated conditions for rated flux ampli-
tude .
For fault current waveform keep sinusoidal character-
istics. In this paper, the basic idea of the identification
principle is: Read a section of the differential waveform
data f, IMF can be attained by EMD for f, where we can
look for all the leading IMF. If the number of leading
IMF is 1,it is fault current; if the number is more than
one, it is magnetizing inrush.

F. Y. ZENG ET AL. 1427
(a) (b)
Figure 4.1. Top wave bump characteristics of the trans-
former.
4.2. Specific Methods and Protection Criteria
4.2.1. Sear ch IMF
The dominant IMF is broken down into component of the
IMF with a large amplitude .In order to search for the
dominant IMF easily, this article defines IMF component
i on the horizontal axis of the projected area as
follows:
cci S

n
o
t
ci i
t
Sctdt (4-2)
discretizing formula (4-2):

1
n
ci i
k
Sck


t
n
(4-3)
According to formula (4-3), the way to get the domi-
nant IMF is: Calculate the various components i c of
IMF，then , if the ci of i
have a difference with in 20%, of IMF is the
dominant IMF.

max max, 1.... ci
SSi
max
SS c
i
c
4.2.2. Pr o t ec tion Criteria
According to this identification principle, we define the
proportion of component coefficient
i
cci
K
is:
1
ci
ci n
ck r
k
S
K
SS



 (4-4)
Assume the largest proportion of coefficients of IMF
is max
K
,
 
1
max 1
1
max
max
n
nci
i
ci n
i
ck r
k
S
KK
SS





 (4-5)
As it can be seen in formula (4-5), the value of max
K
changes between 0~1. When the differential current is
fault current, since it contains only one dominant IMF,
the value of max
K
is very large, almost above 0.9. When
the differential current is inrush current, due to the pres-
ence of two or more similar to the proportion coefficient
leading the IMF, the value of max
K
is 0.5. Additionally,
When the magnitude of the differential current data win-
dow is not greater than the maximum unbalanced cur-
rent，the value of max
K
is 0.
Therefore, we can obtain protection criterion as (4-6)
shows:
max
z
d
K
K (4-6)
Define
z
d
K
= 0.8, respectively calculate three-phase
differential current max
K
.
4.3. Experimental Schematic and Waveform
4.3.1. Transformer Inrush Current Expe riment
Because of the limited laboratory equipment it is impos-
sible to truly imitate inside the short-circuit experiments
of transformer. Because the short circuit current is too
large, and laboratory equipment can not stand the maxi-
mum short-circuit current, otherwise the short-circuit
experiments will burn lines. Therefore, the present study
apply inductive load to simulate the short circuit fault
inside transformer.
4.3.2. Experiment Resulting Waveform and
Processing
Experimental transformer no-load inrush current and
load interterm short-circuit both cases, the two sets of
waveforms, and a group of normal waveform. Since this
article transformer experiment is the presence of har-
monic components in the laboratory, during the test, so
the experimental results from the waveform is not sinu-
soidal waveform, but presents the trend of a square wave.
Transformer inrush current experimental waveform
graph is showed in Figure 4.2. Normal waveform is
showed in Figure 4.3. Inrush current waveform is
showed in Figure 4.4. Short circuit inside waveform is
showed in Figure 4.5.
Figure 4.2. Transformer inrush current experimental
waveform graph.
Figure 4.3. Normal waveform.

F. Y. ZENG ET AL.
1428
Figure 4.4. Inrush current waveform.
Figure 4.5. Short circuit inside waveform.
5. Conclusions
The processing method, fundamentally speaking, is
based on the analysis of the three-phase current funda-
mental and higher harmonics, and then determines the
algorithm of the higher harmonic content, but makes the
method different from the conventional signal due to the
role of the EMD methods of analysis. It is more con-
venient from the principles and experimental methods to
distinguish normal airdrop and fault conditions, but th ere
are also some shortcomings. The main reason is that the
EMD algorithm is still not perfect in the border problem
and envelope fitting: Firstly, there is not a suitable enve-
lope exploded function resulting in fluctuations of max
K
;
secondly, there is no particularly good boundary proc-
essing method.
REFERENCES
[1] T. Y. Li, Y. Zhao and N. Li, “A New Method for Power
Quality Detection Based on HHT,” Proceedings of the
Csee, Vol. 25, No. 17, 2005, pp. 52-56
[2] Z. Ke, J. Jie and T. Q. Zhang, “Distinguishing Magnetiz-
ing Inrush Based on Characteristic of Equivalent Instan-
taneous Inductance,” Power System Protection and Con-
trol, 2010, pp. 12-16
[3] P. Liu, O. P. Malik, D. S. Chen, G. S. Hope and Y. Guo,
“Improved Operation of Differential Protection of Power
Transformers for Intemal Faults,” IEEE Transactions on
Power Delivery, Vo1. 7,1992.
[4] S. H. Jiao, W. S. Liu, J. F. Liu, Z. H. Zhang and Q. X.
Yang, “A New Principle of Discrimination between
Inrrush Current and Fault Current of Transformer Based
on Wavelet,” Proceedings of the CSEE, Jul. 1999, pp.
1-5.
[5] J. A. Sykes and L. F. Morrison, “A Proposed Method of
Harmonic Restraint Differential Protection of Transform-
ers by Digital Computer,” IEEE Transactions on Power
Apparatus and Systems, Vol. PAS-91, pp. 1266-1273.
doi:10.1109/TPAS.1972.293485
[6] F. M. Cao and P. P. Su, “The Application of Wavelet
transform in Transformer’s Differential Protection,”
Electric Power, Vol. 31, No. 11, 1998, pp. 21-24.