Advances in Power and Energy Systems
The transformer inrush currents in large MV-cable installations
FRANCESCO MUZI
Department of Electrical and information Engineering
University of L’Aquila
Monteluco di Roio, L’Aquila 67100
ITALY
francesco.muzi@univaq.it
Abstract:- In large MV-cable installations important problems may occur during the first energization of
transformers, since the consequent relevant inrush current may cause the tripping of the general protection,
and, at the same time, the system’s total blackout. In order to thoroughly investigate this problem, reference
was made to an important underground installation in central Italy, namely the LNGS laboratory, the largest
for astroparticle experiments in the world. A special attention was paid to the phenomenon of inrush
currents, which were examined also with reference to experimental test results, obtained from a sequence of
energizations of an MV/LV power transformer. Moreover, a simulator was implemented in a
Matlab/Simulink environment for an effective evaluation of the behavior of a whole electrical installation.
The same simulator was used to analyze a case study regarding the LNGS laboratory. Finally, possible
solutions aimed at devising a proper selectivity plan for the protection system are proposed and commented.
Key-Words: - MV large electrical installations, Inrush currents, MV power system protection.
1 Introduction
2 A preliminary issue
It is well known that the energization of a
transformer generates a transient with peak
currents that may be many times larger than the
rated transformer current [7]. In case of large MVCable installations, this phenomenon may be
amplified by the presence of line capacitances that
in this situation assume considerable values [9].
As a matter of fact, when the total cable length
exceeds dozens of kilometers at 20 kV, the first
peaks of a transformer’s inrush current can cause
a number of problems, among which particularly
worrying is the onset of the overcurrent protection
installed by the electricity distribution company,
which creates serious problems in the power
supply continuity of the user’s installation.
The present paper was inspired by a study
carried out for a real MV installation located in
central Italy, namely at the Gran Sasso National
Laboratory (LNGS) of the INFN (the Italian
National Institute of Nuclear Physics), which is an
underground laboratory for experiments in
particle physics, particle astrophysics and nuclear
astrophysics. Due to its underground location, the
MV distribution system, extending for about 50
kilometers, is made entirely of 20 kV cables.
The considerations developed in this paper,
although related to a specific installation, are
general and can be applied to any large MV-cable
installation.
A good knowledge of the electromagnetic
transients occurring when a transformer is first
energized is very important to coordinate and
calibrate protection systems in such a way as to
satisfy the requirements of power supply
continuity [4], [5], [8], [10]. Some of the concepts
detailed in later sections are briefly outlined here
to better understand the purpose of the network
simulation carried out with an implemented
MatLab-software code.
In order to calibrate the protection device of a
medium-voltage network it is necessary to know
two type of constraints:
ISBN: 978-1-61804-128-9
1. The limits imposed by the protection
installed by the electricity distribution
company.
2. The value of the transformer inrush
currents.
Fig. 1 shows a comparison between the timecurrent curve of the general protection installed by
the electric utility at the LNGS installation and the
inrush-current curve identified using the data
supplied by the transformer’s manufacturer.
The chart in Fig. 1 shows that the curve
associated with the general protection (step line)
intersects the curve of the inrush current (curved
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Advances in Power and Energy Systems
Time [s]
line). In this condition, the intervention of the
device puts out the entire electrical system.

the rated power, that is to say, the
construction features of the machine: the
associated factors affect the value of the
inductance to be loaded and the damping
resistances.

the short circuit power of the supply
network: the transient will be much
longer and heavier, the greater is the ratio
between the power of the network and
that of the transformer.

the residual flux: the presence of a
residual flux in the transformer’s
magnetic core increases the maximum
value of inrush current.

the instant of energization: this is the
most variable among the parameters
considered, since the current’s maximum
value (from 10 to 20 times the rated one)
occurs when the closure of the circuit
breaker coincides with the voltage zero
crossing, while the minimum value
(about twice the rated current), occurs
when the closure of the circuit breaker
coincides with the passage of the
maximum value of the voltage
waveform.
Current [A]
Fig. 1 - Time-current curve of the general circuit
breaker compared with the evaluated inrush current
obtained from manufacturer data.
In order to estimate the value of the inrush current
in the worst case, two alternatives are possible:
Actually, the technical staff of the LNGS never
observed tripping actions of the general protection
when transformers were inserted, so it was
necessary to study the inrush currents to have
reliable estimates of their actual values.
3 The transformer inrush current
The main phenomenon investigated in this section
is the electromagnetic transient following the first
transformer energization (inrush current). During
the transient following the closure of the circuit
breaker, a transformer acts as an unloaded
inductance absorbing a very high current with a
transient that can last up to 2 seconds. The value
of the current is progressively reduced, thanks to
the dissipative phenomena linked to the resistance
of the winding conductors, until a steady-state
value is reached. Both the maximum value of the
inrush current and the duration of the transient
depend on several parameters:
ISBN: 978-1-61804-128-9

Refer to the manufacturer's data, that
indicate the relationship between the
maximum current peak and the rms value
of the rated current of the transformer and
the value of time constant.

Analyze the behavior of the electrical
system during an energization by means
of specific software simulation.
Since the evaluation performed with the data
supplied by the manufacturer appeared
conservative, as no circuit breaker intervention
was observed on field, the second alternative was
followed, that means a 20 kV network was
modeled and afterwards its behavior was studied
during transients caused by transformer
energizations.
A typical waveform of the inrush current is
shown in Fig. 2 while the data by which
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Advances in Power and Energy Systems
manufacturers evaluate the inrush current of
transformers are reported in Table 1.
2. Reproduction of the experimental test
through the implementation of a MatlabSimulink procedure.
3. Comparison between experimental test
results and those of the simulation.
The rated data of the tested transformer are shown
in Table 2.
Table 2. Data of the tested transformer.
Fig. 2. A typical waveform of the inrush current of a
transformer.
Rated transformer data
Primary
Secondary
Power [kVA]
1500
Voltage [V]
11000
415
Current [A]
78.73
2086.81
Connection
Delta
Wye
Vcc%
6%
Table 1 Coefficients for the calculation of inrush
currents in resin transformers.
Transformer rated
power [kVA]
250
400
630
1250
1600
2000
ki
12
12
11
10
9
8
Time constant τ
[s]
0.22
0.25
0.30
0.35
0.40
0.45
The transformer was tested with a three-phase
supply applied to the primary; the secondary was
maintained
unloaded.
The
laboratory
experimentation consisted of 12 tests of 9 seconds
in duration; for each test the closing angle of the
Vrs line-voltage was varied of 30° and the peak
values of the inrush current were recorded. Tests
were carried out in a network having a 100MVA
short-circuit power at 11 kV. The circuit diagram
used for the laboratory tests is shown in Fig 3.
The inrush current can be calculated at a given
instant by the following formulas:
( )
=
=
where In is the rated current of the transformer on
the primary, I0i is the value of the peak current and
τ is the time constant value. In order to calculate
the inrush current of a group of transformers, it is
necessary to perform the sum of the I0i of the
single machines.
Fig. 3 - Diagram of the experimental circuit.
The parameter values of the equivalent singlephase transformer are shown in Table 3.
4 Experimental test results
In order to develop a reliable simulator,
experimental tests were carried out on a threephase resin encapsulated transformer. The test
involved the measurement of the peak value of
inrush currents.
The performed research work was set according to
the following activities:
Table 3. Parameters of the equivalent single-phase
transformer.
Parameter
Ro
R1
Ld1
R2
Ld2
1. Calculation of an equivalent circuit based
on the test report and testing certificate
supplied by the transformer manufacturer.
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Value
55081 Ω
0.1037 Ω
77
mH
0.511 mΩ
0.011 mH
Advances in Power and Energy Systems
Table 5. Simulation results.
The repeated energizations performed during the
experimental tests were carried out by the closure
of a circuit breaker that was set so as to close in
the first test when the voltage crosses zero, then to
close with a 30° phase shift in each subsequent
test [7], [2]. The results obtained are reported in
Table 4.
Vn=11 kV – An=100 MVA
Vrs closure angle [°]
Table 4. Inrush currents from experimental tests.
Vn=11 kV – An=100 MVA
Vrs closure angle [°]
Ir [A]
Is [A]
It [A]
0
315
729
813
30
580
1086
694
60
760
1076
491
90
1025
653
589
120
1053
432
822
150
381
388
594
180
351
856
937
210
581
889
485
240
816
910
307
270
936
561
587
300
297
75
297
330
371
441
641
Is [A]
It [A]
0
301
768
784
30
601
1045
722
60
771
1031
515
90
978
628
601
120
1013
441
801
150
396
401
588
180
363
843
919
210
597
879
487
240
807
896
317
270
913
542
595
300
311
83
304
330
383
456
631
The analysis of the obtained data shows that
overall the trend of the values obtained from
simulations reflects that of experimental data with
good approximation; for this reason the simulation
model of the saturable three-phase transformer
can be assumed as a valid estimator.
Once the simulation model of the
measurement system of Fig. 3 was tested, the
simulator of the entire LNGS system was
implemented.
For the calculation of the X/R ratio of the
three-phase power source, the following
procedure, derived for Italian standards, was used:
5 Simulation test results
On the basis of the layout of the measuring
system, a simulation model was developed, first
for each individual block, then for the entire
measurement system. Of course, particular
attention was paid to the model of a three-phase
saturable transformer.
Fig. 3 shows the measurement block diagram
implemented in a Simulink environment. The
three-phase bank of inductors, one per each phase,
can be set at the same value with a single
command.
For each test, the oscilloscope named
"currents" records the values of the three currents,
while the oscilloscope named "voltages" registers
the behavior of only the line voltage VRS.
Table 5 shows the results obtained by the
simulation.
ISBN: 978-1-61804-128-9
Ir [A]
.
√
= 0,995
;
= 0,1
;
;
= 10.
A partial simulation model, including
transformers, circuit breakers and MV cables is
shown in Fig 4.
Finally, Fig. 5 shows the result of a
simulation carried out with the simulator of
figure 4 implemented for a zone of the LNGS
system.
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Advances in Power and Energy Systems
Oscilloscope “Currents”
Three-phase ideal
voltage generator
Three-phase
inductor bank
Circuit
breaker
Transformer
1500 kVA
breaker
Oscilloscope “Voltages”
Fig. 3 - Block diagram of the simulation model for the test circuit of Fig 2.
Fig. 4 - The simulator implemented for a partial MV-LNGS network (case study).
Fig 5. An example of the inrush currents estimated by the implemented simulator.
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Advances in Power and Energy Systems
adopting both new kind of relays and proper
protection philosophies.
6 Considerations on the LNGS case
study
As concerns the selectivity of the protection
system, the simulation results obtained allow to
establish the following points:
1. With regard to overload, only a
chronometric selectivity can be adopted and
only on the delayed threshold (short delay);
2. With regard to the short circuit, overcurrent
protections are not selective.
3. The medium voltage cables are fully
protected against both overloads and short
circuits.
4. A three-phase short circuit on the general
switchgear bars involves the opening of the
protection placed upstream the transformer,
causing the total blackout of the LNGS
electrical system.
5. Protections are not selective for ground
faults.
The above statements show that the selectivity of
the adopted protections, in the absence of
interventions on the actual system, is not verified.
For this reason, in order to increase the degree of
selectivity of the protection system, the following
possible solutions are suggested [1], [3], [6]:
1. Avoid parallel operation of substation
transformers.
2. Request the supply company to adopt
appropriate exceptions for line faults.
3. Install directional protections on the rest of
the medium voltage distribution system in
order to improve the selectivity towards the
ground fault.
4. Adopt a logic selectivity for both the line
fault and ground fault.
References
[1] G. Fazio, V. Lauropoli, F. Muzi, G. Sacerdoti,
Variable-window algorithm for ultra-highspeed distance protection, IEEE Transactions
on Power Delivery - Vol. n. 18, NO. 2, April
2003.
[2] Y. Cui, S. G. Abdulsalam, S. Chen, W. Xu, A
Sequential Phase Energization Technique for
Transformer Inrush Current Reduction. IEEE
Transactions on Power Delivery, VOL. 20, No.
2, April 2005.
[3] F. Muzi, A filtering procedure based on least
squares and Kalman algorithm for parameter
estimate in distance protection, International
Journal of Circuits, Systems and Signal
Processing, (a NAUN, North Atlantic
University Union, Journal), Issue 1, Vol. 1,
2007.
[4] F. Muzi, Real-time Voltage Control to
Improve Automation and Quality in Power
Distribution, WSEAS Transactions on Circuits
and Systems, Issue 4, Volume 7, April 2008.
[5] K. P. Basu, A. Asghar, Reduction of
magnetizing inrush current in a delta
connected transformer, Power and Energy
Conference, 2008, PECon 2008.
[6] F. Muzi, Distance relays in conjunction with a
new control algorithm of inverters for smart
grid protection, 2011 CIGRE International
Symposium “The electric Power System of the
future Integrating Supergrids
and
Microgrids”, Bologna, Italy, September 13-15,
2011.
[7] M. Gong, X. Zhang, Z. Gong, W. Xia; J. Wu,
C. Lv, Study on a new method to identify
inrush current of transformer based on wavelet
neural network, Electrical and Control
Engineering (ICECE), 2011.
[8] F. Muzi, A real-time harmonic monitoring
aimed at improving smart grid power quality,
2011 IEEE International Conference on Smart
Measurements for Future Grids (SMFG),
Bologna, Italy, November 14-16, 2011.
[9] F. Muzi, R. Dercosi Persichini, An analysis of
overvoltages in large MV-Cable installation,
15th IEEE-ICHQP International Conference,
17-20 June 2012, Hong Kong.
[10] C. Bartoletti, G. Fazio, F. Muzi, S. Ricci, G.
Sacerdoti, Diagnostics of electric power
components: an improvement on signal
discrimination, WSEAS Transactions on
circuits and systems, Issue 7, Vol. 4, July 2005
7 Conclusions
In MV installations with very long cables, the
transformer inrush currents may cause serious
problems to the continuity of power supply. The
issue was investigated by referring to a real
system, namely an underground laboratory,
although the developed considerations are valid
for any MV installation. As a preliminary step,
experimental test results from the energization of
an MV power transformer were presented and
analyzed. Then a simulator of the whole system,
implemented in a Matlab/Simulink environment,
was illustrated. The results of a case study were
also highlighted by focusing mainly on the
selectivity of the protection system. Moreover,
possible solutions are suggested in order to
achieve the required level of selectivity by
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