ISSN 1068-3712, Russian Electrical Engineering, 2017, Vol. 88, No. 6, pp. 388–393. © Allerton Press, Inc., 2017.
Original Russian Text © M.I. Kuznetsov, D.A. Dadenkov, S.A. Dadenkov, D.S. Dudarev, 2017, published in Elektrotekhnika, 2017, No. 6, pp. 77–81.
Parallel Operation of Three-Phase Power Transformers
with Different Short-Circuit Voltages
M. I. Kuznetsov*, D. A. Dadenkov, S. A. Dadenkov, and D. S. Dudarev
Perm National Research Polytechnic University, Perm, Russia
Received May 16, 2016
Abstract—Parallel operation of three-phase power transformers with different short-circuit voltages has been
studied using a lab bench. The circuit diagram of the bench and experimentally measured vector diagrams of
the currents in primary and secondary windings of the transformers have been presented. It has been found
that, when the difference of short-circuit voltages of parallel operating transformers is more than 10%, both
an arithmetic difference of currents and a great phase shift of secondary-phase voltages occur. As a result, one
of the transformers becomes overloaded, while the other is underloaded. It has experimentally been found
that the load current is determined by the geometrical sum of currents of secondary windings in transformers.
It has been shown that one of the studied transformers works in the conversion mode and its currents are
shifted by 180° with respect to the phase, which is the main reason for failure of the normal operational con-
ditions of parallel transformers.
Keywords: three-phase power transformer, parallel operation of transformers, short-circuit voltage, vector
diagram of current, experimental studies
Division of set transformer power is often needed at
step-down substations. Instead of one transformer
rated to the maximum load of a substation, two or
more transformers, which have the same total load,
operate in parallel [1, 2]. Since the load often contin-
uously increases for some years in a distributive sub-
station, there are no arguments to install at once a
transformer rated to maximum design load of the sub-
The main problem that occurs during parallel
operation of transformers is associated with providing
a uniform load distribution between them. At parallel
switching of the transformers, which have equal power
and similar structure, a uniform load distribution is
automatically achieved due to the symmetry of all the
parallel circuits [3, 4]. Furthermore, the transforma-
tion and short-circuit coefficients should be equal.
However, sometimes, transformers with different
embodiments, unequal powers, and different coeffi-
cients of transformation and short-circuit voltage have
to be connected in practice.
It was shown in [5, 6] that, during parallel opera-
tion, a transformer with a very small coefficient will be
overloaded, such as a transformer with a very small
short-circuit voltage. In [5–7], the arithmetic differ-
ence of secondary voltages was used during the con-
struction of vector diagrams of transformers with dif-
ferent short-circuit coefficients that are connected in
parallel. However, when the difference of short-circuit
voltages is more than 10%, both an arithmetic differ-
ence and a great phase shift of secondary-phase volt-
ages occur, which leads to completely different condi-
tions of parallel operation of transformers, which has
been experimentally confirmed .
For experiments using a bench, two three-phase
transformers with a star-connected circuit of windings
(Y/Y) was used. In this case, the power of the first
transformer (I) was on the level of SHI = 4000 V A,
and that of the second (II) one on that of 2500 V A.
The schematic of the experiment is shown in Fig. 1.
When operating the transformers in parallel, the
admissible difference between the short-circuit volt-
ages should be no higher than 10% [6, 7]. Let us deter-
mine a difference of the short-circuit voltages for the
For transformer I, U
= 6.04%, while for trans-
former II it is 6.798%; thus, the difference of short-
circuit voltages with respect to U
6.419%, which is higher than the admissible value.
This leads to a substantial phase shift of secondary-
phase voltages and, hence, to abnormal conditions of
parallel operation, in which one of them is overloaded