XIX Sympozjum Srodowiskowe PTZE - materialy.pdf

XIX Sympozjum PTZE, Worliny 2009
ANALYTICAL AND NUMERICAL CALCULATION
OF FORCES ACTING ON TRANSFORMER WINDINGS
Miralem Hadžiselimović 1 , Peter Pišek 2 , Peter Virtič 2 , Tine Marčič 2 ,
Bojan Štumberger 1 , Ivan Zagradišnik 1
1 University of Maribor, Faculty of Electrical Engineering and Computer Science
Smetanova ul. 17, SI-2000 Maribor, Slovenia, e-mail: miralem.h@uni-mb.si
2 TECES, Research and Development Centre for Electric Machines, Maribor, Slovenia
Pobreška cesta 20, SI-2000 Maribor, Slovenia, e-mail: peter.pisek@teces.si
The technically useful transformer was developed at the end of the 19th century. The
transformer is a static electromagnetic device with relatively simple geometry and it is used
for transforming primary electrical energy via magnetic field to secondary energy. The rated
values of primary voltages and currents are usually different to the secondary values which
depend on the intended usage of the transformer. Based on Faraday’s induction law, the
frequency of primary and secondary voltages and currents is the same. It is usual that the
consumption of electric energy in the electric power system is quite variable or in some
unwanted cases it is also possible that faults appear which cause the increase of transformer
currents. The worst fault case is the shorting (short-circuit) of secondary windings, where the
transformer’s currents increase rapidly. Due to the Lorentz force law; these short-circuit
currents lead to enormous forces inside the transformer’s windings (Fig. 1). From the theory
of transformers it is well known that three types of forces act on the windings inside an
operating transformer. This paper deals with analytical and numerical calculation of the
aforementioned forces.
F F F
F
a) b)
Fig. 1. Forces on conductors a) opposite current direction b) same current direction
The largest force inside transformer is the normal force F n [1], which acts between the
primary and secondary winding in a manner which tends to increase the air-gap thickness δ
or maximize the air space between the windings (1):
ˆ
ˆ Bσsc
Fn = Iscs N Cm
() 1
2
where Î scs is the short-circuit shock current, N is the winding’s number of turns, ˆB σ sc is the
short-circuit leakage magnetic flux density and C m is the middle circumference of the
winding. The normal force loads a low voltage winding which is placed nearer the pillar with
pressure. On the contrary, the normal force loads the outer high voltage winding with stretch.
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