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14th International Conference on Optimization of
Electrical and Electronic Equipment OPTIM 2014
May 22-24, 2014, Brasov, Romania
Calculation methods for lightning impulse voltage distribution in power transformers
M. A. Boruz, M. P. Mircea, M. Ciontu, I. Mircea
University of Craiova, Romania
This paper aims to present and develop a methodology for calculating the stress to which the internal insulation of
power transformer is subjected during lightning impulse test. The transformer’s insulation must withstand the
voltage testing levels prescribed by the standards. One of the methods for determining the internal stress of various
parts of the power transformer’s insulation is by using mathematical models.
Determination of stress produced by lightning impulse regarding power transformer’s insulation must be as accurate
as possible and the following two aspects should be taken in consideration:
 The internal insulation must withstand the stress that appears during service with a proper safety coefficient;
 Insulation sizing should lead to an economic product.
There are two known theories regarding the analysis of the transient phenomena when testing power transformers
with lightning impulse voltage: the theory of traveling wave and the theory of standing wave (see figures bellow).
Fig. 2. Transformer’s winding equivalent circuit diagram
according to standing wave
Fig. 1. Transformer’s winding equivalent circuit diagram
according to traveling wave
It is considered that on the column of a transformer there are placed “s” concentric coils. In order to determine the
initial voltage distribution every winding of the transformer is expressed as a finite number of elements. Every
element has a serial capacity and more capacities to ground or to the nearby winding (see figure 3).
Minim position
Nominal position
Maxim position
Fig. 3. Equivalent capacitive diagram of a transformer having “s”
concentric coils placed on a column
Fig.4. Comparison between voltage distribution for different position of the
tap changer
This method of splitting the entire transformer in a series of capacities offers the possibility to calculate the initial
voltage repartition for any kind of connection between transformer’s coils and it also takes in consideration the
different types of tap changer [2]. This calculation method can also be applied for any kind of windings: continuous,
interlaced buckets, buckets with or without reinforced insulation etc.
The mathematical algorithm presented can be used by the transformer designer to determine the stress to which the
internal insulation of power transformer is subjected during lightning impulse test. The designer can also check if
the internal transformers distances were chosen correctly. It can be possible to avoid the situations when the
transformer isolation is oversized with a high and unjustified safety coefficient or the situations when safety factor is
too small or sometimes missing.
[1] IEC International Standard, IEC 60076-11, Power Transformers – Part 11: Dry-type Transformers, International
Electrotechnical Commission, Geneve, Switzerland, 2004.
[2] I. Răducanu, Contribution at the transient phenomena study which take place in power transformers when
testing them with lightning impulse voltage - PhD theses, Bucharest 1977, pp 14-17.
[3] C. Ambrozie, Measurement and calculation of the capacities inside continuous windings in power transformers
- PhD theses, Iasi 1972.