Evaluation of the Influence of Non-sinusoidal Conditions on Power Transformers

. The electrical equipment operation is cost-effective and reliable when operating parameters of the electrical network correspond to the rated data of the equipment. The real operation conditions, however, differ from those required for electrical equipment, which negatively affects its efficiency. The non-sinusoidal conditions in electrical networks are currently very common. The paper provides an overview of the characteristics obtained from an analysis of publications, which are used to evaluate the effect of the non-sinusoidal conditions on power transformers. The results of the calculation of these characteristics for a transformer installed at a railway traction substation are presented. Parameters of the non-sinusoidal conditions are obtained as a result of measurements.


Introduction
The operating parameters of electrical networks should ensure their economically viable and reliable operation, which is largely determined by power quality. Power quality, in turn, affects the reliability of electrical equipment, its functioning, and service life. Electrical equipment works most efficiently, cost effectively, and has a long service life, when the operating parameters of the network correspond to the rated data of the equipment. In real conditions, the operating parameters of electrical networks often differ from those required for electrical equipment, in particular, they do not meet the requirements of the State Standard 32144-2013 [1].
At present, a major problem in electrical networks is the non-sinusoidal voltage, which is caused by loads with nonlinear voltage-current characteristic. The authors of [2] note that "the large values of indices U K and ) n ( U K , that characterize the voltage nonsinusoidality, are observed in the electrical networks that power AC railway, aluminum plants and large-scale metallurgical facilities. The problems related to providing the required levels of U K and ) n ( U K … are virtually never stated and solved". Non-sinusoidal conditions cause a large number of negative consequences, which have been reported in numerous publications for more than half a century [3][4][5][6][7][8].
Harmonic voltage and current appearing in nonsinusoidal conditions cause overheating of transformers, damage to capacitors, increased losses in induction motors, erroneous operation of protection and automatic systems, etc. According to [8], the costs associated with harmonics make up 5.4% of all costs related to low quality of electric energy. Power transformers are an important component of electric power systems. In Russia, their total capacity due to several transformation stages is 6-6.5 times higher than the installed capacity of generators. The authors of [9] note that "in the event of an accidental disconnection of a power transformer, the losses are estimated at millions of Euros, excluding the cost of repairing the equipment or replacing it". In the presence of harmonic voltages and currents, the transformers are damaged due to an increase in the heat release in windings and other components. This accelerates the aging process of insulating paper, transformer oil, and magnetic system. Recently, there has been a growing interest in evaluating the influence of harmonics on power transformers, as evidenced by the papers of the international conferences [10][11][12][13][14][15][16]  2 Analysis of non-sinusoidal conditions at the node connecting railway substation to supply network Figure 1 shows a scheme for measuring the power quality indices and the operating parameters. Measurements were carried out for 24 hours with a 1minute time interval between the measurements.     Table 2 gives statistical estimates for some harmonics of phase B. The estimates of the harmonic voltages and currents of three phases with a probability of 0.95 will be used to calculate the parameters characterizing their influence on transformer.

Active power losses in transformer under non-sinusoidal conditions
Harmonics of voltages and currents cause additional losses of active power in transformer. Figure 3 shows a classification diagram of transformer losses [14,17].

No-load losses under non-sinusoidal conditions
In [14], the authors propose calculating the transformer no-load losses under non-sinusoidal conditions

Load losses under non-sinusoidal conditions
According to diagram in Fig. 3  (5) Table 4 presents ohmic losses in high and medium voltage windings that are calculated by (3)- (5). As seen from the Table, the non-sinusoidal current increases total ohmic losses by 14.5 kW.  Table 5 demonstrates eddy current losses in transformer windings and its other components that are calculated by (6)(7)(8)(9)(10). An increase in the eddy current losses under non-sinusoidal conditions compared to the sinusoidal ones is 399.0 kW.

Load losses
Load losses under non-sinusoidal conditions given (4), . (10) The calculated load losses are presented in Table 6. An excess load loss under non-sinusoidal conditions compared to sinusoidal ones is 413.5 kW.

Reduction in the transformer service life
The authors of [8] propose determining the real service life of transformer ( RSL T ) under non-sinusoidal conditions by expression where H  -hot spot temperature of the windings, °С.
Temperature H  is calculated by where ТО   Tables 7 and 8 show the initial data and results of the calculation of reduction in the transformer service life by (12) - (16). As evidenced by Table 8, the non-sinusoidal conditions in phase C can lead to a reduction in the standard transformer service life by 7.5 years.