Identification of interturn faults in power transformers by means of generalized symmetrical components analysis

The paper deals with experimental identification of transformer internal faults, an important factor in reliability and sustainability of power supply systems. Task of identification of transformer internal faults requires increasing sensitivity of relay protection by calculation of components most sensitive to interwire faults from transformer current. In order to study internal faults in transformer, the model in Simulink MATLAB was developed on the basis of transformer constitutive equations. Transformer with short circuited wires was simulated as a multiwinding transformer. We provide the calculation of transformer parameters. Model was applied for analysis of transients in power transformers, such as interwire fault, transformer inrush, and fault in transformer connections. Analysis of power transformer internal faults by means of time-dependent symmetrical components of currents is provided. These symmetrical components were calculated for the first harmonic of current by means of discrimination of firs harmonic by low-pass filter and compensating elements implementing phase shift. Described method allows calculation of symmetrical components during transient and under nonsinusoidal conditions. Simulation results showed the advantage of instantaneous symmetrical components of other direct values. Those components were implemented in relay protection algorithms for identification of internal faults in transformers.


Introduction
Power transformers are important part of any electric power system, and significantly affect the sustainability and reliability of power supply. The transformer reliability is dependent on effective relay protection operation. Main problems in relay protection are failures in case of turn-to-turn fault in the transformer and in unjustified tripping in case of transients in energy system outside the protected zone [1], [2].
As a result of growing energy capacity of modern industry [3], [4], [5], [6], the failure of relay protection in case of interwire fault will lead significant damage caused to the transformer by fault currents and results high repair costs.
The major methods for increasing sensitivity of relay protection are calculation of components most sensitive to interwire faults from transformer currents. Examples of such components are symmetrical components, dq0 transform, wavelet transform and other [7], [8], [9], [10], [11], [12]. In order to estimate and improve algorithms of relay protection, simulation of transformer transients is required.
This study is dedicated to development of transformer model in Simulink MATLAB, which would provide calculation of transformer transients in cases of internal faults and over transients in transformers, and provide means to identify internal faults from other transients.

Methods
Internal short circuits in transformer occur if insulation of transformer windings is damaged. In case of main insulation damage ground faults take place; in case of longitudinal insulation winding end winding fault happen. Interwire fault could happen between coils of same or different phases. Short circuits between coils and wires of transformer windings are most common for early stages of transformer faults.
In cases of interwire fault transformer can be considered as multiwinding transformer [13]. Structural model of ideal single-phase transformer in case of interwire fault is presented on fig.1.

Interwire fault simulation
In case of short circuit between wires of second winding

Simulink MATLAB implementation
In accordance with previously established set of constitutive equations of transformer, structural diagram of the calculation ( fig.2) was developed.
As the simulation of transients in transformer in cases of transients in electric grid is required, it those were implemented by means of SimPowerSystems BlockSet. In order to couple calculation blocks in Simulink with models, made with SimPowerSystems BlockSet library, model of transformer was connected through Controlled Current Source and Voltage Measurement blocks.
Structural diagram of connection of three-phase delta-wye transformer is represented on fig.3.Each phase of three-phase transformer represented by single-phase transformer.
Subsystems Phase_A, Phase_B and Phase_C, are structural diagrams of calculation of single phase transformer constitutive equation

Fault identification
Generalized symmetrical components analysis [14] covers the case of nonsinusoidal and asymmetric dynamic systems of three-phase variables forming the vector: Instantaneous components of positive and negative sequences  . These symmetrical components were calculated for the first harmonic of current by means of discrimination of firs harmonic by low-pass filter and compensating elements implementing phase shift ±120°. Transfer factor of phase-shifting link is calculated as: where 50 1 = f Hz -circuit voltage frequency.
Phase shift at frequency 1 Transfer factor of low-pass filter is calculated as:

Results
Comparative analysis of positive and negative sequences of a differential current has been carried out for the following modes: short circuiting of Results of simulation (Fig.5) demonstrate that an internal fault such as short-circuiting 5% turns of the secondary winding leads to asymmetrical 3-phase differential currents in contrast to the form of a healthy transformer excitation current which is a part of an unbalanced differential current. Fig. 5. Three-phase differential currents due to turn-to-turn short-circuiting 5% of the secondary winding in the background of healthy transformer excitation currents. Fig.5 shows instantaneous curves of negative and positive components of a differential current (Fig. 6) and changing of amplitudes of corresponding sequences resulted from internal short circuiting (Fig.7). As it is seen from Fig. 6 the negative sequence component (curve 2) of the unbalanced differential current is negligibly small as compared to a positive one (curve 1). This is due to a filtering effect of decomposing the current into symmetrical components which results in changing the number of harmonics in compared currents from  To use the obtained results for internal fault identification it is helpful to refer to a complex informative parameter expressed in the form: Dynamics of the parameter behavior during different kinds of faults is shown in Fig. 8.  corresponds to false differential currents caused by external faults, inrush currents, transformer over excitation etc. In this case relay operation is to be prevented.

Discussion
The paper deals with analysis of the power transformer's fault currents under different conditions of operation using Simulink MATLAB. Analysis was carried out on the basis of decomposition of analyzed currents to generalized symmetrical components by means of a sequence analyzer which output signals in the form of dynamic phasors of each harmonic which were used to reconstruct instantaneous values of currents' positive, negative and zero sequences. Low-pass filter with correction link was proposed for calculation of symmetrical components of first harmonic of differential current. Comparative analysis of dynamic phasors shows the sensitivity of amplitudes of negative and positive sequences of differential currents to fault location and allows formulation of algorithm for detecting internal faults in the transformer windings.